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Direct imaging of extrasolar planets with future space-based coronagraphic telescopes may provide a means of detecting companion moons at wavelengths where the moon outshines the planet. We propose a detection strategy based on the positional variation of the center of light with wavelength, "spectroastrometry." This new application of this technique could be used to detect an exomoon, to determine the exomoon's orbit and the mass of the host exoplanet, and to disentangle of the spectra of the planet and moon. We consider two model systems, for which we discuss the requirements for detection of exomoons around nearby stars. We simulate the characterization of an Earth-Moon analog system with spectroastrometry, showing that the orbit, the planet mass, and the spectra of both bodies can be recovered. To enable the detection and characterization of exomoons we recommend that coronagraphic telescopes should extend in wavelength coverage to 3 micron, and should be designed with spectroastrometric requirements in mind. | The Center of Light: Spectroastrometric Detection of Exomoons |
Performance is an important non-functional aspect of the software requirement. Modern software systems are highly-configurable and misconfigurations may easily cause performance issues. A software system that suffers performance issues may exhibit low program throughput and long response time. However, the sheer size of the configuration space makes it challenging for administrators to manually select and adjust the configuration options to achieve better performance. In this paper, we propose ConfRL, an approach to tune software performance automatically. The key idea of ConfRL is to use reinforcement learning to explore the configuration space by a trial-and-error approach and to use the feedback received from the environment to tune configuration option values to achieve better performance. To reduce the cost of reinforcement learning, ConfRL employs sampling, clustering, and dynamic state reduction techniques to keep states in a large configuration space manageable. Our evaluation of four real-world highly-configurable server programs shows that ConfRL can efficiently and effectively guide software systems to achieve higher long-term performance. | Automated Performance Tuning for Highly-Configurable Software Systems |
COVID-19 incidence is analyzed at the provinces of some Spanish Communities during the period February-October, 2020. Two infinite-dimensional regression approaches are tested. The first one is implemented in the regression framework introduced in Ruiz-Medina, Miranda and Espejo (2019). Specifically, a bayesian framework is adopted in the estimation of the pure point spectrum of the temporal autocorrelation operator, characterizing the second-order structure of a surface sequence. The second approach is formulated in the context of spatial curve regression. A nonparametric estimator of the spectral density operator, based on the spatial periodogram operator, is computed to approximate the spatial correlation between curves. Dimension reduction is achieved by projection onto the empirical eigenvectors of the long-run spatial covariance operator. Cross-validation procedures are implemented to test the performance of the two functional regression approaches. | Bayesian surface regression versus spatial spectral nonparametric curve regression |
To clarify the relation of energy shifts to scattering phase shifts in one-body and many-body problems, we examine their relation in a number of different situations. We derive, for a particle in a container of arbitrary shape with a short-range scattering center, a general result for the energy eigenvalues in terms of the s-wave scattering phase shift and the eigenstates in the absence of the scatterer. We show that, while the energy shifts for a spherical container are proportional to the phase shift over large ranges, those for a cubic container have a more complicated behavior. We connect our result to the description of energy shifts in terms of the scattering T-matrix. The general relation is extended to problems of particles in traps with smoothly varying potentials, including, e.g., the interaction of a small neutral atom with a Rydberg atom. We then consider the many-body problem for particles with a two-body interaction and show that the free energy change due to the interaction is proportional to an average of a generalized phase shift that includes the effects of the medium. Finally, we discuss why, even though individual energy levels are very sensitive to boundary conditions, the energy of a many-body system is not. | Calculating energy shifts in terms of phase shifts |
We report on the spectral analysis of the X-ray pulsar LMC X-4 in its high state out of eclipse observed by BeppoSAX. During this observation no coherent pulsations are detected. The primary continuum is well described by a power law with a high energy cutoff (E_cutoff ~ E_fold ~ 18 keV). The addition of a cyclotron absorption line at ~100 keV improves the fit significantly. The inferred magnetic moment is 1.1 10^{31} Gauss cm^3, in agreement with the value estimated assuming that the neutron star is at the spin equilibrium, as it has been proposed for this source. The remaining excess at low energies can be fitted by a Comptonization of soft photons by moderately hot electrons (kT ~0.9 keV), with an optical depth \tau ~ 16. The seed photons for this Comptonization are consistent with black body emission from the accretion disk at the magnetospheric radius. Another possibility is to fit the soft excess with black body and thermal bremsstrahlung. In this case the black body would originate from cold plasma at the magnetosphere while the bremsstrahlung component may be produced by the strong stellar wind from the companion star, ionized by the X-ray emission from the pulsar. | The 0.1-100 keV Spectrum of LMC X-4 in the High State: Evidence for a High Energy Cyclotron Absorption Line |
The third order perturbed Heisenberg Hamiltonian was employed to investigate the spinel thick nickel ferrite films. The variation of energy up to N=10000 was studied. At N=75, the energy required to rotate from easy to hard direction is very small. For film with N=10000, the first major maximum and minimum can be observed at 202 and 317 degrees, respectively. This curve shows some abrupt changes after introducing third order perturbation. The maximum energy of this curve is higher than that of spinel thick ferrite films with second order perturbed Heisenberg Hamiltonian. At some values of stress induced anisotropy, the maximum energy is less than that of spinel thick ferrite films with second order perturbed Heisenberg Hamiltonian derived by us previously. | Third Order Perturbed Heisenberg Hamiltonian of Thick Spinel Ferrite Films |
A long life-time (>0.3 ms) strongly-coupled molecular Rydberg plasma is generated by the excitation of nitric oxide into the high-n Rydberg threshold region in the high-density region of a supersonic jet expansion. After 310 \mus the plasma has expanded to a size of ca. 3 cm. When subjected to very small DC fields from 0.2 to 1.0 V/cm the plasma reveals a much smaller high-density core structure of only 0.6 cm. The molecular Rydberg plasma is observed over a broad range of excitation energies, from threshold down to Rydberg states as low as n = 19. | Some properties of a long lifetime strongly-coupled molecular plasma produced by high Rydberg excitation of nitric oxide in a supersonic free jet |
A correlation inequality is derived from local realism and a supplementary assumption. Unlike Clauser-Horne (CH) inequality [or Clauser-Horne-Shimony-Holt (CHSH) inequality] which is violated by quantum mechanics by a factor of $\sqrt 2$, this inequality is violated by a factor of 1.5. Thus the magnitude of violation of this inequality is approximately 20.7% larger than the magnitude of violation of previous inequalities. Moreover, unlike CH (or CHSH) inequality which requires the measurement of five detection probabilities, the present inequality requires the measurement of only two detection probabilities. This inequality can therefore be used to test locality more simply than CH or CHSH inequality. | A Bell inequality which can be used to test locality more simply than Clauser-Horne inequality and which is violated by a larger magnitude of violation than Clauser-Horne-Shimony-Holt inequality |
Social scientists have criticised computer models of pedestrian streams for their treatment of psychological crowds as mere aggregations of individuals. Indeed most models for evacuation dynamics use analogies from physics where pedestrians are considered as particles. Although this ensures that the results of the simulation match important physical phenomena, such as the deceleration of the crowd with increasing density, social phenomena such as group processes are ignored. In particular, people in a crowd have social identities and share those social identities with the others in the crowd. The process of self categorisation determines norms within the crowd and influences how people will behave in evacuation situations. We formulate the application of social identity in pedestrian simulation algorithmically. The goal is to examine whether it is possible to carry over the psychological model to computer models of pedestrian motion so that simulation results correspond to observations from crowd psychology. That is, we quantify and formalise empirical research on and verbal descriptions of the effect of group identity on behaviour. We use uncertainty quantification to analyse the model's behaviour when we vary crucial model parameters. In this first approach we restrict ourselves to a specific scenario that was thoroughly investigated by crowd psychologists and where some quantitative data is available: the bombing and subsequent evacuation of a London underground tube carriage on July 7th 2005. | Modelling social identification and helping in evacuation simulation |
The application of the deep learning model in classification plays an important role in the accurate detection of the target objects. However, the accuracy is affected by the activation function in the hidden and output layer. In this paper, an activation function called TaLU, which is a combination of Tanh and Rectified Linear Units (ReLU), is used to improve the prediction. ReLU activation function is used by many deep learning researchers for its computational efficiency, ease of implementation, intuitive nature, etc. However, it suffers from a dying gradient problem. For instance, when the input is negative, its output is always zero because its gradient is zero. A number of researchers used different approaches to solve this issue. Some of the most notable are LeakyReLU, Softplus, Softsign, ELU, ThresholdedReLU, etc. This research developed TaLU, a modified activation function combining Tanh and ReLU, which mitigates the dying gradient problem of ReLU. The deep learning model with the proposed activation function was tested on MNIST and CIFAR-10, and it outperforms ReLU and some other studied activation functions in terms of accuracy(upto 6% in most cases, when used with Batch Normalization and a reasonable learning rate). | TaLU: A Hybrid Activation Function Combining Tanh and Rectified Linear Unit to Enhance Neural Networks |
We present a bifurcation analysis of a normal form for travelling waves in one-dimensional excitable media. The normal form which has been recently proposed on phenomenological grounds is given in form of a differential delay equation. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with a saddle-node in a Bogdanov-Takens point, and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We study here the Hopf bifurcation for the propagation of a single pulse in a ring by means of a center manifold reduction, and for a wave train by means of a multiscale analysis leading to a real Ginzburg-Landau equation as the corresponding amplitude equation. Both, the center manifold reduction and the multiscale analysis show that the Hopf bifurcation is always subcritical independent of the parameters. This may have links to cardiac alternans which have so far been believed to be stable oscillations emanating from a supercritical bifurcation. We discuss the implications for cardiac alternans and revisit the instability in some excitable media where the oscillations had been believed to be stable. In particular, we show that our condition for the onset of the Hopf bifurcation coincides with the well known restitution condition for cardiac alternans. | Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible? |
