We present a new universal method to accelerate calculations of transmission function and electrical conductance of 2D materials, the supercell of which may contain hundreds or thousands of atoms. The verification of the proposed method is carried out by exemplarily calculating the electrical characteristics of graphene and graphane films. For the first time, we calculated the transmission function and electrical conductance of pillared graphene, composite film of carbon nanotubes (CNTs)/graphene. The electrical conductance of different models of this material was calculated in two mutually perpendicular directions. Regularities in resistance values were found. The development of technologies for the synthesis of graphene nanomaterials has led to an expansion of the scope of their application. One of the graphene composites that have been actively studied in the last few years is pillared graphene . It is aT(E). The dependence of the transmission function on the energy of the electron in the system is characteristic for each point of the reciprocal lattice. The final form of T(E) depends on the number of k-points in the reciprocal lattice, because T(E) average over these lattice points. Using the convergent transmission function it is possible to find the electrical conductance of the nanostructure. However, in order to obtain a converged form of the averaged transmission function, it may be necessary to calculate it in a set of points in the reciprocal lattice, which is unattainable for a large number of atoms in the considered system. In this connection, the development of methods for accelerating the calculation of the transmission function without a significant loss in the accuracy of calculations has particular relevance and significance for research of the electrical conductive properties of new composite materials. At present, such accelerating techniques are practically absent. We found only one work [The non-equilibrium Green function (NEGF) method with density functional tight-binding (DFTB) scheme or density functional theory (DFT) scheme is used to calculate the electrical conductance of molecular structures consisting of atoms of various elements with high accuracy . Within one work  in whichIn order to calculate the electrical conductance we use the Green–Keldysh functions and the Landauer–Büttiker formalism . The calT(E) is the transmission function characterizing the quantum mechanical transparency of the conducting channel as a function of the energy of the electron moving along it, μ is the Fermi energy of the electrode, e is the charge of the electron, and h is the Planck constant. The thermal broadening function FT(E) is calculated by the formula:where kB is the Boltzmann constant, and T is the temperature. The transmission function is given by:where  and  are, respectively, the advanced and retarded Green matrices (describing the contact with the electrodes), ΓS(E) and ΓD(E) are, respectively, the level broadening matrices for source and drain. The function T(E) is found by summation over the entire Brillouin zone (BZ) and N is the number of points in the reciprocal space. The accuracy of calculating T(E) is determined by the segmentation of the reciprocal space and the considered number of energies values. The calculation will be reliable when the function T(E) does not change with decreasing pitch of the change in the wave number k. For example, for finitely segmented BZ with limits a and b, the function T(E) converges to its true form for N ≥ 103. For materials in which the cell contains of the order of several hundreds or thousands of atoms, the calculation of T(E) at a single point (for a fixed k) takes a rather long time, thus making 103 calculations impossible. For example, for a 2D crystal cell with 472 atoms, the calculation of the transmission function averaged over 288 points of the reciprocal space takes almost four days for the parallel calculation in 24 processes (Intel® Xeon® CPU E5-2660 v2 with a frequency of 2.2 GHz). If the BZ is not a segment, but a 2D or 3D figure, the number N increases by orders of magnitude. In the next section, a method will be described to reduce the number of reciprocal space points and energy values for which a transmission function calculation is required, without substantially losing accuracy of the shape of T(E).where T(E) for two different N by using the example of a graphene monolayer. Figure la shows the considered system, that is, the unit cell connected to the electrodes. Since we calculated the conductance of this material (graphene), the same cells act as electrodes. Electrodes are translated to infinity along the Y-direction, and they are semi-infinite along X. The central cell is also translated to infinity over Y. Thus, the wave number ky varies within , where ay is the unit cell size along the Y-direction (as shown in T(E) from Equations 1–3 with different values of N are shown in k = 0.1 1/Å (N = 15), the function has a step-like form. When the step of the decomposition is reduced to dk = 0.0015 1/Å (N = 984), the curve takes the correct well-known form for a graphene monolayer. The transmission function is represented in conductance quanta e2/h.Let us demonstrate the proposed method for calculating T(E) function is additionally processed. The values of T(E) near the transition area between the steps are refined to make them more abrupt. In many cases, this procedure allows us to eliminate the need for a more detailed decomposition of the energy interval. For this, within transmission-function calculations we used an interval-halving technique, which allows one to obtain a 16-times more accurate boundary value between the steps for four iterations. Each iteration reduces the difference between the energies E1 and E2 by a factor of two , E2 is the first energy value for the same k-point at which T = T(E2) and T(E2) ≠ T(E1)), since the value of the transmission function at the midpoint E3 = 0.5(E1 + E2), which is either T(E1) or T(E2), is determined. Then, the interval  is considered if T(E3) = T(E2), or the interval  if T(E3) = T(E1). Therefore, four similar iterations yield a 16-fold reduction of the energy difference between two adjacent steps of the transmission function.For each point of the reciprocal lattice, the calculated T(E) between two neighbouring points of the reciprocal lattice. T(E) for three different numbers ky. In general, independently of ky, interpolation for each point of the polygonal chain determines the nearest points with energy having the same value of the function T(E) and belonging to the neighbouring polyline. The picture of the distribution of points in this case has the form shown in T(E) = 2 is fixed. Thus, all the points of neighbouring polygonal lines having the same value of T(E) are first found, and then the nearest ones are selected from the energy difference. If a polyline has two adjacent lines, then each point of this polyline can have no more than one near point on each of them. Similarly, in the case of a single neighbouring polyline, there will not be more than one near point for each point on the polygonal chain. If the difference in the values of the transmission function exceeds one, additional points are added. For example, if for some value of ky the transmission function undergoes a jump on passing from a point with energy Ei to a point with energy Ei+1, with Ti+1 − Ti = 2, then an additional point will be added to this polygonal chain. This point is characterized by an energy value of 0.5 (Ei+1 + Ei) and the transmission function at this point is equal to Ti +1. This is necessary in order to find the nearest point with the value of the transmission function Ti + 1.To eliminate the step-like form of the averaged transmission function, we interpolate the function T(E) as the nearest points. The number of points added depends on the length of the segment connecting the nearest points on different polygonal chains. The longer the lengths of the segment, the more additional points are added. If an additional point has not been used to form the connecting segment, it is not used to construct an interpolating function. The starting points and the remaining added points are used to construct the interpolating function.Next, the nearest points found are used to add additional points between them, lying on the segment connecting these points. All additional points have the same value of T1 makes it possible to realize a detailed decomposition over ky values, ensuring smoothing of the initial roughness. T(E): T1. The step-like behaviour of the function T(E) has disappeared everywhere, except for the region near the Fermi level (0.0 eV here). Indeed, there may exist “special regions” for which the original partitioning by ky was too coarse. Special regions are determined by the researcher in the gradient of the image. Areas of smooth colour change indicate the lack of partitioning for this area. Calculations with a more particular partition are additionally carried out for this area, but already in a narrow range of values: from 0 to 0.2 1/Å for ky, and from −0.3 to 0.3 eV for E. The next step is the construction of a new interpolating function T2. T2, T(E) averaged over all ky. The solid curve shows the calculation with the distance between two neighbouring points in reciprocal lattice of 0.0015 1/Å, the dotted line shows the result of applying the developed method. The norm of the difference between the interpolated and the converged values is 0.68%. Time taken to obtain the average transmission function  varies: 34 minutes, 2 seconds per accurate calculation and 2 minutes, 22 seconds to obtain the final values of the interpolated graph. Note that, in general, the time taken to add points depends on the amount of input data, and not on the number of atoms in the considered structure.The interpolating two-dimensional function The proposed method for calculating the transmission function was also tested with the example of graphane. The results of solving the test problems show that the transmission function calculations were accelerated by factor of 14.38 for graphene and of 19.92 for graphane by using the method developed here. Nevertheless, the speed of calculations is limited by the complexity of the dependence of the transmission function on energy and the considered point of the reciprocal lattice. The higher the rate of change in the transmission function, the more detailed calculations are needed.k. The test problems solved for graphene and graphane show that the discrepancy between the values of the transmission function calculated without the developed method and with its application was about 1–2%.The accuracy of the results of the transmission function calculations obtained using the proposed method depends on the size of the unit cell and the chosen reciprocal lattice vector X-axis and 2.13 nm along the Y-axis for each unit cell. X- and Y-directions, as in the case of the graphene monolayer, a central supercell and supercell electrodes are separated  in the left figure, and along Y  in the right figure. In this case the supercell consists of 580 atoms with a distance between the graphene layers of 2.4 nm. The conductance was calculated using the developed method because of the large number of atoms. The plots of the function T(E) averaged over all k in the case of electron transport in the X-and Y-directions are shown in Using the developed method for calculating the transmission function we investigated the transmission functions and electrical conductance of 2D graphene/CNT composites. The investigated film was modelled by two layers of graphene connected by single-layer armchair tubes  with a diameter of 1.23 nm . The distance between the tubes was equal to 2.1 nm, the length of the tubes  ranged from 1.1 to 2.4 nm. The graphene sheet had a length of 2.45 nm along the ated see . The conT(E) were calculated for all models of supercells of a composite on the basis of CNT  at the same distance between tubes of 2.1 nm. The conductance and resistance of the pillared graphene film were calculated based on the calculated T(E). Y-direction for single-layer composites, and around a value of 90 kΩ in the X-direction only with larger amplitude.Similarly, the transmission functions X-axis and 4.12 nm along the Y-axis for each unit cell.Similar investigations were carried out for two-layer pillared graphene . The graY-direction and 29.32 kΩ in the X-direction. The difference between the resistance in the X- and Y-directions is significantly lower for two-layer composite in comparison with single-layer composite. The conductivity in the Y-direction has increased for all the considered situations  varies insignificantly and does not depend on the distance between the graphene layers. For a two-layer composite, the average resistance depends on the axis direction. This can be explained by the high electrical conductance of graphene nanostructures with a zigzag edge. The conductance of these ribbons does not depend on the width of the ribbon and weakly depends on its topology. In the direction of the X-axis (armchair edge of graphene sheet), the electrical conductance of single- and two-layer composites depends significantly on the topology of the film. The resistance changes drastically with the increase in the CNT length.Based on obtained results, we can conclude that for the single-layer pillared graphene film, the resistance in the direction of the k-point sampling or a too coarse energy sampling will lead unrealistic results, in spite of any post-processing scheme.We created a new universal method for calculating the electron-transmission function and electrical conductance at quantum transport in composite nanomaterials. This method allows us to investigate the electrophysical properties of atomic structures, which contain hundreds and thousands of atoms in the transmitted supercell. By the example of monolayer graphene and graphane it was shown that the developed method significantly reduces the calculation time of the transmission function. The error of the calculation was equal to 0.68% and 1.79% for graphene and graphane, respectively. A number of competitive advantages of the proposed approach compared to other methods in the literature are: Our approach does not use the Dijkstra method used in [Using developed method we obtained new knowledge about the electrical conductive properties of a new composite material, namely pillared graphene. The calculated electrical conductance and resistance of the pillared graphene film showed that the current flow is more preferable along the zigzag edge of the graphene sheet both for single-layer and two-layer composites. The average resistance value in this direction was 12 kΩ for the single-layer composite. This value is close to the resistance value of an ideal nanotube. For the two-layer composite, the average resistance was 10.2–29.3 kΩ depending on the direction. This can be explained by the high electrical conductance of graphene nanostructures with a zigzag edge. The conductance of these ribbons does not depend on the width of the ribbon and weakly depends on its topology. In the direction of the armchair edge of the graphene sheet, the electrical conductance depends significantly on the topology of the film. The resistance changes drastically with the increase in CNT length. Using the analogy with graphene nanoribbons, it can be seen that the regularities in the electronic transport along the armchair edge are determined by the width of the ribbon and its morphology. In summary, we can conclude that the pillared graphene films with nanotubes having a diameter of 1.23 nm are characterized by a relatively high electrical conductivity. Due to high strength and conductivity, these films, provided a developed surface and pores for filling with the necessary connections, could be successfully applied in electronic devices and as electrodes of storage batteries.


