With ambitious targets to eliminate lymphatic filariasis over the coming years, there is a need to identify optimal strategies to achieve them in areas with different baseline prevalence and stages of control. Modelling can assist in identifying what data should be collected and what strategies are best for which scenarios.We develop a new individual-based, stochastic mathematical model of the transmission of lymphatic filariasis. We validate the model by fitting to a first time point and predicting future timepoints from surveillance data in Kenya and Sri Lanka, which have different vectors and different stages of the control programme. We then simulate different treatment scenarios in low, medium and high transmission settings, comparing once yearly mass drug administration (MDA) with more frequent MDA and higher coverage. We investigate the potential impact that vector control, systematic non-compliance and different levels of aggregation have on the dynamics of transmission and control.In all settings, increasing coverage from 65 to 80 % has a similar impact on control to treating twice a year at 65 % coverage, for fewer drug treatments being distributed. Vector control has a large impact, even at moderate levels. The extent of aggregation of parasite loads amongst a small portion of the population, which has been estimated to be highly variable in different settings, can undermine the success of a programme, particularly if high risk sub-communities are not accessing interventions.Even moderate levels of vector control have a large impact both on the reduction in prevalence and the maintenance of gains made during MDA, even when parasite loads are highly aggregated, and use of vector control is at moderate levels. For the same prevalence, differences in aggregation and adherence can result in very different dynamics. The novel analysis of a small amount of surveillance data and resulting simulations highlight the need for more individual level data to be analysed to effectively tailor programmes in the drive for elimination.The online version of this article (doi:10.1186/s13071-015-1152-3) contains supplementary material, which is available to authorized users. Wuchereria bancrofti (responsible for 90 % of cases), Brugia malayi or Brugia timori) and can lead to chronic morbidity, such as lymphedema, which is associated with pain, severe disability and resulting social stigmatisation.Lymphatic filariasis (LF) is one of the neglected tropical diseases (NTDs) targeted for local and global elimination as a public health problem within the next decade. The disease is caused by one of a group a mosquito-borne filarial nematodes . These Here we develop a closely related model to both EPIFIL and LYMFASIM, but fit and validate it against recent individual-level surveillance datasets for two quite different MDA programmes in Kenya and Sri Lanka. We then simulate the model across a range of different settings to see how yearly MDA compares with (i) MDA at high coverage, (ii) adding moderate vector control or with (iii) twice-yearly treatment in order to study how these affect the probability of elimination after 5 years. We investigate the role of the main transmitting vector, the level of aggregation of worms amongst people in the population and patterns of non-compliance with the treatment programme on these results. The aim of the analysis is to understand how simulation outcomes are dependent on factors associated with setting. They also will identify the extent to which control programmes need to be informed by local epidemiological data, such as prevalence and the level of aggregation of worms, or the likely coverage of treatment and vector control programmes.Culex and Anopheles uptake curves are implemented depending on setting. The model dynamics are therefore divided into the individual human dynamics, including age and turnover; worm dynamics inside the host; microfilariae dynamics inside the host and larvae dynamics inside the mosquito.We introduce a novel model of filariasis infection in humans, which can broadly be described as a stochastic equivalent to the deterministic EPIFIL model without immunity. A full model description is given in the Additional files, however we shall briefly give a summary of the model development here. The model is a stochastic micro-simulation of individuals with worm burden, microfilaraemia and other demographic parameters relating to age and risk of exposure. Humans are modelled individually, with their own male and female worm burden. The concentration of mf in the peripheral blood is modelled for each individual deterministically and increases according to the number of fertile female worms as well as decreasing at constant rate. The total mf density in the population contributes towards the current density of L3 larvae in the human-biting mosquito population, where the distribution of L3 amongst the human-biting mosquito population is completely homogeneous. An empirically derived relationship is used for the uptake of mf by a mosquito, where both The effect of MDA was simulated for an individual by reducing their mf load and worm numbers according to estimated drug efficacies from the literature  leads to a non-zero endemic equilibrium at lower vector to host ratios than are observed when the bite-rate is more homogeneous. This is a consequence of when the bite risk is more aggregated, there are individuals who are more highly burdened that drive the infection above the breakpoint threshold. When the population is more aggregated the endemic prevalence can occur at lower levels than when the population is more homogeneous.The model parameters that were varied according to the setting were the aggregation of bite exposure and the vector to host ratio. The endemic prevalence of mf is affected by both of these setting parameters Fig. . There in = 808.The model was fitted and validated against two studies of an MDA programme over a number of years. The first is a study of two rounds of MDA using DEC combined with ALB across four sentinel communities in Malindi, Kenya in the years 2002–2004 . BaselinCulex, but where the main drug combination used in MDA is still ALB and DEC. Antigenaemia was measured through ICT and microfilaraemia measured through membrane filtration. Measurements were taken after an MDA round in August 2004 and just prior to another MDA round in late July 2005.Further model fitting was performed on a 2-year study in the districts of Colombo and Gampaha in Western Sri Lanka during an MDA programme . This reThe model was fitted using a maximum likelihood framework. The expected age-prevalence profile was calculated for a set of parameters by averaging across 1000 simulation runs. A likelihood was then constructed assuming binomial sample error for the number of individuals testing positive in each age category of the total population of individuals surveyed. For the Kenyan dataset, the initial time-point was at baseline before intervention. The age-prevalence curve was recorded from the model after reaching endemic equilibrium and used in the model fitting. For the Sri Lankan dataset, the initial time-point used in the model fitting was after the first round of MDA. In order to perform fitting on this dataset, the simulation was run until equilibrium at which point an initial MDA round was simulated. The age-prevalence profile was then taken 2 months after the initial round and used to compute the likelihood.The fitted simulation was then compared to the subsequent time-points in each dataset for both the mf and ICT prevalence. MDA was simulated for coverage taken from the data with efficacy taken from literature estimates. Alongside this the mf intensity distribution was also compared at baseline for the Kenyan dataset. This was not done for the Sri Lankan dataset as no baseline measurements were taken and the number of non-zero mf counts were too few.A number of scenarios are considered that can impact the effectiveness and timeline of a MDA programme. These are where systematic adherence of MDA occurs where individuals either consistently adhere or not adhere to the programme; where correlation exists between bite risk exposure and adherence; where different forms of vector controls occur alongside an MDA programme; and where correlation exists between the MDA and vector control programme  considered for filariasis is the use of Long-lasting insecticide-treated nets (LLINs). LLINs are considered for vector control in ch as in , 20. VecpN) is the original bite rate (λ) multiplied by a factor that determines a random bite being successful, λ(pNsN + (1 ‐ pN)).The modified global bite rate based on coverage of bed nets (σ) added to the mortality probability due to the vector control (dN) and so is σ + λpNdN. It is assumed these effects are constant throughout the whole time the intervention is taking place.The increase in mortality