In this paper, we demonstrate a tunable periodic hourglass-shaped graphene arrays absorber in the infrared (IR) and terahertz (THz) frequency bands. The effects of graphene geometric parameters, chemical potentials, periods, and incident angles on the pure absorption characteristics are studied by using the Finite Difference Time Domain (FDTD) method. In addition, this paper also analyzes the pure absorption characteristics of bilayer graphene arrays. The simulation results show that the maximum absorption reaches 38.2% for the monolayer graphene structure. Furthermore, comparing the bilayer graphene structure with the monolayer structure under the same conditions shows that the bilayer structure has a tunable dual-band selective absorption effect and has a higher maximum absorption of 41.7%. Moreover, it was found that there are dual-band tunable absorption peaks at  OwingD carbon orbitals ,15,16,17orbitals ,19,20. TIn the infrared (IR) and terahertz (THz) range, when graphene interacts with incident light ,26,27,28In the past few years, graphene-based absorbers (GBA) have received much attention. In 2015, Ke et al. reported a cross-shaped graphene array absorber that achieved 20% absorption ; Xiao etOn the basis of these points, this paper proposed a GBA which is composed of periodically patterned “hourglass” graphene metamaterial arrays, and the proposed structure can reach an absorption of 41.7%. For a symmetric dielectric environment, the predicted maximum absorption does not exceed 50% , so the The hourglass-shaped structure consists of two isosceles triangles and two semi-ellipses. These two triangles are symmetrical and intersect with each other. The reason why this structure was chosen are as follows: (1) the two symmetrical and intersecting triangles can realize zero-energy states; (2) the semi-ellipses have two geometric parameters that can be tuned, we can adjust more geometric parameters to adjust its absorption characteristics; (3) the two triangles and two semi-ellipses consist of a continuous graphene structure. In the second section, the hourglass-shaped structure is presented, we also introduce the calculation methods of the absorption spectra. In the third section, we study the influence of different parameters on the absorption characteristics. Then, we analyze the effects of bilayer graphene on absorption. Finally, we summarize the whole project.X and Y directions is P. There are two semi-ellipses and the semimajor and semiminor axis of the semi-ellipse are L and R. The middle part of the graphene structure is composed of two symmetrical isosceles triangles that intersect at the vertices. The graphene arrays are attached to a silicon (Si) substrate separated by a thin silica (SiO2) spacer layer with a thickness of X, Y, and Z directions, respectively. The isosceles triangle of this structure has two sides of length L) and semiminor (R) axis of the ellipse are both 2 (P) of the structure is X and Y directions are adopted as 20 nm, and the Z direction is 1 nm. The relative permittivity of Si and SiO2 are adopted as 1.96 and 3.9 [Z direction with total electric field E polarizing along the X direction. The position of the electric field monitor is placed at the same position of the graphene layer and is larger than the graphene layer boundary.The schematic of the tunable hourglass-shaped GBA is shown in ) method . The ant and 3.9 ,46. The e are the thickness of the SiO2 layer and charge of an electron, respectively. Therefore Equation (1) can be expressed as follows:The chemical potential  that with other parameters are fixed, and T is temperature and is fixed at 300 K, The conductivity of monolayer graphene can be calculated with the random phase approximation (RPA) in the local limit, consisting of intraband and interband contributions ,54,55, wke model , then EqWhen For continuous monolayer graphene, the transmission and reflection are expressed as follows ,57: (8)TIn the range of visible light, ceed 50% . The absL = 0.4 μm, R = 0.4 μm, p = 0.3 μm), the absorption characteristics of different n are both constants. For the gradually changing conductivity of continuous graphene film, the fastest changes are related to Different from other materials, graphene can be dynamically tunable when its geometry is fixed. This dynamic tenability is achieved by changing nly 2.3% , the maxplasmons . In addiR) and absorption spectra of the structure were also studied. Keeping other parameters unchanged  on both sides of the semi-elliptical arc is the main contribution to the wavelength position of the spectra; so with the increase in R, the resonance wavelength experiences blue shift. Then, we can conclude that with the increase in R, the maximum absorption increases and is accompanied by blue shift.L) of the ellipse on absorption characteristics. While keeping other parameters unchanged  are plotted in P has a significant impact on the maximum absorption but less on the wavelength, when other parameters remain unchanged  the filling factor of graphene decreases, leading to the decrease in absorption (the filling factor is defined as the ratio of the graphene resonator to the entire resonant unit cell). The absorption spectra for different periods  theP values are shown in P increases, the electric field intensity concentrated on the ellipse becomes stronger. However, because the filling factor of graphene gradually decreases, and the effect of electric field intensity on the absorption is smaller than that of graphene filling factor on the absorption, the absorption gradually decreases with the increase in P.The distribution of the electric field intensity at maximum absorptions with different P is much smaller than the incident wavelength, the resonance frequency is almost independent of the incident angle We also studied the influence of different incident angles (artition . In the ent of θ . Figure 2 layer with a thickness of We also analyzed the influence of bilayer graphene arrays on absorption characteristics. The results show that the maximum absorption can be further improved using the bilayer graphene arrays. As depicted in R and L of the ellipse, the absorption can be further enhanced. With the increase in R and L, the absorption experiences red shifts and blue shifts, respectively. The variation of P and In this paper, we analyze the tunable absorption enhancement of periodic hourglass-shaped GBA. By increasing


This paper describes a first attempt to quantify LEMG data based on turn number calculation. The results obtained for both healthy and ailing thyroarytenoid (TA) muscles of patients with unilateral vocal fold immobility (UVFI) were compared with the respective qualitative evaluation concerning volitional activity to determine whether the two types of analyses deliver similar results.LEMG data obtained from 44 adults with UVFI were considered for the study. Semiquantitative evaluation of TA volitional activity and turn number were assessed for the ailing and the healthy TA and the difference in percentage was calculated. Paired data were compared with the Wilcoxon signed-rank test. The volitional activity assessment and the turn number evaluation were compared with the Kruskal–Wallis test, and their relationship was tested with the Kendall rank correlation.p = 0.0001), and the Kendall rank correlation a positive relationship  between the volitional activity rating and the turn number assessment.Datasets of 27 patients were considered compatible with turns/s calculation. The results showed that complete paralysis correlated with no turns; single fiber volitional activity with 62–208 turns/s, strongly decreased volitional activity with 198–501 turns/s; and dense volitional activity with 441–1234 turns/s. On the ailing VF only, the Kruskal–Wallis test showed a statistically significant difference (Our preliminary results showed that turn number evaluation is an effective tool to confirm LEMG qualitative analysis, and that, in combination with laryngostroboscopy and voice assessment, can help improving the accuracy of the diagnosis and prognosis and the effectiveness of the chosen therapy. The European Laryngological Society emphasized the need of standardized training and regular practice  at habitual pitch and comfortable loudness for at least 3 s and then to complete forced sniffing inspiration three times, in order to confirm the correct identification of the TA muscle [The LEMG measurements were conducted according to  with disA muscle , and to LEMG qualitative interpretation was completed by a team of experts, immediately after the conclusion of the respective measurement, based on the characteristics of the EMG waveforms . Epochs of 200 ms were displayed on-screen by setting the sweep speed to 10 ms/division. The volitional activity was scored according to .Turns/s calculation was completed offline by a team of experts by means of the built-in algorithm of the Viking Nicolet software (VikingQuest 12.1). Datasets in which the needle electrode could not be placed in the target muscle, or in which the maximum EMG amplitude of the volitional activity was below 100 µV, were excluded from turns analysis. Datasets in which the activity of the targeted TA muscle was found higher between two consecutive phonations than during phonation itself and incompatible with synkinetic reinnervation were likewise excluded to limit the effects of artefacts on the turns/s analysis. The presence of spontaneous motor unit activity, or phonation segments shorter than 3 s were considered exclusion criteria. In short, the number of peaks in the analysis window above the threshold of 100 µV was calculated and normalized to an equivalent time-base of one second (turns/s), as depicted in the example reported in Fig. Patient demographics and outcome variables were analyzed with IBM SPSS statistics software  for medical statistics. Descriptive statistics were used to report demographic data . Quantitative data are presented as mean, standard deviation (SD), range (minimum and maximum), median, and interquartile range (IQR); qualitative data are presented as absolute and relative frequencies. The distribution of turns/s samples was tested by the Kolmogorov–Smirnov test for normality, mean values and standard deviations, median, and IQR, and compared with the results of the qualitative analysis of the volitional activity according to the following rating scale: 4 = dense, 3 = mildly decreased, 2 = strongly decreased, 1 = single fiber, 0 = no activity. Paired data were compared with the Wilcoxon signed-rank test. Kruskal–Wallis test was used to determine whether the results of the qualitative analysis  match or differ from the turn number evaluation. The Kendall rank correlation was performed to determinate whether a relationship exists between volitional activity and the turn number assessment.Datasets of 27 patients were considered compatible with turns/s calculation. 