A $\left(n,\ell,\gamma\right)$-sharing set family of size $m$ is a family of sets $S_1,\ldots,S_m\subseteq [n]$ s.t. each set has size $\ell$ and each pair of sets shares at most $\gamma$ elements. We let $m\left(n,\ell,\gamma\right)$ denote the maximum size of any such set family and we consider the following question: How large can $m\left(n,\ell,\gamma\right)$ be? $\left(n,\ell,\gamma\right)$-sharing set families have a rich set of applications including the construction of pseudorandom number generators and usable and secure password management schemes. We analyze the explicit construction of Blocki et al using recent bounds on the value of the $t$'th Ramanujan prime. We show that this explicit construction produces a $\left(4\ell^2\ln 4\ell,\ell,\gamma\right)$-sharing set family of size $\left(2 \ell \ln 2\ell\right)^{\gamma+1}$ for any $\ell\geq \gamma$. We also show that the construction of Blocki et al can be used to obtain a weak $\left(n,\ell,\gamma\right)$-sharing set family of size $m$ for any $m >0$. These results are competitive with the inexplicit construction of Raz et al for weak $\left(n,\ell,\gamma\right)$-sharing families. We show that our explicit construction of weak $\left(n,\ell,\gamma\right)$-sharing set families can be used to obtain a parallelizable pseudorandom number generator with a low memory footprint by using the pseudorandom number generator of Nisan and Wigderson. We also prove that $m\left(n,n/c_1,c_2n\right)$ must be a constant whenever $c_2 \leq \frac{2}{c_1^3+c_1^2}$. We show that this bound is nearly tight as $m\left(n,n/c_1,c_2n\right)$ grows exponentially fast whenever $c_2 > c_1^{-2}$. | Set Families with Low Pairwise Intersection |
This is the reply to a Comment by I.S.Tupitsyn and P.C.E. Stamp (PRL v92,119701 (2004)) on a letter of ours (J.F.Fernandez and J.J.Alonso, PRL v91, 047202 (2003)). | Reply to Comment on "Magnetization Process of Single Molecule Magnets at Low Temperatures" |
We calculate the QED and QCD radiative corrections to the charged lepton energy distributions in the dominant semileptonic decays of the top quark $t \to b W^+ \to b(\ell^+ \nu_\ell)$ $(\ell=e, \mu, \tau)$ in the standard model(SM), and for the decay $t \to b H^+ \to b(\tau^+ \nu_\tau)$ in an extension of the SM having a charged Higgs boson $H^\pm$ with $m_{H^\pm} < m_t -m_b$. The QCD corrections are calculated in the leading and next-to-leading logarithmic approximations, but the QED corrections are considered in the leading logarithmic approximation only. These corrections are numerically important for precisely testing the universality of the charged current weak interactions in $t$-quark decays. As the $\tau^+$ leptons arising from the decays $W^+ \to \tau^+ \nu_\tau$ and $H^+\to \tau^+ \nu_\tau$ are predominantly left- and right-polarised, respectively, influencing the energy distributions of the decay products in the subsequent decays of the $\tau^+$, we work out the effect of the radiative corrections on such distributions in the dominant (one-charged prong) decay channels $ \tau^+ \to \pi^+ \bar{\nu}_\tau, \rho^+ \bar{\nu}_\tau, a_1^+ \bar{\nu}_\tau$ and $\ell^+ \nu_\ell \bar{\nu}_\tau$. The inclusive $\pi^+$ energy spectra in the decay chains $t \to b(W^+,H^+) \to b (\tau^+ \nu_\tau) \to b (\pi^+ \bar{\nu}_\tau \nu_\tau +X)$ are calculated, which can help in searching for the induced $H^\pm$ effects at the Tevatron and the LHC. | Radiatively corrected lepton energy distributions in top quark decays $t \to bW^+ \to b(\ell^+ \nu_\ell)$ and $t \to bH^+ \to b (\tau^+ \nu_\tau)$ and single charged prong energy distributions from subsequent $\tau^+$ decays |
By using a $q$-analogue of the "magic" matrix introduced by H.Huang in his elegant solution of the sensitivity conjecture, we give a direct generalization of his result, replacing a hypercube graph by a Cartesian power of a directed $l$-cycle. | Induced subgraphs of powers of oriented cycles |
Gravitational collapse of a shell of dust in noncommutative geometry is probed by the renormalized geodesic length, which is dual to probe the thermalization by the two-point correlation function in the dual conformal field theory. We find that larger the noncommutative parameter is, longer the thermalization time is, which implies that the large noncommutative parameter delays the thermalization process. We also investigate how the noncommutative parameter affects the thermalization velocity and thermalization acceleration. | Holographic thermalization in noncommutative geometry |
This letter presents a novel technique to calculate temperatures of building rooftops and other impervious surfaces from high spatial resolution aerial thermal images. In this study, we collected aerial radiance images of 30cm spatial resolution using a FLIR Phoenix imager in long-wave and mid-wave infrared wavelengths for the city of Cedar Falls, USA to estimate building roof temperature loss. Simultaneous ground temperature measurements were made at pre-selected ground targets and roofs using 9 Fluke 561r infrared thermometers. Atmospheric correction of aerial images was performed by Empirical Line Calibration (ELC) method. The resulting ground-leaving radiances were corrected for the emissivity of different roof types and the true kinetic temperature of the building roofs was calculated. The ELC model was observed to perform better when only impervious surface targets were used for the regression. With an R2=0.71 for ELC, the method produced a root mean squared error of 0.74{\deg}C for asphalt roofs. Further, we observed that the microclimate plays a significant role while synchronizing aerial and ground measurements. | Estimation of Building Rooftop Temperature from High Spatial Resolution Aerial Thermal Images |
We construct and study the one-parameter semigroup of $\sigma$-finite measures ${\cal L}^{\theta}$, $\theta>0$, on the space of Schwartz distributions that have an infinite-dimensional abelian group of linear symmetries; this group is a continual analog of the classical Cartan subgroup of diagonal positive matrices of the group $SL(n,R)$. The parameter $\theta$ is the degree of homogeneity with respect to homotheties of the space, we prove uniqueness theorem for measures with given degree of homogeneity, and call the measure with degree of homogeneity equal to one the infinite-dimensional Lebesgue measure $\cal L$. The structure of these measures is very closely related to the so-called Poisson--Dirichlet measures $PD(\theta)$, and to the well-known gamma process. The nontrivial properties of the Lebesgue measure are related to the superstructure of the measure PD(1), which is called the conic Poisson--Dirichlet measure -- $CPD$. This is the most interesting $\sigma$-finite measure on the set of positive convergent monotonic real series. | Invariant measure for the continual Cartan subgroup |
We consider the Casimir effect for quantized massive scalar field with non-conformal coupling $\xi$ in a spacetime of wormhole whose throat is rounded by a spherical shell. In the framework of zeta-regularization approach we calculate a zero point energy of scalar field. We found that depending on values of coupling $\xi$, a mass of field $m$, and/or the throat's radius $a$ the Casimir force may be both attractive and repulsive, and even equals to zero. | Casimir effect in a wormhole spacetime |
Discussed in the paper is a mixed scenario of the charged liquid surface reconstruction in the situation where the 2D surface charge density is close to its saturation value. | Mixed scenario of the charged liquid surface reconstruction |
In the context of the ClearMind project, we measured the scintillating properties, as induced from from gamma ray interactions, of today available PbWO4 crystal. We measured scintillation s yields and time constants by measuring the signal shape measured on a fast photo-multiplier and deconvoluting it from the instrumental effects. For the doped crystals at room temperature, we measured a fast scintillation component, with time constants of 2 ns, 55 percent of the total light yield, and a slow component of 6 ns. We observe a significant increase of the light yield for the slow component when the temperature decreases and simultaneous increase of the time constants, but no increase in the fast component light yield. Our measurements reproduce the main qualitative features of PbWO4 crystals quoted in the literature. Quantitatively though, we measured significantly shorter time constants and larger light yields. This is explained by a rigorous treatment of the instrumental contributions in the measurements. Results are discussed and prospect for future developments, tailored for the ClearMind project, are presented. | Scintillating properties of today available lead tungstate crystals |
We present a study of diffusion of small tagged particles in a solvent, using mode coupling theory (MCT) analysis and computer simulations. The study is carried out for various interaction potentials. For the first time, using MCT, it is shown that for strongly attractive interaction potential with soft core (allowing interpenetration between the solute-solvent pair) the diffusion exhibits a non-monotonic size dependence. This was earlier predicted in simulation and experimental studies and was connected to levitation effect [J. Phys. Chem. B 2005, 109, 5824-5835]. Our MCT analysis reveals that for weak or no attractive interactions, all the small solute particles studied here show levitation through the inter-solvent transient cage. However, for strong attractive interaction the levitation is not present for the smallest particle sizes. It is found that for systems where the interaction potential is hard, not allowing any interpenetration between the solute-solvent pair, the solute cannot explore the inter-solvent cage. Thus these systems will never show any non monotonic size dependence of diffusion. We also show that although levitation is a dynamic phenomena, the effect of levitation can be obtained in the radial distribution function. | Non-monotonic Size Dependence of Diffusion and Levitation Effect: A Mode Coupling Theory Analysis |
Let $X$ be a (two-sided) fractional Brownian motion of Hurst parameter $H\in (0,1)$ and let $Y$ be a standard Brownian motion independent of $X$. Fractional Brownian motion in Brownian motion time (of index $H$), recently studied in \cite{13}, is by definition the process $Z=X\circ Y$. It is a continuous, non-Gaussian process with stationary increments, which is selfsimilar of index $H/2$. The main result of the present paper is an It\^{o}'s type formula for $f(Z_t)$, when $f:\R\to\R$ is smooth and $H\in [1/6,1)$. When $H>1/6$, the change-of-variable formula we obtain is similar to that of the classical calculus. In the critical case $H=1/6$, our change-of-variable formula is in law and involves the third derivative of $f$ as well as an extra Brownian motion independent of the pair $(X,Y)$. We also discuss briefly the case $H<1/6$. | An It\^o's type formula for the fractional Brownian motion in Brownian time |
Genuine leather, such as the hides of cows, crocodiles, lizards and goats usually contain natural and artificial defects, like holes, fly bites, tick marks, veining, cuts, wrinkles and others. A traditional solution to identify the defects is by manual defect inspection, which involves skilled experts. It is time consuming and may incur a high error rate and results in low productivity. This paper presents a series of automatic image processing processes to perform the classification of leather defects by adopting deep learning approaches. Particularly, the leather images are first partitioned into small patches,then it undergoes a pre-processing technique, namely the Canny edge detection to enhance defect visualization. Next, artificial neural network (ANN) and convolutional neural network (CNN) are employed to extract the rich image features. The best classification result achieved is 80.3 %, evaluated on a data set that consists of 2000 samples. In addition, the performance metrics such as confusion matrix and Receiver Operating Characteristic (ROC) are reported to demonstrate the efficiency of the method proposed. | Efficient Neural Network Approaches for Leather Defect Classification |
For the classical Shiryaev--Roberts martingale diffusion considered on the interval $[0,A]$, where $A>0$ is a given absorbing boundary, it is shown that the rate of convergence of the diffusion's quasi-stationary cumulative distribution function (cdf), $Q_{A}(x)$, to its stationary cdf, $H(x)$, as $A\to+\infty$, is no worse than $O(\log(A)/A)$, uniformly in $x\ge0$. The result is established explicitly, by constructing new tight lower- and upper-bounds for $Q_{A}(x)$ using certain latest monotonicity properties of the modified Bessel $K$ function involved in the exact closed-form formula for $Q_{A}(x)$ recently obtained by Polunchenko (2017). | On the Convergence Rate of the Quasi- to Stationary Distribution for the Shiryaev-Roberts Diffusion |
We investigate the sensitivity of future photon-photon colliders to low scale gravity scenarios via the process $\gamma\gamma \to ZZ$ where the Kaluza-Klein boson exchange contributes only when the initial state photons have opposite helicity. We contrast this with the situation for the process $\gamma \gamma \to \gamma \gamma$ where the $t$ and $u$ channel also contribute. We include the one-loop Standard Model background whose interference with the graviton exchange determines the experimental reach in measuring any deviation from the Standard Model expectations and explore how polarization can be exploited to enhance the signal over background. We find that a 1 TeV linear collider has an experimental reach to mass scale of about 4 TeV in this channel. | Signals for Low Scale Gravity in the Process $\gamma \gamma \to ZZ$ |