On the other hand, the BP-based humidity sensor is less repeatable due to the instability of BP with water molecules and the stability of the sensor is reduced. In this study, this limitation of the BP-based humidity sensor was overcome by preparing a BP/graphene hybrid as a novel humidity sensing nanostructure. The BP/graphene interface improved the stability of the humidity sensor after a few weeks with a linear response within the relative humidity (RH) range of 15–70%. The sensor’s response/recovery speed of the humidity sensor was extremely fast within few seconds. The response (S) of the humidity sensor based on the BP/graphene hybrid is 43.4% at RH = 70%. The estimated response and recovery time of the sensor is only 9 and 30 seconds at RH = 70% at room temperature. The experimental investigation reveals that the BP/graphene hybrid not only improves the reversibility and hysteresis factors but also enhances the stability of the humidity sensor.Black phosphorus (BP) materials have attracted considerable attention owing to their ultra-sensitive humidity sensing characteristics because of the natural absorption of water (H Various humidity sensor technologies have been developed, such as those based on resistive1, semiconductor1, optical2, and surface acoustic wave technologies3. Among these devices, resistive sensors have several advantages compare with other types such as simple structure, high sensitivity, rapid response, low cost and low power consumption1. Popular humidity sensing materials include polymers4, semiconducting metal oxides1, and carbon-based materials (carbon nanotube and graphene oxide)5. These conventional materials with a range of nanostructures offer many advantages for use in humidity sensing. On the other hand, humidity sensors from these conventional nanomaterials still exhibit a slow response/recovery time and in some cases require heating temperatures for operation5. Recently, new two dimension (2D) nanomaterials have demonstrated many advantages in the sensing area with a planar crystallite structure, large surface-to-volume, and low electronic noise6. The unique properties of new 2D materials, such as graphene7, black phosphorus (BP)10, and tin disulfide (SnS2)11, provided superior sensing factors including single molecules agents, ultra-fast super sensitivity and low power consumption.Humidity sensing techniques have been investigated in many areas such as the industrial processing, environment, food, agricultural, and indoor applications13. In particular, BP is a new excellent humidity sensing material with ultra-sensitivity and a rapid response12. However, BP has low stability and reacts naturally with water molecules, limiting its long-term stability in humid environment12. To overcome this limitation, there have been some attempts to passivate the surface of BP14, encapsulate it with graphene15, or use a composite/hybrid with other materials18. In particular, chemical bonding between phosphorus and carbon (P-C) has been reported to play a significant role in stabilizing BP/graphene composites/hybrids for practical applications17. On the other hand, the conventional composites/hybrids are usually limited due to defect formation at the interface, leading to lower stability of the electronic device. Graphene-based heterojunction presents an interesting alternative way to overcome this limitation because of excellent properties of graphene as a support material. In addition, the combination of these new 2D materials on graphene to form heterojunctions between 2D materials has advantages in 2D electronic device such as low electronic noise, low power consumption, and good stability at the interfaces15. The new 2D material and graphene heterojunction control provides the latest advantages of 2D electronics, such as low electronic noise, low power consumption and excellent stability interfaces.BP has been reported as a novel material for gas and humidity sensing with excellent properties13. However, to take advantage of unique characteristics of scalable technologies, it is essential to establish a mass production process for 2D materials synthesis and sensor device fabrication. This very exciting challenge will be addressed in the current work. In this study, a large quantity of BP materials was synthesized in powder form  with a novel technique of high energy ball milling (HEBM). The BP powder was exfoliated by a mild ultrasonication process and BP/graphene heterojunction was formed on the graphene surface using an electrospray system for humidity sensor. The humidity sensing performances of the sensors prepared with a pure BP and BP-graphene heterojunction were investigated and compared in terms of the sensitivity, reversibility, and stability. The role of graphene and the interface between BP/graphene for humidity sensors was investigated in detail.To date, exfoliated 2D layers, particularly BP, could only be transferred in small sizes onto substrates in basic and proof-of-concept studies2/Si with wafer-level. Then, the platform of humidity sensor chip comprise patterned graphene between two gold (Au) electrode. The BP powder was synthesized by a HEBM method and deposited on the patterned graphene by electro-spray (see in Supplementary data for more detail). Figure g1, B2g, and Ag2 peaks of BP are clearly visible at 359, 432, and 462 cm−1, respectively19. The Ag1 and Ag2 peaks of the pure BP sample were observed at 356 and 459 cm−1, respectively. The Raman spectrum of single layer graphene consisted of two major sharp peaks (G and 2D peaks) at 1584 and 2674 cm−1. The major peaks (G and 2D peaks) originated from the doubly degenerate zone center E2g mode and the second order zone boundary phonons, respectively20. The D peak at 1350 cm−1 is related to the defects present20. The features of those peaks are indicators of the quality of graphene, such as doping and strain. The G and 2D peaks in BP/graphene were 1590 and 2689 cm−1, respectively. No obvious increase in the D peak in the Raman spectra before and after depositing BP powder on graphene was observed. The as-synthesized single layer graphene has Raman spectra with 2D/G ratio > 1. However, the 2D/G ratio value was reduced (2D/G < 1) after the sensor fabrication process  when the sensor is exposed to a given humidity. The recovery time is defined as the time needed to recover to 90% of the initial baseline after turning-off the humidity. The responses S (%) of the humidity sensor based on BP-graphene heterojunction calculating from Fig. 21 and 5/5 seconds12. Meanwhile, the response/recovery time of our humidity sensor using pure BP was 24/72 seconds. The results showed that the humidity sensor using BP/graphene heterojunction is better than that using pure BP with a 2-fold faster response time. Moreover, the humidity sensor using pure BP without a passivation method showed large degradation after a few cycles (within 2 hours)21. Fig. 2O) molecules withdraw a free electron from the BP flakes and increase the hole density in BP. The BP exhibits a p-type semiconductor behavior15. Therefore, the increasing hole density in p-type BP leads to decreasing resistance in the humidity sensor of the pure BP sample  is defined as the percentage resistance change of the resistivity sensor by exposure to humidity:12, the BP-graphene heterojunction humidity sensor in this study has the advantageous features of a fast response/recovery time, linearity and mass production process of sensor. The degradation of the BP only sensor was caused by lower stability of the surface of the BP flake in moisture and humidity14. In this case, pure BP played a role both as a humidity sensing material and conducting patch between the Au electrodes in the sensor device, leading to higher noise and degradation during humidity absorption/desorption. The sensing mechanism of BP/graphene heterojunction involves charge transfer at the interface between BP/graphene and graphene playing a role as a stable conducting path. In addition, due to the good stability at the BP/graphene interface17, the humidity sensor could show better stability and reversibility, compared to the sensor using the BP only sample. Passivation of BP surface is essential for sensing applications22, and electronic devices15 based on BP materials. This is the greatest challenge for applying BP as a sensing material because the passivated BP process reduced the sensitivity of the BP surface, leading to the complicated fabrication of the sensor. However, the sensor based on passivated BP showed a long-term stability up to one month22 or three months12. In this study, the BP/graphene heterojunction humidity sensor showed high sensitivity, fast/response recovery owing to BP without a passivation process and acceptable stability for up to two-weeks, which is better than that of the sensor using the pure exfoliated BP material with stability for only a few hours.Figure A humidity sensor based on BP/graphene heterojunction was developed using a large scale fabrication technique. The role of graphene in the heterojunction of the humidity sensor was investigated by comparing the sensor performance of the BP and BP/graphene sample. The BP-only samples showed good sensitivity to humidity with the advantages of a strong response and rapid response/recovery time, but were less stable, non-linear and reversible. On the other hand, the BP/graphene heterojunction-based humidity sensor overcomes these limitations and has excellent sensing properties with a response of 43.4% and a response/recovery time of 9/30 seconds with a RH of 70%. In addition, the humidity sensor has good repeatability, low hysteresis and long-term stability over two weeks by forming a BP-graphene heterojunction. Moreover, it solves the instability of the BP-only sensor.23. The wafer-scale of single layer graphene was synthesized by chemical vapor deposition (CVD)20. The sensor chip (graphene chip) with patterned graphene between the two gold (Au)-electrodes (distance of 100 µm) was fabricated in wafer-scale level by