16/27 (59.3%) patients were male and 11/27 (40.7%) were female. The average age was 57.2 ± 15.6 with patients between 18 and 80 years. Details about the UVFI etiology and duration until the time the EMG was performed are provided in Tables p ≤ 0.05).Turns/s could be calculated in 27/27 (100%) healthy and in 20/27 (74.1%) of the ailing TA muscles. In 7/27 (25.9%) of the ailing TA muscles, the resulting amplitude resolution of the EMG signal was below the threshold and therefore could not be used for analysis. In 6/20 ailing TA muscles EMG activity was absent resulting in 0 turns. The distribution of the turns in both cases showed a non-Gaussian shape according to the one-sample Kolmogorov–Smirnov Test (p ≤ 0.0001). The qualitative analysis performed according to [The average number of turn/s characterizing the ailing VFs was 210 ± 264, while on average the turn number of the healthy VFs was 720 ± 297. The Wilcoxon Signed Rank Test showed that this difference in this pattern of turns/s distribution between the ailing and the healthy VF was significant (p = 0.001), but not on the healthy TA muscles (p = 0.226). The Kendall rank correlation showed a strong, positive relationship between the volitional activity rating and the turn number assessment on the ailing , but not on the healthy TA muscles . The relationship between the turn number and qualitative results of the volitional activity evaluation is depicted in detail in Fig. The Kruskal–Wallis Test showed that there is a statistically significant difference between the volitional activity rating and the turn number assessment performed on the ailing (In 20/27 (74.1%) of the evaluated subjects both the ailing and the healthy VFs were evaluated in the same session. In the remaining 7/27 (25.9%) subjects, the resulting amplitude resolution of the EMG signal of the ailing VF was below the threshold and therefore could not be used for analysis. The results of the qualitative and quantitative analysis are summarized in Table In 1/20 (5%) case for which the UVFI had an idiopathic case, the qualitative analysis rated the healthy VF volitional activity mildly decreased. In this case, these results were confirmed by the turns/s analysis.Considering only the ailing VFs, single fiber volitional activity correlated with a very low number of turns/s comprised between 62 and 208, while strongly decreased volitional activity correlated with an increased number of turns/s comprised between 198 and 501 (if excluding the stenosis case).As expected, the percentage decrease in turn numbers when comparing the healthy with the ailing VF is 100% when the latter is completely paralyzed. Single fiber volitional activity correlates with a turn number decrease comprised between 60 and 88%. Strongly decreased volitional activity associates with a turn number decrease comprised between 51 and 72% and mildly decreased volitional activity with a turn number decrease of 35%.Our preliminary data confirmed previous works describing the possibility to use turn number count to objectify the LEMG results. Statham et al.  already Smith et al.  reportedHo et al.  showed aAnother clinically relevant aspect linked to the turn number calculation, is the better understanding and interpretation of qualitative LEMG results. In particular, in 6/27 cases (22%), the qualitative volitional activity of the healthy VF was rated dense, i.e. normal, while the turn number calculated was comprised between 441 and 529 suggesting a mild decrease in the VF functionality. The VFI etiology for these cases was total thyroidectomy, mediastinoscopy or lung transplantation, i.e. an iatrogenic cause that in principle could have affected both VFs, with the less affected VF being asymptomatic at the time of the LEMG. Since 4/6 cases (66.7%) were evaluated between 1 and 4 months upon UVFI onset, this piece of information would help the medical staff to schedule the upcoming control visits and plan the conservative therapy for the patient as well as to formulate a more accurate prognosis. In this study, we did not focus on the MUAP morphology, which has been previously introduced by other authors to discriminate between healthy and ailing VFs , 15. WhiThere are some limitations that could have affected the results of our study. In the first place, it was conducted monocentric and on a limited number of patients. In the second place, it is possible that although the turn number was calculated on the TA, it may include some values generated on the lateral cricoarytenoid (LCA) instead, due to the extreme proximity of the two muscles. Since our results are in line with previously published works, we expect that such potential error did not constitute a significant bias for our result analysis.Our study is one of the first attempts to compare the results of qualitative vs. semi-quantitative analysis applied to LEMG.Our initial results on a limited sample of data sets seem to confirm that the implementation of turn calculation could become a useful tool to confirm volitional activity assessment and help discriminating UVFI due to dysfunctionalities of the thyroarytenoid muscle from those caused by glottic gap reduction due to mechanical causes such as stenosis.Future studies in larger cohorts and including standard voice assessments and/or laryngostroboscopy should be considered confirming these results.


In this study, nine kinds of samples were sintered, to investigate the effects of graphene and nano-TiC on the reinforcing mechanisms of Al2O3-based ceramics. The experimental results indicated that adding 0.5 vol% graphene and 10 vol% nano-TiC can obtain the optimum flexural strength, fracture toughness, and Vickers hardness, which were 705 ± 44 MPa, 7.4 ± 0.4 MPa m1/2, and 20.5 ± 0.8 GPa, respectively. Furthermore, the reinforcing mechanisms of crack bridging, pull-out of graphene, and pull-out of nano-TiC are identified, which are contributed to improving the mechanical properties of ceramics. Meanwhile, other reinforcing mechanisms induced by graphene  and nano-TiC  are discussed. These reinforcing mechanisms are coupled together, while decoupling is hard to work out. Thus, further quantitative studies of reinforcing effects of graphene and nano-TiC on Al2O3-based ceramic-tool materials are necessary to be carried out.Graphene and nano-TiC, which have good reinforcing effects on Al Some methods have been proposed, such as whisker toughening, phase transformation, the particle dispersion, and synergistic effects by various reinforcing mechanisms [Cutting-tool material, attracting much attention of researchers, is an extremely important factor in the fields of high-speed machining. Among cutting-tool materials, Aloperties ,2,3. Untchanisms ,5,6,7.2O3, SiC, TiN, ZrO2, etc.) is an effective method to reinforce Al2O3-based ceramics, due to their small grain size and more grain boundaries of the nanoparticles. Pezzotti et al., who explored the strengthening mechanisms of Al2O3/SiC composites, found that SiC particles tightened the grain boundary and shielded it from possible grain-boundary defects [2 particles and SiC whiskers into the Al2O3 matrix and discovered that the fracture toughness was significantly increased, which was induced by the additive phases [The addition of nanoparticles  sintering ,20, micr2O3-based ceramic-tool materials could be found. In this study, HP was used to fabricate Al2O3-based samples, under vacuum conditions. The effects of graphene and nano-TiC on the microstructure were studied, and the optimal material composition was obtained. Finally, some reinforcing mechanisms induced by graphene and nano-TiC were analyzed.At present, few studies on graphene/nano-TiC-reinforced Al2O3 (0.5 µm), nano-Al2O3 (0.1 µm), and nano-TiC (0.04 µm), with a purity of 99.9%, were all bought from Shanghai Chaowei nanotechnology Co. Ltd., Shanghai, China. The graphene was purchased from XFNANO Materials Technology Co. Ltd., Nanjing, China, and it had a diameter and thickness of 0.5–5 µm and 0–0.8 nm, respectively. The materials used are briefly described as follows: Micro-Al2O3  were used as sintering aids. Ni  and Mo  were used as metal binders. Ni has good ductility and moderate hardness, which can form a liquid phase to promote the sintering process. Adding a certain amount of Mo to Ni could significantly improve the wettability of Ni to nano-TiC. In addition, Polyvinylpyrrolidone , which was an effective dispersant for graphene, was used to disperse graphene with absolute alcohol  for 2 h. Then, nano-TiC was added into the solution of absolute alcohol and polyethylene glycol , and was ultrasonically dispersed for 0.5 h at the pH of 9–10. To mix the suspension evenly and grind