is similarly calculated, however the mortality under intervention is the natural mortality , the reV: H and the shape parameter corresponding to the heterogeneity of exposure risk among individuals, k. The maximum likelihood parameters were estimated to be V: H = 120 and k = 0.08.The model was fitted to the Malindi, Kenya dataset using the maximum likelihood fitting procedure. The fitted parameters were the vector to human ratio n = 740). For 91 out of 100 re-samplings the Kolmogorov-Smirnov test statistic returned a p-value greater than 0.01 confirming that the two samples are drawn from the same underlying distribution. A visual comparison of the two distributions also confirms the similarity between the two distributions.As a further step to compare the model fit to the data, the distribution of mf between individuals was compared between the recorded mf count data and the predicted distribution by the model Fig. . The disFor further validation, the estimates of the ICT prevalence from the simulated MDA campaign were also compared to the data Fig. . The antV: H = 55 and the population bite-risk aggregation k = 0.06. The resulting simulated age-prevalence profiles match reasonably well with the data and fall within the confidence intervals of all points, except for the first two age groups  and the same for bite risk and MDA (reflecting a scenario in which poor access to interventions is particularly acute for the high risk group). There is little information available on the realism, or otherwise, of this type of scenario, but we include it to illustrate the potential importance of these types of effects on the efficacy of a control programme. The results show that the effectiveness of these interventions can be undermined when these type of issues exist Fig. . MDA witone Fig. .Fig. 7CoIn order to investigate the impact of these types of correlations further, we look across a range of parameter values. When a higher bite exposure is associated with a tendency to not adhere to intervention decreases the success of an MDA programme, when a correlation exists between higher bite exposure and adherence, the probability of elimination can be dramatically increased. For example, annual MDA at 80 % coverage with high endemicity can increase the elimination probability from 2 to 48 % Fig. .Fig. 8Imρ = 0.75), a correlation between individuals who use LLIN and receive MDA treatment can dramatically decrease the probability of elimination. For example, with LLIN coverage of 65 %, a correlation can decrease the probability of elimination within 5 years from 80 to 30 %  has rapidly become the more popular method of estimating prevalence compared to measuring mf in the peripheral blood due to its cheaper cost, easier implementation and relatively little training to perform . Open quThe modelling work has identified a number of key areas that are important to address with regards to an elimination prgramme. In a timeline of 5 years bi-annual MDA at 65 % is the most effective of all strategies considered. However, if bi-annual MDA is not feasible, then an MDA programme combined with vector control can also have a similarly high probability of success in all settings. Annual MDA at 80 % with no VC is only effective in low and medium settings and annual MDA at 65 % is only effective for lower endemic settings. A number of systematic adherence issues can impact the success of a programme such as individuals who don’t adhere having higher burden, use of LLINs being correlated with adherence to MDA for an individual and systematic compliance to MDA. Where there are units that have not met goals within a specified timeline these would be the main sources to investigate.How exposure is distributed among individuals due to proximity to breeding sites etc. also has large implications for the success of a programme. A proxy of this can be taken from understanding the distribution of intensity of infection. Therefore using mf or antigen count data, which is already collected, should be used to inform modelling work and threshold targets for prevalence.Differences between Anopheles & Culex uptake curves also have important implications for elimination. Big differences in competence have also been observed for closely related species. Data on vector competence, behaviour, ecology and species distributions would allow for more accurate modelling work and aide in elimination strategies.We have considered the question of whether mass drug administration alone is capable of achieving elimination within the ambitious 2020 goals. To this end we developed a novel model of filariasis infection where an individual’s treatment, use of vector control and ability to adhere or not to interventions may be explicitly modelled. We have found that in most settings elimination may be achieved if the intervention is intensive enough. For areas with higher endemicity, this ambitious goal may not be achieved and other forms of intervention would need to be considered, principally higher coverage of both MDA and possibly additional vector control. We identified a number of issues that may inhibit an elimination campaign however. Chiefly, the aggregation of bite risk amongst a population can limit the reduction in prevalence due to MDA. Systematic adherence when coupled with exposure and adherence to other interventions can also have a large negative impact on a campaign. There is therefore a need to produce more accurate estimates of population aggregation by fully utilising individual-based data in models for elimination.Wim and Wif. The density of mf in the peripheral blood is also modelled for each individual and denoted Mi. The total mf density in the population contributes towards the current density of L3 larvae in the human-biting mosquito population. The model dynamics are divided into the individual human dynamics, including age and turnover; worm dynamics inside the host; microfilariae dynamics inside the host and larvae dynamics inside the mosquito.We introduce a novel model of filariasis transmission. The model is a stochastic micro-simulation of individuals with worm burden, microfilaraemia and other demographic parameters relating to age and risk of exposure. Humans are modelled individually, with their own male and female worm burden denoted i both male and female worms are added according to their bite risk bi that is individually drawn from a gamma distribution with mean 1 and shape parameter k . The rate at which worms are acquired depends on a number of stages of larvae life cycle as well as characteristics of the host. These are the mean total number of bites per individual per month b; the number of bites per mosquito λ; the ratio of vectors to hosts V: H; the probability that an L3 larvae leaves the host during a biting event ψ1; the probability that the L3 enters the host ψ2; the proportion of L3 within the host that develop into adult worms s2; and the age-dependent biting rate h(a) that increases with body size to saturate at age nine [i acquires an adult worm is thereforek and the vector to host ratio V:H . Therefore both of these parameters need to be fitted for each setting. Each worm has a constant rate of death μ, which is the same for males and females. Therefore the number of deaths in a time-step is Poisson-distributed with rate μWim and μWif for male and female worms respectively.For each individual age nine . The ratW. bancrofti is assumed to be completely polygamous [і are thereforeThe microfilariae dynamics are dependent on the total number of adult male and female worms. lygamous  and hencCulex, where the cibarial armature is less-developed than in other species, mf can survive at lower densities [The larvae develop from the mf that enter the mosquito during a blood meal from an infected host. There are two functional forms of this relationship that differ according to mosquito genus. For ensities . The relAnopheles larvae survival and development is facilitated at higher densities of mf. This relationship is given bym here is concentration of mf per 20 μL taken during a blood meal and r, κ are parameters relating to the functional form of the uptake curve [bi. The uptake of mf that develop into larvae is an average of all individual’s mf concentration weighted by their bite-risk i.e.For ke curve . Each inλ, the proportion of mosquitoes which pick up infection when biting an infected host ɡ; the death rate of L3, which is dominated by mosquito death σ1 and the proportion of L3 leaving the mosquito per bite, ψ1. The average number of larvae taken up in the mosquito population The dynamics of larvae in the mosquito are developed in very similar vain to EPIFIL . The dynFinally the equilibrium value for L3 in a mosquito is given byHence the equilibrium value of the larvae is a scaling of the uptake of mf that develop into larvae.k. The shape parameter defines how aggregated bites are amongst