a dry-etching technique and conventional MEMS process (see the Supplementary data). The BP powder dispersed in dimethyl sulphonate  by an ultrasonic treatment was deposited on a graphene chip to fabricate a humidity sensor via an electrospray system. DMSO was used as the solvent for BP in the electrospray experiment, where BP was deposited on the patterned graphene surface. The water flow rate was controlled precisely by a syringe pump . The electric potential was adjusted using a power supply  connected to the metal capillary. The metal capillary was used as an electrospray emitter with an inner diameter of 250 μm. The nozzle tip- to-substrate distance was fixed to 10 mm. For rapid evaporation of the solvent, the surface temperature of the substrate was adjusted using a hot plate . For comparison, the humidity sensor using pure BP powder was fabricated but without graphene between the Au electrodes. Humidity sensors using pure BP powder for comparison were fabricated under the same conditions but without graphene between the Au electrodes. In the wire-bonding process, the humidity sensor was mounted on the TO-39 chip to finish the sensor fabrication process.The BP powder was synthesized using the HEBM technique at ambient temperature and pressure. The detail experimental conditions for the synthesis of BP powder by HEBM can be found elsewhere (see the Supplementary data)The surfaces of the BP/graphene hybrid were characterized by field emission scanning electron microscope . Transmission electron microscopy (TEM) and high resolution TEM (HRTEM) images of the BP were captured using an ultra-high resolution field emission electron microscope (JEOL JEM-2100). The crystalline characteristics of the BP were investigated by X-ray diffraction . Raman spectroscopy was performed in a back scattering configuration using a 532 nm laser source and holographic grating of 1200 grooves/mm.2 gas. A computerized mass flow controller  was used to change the humidity and concentration of N2 gas. The relative humidity (RH%) was varied from 15 to 70%. N2 gas with different humidity level was delivered to the chamber at a constant flow rate of 100 standard cubic centimeters per minute (sccm). The gas chamber was purged with N2 gas between each humidity pulse, allowing the surfaces of the sensors to return to the standby state.The sensors were mounted inside an enclosed environmental chamber and a multi-meter (Fluke 8846 A) connected to the computer was used to record the resistance of the sensors. The humidity in gas chamber was generated using a water bubble controller and introduced into the chamber by NSupplementary Info


Quantum decision theory (QDT) is a recently developed theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of uncertainty and other effects that are particularly manifest in cognitive processes, which makes it well suited for the study of decision making. QDT describes a decision maker’s choice as a stochastic event occurring with a probability that is the sum of an objective utility factor and a subjective attraction factor. QDT offers a prediction for the average effect of subjectivity on decision makers, the quarter law. We examine individual and aggregated (group) data, and find that the results are in good agreement with the quarter law at the level of groups. At the individual level, it appears that the quarter law could be refined in order to reflect individual characteristics. This article revisits the formalism of QDT along a concrete example and offers a practical guide to researchers who are interested in applying QDT to a dataset of binary lotteries in the domain of gains. For example, a typical question could be to choose between the following options: “option 1: get CHF 50 with a 40% chance (or nothing with a 60% chance); option 2: get CHF 10 for sure.” Our dataset includes the 200 decisions performed by each of 27 subjects with various values of p and x.In this article, we apply quantum decision theory (QDT) to a dataset of choices between a certain and a risky lottery, both in the domain of gains. Each decision task consists in a choice between (1) a risky option in which the decision maker can win a fixed amount, here QDT offers a quantitative prediction, the so-called quarter law, which concerns the average effect of subjectivity on people’s decisions. In the present case, the quarter law allows us to predict the frequency with which either of two options will be chosen.With this article, our aim is to provide a practical how-to guide for QDT in its present state, not to resolve paradoxes of human decision making (as has been done in QDT articles –3) or exAnother contribution is to offer a practical illustration of how to apply QDT to a dataset of binary lotteries in the domain of gains, so as to test the quarter law at the level of individuals and groups when each subject is faced with a number of different decisions. Previous QDT publications, e.g. , 3, typiWe examine individual and aggregated (group) results, and find that our results are in good agreement with the quarter law at the level of groups. At the individual level, it appears that the quarter law could be refined in order to reflect individual characteristics. We use gender to distribute subjects into two groups and apply QDT to compare these groups and test the quarter law within each group. Gender is a convenient variable on which to test the aggregation of individual data. Indeed, it is a readily available individual characteristics that splits the sample in two sets of almost equal size. Moreover, there is a vast literature on gender-specific risk-taking behavior –17. The Let us stress that QDT does not suppose that the brain is a quantum object. The mathematical formalism of quantum mechanics, rigorously developed by von Neumann , is thatWe thus use the same mathematical formalism as that of quantum mechanics, but do not claim that neurological processes are quantum in nature. For clarity, let us give a parallel example. Newton (1642-1726/7) was interested in planetary motion and developed calculus to establish the laws of movement and gravitation. That does not mean that there is anything fundamentally planetary to calculus. This formalism very generally allows the study of change. In the case of planetary motion, calculus describes the change of position and speed along physical trajectories in space and time. Meanwhile, calculus has been used in every scientific domain concerned with change. In the same way, the mathematical framework of Hilbert spaces is known in physics for its application to quantum mechanics, but it can be said to generally apply to the study of uncertainty, and this is what motivates us to make use of it for decision making processes.Others have recently followed a similar path, most notably Busemeyer and collaborators e.g. –24); see; see24])j) is characterized by a set of outcomes and their probability of occurrence, and is written aspj is a probability measure over the set of payoffs {xn} and thus belongs to the interval  and is normalized to one.Let us now give a few elements of decision theory that help understand how QDT relates to classical theories of that field that are well known in the fields of psychology and behavioral economics. For this review, we consider how classical theories evaluate simple gambles. Simple gambles, as Kahneman  (p.269) In experimental settings, it is common for decision makers to have to choose between two simple gambles or between a gamble and a sure thing, as in “would you rather have a 20% chance to win CHF 50 (with an 80% chance to get nothing), or get CHF 10 for sure?”. We call this a “decision task” . We write the former example asIn decision theory, such decision tasks serve as simple models for the more complex decisions we face in everyday life. In real situations, outcomes are often not expressed in monetary terms, and their probabilities are unknown. For instance, we are unable to assign a probability to the event that our happiness will increase if we get a new job and move, nor do we assign an exclusively quantitative value to this change of happiness. Nevertheless, it is the consensus of the field that simple choice problems such as the above elicit risk preferences, and we will focus on lotteries of that form.A few risk elicitation methods are reviewed by . The metIn accordance with probability theory, Pascal  expresseu transforming values in u(x) = ln(x), such as to reflect that we become more indifferent to changes of wealth as the initial amount of wealth increases. For example, an increase of wealth from 1 to 4 million has a higher psychological value than an increase from 4 to 7 million.Later on, Bernoulli  examinedu(x)) remained dominant for a very long time. Von Neumann and Morgenstern  .Hence, we identify the probability that the lottery p(Lj)  is to be understood as the theoretical frequency of the prospect Lj being chosen over a large number of times. Two types of setups can be put in place. The first setup involves a number of agents; in that case p(Lj) gives the fraction of agents expected to choose Lj. In the second setup, a single decision maker is faced with a number of decision tasks, among which the same decision task appears several times. This setup is designed such that each repetition of the same decision task can be assumed to be independent of previous occurrences. That is, we assume negligible memory and influence of previous decisions. In this second setup, the option Lj is chosen a fraction p(Lj) of the time by the same decision maker. QDT treats similarly these two setups.The probability ψ|πj〉|2 in terms of the coefficients given in Eqs ψ|πj〉|2 iutility factor,The classical terms become the so-called f(Lj) remains in p(Lj). When q(Lj) = 0, the standard classical correspondence principle , q(Lj) lies in the interval . These two conditions are called in QDT the alternation conditions:Since q equal to L (the number of prospects in each decision task) multiplied by the number of choices made. Let us introduce