up the large particles, we ball-milled the prepared materials for 48 h, with Al2O3 ceramic grinding balls. After the grinding, the materials were dried in a vacuum drying furnace, at 120 °C, for about 3 h. After we sieved it, the graphite mold was used to load the materials. The vacuum sintering furnace was used for HP, with a sintering temperature, pressure, and hold time of 1650 °C, 30 MPa, and 10 min, respectively. The brief experimental process of composite materials is shown in MgO  and YAs presented in ICK, c, and d are the fracture toughness, the average diagonal crack length, and average diagonal line length of indentation, respectively. In this paper, each group of samples was tested five times, and the average value was taken as the final result.The sintered composites were cut into long strips that were 30 mm × 3 mm × 4 mm, by an inner circle slicer. After grinding and polishing the strips, a three-point bend tester  was used to obtain the flexural strength. Vickers hardness was calculated from a hardness tester , with 20 kg force, for 15 s. In addition, the fracture toughness was acquired according to the Vickers indentation method, with the following formula :(1)KIC=02O3  and nano-TiC  are stable and no new phases are generated at 1650 °C for 10 min by HP. Because graphene is not detected with XRD, due to its low content [As shown in  content ,26, the 2O3, and nanoscale grains are nano-Al2O3 and nano-TiC. Furthermore, graphene is embedded along grain boundaries. From pV, and fracture surface energy, fE, is given by the following equation:0E is the fracture surface energy when p =V 0, and b is the constant associated with pores. From Equation (2), it can be observed that pores are not conducive to the dissipation of the fracture surface energy. Thus, we can conclude that reducing porosity is helpful in improving the mechanical properties of ceramics. As graphene content increased, the number of pores decreased, as shown in The fracture morphology of composites A, C, and E is illustrated in 2O3 matrix, providing spaces for grains to grow. Different shrinkage rates and weak interface bonding strength could be the reason for this phenomenon. Furthermore, graphene agglomeration leads to a reduced “binding effect” along grain boundaries, resulting in an increase in grain size. Therefore, to obtain the fine mechanical properties of ceramic materials, the appropriate graphene content must be considered.It is believed that graphene is uniformly distributed along the grain boundaries, restraining excessive grain growth . UniformPull-out of graphene e and a r−1 and ~1590 cm−1, which are D band and G band, respectively. The D band implies the disordered structure and lattice distortion, while the G band confirms the carbon–carbon band in graphene. Two characteristic peaks of graphene appear in the composites, indicating that the original characteristic structure of graphene has been retained after sintering at a high temperature and high pressure, which provides a good guarantee for the reinforcing effect of graphene on ceramic materials. The peak value of D/G of Raman intensity (D/IGI) are calculated, which are 0.23, 1.46, and 0.69 for raw graphene, composite B, and composite D, respectively. Interestingly, the D/IGI value of the composite B is higher than that of composite D, which may indicate a graphene agglomeration in composite D  and flexural strength . Graphene and nano-TiC are capable of reinforcing Al2O3-based ceramic-tool materials were fabricated at same sintering conditions in HP. The effects of graphene and nano-TiC on the microstructure, mechanical properties, and reinforcing mechanisms were discussed. The main conclusions were presented.Graphene was well-dispersed and stable. However, too much graphene, which may cause some pores and weaken the “binding effect” of grains, had adverse effects on the mechanical properties. Meanwhile, PEG and ultrasonic dispersion were effective methods to disperse nano-TiC. By adding a little graphene and nano-TiC, the microstructure was much finer, which showed excellent compactness.1/2, and 20.5 ± 0.8 GPa, respectively.The optimal mechanical properties were obtained. After we added 0.5 vol% graphene and 10 vol% nano-TiC, the flexural strength, fracture toughness, and Vickers hardness were 705 ± 44 MPa, 7.4 ± 0.4 MPa m2O3-based ceramic-tool materials.Graphene and nano-TiC synergistically induced some reinforcing mechanisms. The strong bonding interface induced by graphene caused crack bridging and graphene break, whereas the weak bonding interface caused crack guiding and pull-out of graphene. Nano-TiC also induced crack deflection and crack branching. Similarly, more pores could be found with the addition of more graphene and nano-TiC. Therefore, the appropriate amounts of graphene and nano-TiC were important for reinforcing AlGraphene/nano-TiC reinforced Al


The refractive indices of GST layers can be manipulated by the external electrical pulses applied to microheaters. The amplitude and duration of electrical pulses define the crystallinity ratio of the used GST mediums. The results revealed achieving perfect absorption (> 99%) in the visible and infrared (IR) regimes of the electromagnetic spectrum upon incorporating two thin GST layers of different thicknesses (in the stack) in the amorphous state. The proposed configuration showed the capability of introducing independent transition state  for each GST layer—the visible regime could be extended to the IR regime, and the perfect absorption peak in the IR regime could be broadened and red-shifted. It is expected that the structure would find potential applications in active photonic devices, infrared imaging, detectors and tunable absorbers.Investigation was made of the optical response of metal-dielectric stacks-based cavity structures embedded with graphene microheaters for the purpose of perfect absorption. The absorber configuration exploits the Ge This is because of their ability to provide scalable and cost-effective schemes to devise photonic components for varieties of technological applications5. The significance of metamaterials and plasmonic absorbers remains primarily due to the possibility of achieving near-to-perfect absorption (> 99%) with superb control over the spectral characteristics13, thereby making them potential candidates for building blocks of future optical systems with enormous applications, such as energy harvesters16, IR imaging systems17, label-free sensors18, etc. Attempts have been made to broaden the absorption spectrum by employing different strategies16 and techniques, such as exploiting the hyperbolic metamaterials18 or multiplexed patterned metallic structures19. However, the complexity of nanofabrication processes, scarcity of natural materials22 and incompatibility with large-scale manufacturing remain the determining factors for relatively less use of these in the terahertz (THz) and IR regimes.Investigation of the electromagnetic behavior of metal-dielectric stacks-based cavity systems attracted significant attention by the R&D community toward realizing perfect absorption in the range extended from the visible light to the infrared (IR) regime25 and phase changing mediums (PCMs)30, into the design of active metamaterials allows them to be useful in many photonic applications. Within the context, graphene- and liquid crystal-based devices are tuned by external electrical stimulus, whereas the PCMs (such as the VO2 and G2Se2Te5 (GST) mediums)-based devices can be tuned electrically26, thermally29, and/or optically32. These mediums have been mostly used in designing absorbers30. Ghosh et al.34 reported almost unity absorption over a broad bandwidth in the THz and low IR regimes where graphene shows metallic behavior. They employed patterned graphene layers on the top of the dielectric-metal stack to enhance the absorption characteristics. However, this approach is not suitable in the UV and visible regimes.Tunable materials have been attractive in designing active metamaterials and plasmonic absorbers. The integration of tunable materials, such as graphene2-based systems are more useful to exhibit perfect absorption in the IR wavelengths, whereas the GST-based systems provide nearly perfect absorption in the IR and visible light regimes. However, the major drawback of VO2 medium is the phase transition that happens at a relatively low temperature (68 °C) under continuous temperature control36. On the other hand, the phase of GST remains stable in maintaining the primary state—the amorphous or crystalline—even in the absence of control stimulus. More importantly, GST is extremely scalable, and can be easily integrated in technology-based devices of commercial potentials.Among the PCMs, the VO38. Taghinejad et al.38 reported that ITO-based microheaters can be employed to realize fast and reversible switching between the two GST states by applying a low voltage (~ 20 V). The authors demonstrated that applying 200 ms electrical pulses of different amplitudes gradually decreases the resistivity of GST layer from high (the amorphous state) to low  values38. They determined that the intermediate crystalline states can be configured through adjusting the excitation pulse amplitude.Microheating systems have been of significant importance in various need-based miniaturized photonic devices owing to exhibiting high Joule heating performance—the ability of providing adequate heat in minuscule Joules38. This process also reduces the optical loss of ITO layer to a value < 20%, which is very high, as compared to graphene that shows the optical loss of about 2.7% only. In addition, the ITO suffers from many other issues, such as being expensive, having difficulties in patterning, easily being wore out or cracked39. The ITO can be