Delayed comparison tasks are widely used in the study of working memory and perception in psychology and neuroscience. It has long been known, however, that decisions in these tasks are biased. When the two stimuli in a delayed comparison trial are small in magnitude, subjects tend to report that the first stimulus is larger than the second stimulus. In contrast, subjects tend to report that the second stimulus is larger than the first when the stimuli are relatively large. Here we study the computational principles underlying this bias, also known as the contraction bias. We propose that the contraction bias results from a Bayesian computation in which a noisy representation of a magnitude is combined with a-priori information about the distribution of magnitudes to optimize performance. We test our hypothesis on choice behavior in a visual delayed comparison experiment by studying the effect of (i) changing the prior distribution and (ii) changing the uncertainty in the memorized stimulus. We show that choice behavior in both manipulations is consistent with the performance of an observer who uses a Bayesian inference in order to improve performance. Moreover, our results suggest that the contraction bias arises during memory retrieval/decision making and not during memory encoding. These results support the notion that the contraction bias illusion can be understood as resulting from optimality considerations. Comparing magnitudes of two temporally separated stimuli is one of the fundamental tools of experimental psychology and neuroscience. Interestingly, choice behavior in these experiments reveals a fundamental bias: when the first stimulus is small, subjects tend to overestimate it, whereas when it is large, they tend to underestimate it. The first account of this bias, known as the contraction bias, was published a century ago by Harry Levi Hollingworth who later became one of the pioneers of applied psychology. Hollingsworth presented subjects with square cards of various sizes for a brief period of time and asked them to memorize their sizes perceived magnitude of a stimulus is a weighted combination of its veridical magnitude and a reference magnitude, such as an average of all contextually relevant stimuli, that serves as an anchor The customary explanation for the contraction bias is that the There is a growing body of literature suggesting that the brain utilizes Bayes' rule to optimally combine information from different sources In order to test this hypothesis, we conducted an experiment in which we instructed subjects to memorize the length of a bar presented on a computer screen and then compare this memorized length to the length of a probe bar. We show that contraction bias depends on the prior distribution of bar lengths, and increasing the uncertainty in the memory of bar lengths enhances the contraction bias, both of which are consistent with the Bayesian hypothesis.after memory encoding and measuring the magnitude of the contraction bias we demonstrate that prior information is introduced during memory retrieval/decision making rather than when the first stimulus is encoded in memory.When within a trial does the Bayesian computation take place? Is the encoded memory biased or does the prior information bias the result of the length comparison? By manipulating uncertainty in the memory of bar lengths Some of the findings presented here have appeared previously in abstract form 1L) for 1 sec and were instructed to memorize its length. After a delay of 1 sec, during which screen remained blank, they viewed a probe bar (2L). The probe bar remained visible on the screen until subjects reported which of the two bars was longer by pressing dedicated keys on the keyboard. The first bar, L1, was drawn from a uniform distribution in the logarithmic scale between 150 and 600 pixels. The difference in length between 1L and 2L varied between −30% and +30%. Both bars were presented at random locations on the screen and no feedback was provided to the subjects on performance on individual trials (See L1>L2’ responses as a function of the difference between the memorized and probe stimuli. The average psychometric curve of the subjects (n = 9) is plotted in L1 and L2 increased.In the standard task , subjectials See . We quanpattern of errors made by subjects depends on the magnitude of the memorized stimulus. When the memorized stimulus is small, subjects tend to make more errors in trials in which the probe stimulus is larger than the memorized stimulus, compared to trials in which the probe is smaller than the memorized stimulus. The opposite behavior is observed when the magnitude of the memorized stimulus is large L1 and L2 in our experiments) relative to the width of the psychometric curve. We used a different approach to overcome this limitation: Unbeknownst to the subjects, we included a subset of trials in which the lengths of the two bars were identical. We term these trials “impossible trials” because there is no correct answer to the question “which bar (L1 or L2) was longer”. Impossible trials are well suited for the analysis of the contraction bias because performance on these trials is independent of the proficiency of individual subjects in distinguishing the difference in the length of the two bars.Our purpose is to quantify the contraction bias in these experiments. Previous studies have demonstrated a contraction bias in delayed comparison tasks by showing that the L1>L2’ as a function of the length of L1 (L1 = L2). Note that despite the fact that L1 and L2 were identical on these trials, subjects reported that L1 was longer than L2 on roughly 60% of the shortest trials  the control region knows that the neural representations of L1 and L2 are noisy, e.g. due to noise in the sensory pathway. Moreover the representation of L1 is noisier than that of L2 because L1 has to be stored in memory, a process that may contribute additional noise to the representation of L1; (2) the control region has information about the marginal distribution of bar lengths. This distribution can be approximated based on the history of the experiment; (3) the control region utilizes Bayes' rule and combines the noisy representations of L1 and L2 with knowledge about the prior distribution in order to construct the posterior distributions for the two bar lengths. These posteriors are then used to minimize error in judgment. A formal description of this process appears in the Our aim is to account for the contraction bias in a Bayesian framework of decision making. In order to see how the contraction bias emerges from Bayesian inference, we consider a control region in the brain, such as the prefrontal cortex L1 is unknown, L2 is known. Consider a hypothetical subject who forgets the length of L1, but has no ambiguity about the length of L2, i.e., the neural representation of L1 is infinitely noisy whereas there is no noise in the neural representation of L2. In this case, the posterior of L1 is the prior distribution. In contrast, the prior distribution makes no contribution to the posterior of L2. Therefore, the optimal strategy would be to report ‘L1>L2’ in trials where L2 is smaller than the median of the prior distribution and to report ‘L1<L2’ in trials in which L2 is larger than the median. Therefore, in the impossible trials in which L1 = L2, the subject would report ‘L1>L2’ if L1 is smaller than the median of the prior distribution and would report ‘L1<L2’ otherwise, as depicted in L1 and underestimating relatively large L1.L1 and L2 are equally uncertain. Consider a case where the estimated uncertainties in the representations of L1 and L2 are equal. This would be true if the only uncertainty in the representations of L1 and L2 results from sensory noise, and memory storage does not add any additional noise to the representation of L1. In the impossible trials in which the two bars are physically identical, the contribution of the prior distribution to the posteriors of L1 and L2 is equal. Symmetry considerations indicate that the subject would report that ‘L1>L2’ at chance level for all bar lengths, i.e., there is no contraction bias, as depicted in L1 is less certain than L2. In intermediate cases where the level of uncertainty in L1 is larger than that of L2, for example, as a result of added noise due to memory storage, we expect the resultant response curve to reside between the response curves of L1 is reported to be larger than L2 as a function of the lengths of L1 and L2 . Similar to the first experiment, all lengths were presented in logarithmic scale to satisfy the assumption of independence of noise and bar length. We compared the responses of this group to the original group who saw stimuli that were drawn from a uniform distribution in the logarithmic scale between 150 to 600 pixels. The accuracy of subjects in the trials in which L1≠L2  was indistinguishable between the two groups , supporting the assumption that the level of noise in the neural representation of the bars is independent of bar length in these ranges. Response curves for the two groups in the impossible trials are depicted in If the contraction bias results from Bayesian inference, then changing the prior distribution is expected to change the response curve. In particular, assuming that noise is independent of the length of the bars, a translational shift in the prior distribution would result in an equal translational shift in the response curve without changing its shape. To test this prediction, we asked a new group of naïve subjects to participate in the experiment of L1 is 30% higher than the uncertainty in L2 , the intermediate trials in which the difference between L1 and L2 was ±15% (t-test) and the most difficult trials in which the difference between L1 and L2 was ±7.5% (t-test).The distracting task was designed to interfere with the memory of the first bar. In the Bayesian framework, it was intended to add ‘noise’ to the representation of ary task . This dep = 0.0002, two-tailed), supporting the assertion that a decrease in performance is associated with an increase in the magnitude of the contraction bias.In order to characterize the effect of the secondary task on the contraction bias, we compared the response curve of subjects in the impossible trials with interference from the secondary task  the subjects could not know whether they would be presented with an interfering task and therefore could not know what weight to give to the prior distribution. Therefore, if the computation had taken place at the time of the encoding of L1, we would have observed no difference in the slope of the response curve between the two conditions. Therefore, the Bayesian computation necessarily took place after the interfering task, at the time of L1 retrieval or later, when L1 and L2 were compared.Within a single trial, when does information about the prior distribution combine with the sensory measurement? One possibility is that it takes place during the encoding of d trials . In otheHow do subjects learn the prior distribution? In order to address this question, we compared the level of contraction bias, as measured by the slope of the response curve, in the first 20 impossible trials to the slope in the last 20 impossible trials for subjects who completed the experiment in In this study we examined the effect of a translational shift in the prior, but we did not alter the shape of the prior distribution. Previous studies have shown that subjects are sensitive to the shape of the prior distribution in category and sensimotor learning Contraction bias in delayed comparison tasks is a common cognitive illusion observed in many different modalities and under different experimental conditions All subjects gave written informed consent using methods approved by the Massachusetts Institute of Technology Committee on the Use of Humans as Experimental Subjects.Subjects were undergraduate and graduate students from the