individuals and consequently defines the aggregation of infection amongst individuals. The human death rate τ is assumed to be constant throughout an individual’s lifetime with a cut-off at age 100. This results in a truncated exponential for the ages of inidividuals in a simulation.Each individual begins with zero infection and a bite-rate exposure that is drawn from a Gamma-distribution with mean 1 and shape parameter ui drawn from a normal distribution with mean u0 and variance σ2,Systematic adherence of individuals to mass-drug administration was modelled by assigning an individual a probability of receiving an effective dose during a treatment round z is less than zero. This random variable is drawn from a normal distribution with mean ui and variance 1.During each treatment round an individual is treated according to whether a randomly assigned variable p, the following must hold,Φ is the standard normal cumulative distribution function. The value for u0 may therefore be calculated using a pre-defined treatment coverage asFor there to be a coverage of σ2, which is defined asThe amount of systematic adherance is controlled through the variance ρ = 0 the variance is also zero and hence the receiving treatment is uncorrelated between individuals. This would be when there is no systematic adherance. As ρ increases to 1, the variance for an individual’s random choice value ui increases meaning it is more likely to be far above or below zero and hence means that adherence is more strongly correlated for an individual. This provides a method for changing the amount of systematic adherence without altering the total treatment coverage.For We simulated a number of scenarios of intervention alongside potential complexities which may limit the effectiveness of the intervention. The initial group of scenarios studied are for MDA coverage at 65, 80 and 95 % along with systematic adherence levels of 0.0, where each round of treatment has random coverage which is not correlated with previous rounds; 0.5, where an individual’s decision to comply is the same as in the previous round 50 % of the time and 1.0, where an individual either always complies or never complies with MDA. These scenarios are considered for low, medium and high endemic settings and for Anophelene and Culicine dominated regions.Anopheles vector, coverage rapidly speeds up the time to elimination in low and medium settings  of the standard normal is first applied converting into a uniformly distributed random number. The inverse of the gamma CDF is then applied to this random variable, producing a gamma distributed random variable that is still correlated with the tendency to comply or not comply with MDA.In order to convert the normal-distributed bite-riskThe probability of achieving elimination was explored if there is a positive, or negative correlation between an individual’s bite risk and their adherence with an MDA programme  were modelled for coverages of 65, 80 and 95 %. These were assumed to not be correlated with the MDA programme, which had coverage of 65 % with both annual and bi-annual interventions modelled.The probability of elimination was measured for each setting, LLIN coverage and annual and bi-annual MDA. For the annual intervention setting, bed net coverage alters the probability to elimination from the baseline  and a range of coverage levels  for high medium and low prevalence . We compare the reductions in prevalence 5 years into the programme probability of elimination for each of these settings, where elimination is defined as when transmission has been broken and no bounce back to pre-intervention levels can occur, even when intervention has been stopped. Systematic adherence alone has a marginal impact on the outcome of a MDA programme (Additional file In order to investigate the effect of these different correlations on the dynamics of an MDA programme, we consider a range of systematic adherence parameters (For annual MDA at 65 %, coverage of 65 % is only able to achieve elimination after 5 years for a low endemicity and after 10 years for medium endemicity (Additional file V: H. We therefore calculated the mean prevalence over 200 simulation runs or a range of vector to human ratios and used the resulting relationship to calculate the required parameter for a given prevalence value (Additional file Anopheles and Culex. For a large vector to host ratio there is no significant difference in prevalence, however a lower ratios there is an appreciable difference, where Culex has a breakpoint lower than Anopheles. For a range of values, high, medium and low transmission settings were required. The prevalences taken were 10, 15 and 20 % with the corresponding V: H estimated by using the first value for which that prevalence is achieved. These were estimated as 39, 60 and 120.In order to simulate a number of diverse scenarios, we required simulations to have endemic states at a number of different prevalences. As prevalence is not a free parameter in the model, this was done by changing the vector to human ratio


Skin cancers account for less than 1 % of all malignancies in India. Squamous cell carcinomas occurring over the waistline due to tying of cotton cloth called dhoti in males and sarees in females are predominantly seen in traditional Indian population. On wearing of these clothes for years, there is a constant irritation which produces depigmentation, glazing of the skin, acanthosis, scar formation, and later on malignant transformation. Presenting a case of a 65-year-old male with 7 × 5 cm ulceroproliferative growth over the right waistline with a history of prolonged use of dhoti. Wide local excision of the growth with 2-cm margin and primary closure of wound by mobilizing the skin was carried out. Histopathology showed well-differentiated squamous cell carcinoma. The patient is clinically disease free after postoperative follow-up of 1 year. Waistline cancer is a rare type of squamous cell cancer occurring over the waistline predominantly in Indian males and females wearing a piece of cotton cloth used to cover the lower part of the body. This cloth is called dhoti in men and saree in women. The dhoti is worn tightly around the waist with one of the shorter ends carried under the groin and tucked at the back, and the saree is adorned with a petticoat worn underneath by women, which is secured tightly to the waist by a cord. The tight knot around the waist at a similar position causes long-term friction and along with perspiration leads to pigmentation and scale-like changes in the skin which eventually undergo malignant transformation. The knowledge and existence of such malignancy is sparse in Indian medical fraternity  where itA 65-year-old male patient presented with a progressively increasing painless ulcer on the right side of the waist with a 6-month duration. Patient gave history of tightly tying a cotton dhoti over the waistline for the last 40 years. On local examination, there was a hypopigmented skin patch with scaling and ulceroproliferative growth of 7 × 5 cm with everted edges Fig. . There wHistopathology reports confirmed the presence of squamous cell carcinoma with tumor-free margin Fig. . PostopeThe term dhoti cancer was coined in 1945 by Khanolkar and Suryabai  which isThe exact causation of dhoti cancer is ill understood, and there are many hypothesis put forward to explain its probable mode of causation. Constant friction at the site of tying of dhoti or saree causes friction of the waistline which is associated with dermatoses . Other hAnother hypothesis put forward is depressed immunological state produced by the surrounding scar tissue  and absedhoti users for any malignant transformation.The age of presentation in the present case that was 65 years with more than 40 years of wearing dhoti is quite consistent with its occurrence in the age group after 50 years as reported in literature. This suggests a prolonged exposure of more than 40 years before malignant transformation . The feadhoti cancer will become further rare, but clinicians in India need to remember this condition as dhoti will continue to be a dress of traditional Indian males. The presence of acanthotic lesion in the waistline should be viewed with suspicion, and a constant monitoring to the patient is recommended.A rare case of squamous cell carcinoma due to chronic friction by wearing dhoti is presented with a treatment plan. It is expected that with change of lifestyle and lesser use of dhoti in new-generation Indians, the occurrence of The patient has given a written consent. Written and informed consent was obtained from the patient for the publication of case report and accompanying images. A copy of written consent obtained in vernacular language (Marathi) is available with us and is being held back to protect patient’s identity. It could be submitted with name blocked if the journal requires it.


Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models  and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa −1.5 for linear and −1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks. Connecting network theory with thermodynamics was an idea already present more than 40 years ago under the term network thermodynamics . DespiteWe look at reaction networks as thermodynamic systems that transforms two chemical species into one another . The env2O into H2O. Even if the artificial networks we create are comparable in density, they are not created with this constraint. This is due to the implications this constraint would have on the complexity of the boundary conditions. Omitting it leads to the existence of many transformation pathways between most pairs of randomly chosen boundary species, otherwise almost all pairs of boundary species would just have a steady state flow of zero between them.Our basic assumption is that the network is able to transform the two boundary species into each other. This is not always possible in real reaction networks where the transformations are constrained by stoichiometry of chemical constituents. For example, any chemically sound reaction model will implicitly forbid pathways that transform NWe study different quantitative properties of the networks at steady state. In particular, because cycles have been reported to have important functions in networks –11, we lIn the next section we describe our method for generating reaction networks so they resemble different complex network models and how we simulate them to find their non-equilibrium steady state. We then present our results concerning the flow through the networks, the distribution of entropy production of individual reactions, and the dependency of cycle number from flow through the nonlinear networks.L and R. Lij is the coefficient of the i-th species on the left side of the j-th reaction and Rij is the coefficient of the i-th species on the right side of the j-th reaction. Combining both matrices gives the stoichiometric matrix N = R−L, for which the element Nij in i-th row and j-th column gives the effective change of species i by reaction j. Given a relation v = v(x) between reaction rates v and species concentrations x, one can associate the reaction network with the dynamics of an ordinary differential equation (ODE):Reaction networks  consist In complex network science instead of looking at a bipartite graph, where reactions and species are represented by different types of nodes which are connected by edges, often the substrate graph is used. In this simplified view the nodes represent the species and an edge between two species is present if and only if there is a reaction having those two species on different sides of the reaction equation  13, 14], 1413, 1V of N nodes and a multiset E ⊂ V×V of M edges. These networks are generated following the models of Erdős-Rényi [Our artificial reaction networks are generated in three steps. We first generate a simple directed network (graph) consisting out of a set ős-Rényi , Barabásős-Rényi  .Thermodynamic properties of reaction networks can be described by non-equilibrium thermodynamics , 21. FordS can be separated into the exchange of the system with the environment deS and change through processes in the system diS:The change of entropy dexk being the change of concentration due to interaction with the environment and μk being the chemical potential. The entropy change through internal processes diS is given accordingly:The entropy exchange with the environment (with constant temperature and pressure) is given byσi of all individual reactions with σi = ∑mμmNmivi:From this equation the rate of entropy production can be calculated. By rewriting we see that the entropy production of the network i can be also written as function of forward and backward reaction rates vi,+ and vi, −[In steady state the entropy production of individual reaction nd vi, −:σi= we can replace the entire network with one imaginary linear reaction b1⇋b2. If we assume the Gibbs energies of formation of boundary species to be zero, the forward and backward rate coefficients are equal and we obtain the equationThis relation can be applied to calculate the total entropy production rate dS = deS+diS.Alternatively one could also get this result by calculating the boundary species entropy exchange with the environment, because in steady state 0 = N. Reaction rates are calculated using the Arrhenius equation (with the prefactor A set to 1):The Gibbs energies of formation of the species Ea is the activation energy which is sampled from the distributionEa just once for every reaction and assign it to that reaction direction which respective products have a higher Gibbs energy of formation, either Here, he right . We simub1, b2 at fixed concentration c1, c2. To remove the effects of the energy difference between the boundary species on the flow, we set their Gibbs energy of formation c1−c2∣ as standard deviation. Dynamics are simulated up to a time t of 50000 or up to the time when the mean square change of concentration (per species and time-step size) is smaller than 10−20.As we are interested in the steady state of the network under thermodynamic boundary conditions we solve the reaction equation while keeping the concentration of two selected chemical species We assume that the greatest topological factor influencing flow through the reaction network is the shortest path distance between the boundary species. Because we cannot perform simulation and analysis for one million pairs of boundary species, we sample 50 pairs of boundary species for all values of the shortest path occurring in the network.c1 = 0.1 and c2 = 1. To get an error estimate, we generate 10 independent samples of every network type.A simple investigation of network flow and entropy distribution is done with boundary species concentrations set to c1 at 0.1 while varying c2 from 0.2 up to 60. With higher values of boundary concentrations we notice an extreme increase of computational time needed to solve the individual ODEs. Thus, we are only able to simulate one network sample of every type for this setup.To investigate the response of the nonlinear networks to an increase in thermodynamic disequilibrium we vary the boundary conditions accordingly. For this we keep https://github.com/jakob-fischer/jrnf_tools), running (https://github.com/jakob-fischer/jrnf_int), and analyzing (https://github.com/jakob-fischer/jrnf_R_tools) the simulations is developed in R and C++ and freely available through the platform github.The software for generating  of reactions in glycolysis [For a comparison of the artificial reaction networks with real thermodynamic data we use a table of reaction free energies  while for larger values of d, they have generally a larger flow than the other networks. We hypothesize that the flow for boundary points whose distance is close to the diameter is limited by the sparse connection of those boundary species to the network. The high clustering of Watts-Strogatz networks  shows to be especially weakly dependent on boundary species distance orks cf.  apparentThe linear networks generated out of the Erdős-Rényi model and those generated with the Pan-Sinha model show a strikingly similar behavior. This may be due to their similar degree distribution (not shown).Unlike in linear networks, the flow and dissipation distribution in nonlinear networks depend on the absolute concentrations of the boundary species. For the variation of boundary concentration flow dependency of the concentration difference is in an intermediate regime  and the μ = μ0+ln(xi) inside the reaction network for different strengths of the boundary condition. In P(μ) are shown for the simulated Barabási-Albert (BA) reaction networks with boundary species distance d of 3. The distributions in general are localized between the chemical potentials of the boundary species μb1 = ln(xb1) and μb2 = ln(xb2) (remember that μ0 for boundary species is set to zero). While the distributions are almost uniform in this range for low flows, at higher flows the distributions are more shifted towards the upper part. Normalizing the standard deviation σμ by Δμ = ∣μb2−μb1∣ confirms this finding . We see that with higher flows the fraction of dissipation explained by these 10 percent of the network decreases (fσ(0.1) for lower values, but above a flow of around 5 they also decrease. Explained differently, for higher flows one needs a larger part of the network to explain a given fraction of its dissipation. Together with the narrower distribution of chemical potentials we interpret this as the thermodynamic disequilibrium leading to a tighter coupling of the reaction network. This coupling leads to the chemical potential of different species to be closer and to the dissipation being more evenly distributed among reactions.The distributions of dissipation values of the reactions are to noisy to find out if they also get narrower for higher flows. Thus, we calculate the fraction of the dissipation explained by the 10% of reactions with the highest dissipation, ecreases . The netv. Note, that even if the simulated reactions do not change, a change in the effective flow of a reaction can imply a change of direction and by this a change in the directed substrate graph.There are many indicators that cycles have an important function in networks –11. CyclThe number of small cycles is dependent on local topological properties of the network models. Thus, for evaluation we subtract the number of cycles found in networks with randomly chosen reaction directions . For allσ (σ[P(σ).To see how dissipation is distributed inside of the networks, we calculate the entropy production rate for the individual reactions σ  and looker than σ instead P(σ) follows a power law, we get an exponent of about −1.5 for linear networks and of −1.66 for nonlinear networks. The steeper slope of the nonlinear networks can be interpreted as an effect of their reactions being better coupled. This can be seen by the fact that nonlinear (A+B⇋C+D) reactions are not depleting a potential between two species directly but there is always the probability that they increase the potential between two other species. The coupling implies a stronger connection of the flow between individual reactions and by this a stronger connection with the magnitude of dissipation.The distributions show no large qualitative differences between the different network models . The powTo evaluate how the dissipation of