The axion or axion-like particle motivated from a natural solution of strong CP problem or string theory is a promising dark matter candidate. We study the new observational effects of ultralight axion-like particles by the space-borne gravitational wave detector and the radio telescope. Taking the neutron star-black hole binary as an example, we demonstrate that the gravitational waveform could be obviously modified by the slow depletion of the axion cloud around the black hole formed through the superradiance process. We compare these new effects on the binary with the well-studied effects from dynamical friction with dark matter and dipole radiation in model-independent ways. Finally, we discuss the constraints from LIGO/Virgo and study the detectability of the ultralight axion particles at LISA and TianQin. | Imprints of ultralight axions on the gravitational wave and pulsar timing measurement |
We show by quantum Monte Carlo simulations of realistic Kondo lattice models derived from electronic--structure calculations that multiple quantum critical points can be realized in Plutonium--based materials. We place representative systems including PuCoGa5 on a realistic Doniach phase diagram and identify the regions where the magnetically mediated superconductivity could occur. Solution of an inverse problem to restore the quasiparticle renormalization factor for f-electrons is shown to be sufficiently good to predict the trends among Sommerfeld coefficients and magnetism. Suggestion on the possible experimental verification for this scenario is given for PuAs. | Multiple Quantum Phase Transitions of Plutonium compounds |
In this paper we consider a reducible degeneration of a hyperelliptic curve of genus $g$. Using the Sato Grassmannian we show that the limits of hyperelliptic solutions of the KP-hierarchy exist and become soliton solutions of various types. We recover some results of Abenda who studied regular soliton solutions corresponding to a reducible rational curve obtained as a degeneration of a hyperelliptic curve. We study singular soliton solutions as well and clarify how the singularity structure of solutions is reflected in the matrices which determine soliton solutions. | On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions |
The recent rising popularity of ultra-fast delivery services on retail platforms fuels the increasing use of urban warehouses, whose proximity to customers makes fast deliveries viable. The space limit in urban warehouses poses a problem for the online retailers: the number of products (SKUs) they carry is no longer "the more, the better", yet it can still be significantly large, reaching hundreds or thousands in a product category. In this paper, we study algorithms for dynamically identifying a large number of products (i.e., SKUs) with top customer purchase probabilities on the fly, from an ocean of potential products to offer on retailers' ultra-fast delivery platforms. We distill the product selection problem into a semi-bandit model with linear generalization. There are in total $N$ different arms, each with a feature vector of dimension $d$. The player pulls $K$ arms in each period and observes the bandit feedback from each of the pulled arms. We focus on the setting where $K$ is much greater than the number of total time periods $T$ or the dimension of product features $d$. We first analyze a standard UCB algorithm and show its regret bound can be expressed as the sum of a $T$-independent part $\tilde O(K d^{3/2})$ and a $T$-dependent part $\tilde O(d\sqrt{KT})$, which we refer to as "fixed cost" and "variable cost" respectively. To reduce the fixed cost for large $K$ values, we propose a novel online learning algorithm, which iteratively shrinks the upper confidence bounds within each period, and show its fixed cost is reduced by a factor of $d$ to $\tilde O(K \sqrt{d})$. Moreover, we test the algorithms on an industrial dataset from Alibaba Group. Experimental results show that our new algorithm reduces the total regret of the standard UCB algorithm by at least 10%. | Shrinking the Upper Confidence Bound: A Dynamic Product Selection Problem for Urban Warehouses |
Let $I$ be an ideal of a polynomial algebra $S$ over a field generated by square free monomials of degree $\geq d$. If $I$ contains more monomials of degree $d$ than $(n-d)/(n-d+1)$ of the total number of square free monomials of $S$ of degree $d+1$ then $\depth_SI\leq d$, in particular the Stanley's Conjecture holds in this case. | Depth and minimal number of generators of square free monomial ideals |
The dynamics of droplet fragmentation in turbulence is described in the Kolmogorov-Hinze framework. Yet, a quantitative theory is lacking at higher concentrations when strong interactions between the phases and coalescence become relevant, which is common in most flows. Here, we address this issue through a fully-coupled numerical study of the droplet dynamics in a turbulent flow at high Reynolds number. By means of time-space spectral statistics, not currently accessible to experiments, we demonstrate that the characteristic scale of the process, the Hinze scale, can be precisely identified as the scale at which the net energy exchange due to capillarity is zero. Droplets larger than this scale preferentially break up absorbing energy from the flow; smaller droplets, instead, undergo rapid oscillations and tend to coalesce releasing energy to the flow. Further, we link the droplet-size-distribution with the probability distribution of the turbulent dissipation. This shows that key in the fragmentation process is the local flux of energy which dominates the process at large scales, vindicating its locality. | The interaction of droplet dynamics and turbulence cascade |
An object detector performs suboptimally when applied to image data taken from a viewpoint different from the one with which it was trained. In this paper, we present a viewpoint adaptation algorithm that allows a trained single-view object detector to be adapted to a new, distinct viewpoint. We first illustrate how a feature space transformation can be inferred from a known homography between the source and target viewpoints. Second, we show that a variety of trained classifiers can be modified to behave as if that transformation were applied to each testing instance. The proposed algorithm is evaluated on a person detection task using images from the PETS 2007 and CAVIAR datasets, as well as from a new synthetic multi-view person detection dataset. It yields substantial performance improvements when adapting single-view person detectors to new viewpoints, and simultaneously reduces computational complexity. This work has the potential to improve detection performance for cameras viewing objects from arbitrary viewpoints, while simplifying data collection and feature extraction. | Viewpoint Adaptation for Rigid Object Detection |
Using methods of formal geometry, the Poisson sigma model on a closed surface is studied in perturbation theory. The effective action, as a function on vacua, is shown to have no quantum corrections if the surface is a torus or if the Poisson structure is regular and unimodular (e.g., symplectic). In the case of a Kahler structure or of a trivial Poisson structure, the partition function on the torus is shown to be the Euler characteristic of the target; some evidence is given for this to happen more generally. The methods of formal geometry introduced in this paper might be applicable to other sigma models, at least of the AKSZ type. | The Poisson sigma model on closed surfaces |
This work introduces RadVR, a virtual reality tool for daylighting analysis that simultaneously combines qualitative assessments through immersive real-time renderings with quantitative physically correct daylighting simulations in a 6DOF virtual environment. By taking a 3D building model with material properties as input, RadVR allows users to (1) perform physically-based daylighting simulations via Radiance, (2) study sunlight in different hours-of-the-year, (3) interact with a 9-point-in-time matrix for the most representative times of the year, and (4) visualize, compare, and analyze daylighting simulation results. With an end-to-end workflow, RadVR integrates with 3D modeling software that is commonly used by building designers. Additionally, by conducting user experiments we compare the proposed system with DIVA for Rhino, a Radiance-based tool that uses conventional 2D-displays. The results show that RadVR can provide promising assistance in spatial understanding tasks, navigation, and sun position analysis in virtual reality. | RadVR: A 6DOF Virtual Reality Daylighting Analysis Tool |
High-resolution specific-heat measurements of the organic superconductor kappa-(BEDT-TTF)_2Cu[N(CN)_2]Br in the superconducting (B = 0) and normal (B = 14 T) state show a clearly resolvable anomaly at Tc = 11.5 K and an electronic contribution, Ces, which can be reasonably well described by strong-coupling BCS theory. Most importantly, Ces vanishes exponentially in the superconducting state which gives evidence for a fully gapped order parameter. | kappa-(BEDT-TTF)_2Cu[N(CN)_2]Br: a Fully Gapped Strong-Coupling Superconductor |
Let $0<p,q\leq \infty$ and denote by $\mathcal{S}_p^N$ and $\mathcal{S}_q^N$ the corresponding Schatten classes of real $N\times N$ matrices. We study the Gelfand numbers of natural identities $\mathcal{S}_p^N\hookrightarrow \mathcal{S}_q^N$ between Schatten classes and prove asymptotically sharp bounds up to constants only depending on $p$ and $q$. This extends classical results for finite-dimensional $\ell_p$ sequence spaces by E. Gluskin to the non-commutative setting and complements bounds previously obtained by B. Carl and A. Defant, A. Hinrichs and C. Michels, and J. Ch\'avez-Dom\'inguez and D. Kutzarova. | Gelfand numbers of embeddings of Schatten classes |
The maximum entropy technique (MENT) is used to determine the distribution functions of physical values. MENT naturally combines required maximum entropy, the properties of a system and connection conditions in the form of restrictions imposed on the system. It can, therefore, be employed to statistically describe closed and open systems. Examples in which MENT is used to describe equilibrium and non-equilibrium states, as well as steady states that are far from being in thermodynamic equilibrium, are discussed. | The maximum entropy tecniques and the statistical description of systems |
For noncorrelated random variables, we study a concentration property of the family of distributions of normalized sums formed by sequences of times of a given large length. | Concentration of normalized sums and a central limit theorem for noncorrelated random variables |
Supersymmetry and more specifically supergravity grand unification allow one to extrapolate physics from the electroweak scale up to the grand unification scale consistent with electroweak data. Here we give a brief overview of their current status and show that the case for supersymmetry is stronger as a result of the Higgs boson discovery with a mass measurement at $\sim 125$ GeV consistent with the supergravity grand unification prediction that the Higgs boson mass lie below 130 GeV. Thus the discovery of the Higgs boson and the measurement of its mass provide a further impetus for the search for sparticles to continue at the current and future colliders. | A Stronger Case for Superunification Post Higgs Boson Discovery |
Contemporary high-resolution sonar systems use broadband pulses and long arrays to achieve high resolution. It is important to understand effects that high-resolution sonar systems might have on quantitative measures of the scattered field due to the seafloor. A quantity called the broadband scattering cross section is defined, appropriate for high-resolution measurements. The dependence of the broadband scattering cross section, $\sigma_{bb}$ and the scintillation index, $SI$ on resolution was investigated for one-dimensional rough surfaces with power-law spectra and backscattering geometries. Using integral equations and Fourier synthesis, no resolution dependence of $\sigma_{bb}$ was found. The incoherently-averaged frequency-domain scattering cross section has negligible bandwidth dependence. $SI$ increases as resolution increases, grazing angle decreases, and spectral strength increases. This trend is confirmed for center frequencies of 100 kHz and 10 kHz, as well as for power-law spectral exponents of 1.5, 2, and 2.5. The hypothesis that local tilting at the scale of the acoustic resolution is responsible for intensity fluctuations was examined using a representative model for the effect of slopes (inspired by the composite roughness approximation). It was found that slopes are responsible in part for the fluctuations, but other effects, such as multiple scattering and shadowing may also play a role. | Resolution dependence of rough surface scattering using a power law roughness spectrum |