Massachusetts Institute of Technology. All subjects had normal or corrected-to-normal vision and no subjects took part in more than one of the experiments. Each subject received $10 plus 1 cent for every correct trial in the experiment for a session lasting less than an hour.Stimuli were white horizontal bars on a black background displayed on a 17″ computer screen with a resolution of 1024×768. All bars were 3 pixels wide.L1 at a random location on the screen for 1 sec. After a delay period of 1 sec, during which screen remained blank, L2 appeared at another random location on the screen. L2 remained visible until the subjects pressed one of two keys indicating which bar was longer. The difference in length between 1L and 2L varied between −30% and +30%. Unbeknownst to the subjects, in roughly 50% of the trials, the lengths of the first and second bars were equal (L1 = L2). Subjects did not receive feedback on performance on individual trials. Each trial was followed by a 2 sec intertrial interval during which the screen remained blank. Two distinct groups of subjects completed the standard task. One group (n = 9) saw L1 bars chosen uniformly in the logarithmic scale from the  pixel interval, while the other group (n = 10) saw bars chosen from the  pixel interval.Subjects sat approximately 60 cm from a computer screen in a dimly lit room. Each subject completed 400 to 600 trials in one hour and received feedback on their overall performance after every 20 trials. No other feedback was provided. In the standard task, each trial started with the presentation of a L1 bars were chosen uniformly in the logarithmic scale from the  pixel interval; (2) subjects completed a distracting memory task between the presentation of L1 and L2 in a randomly selected 50% of the trials: 500 msec after L1 disappeared, a random sequence of four colors  were displayed on the screen for 400 msec each. 400 msec after the disappearance of the last color, a number from 1 to 4 appeared in yellow on the screen. Subjects were instructed to recall the color that corresponded to the number and press one of four dedicated keys to indicate this color. L2 appeared 500 msec after subjects made their color choice.The modified task was identical to the standard task with two exceptions: (1) According to our Bayesian hypothesis, the contraction bias emerges because subjects use Bayes' law to combine noisy information about the lengths of the bars with knowledge about the prior information in order to optimize performance. In this section we formalize this intuition.iL and iR be the logarithm of the length of bar i and its neural representation, respectively. We assume that this representation is noisy such that iz is drawn from a zero-mean Gaussian distribution with variance iR for a given representation of bar length In accordance with Weber's law, the lengths of the bars are measured in logarithmic scale. Let  uniform . Bayes' niform  such that L1 has to be stored in memory, a process that may contribute additional noise to the representation of L1. An ideal Bayesian observer, who has access to R1 and R2, would report ‘L1>L2’ in trials in which L1<L2’ in trials in which L1>L2’ in a trial in which L1 and L2 are presented is given byGiven a pair of neural representations, L1 is infinite, whereas there is no uncertainty in the representation of L2. In other words, L1>L2’ if R2 is larger than the median of L1. In trials in which L1 = L2, Eq. (3) dictates that he would report ‘L1>L2’ in trials in which L2 is larger than the median and ‘L1<L2’ otherwise.In order to construct the response curve we compute  . For furAll slopes were computed after normalizing the range of lengths to 0 and 1 in the logarithmic space.We used a pairs bootstrap resampling procedure In order to compare the response curve slopes between subjects who saw 50–200 pixel lines and those who saw 150–600 pixel lines we sampled from each group independently using the algorithm above, and then constructed a 95% confidence interval on the difference between the bootstrap slopes of the two groups.In order to compare trials with and without the interference task we calculated the difference in the bootstrap slope of each subjects' standard and interfered trials, and found the 95% confidence interval of this difference. The same method was also used to compare the slope of the response curve in the first 20 impossible trials of the experiment to the slope of the response curve in the last 20 impossible trials of the experiment.In order to compare behavioral performance to that predicted by the model, we used the model presented above to generate a set of response curves of ideal observers characterized by different values of L2>L1’ in the 50–200 and 150–600 standard experiments. Subjects reported that ‘L1>L2’ in the impossible trials in 41% and 46% respectively. This tendency has been reported previously p = 0.58, two tailed t-test). More importantly, this explanation is circular because a bias in the opposite direction could equally well have been explained by arguing that the prior distribution is biased in favor of large magnitudes. Therefore we did not attempt to account for the global bias and subtracted it before fitting, assuming that it is generated by a different mechanism. Thus, for the purpose of finding the parameters we added a constant to each of the response curves to normalize them such that mean(Pr[‘L1>L2’]) = 0.5. For purposes of comparison, the range of the logarithm of bar lengths was normalized to lie between 0 and 1 and we used a least square fit to find the parameters that best fit the population-average experimental data. We found that the best fit model parameters for the groups who saw 50–200 and 150–600 pixel-long bars were given by Note that subjects exhibited a small bias in favor of reporting ‘


The neutral assumption that individuals of either the same or different species share exactly the same birth, death, migration, and speciation probabilities is fundamental yet controversial to the neutral theory. Several theoretical studies have demonstrated that a slight difference in species per capita birth or death rates can have a profound consequence on species coexistence and community structure. Whether asymmetry in migration, a vital demographic parameter in the neutral model, plays an important role in community assembly still remains unknown. In this paper, we relaxed the ecological equivalence assumption of the neutral model by introducing differences into species regional dispersal ability. We investigated the effect of asymmetric dispersal on the neutral local community structure. We found that per capita asymmetric dispersal among species could reduce species richness of the local community and result in deviations of species abundance distributions from those predicted by the neutral model. But the effect was moderate compared with that of asymmetries in birth or death rates, unless very large asymmetries in dispersal were assumed. A large difference in species dispersal ability, if there is, can overwhelm the role of random drift and make local community dynamics deterministic. In this case, species with higher regional dispersal abilities tended to dominate in the local community. However, the species abundance distribution of the local community under asymmetric dispersal could be well fitted by the neutral model, but the neutral model generally underestimated the fundamental biodiversity number but overestimated the migration rate in such communities. The unified neutral theory, an intriguing and yet controversial explanation for species diversity patterns, has attracted much attention and has stimulated much new thinking about diversity The assumption of ecological equivalence or ecological symmetry is fundamental to the neutral theory, but it is also one of the main causes of the controversy. In real communities, species can be quite different from each other in their life history traits that contribute to their demographic rates. Some theoretical studies have examined the robustness of the neutral model against the differences in species fecundity or mortality rates However, Hubbell suggested that the ecological equivalence assumption works well as a first approximation To our knowledge, only one theoretical study tested the robustness of the neutral model against variance in migration rate In this paper, we considered a local community embedded within a metacommunity. We relaxed the ecological equivalence assumption of the neutral model by introducing differences into species' natural dispersal ability from the metacommunity to the local community. Diversity of such a local community was maintained by the balance among local birth, death and immigration from the outer metacommunity. The local community was neutral. Asymmetry only existed in the input of individuals and species by immigration from the corresponding metacommunity. We investigated by simulation the relative importance of dispersal asymmetry among species versus the ecological drift in shaping local community structures. We also recorded the relationship between species per capita dispersal ability from the metacommunity to the local community and species relative abundance in the local community. Finally, we evaluated the ability of the neutral model in fitting species abundance distributions of local communities with dispersal asymmetries.m and no deviation (σ = 0). In this case, there appear a few species with very high abundances, whereas the number of species with rare and medium abundances decreases.Contrary to the neutral model, there is a positive correlation between species per capita dispersal factor and species rank in abundance for especially common species . With thθ) for the local communities with large differences in species regional dispersal abilities. The larger the variance in species dispersal abilities, the greater the underestimates of the fundamental biodiversity number will be. The neutral theory also overestimates the migration rate when species differ largely in their dispersal abilities.Besides the effects of dispersal asymmetries on community structures described above, the neutral model fits the local neutral communities with dispersal asymmetries very well . For exai is ip = iP/mJ in the metacommunity. The probability that an immigrant to the local community belongs to species i is proportional to ip. Let us denote it as a ip-metacommunity. With dispersal asymmetry introduced in the model, an immigrant is from species i with probability i is iq (iq–metacommunity). But both the diversity and evenness of such a iq –metacommunity decrease with increasing σ . The Simpson diversity index is 0.98 and θ is 50 for σ = 0. The average Simpson diversity index is 0.98, 0.97, and 0.94, and the average value of the fundamental biodiversity number is 50.35, 48.46, and 42.74, for the iq–metacommunity with σ = 0.1, 1, and 4 respectively. Reduced biodiversity and evenness in the iq–metacommunity directly result in lower fundamental biodiversity numbers of the local communities when σ is large  rainforest varied from 0.44 to 16.4% per year for the 63 species with over 50 individuals ≥10 cm dbh On the one hand, large differences among species migration probability could have significant effects on local community structures . ExtremeOn the other hand, more realistic dispersal processes and dispersal asymmetries may produce different conclusions compared with what we have reported here. In this paper, the migration process is modeled as a spatially implicit process from the metacommunity to the local community, which is the same as spatially implicit neutral models did In this study, we relaxed the strict symmetry assumptions of the neutral model by incorporating differences in species dispersal rate from the metacommunity into local communities. As in the neutral model, diversity in the local community is maintained as a dynamic equilibrium between the extinction