φ(q), the normalized distribution of q, and writeArising from interference effects between prospects in the mind of the decision maker, the attraction factor can be seen as a random quantity varying across decision makers and over time for a single decision maker. Thus, the choices made by different individuals or by the same person at different times constitute a number of realizations of L = 2 prospects, the distribution of q is symmetrical around zero and the mean of q is zero:Because of the alternation conditions Let us define the quantitiesFrom the alternation conditions q is equiprobable, i.e. the distribution φ(q) is uniform. From In the absence of any information, the variable L1 is the most attractive prospect, we haveL2 is the most attractive prospect. In QDT, this is called the quarter law and constitutes a quantitative prediction on the average value of the attraction factors in any given experiment, under the assumption of no additional prior information.Applied to a binary lottery choice, this yields the prediction that, when φ(q) yield the same average value of 1/4 for the attraction factor, which makes this result quite general, as pointed out by Yukalov and Sornette in , with α > 0 and Γ(α) the gamma function. The beta distribution is employed in many applications, for example in Bayesian inference as a prior probability distribution. The quarter law also follows from several other distributions normalized on the interval , such as the symmetric quadratic distribution,Several families of distributions nette in . For exaTypical values of the attraction factors are derived by Yukalov and Sornette in  in the gA rule has been expressed by Yukalov and Sornette in  (p.1162)This rule considers two lotteriesThe maximal and minimal gains are denoted asg(L1) of the first prospect, the risk factor r(L2) of choosing the second prospect, and the quantity α(L1) are then defined as follows:The gain factor q(L1), is defined by the ruleUsing these quantities, the sign of the first prospect attraction factor, L1, is risky: subjects can win either CHF 50, with a probability p, or nothing, with a probability 1-p. In the other lottery L2, subjects get the sure amount x in CHF . This can be seen as a “certain lottery.” The condition 0 < x < 50 is always ensured, otherwise there would be no point in choosing the risky lottery. The two lotteries are writtenx < y and in the experiment, y = 50 CHF.In the dataset we are analyzing, subjects have to choose between one of two lotteries. One lotteries, L1 as p, x with probability 0 and y with probability p. Similarly, writing L2 as x with probability 1 and y with probability 0. This way of expressing the two prospects captures the fact that decision makers compare the two lotteries as they are making up their mind.Note that the same amounts appear in both prospects. Writing p (the probability of winning the fixed amount CHF 50 in the risky lottery L1) and x (the guaranteed payoff in the certain lottery L2). In the experiment that generated the dataset, pairs of  values were randomly generated and the corresponding decision tasks  were submitted to subjects.In this dataset, a decision task is characterized by the values of the two parameters p was varied between 0.05 and 0.9 by steps of 0.05, and the sure amount x between 0 and 49 by steps of 1. At most 900 different  pairs could thus be generated.Each of 27 participants was given 200 randomly generated decision tasks, in 4 runs of 50 questions each. This amounts to 5,400 data points. Overall, the probability The detailed method of the experiment in given in  (chap. 7The mean age of participants was 25.8 ± 3.6 years. Thirteen women (mean age 25 ± 3.3 years) and fourteen men (mean age 27 ± 3.7 years) were included in the study. The decisions were contextualized, in the sense that participants were asked to imagine a bank investment. Each decision was equally important, as participants were promised to receive, at the end of the experiment, the amount resulting from one randomly chosen decision task. The Ethics Committee of the Canton of Zurich approved the study. All participants provided written, informed consent and were compensated for their participation.We now present how QDT specifically applies to the empirical dataset under study. The theoretical correspondence was carried out in the section that follows the introduction. Indeed, this section considers a decision problem whose structure corresponds to that of the decision tasks generating the dataset.As stated earlier, we equate prospect utilities with expected values given by Then, according to p(Lj). As is the case of other datasets available to researchers, the present dataset was not generated with QDT in mind. We suggest in the discussion how to design decision tasks more suitable for testing QDT. There are several ways to aggregate the decision tasks, of which the following:Since QDT is a probabilistic theory, a decision task must be offered several times in order to obtain an empirical choice frequency approximating (i)p, x) values, i.e. the same utilities U(L1), U(L2).Only aggregate decisions presenting the same ((ii)p, x) values. For example,  and  present the same value of p and close values of x, and could be considered so similar as to represent the same decision task.Aggregate decisions with close ((iii)f(L1), f(L2). For instance, the  pairs A, B and C give respectively f(L1) = 0.1.Aggregate decisions presenting the same utility factors p, x) pairs (option (i)) is that the available empirical dataset does not always present a sufficient number of realizations of each  pair to perform a meaningful probabilistic analysis. For instance, in our dataset, 10.7% of all  pairs were offered only once; 11.5% were offered twice; 30.4% were offered three times or less. At most, one  pair was offered 126 times. Ignoring decision tasks with less than a minimum number of realizations is possible, but means giving up a substantial amount of data.The issue with only aggregating identical (f(L1) to the lowest 0.01, no decision task characterized by its utility factor f(L1) was offered less than three times, and only 1.3% of all values of f(L1) were submitted exactly three times. At most, a given value of f(L1) was submitted 274 times. The number of decision tasks given per value of f(L1) is shown in Aggregating by utility factor (option (iii)) partly resolves this issue. When rounding p and x from different  pairs have to be in order to aggregate the pairs. This option can bring an intermediate result between options (i) and (iii). In this analysis, we use option (iii).In option (ii), one has to decide how close values of Nj a prospect was chosen by one or several decision makers over the N times the same decision task was offered. Since the probabilities, utility factors and attraction factors for the two prospects  are related by Eqs  an anNj a pd by Eqs , the entp(L1). In what follows, we identify pexp(L1) with p(L1).The empirical frequency is given byX such that, at the k-th realization of a given decision task,p(L1) is thus the Bernoulli distribution of X.Let us introduce a random variable retract function, which retracts a variable z into an interval :Let us additionally introduce the p(L1), the utility factor f(L1) and the attraction factor q(L1):p(L1) lies in .Empirically, based on p(L1)<1, because of the retract function in p(L1) = 0 and p(L1) = 1, q(L1) can have taken any value such that f(L1) + q(L1)≤0 or f(L1) + q(L1)≥1, respectively. Hence, the exact value of q(L1) that guided the decision maker(s) cannot be retrieved in these two cases; applying q(L1).The attraction factor can be deduced from experimental results asf(L1) in . In order to visualize to which extent empirical data conforms to the quarter law through p(L1) as a function of f(L1). Then q(L1) is given by the difference between p(L1) and the lower left to upper right diagonal of the graph (p(L1) = f(L1)), as long as 0 < p(L1)<1. The absolute value of this distance is predicted by the quarter law to be equal to 0.25, on average. The dataset consists in decision tasks with various values of r(L2) = 0, α(L1) = −1 and sgn q(L1) = −1. In other words, at and around f(L1) = f(L2) = 0.5, the risky prospect’s attraction factor should be negative and the certain prospect should be preferred, in accordance with the principle of risk aversion.The rule for the sign of the attraction factor in the case of close utility factors given by For clarity, we summarize here the few steps necessary to obtain the attraction factors and test the quarter law in a dataset of choices between two lotteries in the domain of gains.f(Lj) ∈  ∀j = 1, 2.Choose a form for the utility factors satisfying Decide on an aggregation of decision tasks .Lj being chosen, p(Lj).For each aggregate, compute the frequency of a lottery p(Lj) in , compute for each aggregate the attraction factor q(Lj) = p(Lj) − f(Lj).For p(Lj) as a function of f(Lj).Represent f(Lj), or averaged over intervals of f(Lj)), |q(Lj)|, to the value 1/4 predicted by the quarter law.Compare the absolute value of the attraction factor , as a function of the utility factor of this prospect, f(L1). In the left panel, each point comprises the results of decision tasks presenting the same  values. The area of the markers is proportional to the number of decision tasks per point, which varies between 1 and 4. It is apparent in this panel that the majority of decision tasks were given only once, based on markers area as well as the fact that most points are situated at p(L1) = 0 or p(L1) = 1.f(L1), the same individual may not consistently choose the same prospect, especially at intermediary values of f(L1). Yet, at low and high values of f(L1), decisions tend to be consistent, as may be expected.The left panel of p(L1)) as a function of a quantity depending on the question’s parameters, which in our case is f(L1). To these data points is then typically fitted a logistic (S-shaped) function whose parameter can be interpreted as partly characterizing a decision