a reaction depends on the connectivity of the involved species, for every species we calculate the mean dissipation of all reactions connected to it. Plotting the mean dissipation depending on the degree centrality of the species (in the substrate graph) shows a relatively high dissipation for reactions adjacent to lowly connected species . This efWe have simulated random reaction networks under thermodynamic constraints in order to provide insight into how energy is dissipated in complex reaction networks in thermodynamic disequilibrium. We observe a clear difference between linear and nonlinear networks. The power law has an exponent of ≈ −1.5 for linear and a slightly lower exponent of ≈ −1.66 for nonlinear networks. However, there are no qualitative differences between the distributions of entropy production rate for different complex network models like Erdős-Rényi, Barabási-Albert, etc. . The difWe found that a greater disequilibrium in nonlinear reaction networks is associated with a more tightly coupled network. For a greater flow, the network self-organizes and maintains a greater number of cycles . A greatFinally, we found that reactions involving lowly connected species tend to dissipate more energy, which is more pronounced in nonlinear networks, but is also found in linear networks . This miWe also showed how our artificial networks share topological properties with real reaction networks. The artificial networks are toplogically more similar to Earth’s atmospheric chemistry and Yeast’s metabolism than to the two investigated combustion chemistries. The main discriminating factor here is the high density of those two combustion chemistries. The distribution of thermodynamic parameters in the artificial networks only roughly matches data from reactions of glycolysis . ObviousNevertheless, a fundamental problem of such a comparison remains. It is the way the data of reaction networks is obtained. In networks from chemical models, experimentalists and modelers have made a decision on which reactions are relevant. Experimentalists only find reactions that are occurring and are measurable in the systems they investigate. Also the modelers might just decide to exclude reactions with low reaction rates from their models. Hence, the reaction network taken from a model is already biased with respect to the model’s intention. Our approach with artificial networks, however, assumes the artificial network is a set of  possible reactions; which reactions become important emerges from the dynamics and can be different depending on the boundary conditions.Thus, we suggest to investigate such emergent phenomena in the future. This is possible by taking smaller artificial reaction networks and then looking at their reaction pathways using elementary flux modes . This wo


In many modern applications data is represented in the form of nodes and their relationships, forming an information network. When nodes are described with a set of attributes we have an attributed network. Nodes and their relationships tend to naturally form into communities or clusters, and discovering these communities is paramount to many applications. Evaluating algorithms or comparing algorithms for automatic discovery of communities requires networks with known structures. Synthetic generators of networks have been proposed for this task but most solely focus on connectivity and their properties and overlook attribute values and the network properties vis-à-vis these attributes. In this paper, we propose a new generator for attributed networks with community structure that dependably follows the properties of real world networks. A variety of present-day applications requires interrelated data with relationships between data points. The structures in these interrelated data are typically modeled by a graph of interconnected nodes, known as complex networks or sometimes social networks or information networks. Examples of such networks are citation or collaboration networks of scholars, or trust and social networks of humans. Although drawn from a wide range of domains, most real world networks exhibit common statistical properties, such as power law degree distribution, and small world characteristic, which enable implementing a generic set of techniques for analyzing these networks .One fundamental property of many real networks is that they tend to organize according to an underlying modular structure . These sTherefore we believe that there is a need for developing a more realistic benchmark generator to generate authentic networks with built-in community structures and attributed nodes, faithfully following the known properties of real-world attributed networks and closely ensuring intrinsic characteristics such as preferential attachment requiring nodes with high connectivity to have a higher chance to attract links with other nodes, and homophily, the tendency of nodes to associate with higher probability with nodes having similar attribute values. We propose herein a generator for attributed networks with community structure, show the parameters of the model and highlight some of the experiments to demonstrate reliability and flexibility of our model.Section is dedicated to the state of the art, while the model is presented in Section. The experiments are described in Section and Section concludes.There are many generative network models proposed for real world networks , 12–15. β. The WS model is therefore able to generate small world graphs with high transitivity. The degree distribution, however, does not follow a power law, and therefore this model is not scale-free.The classical Erdős-Rényi (ER) model  generateThe Barabási-Albert (BA) model  is one oIn , 22 the Other notable synthetic generators are the mathematical tractable models, such as the Stochastic Kronecker Graph model , and itszin and 1 − zin respectively where zin ∈ . Since all the vertices have the same expected degree and equal communities size, this model is not accordant to real social network properties.The GN benchmark  is the fμ of its links with the other vertices of its community and a fraction μ with the other vertices of the network. An extension of this benchmark for overlapping communities is presented in [LFR benchmark  amends tented in .The process of generating the commonly used LFR benchmarks  could beThis generation process has two main issues. First, the original network is generated with a very simple network model, i.e., the configuration model . TherefoThe second issue with the LFR benchmark generators is enforcing communities later on the network which is in contrary to their definition as the natural structure underlying the networks. Orman and Labatut also mention this fact that the rewiring process in general changes the network structure chaotically, but leave it untackled . MoussiaThe block two-level Erdős-Rényi (BTER) model proposed in , 33, dirEvidences of homophily in most real networks suggest that connections are formed with a bias in favor of similar attributes of vertices (including their degrees). Some network generator models assume that links between vertices are formed solely based on their attributes , 35.u and a vertex v depends on the degree of vertex v as well as the number of attributes u and v have in common) and attribute-augmented triangle-closing .To take into account this behavior, another possibility is to consider attributes as vertices within an augmented network. Social-Attribute Network (SAN) proposed by  follows Another approach has been proposed in  using raVery few generators allow one to build a network having both a community structure and attributes associated with the vertices. In  the authWhile not being dedicated to the generation of networks, several articles , 40 haveGiven the interest of discovering communities in a social network where vertices are associated with attributes, we believe that a generator of networks following real networks properties and allowing to assess the quality of the obtained results using a ground truth is valuable.v ∈ 𝓥 is described by an attribute value vector vA[We provide a new attributed network with community structure generator. Such networks can be represented by an attributed graph 𝓖 = , where 𝓥 is a set of vertices, 𝓔 a set of edges and 𝓐 a set of real attributes associated with the vertices such that each vertex ector vA.C1, C2) ∈ 𝓟×𝓟, C1∩C2 = ∅; (2) ∀C ∈ 𝓟,C ≠ ∅; and (3) The network has a community structure if the nodes are grouped into sets densely connected and relatively homogeneous regarding the attributes. We suppose that these communities are not overlapping and consequently, they define a partition 𝓟 of 𝓥 such that (1) ∀(The proposed attributed network with community structure generator is based on the following hypothesis.P(k) having a degree k follows P(k) ∼ kγ− where γ ranges typically between 2 and 3 [It respects the preferential attachment according to which new nodes prefer to join to the more connected nodes existing in the network. Thus, each node is connected to an existing node with a probability proportional to the number of links of the chosen node. Given this hypothesis, our model can be considered as an extension of the Barabasi-Albert model: it leads to scale-free networks characterized by a degree distribution with a heavy tail which can be approximated by a power law distribution such that the fraction of vertices  2 and 3 . However 2 and 3 , usuallyThe second hypothesis underlying our model is that the membership to a community depends on the structural links and the attributes in such a way that firstly, there should be more edges between two vertices belonging to a same community than between vertices from different communities and secondly, two vertices belonging to the same community are likely to be more similar in terms of attributes as two vertices belonging to different communities.Finally, our model is based on the homophily hypothesis, according to which two vertices are more likely to be connected if they share common characteristics and this property is verified inside the communities but also between communities , 42. So,Given these hypotheses, the proposed model allows us to generate attributed graphs having the following properties.P1. Local preferential attachment: The local preferential attachment states that a vertex is more likely to create connections with vertices having a high degree and which are close [re close .P2. Small world: This property indicates that most vertices can be reached from every other through