replaced with graphene owing to its being a transparent and flexible material, which can be easily patterned by exploiting lithography techniques. Apart from this, the low intrinsic optical loss, high in-plane thermal conductivity, and low heat capacity remain the additional advantages39.The quality of microheating systems relies on the key factor to achieve high Joule heating performance that essentially depends on the low resistivity value of heater. The ITO has a sheet resistance of approximately 100 Ω/sq—the value which can heat the monolayer graphene having a sheet resistance of 10 kΩ/sq. However, the ITO requires rapid thermal annealing process in which the thin film undergoes heating to a high temperature of 450 °C for ~ 15 min43. In this stream, Rios et al.37 demonstrated the optoelectronic framework incorporating undoped monolayer graphene heater to perform reversible and controllable switching between four different levels of crystallinity for a large area of GST medium. Ref.41 discusses the techniques to enhance the Joule performance of graphene heater, and reports on decreasing the sheet resistance and minimizing the contact resistance between graphene layer and electrodes. Within the context, the sheet resistance of graphene is inversely related to its bidimensional conductivity—the factor that can be defined by the electron relaxation time and the numbers of layers42. Hung et al.42 showed that increasing the number of graphene layers up to 4, thereby contributing to nearly 1 nm total thickness, would increase the Joule performance; a high temperature up to 600 °C can be achieved at a low voltage of 4.3 V. However, they showed that the use of graphene layer thickness > 1 nm slightly increases the sheet resistance (of heater) since the increased edge structure would reduce the heating efficiency. Luo et al.43 demonstrated that a high lattice temperature up to 1397 °C can be achieved by encapsulating the graphene layers with hexagonal boron nitride.Investigators have reported various techniques to exploit graphene as the microheater for GST mediums42. We also present the optimum dimensions of the geometrical parameters that would yield high absorption (by the structure) in the visible and IR regimes of the electromagnetic spectrum. The study includes the effect of operational conditions on the absorption characteristics by exploiting the transfer matrix method (TMM). The effect of two different phases of GST  on the absorption characteristics are also studied. The obtained results demonstrate achieving dual broad-band absorption spectra—the feature that would be promising in many optical applications, such as bolometer, color displays, IR detectors, tunable camouflages, energy harvesters and optical communications.In view of the use of graphene layer(s) as microheater for GST medium, the present work is aimed at investigating the tunable absorption characteristics of a specially designed multilayered planar structure that incorporates graphene as well as GST. In particular, we use metal-dielectric-based cavity structures embedded with two graphene microheaters each having a thickness of 1 nm, which is corresponding to nearly a trilayer graphene sheet. The refractive indices of GST layers can be manipulated by the external electrical pulses applied to graphene microheater layers. We obtain the simulated/numerical results by using the equivalent circuit model in Ref.2 mediums as space layers, and finally, a thin layer of SiO2 on top to serve the purpose of capping. This protects the upper planar GST medium from evaporation as well as provides more heat confinement within the structure. We use the SiO2 medium because of its stable interaction with graphene sheets, and also, low amount of loss in the IR regime44. The bottom silver layer acts as a reflective mirror which introduces critical coupling conditions.Figure 237. A graphene medium having 1 nm thickness normally corresponds to trilayer graphene structure, which can be synthesized on a ceramic substrate by the CVD method, and then transferred on the SiO2 layer42. We consider the trilayer graphene sheets as microheaters for the used GST layers. The bottom Ag layer can be deposited over the Si substrate by thermal evaporation. The same process can be exploited to deposit the GST layers on the SiO2 mediums42. It has been reported before that 100 nm thick Ti/Au metal pads on graphene layers can be used as metal connectors to induce the required electrical current for heating the GST layers41.The proposed multilayered structure can be fabricated exploiting the chemical vapor deposition (CVD) technique without undergoing complex lithography process. Multilayered graphene medium can be deposited over a thin layer of SiO45, Fig. c) states with wavelength. These components of permittivity are, respectively, shown by c- and Using the optical constants of mediums4747. In the present work, we take 48.On the other hand, the conductivity Figure 48. In the treatment, we consider plane waves of either transverse electric (TE) polarization with x–y plane. Now, the wavenumbers corresponding to the TE- and TM-polarized waves propagating in the 49We study the propagation of electromagnetic waves through the proposed structure using a TMM-based numerical approachmentclass2pt{minimIn these equations, 48:We now exploit Maxwell’s equations to satisfy the boundary conditions at the two interfaces of each layer. Then the equations are reorganized in the form of a In Eq. , \documeFor an N-layer model, the total transfer matrix (mentclass2pt{minim49:The reflection In Eqs.  and 7),,7), \doc42. Within the context, one may think of the effects due to the cross-polarized component, which may alter the total absorptivity50. However, we neglect the cross-polarization effect because the medium is considered as uniaxial homogeneous, as stated before.The absorbance (or the absorption coefficient) 2 surface normally . Moreover, we observe red-shifts in the absorption peak upon increasing the value of Figure We now consider the effect of varying the value of 51.We clearly observe in Fig. 2 layer thicknesses. To perform this, we first sweep the value of the upper SiO2 layer thickness perfect absorption condition corresponding to the largest chosen value of Next, we attempt to study the effect of SiO2 layer thickness 2 layer increases, the optical length of cavity also undergoes increase, thereby resulting in red-shifts of the absorption peaks. However, the thicker the SiO2 layer is, the thinner the GST layer becomes in a cavity, which results in lower absorption property. We also observe that the absorption span gradually increases with increasing thicknesses of the SiO2 layer—the feature that the inset of Fig. We now focus on the effect of the lower SiOperfect absorption, while the span is decreased upon increasing perfect condition (100% absorption) to 99%  edge coupling41. Furthermore, the hexagonal boron nitride encapsulated graphene devices or multilayer graphene structures can be used to increase the carrier density of graphene42. In the present work, however, we use multilayer graphene sheets  to increase the carrier density as well as to avoid the high voltage requirement.The efficiency of graphene microheaters can be enhanced by reducing the contact resistance between the electrodes and graphene sheets. This ultimately reduces the total voltage required, and also, avoid the current saturation to reach high temperaturesSince we are exploiting the trilayer graphene sheets as microheaters, it would be interesting to study the effect of graphene on the optical properties of the structure. In such an attempt, we now increase the number of graphene sheets from 1 to 10 layers—the situations that correspond to the use of monolayer graphene to graphite; Fig. To further study the effect of graphene layers on the absorption spectra, we now observe the impact of chemical potential So far, we discussed the results in respect of the absorption/reflection spectra of the structure under the normal incidence  of GST layer(s) in both the c- and Here c-state  against the incidence obliquity of waves. A wide range of absorption in either the visible or mid-IR regime can be governed by controlling the crystallinity ratio of GST layers, while the thickness of the structure is comparable with other multilayer kind of absorbers.Table The investigation is pivoted to the optical response of specially designed multilayered structure comprised of dielectric, GST alloys in amorphous and crystalline states and trilayer graphene sheets. The results reveal the presence of absorption spectra in the visible and IR regimes. Under different parametric and operational conditions, the incorporation of two GST layers in the structure results in perfect absorption. The width and position of absorption bands can be governed by suitably controlling the layer thicknesses of different mediums and incidence obliquity. The embedded graphene microheaters can be utilized to achieve phase transition of GST layers, thereby introducing additional tunability feature of the structure. It has been found that the graphene layer has no disruptive effect on the optical properties as the relevant functional parameters, namely the number of sheets (in the structure) and chemical potential, do not affect the spectral performance. The results demonstrate that the use of 10 graphene layers and 0.9 eV chemical potential slightly improves absorption. The GST crystallization process has been simulated by introducing the crystalline-to-amorphous ratio—the feature that adds more tunability of the absorption spectra. The obtained results indicate the usefulness of the structure in various photonic applications, such as bolometry, label-free biosensors, IR detectors, and tunable wide-band absorbers.