maker’s risk behavior . Th. Thp(L1)p(L1) as a function of f(L1) for the same individual, but here we aggregated  values yielding the same f(L1) value rounded to the lowest 0.01. As noted in the methods, there are thus more decision tasks per point, which motivates us to continue the analysis based on this aggregation. In contrast to aforementioned fitting approaches, we are interested in examining whether these data points follow the QDT prediction given by the quarter law, expressed by p(L1) is situated at f(L1) ± 0.25 on average.The right panel of It is instructive to take a closer look at individual results. f(L1). The participant from the bottom left panel shows a strong preference for the certain prospect until high values of f(L1). In the bottom right panel, a relatively large number of choices seem to be random, although there is overall a transition from the certain to the risky prospect. Second, it appears that individuals behave quite differently from one another. For example, the participant in the top left panel appears to have calculated the expected values of each prospect and consistently chosen the one with the highest expected value. By contrast, in the top right panel, the transition from the certain to the risky prospect is noisier and takes place along a longer interval of In this section, we carry out an aggregation of individual results by gender and examine whether the quarter law holds at this level and whether gender differences can be observed in our sample. We use gender out of convenience, because it is a readily available characteristics of subjects that splits the sample in two sets of almost equal size. Moreover, it is common to observe gender differences in risk-taking behavior –17, as bpW(L1)) and men (pM(L1)) separately, as functions of the utility factor f(L1).qW(L1) (for women) and qM(L1) (for men). We use the SciPy script scipy.stats.ks_2samp  for men, as compared to f(L1) ∈  for women. Namely,f(L1) than men, andwomen (as a group) transition from the certain to the risky prospect at a higher value of f(L1) than men.women (as a group) transition over a longer interval of f(L1) = 0.5 and the preference transition to the risky prospect reflects the population’s average risk aversion. The larger distance for women suggests that women in the sample show a stronger risk aversion than men, on average. However, let us stress that the sample size of thirteen women and fourteen men is too small to generalize these results to genders in general. We come back to this point in the discussion.The distance between the risk-neutral value The interval length, for its part, can have two different interpretations.f(L1) (homogeneous population), a longer interval reflects that decision makers show little discrimination between different values of f(L1) along that interval, and are inconsistent in their choices, leading to intermediary values of p(L1).If individual transitions all start and end at roughly the same values of Alternatively, if individual transitions occur at different points or along intervals of different length (heterogeneous population), averaging over individuals will yield a broad transition at the level of the group. In that case, the transitional interval length at the group level reflects inter-individual variability.The analysis performed in the next section suggests that inter-individual variability is higher among women than men and is likely to contribute to the longer transition observed in q(L1). This yields one p-value per pair of individuals. Small p-values indicate that individuals in a pair make significantly different decisions.We now compare the distributions of attraction factors in pairs of individuals, separating between same-gender and cross-gender pairs. We thus make three types of pairings, man-man, woman-woman and woman-man. For each pair, we perform a Kolmogorov-Smirnov test on the individual distributions of attraction factors p = 0.025) and from the woman-woman distribution (p = 0.05), but the woman-woman distribution is quite similar to the woman-man distribution (p = 0.68).We also compare these distributions of p-values, using again Kolmogorov-Smirnov tests, and find that the man-man distribution is very different from the man-woman distribution | over all decision tasks for women and men separately. Let us recall that one has to exclude from the analysis the decision tasks with p(L1) = 0 or p(L1) = 1, as explained in the methods.In this section, we test the validity of the quarter law at the level of each gender. According to QDT, the absolute value of the attraction factor of either option in a binary lottery should be equal to 1/4 on average. We thus compute the average of |q(L1)| at the level of a group, as well as two different measures of variability. For completeness, we present all of these computations, as each gives a different perspective on the empirical results.We may use two different aggregations of individual results to obtain the mean of |Ns subjects to illustrate the different computations. Say that overall Nf different values of f(L1) were offered to this sample. Each value of f(L1) is associated with the choices made by different individuals. These choices can be aggregated to get one value of q(L1) per value of f(L1), without differentiating between individuals. This amounts to interpreting the sample as a set of homogeneous individuals, or equivalently as a single entity. We then average these Nf values of |q(L1)| . The standard deviation measures the variation of |q(L1)| across all decisions and sample subjects aggregated.Let us consider a sample of q(L1)| over the different values of f(L1) submitted to this subject alone. We thus get Ns values of Another approach is to first isolate each individual’s choices so as to obtain the subject’s average value of |Nf or Ns) whose variability is being measured and thus depends on the chosen aggregation.An alternative measure of variability to the standard deviation is the standard error of the mean (SEM). The SEM (that can only be estimated here) measures the variation between same-size samples compared to the full population from which the sample is drawn. Here, the “full population” is not the world human population. It is the comparable population in terms of age, gender (if the sample is restricted to one gender), socio-economic situation, education level, and culture. It may be qualified as WEIRD , as coined by . The estThese approaches yield the following attraction factors, standard deviations and SEM (in brackets), for women (W) and men (M). Without differentiating between subjects, we getWith a single value of q(L1)| is reasonably close to the value of 0.25 predicted by the quarter law, and this is formally evaluated by the standard deviation or SEM. When we consider each aggregate as an entity and use the standard deviation, the results for both genders are in agreement with the quarter law prediction of 0.25 on average. We interpret in the discussion the relatively large standard deviations found in this case.In all cases, the mean value of |When we average over each subject first and thus get a single value of With both approaches, the SEM does not cover the difference between the empirical and the theoretical value. This can be expected because, as noted above, the sampled population is biased and thus does not satisfy the no prior information hypothesis at the basis of the quarter law. We briefly come back to this point in the discussion.q(L1)| and the theoretical value of 0.25. However, the sample is overall biased. It could be the case that a larger sample would bring the mean absolute of the attraction factor nearer to 0.25 so that the SEM would cover the difference. This would occur if the bias of the mean decreases faster than the SEM as the sample size increases. Yet this is rather unlikely, as more of the same “kind” of subjects  would still constitute a biased sample.Overall, these results indicate that individual choices vary sufficiently to span the difference between the empirical value of |In this section, we aggregate individual results with the aim to test the quarter law at the population level.f(L1) = 0.5, we find the following attraction factor, based on 224 decision tasks:f(L1) = 0.5, expressed by . A rounding of f(Lj) should be chosen such as to allow this repetition over the N decision tasks and have the distribution of f(Lj) cover the interval . The lotteries should be generated beforehand and the distribution of games should be controlled to reflect the desired distribution. The order in which  games are presented to subjects should be randomized so that participants are unlikely to answer very similar questions consecutively.One of the practical challenges we encountered was to choose an adequate aggregation of decision tasks in order to carry out a meaningful probabilistic analysis guided by QDT, given the empirical distribution of . As a comparison, prospect theory founders Kahneman and Tversky typically ran experiments on 50 to 300 subjects , 63, 64.We offer in this work a guide and illustration of how to apply quantum decision theory (QDT) to an empirical dataset of binary lotteries in which decision makers had to choose between a certain and a risky option involving gains. Through this, we hope to promote the empirical investigation of QDT, in order to test its current claims, but also challenge it and indicate new research directions. One such direction could be to calibrate the attraction factor and characterize individual decision makers in terms of type of strategy and degree of predictability.S1 FileEach row in the dataset represents a decision task and includes an individual identifier (1 to 27), the gender of the participant (F or M), the probability with which the amount CHF 50 would be obtained in the risky option, the amount guaranteed by the certain option, and the decision made by the participant . There are 200 decision tasks per participant, resulting in 5,400 data rows.(CSV)Click here for additional data file.