of resident species and immigration of new species from the metacommunity Based on the results of our simulation and those achieved by Zhou and Zhang One vital weakness of the neutral model is that it cannot provide any information about species composition and the relationship between species richness and the ecosystem function, which must be answered by community ecologists. Once species differences are introduced into the neutral model, species can also dynamically coexist despite the asymmetry in competitive ability or migration and positive relationships between the species competition ability or migration rate and its abundance emerge mJ and with the fundamental biodiversity number θ following the algorithm described by Hubbell im the per capita dispersal factor of species i into a local community. σ = 0 is the neutral case with all im being equal to1.We constructed a neutral metacommunity of size J, with the Hubbell's migration parameter equaling m. Contrasted with the neutral model, the initial relative abundance of species i in the local community is proportional to iPim, where iP is the abundance of species i in the corresponding metacommunity. The dynamics of the local community were determined by local birth, death and immigration from the metacommunity as described below.With the background metacommunity formed as described above, we explored the effect of asymmetric dispersal limitation from the metacommunity to the local community on species richness and species abundance distributions in the local community. We sampled local communities of size m (migration coefficient) the vacant site was occupied by an immigrant, and the immigrant belonged to species i with probability i, where in is the abundance of species i in the local community. The local dynamics were iterated for 20 000 turnovers of the local community, which was long enough for the community to reach a stochastic equilibrium.To model the dynamics of a local community, we first randomly eliminated an individual from the local community. With the probability mJ = 1×106, θ = 50, J = 1×104, m = 0.01, 0.1 and 0.3 respectively. For each value of m, we selected the value of standard deviation of species per capita dispersal factor σ to be 0 , 0.1, 1, and 4 respectively. The values of m were similar to that estimated for tropical rainforest m and the standard deviation σ were the same. Additionally, while calculating the distribution of species' abundance in the local community, we recorded the relationship between species' per capita dispersal factors and their relative abundances in the local community at equilibrium. Then we fitted the simulated communities with Hubbell's neutral model and tested the goodness of fit as follows. For each simulated abundance data set, we estimated the fundamental biodiversity number, migration rate and the log-likelihood value (LV) using the method proposed by Etienne i, i = 1, …, 100). We obtained a percentage value by comparing the LV and LVi . A percentage value that is around or larger than 0.5 means the simulated abundance data set can be well fitted by the neutral model In the simulations, we assumed that


From measurements of the surface tension, density, viscosity and light scattering of aqueous solutions of methanol, ethanol and propanol at 293 K, their activity in the surface monolayer, surface excess concentration, and apparent and partial molar volume were determined. The surface excess concentration of alcohols at the water–air interface was determined from the Gibbs equation by using both the alcohol's activity and their molar fraction in the bulk phase and recalculated by using the Guggenheim–Adam equation. The values of the surface excess concentration determined from the Gibbs equation were also applied to determine the standard Gibbs energy of alcohol adsorption at the water–air interface from Langmuir’s equation and compared to those determined from that of Aronson and Rosen.The online version of this article (doi:10.1007/s10953-012-9935-z) contains supplementary material, which is available to authorized users. Short chain alcohols are applied as solvents, co-solvents or co-surfactants and, among other things, they can change volumetric and surface properties of surfactants –8. AlcohThe microstructure of the bulk phase of aqueous solutions of alcohols is governed by the hydrogen bond, hydrophobic interaction and hydration, which are reflected in the enthalpy and entropy contributions in the free enthalpy of solution . For a dFrom fluorescence probe investigations Zana and Eljebari  stated tYoshida and Yamaguchi  using lon-propanol at room temperature, also stated that both water and n-propanol form single-component aggregates in solution.Roney et al. , based oHowever, in contrast to these conclusions, Alavi et al.  suggesteIndependently of the opinions about the structure of the aqueous solutions of short chain alcohols, it is known that their structure influences the volumetric properties of solutions, which is reflected, among other things, by the density and viscosity values. Using the density data it is possible to calculate the apparent and partial molar volumes of both water and the alcohols, and deviations from ideality can be observed. In the literature it is possible to find many data for partial and excess volume changes as a function of composition of aqueous solutions of short chain alcohols –23. ManyIt is known that there is a correlation between the structure of aqueous solution of a surface active agent and its tendency to adsorb at the water–air interface , 24, 25.Among other things, Yano  stated tThe surface excess concentration of alcohol at water–air interface is commonly determined from the Gibbs adsorption equation. To evaluate this concentration quantitatively a reliable data set of two parameters, the surface tension and the activity of alcohol in the bulk phase should be known. In most previous works the surface excess of alcohol concentration was calculated using the molar concentration instead of the alcohol's activity. Strey et al. , Lavi anGS is the Gibbs energy of the surface region, SS is the entropy of the surface region, VS is the volume of the surface region, γ is the surface or interface tension, A is the interfacial area, μi is the chemical potential of the i component in the surface region and i.For muliticomponet systems, including two phases in isobaric and isothermal processes, according to the Gibbs theory, the following equation is fulfilled for the surface region :1\documeT and p, in the equilibrium state of the reversible adsorption process, from Eq. i in the surface region. Equation For constant In the literature it is possible to find improper applications of this equation for determination of surface excess concentration of some surface active agents at the water–air or water–oil interface. It is particularly evident in the case of solutions in which the components are mixing in their total concentration range, for example, aqueous solutions of short chain alcohols.S and bulk B phase the chemical potential can be expressed by the following equations, respectively , Rosmuir Eq.  35].Tab.Tab2 groThe changes of the structure of aqueous solutions of alcohols should be reflected in the changes of their density and viscosity Fig. , 4, it iϕv) and partial , but if we assume the length of alcohol molecule is equal to the value given by Raina et al. [2. Thus, the question is which distance between alcohol molecules is more realistic in the bulk phase. It is known that molecules of short chain alcohols can be associated by hydrogen bonding. In such cases the average molecule length which results from its volume in the bulk phase, determined from the density data, is lower than that calculated on the basis of the distance between the particular atoms in the molecule; therefore, the distance between molecules equal to 2 Å is more justified than that based on d = 1.58 Å. If so, then the contraction of the molar volume of alcohol in water can result from possible changes of the d value from 2 to 1.58 Å. The minimal and maximal values of the mole volume of alcohol calculated from Eq. It appears that the volumes of qual 2 Å  are near = 2.6 Å , 51, d =[d = 2 Å  and V eqa et al.  . Supplementary Fig. S9 shows that if m3·mol−1 , which ix2 = 0.5 and depends on enthalpy and entropy effects. Thus, if mixtures of alcohol with water are made, some hydrogen bonds are broken endothermically and new ones are made exothermically, the enthalpy will be the difference between two much larger thermal effects. Simultaneously a loss of entropy takes places. In aqueous solutions of alcohols, alcohol–alcohol, water–water and alcohol–water molecules joined by hydrogen bonds and aggregates of alcohol formed by hydrophobic interactions are present. The measurements of the size of alcohol molecules by the Zetasizer Nano at x2 = 0.5 indicate that there are not large aggregates of alcohols. Probably dimers of alcohols are present, but also the formation of the alcohol–water hydrogen bonds cannot be excluded. From the thermodynamic properties of water–ethanol mixtures it results that the entropy effect is decisive for the changes of excess Gibbs energy of mixing. Thus a proper order of the associated alcohol and hydrated water molecules at x2 = 0.5 has a higher contribution to the excess Gibbs energy than disruption and formation of hydrogen bonds in comparison to “pure” water and alcohol. Therefore, probably a minimal excess of the sum of water and alcohol molar volumes is observed at x2 = 0.5.From this figure it is seen that the shape of the curves showing the changes of the sum of the partial molar volumes of alcohol and water as a function of alcohol mole fraction in the bulk phase is similar for each alcohol solutions and the maximum corresponding to l mixing , 55. ThiMeasurements of the isotherm of surface tension, density, viscosity and the light scattering show clearly that even methanol forms some aggregates, which for ethanol and propanol are like small micelles at some solution concentrations.In contrast to other investigators, aqueous solution ideality of short chain alcohols in the range of their concentration from zero to that corresponding to the maximal value of alcohol surface excess concentration was not proved, but a dependence between the maximal value of alcohol surface excess concentration at the solution–air interface and kind of alcohol was observed.Contrary to expectation, the activity of alcohol in the surface monolayer cannot be determined on the basis of the Sprow and Prausnitz equation, taking into account the activity of alcohol in the bulk phase determined from the Laar equation on the basis of partial pressure of alcohol over the solution and the constant value of the molar area of alcohol in the surface layer. However, it is possible to predict the alcohol activity from these equations, taking into account the activity of water in the bulk phase and the constant value of the water molar area.The standard Gibbs energy of alcohol adsorption at the water–air interface can be determined successfully both by Langmuir and Rosen and Aronson equations only in the case where asymmetric definitions of the activity are taken into account and, if according to this definition, the solution does not deviate from the ideality in the range of the surface active agent concentrations at which saturated adsorbed monolayer is formed.There is a contraction minimum of the volume of solutions after mixing alcohol with water if the ratio of their molecules is 1:1, which correlate with the maximum of the surface free enthalpy excess of alcohol and water mixing and is close to the minimal enthalpy and entropy effects, indicating that the decisive contribution of the entropy to volume excess of sum of water and alcohol volumes at molar fraction of alcohol equal to 0.5.Supplementary material 1 (DOC 33253 kb)Below is the link to the electronic supplementary material.