Here we show that, in graphene-on-boron-nitride superlattices, Brown-Zak fermions can exhibit mobilities above 106 cm2 V−1 s−1 and the mean free path exceeding several micrometers. The exceptional quality of our devices allows us to show that Brown-Zak minibands are 4q times degenerate and all the degeneracies  can be lifted by exchange interactions below 1 K. We also found negative bend resistance at 1/q fractions for electrical probes placed as far as several micrometers apart. The latter observation highlights the fact that Brown-Zak fermions are Bloch quasiparticles propagating in high fields along straight trajectories, just like electrons in zero field.In quantizing magnetic fields, graphene superlattices exhibit a complex fractal spectrum often referred to as the Hofstadter butterfly. It can be viewed as a collection of Landau levels that arise from quantization of Brown-Zak minibands recurring at rational ( 6 cm2/V s and micrometer scale ballistic transport.Here, the authors show that Brown-Zak fermions in graphene-on-boron-nitride superlattices exhibit mobilities above 10 One of the simplest and most studied van der Waals heterostructures is graphene encapsulated between two hexagonal boron nitride (hBN) crystals. The encapsulation protects graphene from extrinsic disorder5, allowing ultra-high electronic quality and micrometer-scale ballistic transport often limited only by edge scattering7. A special case of encapsulated graphene heterostructures is graphene superlattices, where crystallographic axes of graphene and hBN are intentionally aligned. A small (1.8%) mismatch between graphene and hBN crystal lattices results in a periodic moiré potential acting on charge carriers in graphene and leading to the formation of electronic minibands17.Van der Waals assembly offers a possibility to create materials by stacking atomically-thin layers of different crystalsϕ per superlattice unit cell to be comparable to the flux quantum ϕ0 in experimentally-accessible magnetic fields B. At B = Bp/q corresponding to ϕ = ϕ0p/q, where p and q are integer, the translational symmetry of the electronic system is restored (despite the presence of a quantizing magnetic field) and the superlattice’s electronic spectrum can again be described in terms of Bloch states29, just like in B = 0. These high-field Bloch states are characterized by their own miniband spectra29 different from the zero-B spectrum of graphene-on-hBN superlattices. The associated quasiparticles are referred to as Brown-Zak (BZ) fermions. According to the group-theory analysis, an electronic spectrum for each realization of BZ fermions should have an additional q-fold degeneracy31 . This degeneracy is additional to the 4-fold spin and valley degeneracy of graphene’s original spectrum. Importantly, BZ fermions are Bloch quasiparticles, like electrons in solids or Dirac fermions, and, at B = Bp/q, they move through the superlattice as if the applied field is zero. Away from these exact values, BZ fermions experience an effective magnetic field Beff = B − Bp/q (refs. 31).A relatively large (∼14 nm) periodicity of graphene-on-hBN superlattices has also made it possible to study the regime of Hofstadter butterflies, which requires the magnetic flux p and q using high-quality graphene superlattices. These devices were fabricated using the standard dry transfer procedures, where the studied graphene crystal was carefully aligned with one of the encapsulating hBN crystals using the crystallographic edges11. The alignment was verified by Raman spectroscopy32 prior to encapsulation with the second hBN crystal. The latter was intentionally misaligned to avoid competing moiré patterns35. The assembled stacks were placed on an oxidized Si wafer, which allowed us to apply the back-gate voltage Vg to control the carrier density n. We studied six devices that were shaped into the multiterminal Hall bar geometry and had the main channel widths W ranging from 2 to 17 μm  dependences, except for gate voltages close to the neutrality points (NPs) and van Hove singularities (vHS), where ρxy reversed its sign and could no longer be described by the standard dependence ρxy = B/ne (e is the electron charge). All our devices exhibited very high carrier mobilities μ = (ρxxne)−1 of the order of 106 cm2 V−1 s−1, which were still somewhat reduced by edge scattering because of finite W  fanning out from the main and secondary NPs (miniband edges) which are located at Vg near 0 and ±45 V, respectively. There are also pronounced funneling features near van Hove singularities at Vg ≈ −60, −35, +40 and +55 V in both hole (−) and electron (+) parts of the spectrum. Another important attribute of the map is horizontal yellow streaks that occur at ϕ/ϕ0p/q  and ρxx (B) at a constant Vg. Their 1/B frequency is independent of n, and they were named BZ oscillations28. The horizontal streaks are seen in Fig. xx and zeros in ρxx and, as explained in the introduction, reflect the recovery of translational symmetry (p flux quanta penetrate through q superlattice unit cells) and the emergence of Bloch states experiencing zero Beff. Along each horizontal streak, one can find numerous NPs and vHS, which reflect different realizations of BZ fermions at each Bp/q. Landau mini-fans radiate from these NPs in both directions along the B axis 29. Another notable feature of the shown σxx map is a repetitive triangular-like pattern seen most clearly between 2 and 12 T, especially for positive Vg. The yellow triangles are made of horizontal streaks at zero Beff, vertical streaks emerging from NPs for BZ fermions and slanted streaks originating from vHS.Figure p/q Fig. . If tempxis Fig. , represeϕ/ϕ0 = 1/2 and show that, away from NPs and vHS, BZ fermions in our devices exhibit μ reaching a few 106 cm2 V−1 s−1. This is comparable to μ of Dirac fermions in zero B. Another important characteristic of charge carrier transport is the mean free path l. It can be evaluated for both Dirac and BZ fermions, using the standard expression h is the Planck constant, kF is the Fermi momentum and g is the degeneracy. In zero B, g = 4 because of the spin and valley degeneracy of Dirac fermions. BZ fermions are expected to have an additional, mini-valley degeneracy31, which is equal to q  in contrast to its conventional, positive sign for diffusive (ohmic) transport. As expected from very long l of Dirac fermions, Rb was negative in zero B everywhere away from NPs and vHS  appeared only around B corresponding to ϕ/ϕ0 = 1/2, 1/3, 1/4 and 1/5. This is the regime where the existence of BZ fermions, experiencing zero Beff, was previously inferred29 from maxima in σxx and zeros in ρxy. The possibility of ballistic transport of BZ fermions was also suggested using numerical simulations15. The observed negative Rb prove the previous conjectures unequivocally. The negative pockets in Fig. B = Bp/q, non-zero Beff bends the BZ fermion trajectories and the negative signal disappeared  for both negative and positive Beff. For clarity, the conductivity map in Fig. xx. Each minimum can be described by its integer filling factor ν, which we calculated from the minimum’s slope. This representation of the Hofstadter spectrum, where LLs are plotted as a function of n or Vg rather than energy, is usually referred to as the Wannier diagram22. In the diagram of Fig. q = 2, 3, 4, 5, 7, 8, 9, and 11, and for p = 1, 2, 3, 4, and 5. The difference in ν between the nearest LLs yields directly their g. For example, all LLs found for ϕ/ϕ0 = 1/2 were separated by Δν = 2 whereas those at ϕ/ϕ0 = 1/3 and 1/4 by Δν = 3 and 4, respectively  was also observed in other parts of the Wannier diagram for both electron and hole doping 16 or symmetry-broken Chern insulator (SBCI)17. Theoretically, the many-body states can arise from interaction effects that lift the mini-valley degeneracy of BZ fermions. This may happen via mini-valley mixing due to the formation of charge-density waves (commensurate with the magnetic superlattice composed of q unit cells of the underlying moiré pattern) or a Wigner crystal37 . Alternatively, the fully lifted degeneracy may occur through spontaneous mini-valley polarization of BZ LLs, analogous to spin/valley ferromagnetism in graphene14. In the latter case, the BZ fermion states localize in the momentum space around one of the mini-valleys but remain delocalized across the magnetic supercell.There is, however, one notable exception, which was observed for T, which cannot be understood either within the Hofstadter-Wannier model or by considering LLs of non-interacting BZ fermions and, to the best of our knowledge, was never reported before. From either perspective, individual LLs must evolve linearly in Vg and B, as indeed seen in most cases  distance from graphene to the gate in our devices makes quantum capacitance corrections39 negligible, leading to the n ∝ Vg dependence. Unexpectedly, we found that some Landau fans of BZ fermions exhibited bending and staircase-like features. Figure B axis). The anomalous behavior is possibly due to an interplay of BZ-fermion LLs with quantized states originating from nearby vHS, which would lead to redistribution of charge carriers between states with the light and heavy effective masses. One possible scenario is localization of electrons within some parts of the magnetic supercell, because its size becomes notably larger than the magnetic length at B > 10 T . Unfortunately, we could not find any additional features that would enable us to decipher origins of the described anomalies and, therefore, have to leave them for further investigation.Some Landau mini-fans exhibited highly anomalous behavior at low 7. The thicknesses of the used hBN crystals was between 20 and 70 nm. After the trilayer stack was assembled, we used the standard electron beam lithography and reactive ion etching to define trenches for electrical contacts. Cr/Au films were evaporated into the trenches. Finally, using ion etching again, the trilayer stack was shaped into a Hall bar mesa.The reported graphene-on-hBN superlattices were assembled using the standard dry transfer procedures and polydimethylsiloxane (PDMS) stamps coated with a polypropylcarbonate (PPC) layerT. The carrier concentration was controlled by applying a DC gate voltage between graphene and the silicon substrate.For electrical measurements, the standard low-frequency lock-in technique was employed. At temperatures below 100 mK, we used excitation currents of ∼10 nA, and between 0.1 to 1 μA at higher Supplementary Information