Zika virus RNA was detected at high levels in 12 (52.2%) samples and was not detected in 10 (43.5%) samples from 43 patients. The article has been corrected online (


Idiopathic pulmonary fibrosis (IPF) is a progressive and lethal lung disease of unknown origin whose incidence has been increasing over the latest decade partly as a consequence of population ageing. New anti-fibrotic therapy including pirfenidone and nintedanib have now proven efficacy in slowing down the disease. Nevertheless, diagnosis and follow-up of IPF remain challenging.This review examines the recent literature on potentially useful blood molecular and cellular biomarkers in IPF. Most of the proposed biomarkers belong to chemokines , proteases (MMP-1 and MMP-7), and growth factors (IGBPs) families. Circulating T cells and fibrocytes have also gained recent interest in that respect. Up to now, though several interesting candidates are profiling there has not been a single biomarker, which proved to be specific of the disease and predictive of the evolution .Large scale multicentric studies are eagerly needed to confirm the utility of these biomarkers. Idiopathic pulmonary fibrosis is a rare lung disease of unknown origin which leads rapidly to death . EpidemiBiological markers, often referred as biomarkers, are commonly defined as objectively measured elevated indicators of physiological / pathological processes or pharmacological response to therapeutic interventions . BiomarkIPF is defined as a chronic progressive fibrosing interstitial pneumonia of unknown origin . The disHere we have performed a systematic search in pubmed by typing the words “biomarkers” and “IPF” and selecting those measured in blood. Publications dates of selected papers range from 1993 until 2016.Many biomarkers have been studied in BALF and in serum as potential diagnostic or prognostic tools. Their utility for monitoring the disease has to be assessed .The main biomarkers associated with the alveolar epithelial cell damage (or dysfunction) are the Krebs von den Lungen-6 (KL-6) antigen and the surfactant protein A and D (SP-A and SP-D). Compared to SP-A and SP-D, serum KL-6 has a highest accuracy for diagnosis of interstitial lung diseases (IPF and ILD associated with connective tissue diseases) .KL-6 is a high molecular weight glycoprotein classified as a human transmembrane mucin 1 (MUC1). That glycoprotein is mainly expressed at the extracellular membrane surface of type II pneumocytes –14. It hSurfactant proteins are lipoprotein complexes synthesized and secreted by type II pneumocytes to decrease surface tension at the air–liquid interface. They have also a role in the lung host defence. Serum SP-A and SP-D are known as being elevated in patients with ILD with a greater extend in IPF –25. SomeThe main biomarkers identified in IPF focusing on fibrogenesis are matrix metalloproteinases (MMP)-1 and -7, Lysyl oxidase-like 2 (LOXL2) and Periostin.Matrix metalloproteinases are a collection of zinc-dependent proteases involved in the breakdown and the remodelling of extracellular matrix components . MMP-1 aConcentrations of protein fragments generated by MMP activity are increased in the serum of individuals with IPF compared with healthy controls. Increased neoepitope concentrations were associated with disease progression as defined by death or decline in FVC > 10% at 12 months after study enrolment and the rate of this increase predicted survival , 34. We Lysyl oxidase-like 2 (LOXL2) is expressed in fibrotic lung and is thought to play a crucial role in matrix remodelling and fibrogenesis . Serum lp = 0.005) [CC motif chemokine ligand 18 (CCL18) is a small protein derived from alveolar macrophages that acts as a chemo-attractant. CCL18 is mainly secreted by antigen-presenting cells such as monocytes, macrophages and dendritic cells . In the = 0.005) . Moreove= 0.005) . TherefoIL-8 is a cytokine, which is highly chemo-attractant for neutrophils and known to be elevated in serum of IPF patients. A study identified a negative correlation between IL-8 and pulmonary function tests  , 47 and p < 0.01) [YKL-40 is a chitinase-like protein that regulates cell proliferation and survival and has previously been described in liver fibrosis. YKL-40 has also been well studied in multiple ILDs . Its mec < 0.01) . TherefoIGFBP-2 is a member of a highly conserved family of six insulin-like growth factor (IGF) binding proteins, which has recently been identified in IPF , 52. IGFIntracellular adhesion molecule-1 and -2 (ICAM-1 and ICAM-2) are also elevated  in serum from patient with IPF. ICAM-1 has been found to be overexpressed on pulmonary epithelial cells of patients with IPF , 54, whe2. In this study, serum levels of VEGF in severely hypoxemic IPF were similar to those found in non-small cell lung carcinoma [Vascular endothelial growth factor (VEGF) is a glycoprotein expressed in alveolar epithelial cells . Increasarcinoma . Serum Varcinoma .The heat shock protein 70 (HSP 70) is a molecular chaperone that is expressed in response to stress. IgG autoantibodies directed to HSP70 have been associated with a poorer prognostic in IPF . In addin = 86, validation cohort n = 63) that a biomarker index composed of SP-D, MMP-7 and osteopontin enhanced diagnostic accuracy for IPF compared to other ILDs (rheumatoid arthritis associated ILD (n = 33); alternative idiopathic ILD (n = 41)) [A recent study focusing on biomarkers that might assist in distinguishing IPF from non-IPF-ILDs have identify in the plasma of 149 IPF patients (derivation cohort n = 41)) . This thn = 41)) .+ on T-regulatory cells in IPF [+CD25+FOXP3+ T reg cells in IPF [T-cells are also involved in the pathophysiology of IPF. Semaphorin 7a (Sema 7a), a membrane-bound protein expressed in activated Tcells, also regulates inflammatory responses via stimulation of macrophage chemotaxis and cytokine production chemokine expression, modulation of T-cell function and regulation of collagen production by fibrocytes. Hematopoietic expression of Sema 7a is sufficient to induce fibrosis in TGF-β1–induced murine lung fibrosis . There is in IPF –64. Its s in IPF . As it hs in IPF . Other ts in IPF .+Col-1+ fibrocytes are circulating bone-marrow derived mesenchymal progenitor cells which can differentiate into fibroblast and myofibroblasts [Circulating CD45roblasts . They arroblasts , 70.Genomic, epigenetic and molecular phenotyping are widely used in clinical research. It is getting more and more clear that genetic polymorphisms, whole blood transcriptomic profile, as well as lung microbiome are predicting groups of diverse disease behaviour and response to treatment . ExtraceOne of the limitations of our review is that we have chosen candidate biomarkers in IPF according to our thinking and their potential usefulness. Another limitation is the lack of longitudinal studies for some of the biomarkers, which reduces the clinical impact of the finding because of a lack of assessment of treatment response. We believe that further longitudinal multicentre studies are highly needed to evaluate the real clinical impact of most of the biomarkers in a single or multivariate analysis as diagnostic and prognostic tools.Diagnosis of IPF remains challenging and requires a multidisciplinary approach. Treatments currently available have a limited efficacy and the overall prognosis of the disease remains poor. Recent advance in pathophysiological process are promising for further therapies; nevertheless, the most important point for now is the early diagnosis as a mean to early treatment. So far, there is no easy to use biomarker available for clinical practice. It is now obviously clear that genetic and epigenetic variations are involved in the pathogenesis giving us different information for the morbi-mortality in IPF. Furthermore, prospective longitudinal studies have started to identify blood biomarkers to be used in clinical practice.


Idiopathic pulmonary fibrosis (IPF) is a chronic, progressive disease characterized by the aberrant accumulation of fibrotic tissue in the lungs parenchyma, associated with significant morbidity and poor prognosis. This review will present the substantial advances achieved in the understanding of IPF pathogenesis and in the therapeutic options that can be offered to patients, and will address the issues regarding diagnosis and management that are still open.Over the last two decades much has been clarified about the pathogenic pathways underlying the development and progression of the lung scarring in IPF. Sustained alveolar epithelial micro-injury and activation has been recognised as the trigger of several biological events of disordered repair occurring in genetically susceptible ageing individuals. Despite multidisciplinary team discussion has demonstrated to increase diagnostic accuracy, patients can still remain unclassified when the current diagnostic criteria are strictly applied, requiring the identification of a Usual Interstitial Pattern either on high-resolution computed tomography scan or lung biopsy.Outstanding achievements have been made in the management of these patients, as nintedanib and pirfenidone consistently proved to reduce the rate of progression of the fibrotic process. However, many uncertainties still lie in the correct use of these drugs, ranging from the initial choice of the drug, the appropriate timing for treatment and the benefit-risk ratio of a combined treatment regimen. Several novel compounds are being developed in the perspective of a more targeted therapeutic approach; in the meantime, the supportive care of these patients and their carers should be appropriately prioritized, and greater efforts should be made toward the prompt identification and management of relevant comorbidities.Building on the advances in the understanding of IPF pathobiology, the further investigation of the role of gene variants, epigenetic alterations and other molecular biomarkers reflecting disease activity and behaviour will hopefully enable earlier and more confident diagnosis, improve disease phenotyping and support the development of novel agents for personalized treatment of IPF. The landscape of Idiopathic Pulmonary Fibrosis (IPF), a chronic interstitial pneumonia characterized by the invariably progressive deposition of fibrotic tissue in the lungs and overall poor prognosis, has been revolutionized over the last decades by substantial advances in the understanding of disease pathobiology, the standardization of the diagnostic processes and the availability of the first treatments that modify the disease course. The increased awareness of IPF patients’ care needs, together with a thriving scenario of novel biological markers and potentially effective treatments, brought new important challenges to the surface: the need for an earlier, non-invasive and confident diagnosis, a more accurate disease stratification, and a personalized, comprehensive therapeutic approach are only some of the issues researchers and physicians will deal with over the next years. In this review, we summarize the current knowledge on pathogenesis and management of IPF, with a focus on the future perspectives in IPF care and on the challenges encountered in the translation of research outputs into clinical practice.Despite the comprehensive understanding of IPF pathogenesis remains elusive, research efforts in the last few years have reached important milestones. Several environmental and microbial exposures have been proposed as playing roles in IPF pathobiology that might be far from collateral, making the concept of “idiopathic” less compelling. Individual genetic and epigenetic factors remain the most important for the development of the fibrotic process, although the contribution of the variants so far identified, or their interaction with the putative external factors has yet to be clarified. In this context of genetic susceptibility, the repeated micro-injury of the alveolar epithelium has been recognized as the first driver of an altered repair process where several