Model predictive control (MPC) schemes are commonly designed with fixed, i.e., time-invariant, horizon length and cost functions. If no stabilizing terminal ingredients are used, stability can be guaranteed via a sufficiently long horizon. A suboptimality index can be derived that gives bounds on the performance of the MPC law over an infinite-horizon (IH). While for time-invariant schemes such index can be computed offline, less attention has been paid to time-varying strategies with adapting cost function which can be found, e.g., in learning-based optimal control. This work addresses the performance bounds of nonlinear MPC with stabilizing horizon and time-varying terminal cost. A scheme is proposed that uses the decay of the optimal finite-horizon cost and convolutes a history stack to predict the bounds on the IH performance. Based on online information on the decay rate, the performance bound estimate is improved while the terminal cost is adapted using methods from adaptive dynamic programming. The adaptation of the terminal cost leads to performance improvement over a time-invariant scheme with the same horizon length. The approach is demonstrated in a case study. | On performance bound estimation in NMPC with time-varying terminal cost |
This paper presents a methodology for selecting the mini-batch size that minimizes Stochastic Gradient Descent (SGD) learning time for single and multiple learner problems. By decoupling algorithmic analysis issues from hardware and software implementation details, we reveal a robust empirical inverse law between mini-batch size and the average number of SGD updates required to converge to a specified error threshold. Combining this empirical inverse law with measured system performance, we create an accurate, closed-form model of average training time and show how this model can be used to identify quantifiable implications for both algorithmic and hardware aspects of machine learning. We demonstrate the inverse law empirically, on both image recognition (MNIST, CIFAR10 and CIFAR100) and machine translation (Europarl) tasks, and provide a theoretic justification via proving a novel bound on mini-batch SGD training. | Optimal Mini-Batch Size Selection for Fast Gradient Descent |
The Leuven workshop on the `Quantum Structure of Space-time and the Geometrical Nature of the Fundamental Interactions' had a special session dedicated to the memory of Sonia Stanciu. This is the summary of a talk delivered by the author on this occasion. | The scientific work of Sonia Stanciu |
A lifelong reinforcement learning system is a learning system that has the ability to learn through trail-and-error interaction with the environment over its lifetime. In this paper, I give some arguments to show that the traditional reinforcement learning paradigm fails to model this type of learning system. Some insights into lifelong reinforcement learning are provided, along with a simplistic prototype lifelong reinforcement learning system. | Some Insights into Lifelong Reinforcement Learning Systems |
We consider a family $\{\Omega^\varepsilon\}_{\varepsilon>0}$ of periodic domains in $\mathbb{R}^2$ with waveguide geometry and analyse spectral properties of the Neumann Laplacian $-\Delta_{\Omega^\varepsilon}$ on $\Omega^\varepsilon$. The waveguide $\Omega^\varepsilon$ is a union of a thin straight strip of the width $\varepsilon$ and a family of small protuberances with the so-called "room-and-passage" geometry. The protuberances are attached periodically, with a period $\varepsilon$, along the strip upper boundary. For $\varepsilon\to 0$ we prove a (kind of) resolvent convergence of $-\Delta_{\Omega^\varepsilon}$ to a certain ordinary differential operator. Also we demonstrate Hausdorff convergence of the spectrum. In particular, we conclude that if the sizes of "passages" are appropriately scaled the first spectral gap of $-\Delta_{\Omega^\varepsilon}$ is determined exclusively by geometric properties of the protuberances. The proofs are carried out using methods of homogenization theory. | Spectrum of a singularly perturbed periodic thin waveguide |
The three-dimensional Schr\"odinger equation with a position-dependent (effective) mass is studied in the framework of Supersymmetrical (SUSY) Quantum Mechanics. The general solution of SUSY intertwining relations with first order supercharges is obtained without any preliminary constraints. Several forms of coefficient functions of the supercharges are investigated and analytical expressions for the mass function and partner potentials are found. As usual for SUSY Quantum Mechanics with nonsingular superpotentials, the spectra of intertwined Hamiltonians coincide up to zero modes of supercharges, and the corresponding wave functions are connected by intertwining relations. All models are partially integrable by construction: each of them has at least one second order symmetry operator. | SUSY Method for the Three-Dimensional Schr\"odinger Equation with Effective Mass |
Landauer's principle laid the main foundation for the development of modern thermodynamics of information. However, in its original inception the principle relies on semiformal arguments and dissipative dynamics. Hence, if and how Landauer's principle applies to unitary quantum computing is less than obvious. Here, we prove an inequality bounding the change of Shannon information encoded in the logical quantum states by quantifying the energetic cost of Hamiltonian gate operations. The utility of this bound is demonstrated by outlining how it can be applied to identify energetically optimal quantum gates in theory and experiment. The analysis is concluded by discussing the energetic cost of quantum error correcting codes with non-interacting qubits, such as Shor's code. | Energetic cost of Hamiltonian quantum gates |
The sensitivity of momentum distributions, recoil polarization observables, and response functions for nucleon knockout by polarized electrons to channel coupling in final-state interactions is investigated using a model in which both the distorting and the coupling potentials are constructed by folding density-dependent effective interactions with nuclear transition densities. Calculations for $^{16}$O are presented for 200 and 433 MeV ejectile energies, corresponding to proposed experiments at MAMI and TJNAF, and for $^{12}$C at 70 and 270 MeV, corresponding to experiments at NIKHEF and MIT-Bates. The relative importance of charge exchange decreases as the ejectile energy increases, but remains significant for 200 MeV. Both proton and neutron knockout cross sections for large recoil momenta, $p_m > 300$ MeV/c, are substantially affected by inelastic couplings even at 433 MeV. Significant effects on the cross section for neutron knockout are also predicted at smaller recoil momenta, especially for low energies. Polarization transfer for proton knockout is insensitive to channel coupling, even for fairly low ejectile energies, but polarization transfer for neutron knockout retains nonnegligible sensitivity to channel coupling for energies up to about 200 MeV. The present results suggest that possible medium modifications of neutron and proton electromagnetic form factors for $Q^2 \gtrsim 0.5 (GeV/c)^2$ can be studied using recoil polarization with relatively little sensitivity due to final state interactions. | Channel Coupling in $A(\vec{e},e' \vec{N})B$ Reactions |
Attention mechanism has been shown to be effective for person re-identification (Re-ID). However, the learned attentive feature embeddings which are often not naturally diverse nor uncorrelated, will compromise the retrieval performance based on the Euclidean distance. We advocate that enforcing diversity could greatly complement the power of attention. To this end, we propose an Attentive but Diverse Network (ABD-Net), which seamlessly integrates attention modules and diversity regularization throughout the entire network, to learn features that are representative, robust, and more discriminative. Specifically, we introduce a pair of complementary attention modules, focusing on channel aggregation and position awareness, respectively. Furthermore, a new efficient form of orthogonality constraint is derived to enforce orthogonality on both hidden activations and weights. Through careful ablation studies, we verify that the proposed attentive and diverse terms each contributes to the performance gains of ABD-Net. On three popular benchmarks, ABD-Net consistently outperforms existing state-of-the-art methods. | ABD-Net: Attentive but Diverse Person Re-Identification |
High parallel framework has been proved to be very suitable for graph processing. There are various work to optimize the implementation in FPGAs, a pipeline parallel device. The key to make use of the parallel performance of FPGAs is to process graph data in pipeline model and take advantage of on-chip memory to realize necessary locality process. This paper proposes a modularize graph processing framework, which focus on the whole executing procedure with the extremely different degree of parallelism. The framework has three contributions. First, the combination of vertex-centric and edge-centric processing framework can been adjusting in the executing procedure to accommodate top-down algorithm and bottom-up algorithm. Second, owing to the pipeline parallel and finite on-chip memory accelerator, the novel edge-block, a block consist of edges vertex, achieve optimizing the way to utilize the on-chip memory to group the edges and stream the edges in a block to realize the stream pattern to pipeline parallel processing. Third, depending to the analysis of the block structure of nature graph and the executing characteristics during graph processing, we design a novel conversion dispatcher to change processing module, to match the corresponding exchange point. | An Efficient Dispatcher for Large Scale GraphProcessing on OpenCL-based FPGAs |
Perturbation theory plays a central role in the approximate solution of nonlinear differential equations. The resultant series expansions are usually divergent and require treatment by singular perturbation methods to generate uniformly valid solutions. However, applying these methods is a subtle art owing to the lack of globally applicable algorithms. Inspired by the fact that all exact solutions of differential equations are consequences of (Lie) symmetries, we reformulate perturbation theory for differential equations in terms of approximate symmetries, via expansions of the Lie symmetries of the solutions. This is a change in perspective from the usual method for obtaining series expansions of the solutions themselves. We show that these approximate symmetries are straightforward to calculate and are never singular; their integration is therefore a powerful way of constructing uniformly convergent solutions. This geometric viewpoint naturally implies that several key singular perturbation methods such as the general perturbative RG-inspired approach of Chen, Goldenfeld and Oono (CGO RG), the method of multiple scales (MMS), and the Poincare-Lindstedt method (PLM), exploit a fundamental class of approximate symmetries that we term ``hidden scale symmetries''. In turn, this clarifies when and why these methods succeed and just as importantly, when they fail. Our algorithmic method directly identifies and integrates these hidden scale symmetries, making it often simpler to implement, and permitting solution of problems where other methods are impractical. Finally, we show how other kinds of approximate symmetry can be exploited to solve systems that do not possess integrable hidden scale symmetries. | Approximate Lie symmetries and singular perturbation theory |
Although there is a growing consensus that a low-carbon transition will be necessary to mitigate the accelerated climate change, the magnitude of transition-risk for investors is difficult to measure exactly. Investors are therefore constrained by the unavailability of suitable measures to quantify the magnitude of the risk and are forced to use the likes of absolute emissions data or ESG scores in order to manage their portfolios. In this article, we define the Single Event Transition Risk (SETR) and illustrate how it can be used to approximate the magnitude of the total exposure of the price of a share to low-carbon transition. We also discuss potential applications of the single event framework and the SETR as a risk measure and discuss future direction on how this can be extended to a system with multiple transition events. | Single Event Transition Risk: A Measure for Long Term Carbon Exposure |
We present some properties of positive closed currents of type $(1,1)$ on compact non-k\"ahlerian surfaces related to our previous study of these objects started in \cite{ChiTo2}. | Positive currents on non-k\"ahlerian surfaces, II |