Conferences with contributed talks grouped into multiple concurrent sessions pose an interesting scheduling problem. From an attendee’s perspective, choosing which talks to visit when there are many concurrent sessions is challenging since an individual may be interested in topics that are discussed in different sessions simultaneously. The frequency of topically similar talks in different concurrent sessions is, in fact, a common cause for complaint in post-conference surveys. Here, we introduce a practical solution to the conference scheduling problem by heuristic optimization of an objective function that weighs the occurrence of both topically similar talks in one session and topically different talks in concurrent sessions. Rather than clustering talks based on a limited number of preconceived topics, we employ a topic model to allow the topics to naturally emerge from the corpus of contributed talk titles and abstracts. We then measure the topical distance between all pairs of talks. Heuristic optimization of preliminary schedules seeks to balance the topical similarity of talks within a session and the dissimilarity between concurrent sessions. Using an ecology conference as a test case, we find that stochastic optimization dramatically improves the objective function relative to the schedule manually produced by the program committee. Approximate Integer Linear Programming can be used to provide a partially-optimized starting schedule, but the final value of the discrimination ratio (an objective function used to estimate coherence within a session and disparity between concurrent sessions) is surprisingly insensitive to the starting schedule. Furthermore, we show that, in contrast to the manual process, arbitrary scheduling constraints are straightforward to include. We applied our method to a second biology conference with over 1,000 contributed talks plus scheduling constraints. In a randomized experiment, biologists responded similarly to a machine-optimized schedule and a highly modified schedule produced by domain experts on the conference program committee. Researchers and educators depend upon professional conferences to showcase their work and stay current on the work of their peers. Thousands of such conferences are held each year worldwide, and conferences that feature of hundreds of oral presentations are not unusual. Such large conferences often schedule oral presentations in concurrent sessions so that each presentation can be allocated adequate time while keeping the overall conference duration to only a few days.Conference scheduling is typically done manually by program organizers who review the large volume of talk submissions, decide which talks are similar to each other, and group similar talks into sessions accordingly . They doA might be more similar to talk B on one dimension but more similar to talk C on a different dimension. Depending on their areas of expertise, different organizers might weight those dimensions differently, and the weights of the organizers may or may not be representative of the conference attendees.In practice, identifying similarity among talks is a highly subjective process. Research talks often have several dimensions; a talk presenting an efficient key distribution scheme for asymmetric cryptography is related to key distribution algorithms, network security, and cryptographic algorithms. Talk Even if the measure of similarity were not subjective, ensuring a high level of dissimilarity among concurrent sessions, each with multiple talks, is a challenging task for humans, as it requires perception of the distribution of many points in a highly multidimensional space. This can lead to schedules with conflict between concurrent sessions even when the talks within each individual session appear similar. Ensuring a high level of dissimilarity among concurrent sessions is important to minimize participants having to move between sessions, or having to choose between co-occurring talks of equal interest. Adding to the complexity of the conference scheduling task is the fact that organizers typically have to accommodate idiosyncratic scheduling constraints due to the travel schedules and other obligations of individual presenters. Efficient and automated data-driven solutions to overcome the problems would be desirable.Q talks scheduled across W days with a maximum of N timeslots per day, each with a maximum of Cmax concurrent sessions. A session is defined as a sequence of talks scheduled during one timeslot in one room. The maximum number of talks in a session is predefined by the organizers and does not vary across the schedule. Sessions are considered concurrent when they are scheduled in the same timeslot. Timeslots are non-overlapping.Imagine a conference with We define the conference scheduling problem as the task of assigning talks to timeslots and concurrent sessions so as to maximize coherence within a session and minimize similarity between concurrent sessions . In this work, we describe a heuristic solution to the conference scheduling problem that creates optimized conference schedules with multiple concurrent sessions in a fully automated fashion.First, we propose the use of a data-driven machine-learning approach, topic modeling , to infeSecond, we present a suite of heuristic schedule creation approaches designed to maximize an objective function that quantifies session coherence and dissimilarity between concurrent sessions in a single metric. We explore different strategies to create initial schedules, including a greedy heuristic, random assignment, and Integer Linear Programming. We then explore different stochastic optimization strategies to further improve upon the initial schedules , and invWe selected a high-performing combination of approaches that improved upon a manually produced schedule for a recently held ecology conference. Using this combination of approaches, we then created an automated schedule for a large evolutionary biology conference that had not yet been held, in collaboration with the conference organizing committee. The organizing committee made major, manual modifications to produce the final schedule that was used.After the evolutionary biology conference was held, we conducted an experiment where biologists with expertise in that field were presented with samples of the concurrent sessions from both the machine-generated and manually-modified schedules in order to elicit their subjective opinions about session coherence and conflict among concurrent sessions. This provided an evaluation of how well the discrimination ratio captured the topic dimensions that mattered to experts in the field who would be representative of conference attendees.Surprisingly, given the pervasive exposure of academics to the challenges of conference scheduling, there is a relatively small literature on the problem  used through ‘Methods’. Then, we present details about creating the corpus of documents (‘Creating the corpus for topic modeling) for topic modeling along with topic modeling algorithms used (‘Topic modeling’). Next, we describe how similarity between talks and sessions will be computed using outputs from the topic model . An objective function called the Discrimination Ratio to quantify the similarity of talks within a session vs. disparity between concurrent sessions will be presented (‘An objective function for conference scheduling ’An objective function for conference scheduling’). Finally, we outline heuristic approaches for creating initial schedules  and for optimizing the initial schedules (‘Stochastic optimization’).W days, each with N timeslots, with a total of Q talks. Each timeslot is further divided into a maximum of Cmax concurrent sessions. Two sessions are considered to be concurrent if the starting and ending time of the sessions are the same. The number of concurrent sessions in any given timeslot i is represented by Ci. Each session can contain a maximum of Tmax talks. A session is a sequence of talks scheduled during one timeslot in one room. For a given session j, the number of talks in the session is represented by Tj. Talks in a particular timeslot and a particular session can be referred to in the order in which they’re scheduled. ti,j,k represents the kth talk in session j of timeslot i.A conference schedule is composed of G) to be generated from the corpus of Q talks. The algorithm outputs a vector representation . A pairwise similarity matrix (M) is computed from the above vector representation that contains the cosine similarity (S) between vectors , is defined as the ratio of the mean talk similarity within a session (Sw) to the mean talk similarity between concurrent sessions (Sb) across the full schedule.The topic modeling algorithm takes as input the number of topics (W), number of timeslots per day (N), maximum number of concurrent sessions in a timeslot (Cmax), maximum number of talks in each concurrent session (Tmax), and the pairwise talk similarity matrix (M).Initial schedules can be created using the Random, Greedy, or ILP approaches . These approaches take the number of days in the conference (HC) and a Simulated Annealing (SA) algorithm that further optimize the initial schedules. For the HC and SA approaches, we experiment with a version  that optimizes the objective function directly and another  that splits the optimization into two stages - first maximizing within-session similarity and then minimizing between-session similarity. All four variants  take a starting schedule (I), the number of parallel optimization runs (R), the maximum number of swaps (e), and a pairwise talk similarity matrix (M). The approaches can optionally take a list of scheduling constraints encoded as a dictionary (L). In addition, the SA versions (SAASAB) take an initial temperature (Z) and a constant (α = 0.99). These parameters are further defined in ‘Simulated annealing’.We present two variants each of a Hill Climbing  provides a set of 179 commonly used english words that was used as the initial stop word list.The corpus of documents that is input to the topic model is the set of talks for a conference. In our implementation, each document included the title and abstract for a single talk. To ensure that the corpus only contained meaningful words that reflect the semantic content of talks, stemming and stop word removal were applied. Stemming reduces variants of words to their base or root form , making For the second conference, Evolution 2014, domain experts on the conference organizing committee added additional stop words, leading to a total of 952 stop words.We used Latent Dirichlet Allocation (LDA), a generative probabilistic model often used to describe collections of text corpora and one of the most widely used topic modeling algorithms . LDA modOne of the input parameters to the LDA algorithm is the number of topics to identify from the corpus. Several preliminary topic models were created using different numbers. We developed a metric, the Match Percentage, to compare the fit of different models. For each model, the top two words from each of the top three topics of a talk were used to create a set of six keywords. The fraction of keywords found within the title and abstract was computed for each talk and the Match Percentage was computed as the mean of this fraction across all talks, expressed as a percentage. The topic model with the highest Match Percentage was chosen for subsequent analyses.While there are automated metrics, such as perplexity , to evalG topics, the vector ti is defined as LDA outputs a representation of each talk in the corpus as a weighted vector over all the latent topics. In a model with M, is computed by calculating the cosine similarity (S) of the two vectors, From this, a pairwise similarity matrix, D, to quantify in one measure the similarity of talks within each session and the disparity between talks in concurrent sessions. D is defined as the ratio of the mean within-session similarity to the mean between-session similarity across the full schedule. D is higher (>1) when the mean within-session similarity is higher as compared to mean between-session similarity in a schedule. Lower D values (<1) indicate that the mean within-session similarity is lower as compared to mean between-session similarity in a schedule. D is 1 when the mean within-session similarity is same as the mean between-session similarity.We introduce an objective function called the Discrimination Ratio, Sw, is the mean of the pairwise