Hebbian plasticity precisely describes how synapses increase their synaptic strengths according to the correlated activities between two neurons; however, it fails to explain how these activities dilute the strength of the same synapses. Recent literature has proposed spike-timing-dependent plasticity and short-term plasticity on multiple dynamic stochastic synapses that can control synaptic excitation and remove many user-defined constraints. Under this hypothesis, a network model was implemented giving more computational power to receptors, and the behavior at a synapse was defined by the collective dynamic activities of stochastic receptors. An experiment was conducted to analyze can spike-timing-dependent plasticity interplay with short-term plasticity to balance the excitation of the Hebbian neurons without weight constraints? If so what underline mechanisms help neurons to maintain such excitation in computational environment? According to our results both plasticity mechanisms work together to balance the excitation of the neural network as our neurons stabilized its weights for Poisson inputs with mean firing rates from 10 Hz to 40 Hz. The behavior generated by the two neurons was similar to the behavior discussed under synaptic redistribution, so that synaptic weights were stabilized while there was a continuous increase of presynaptic probability of release and higher turnover rate of postsynaptic receptors. Even though Hebbian synaptic plasticity is a powerful concept which explains how the correlated activity between presynaptic and postsynaptic neurons increases the synaptic strength, its value has been diminished as a learning postulate because it does not provide enough explanation how synaptic weakening occurs. In simple mathematical interpretation of Hebbian learning algorithm, an increase of the synaptic strength between two neurons can be seen if their activity is correlated otherwise it is decreased . This inpr) according to the history of short-term activity [However, the specifics of a biologically plausible model of plasticity that can account for the observed synaptic patterns have remained elusive. To get biologically plausible model and remove the instability in Hebbian plasticity many mechanisms have been discussed in recent findings. One remarkable suggestion is to combine STDP with multiple dynamic and stochastic synaptic connections which enable the neurons to contact each other simultaneously through multiple synaptic communication pathways that are highly sensitive to the dynamic updates and stochastically adjust their states according to the activity history. Furthermore, strength of these individual connections between neurons is necessarily a function of the number of synaptic contacts, the probability of neurotransmitter release, and postsynaptic depolarization . These sactivity , 21 whicactivity . Based oactivity , 24; herA fully connected neural network was developed with two neurons in which each neuron consisted of thousands of computational units. These computational units were categorized as transmitters and receptors according to the role they played on the network. A unit was called a transmitter if it transmitted signals to other neurons and a unit was called a receptor if it received the signals into the neuron. The receptors of a given neuron were clustered into receptor groups. According to the excitation and the inhibition of the model neuron these computational units could update their states dynamically from active state to inactive state or vice versa. Only when a computational unit was in active state it could successfully transmit signals between neurons. Transmitters from presynaptic neuron and receptors of the corresponding receptor group of the postsynaptic neuron together simulated the process of a single synapse. Transmitter at presynaptic neuron can be considered as a synaptic vesicle which can release only a single neurotransmitter at a time and the model receptors can be considered as postsynaptic receptors at synaptic cleft. With these features, excitation of a neuron at a particular synapse in our network was determined by the function of the number of active transmitters in the presynaptic neuron, transmitters' release probability, and the number of active receptors at the corresponding receptor group of the postsynaptic neuron. First, in order to analyze how network with two neurons could balance the excitation when Poisson inputs with mean rates 10 Hz and 40 Hz were applied, Only one neuron was fed by Poisson inputs while letting the other neuron to adjust itself according to the presynaptic fluctuations. Neurons stabilized its weight for both Poisson inputs while the weight values of Poisson inputs with mean rate 10 Hz were stabilized into higher range compared to when Poisson inputs with mean rate 40 Hz was applied. The analysis into internal dynamics of neurons shows that neurons have behaved similar to the process discussed in synaptic redistribution when long-term plasticity interacts with short-term depression. Further, neurons have played complementary roles to maintain the network's excitation in an operational level. These compensatory roles have not damaged the network biological plausibility as we could see that neurons worked as integrators that integrate higher synaptic weighted inputs to lower output and vice versa. Finally the network behavior was evaluated for other Poisson inputs with mean rates in the range of 10 Hz to 40 Hz and observed as the mean rate of the Poisson inputs increases, the immediate postsynaptic neuron increases its synaptic weights, while the immediate presynaptic neuron of those inputs was settle, into a complementary state to the immediate postsynaptic neuron. A, with n receptor groups and a transmitter set. Moreover, transmitters in our presynaptic neurons were similar to the synaptic vesicles in real neurons with a single neurotransmitter. The states, either active or inactive, of these transmitters and receptors were modeled using two-state stochastic process as explained in the next section. Only when the units were in active states, they were reliable to successfully transmit or receive the signals to or from other neurons. A fully connected network with two neurons was created. Each neuron was attached to thousands of computational units which were either in active state or inactive state according to the excitation and the inhibition of the attached neuron. Units attached to a neuron were classified into two groups based on the role they played on the neuron. A computational unit that transmitted the signal from the attached neurons to other neurons was called a transmitter and a computational unit that received the signals to the attached neurons from other neurons was called a receptor. Further, receptors attached to a neuron were clustered into groups so that transmitters from presynaptic neuron could contact the postsynaptic neuron simultaneously through multiple synaptic connections. R of postsynaptic neuron and transmitter set T of presynaptic neuron jointly measured the excitation at the attached synapse w and balanced the excitation using threshold θ as discussed in the next section. The transmitters from presynaptic neurons contacted the receptors of a particular receptor group of postsynaptic neurons by forming a synapse between the two neurons; see +2 ions that influx to the biological synapse after arriving of an action potential and residual ca+2 ion concentrations that the synapse already has. And depletion has no influence on ca+2  ion concentrations and merely depends on use activity of the synapse. Then signal release probability at a transmitter in a synapse was adopted by the model proposed in [pr as a function of ca+2  ions influx to synapse, vesicle depletion, and signal arriving time to the transmitter. Only the influx of ca+2  ions after arriving of neurotransmitters into receptors of postsynaptic neuron was considered when determining states of the receptors. When defining the process under dynamic stochastic synapses we have only concerned with the properties and mechanisms of use-dependent plasticity from the few milliseconds to several minutes time scales. Therefore, use-dependent activity to our modeled network was introduced using short-term plasticity; facilitation and depletion , 26. Wheposed in  which dePs(ti) is the probability that signal is released by a transmitter S at time ti and train S, S(t) consists of the sequences of times where S has successfully released the signals. The map S forms a stochastic process with two states, that is, Release (R) for ti ∈ S(t) and Failure of Release (F) for ti ∉ S(t). The probability Ps(ti) in (ti by S as a function of facilitation C(t) ≥ 0 in (V(t) > 0 in  given in (C(t) to presynaptic signal that had reached to S at time t − s; α is the magnitude of the response. Similarly V′(s) given in (V(t) to the preceding releases of the synapse S at time t − s ≤ t and τc and τv are time decay constants of facilitation and depression. Maass and Zador [S to release the received signal at time t, if Ps(ti) > 0. We updated this rule by introducing a new θ threshold so that if Ps(ti) > θ, a transmitter S is allowed to release the received signal. And we called it as in active state. Receptors in the postsynaptic neuron were modeled using the same model of Maass and Zador except that they were not involved in the process of vesicle depletion. Therefore, the states of the receptors were determined by setting the depletion V(t) in  > 0 in  at time given in  defines given in  models tnd Zador  allowed θ for each receptor groups and set of transmitters. Let RJjI denote the jth receptor group in postsynaptic neuron J that contact transmitters in the presynaptic neuron I, and let XJjI(t) the output and θJjI(t) be the threshold value of RJjI at time step t. Similarly let TI denote the transmitters in neuron Iand let OI(t) be the output and θI(t) the threshold value of TI at time step t. The threshold value of the receptor group RJjI was defined as in (RJjI to TI is increasing (or decreased when the activity of RJjI to TI is decreasing). Threshold value for transmitters in neuron I, that is, TI, was defined as a function of total synaptic inputs from all its synaptic connections to the neuron I into the total output of the neuron as in  = 1/(1 − ex−), XJjI(t) = |RJjIAct(t)|/|RJjI|;  i = 1,2,…, g; OI(t) = |TIAct(t)|/|TI|.  |G| is the number of components in G and |GAct(t)| is the number of active components in G at time step t. A modeled neuron maintained threshold values ed as in  and it won as in . Every 6Moreover, according to the following predefined behavioral rule signal was propagated between neurons. Rule  1. When a receptor receives a signal from the corresponding presynaptic neuron at time step t, the signal is propagated within the network according to the following conditions. Once a received signal is applied to a receptor if the receptor is updated to inactive state then the received signal is inactivated otherwise the signal is propagated to a randomly selected transmitter of the same neuron. t, the signal is transmitted to a randomly selected receptor of the randomly selected receptor group of the postsynaptic neuron if updated state of the transmitter is active otherwise the received signal is inactivated. Once a transmitter of a particular neuron receives a signal at time step The above behavioral rule defines the underlying mechanism of signal transmission between the presynaptic neuron and the postsynaptic neuron; that is, when the related computational units from the two neurons are active only, the signal is successfully transmitted. Therefore, the number of active receptors in a receptor group of the postsynaptic neuron and the number of active transmitters in the presynaptic neuron jointly define the efficacy at a given synapse. In addition to this short-term plasticity and homeostatic synaptic plasticity , 29 adjunb = 7, which stored data of a given synapse of successive seven time steps. A single cell of a bin contains data at a time step t, namely, the number of active transmitters in the presynaptic neuron, the number of active transmitters in the postsynaptic neuron, the number of active receptors in the corresponding receptor group of the postsynaptic neuron, and the mean release probability of transmitters in presynaptic neuron. Let Ci be ith cell of kth bin, the time gap between two consecutive cells is set to 5 ms as in <(τ+ = τ− = 20 ms)<(tc7     = 30 ms), where τ+ and τ− are membrane constants for potentiation and depression (discussed later):This allowed us to define the time represented by each cell in a bin from its first cell as in ; see Figs that correspons to synapse s in kth bin (Bk). Since the activity between the presynaptic transmitters and receptors in receptor group s is not independent, we defined mean, μBk,s, and variance, σBk,s  2, of the kth bin on synapse s as in ATpre_={As as in μ^BBk, can be defined as in  × 5  ms and tpost to (cpost − 1) × 5  ms. Therefore, if postsynaptic hitter occurs after the presynaptic hitter, it leads to the potentiation, and if presynaptic hitter is followed by the postsynaptic hitter, it depresses the synapses during the given bin:Here  on STDP . Further on STDP  have estfined in . Similarfined in . Then STμSks and variance σSks2 of the sth synapse (Ss) can be defined as in (kth bin (Bk) is interacted with the synapse. The mean μSks and the variance σSks2 of the synapse Ss were estimated using maximum likelihood estimators as shown in μSks andshown in  and 22)μSks andes as in :(19)μSkBk is greater than the average output it had produced so far. That is, if the current mean number of active transmitters of a particular neuron is less than the mean number of active transmitters during the kth bin, neuron was recognized as in a nonquiescence state at bin Bk. That is mathematically if MATpreSk−1s ≤ MATpreBk and MATpostSk−1s ≤ MATpostBk, the weight was updated on the synapse Ss at bin Bk as discussed next.  In order to generate action potentials real neurons are necessary to be in a nonquiescence state. If a neuron is in a quiescence state, it is not possible for the neuron to generate action potentials that can change the synaptic strength significantly. Therefore, STDP was applied on synapses only if model presynaptic and postsynaptic neurons were not in quiescence states. We defined that a neuron is not in a quiescence state when the average output produced by the neuron during bin Ak of the kth spike in a spike train is proportional to the weight at that synapse and the release probability at the kth spike. In our approach Ak is proportional to the impact that made by transmitters in the presynaptic neuron and receptors in the corresponding receptor group of the postsynaptic neuron during Bk on the synapse Ss. If we applied the model proposed in [kth bin instead of kth spike, we can express Ak as in  as in  as in  if WSs,kth bin at synapse Ss, WSs(Δk), can be defined as in  during the kth bin to the coefficient variation of the synapse Ss has as given in , a, a24), aed as in  and the ed as in :(26)WSsng rates . The ampgiven in . The relas as in . Median p as in . This isA and neuron B, was developed; each neuron had ten receptor groups, making a presynaptic neuron to contact the postsynaptic neuron through ten dynamic stochastic synapses simultaneously. Both neurons, A and B had equal number of transmitters nT = 30000 and receptors nR = 30000; and receptors attached to neurons were uniformly distributed among receptor groups. At the onset one percent of transmitters and one percent of receptors in each receptor-group was set to active state. Poisson inputs with mean firing rates (λ) 10 Hz and 40 Hz were applied to all the receptor groups of neuron Asimultaneously while giving enough space for neuron B to adjust itself according to the feedbacks of neuron A,see A; and the behavior of the network was analyzed after the synaptic connections have established the effect of the altered activity and network activity has developed. The values were fed to the system according to following rule: the generated Poisson distribution was converted to byte stream by the following rule: if generated value is greater than the median of the Poisson distribution then it was considered to represent value 1 otherwise it was considered to represent value 0. Only when the represented value is equal to one, the signal was generated and fed to neuron A.An experiment was arranged to find the possibility that can STDP and short-term plasticity together balance the excitation of a network with two Hebbian neurons without defining any constraints on the weight learning algorithm. A fully connected network with two neurons, say neuron A and B at Poisson inputs with mean rates 10 Hz and 40 Hz. As shown in these figures, the weight distributions of both neurons at each, synapse have stabilized around 175 bins. After the weights distribution was stabilized, the median of the weight distribution was calculated and these calculated median values are shown in Figures A and B in terms of their mean release probability (the mean of the release probabilities of transmitters attached to the neuron) and the coefficient variation which measures the given synapse's excitation  in termMoreover, if the difference of the value of CVs between two neurons was considered, it is clearly shown in the Figures A's receptor groups and studied the behavior of the both neurons on the same network. λ, the medians of the stabilized synaptic weights of synapses of neuron B as the immediate postsynaptic neurons of external inputs have continuously increased as the mean rate of Poisson inputs is increased. Again the compensatory behavior from neuron A could be seen as it has generally decreased its medians of the stabilized synaptic weights as the mean rate is increasing. These complementary behaviors of two neurons seem to be necessary to stabilize the overall network activity. When 20 > λ, both neurons have worked together to control the overall excitement of the network. Intriguingly, when  λ = 20 and λ = 25, the excitation of the entire network was equally balanced between the two neurons as their average value of the medians of the stabilized synaptic weights becomes almost equal to each other. This might be because of the effect of τ+ = τ_ = 20 ms that we selected for STDP potentiation and depression time constant. This is important observation which provides the possibilitythat postsynaptic neurons could excited and stabilized into the same level of the presynaptic neuron if STDP time constants are highly correlated with the mean rate of the Poisson inputs applied. Therefore, STDP with different time constants for potentiation and depression might be a good solution to scale down external inputs effectively into neuronal level. Finally we would like to understand the behavior of the network when applying Poisson inputs in the range of 10 Hz and 40 Hz. The Poisson inputs with mean rates, 15 Hz, 20 Hz, 25 Hz, 30 Hz, and 35 Hz were also presented to neuron Bas the immediate postsynaptic neuron of the external inputs has scored the higher synaptic weights compared to neuron A. That is, its synapses, where the transmitters from immediate presynaptic neuron A contacted each receptor group of the postsynaptic neuron B, have scored higher weights compared to the other neuron. The presynaptic neuron A in this functional process has maintained higher mean release probability. Therefore, first, the synaptic weights of neuron Bhave been increased presynaptically by increasing the probability of neurotransmitter release. Second, the analysis of CV of these synapses of postsynaptic neuron B shows that it is laying higher range than the function of CV of neuron A, confirming the possibility of increasing the synaptic weights by higher turnover rate of active receptor component of postsynaptic neuron. This behavior of postsynaptic neuron B is also supported at Poisson inputs with mean firing rate 40 Hz. Intriguingly, if the behavior of postsynaptic neuron B at 40 Hz after neuron has adjusted to the external inputs and stabilized, was analyzed, the higher fluctuations of CV and comparatively lesser synaptic weights of neuron B at Poisson inputs with mean rate 40 Hz were observed compared to the postsynaptic neuron B's behavior at Poisson inputs with mean rate 10 Hz, showing the possibility that synaptic redistribution can increase the synaptic weights for Poisson inputs with low mean rate at steady state and not for Poisson inputs for higher mean rate. And for higher mean rates it is