The development and progress of the studies of winds and mass loss from hot stars, from about 1965 up to now, is discussed in a personal historical perspective. The present state of knowledge about stellar winds, based on papers presented at this workshop, is described. About ten years ago the mechanisms of the winds were reasonably well understood, the mass loss rates were known, and the predictions of stellar evolution theory with mass loss agreed with observations. However, recent studies especially those based on FUSE observations, have resulted in a significant reduction of the mass loss rates, that disagrees with predictions from radiation driven wind models. The situation is discussed and future studies that can clarify the situation are suggested. I also discuss what is known about the dissolution of star clusters in different environments. The dissolution time can be derived from the mass and age distributions of cluster samples. The resulting dissolution times of clusters in the solar neighborhood (SN) and in interacting galaxies are shorter than predicted by two-body relaxation of clusters in a tidal field. Encounters with giant molecular clouds can explain the fate of clusters in the SN and are the most likely cause of the short lifetime of clusters in interacting galaxies. | Mass Loss and Evolution of Stars and Star Clusters: a Personal Historical Perspective |
Image-based three-dimensional (3D) reconstruction utilizes a set of photos to build 3D model and can be widely used in many emerging applications such as augmented reality (AR) and disaster recovery. Most of existing 3D reconstruction methods require a mobile user to walk around the target area and reconstruct objectives with a hand-held camera, which is inefficient and time-consuming. To meet the requirements of delay intensive and resource hungry applications in 5G, we propose an edge computing-based photo crowdsourcing (EC-PCS) framework in this paper. The main objective is to collect a set of representative photos from ubiquitous mobile and Internet of Things (IoT) devices at the network edge for real-time 3D model reconstruction, with network resource and monetary cost considerations. Specifically, we first propose a photo pricing mechanism by jointly considering their freshness, resolution and data size. Then, we design a novel photo selection scheme to dynamically select a set of photos with the required target coverage and the minimum monetary cost. We prove the NP-hardness of such problem, and develop an efficient greedy-based approximation algorithm to obtain a near-optimal solution. Moreover, an optimal network resource allocation scheme is presented, in order to minimize the maximum uploading delay of the selected photos to the edge server. Finally, a 3D reconstruction algorithm and a 3D model caching scheme are performed by the edge server in real time. Extensive experimental results based on real-world datasets demonstrate the superior performance of our EC-PCS system over the existing mechanisms. | An Edge Computing-based Photo Crowdsourcing Framework for Real-time 3D Reconstruction |
The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair Entropy-Statistical Complexity for a large class of time series models would allow statistical tests that are unavailable to date. Working in this direction, we characterize the asymptotic distribution of the empirical Shannon's Entropy for any model under which the true normalized Entropy is neither zero nor one. We obtain the asymptotic distribution from the Central Limit Theorem (assuming large time series), the Multivariate Delta Method, and a third-order correction of its mean value. We discuss the applicability of other results (exact, first-, and second-order corrections) regarding their accuracy and numerical stability. Within a general framework for building test statistics about Shannon's Entropy, we present a bilateral test that verifies if there is enough evidence to reject the hypothesis that two signals produce ordinal patterns with the same Shannon's Entropy. We applied this bilateral test to the daily maximum temperature time series from three cities (Dublin, Edinburgh, and Miami) and obtained sensible results. | Statistical Properties of the Entropy from Ordinal Patterns |
We compute the gradient expansion for anisotropic hydrodynamics. The results are compared with the corresponding expansion of the underlying kinetic-theory model with the collision term treated in the relaxation time approximation. We find that a recent formulation of anisotropic hydrodynamics based on an anisotropic matching principle yields the first three terms of the gradient expansion in agreement with those obtained for the kinetic theory. This gives further support for this particular hydrodynamic model as a good approximation of the kinetic-theory approach. We further find that the gradient expansion of anisotropic hydrodynamics is an asymptotic series, and the singularities of the analytic continuation of its Borel transform indicate the presence of non-hydrodynamic modes. | Gradient expansion for anisotropic hydrodynamics |
The understanding of interaction effects between marine energy converters represents the next step in the research process that should eventually lead to the deployment of such devices. Although some a priori considerations have been suggested recently, very few real condition studies have been carried out concerning this issue. Trials were run on 1/30th scale models of three-bladed marine current turbine prototypes in a flume tank. The present work focuses on the case where a turbine is placed at different locations in the wake of a first one. The interaction effects in terms of performance and wake of the second turbine are examined and compared to the results obtained on the case of one single turbine. Besides, a three-dimensional software, based on a vortex method is currently being developed, and will be used in the near future to model more complex layouts. The experimental study shows that the second turbine is deeply affected by the presence of an upstream device and that a compromise between individual device performance and inter-device spacing is necessary. Numerical results show good agreement with the experiment and are promising for the future modelling of turbine farms. | Numerical and experimental study of the interaction between two marine current turbines |
Nonlinear kinetic theory of cosmic ray (CR) acceleration in supernova remnants (SNRs) is used to investigate the properties of Kepler's SNR and, in particular, to predict the gamma-ray spectrum expected from this SNR. Observations of the nonthermal radio and X-ray emission spectra as well as theoretical constraints for the total supernova (SN) explosion energy E_sn are used to constrain the astronomical and particle acceleration parameters of the system. Under the assumption that Kepler's SN is a type Ia SN we determine for any given explosion energy E_sn and source distance d the mass density of the ambient interstellar medium (ISM) from a fit to the observed SNR size and expansion speed. This makes it possible to make predictions for the expected gamma-ray flux. Exploring the expected distance range we find that for a typical explosion energy E_sn=10^51 erg the expected energy flux of TeV gamma-rays varies from 2x10^{-11} to 10^{-13} erg/(cm^2 s) when the distance changes from d=3.4 kpc to 7 kpc. In all cases the gamma-ray emission is dominated by \pi^0-decay gamma-rays due to nuclear CRs. Therefore Kepler's SNR represents a very promising target for instruments like H.E.S.S., CANGAROO and GLAST. A non-detection of gamma-rays would mean that the actual source distance is larger than 7 kpc. | Gamma-ray emission expected from Kepler's SNR |
We describe and analyze a finite element numerical scheme for the parabolic-parabolic Keller-Segel model. The scalar auxiliary variable method is used to retrieve the monotonic decay of the energy associated with the system at the discrete level. This method relies on the interpretation of the Keller-Segel model as a gradient flow. The resulting numerical scheme is efficient and easy to implement. We show the existence of a unique non-negative solution and that a modified discrete energy is obtained due to the use of the SAV method. We also prove the convergence of the discrete solutions to the ones of the weak form of the continuous Keller-Segel model. | Scalar auxiliary variable finite element scheme for the parabolic-parabolic Keller-Segel model |
The effect of the full treatment is a primary parameter of interest in policy evaluation, while often only the effect of a subset of treatment is estimated. We partially identify the local average treatment effect of receiving full treatment (LAFTE) using an instrumental variable that may induce individuals into only a subset of treatment (movers). We show that movers violate the standard exclusion restriction, necessary conditions on the presence of movers are testable, and partial identification holds under a double exclusion restriction. We identify movers in four empirical applications and estimate informative bounds on the LAFTE in three of them. | Instrument-based estimation of full treatment effects with movers |
We consider the Cauchy problem for a second-order nonlinear evolution equation in a Hilbert space. This equation represents the abstract generalization of the Ball integro-differential equation. The general nonlinear case with respect to terms of the equation which include a square of a norm of a gradient is considered. A three-layer semi-discrete scheme is proposed in order to find an approximate solution. In this scheme, the approximation of nonlinear terms that are dependent on the gradient is carried out by using an integral mean. We show that the solution of the nonlinear discrete problem and its corresponding difference analogue of a first-order derivative is uniformly bounded. For the solution of the corresponding linear discrete problem, it is obtained high-order a priori estimates by using two-variable Chebyshev polynomials. Based on these estimates we prove the stability of the nonlinear discrete problem. For smooth solutions, we provide error estimates for the approximate solution. An iteration method is applied in order to find an approximate solution for each temporal step. The convergence of the iteration process is proved. | On Stability and Convergence of a Three-layer Semi-discrete Scheme for an Abstract Analogue of the Ball Integro-differential Equation |
We study the intrinsic superconductivity in a dissipative Floquet electronic system in the presence of attractive interactions. Based on the functional Keldysh theory beyond the mean-field treatment, we find that the system shows a time-periodic bosonic condensation and reaches an intrinsic dissipative Floquet superconducting (SC) phase. Due to the interplay between dissipations and periodic modulations, the Floquet SC gap becomes "soft" and contains the diffusive fermionic modes with finite lifetimes. However, bosonic modes of the bosonic condensation are still propagating even in the presence of dissipations. | Intrinsic dissipative Floquet superconductors beyond mean-field theory |
Auto-correlated noise appears in many solid state qubit systems and hence needs to be taken into account when developing gate operations for quantum information processing. However, explicitly simulating this kind of noise is often less efficient than approximate methods. Here, we focus on the filter function formalism, which allows the computation of gate fidelities in the presence of auto-correlated classical noise. Hence, this formalism can be combined with optimal control algorithms to design control pulses, which optimally implement quantum gates. To enable the use of gradient-based algorithms with fast convergence, we present analytically derived filter function gradients with respect to control pulse amplitudes, and analyze the computational complexity of our results. When comparing pulse optimization using our derivatives to a gradient-free approach, we find that the gradient-based method is roughly two orders of magnitude faster for our test cases. We also provide a modular computational implementation compatible with quantum optimal control packages. | Analytic Filter Function Derivatives for Quantum Optimal Control |
We use holography to analyze the evolution of an ensemble of jets, with an initial probability distribution for their energy and opening angle as in proton-proton (pp) collisions, as they propagate through an expanding cooling droplet of strongly coupled plasma as in heavy ion collisions. We identify two competing effects: (i) each individual jet widens as it propagates; (ii) the opening angle distribution for jets emerging from the plasma within any specified range of energies has been pushed toward smaller angles, comparing to pp jets with the same energies. The second effect arises because small-angle jets suffer less energy loss and because jets with a higher initial energy are less probable in the ensemble. We illustrate both effects in a simple two-parameter model, and find that their consequence in sum is that the opening angle distribution for jets in any range of energies contains fewer narrow and wide jets. Either effect can dominate in the mean opening angle, for not unreasonable values of the parameters. So, the mean opening angle for jets with a given energy can easily shift toward smaller angles, as experimental data may indicate, even while every jet in the ensemble broadens. | Evolution of the jet opening angle distribution in holographic plasma |