a small number of edges. According to [rding to , in a smrding to , 44.P3. Community structure: A community structure appears when vertices can be grouped in a way such that vertices in a group are more connected to vertices in the same group compared to other vertices. While there is no formal definition of a network community, several measures have been proposed to control the community structure. In this article, we consider the modularity measure from [ure from . Moreoveure from  is givenP4. Community homogeneity: This property occurs when the vertices inside a community are more similar according to their attribute values compared to vertices in a different community. To measure this property, one can use the within inertia ratio. Given 𝓟, a partition of vertices and d, the euclidean distance between the real attribute vectors associated with the vertices v1 and v2, the within inertia ratio is gC is the center of gravity of the vertices in C, PC the weight of C and g is the center of gravity of all the vertices.P5. Homophily: This property is verified in networks where similar vertices according to their properties tend to be more connected than dissimilar vertices. To measure this property, we adapted the test introduced by [expected homophily measure corresponding to the probability for two vertices to be similar with an observed homophily measure defined as the probability that two linked vertices are similar. If the expected measure is significantly less than the observed measure, then there is evidence for homophily.duced by  for numeThe previously described network properties can be controlled by the user using the model parameters summarized in Vertices: Each generated graph has a fixed number of vertices controlled by the parameter N = ∣𝓥∣.Edges: Three parameters control the edge insertion. Parameter MTE allows to set the minimal number of edges in the graph and consequently to control the density of the network. To reach this threshold, edges are inserted within the communities at the end of the process to reinforce the community structure by triadic closure i.e. by increasing the number of three fully connected vertices.Attributes: The numeric attribute values associated with the vertices are generated according to normal laws defined by two parameters: ∣𝓐∣, the number of attributes and 𝓐, the set of attribute descriptors. An attribute descriptor is a standard deviation σA, according which a component of the attribute vector associated with the vertices is generated following a normal law 𝓝. Note that using centered values does not change the distance between the vertices, so the mean is fixed to 0.Communities: The number of communities is set using parameter K. Parameter θ allows to associate a vertex with a random community instead of a community formed by vertices sharing similar attributes. It models the hypothesis that community selection is not necessarily based on available attributes and thus seems stochastic. A low value of θ will generate highly homogeneous communities, while on the other hand, a higher value will decrease the community homogeneity. Finally, to reduce algorithm complexity, a set of representatives is built for each community to compare similarity with newcomers. Parameter NbRep defines the maximal number of representatives for each community.Algorithm 1 which stands for Attributed Networks with Communities Generator. It returns:vA denotes the attribute vector associated with a vertex v ∈ V;An attributed graph 𝓖 = , where 𝓥 is a set of vertices, 𝓔 a set of edges, 𝓐 a set of attributes and where C1,C2) ∈ 𝓟×𝓟,C1∩C2 = ∅; (2) ∀C ∈ 𝓟,C ≠ ∅; and (3) A partition 𝓟 of 𝓥, corresponding to the generated attributed network, such that (1) ∀(Our generator is named MTE). The vertex insertion step is also split into two subparts: community selection and edge insertion.The main algorithm is divided into four parts. Vertices and attribute values are first generated, then communities are initialized. Vertices are then added by batch into the graph and finally an optional step allows to control the density of the network in ensuring a minimum number of edges . It is described in Algorithm Algorithm 2 in Algorithm 1 in Vinit of K × NbRep vertices is drawn from 𝓥 to build the initial communities    returns an element of S selected uniformly and randomly.3. Batch vertex insertion: This step iteratively adds vertices in the graph by batches of random size until all the vertices generated at step 1 have been inserted. The set of remaining vertices VtoAdd is first initialized  is minimized where dist is defined by C  and its between degree (Ebth) are firstly selected with the function RandPL according to a power law with respect to the parameters Algorithm 3 in RandPL(m) returns a natural number belonging to {1,…,m} randomly selected using the probability density function RandEdgeWth in order to ensure the local preferential attachment P1. The function RandEdgeWth(V) returns a vertex u from V randomly selected according to the probability density function deg(u) denotes the degree of vertex u. The other neighbors are selected with function RandEdgeBtw among the representatives of the other communities in such a way that they are more likely to be connected if they are similar to the vertex (cf. property P5). Indeed, the function RandEdgeBtw returns a vertex u from V according to the probability density function 4. Final edges insertion: The last step occurs only if the number of edges added at steps 2 and 3.b. does not reach MTE, the minimum number of edges in the resulting graph, fixed by the user. As the edges are only inserted within communities, this step allows reinforcing the community structure and increasing the average clustering coefficient (cf. P3). The insertion is performed as follows. A vertex v is selected at random ). Several triangle closing models have been proposed in [posed in . In our posed in  that desMTE edges or until each community forms a clique  as well as within communities (colored dots) for the reference graph are given in The aim of the first set of experiments is to demonstrate how, starting from a reference graph, the parameters can be used to either weaken or strengthen the community structure. The reference graph is generated using the following parameters: In the following set of experiments unless stated otherwise the parameters used to generate a graph correspond to those of the reference graph. The values of the measure plotted for different values of each parameter are the mean and standard deviation of the measure computed on 10 generated graphs with the same setting.θ which controls the probability to randomly assign a vertex to a community. θ. As expected, the increasing within inertia and decreasing observed homophily  indicate that the homogeneity property is weakened. This behavior is also in agreement with the results presented in 2 of the attribute values along two axis (one for each attribute). The higher the value of θ, the more heterogeneous the communities are.As mentioned in the introduction, the community structure in an attributed graph relates to both the edges density and the attribute homogeneity inside the communities. To degrade the community homogeneity, we ran experiments in varying the values of the parameter In the aim to degrade the community structure in such a way to have a number of within edges lower than the number of between edges, we performed experiments in varying the values of the parameter θ = 0.5, Moreover, in experiments where the attributes and the relations are degraded, using a tuning for the parameters θ = 0), we cannot improve it and we consider the community structure based on links. We increased the number of within edges while keeping a fixed number of between edges. Two parameters allow to control the number of within edges, MTE which correspond respectively to the maximum number of edges connecting an inserted vertex to vertices in its community and the minimum number of edges in the final graph.Opposite to the previous set of experiments, the community structure of the generated graphs can be improved compared to the reference graph. However, as the community homogeneity is already high in the reference graph . It is implemented in Java and it can be executed on any platform with a Java virtual machine. A screen copy of the user interface of the generator is presented in P5);The difference between the expected and observed homophily allows to measure if similar vertices according to the attributes tend to be more connected than dissimilar vertices (cf P4). A low within inertia indicates that the communities are highly homogeneous with regard to the attribute values;The within inertia measures the dispersion of the attribute values inside the communities (cf. P3);The modularity defined by Newman  (cf. P3)P3). This observed value can be compared with an expected value computed on a random graph having the same vertex set: an observed value higher than the expected value confirms the community structure;The network average clustering coefficient is a measure of the clustering tendency of the network (cf. P1);The average degree is the average number of neighbors of a vertex (cf. P2). It is not computed when the graph is formed by several disconnected components ;The diameter is the longest shortest path between any two vertices (cf. P3);The number of between edges and the number of within edges are respectively the number of edges connecting vertices in the same community and the number of edges connecting vertices in different communities (cf. The number of edges in the graph, i.e., ∣𝓔∣.In this article we proposed a network generator having a known community structure and where vertices are associated with numeric attributes. This generator constructs graphs with real networks properties both with respect to the structure, i.e., local preferential attachment, small world property, community structure, and with respect to the attributes, i.e., homogeneous communities and homophily. Several parameters allow the user to control the structure of the graph. We performed experiments to study how these parameters can impact the generated graph and demonstrated that they allow a degradation of the structure of the network on the one hand, and the deterioration of the homogeneity of the communities on the other hand. Regarding runtime, our generator is able to provide graphs having one million vertices. A possible extension of this work is to generate graphs where the attributes can be either numeric or categoric.