similarities between all the talks within each session. N is the number of timeslots in the schedule, Ci is number of concurrent sessions in timeslot i, Tj is number of talks in session j, and S  from  is the cSb, is the mean of the pairwise similarities between all the talks in different concurrent sessions. The mean between-session similarity, D = Sw∕Sb. D is inspired by other commonly used metrics used to evaluate the quality of clusters generated by clustering algorithms, such as k-means. Such commonly used metrics include the Error Sum of Squares (SSE)—the sum of the squared differences between each observation and its cluster’s mean .The Random assignment algorithm provides a baseline against which to compare the performance of approaches that explicitly optimize the objective function. Given a set of talks and scheduling parameters as in ‘Preliminaries’, this algorithm assigns talks to sessions through sampling with replacement with no consideration of talk similarities or the value of the objective function.Y seed talks that are selected based on an input threshold of minimum dissimilarity between each other. First, the algorithm finds a session for each seed talk such as to maximize the objective function. Next, the rest of the talks are assigned to sessions by choosing the most locally optimal solution at each step.The Greedy assignment algorithm generates a semi-optimal schedule for further stochastic optimization. In addition to the parameters in ‘Preliminaries’, the algorithm requires a set of http://www.cplex.com).We cast the problem of scheduling the conference as an Integer Linear Program (ILP) using a variable reduction technique that was solved using AMPL  with theAn Integer Linear Program (ILP) consists of variables, constraints, and an objective function where some or all of the variables take on integer values . Non-intX clusters of similar talks using a modified version of Kruskal’s algorithm , is then chosen from each of the X clusters. The aim is to produce a set of initial input talks for the ILP that are highly different from each other, while ensuring that each attractor has many other talks similar to it. We choose as the attractor the talk that has the highest similarity to all other talks in its cluster. If there are multiple talks that qualify as attractors, one of those talks is chosen randomly. We calculate a fit score (F) for each talk tj in cluster Xi as follows. tj with the maximum value of F is chosen as the attractor for cluster Xi.A representative talk called the attractor  approaches accept solutions from a swap only when they increase the discrimination ratio, and are thus susceptible to being trapped in local optima. By contrast, the simulated annealing (SA) approaches will accept solutions that decrease D with a certain probability, and thus have the potential/possibility to escape local optima  by iteratively proposing swaps in the positions of talks in the schedule. The Hill Climbing  that maps each talk to a set of sessions in which the talk can be placed without violating any scheduling constraints. For example, in a schedule with five sessions (labeled 1 through 5), if a constraint prevents talk ti from being scheduled in session 5, the constraint would be encoded in the dictionary as L[ti]={1,2,3,4}. Each proposed swap was checked for constraint violations before being accepted. If there is no feasible solution due to conflicting constraints, no solution is returned.These constraints can be accommodated by the optimization approaches described above by requiring them to be satisfied in any solution obtained. In our implementation, such scheduling constraints were encoded as a dictionary  ____________________________________________________________________________   Input:   Initial schedule   Output:   Optimized schedule   set current schedule to input schedule;   set e to maximum number of swaps;   while discrimination ratio (D) increases or e > 0  do     select two talks from the current schedule at random;     swap the two talks;     if  updated schedule does not violate constraints  then          compute D of updated schedule;          if  updated D > current D then               accept changes;               set current schedule to updated schedule;          end     else         discard changes;     end     e = e − 1;   end   return current schedule; ____________________________________________________________________________     ________________________________________________________________________________  Algorithm 2: Hill Climbing optimization algorithm (HCB) ________________________________________________________________________________    Input:   Initial schedule    Output:   Intra-session optimized schedule    set current schedule to input schedule;    set e to maximum number of swaps;    while mean intra-session similarity (Sw) increases or e > 0  do        select two talks from the current schedule at random;        swap the two talks;        if  updated schedule does not violate constraints  then             compute Sw  of updated schedule;             if  updated Sw > current Sw  then                  accept changes;                  set current schedule to updated schedule;             end         else             discard changes;         end         e = e − 1;    end    set Intra-session optimized schedule to current schedule;    Input:   Intra-session optimized schedule    Output:   Optimized schedule    set e to maximum number of swaps;    set current schedule to input schedule;    while mean inter-session similarity (Sb) decreases or e > 0  do         select two sessions from the input schedule at random;         swap the two sessions;         if  updated schedule does not violate constraints  then              compute Sb  of updated schedule;              if  updated Sb < current Sb  then                   accept changes;                   set current schedule to updated schedule;              end         else              discard changes;         end         e = e − 1;    end    return current schedule ; ________________________________________________________________________________    Topic models were created using the LDA algorithm for 60, 80, 100, and 120 topics on the corpus of 324 talks. Each topic model was evaluated based on two criteria: (1) Match Percentage and (2) manual examination of the topics and topic words associated with each talk. We obtained Match Percentages of 70.5% (for 60 topics), 74.6% (80), 75.2% (100) and 75% (120). The topic model with 100 topics was judged to be the best model for the data. Subsequently, this topic model was used to compute a talk similarity matrix that contained a similarity score for all pairs of talks in the dataset. The talk similarity matrix was computed using cosine similarity between the topic relevance vectors of any two talks . ____________________________________________________________________________________  Algorithm 3: Simulated Annealing optimization algorithm (SAA) ____________________________________________________________________________________   Input:   Initial schedule   Output:   Optimized schedule   set e to maximum number of swaps;   set best D to D of input schedule;   set current schedule, best schedule to input schedule;   while discrimination ratio (D) increases or e > 0  do     select two talks from the input schedule at random;     swap the two talks;     if  updated schedule does not violate constraints  then          compute D of updated schedule;          compute probability of accepting updated schedule using Kirkpatrick accep          tance probability function;         r=random number between 0 and 1;         if  acceptance probability > r  then               accept changes;               set current schedule to updated schedule;               compute D of updated schedule;               if  updated D > current D then                    set best schedule to updated schedule               end         else            discard changes;         end     else        discard changes;     end     e = e − 1;   end   return best schedule; ______________________________________________________________________________________          ______________________________________________________________________________________________________  Algorithm 4: Simulated Annealing optimization algorithm (SAB)  _____________________________________________________________________________________________________   Input: Initial schedule   Output: Optimized schedule   set e to maximum number of swaps;   set best Sw to Sw of input schedule;   set current schedule, best schedule to input schedule;   while mean inter-session similarity (Sw) increases or e > 0 do       select two talks from the current schedule at random;       swap the two talks;       if updated schedule does not violate constraints then            compute Sw of updated schedule;            compute probability of accepting updated schedule using Kirkpatrick acceptance probability             function;            r=random number between 0 and 1;            if acceptance probability > r then                 accept changes;                 set current schedule to updated schedule;                 if updated Sw > best Sw then                     best Sw = updated Sw;                     best schedule = updated schedule;                 end            else                discard changes;            end        else            discard changes;        end        e = e − 1;   end   set Intra-session optimized schedule = best schedule;   Input: Intra-session optimized schedule   Output: Optimized schedule   set e to maximum number of swaps;   set current schedule, best schedule to input schedule;   set best Sb to Sb of input schedule;   while mean inter-session similarity (Sb) decreases or e > 0 do       select two talks from the current schedule at random;       swap the two talks;       if updated schedule does not violate constraints then            compute Sb of updated schedule;           compute probability of accepting updated schedule using Kirkpatrick acceptance probability            function;           r=1-(random number between 0 and 1);           if acceptance probability > r then                accept changes;                set current schedule to updated schedule;                if updated Sb < best Sb then                    best Sb = updated Sb;                    best schedule = updated schedule;                end           else               discard changes;           end       else           discard changes;       end       e = e − 1;   end   return best schedule;   _________________________________________________________________________________________________________     Fifty each of Random, Greedy, and ILP schedules were created in addition to the manually created Ecology 2013 schedule. The schedule with the highest discrimination ratio among the 50 runs was taken to be the solution for each combination of starting schedule and stochastic optimization algorithm.SAA, closely followed by HCA, on all initial schedules. Thus, the two approaches optimizing directly and continuously for D outperformed those that sequentially optimized for within-session similarity followed by between-session disparity.The discrimination ratios of the initial and final optimized schedules are shown in D distributions using a Student’s t-test across 50 final schedules created HC and SA approaches with different initial schedules to investigate if there are any significant