We improve on recent results that establish the existence of solutions of certain semilinear wave equations possessing an interface that roughly sweeps out a timelike surface of vanishing mean curvature in Minkowski space. Compared to earlier work, we present sharper estimates, in stronger norms, of the solutions in question. | A refined description of evolving interfaces in certain nonlinear wave equations |
The notion of incompatibility of measurements in quantum theory is in stark contrast with the corresponding classical perspective, where all physical observables are jointly measurable. It is of interest to examine if the results of two or more measurements in the quantum scenario can be perceived from a classical point of view or they still exhibit non-classical features. Clearly, commuting observables can be measured jointly using projective measurements and their statistical outcomes can be discerned classically. However, such simple minded association of compatibility of measurements with commutativity turns out to be limited in an extended framework, where the usual notion of sharp projective valued measurements of self adjoint observables gets broadened to include unsharp measurements of generalized observables constituting positive operator valued measures (POVM). There is a surge of research activity recently towards gaining new physical insights on the emergence of classical behavior via joint measurability of unsharp observables. Here, we explore the entropic uncertainty relation for a pair of discrete observables (of Alice's system) when an entangled quantum memory of Bob is restricted to record outcomes of jointly measurable POVMs only. Within the joint measurability regime, the sum of entropies associated with Alice's measurement outcomes - conditioned by the results registered at Bob's end - are constrained to obey an entropic steering inequality. In this case, Bob's non-steerability reflects itself as his inability in predicting the outcomes of Alice's pair of non-commuting observables with better precision, even when they share an entangled state. As a further consequence, the quantum advantage envisaged for the construction of security proofs in key distribution is lost, when Bob's measurements are restricted to the joint measurability regime. | Joint measurability, steering and entropic uncertainty |
There is resurging interest, in statistics and machine learning, in solvers for ordinary differential equations (ODEs) that return probability measures instead of point estimates. Recently, Conrad et al. introduced a sampling-based class of methods that are 'well-calibrated' in a specific sense. But the computational cost of these methods is significantly above that of classic methods. On the other hand, Schober et al. pointed out a precise connection between classic Runge-Kutta ODE solvers and Gaussian filters, which gives only a rough probabilistic calibration, but at negligible cost overhead. By formulating the solution of ODEs as approximate inference in linear Gaussian SDEs, we investigate a range of probabilistic ODE solvers, that bridge the trade-off between computational cost and probabilistic calibration, and identify the inaccurate gradient measurement as the crucial source of uncertainty. We propose the novel filtering-based method Bayesian Quadrature filtering (BQF) which uses Bayesian quadrature to actively learn the imprecision in the gradient measurement by collecting multiple gradient evaluations. | Active Uncertainty Calibration in Bayesian ODE Solvers |
The influence of $\Delta$ isobar components on the ground state properties of nuclear systems is investigated for nuclear matter as well as finite nuclei. Many-body wave functions, including isobar configurations, and binding energies are evaluated employing the framework of the coupled-cluster theory. It is demonstrated that the effect of isobar configurations depends in a rather sensitive way on the model used for the baryon-baryon interaction. As examples for realistic baryon-baryon interactions with explicit inclusion of isobar channels we use the local ($V28$) and non-local meson exchange potentials (Bonn$_{2000}$) but also a model recently developed by the Salamanca group, which is based on a quark picture. The differences obtained for the nuclear observables are related to the treatment of the interaction, the $\pi$-exchange contributions in particular, at high momentum transfers. | $\Delta(1232)$ Isobar Excitations and the Ground State of Nuclei |
In order to better understand the variation mechanism of ozone abundance in the middle atmosphere, the simultaneous monitoring of ozone and other minor molecular species, which are related to ozone depletion, is the most fundamental and critical method. A waveguide-type multiplexer was developed for the expansion of the observation frequency range of a millimeter-wave spectroradiometer, for the simultaneous observation of multiple molecular spectral lines. The proposed multiplexer contains a cascaded four-stage sideband-separating filter circuit. The waveguide circuit was designed based on electromagnetic analysis, and the pass frequency bands of Stages 1-4 were 243-251 GHz, 227-235 GHz, 197-205 GHz, and 181-189 GHz. The insertion and return losses of the multiplexer were measured using vector network analyzers, each observation band was well-defined, and the bandwidths were appropriately specified. Moreover, the receiver noise temperature and the image rejection ratio (IRR) using the superconducting mixer at 4 K were measured. As a result, the increase in receiver noise due to the multiplexer compared with that of only the mixer can be attributed to the transmission loss of the waveguide circuit in the multiplexer. The IRRs were higher than 25 dB at the center of each observation band. This indicates that a high and stable IRR performance can be achieved by the waveguide-type multiplexer for the separation of sideband signals. | Waveguide-Type Multiplexer for Multiline Observation of Atmospheric Molecules using Millimeter-Wave Spectroradiometer |
The gravitational and electromagnetic multipole moments of the charged rotating disc of dust, which is an axisymmetric, stationary solution of the Einstein-Maxwell equations in terms of a post-Newtonian expansion, are calculated and discussed. It turns out that the individual mass, angular momentum, electric and magnetic moments are ordered in the sense that higher moments have a lower absolute value. There is an interesting conjecture stating that the absolute values of all higher multipole moments of a uniformly rotating perfect fluid body are always greater than those of the corresponding Kerr spacetime, which we generalize to include charged bodies. We find that for the charged rotating disc of dust the conjecture holds (within the limits of accuracy of the post-Newtonian expansion). | Multipole moments of a charged rotating disc of dust in general relativity |
In this work, we present a unified performance analysis of a free-space optical (FSO) link that accounts for pointing errors and both types of detection techniques (i.e. intensity modulation/direct detection (IM/DD) as well as heterodyne detection). More specifically, we present unified exact closed-form expressions for the cumulative distribution function, the probability density function, the moment generating function, and the moments of the end-to-end signal-to-noise ratio (SNR) of a single link FSO transmission system, all in terms of the Meijer's G function except for the moments that is in terms of simple elementary functions. We then capitalize on these unified results to offer unified exact closed-form expressions for various performance metrics of FSO link transmission systems, such as, the outage probability, the scintillation index (SI), the average error rate for binary and $M$-ary modulation schemes, and the ergodic capacity (except for IM/DD technique, where we present closed-form lower bound results), all in terms of Meijer's G functions except for the SI that is in terms of simple elementary functions. Additionally, we derive the asymptotic results for all the expressions derived earlier in terms of Meijer's G function in the high SNR regime in terms of simple elementary functions via an asymptotic expansion of the Meijer's G function. We also derive new asymptotic expressions for the ergodic capacity in the low as well as high SNR regimes in terms of simple elementary functions via utilizing moments. All the presented results are verified via computer-based Monte-Carlo simulations. | Performance Analysis of Free-Space Optical Links Over M\'{a}laga ($\mathcal{M}$) Turbulence Channels with Pointing Errors |
The dependence of the $q$ and $T$ parameters of the Tsallis-distribution-shaped fragmentation function (FF) on the fragmentation scale (found to be equal to the jet mass) is calculated via the resummation of the branching process of jet fragmentation in the leading-log appriximation (LLA) in the $\phi^3$ theory. Jet and hadron spectra in electron-positron ($e^+e^-$) annihilations with 2- and 3-jet final states are calculated using virtual leading partons. It is found that jets, produced earlier in the branching process, are more energetic, and the energy, angle and multiplicity distributions of hadrons stemming from them are broader. It is also found that replacing the LL resummation in the branching process by a single splitting provides good approximation for the jet energy distribution in 2-jet events. Furthermore, a micro-canonical statistical event generator is presented for the event-by-event calculation of hadron momenta in $e^+e^-$ annihilations. | Scale dependence of the q and T parameters of the Tsallis distribution in the process of jet fragmentation |
Distribution shifts are a serious concern in modern statistical learning as they can systematically change the properties of the data away from the truth. We focus on Wasserstein distribution shifts, where every data point may undergo a slight perturbation, as opposed to the Huber contamination model where a fraction of observations are outliers. We formulate and study shifts beyond independent perturbations, exploring Joint Distribution Shifts, where the per-observation perturbations can be coordinated. We analyze several important statistical problems, including location estimation, linear regression, and non-parametric density estimation. Under a squared loss for mean estimation and prediction error in linear regression, we find the exact minimax risk, a least favorable perturbation, and show that the sample mean and least squares estimators are respectively optimal. This holds for both independent and joint shifts, but the least favorable perturbations and minimax risks differ. For other problems, we provide nearly optimal estimators and precise finite-sample bounds. We also introduce several tools for bounding the minimax risk under distribution shift, such as a smoothing technique for location families, and generalizations of classical tools including least favorable sequences of priors, the modulus of continuity, Le Cam's, Fano's, and Assouad's methods. | Statistical Estimation Under Distribution Shift: Wasserstein Perturbations and Minimax Theory |
Recently achieved two-component dipolar Bose-Einstein condensates open exciting possibilities for the study of mixtures of ultra-dilute quantum liquids. While non-dipolar self-bound mixtures are necessarily miscible with an approximately fixed ratio between the two densities, the density ratio for the dipolar case is free. As a result, self-bound dipolar mixtures present qualitatively novel and much richer physics, characterized by three possible ground-state phases: miscible, symmetric immiscible and asymmetric immiscible, which may in principle occur at any population imbalance. Self-bound immiscible droplets are possible due to mutual non-local inter-component attraction, which results in the formation of a droplet molecule. Moreover, our analysis of the impurity regime, shows that quantum fluctuations in the majority component crucially modify the miscibility of impurities. Our work opens intriguing perspectives for the exploration of spinor physics in ultra-dilute liquids, which should resemble to some extent that of 4He-3He droplets and impurity-doped helium droplets. | Quantum droplets of dipolar mixtures |