lung cells develop aberrant behaviours, leading to the development and sustainment of the fibrotic process. This section will cover in detail the current evidence on the contribution of these factors to IPF pathogenesis and the main goals of research for the years to come. The main pathogenetic actors in IPF are also illustrated in Fig. Several epidemiological studies have demonstrated that environmental exposures are involved in the pathogenesis of IPF. Although evidences of dose-response relationship are limited, findings have strongly associated cigarette smoking and metal dust with the risk of IPF, even for the familial form of pulmonary fibrosis . Even afFurther significant correlations have been established among IPF and agriculture and farming, livestock, wood dust and stone, sand and silica .Microbial agents  play a potential role in the pathogenesis of IPF . An imbaMoreover, Huang and co-workers analysed the patients enrolled in the COMET-IPF study and demonstrated a relationship between peripheral blood immune gene expression and bronchoalveolar lavage (BAL) microbiome features in IPF . Viral iStudies investigating drugs as antivirals, antibiotics, and antifungals have shown a great promise for IPF treatment, consolidating the link between microbiome and IPF .Susceptibility to IPF is probably related to several genetic features characterized by a combination of gene variants and transcriptional changes, that result in the loss of epithelial integrity. Familial interstitial pneumonia (FIP) is identified when two or more member of the same biological family are affected . FIP is Any process that modifies gene activity without changing the underline genetic code is defined as epigenetic alteration . TraditiCigarette smoking and ageing are the main effectors of epigenetic modifications, given their association with IPF and the relationship between them and DNA methylation , 27. StoAgeing is a physiological progression to the death, through loss of function and increasing weakness. Cellular and clinical age-related changes play a leading role in IPF . Age-relIn the last years research efforts have been oriented to the pathobiology of IPF. Previously defined an inflammatory disease, IPF is currently considered an epithelium-driven disease, in which a dysfunctional, ageing lung epithelium exposed to recurrent microinjuries lead to defective attempts of regeneration and aberrant epithelial-mesenchymal crosstalk, creating an imbalance between profibrotic and antifibrotic mediators, maintaining an environment supportive of exaggerated fibroblast and myofibroblast activity and hijacking the normal reparative mechanisms to chronic fibroproliferation. In this section we will focus on the different cell type and mediators involved in IPF pathogenesis .It is postulated that fibrosis evolves over a long interval of time in patients with IPF; when diagnosed, lung structure is importantly modified by disease, and pathological features are characterized by different stages of epithelial damage, AEC2s hyperplasia, dense fibrosis, abnormal proliferating mesenchymal cells. What happens before diagnosis is still partly unclear, but the current theory is that a dysfunctional ageing epithelium is the key to understand IPF pathogenesis .In normal lungs, loss of AEC1s after an injury is followed by proliferation and differentiation of AEC2s and stem cells, that restore alveolar integrity involving several mechanisms: coagulation cascade, new vessels formation, fibroblast activation and migration, collagen synthesis and proper alignment. Many chemokines, as TGF-β1, platelet-derived growth factor (PDGF), vascular endothelial growth factor (VEGF) and fibroblast growth factor (FGF), lead the process. If injury persists, or the ability to restore normality is impaired, the wound healing process will pass through an inflammatory phase, with increased levels of interleukin-1 (IL-1) and tumor necrosis factor-alpha (TNF-α), creating a biochemical environment leading to chronic abortive regeneration and tissue remodelling .In IPF patients lung epithelium is thought to be dysfunctional, and genetically susceptible to aberrant response to injuries. Possible genetic causes of dysfunction have been discussed in the precedent section. These mutations affect genes expressed in AECs. Altered genetic expression, with consequent aberrant transcription and translation, leads to abnormal protein production, potentially able to damage cellular environment and alterate cellular behaviour, and to accelerated cellular senescence. The result of these abnormalities is a fragile epithelium, with reduced ability to respond to an injury , 35, 36.The repetitive exposure of alveolar epithelium to microinjuries, as infections, cigarette smoke, environmental inhaled toxics, gastro-oesophageal reflux lead to damage of AEC1s. Dysfunctional AEC2s should regenerate damage cells, but their ability to re-establish normality is seriously impaired; this is the crucial moment of IPF pathogenesis , 38.The cellular activity leads to protein over-expression and endoplasmic reticulum stress (ERS), a protective pathway that occurs when there is an imbalance between cellular demand for protein synthesis and the endoplasmic reticulum capacity to work properly. The consequence is the activation of another protective pathway, the unfolded protein response (UPR), designed to re-establish normality in endoplasmic reticulum(ER) work inhibiting proteins translation and targeting them for degradation, but also to lead cell to apoptosis if stress persists. The activation of UPR has several consequences on cellular behaviour, not completely understood. A relevant consequence is the activation of intracellular apoptotic pathways; furthermore, UPR stimulates the production of profibrotic mediators, as TGF-β1, PDGF, CXCL12 (C-X-C motif chemokine 12), CCL2 (chemokine C-C motif ligand 2) , 39.TGF-β1 is probably the most important mediator involved in IPF pathogenesis. AEC2s may produce it as a consequence of actin/myosin-mediated cytoskeletal contraction induced by UPR, through ανβ6 integrin activation. Theανβ6 integrin/TGF-β1 pathway is a fundamental biological process: the molecules are constitutively bound, suggesting that the system is primed to detect injurious stimuli. TGF-β1 may be activated even by lysophosphatidic acid (LPA), whose production is controlled by autotaxin. TGFβ1 is a strong pro-fibrotic mediator: it promotes epithelial cell apoptosis, epithelial mesenchymal transition (EMT), epithelial cell migration, production of other profibrotic mediators, circulating fibrocytes recruitment and fibroblasts activation, proliferation and transformation into myofibroblasts, production of VEGF, CTGF (connective-tissue growth factor) and other pro-angiogenic mediators and several other pathways .The EMT is a molecular reprogramming of AEC2s, induced by UPR and enhanced by pro-fibrotic mediators and pathways. Epithelial cells express mesenchymal cell-associated genes, become detached from basement membrane, migrate and down-regulate their typical markers. The most characteristic marker of these transitional cells is αSMA , typical of myofibroblasts. Such an event may occur in three different moment of cellular and tissue life: development, cancer and fibrosis, whereas it is not required to restore normality during wound healing response .Other key pathways in IPF are a group of deregulated embryological programs, as the Wnt-β-catenin signalling, involved in EMT and fibrogenesis and activated by TGF-β1, Sonic Hedgehog (Shh), gremlin-1, and phosphatase and tensin homologue (PTEN). Deregulation of these pathways confers resistance to apoptosis and proliferative advantages to cells .Evans and co-workers [The UPR, TGF-β, and EMT are activated in patients with IPF, but how this activation occurs is still widely undefined. Many possible causes of ERS and UPR have been identified, as Herpes virus infection end epigenetic effects of inhaled toxic . An intr-workers , 41.Malli and co-workers demonstrated that IPF patients present significantly decreased EPCs, with important consequences as failure of re-endothelization, that may lead to a dysfunctional alveolar-capillary barrier, inducing a pro-fibrotic response, and compensative augmented levels of VEGF, that might consequently stimulate fibrotic process and abnormalities of vessels function, contributing to cardio-respiratory physiologic consequences typical of advanced stage of disease. Furthermore, endothelial cells may undergo a mesenchymal transition, with the same consequences of EMT [The damage to alveolar structure and the loss of AECs, with disruption of basement membrane, involves alveolar vessels and leads to increased vascular permeability. This early phase of wound healing response is characterized by the formation of wound clot; consequently, new vessels should be formed and endothelial cells should proliferate, involving endothelial progenitor cells (EPCs). s of EMT .Endothelial and epithelial damage lead to activation of the coagulation cascade in the early phases of wound healing process. Coagulation proteinases have several effects on cells involved in wound healing. The tissue factor (TF)-dependent pathway is the most important in IPF pathogenesis, leading to a pro-coagulation state enhanced by increased levels of plasminogen activation-inhibitors as PAI1 and PAI2, active fibrinolysis inhibitors and protein C-inhibitors. The pro-coagulation environment reduces the degradation of extracellular matrix(ECM), resulting in a profibrotic effect, and inducing differentiation of fibroblasts into myofibroblasts via proteinase-activated receptors , 35.AECs are not the unique cells whose behaviour is modified during IPF pathogenesis: also airway basal cells change their biological program to respond to persistent injuries and epithelial damage. This regenerative response activates developmental pathways and leads to an aberrant proliferation with irreversible changes in alveolar spaces architecture. This phenomenon, known as bronchiolisation of alveolar spaces, has important functional consequences and is one of the pathological features of usual interstitial pneumonia (UIP) .The contribution of mesenchymal cells, and particularly of fibroblasts and myofibroblasts is crucial for IPF pathogenesis; these cells are recruited, activated and induced to differentiate, trans-differentiate and proliferate by the abnormal biochemical environment created by activated epithelial and endothelial cells. It is still unknown the initial trigger and source of mesenchymal cell recruitment, but current literature agrees to define fibroblasts and myofibroblasts as the key player cells of IPF pathogenesis. Mesenchymal cell-type involved are circulating fibrocytes, pulmonary fibroblasts and myofibroblasts .Fibrocytes are circulating bone-marrow derived mesenchymal cell progenitors, co-expressing CD45 or CD34 withtype-1 collagen. They could be recruited by damaged tissues when pathological processes significantly deplete local mesenchymal cells. The activated epithelium recruits them exposing CXCL12, CCL2 and secreting TGF-β1, a strong fibrocytes activator that induces αSMA production. In damaged lung, fibrocytes contributes to IPF through ECM production differentiating into fibroblasts and myofibroblasts and enhancing profibrotic environment by secreting profibrotic cytokines. Furthermore, there are increasing evidences that percentage of circulating fibrocytes increases during acute exacerbation of IPF (AEIPF), and afterwards decreases when the hyper-acute phase ends. Therefore, they could be considered promising biomarkers, with prognostic implications .Fibroblasts are tissue mesenchymal cells committed to re-establish a normal and well-structured ECM in wound healing repair process. During IPF pathogenesis both lung and fibrocytes-derived fibroblasts are persistently exposed to profibrotic mediators secreted by activated fibroblasts, leading to ECM production and trans-differentiation to myofibroblasts. The most