only a higher turnover rate of active receptor components. Further, STDP potentiation and depression time constants have made higher impact on the behavior of those two neurons; that is, it has controlled the level of excitation of each neuron equally when the magnitude of the mean rate laid near the magnitude of the STDP time constants. As the mean rate of the Poisson inputs is increasing, the complementary roles have been initiated into the two neurons.As per the literature, a synapse can be strengthened either by increasing the probability of transmitter release presynaptically or by increasing the number of active receptors postsynaptically. This general functionality at the synapses can be varied by the interplay between long-term plasticity and short-term dynamics, especially short-term depression. Short-term depression is mainly based on vesicle depletion which is the use-dependent reduction of neurotransmitter release in the readily releasable pool . When loSTDP has successfully interplayed with short-term plasticity to control the excitation or inhibition of neural network according to external adjustments. Notably, these adjustments are consistent and are also biologically plausible. The stabilization of synaptic weights in an operational level without controlling constraints seems to be possible if STDP as long-term plasticity interacts with the short-term dynamics. The dynamic behavior of short-term activity is necessary to propagate and balance the excitation of neural network without damaging the synaptic weight distribution; similar to how CV and probability of release have played with STDP to balance the excitation. When compared to Luz and Shamir  findingsThe model proposed in this research is a computational model to investigate the internal dynamics of neural networks when STDP, Hebbian plasticity and short-term plasticity, are interacting with each other. The model itself has few drawbacks; mainly the neural network of our model has spent around 150 bins to show the adjustment to external modifications; this is mainly because we selected the median of the weight distribution as the amount of synaptic potentiated as a response to the pair of presynaptic and postsynaptic spike (in ). This s


Shift work has become an integral part of our life with almost 20% of the population being involved in different shift schedules in developed countries. However, the atypical work times, especially the night shifts, are associated with reduced quality and quantity of sleep that leads to increase of sleepiness often culminating in accidents. It has been demonstrated that shift workers’ sleepiness can be improved by a proper scheduling of light exposure and optimizing shifts timing. Here, an integrated physiologically-based model of sleep-wake cycles is used to predict adaptation to shift work in different light conditions and for different shift start times for a schedule of four consecutive days of work. The integrated model combines a model of the ascending arousal system in the brain that controls the sleep-wake switch and a human circadian pacemaker model. To validate the application of the integrated model and demonstrate its utility, its dynamics are adjusted to achieve a fit to published experimental results showing adaptation of night shift workers (n = 8) in conditions of either bright or regular lighting. Further, the model is used to predict the shift workers’ adaptation to the same shift schedule, but for conditions not considered in the experiment. The model demonstrates that the intensity of shift light can be reduced fourfold from that used in the experiment and still produce good adaptation to night work. The model predicts that sleepiness of the workers during night shifts on a protocol with either bright or regular lighting can be significantly improved by starting the shift earlier in the night, e.g.; at 21∶00 instead of 00∶00. Finally, the study predicts that people of the same chronotype, i.e. with identical sleep times in normal conditions, can have drastically different responses to shift work depending on their intrinsic circadian and homeostatic parameters. Shift work has become an essential part of our 24-h society. However, along with benefits of around-the-clock service, it leads to increased sleepiness of shift workers, which leads to accidents and work-related injuries. This can have detrimental consequences not only for the shift workers themselves, but also for people around them. This is especially the case in health care, transport, and public safety systems, where shift work is widespread, and lives depend on workers’ performance Increased sleepiness during the shifts is likely to be associated with misalignment of the circadian system and enforced sleep-wake schedules Together, the homeostatic and circadian processes contribute to the level of the total sleep drive and determine the timing of sleep-wake transitions. Shift work leads to changes in the light exposure and sleep times, thereby affecting both the homeostatic and circadian processes. Ideally, the workers’ circadian oscillators need to re-entrain in accord with the shift schedule; e.g., on the night shifts the maximum of circadian activity should appear during the night and minimum during the day, thus also allowing sufficient sleep time and recovery of the homeostatic sleep pressure. However, most of the time such re-entrainment does not happen even after many years of shift work, and the workers constantly perform in conditions of increased sleepiness and risk The problem of adaptation to shift work had been intensively studied in the last decades. It has been demonstrated that increased light intensity during the shifts and darkness during the breaks can significantly improve adaptation to shifts and decrease sleepiness. Likewise, some shift schedules are expected to be easier to adapt to than others , thereby controlling the transitions between sleep and wake . The homeostatic drive H is assumed to accumulate during wakefulness and dissipate during sleep according toThe homeostatic x is approximately sinusoidal and changes between −1 and 1. In our model C cannot be negative because it is related to the firing rate of the SCN. Therefore, we introduce the following relationship between C and x, in the same way as it was done in x is calculated fromThe circadian pacemaker model simulates the activity of the master circadian clock in the suprachiasmatic nucleus of the hypothalamus (SCN) under the effects of light and non-photic inputs Ω scales the period to 24 hours, and cx follows the equationk and q are responsible for the sensitivity of the circadian pacemaker to light, and cτ is the internal circadian period. The variable sN is responsible for the non-photic influences on the phase of the circadian pacemaker, such as meals and locomotion withρ reflects the strength of the non-photic stimulation, and r modulates timing of the non-photic effects in respect to the core body temperature minimum (see below). The parameter s = 1 during wakefulness, and s = 0 during sleep, provides state dependency of the non-photic effects.The parameters B is assumed to be proportional to the rate α for the conversion of the photoreceptors in the retina from the ready state to the activated state, and to the number of receptors ready to be activated (1-n):G and ε were previously adjusted to fit experimental data n are converted back to the ready state at a rate β:In the St. Hilaire et al. (2007) model the photic drive 0p, I, and 1I are constants, and I is the actual light input into the model, which is reduced during sleep due to eyelid closure:wake see .In the experimental study that we simulate effects of bright versus regular light during night shifts were examined in healthy male volunteers Each protocol consisted of one baseline week during which the men were asked to maintain regular bedtimes between 00∶00 and 08∶00, and their sleep-wake logs were recorded and verified. At the end of the baseline week the core body temperature (CBT), and several other measures were recorded during at least 27 hours of the so-called constant routine (CR) at 150 lux lighting. CR was also performed a second time after the shift work schedule was completed, and its purpose was to measure and compare endogenous circadian phase unperturbed by periodic environmental inputs, such as light/dark cycle, and influences due to periodic changes in behavior, such as sleep-wake cycle. Constant routine requires subjects to remain awake throughout, in a constant posture, restricted to very low activity levels, with nutritional intake distributed throughout day and night (for more detail on CR see CBTmint) during the second CR relative to the first was calculated and compared between the groups.Starting the next day after these initial CR recordings the night shifts (00∶00–08∶00) were imposed for four consecutive days. In the control group lighting during the shift was set to normal indoor intensity of 150 lux. For the treatment group lighting during the shifts was bright with intensity between 7000 and 12 000 lux, and a period of constant darkness was scheduled for 8 hours starting one hour after the shift end (09∶00–17∶00). During the one hour commute home from work both groups were exposed to outdoor lighting, but the light exposure during the breaks was not controlled. CR was again performed starting on the last day of the shifts schedule following natural awakening, and the CBT was measured. The time shift of the CBT minimum , shift times (150 or 12 000 lux at 00∶00–08∶00 on the shift days), and the timings of scheduled darkness . However, other information required for simulations, such as light exposure during baseline and during commute to and from work was not provided in the publication In particular, the experimental study did not provide information about the light profile during the baseline week. Therefore, we had to assume a reasonable light profile during the baseline and the times where lighting was not controlled in the experiment. For this purpose, we use a light profile with intensity of 500 lux between 09∶00 and 20∶00 and lower lighting of 150 lux outside these times during wakefulness, as shown for days 1–5 in In accord with the experimental protocol constant routine on days 6–7 of the study is realised