Motivated by queues with many servers, we study Brownian steady-state approximations for continuous time Markov chains (CTMCs). Our approximations are based on diffusion models (rather than a diffusion limit) whose steady-state, we prove, approximates that of the Markov chain with notable precision. Strong approximations provide such "limitless" approximations for process dynamics. Our focus here is on steady-state distributions, and the diffusion model that we propose is tractable relative to strong approximations. Within an asymptotic framework, in which a scale parameter $n$ is taken large, a uniform (in the scale parameter) Lyapunov condition imposed on the sequence of diffusion models guarantees that the gap between the steady-state moments of the diffusion and those of the properly centered and scaled CTMCs shrinks at a rate of $\sqrt{n}$. Our proofs build on gradient estimates for solutions of the Poisson equations associated with the (sequence of) diffusion models and on elementary martingale arguments. As a by-product of our analysis, we explore connections between Lyapunov functions for the fluid model, the diffusion model and the CTMC. | Diffusion models and steady-state approximations for exponentially ergodic Markovian queues |
Compactifications of type II theories on Calabi-Yau threefolds including electric and magnetic background fluxes are discussed. We derive the bosonic part of the four-dimensional low energy effective action and show that it is a non-canonical N=2 supergravity which includes a massive two-form. The symplectic invariance of the theory is maintained as long as the flux parameters transform as a symplectic vector and a massive two-form which couples to both electric and magnetic field strengths is present. The mirror symmetry between type IIA and type IIB compactified on mirror manifolds is shown to hold for R-R fluxes at the level of the effective action. We also compactify type IIA in the presence of NS three-form flux but the mirror symmetry in this case remains unclear. | Type II Theories Compactified on Calabi-Yau Threefolds in the Presence of Background Fluxes |
The alternating direction method of multipliers (ADMM) is a popular method for solving convex separable minimization problems with linear equality constraints. The generalization of the two-block ADMM to the three-block ADMM is not trivial since the three-block ADMM is not convergence in general. Many variants of three-block ADMM have been developed with guarantee convergence. Besides the ADMM, the alternating minimization algorithm (AMA) is also an important algorithm for solving the convex separable minimization problem with linear equality constraints. The AMA is first proposed by Tseng, and it is equivalent to the forward-backward splitting algorithm applied to the corresponding dual problem. In this paper, we design a variant of three-block AMA, which is derived by employing an inertial extension of the three-operator splitting algorithm to the dual problem. Compared with three-block ADMM, the first subproblem of the proposed algorithm only minimizing the Lagrangian function. As a by-product, we obtain a relaxed algorithm of Davis and Yin. Under mild conditions on the parameters, we establish the convergence of the proposed algorithm in infinite-dimensional Hilbert spaces. Finally, we conduct numerical experiments on the stable principal component pursuit (SPCP) to verify the efficiency and effectiveness of the proposed algorithm. | Convergence analysis of a relaxed inertial alternating minimization algorithm with applications |
We propose a new per-layer adaptive step-size procedure for stochastic first-order optimization methods for minimizing empirical loss functions in deep learning, eliminating the need for the user to tune the learning rate (LR). The proposed approach exploits the layer-wise stochastic curvature information contained in the diagonal blocks of the Hessian in deep neural networks (DNNs) to compute adaptive step-sizes (i.e., LRs) for each layer. The method has memory requirements that are comparable to those of first-order methods, while its per-iteration time complexity is only increased by an amount that is roughly equivalent to an additional gradient computation. Numerical experiments show that SGD with momentum and AdamW combined with the proposed per-layer step-sizes are able to choose effective LR schedules and outperform fine-tuned LR versions of these methods as well as popular first-order and second-order algorithms for training DNNs on Autoencoder, Convolutional Neural Network (CNN) and Graph Convolutional Network (GCN) models. Finally, it is proved that an idealized version of SGD with the layer-wise step sizes converges linearly when using full-batch gradients. | Layer-wise Adaptive Step-Sizes for Stochastic First-Order Methods for Deep Learning |
In molecular devices electronic degrees of freedom are coupled to vibrational modes of the molecule, offering an opportunity to study fundamental aspects of this coupling between at the nanoscale. To this end we consider the nonequilibrium heat exchange between a conduction band and a bosonic bath mediated by a single molecule. For molecules large enough so that on-site interactions can be dropped we carry out an asymptotically exact calculation of the heat current, governed by the smallness of the electron-phonon coupling, and obtain the steady state heat current driven by a finite temperature drop. At low temperatures the heat current is found to have a power-law behavior with respect to the temperature difference with the power depending on the nature of the bosonic bath. At high temperatures, on the other hand, the current is linear in the temperature difference for all types of bosonic baths. The crossover between these behaviors is described. Some of the results are given a physical explanation by comparing to a perturbative Master equation calculation (whose limitation we examine). | Single-molecule-mediated heat current between an electronic and a bosonic bath |
The aim of this paper is to obtain an upper bound to the second Hankel the determinant for starlike and convex functions of order. | Hankle determinant for starlike and convex functions of order |
This manuscript presents a diagnostic analysis of three dark energy models resulting from the parametrization of the deceleration parameter. These models exhibit intriguing features, including late-time acceleration and a cosmological phase transition from early deceleration to late acceleration. The analysis utilizes parametrizations of the deceleration parameter, $q(z)$, and employs Cosmic Chronometers (CC), Type Ia supernovae (SNIa), Gamma Ray Bursts (GRB), Quasar (Q) and Baryon Acoustic Oscillations (BAO) datasets to constrain the models and determine the best-fitting values of the model parameters. Additionally, the evolution of kinematic cosmographic parameters is investigated. The study focuses on discussing the statefinder and Om diagnostic analyses of the considered models, comparing them with the well-established $\Lambda$CDM and SCDM models. By utilizing information criteria, the viability of the models is examined, assessing their goodness of fit and their ability to explain the observed data. The results provide valuable insights into the behavior and characteristics of the dark energy models. The comparison with the standard models sheds light on the similarities and differences, while the information criteria analysis offers a quantitative assessment of their suitability. This analysis contributes to our understanding of the dynamics and evolution of the universe, furthering our knowledge of dark energy and its role in shaping the cosmos. | Diagnostic and Comparative Analysis of Dark Energy Models with $q(z)$ Parametrizations |
This paper proposes an adaptable path tracking control system based on Reinforcement Learning (RL) for autonomous cars. A four-parameter controller shapes the behavior of the vehicle to navigate on lane changes and roundabouts. The tuning of the tracker uses an educated Q-Learning algorithm to minimize the lateral and steering trajectory errors. The CARLA simulation environment was used both for training and testing. The results show the vehicle is able to adapt its behavior to the different types of reference trajectories, navigating safely with low tracking errors. The use of a ROS bridge between the CARLA and the tracker results (i) in a realistic system, and (ii) simplifies the replacement of the CARLA by a real vehicle. An argument on the dependability of the overall architecture based on stability results of non-smooth systems is presented at the end of the paper. | Tuning Path Tracking Controllers for Autonomous Cars Using Reinforcement Learning |
Electromagnetic properties of neutrinos, if ever observed, could help to decide the Dirac versus Majorana nature of neutrinos. We show that the magnetic moments of Majorana neutrinos have to fulfill triangle inequalities, $|\mu_{\nu_\tau}|^2 \leq |\mu_{\nu_\mu}|^2 +|\mu_{\nu_e}|^2$ and cyclic permutations, which do not hold for Dirac neutrinos. Observing a violation of these inequalities, e.g. by measuring the magnetic moment of $\nu_\tau$ at SHiP, would thus strongly hint either at the Dirac nature of neutrinos or at the presence of at least one extra light sterile mode. | Triangle Inequalities for Majorana-Neutrino Magnetic Moments |
In the present paper, we will characterize the boundedness of the generalized fractional integral operators $I_{\rho}$ and the generalized fractional maximal operators $M_{\rho}$ on Orlicz spaces, respectively. Moreover, we will give a characterization for the Spanne-type boundedness and the Adams-type boundedness of the operators $M_{\rho}$ and $I_{\rho}$ on generalized Orlicz--Morrey spaces, respectively. Also we give criteria for the weak versions of the Spanne-type boundedness and the Adams-type boundedness of the operators $M_{\rho}$ and $I_{\rho}$ on generalized Orlicz--Morrey spaces. | Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz--Morrey spaces of the third kind |
A review of Lorentz and CPT tests performed in atomic systems is presented. A theoretical framework extending QED in the context of the standard model is used to analyze a variety of systems. Experimental signatures of possible Lorentz and CPT violation in these systems are investigated. Estimated bounds attainable in future experiments and actual bounds obtained in recent experiments are given. | Lorentz and CPT Tests in Atomic Systems |
The recently reported Rutherford backscattering and particle-induced X-ray emission experiments have revealed that in low-temperature MBE grown GaMnAs a significant part of the incorporated Mn atoms occupies tetrahedral interstitial sites in the lattice. Here we study the magnetic properties of these interstitial ions. We show that they do not participate in the hole-induced ferromagnetism. Moreover, Mn interstitial double donors may form pairs with the nearest substitutional Mn acceptors - our calculations evidence that the spins in such pairs are antiferromagnetically coupled by the superexchange. We also show that for the Mn ion in the other, hexagonal, interstitial position (which seems to be the case in the GaMnBeAs samples) the p-d interactions with the holes, responsible for the ferromagnetism, are very much suppressed. | Spin interactions of interstitial Mn ions in ferromagnetic GaMnAs |
We propose a new model of the D-term hybrid inflation in the framework of supergravity. Although our model introduces, analogously to the conventional D-term inflation, the inflaton and a pair of scalar fields charged under a $U(1)$ gauge symmetry, we study the logarithmic and exponential dependence on the inflaton field, respectively, for the K\"ahler and superpotential. This results in a characteristic one-loop scalar potential consisting of linear and exponential terms, which realizes the small-field inflation dominated by the Fayet-Iliopoulos term. With the reasonable values for the coupling coefficients and, in particular, with the $U(1)$ gauge coupling constant comparable to that of the Standard Model, our D-term inflation model can solve the notorious problems in the conventional D-term inflation, namely, the CMB constraints on the spectral index and the generation of cosmic strings. | A viable D-term hybrid inflation |
In order to grasp the features arising from cellular discreteness and individuality, in large parts of cell tissue modelling agent-based models are favoured. The subclass of off-lattice models allows for a physical motivation of the intercellular interaction rules. We apply an improved version of a previously introduced off-lattice agent-based model to the steady-state flow equilibrium of skin. The dynamics of cells is determined by conservative and drag forces,supplemented with delta-correlated random forces. Cellular adjacency is detected by a weighted Delaunay triangulation. The cell cycle time of keratinocytes is controlled by a diffusible substance provided by the dermis. Its concentration is calculated from a diffusion equation with time-dependent boundary conditions and varying diffusion coefficients. The dynamics of a nutrient is also taken into account by a reaction-diffusion equation. It turns out that the analysed control mechanism suffices to explain several characteristics of epidermal homoeostasis formation. In addition, we examine the question of how {\em in silico} melanoma with decreased basal adhesion manage to persist within the steady-state flow-equilibrium of the skin.Interestingly, even for melanocyte cell cycle times being substantially shorter than for keratinocytes, tiny stochastic effects can lead to completely different outcomes. The results demonstrate that the understanding of initial states of tumour growth can profit significantly from the application of off-lattice agent-based models in computer simulations. | A modelling approach towards Epidermal homoeostasis control |