Introduction The complexity of the process and outcome of vocational rehabilitation yearns for a multifaceted approach. This article investigates whether importance of participation in major life areas for men and women predicts the outcome of vocational rehabilitation. Methods This longitudinal study provides measure points at the start of the intervention (T1), at the end of the intervention (T2) and at a follow-up 6–12 months after completing the rehabilitation program (T3). Associations were assessed by nominal logistic regression. Results The importance of participation in work was positively associated to return to work (RTW), while the importance of participation in leisure activities and importance of participation in family was negatively associated with RTW after the rehabilitation. Gender and number of children also contributed significantly to the regression model. Conclusion To identify individuals’ subjective evaluation of the importance of participation may be of value in explaining return or not RTW and contribute to explain gender differences in outcomes. It may also inform rehabilitation counselors in collaboration with clients and facilitate tailoring interventions to the individual’s needs. Existing evidence on the impact of vocational rehabilitation on return to work (RTW) for men and women with musculoskeletal pain is diverse. The complexity of the rehabilitation process and in predicting outcome is widely agreed. The wide range of factors associated with the outcome of vocational rehabilitation include demographic, psychological, social, medical, rehabilitation characteristics, work-place characteristics, factors related to the social security system, and general unemployment .Several studies have found that men more often RTW after vocational rehabilitation than women , 3. PrevIt has been argued that one has to take into consideration what matters to the individuals to be able to assess the problems in an useful way, be it in therapy or research . StudiesIn many studies individual’s own expectations of recovery and outcome of vocational rehabilitation have been shown to be a stable and important predictor of RTW –22. WithThis study aims to illuminate whether men and women’s evaluation of importance of participation in major life areas predicts RTW following vocational rehabilitation.This study was longitudinal with measure points at the start of the intervention (T1), at the end of the intervention (T2) and at a follow-up 6–12 months after completing the rehabilitation program (T3). Approval was obtained from the Norwegian Social Science Data Service (NSD).N = 168), had upper secondary education and training while 23 % (N = 51) had higher education. For further characteristics of the sample see Table A total of 270 individuals participated; 191 were women and 79 were men, aged 21–64 . The majority, 77 % (The program was free of charge and participants were compensated for lost income by the Norwegian Labor and Welfare Service (NAV). All participants had an individual plan prepared in collaboration with rehabilitation staff at the start of the intervention. The program comprised of individual activities, group activities and work-related activities at the rehabilitation premises and at the workplace. Education in health- and work-related themes and adaptation at the workplace were implemented to enhance participation in work as outcome. The intervention aimed at changing the individual’s focus from pain and disability to recourses and competencies.N = 270) and at T2 (N = 140). In the period from October 2010 to December 2011 an additional measure, comprised of participation-related questions, was integrated into the ordinary data collection. The follow-up survey was administered to the 270 participants by regular post 6–12 months after finishing rehabilitation. A total of 109 participants responded at first notice and the remainder were contacted by phone after 4–6 weeks and asked if they would answer the survey orally. This procedure ended in a response rate of 69 % (N = 187) at T3. There were no significant differences with regard to gender or age between the dropouts and those who completed the questionnaire at T1, T2 and T3  importance of participation in work, family life and leisure activities at the measure point, 2) importance of participation in work, family life and leisure activities before sick leave, 3) perceived barriers for RTW, 4) perceived issues with regard to the importance of having a job, 5) expectations of work participation in the future and 6) issues concerning perceived optimal participation in general. The internal consistency of the whole instrument was good with a Cronbach’s alpha coefficient of 86 .In the current study the items in subscale 1 were used as independent variables. The items of the subscale were importance of participation in work (IPW), importance of participation in family (IPF) and importance of participation in leisure activities (IPL) at measure point. Responses were captured by a Likert scale ranging from 1 to 7 (participation is very important) and measured at T1 and T2. The internal consistency of subscale 1 was acceptable with a Cronbach’s alpha coefficient of 73 .Change in IPW, family and leisure activity variables were computed by subtracting level of importance at T1 from T2.The follow-up survey consisted of 13 questions considering the situation at T3. The variables full-time work, part-time work, full work assessment allowance (WAA) and full disability pension were computed into a new variable scoring 1 for full-time work, 2 for part-time work and 3 for full WAA and full disability pension. The rationale for the construction of this outcome variable was to include individuals who selected only one of the response alternatives, while, at the same time, capturing some nuances of outcome alternatives by differentiating between full RTW and partial RTW.t tests were conducted to investigate prospective changes in importance of participation and changes in perceived overall health from T1 to T2; the analysis were conducted for all and for men and women separately. The results from the bivariate analyses , together with theoretical and empirical findings from previous research, guided the decision of which independent variables to include in the final regression model. Independent variables examined were IPW, IPF, IPL, change in IPW, change in IPF, change in IPL, gender, number of children, age, overall health, and education.SPSS version 20.0  for Windows was used for the statistical analyses. Initially, frequencies were examined and bivariate associations estimated. Paired sampled Because the outcome measure in this study was a variable with three categories, multinominal logistic regression was performed. The reference category was full long term benefits (WAA and disability pension). To estimate the odds of membership to the outcome group, odds ratios (OR) and their 95 % confidence intervals (95 % CI) were used. Multivariate logistic regression was finally performed with all retained independent variables in the final regression model.2  = 13.01, p = .001. No significant associations were found between gender, part-time work, WAA and disability pension. With regard to education the Chi square test showed no association to either of the categories of the outcome variable and education was, therefore, excluded from further analysis. The “change in participation” variables did not correlate to any of the other variables nor significantly contribute in the bivariate regressions. Neither did the paired sample t test comparing T1 and T2 yield any significant mean change in the importance of participation variables, a finding also applicable when running the analyses by gender. Therefore, the “change in participation” variables were excluded from further analysis.A Chi square test for independence indicated a significant association between gender and working full-time after the rehabilitation, χp = .001) and negatively correlated to gender . Previous research has indicated that importance of family might for women indicate being present for children while for men importance of family is more linked to providing for children [The variable, participation in family, had the least correlation to the items in the outcome variable (positively correlated to disability pension at T2); however, at T1 it was also positively correlated with the number of children  to T2 , t (134) = 3.30, p < .005 (two-tailed). The eta square statistic (.07) indicated a moderate effect size. When running the analyses by gender, we found that the positive change in perceived overall health applied to women from T1  to T2 , t (99) = 2.97, p < .005 (two-tailed). The eta squared statistic (.08) indicated a moderate effect size. No significant change was found for men.The paired sample In bivariate regression analyses the variables IPW, IPF, IPL, overall health and gender were statistically associated to the outcome variable. Individuals who demonstrated a higher evaluation of participation in work were more likely to be found in “Full RTW”  or in the “Partly RTW”  categories. Those reporting low IPL were more likely to be found in the “Full RTW”  category. With regard to gender men were far more likely than women to be found in the “Full RTW”  category  and  respectively. Consequently, to evaluate participation in work highly remains equally important for RTW when bringing the other variables into the equation. Also IPL is significantly contributing to the multivariate model. Individuals reporting lower evaluation of IPL  were more likely to RTW full time. Likewise gender remained statistically associated with “full time RTW”  showing that men were much more likely than women to be found in the “full time RTW” category. In this sample 9 men and none of the women returned to full time work. Due to the relatively few persons in the “Full time RTW” group the confidence intervals around the estimated odds ratio were very wide. In summary, when comparing the likeliness to belong to the “Full RTW” category or the “Full benefit” category 6–12 months after rehabilitation, the model indicates that being male and evaluating IPW highly and IPL as less important increases the probability of a full RTW. None of the other variables contributed to the model. When comparing the likeliness to be found in the “Partly RTW” group or the “Full benefit” group the results in the multivariate analysis differ from the bivariate analysis. First, we see that IPF becomes statistically associated  with the “Partly RTW” category. Low evaluation of the IPF slightly increases the likeliness for RTW in a part time position. In the opposite direction having (more) children increases the likeliness  to be found in the partly RTW category. Gender, IPL, age and overall health was not statistically associated to the outcome categories when comparing “Partly RTW” and “Full benefit” 6–12 months subsequent to rehabilitation (Table This study aimed to investigate simultaneously the role of importance of participation in major life areas and the variables gender, number of children, age and overall health to explain the outcome 6–12 months after conducting vocational rehabilitation.The