by having constant light of 150 lux and forced waking for 27 hours starting immediately after awakening on day 6   and 25 lux in the night (23∶00–00∶00), as illustrated with different shades of gray in One hour travel time is allowed for commute to and from work, and, thus, wakefulness is enforced during this time as shown in m = 1.18 VmV and v = V−10 mV (see example of mV in H and C according to Eqs (5)-(12) and, therefore, also tracking of the changes of the total sleep drive.Forced wakefulness during shifts, travel, and constant routines is introduced by keeping the mean membrane potentials of the MA and VLPO populations at their mean wake values: The difference between the control and treatment protocols can be seen during the days 8–11 in In both groups sleep is allowed at any time between coming home (09∶00) and going to work (23∶00) and the light during this time corresponds to the baseline light with the difference that in the treatment study darkness is enforced until 17∶00. On the last day of shift work  minimum from the dynamics of the circadian variables according to the formula introduced in with0t = 0.97 h is a constant, and critφ is phase difference between the circadian variables x and cx of the pacemaker model, given in radians. In the experiment recordings of the CBTmint are compared between the 7th and 12th days of the protocol  during the first constant routine, and CBTminCR2t during the second.Here In the following we first demonstrate the dynamics of the model on the experimental protocol CBTminΔt in the control case was slightly delayed instead of being advanced. Such slight differences can be expected since the default parameter values were chosen for a case of typical sleep-wake dynamics in the population at large, whereas here the model parameters need to be adjusted to a particular set of subjects that took part in the experiment. Therefore, in order to achieve a closer fit to the experimental observations averaged across the subjects in the study we needed to find parameter sets that satisfied two conditions: (i) sleep at the baseline should appear in the range of experimentally observed mean ± SEM taking into account both control and treatment groups. This implies that sleep start time should be in the region between 23∶43 and 00∶40, as can be derived from CBTminΔt in response to the control protocol should likewise be in the range of the experimentally observed mean ± SEM, which, according to CBTminΔt on the treatment protocol. Instead we use the data for treatment protocol to additionally test the validity of the adjusted parameter set by comparing model prediction with experimental observations during treatment, as shown in the next section.The parameter values for both parts of the integrated model have been calibrated previously and tested on a number of experimental studies χ, k, and q, as they constitute a minimal set required to achieve the fit. We aimed to keep existing parameter values wherever possible. Thus we have chosen to adjust only three of the model’s parameters: χ that would satisfy both conditions at the original values of k = 0.55 and q = 1/3 as used in χ <57 h, as indicated by the yellow area in χ above 57 hours or its decrease below 48 hours does not allow both conditions to be satisfied with baseline sleep appearing too late for high χ or too early for low χ.It is obvious from the figure that for the chosen ambient light profile there is no χ = 51 h, k = 0.51, and q = 0.6). All the parameter values are listed in In the supplementary material .D has increased significantly due to increased homeostatic sleep pressure H, so sleep starts immediately after the forced wakefulness is removed. However, high circadian activity C during daylight hours leads to awakening after only short time of sleep, even though the homeostatic sleep pressure has not yet significantly decreased. Sleep is thus again induced briefly before waking is enforced to travel to work.After the CR is over, sleep on both protocols is freely allowed. At this point the sleep drive CBTmint appears 2–3 hours before natural awakening.Night shift starts on the 8th day of the protocols and is repeated for 4 consecutive days, with work between 00∶00 and 08∶00. In the control case sleep is fragmented and shorter than in the treatment. This is related to the fact that the maximum of the circadian activity still appears during daytime and induces wakefulness even though the homeostatic sleep pressure has not yet fully recovered CR is again performed on the last day of shift work starting at 17∶00 on both control and treatment schedules. After the CR, sleep is freely allowed. In both control and treatment cases sleep starts immediately after the forced wakefulness is over. In the control case it continues until the next morning, indicating the lack of re-entrainment to the shift schedule. In the treatment case the sleep episode after the second CR is short, and the model is in the wake state from ∼23∶00 to about 07∶00 the next morning, indicating good entrainment to the night shift schedule.CBTtmin via Eq. (15). Comparison between the model predictions and experimental outcomes is shown in CBTtmin on the control and treatment protocols such that the theoretical values fall in the range of the experimentally observed mean ± SEM. As the result of this adjustment also the sleep times during the shifts agree well with experiment having full-scale accuracy of 2.5% for treatment and 3.33% for control protocol as shown in In the experiment the measurements of the CBT minimum were compared between the first and second constant routines. Therefore, here we do the same, and calculate Δst and 2nd constant routines, i.e., average sleep drive D between 00∶00 and 08∶00 on days 7 and 12, in order to estimate the effects of control and treatment protocols on sleepiness. This measure was not assessed in the experiment, so it cannot be directly compared with the data provided in We have also compared mean sleep drives during the shift times Since the model dynamics agree well with the experimental observations we can use it to explore and predict adaptation to night shifts in other conditions and to design shift schedules with lower sleep drive.CBTtmin and mean shift sleep drive on the treatment protocol change depending on the lighting intensity during the shifts, while all other conditions are kept the same as in Lighting intensities used at workplaces generally vary between about 10–50 lux for patrolling police officers or truck drivers on night shifts and up to 350–500 lux in offices, clinics, and factories. The treatment light intensity used in the experiment (7000–12 000 lux) is high, and would be expensive, and sometimes impossible, to use at workplaces. Therefore, in order to see whether light intensity can be reduced we examine how different shift light intensities affect entrainment to the shifts in the treatment conditions. CBTtmin on the lighting is nonlinear and the slope of the ΔCBTtmin change is significantly reduced for I ≥1000 lux. The difference in ΔCBTtmin between 1000 lux and the 12 000 lux used in the experiment, is 1.5 h, and still leads to quite good adaptation and reduced sleep drive. The light intensity of 3000 lux, which is still fourfold lower than that used in the experiment, leads to an only half an hour smaller shift of the CBT minimum compared to 12 000 lux (−8.4 h vs. −8.9 h). Given that in reality shift workers are also affected by various random inputs, such a difference can be considered as minor. On the other hand, light intensities below 100 lux lead to high sleep drive and phase advance of the temperature rhythms and, thus, advance of the circadian pacemaker (ΔCBTtmin >0). According to CBTtmin = −0.79 h. However, in the control case, where the same shift light intensity is used, ΔCBTtmin = 1.2 h  the parameter k that regulates circadian sensitivity to light and is responsible for the fulfillment of the Aschoff rule postulating that diurnal animals (k>0) delay in constant light conditions q, which is also responsible for the sensitivity of the circadian pacemaker to light; and (iv) the internal circadian period cτ. The first three parameters have been chosen because they were initially tuned to achieve a good fit to the averaged experimental data, and the internal circadian period was chosen because this characteristic often differs in people and can significantly affect response to night shifts.To study how the different response to the experimental protocol can be achieved we examine how change of the model’s parameters affects the dynamics. In particular we estimate the effects of (i) the parameter Since we do not have detailed information about sleep times of different subjects at the baseline, but know that they were asked to sleep between 00∶00 and 08∶00, we have to assume that this is their baseline sleep time. However, we found that change of any single control parameter leads to change of the baseline sleep time. Therefore, in order to keep baseline sleep times constant, and in line with the previous simulations, we have to balance such a change by tuning another parameter. In this way we always change two parameters and have the same baseline conditions, but different responses to shift protocols.