differences in performances. We found statistically significant differences between SA and HC versions for the majority of starting schedules at the Bonferroni-corrected threshold of α = 0.002 , 76.8% (100), 79.3% (150) and 77.2% (250). Based on the match percentage of the four models and manual inspection of the generated topics, the model with 150 topics was chosen to compute talk similarity for the Evolution 2014 corpus.During the test runs conducted on the Ecology dataset, we observed that there was little variation between different parallel runs within the same algorithm . KnowingSAA followed closely by HCA. Interestingly, the inclusion of constraints did not lead to a reduction in the discrimination ratios; in fact, the highest discrimination ratio (6.7) was obtained in the presence of constraints.The results are shown in D distributions using a Student’s t-test across 10 final schedules created HC and SA approaches with a Random initial schedule. Statistically significant differences were found between SA and HC versions with a Random initial schedule both with and without additional scheduling constraints  that represent each talk. The most frequently occurring words among the talks can be used to create a preliminary label, which can then be used to construct a session name by program organizers.SAA schedule with constraints, reported above, was then given to the Evolution 2014 program committee as a starting point. The program committee consisted of ten evolutionary biologists. Based on their subjective judgments, and following manual procedures that elude easy description, the committee members made a large number of changes to the placement of talks and sessions before finalizing the schedule for the conference. In addition, the program committee added extra sessions for special symposia that were not part of the pool of contributed talks.The D for the original automated schedule was 6.7, while that for the manually modified schedule was 3.2.The changes made by the program committee were substantial; 0.50% of talk pairs that shared a session in the automated schedule were retained within the same session in the modified schedule, while 4.40% of talk pairs placed in concurrent sessions in the modified schedule had originally been placed together in the automated schedule. The value of The differences between the automated and manually modified Evolution 2014 schedule provided an opportunity to conduct a human evaluation. We were particularly interested in comparing how tempted users would be to hop between sessions in each case. To that end, we presented a set of 29 volunteers with expertise in evolutionary biology, none of whom served on the program committee, with faux schedules compiled from the two different sources. Responses were captured via an online survey . The respondents, recruited individually, included twenty-four early career researchers  and five faculty.Respondents were presented with one of eight faux schedules. Each schedule consisted of two timeslots. First, two timeslots each were randomly selected from the automated schedule and the manually modified schedule. These were then combined to produce all eight possible schedules consisting of one timeslot from the automated schedule and one from the modified schedule . Each tiThe survey contained two groups of questions. First, we asked respondents to select the five talks they would like to attend within each timeslot, irregardless of whether they were assigned to the same session. We could then compare the automated or modified timeslots with respect to how the selected talk pairs were grouped into common sessions.Secondly, we asked respondents to choose one session to attend in its entirety in each timeslot and report on the difficulty of finding a session where all the talks interested them. Responses were scored on a Likert scale of one to five with one being “very difficult”, and five being “very easy”. These responses could then be used to compare the topical coherence of the sessions from the automated and modified schedules.t-test t =  − 0.720, p = 0.474, n = 29). With respect to (b), the responses for the automated and manually modified timeslots were quite similar in distribution (If either of the schedules (automated or modified) were more effective than the other at capturing the topics of relevance to our sample of mock conference attendees, we would expect to see respondents (a) select more talks in the same session(s) and (b) select higher values on the Likert scale for timeslots from that schedule. With respect to (a), we found no significant difference in the number of same-session talk pairs between the automated and manual timeslots . We would expect some difference between human perception of talk similarity and the inference of the same based on a topic model. And we would also expect a difference in how humans weigh coherence within sessions and disparity between sessions.D scores for schedules produced using these approaches.In fact, we did receive feedback from Evolution 2014 organizers that we should consider coherence first and disparity second. However, we saw that schedules produced in this way were inferior as judged by the discrimination ratio, although we do not know if they would be judged inferior by humans. This might be due to the way the algorithm operates—optimizing coherence within sessions first without regard to disparity between concurrent sessions. Once the coherence with sessions has been optimized, the algorithm is not allowed to change the placement of talks in sessions to maximize disparity but can only change the placement of the concurrent sessions with respect to each other. This results in a smaller search space for increasing disparity between concurrent sessions which might lead to lower Scheduling constraints are a regular feature of conferences, and initially we anticipated that they would be more troublesome than they ultimately proved to be. We found no decrease in discrimination ratio when incorporating constraints in the Evolution 2014 schedule. We hypothesize that the applied scheduling constraints were not restrictive enough to substantially limit the search space. For context, while approximately 24% of the talks had scheduling constraints, the majority could still be placed in 91% of sessions. In cases where constraints are more restrictive, one could modify the approach here to accept solutions that minimize the number of constraints violated, or weight the constraints such that solutions aim to minimize the total weight of violated constraints.With the Evolution 2014 schedule, we took advantage of the opportunity to conduct a preliminary investigation into how much session-hopping users felt would be necessary in the automated schedule versus the manually modified one. By the two measures we looked at, prospective conference goers with expertise in the field found the two schedules to be comparable. Given the substantial changes made to the automated schedule, it was perhaps surprising that results did not show greater differences.community of conference attendees with diverse interests. This also suggests that it would be reasonable for future conference organizers to use an automated schedule as is, without expending additional human effort vainly trying to improve upon it. However, a number of limitations with this experiment should be noted. The sample size was small and a limited array of schedules were presented for evaluation. While all survey participants had expertise in some area of evolutionary biology, we might have been asking them to evaluate sessions outside of their specific interests. And they were tested in an artificial setting; their behavior in navigating a real conference schedule may differ.One possible interpretation of this result is that while the conference organizers may have modified the schedule in an effort to optimize their own subjective similarity and disparity measures, they did not improve upon the automated schedule from the perspective of a D is a reasonable objective function, though a difficult one for humans to manually optimize. It’s value lies in capturing both similarity within and dissimilarity between sessions, the latter of which has been previously neglected. Third, we have identified fast heuristics for optimizing D.Taken together, we believe this work makes a number of contributions. First, topic modeling provides a reasonable input for automated clustering of conference abstracts. The scalability of this approach is attractive for large conferences. Secondly, Would it be possible to improve upon this approach such that an automated schedule would be preferred by a future organizing committee to a manually generated, or manually modified, schedule? One area for potential improvement would be to customize the weights given to topics based on the perceived importance of conference attendees. In the approach described here, each topic received equal weight. However, a community of scientists may consider some topics more important than others. Values for the weights could be gathered by means of a survey or other user-contributed data. If topics were mapped to an ontology, weights related to the information content of topics could provide an indirect measure of importance  without D, or to independently varying levels of similarity within sessions and dissimilarity between sessions.Given the comparable performance of the automated and manually modified Evolution 2014 schedules, it would be of interest to further examine how well statistical measures of topic similarity between talks match human perception. For similarity measures that do match well, it would then be of interest to see how sensitive humans are to schedules with very different levels of Another pair of factors not considered was co-author and co-citation networks. Intuitively, talks that are closely linked in either kind of network may be similar in ways that are somewhat independent of how they are related by the topic model . Use of Our implementation limits concurrent sessions to those that overlap fully. Conferences sometimes schedule sessions of differing lengths that partially overlap with one another, and accommodating this in future versions could allow for greater flexibility.The heuristic approaches presented here have not been evaluated with respect to an exact approach with an optimality guarantee. Future work may consider developing exact approaches, such as Mixed-Integer Linear Programming, to better understand the computational bounds of these approaches and investigate if the heuristics proposed here are substantially faster as compared to exact approaches and if the solutions are comparable.Automated scheduling of large conferences is a problem of great interest and utility to scientists across various domains. Here, we presented heuristic algorithms for the creation and optimization of conference schedules with concurrent sessions based on an objective function. The methods presented here are capable of “reading” conference talks, assessing similarities between the talks, and using those similarities to populate conference sessions. While these methods are a step forward in the field of automated conference scheduling, further work is needed to develop objective functions that accurately reflect user perception of “good” conference schedules.https://doi.org/10.5281/zenodo.2860367.Data and software for this work are available at 10.7717/peerj-cs.234/supp-1Appendix S1Click here for additional data file.