important stimulating factor for trans-differentiation is TGF-β1, but also PDGF plays a significant role. The activation of these cells has important consequences on their intra and extracellular behaviour: IPF lung fibroblasts share unique properties, as a hyper-methylated DNA profile, that enhance genetic transcriptions; this behaviour has similarity to lung cancer biology .It is still debated if deregulated AECs undergoing EMT and expressing αSMA could be considered myofibroblasts or not. Myofibroblasts synthesize more ECM than fibroblasts. The matrix produced by myofibroblasts is poorly organized but very dense. Moreover, they persist longer than fibroblasts in damaged tissue. Myofibroblasts have contractile properties due to αSMA, similarly to smooth muscle cells (SMCs); the main difference between these cells is the irreversibility of contraction of myofibroblasts, that may regulate collagen remodelling, inducing a spatial re-organization of collagen fibrils, increasing mechanical stress and leading to a stiffer ECM. The mechanical characteristics of deposed ECM is probably the most important factor in regulation of myofibroblasts activity: in fact, their synthesis activity is enhanced by contact with a stiffer matrix, creating a positive feedback loop, whereas a healthy soft substrate strongly inhibits myofibroblasts and leads to reduction of their number. This is probably the reason of absence of myofibroblasts in normal tissues , 45, 46.A typical pathological feature of UIP is the presence of fibroblastic foci (FF), small clusters of active fibroblasts and myofibroblasts, very close to hyperplastic AEC2s. The strict association between AEC2s and mesenchymal cells inside the FF favours aberrant crosstalk, and enhances effects of TGF-β1, PDGF, Wnt pathway, amplifying the profibrotic environment and leading to a greater trans-differentiation rate, acquisition of invasive characteristics and exaggerated matrix production, with an imbalance between deposition and degradation of collagen.The pathobiology of IPF is leaded by aberrant epithelial-mesenchymal crosstalk, but the inflammation may play an important role. Inflammatory cells are involved in normal wound healing since early phases. Macrophages immediately produce cytokines that stimulate an inflammatory response, and later participate to the transition to a reparative environment, recruiting fibroblasts, epithelial and endothelial cells. When injury persists, neutrophils and monocytes are recruited. The production of reactive oxygen species (ROS) worsens epithelial damages, and an imbalance between antioxidants and pro-oxidants may lead to epithelial cells apoptosis and dysfunctional pathways activation. Monocytes and macrophages produce PDGF, a strong profibrotic mediator; furthermore, CCL2 and the macrophage colony stimulating factor (M-CSF), also known as colony stimulating factor 1 (CSF1) may have direct profibrotic effects , 39.Kotsianidis and co-workers [The role of lymphocytes is still debated; certain lymphocytic cytokines are considered profibrotic, with direct effects on fibroblasts and myofibroblasts activity. Th-1, Th-2 and Th-17 T-cells have been linked to IPF pathogenesis. Th1 subset produces IL-1α, TNF-α, PDGF andTGF-β1, with a final profibrotic effect, butTh2 and Th17 responses seems to be more important in IPF pathogenesis. Th2 subset typical interleukin is IL-4. This interleukin induces increased levels of IL-5, IL-13 and TGF-β1, recruiting macrophages, mast-cells, eosinophils and mesenchymal cells, and is directly implied in fibroblasts activation. Furthermore, fibroblasts isolated from patients with IPF show hyper-responsiveness to IL-13; this interleukin has a positive effect on fibroblasts’ activity, enhancing ECM production. Th17 subset indirectly promotes fibrosis, increasing TGF-β1 levels; it is positively regulated by TGF-β1, creating a positive feedback loop . In both-workers .In IPF lung levels of Interferon-γ (IFN-γ) are low. IFN-γ inhibits fibroblastic activity and switch off Th2 response. However, novel studies on the role of inflammation in IPF pathobiology are needed, and their results will probably either help to understand what happen in the early stages or contribute to clarify the mechanisms of disease progression .According to the 2011 joint statement by the American Thoracic Society (ATS), European Respiratory Society (ERS), Latin America Thoracic Association (ALAT) and Japanese Respiratory Society (JRS) , the diaFirstly, around 10% patients presenting with an atypical UIP pattern on HRCT cannot undergo surgical lung biopsy due to age, advanced disease, or poor clinical conditions . These pFinally, despite the universally recognized utility of MDD, there is no reference standard to measure its validity, and a consensus on what constitutes reasonable purposes, structure, and governance of MDD meetings has been recently advocated . MoreoveThe recent advances in the treatment of IPF make the need to ameliorate the diagnostic process more compelling than ever, with the goal of limiting the number of unclassifiable ILD and enhancing the identification of patients who can benefit from treatment. Groups of experts have recently indicated the need for a more comprehensive and dynamic diagnostic process, integrating the contributions of all available clinical data and diagnostic techniques. Physicians should be allowed establish diagnoses when diagnostic confidence is sufficiently high based on available criteria and clinical judgment, while provisional diagnoses should be made when there is a leading diagnosis which does not strictly meet all the criteria. In order to address the issue of unclassifiable cases, complementary information to traditional histopathology might be provided by modern technologies such as micro-computed tomography (micro-CT or μCT), a novel imaging technique that allows the three-dimensional study of paraffin-embedded tissue blocks . PrelimiSince the conduction of the first trial almost 30 years ago , the lanPirfenidone, an orally administered pyridine, demonstrated combined anti-inflammatory, anti-oxidant and anti-fibrotic actions both in vitro and in animal models of pulmonary fibrosis, consisting in the regulation of the expression of TGF-β and inhibition of fibroblast and collagen synthesis. However, the precise mechanism of action remains unknown.Four placebo-controlled randomized trials –84 exploNintedanib is a multiple inhibitor of tyrosine kinase receptors implicated in lung fibrosis pathogenesis, including PDGF receptors α and β, VEGF receptors 1, 2 and 3, and FGF receptors 1, 2 and 3 , which wEvidence from real-life experiences of nintedanib use is very limited. Data from a German multicenterstudy on the compassionate use program of nintedanib in IPF  reportedFor the first time after decades of disappointing results, physicians have now two equally effective treatment options to offer to patients with IPF. Translating the results of the trials into clinical practice proved to be not straightforward though, and some uncertainties are still limiting the management of the heterogeneous IPF population.The timing for starting treatment might represent the first challenge for physicians approaching those patients newly diagnosed with IPFwho are asymptomatic and have little or no functional impairment. In fact, it is unclear whether they might benefit from any treatment since there is no marker to ascertain the future clinical course of these patients. Recent post-hoc analyses of pooled data from the late phase trials on the efficacy of both nintedanib and pirfenidone showed that in the placebo arms subgroups of patients with more preserved lung function at baseline had a similar rate of progression of the disease as compared to patients with more impaired lung function, while the treated subgroups showed to receive the same benefit from both drugs , 96. ThiDuration of treatment represents a matter of debate, as it is unknown whether pirfenidone or nintedanib maintain their efficacy for periods longer than 2 years and whether they should be discontinued in those patients experiencing significant disease progression, as there are no markers of response to treatment available yet. A subgroup analysis of data from the CAPACITY and the ASCEND trials showed that in patients who progressed significantly during treatment (predicted FVC decline > 10% after 6 months), those who continued pirfenidone had a lower risk of subsequent FVC decline or death . As for This trial also allowed to enter patients with more severe disease  and will hopefully clarify whether the beneficial effects of these drugs may be generalized to the whole IPF population. The interim analysis showed that patients with FVC ≤ 50% and > 50% predicted at baseline had a similar decline in FVC to week 48, suggesting that nintedanib may offer similar benefits in patients with advanced disease . HoweverWith two drugs available, which should be chosen when starting treatment? Indeed, pirfenidone and nintedanib appear to have comparable efficacy and tolerability, as well as a partially overlapping spectrum of potential side effects , 99. As When available and appropriate, the option of participating in a clinical trial should always be considered and discussed with the patient. This can give access to new, potentially beneficial therapies and gives the patients the opportunity to play an active role in their management and to be followed by expert medical staffs in specialized centers.Following the example of most fields of respiratory medicine, such as asthma, chronic obstructive pulmonary disease, pulmonary hypertension and lung cancer, combination therapy that includes the use of different molecules in a synergic has a strong rationale . Indeed,https://clinicaltrials.gov/ct2/show/NCT02606877 Identifier: NCT02606877). For the time being, it is advisable to avoid the concomitant use of the two drugs given the risk associated with the partly overlapping side effect profiles.A larger, multicenter phase 2 open-label, multiple dosing trial to investigate the pharmacokinetics of nintedanib and pirfenidone when administered separately or in combination has been recently conducted in the UK , lung cancer, pulmonary hypertension, obstructive sleep apnoea, while non-respiratory comorbidities include ischemic heart disease and gastro-oesophageal reflux  The greaThe prevalence of COPD in IPF ranges from 6% to 67% across 23 different studies . A syndrLung cancer is more frequent in patients with IPF than in the general population, suggesting a predisposition to developing neoplasm in IPF. This could be explained both by common risk factors such as tobacco-smoking and by the sharing of pathogenic pathways and molecular alterations . The prePulmonary hypertension (PH), usually defined as mean pulmonary arterial pressure (mPAP) ≥ 25 mmHg, is one of the conditions more frequently associated to IPF and has been widely demonstrated to increase mortality in this population , 139. ThModerate to severe OSA affects up to 65% IPF patients , 149. PaGERD is common in IPF patients, and the use of proton pump inhibitors (PPI) demonstrated to improve survival in retrospective studies , 154. BaThe coexistenceof coronary artery disease deservesattentionis observed in up to 30% of patients with IPF and increases mortality . The manAnxiety-depressive disorder considerably affects patients with IPF with a prevalence of 11–50% . DepressNowadays, substantial advances have been achieved in the understanding of IPF pathogenesis and in the therapeutic possibilities that can be offered to patients. Nevertheless, major issues regarding diagnosis and management are still open. The process leading to a confident diagnosis of IPF is far from being straightforward. Currently, only morphological data coming from HRCT or SLB are available for discussion, and their interpretation can significantly vary between clinicians, even if experts. Several different genetic and biological markers have been proposed for aiding diagnosis and prognosis , however