χ to adjust the baseline sleep time when one of the circadian parameters  is tuned. Increase of χ normally leads to a later sleep onset, while its reduction yields an earlier one. χ at which sleep at the baseline is achieved between 00∶00 and 08∶00 when varying one of the parameters k, q, and cτ. For each of the figures the rest of the parameters are kept constant at the values corresponding to the fit to the average experimental case as shown in In this study we use the homeostatic time constant k alone leads to earlier sleep onset; therefore, in order to keep sleep during baseline week the same in all simulations the parameter χ must be increased to delay the sleep onset accordingly. χ and k lead to the same baseline conditions  the control protocol does not shift the CBT minimum. Below this value the system shows phase delay of the circadian pacemaker, and phase advance above this point. The response to the treatment study is more stable, demonstrating strong phase delay of the circadian pacemaker across all the k values, with slight decrease of ΔCBTtmin at higher values of k and χ.Increase of the parameter q from the original value of 0.3, used in q has to be compensated by decrease of χ in order to achieve the same baseline sleep conditions. Second, increase of q leads to stronger delay of the CBTmint in both control and treatment cases. In the control case, increase of q from 0.1 to 0.9 leads to a monotonous decrease of ΔCBTtmin from advancing to delaying values, while in the treatment case there is a maximum  of ΔCBTtmin at q = 0.3.Increase of the parameter k. In order to compensate for the delay of the sleep onset at higher values of cτ, the homeostatic time constant χ has to be reduced, as seen in cτ, ΔCBTtmin is decreasing for both control and treatment protocols. However, the response in the treatment protocol is much less pronounced than in the control. By choosing appropriate parameter values based on CBTtcontrolmin  = −1.2 h, and ΔCBTttreatmentmin  = −9.2h  and good adaptation with decreased sleepiness for the case of high lighting during the shifts (12 000 lux). This result is observed even without specific parameter adjustment, confirming that qualitative model predictions can be trusted even with the default parameter set. We find that the parameters can be adjusted to fit the particular set of subjects in the experimental study, thus allowing quantitative predictions for this group. This can be done with a number of different parameter sets, but these parameter combinations lead to similar predictions. Further, using the adjusted model, we have demonstrated its utility for prediction of shift times resulting in lower sleep drive and faster adaptation in lower light conditions. For example, we find that treatment light intensity can be reduced to 3000 lux, while still leading to similar adaptation as observed at 12 000 lux, and that starting shifts on this schedule at 21∶00 instead of 00∶00 significantly decreases sleep drive in both control and treatment cases. Finally, we have demonstrated that the model parameters can be adjusted to fit the dynamics of specific individuals on this protocol, and that individuals with the same baseline sleep characteristics can have drastically different response to shift work.Due to the low number of subjects in the experimental study It is noteworthy that the model parameters cannot be further calibrated based on the existing published experimental shift work studies, because, as far as we are aware, they do not provide complete information required for simulations. In the present study, for example, we had to make assumptions for ambient light profile, which affects the choice of parameter sets that match experimental observations. However, our study also indicates that such precise information may not even be needed, since the predictions for optimal and worst shift conditions remain similar for different examined light profiles once the parameters are adjusted . This may not be the case for other predictions and light conditions and has to be further investigated. Therefore, in the future it will be of advantage to further narrow down the parameter ranges provided a more complete experimental data for large number of subjects. We elaborate on the key findings of the present study below.The model predicts that the light intensity during the shifts in the treatment protocol can be reduced to ≈3000 lux, while giving practically the same adaptation as that in the case of 12 000 lux. Lower lighting level at the workplace that still allows good adaptation to shifts is highly preferable because it makes less damage to the retina, and is cheaper in terms of electric power. The above results support experimental findings of Boivin et al. Our simulations have demonstrated that adaptation to the night shift schedule in the control case strongly depends on the light intensity during the morning commute home from work, with lower light intensity leading to better adaptation and lower mean sleep drive. This is in good agreement with experimental studies showing that use of sunglasses or other ways of reducing light exposure during morning commute improves shift workers’ adaptation  reduce outdoors light exposure, which we have shown to be beneficial for adaptation to shift work , and . This can contribute to the variety of individual results observed in the experiment, where two out of five subjects demonstrated delay of the CBT minimum, while the other three advanced. Such variety was not observed in the treatment case because the shift start time used in the experiment was quite far from the critical point of the treatment case (01∶45). However, one of the subjects had demonstrated an unusually large shift in the ours see . It is pSuch a critical point for shifts starting time exists for every light protocol, according to the human phase response curve. Although the transition can be of either type 1 (as in the control case) or 0 (as in the treatment case), it nevertheless leads to an increased sleep drive, and therefore increases risk of work-related injuries and reduces the overall quality of life. Thus, it is important to know where the critical point is located for specific work conditions in order to avoid scheduling of the shift onsets near this time. This is specifically the case for the control protocol, where variations of sleep drive depending on the shift start time are much larger than in the treatment case where the mean sleep drive curve is flatter see ,8. This Using the information obtained from χ, k, and q. Additionally we have chosen to study how the model dynamics depend on the internal circadian period cτ because this parameter is often different in individuals.Finally, because of natural variability among subjects, we have examined how the model dynamics depend on model parameters. Since we have aimed to keep the original parameter values wherever possible, here again we have chosen to change parameters that were needed for initial fit of the model to experimental data: χ and cτ, while other are constrained based on the model dynamics, such as k and qk can lead to the same dynamics as difference in the internal circadian period cτ. This demonstrates flexibility of the integrated model, but it also means that the data provided by the protocol in χ can be estimated from polysomnographic recordings cτ can be measured in forced desynchrony protocols We have demonstrated that the model can be adjusted to required individual dynamics by means of different slight parameter changes. However, the ranges of the parameter values from which we can choose are not free, but determined by physiological characteristics, many of which can be directly measured experimentally, such as The model also suggests that the individuals showing the same dynamics at the baseline can have significantly different response to the shift schedules. In other words this means that people with seemingly the same chronotype in normal conditions can have very different responses when sleep-wake cycles are perturbed by shift work. At the same time, we have demonstrated that whenever the sleep timing at baseline and response to the midnight shift are both preserved, even different parameter sets lead to the same overall predictions . This indicates that the knowledge of chronotype alone may be insufficient to estimate how well people adapt to shifts, but the knowledge of chronotype together with the data on response to perturbation, such as night shift, can be enough to make predictions for individuals. In this study baseline sleep was adjusted to appear between 00∶00 and 08∶00 which corresponds to midsleep time around 04∶00, which is one of the most common chronotypes In the present study we have demonstrated that the integrated model can be adjusted to quantitatively match experimental shift work data, and have shown how adaptation to shift work can be improved by changing such external factors as lighting and timing of the shifts. However, it has to be noted that there is an infinite number of possible conditions affecting adaptation, including different shift work schedules, light profiles, and intrinsic workers’ sleep properties. Obviously, they cannot all be examined in advance even using a mathematical model. However, a physiologically based model can be calibrated on a number of specific core studies, and then applied to other conditions as desired by users.Figure S1Parameter sets satisfying the conditions for fit to the experiment. Values of k and q are shown for each χ between 48 and 57 hours leading to a fit of the model dynamics to the experimental data at the baseline and in response to the control protocol. Solid lines are plotted for constant values of χ, with dashed lines for χ = 48 h and χ = 57 h representing the border cases at which baseline sleep condition is no longer fulfilled. Point A indicates the parameter set used throughout the paper, B - default values of k and q as used in χ = 49 h, k = 0.5, q = 0.65), D , E , F  – indicate the parameter sets used in simulations in (TIF)Click here for additional data file.Figure S2Dependence of adaptation on shift start times for different parameter sets allowing fit to the experimental data. The colors of the lines correspond to the parameter sets from (TIF)Click here for additional data file.Figure S3Examples of the examined ambient light profiles. Note, that these light profiles are additionally modified by the dynamics of the model, as the light is gated during sleep, and are further modified during the shift protocols(TIF)Click here for additional data file.Figure S4Dependence of adaptation on shift start times for different ambient light profiles and parameter sets according to  The colors correspond to the different light profiles: red – profile 1, black – profile 2, green – profile 3, blue – profile 4. The black line for light 2 is the same as in (TIF)Click here for additional data file.Table S1Parameter values corresponding to the ambient light profiles shown in  The parameter sets are chosen in accord with conditions outlined in “Parameter adjustment” section. Profile 2 and the corresponding parameter set (set A in set A in  are the (DOC)Click here for additional data file.Text S1Supporting information on adjustment of the model parameters and model dynamics at different ambient light profiles.(DOC)Click here for additional data file.