We demonstrate an all-optical phase regeneration technique based on Kerr soliton combs, which can realize degraded quaternary phase shift keying (QPSK) signal regeneration through phase-sensitive amplification. A Kerr soliton comb is generated at the receiver side of optical communication systems based on a carrier recovery scheme and is used as coherent dual pumps to achieve phase regeneration. Our study will enhance the relay and reception performance of all-optical communication systems. | Phase regeneration of QPSK signals based on Kerr soliton combs in a highly nonlinear optical fiber |
The aim of this paper is to study the dimensions and standard part maps between the field of $p$-adic numbers ${{\mathbb Q}_p}$ and its elementary extension $K$ in the language of rings $L_r$. We show that for any $K$-definable set $X\subseteq K^m$, $\text{dim}_K(X)\geq \text{dim}_{{\mathbb Q}_p}(X\cap {{\mathbb Q}_p}^m)$. Let $V\subseteq K$ be convex hull of $K$ over ${{\mathbb Q}_p}$, and $\text{\st}: V\rightarrow {{\mathbb Q}_p}$ be the standard part map. We show that for any $K$-definable function $f:K^m\rightarrow K$, there is definable subset $D\subseteq{{\mathbb Q}_p}^m$ such that ${{\mathbb Q}_p}^m\backslash D$ has no interior, and for all $x\in D$, either $f(x)\in V$ and $\text{st}(f(\text{st}^{-1}(x)))$ is constant, or $f(\text{st}^{-1}(x))\cap V=\emptyset$. We also prove that $\text{dim}_K(X)\geq \text{dim}_{{\mathbb Q}_p}(\text{st}(X\cap V^m))$ for every definable $X\subseteq K^m$. | On Dimensions, Standard Part Maps, and $p$-Adically Closed Fields |
We present a novel active learning algorithm, termed as iterative surrogate model optimization (ISMO), for robust and efficient numerical approximation of PDE constrained optimization problems. This algorithm is based on deep neural networks and its key feature is the iterative selection of training data through a feedback loop between deep neural networks and any underlying standard optimization algorithm. Under suitable hypotheses, we show that the resulting optimizers converge exponentially fast (and with exponentially decaying variance), with respect to increasing number of training samples. Numerical examples for optimal control, parameter identification and shape optimization problems for PDEs are provided to validate the proposed theory and to illustrate that ISMO significantly outperforms a standard deep neural network based surrogate optimization algorithm. | Iterative Surrogate Model Optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networks |
In this paper, we investigate the minimax properties of Stein block thresholding in any dimension $d$ with a particular emphasis on $d=2$. Towards this goal, we consider a frame coefficient space over which minimaxity is proved. The choice of this space is inspired by the characterization provided in \cite{BorupNielsen} of family of smoothness spaces on $\mathbb{R}^d$, a subclass of so-called decomposition spaces \cite{Feichtinger}. These smoothness spaces cover the classical case of Besov spaces, as well as smoothness spaces corresponding to curvelet-type constructions. Our main theoretical result investigates the minimax rates over these decomposition spaces, and shows that our block estimator can achieve the optimal minimax rate, or is at least nearly-minimax (up to a $\log$ factor) in the least favorable situation. Another contribution is that the minimax rates given here are stated for a general noise sequence model in the transform coefficient domain beyond the usual i.i.d. Gaussian case. The choice of the threshold parameter is theoretically discussed and its optimal value is stated for some noise models such as the (non-necessarily i.i.d.) Gaussian case. We provide a simple, fast and a practical procedure. We also report a comprehensive simulation study to support our theoretical findings. The practical performance of our Stein block denoising compares very favorably to the BLS-GSM state-of-the art denoising algorithm on a large set of test images. A toolbox is made available for download on the Internet to reproduce the results discussed in this paper. | Stein Block Thresholding For Image Denoising |
We propose the ViNet architecture for audio-visual saliency prediction. ViNet is a fully convolutional encoder-decoder architecture. The encoder uses visual features from a network trained for action recognition, and the decoder infers a saliency map via trilinear interpolation and 3D convolutions, combining features from multiple hierarchies. The overall architecture of ViNet is conceptually simple; it is causal and runs in real-time (60 fps). ViNet does not use audio as input and still outperforms the state-of-the-art audio-visual saliency prediction models on nine different datasets (three visual-only and six audio-visual datasets). ViNet also surpasses human performance on the CC, SIM and AUC metrics for the AVE dataset, and to our knowledge, it is the first network to do so. We also explore a variation of ViNet architecture by augmenting audio features into the decoder. To our surprise, upon sufficient training, the network becomes agnostic to the input audio and provides the same output irrespective of the input. Interestingly, we also observe similar behaviour in the previous state-of-the-art models \cite{tsiami2020stavis} for audio-visual saliency prediction. Our findings contrast with previous works on deep learning-based audio-visual saliency prediction, suggesting a clear avenue for future explorations incorporating audio in a more effective manner. The code and pre-trained models are available at https://github.com/samyak0210/ViNet. | ViNet: Pushing the limits of Visual Modality for Audio-Visual Saliency Prediction |
We obtained BVIc photometry of IRC-10443 on 85 different nights distributed over two years, and in addition low resolution absolute spectro- photometry and high resolution Echelle spectroscopy. Our data show that IRC-10443, which was never studied before in any detail, is a SRa variable, characterized by Delta(B)=1.27, Delta(V)=1.14 and Delta(I)=0.70 mag amplitudes and mean values <B>=13.75, <V>=11.33 and <Ic>=6.18 mag. Two strong periodicities are simultaneously present: a principal one of 85.5 (+/-0.2) days, and a secondary one of 620 (+/-15) days, both sinusoidal in shape, and with semi-amplitudes Delta(V)=0.41 and 0.20 mag, respectively. IRC-10443 turns out to be a M7III star, with a mean heliocentric radial velocity -28 km/s and reddened by E(B-V)=0.87, a third of which of circumstellar origin. The same 0.5 kpc distance is derived from application of the appropriate period-luminosity relations to both the principal and the secondary periods. The long secondary period causes a sinusoidal variation in color of 0.13 mag semi-amplitude in V-Ic, with IRC-10443 being bluest at maximum and reddest at minimum, and with associated changes in effective temperature and radius of 85 K and 6%, respectively. This behavior of colors argues in favor of a pulsation nature for the still mysterious long secondary periods in AGB stars. | IRC-10443: a multi-periodic SRa variable and the nature of long secondary periods in AGB stars |
Neural networks have been used successfully in a variety of fields, which has led to a great deal of interest in developing a theoretical understanding of how they store the information needed to perform a particular task. We study the weight matrices of trained deep neural networks using methods from random matrix theory (RMT) and show that the statistics of most of the singular values follow universal RMT predictions. This suggests that they are random and do not contain system specific information, which we investigate further by comparing the statistics of eigenvector entries to the universal Porter-Thomas distribution. We find that for most eigenvectors the hypothesis of randomness cannot be rejected, and that only eigenvectors belonging to the largest singular values deviate from the RMT prediction, indicating that they may encode learned information. In addition, a comparison with RMT predictions also allows to distinguish networks trained in different learning regimes - from lazy to rich learning. We analyze the spectral distribution of the large singular values using the Hill estimator and find that the distribution cannot in general be characterized by a tail index, i.e. is not of power law type. | Random matrix analysis of deep neural network weight matrices |
Vertical Federated Learning (VFL) enables multiple data owners, each holding a different subset of features about largely overlapping sets of data sample(s), to jointly train a useful global model. Feature selection (FS) is important to VFL. It is still an open research problem as existing FS works designed for VFL either assumes prior knowledge on the number of noisy features or prior knowledge on the post-training threshold of useful features to be selected, making them unsuitable for practical applications. To bridge this gap, we propose the Federated Stochastic Dual-Gate based Feature Selection (FedSDG-FS) approach. It consists of a Gaussian stochastic dual-gate to efficiently approximate the probability of a feature being selected, with privacy protection through Partially Homomorphic Encryption without a trusted third-party. To reduce overhead, we propose a feature importance initialization method based on Gini impurity, which can accomplish its goals with only two parameter transmissions between the server and the clients. Extensive experiments on both synthetic and real-world datasets show that FedSDG-FS significantly outperforms existing approaches in terms of achieving accurate selection of high-quality features as well as building global models with improved performance. | FedSDG-FS: Efficient and Secure Feature Selection for Vertical Federated Learning |
Environmental microorganism (EM) offers a high-efficient, harmless, and low-cost solution to environmental pollution. They are used in sanitation, monitoring, and decomposition of environmental pollutants. However, this depends on the proper identification of suitable microorganisms. In order to fasten, low the cost, increase consistency and accuracy of identification, we propose the novel pairwise deep learning features to analyze microorganisms. The pairwise deep learning features technique combines the capability of handcrafted and deep learning features. In this technique we, leverage the Shi and Tomasi interest points by extracting deep learning features from patches which are centered at interest points locations. Then, to increase the number of potential features that have intermediate spatial characteristics between nearby interest points, we use Delaunay triangulation theorem and straight-line geometric theorem to pair the nearby deep learning features. The potential of pairwise features is justified on the classification of EMs using SVMs, k-NN, and Random Forest classifier. The pairwise features obtain outstanding results of 99.17%, 91.34%, 91.32%, 91.48%, and 99.56%, which are the increase of about 5.95%, 62.40%, 62.37%, 61.84%, and 3.23% in accuracy, F1-score, recall, precision, and specificity respectively, compared to non-paired deep learning features. | A New Pairwise Deep Learning Feature For Environmental Microorganism Image Analysis |
As autonomous vehicles and autonomous racing rise in popularity, so does the need for faster and more accurate detectors. While our naked eyes are able to extract contextual information almost instantly, even from far away, image resolution and computational resources limitations make detecting smaller objects (that is, objects that occupy a small pixel area in the input image) a genuinely challenging task for machines and a wide-open research field. This study explores how the popular YOLOv5 object detector can be modified to improve its performance in detecting smaller objects, with a particular application in autonomous racing. To achieve this, we investigate how replacing certain structural elements of the model (as well as their connections and other parameters) can affect performance and inference time. In doing so, we propose a series of models at different scales, which we name `YOLO-Z', and which display an improvement of up to 6.9% in mAP when detecting smaller objects at 50% IOU, at the cost of just a 3ms increase in inference time compared to the original YOLOv5. Our objective is to inform future research on the potential of adjusting a popular detector such as YOLOv5 to address specific tasks and provide insights on how specific changes can impact small object detection. Such findings, applied to the broader context of autonomous vehicles, could increase the amount of contextual information available to such systems. | YOLO-Z: Improving small object detection in YOLOv5 for autonomous vehicles |