rehabilitation intervention did not seem to have an impact on the individual’s evaluation of the IPW as IPW was stable during rehabilitation, and showed strong association to RTW fully and partly. It is possible that the rehabilitation reinforced the individual’s goal orientation toward RTW for those already perceiving work as important, while the opposite might apply to those who did rate participation in work as less important. Both scenarios are relevant from the rehabilitation professional’s point of view; it is of interest to reflect on which working mechanisms push some toward work disability and others toward RTW. To see participation in work as important most likely strengthens the motivation to RTW. Indeed, motivation is argued to be an important predictor of rehabilitation outcomes , 42 as iHealth problems are among the factors which have been found to significantly predict the outcome of vocational rehabilitation . HoweverThose who had children were more prone to RTW partly in the current study. When providing for children, the economic incentive to work is obvious. However, we did not control for the children’s ages. A dimension of the effect of having children on partial RTW might be that individuals still providing for children are more inclined to go back to work compared to those having older children or who do not have children at all. Returning to work part-time instead of full-time can also be a result of wanting to be present for the children, hence, a combination of providing for and being present for children. On the other hand, to see participation in family as important reduced the odds of returning to work part-time compared to receiving full benefits. A recent study on sickness absence found that the risk for work absenteeism is higher among women with children than without children. The risk decreased by age and was not found after the age of 35, except for single mothers who had a higher risk irrespective of age . The effIn the current study age did not predict either full or partial RTW, a finding which is not in line with the majority of other studies , 50, 51.Low importance of leisure activities was associated to a full RTW, but was not predictive of a partial RTW. A simple explanation may be that some individuals struggling with prolonged health problems cannot manage both full-time work and being active in their spare time. A study investigating vocational and leisure outcomes subsequent to spinal cord injuries found that loss of participation in work tended to be replaced by domestic and leisure activities . When prA characteristic of the results in this study is that the significant associations from the bivariate analyses remained stable when conducting multivariate analysis were the variables IPF and number of children also became statistically associated to the outcome. This may underline the interactive aspect of factors playing a role for RTW and indicate that considering multiple aspects is required when aiming at understanding and explaining mechanisms in work in the process and outcome of vocational rehabilitation.A common limitation to logistic regression analyses is that the estimates are affected by omitted variables, even when these variables are unrelated to the independent variables in the model. Thus, the effects reflect unobserved heterogeneity, and it is, therefore, problematic to interpret OR as substantive effects . In the Another possible limitation was the construction of the outcome variable because although WAA and disability pensions are long time benefits they are intended for individuals with RTW prospects and individuals who have no chance of RTW, respectively. However, we argue that the merging of the two categories were appropriate considering the purpose, which was to study specifically individuals who were not working at all at T3.The finding that IPW, family and leisure activities, together with other factors, contributed to the prediction of RTW, illuminates how attention to everyday life and what matters to people can help to explain RTW and failure to RTW. For rehabilitation the results point to a need for identifying the individual’s subjective evaluation of importance of participation in different life domains, in order to tailor the rehabilitation to each person to optimize RTW. The attempt to capture perceived importance of participation in different life domains does, in our view, contribute to the development and conceptualizing of the application of a bio-psycho-social perspective in RTW research. Thus, it delineates how RTW, which is the goal of vocational rehabilitation, is reciprocally influenced by health conditions, environmental factors and personal factors. Consequently, the approach may be useful in capturing issues that are difficult to explain, such as gender differences in outcome of vocational rehabilitation. Finally this study has indicated that measuring importance of participation may be of value both to explain RTW or not, and to rehabilitation staff as a helpful tool in the collaboration with clients. There is, however, a need to develop more nuanced participation instruments that better capture the broad specter of participation, and which also ensure the value, context and situational aspects to enable clinical and scientific use of the subjective evaluation of importance of participation. In order to increase clinical utility of the research, a deeper knowledge regarding the interactive aspects of the domains comprised in the ICF is needed. Thus, and based on the current body of knowledge, it is of interest to include self-efficacy variables together with participation variables in statistical models to expand on the knowledge of the formation of expectations of RTW in a truly bio-psycho-social and interdisciplinary perspective.


Reservoir computing is a recently introduced brain-inspired machine learning paradigm capable of excellent performances in the processing of empirical data. We focus in a particular kind of time-delay based reservoir computers that have been physically implemented using optical and electronic systems and have shown unprecedented data processing rates. Reservoir computing is well-known for the ease of the associated training scheme but also for the problematic sensitivity of its performance to architecture parameters. This article addresses the reservoir design problem, which remains the biggest challenge in the applicability of this information processing scheme. More specifically, we use the information available regarding the optimal reservoir working regimes to construct a functional link between the reservoir parameters and its performance. This function is used to explore various properties of the device and to choose the optimal reservoir architecture, thus replacing the tedious and time consuming parameter scannings used so far in the literature. The increase in need for information processing capacity, as well as the physical limitations of the Turing or von Neumann machine methods implemented in most computational systems, have motivated the search for new brain-inspired solutions some of which present an outstanding potential. An important direction in this undertaking is based on the use of the intrinsic information processing abilities of dynamical systems2reservoir computing (RC)45678911time-delay reservoirs (TDRs). Physical implementations of this scheme carried out with dedicated hardware are already available and have shown excellent performances in the processing of empirical data: spoken digit recognition1314151611The contributions in this paper take place in a specific implementation of this idea that is obtained as a melange of a recently introduced machine learning paradigm known under the name of θ of the nonlinear kernel used to construct the RC (see below). More specifically, small deviations from the optimal parameter values can seriously degrade the performance and moreover, the optimal parameters are highly dependent on the task at hand. This observation makes the kernel parameter optimization a very important step in the RC design and has motivated the introduction of alternative parallel-based architectures19A major advantage of RC is the linearity of its training scheme. This choice makes its implementation easy when compared to more traditional machine learning approaches like recursive neural networks, which usually require the solution of convoluted and sometimes ill-defined optimization problems. In exchange, as it can be seen in most of the references quoted above, the system performance is not robust with respect to the choice of the parameter values The main contribution of this paper is the introduction of an approximated model that, to our knowledge, provides the first rigorous analytical description of the delay-based RC performance. This powerful theoretical tool can be used to systematically study the delay-based RC properties and to replace the trial and error approach in the choice of architecture parameters by well structured optimization problems. This method simplifies enormously the implementation effort and sheds new light on the mechanisms that govern this information processing technique.TDRs are based on the interaction of the time-dependent input signal f is a nonlinear smooth function  that depends on the K parameters in the vector τ > 0 is the delay, z(t) that we explain later on. We note that, even though the differential equation takes values in the real line, its solution space is infinite dimensional since an entire function where In order to visualize the TDR construction using a neural networks approach it is convenient, as in12virtual neurons and of an adapted input maskz(t) at a given time t is multiplexed over the delay period by setting neuron layers x(t) parametrized by a discretized time The design starts with the choice of a number xi(t) and Ii(t) stand for the ith-components of the vectors x(t) and I(t), respectively, with xi(t) is the ith neuron value of thetth layer of the reservoir and d is referred to as the separation between neurons. With this convention, the solutions of (2) are described by the following recursive relation:where d is small, the neuron value xi(t) is mainly influenced by the previous neuron value xi−1(t), while large distances between neurons give predominance to the previous layer and foster the input gain. The recursions (4) uniquely determine a smooth map that shows how, as depicted in Module B in F is constructed out of the nonlinear kernel map f that depends on the K parameters in the vector θ; F is referred to as the reservoir map.where reservoir or the time-delay reservoir (TDR) and to the collection of the three modules as the reservoir computer (RC) or the TDR computer. A TDR based on the direct sampling of the solutions of (1) will be called a continuous time TDR and those based on the recursion (5) will be referred to as discrete time TDRs.The construction of the TDR computer is finalized by connecting, as in Module C of θ and, in some cases, on the entries of the input mask c used for signal multiplexing. When comparing RC to standard neural networks and thinking of it as a machine learning paradigm, the RC training phase can be assimilated to the determination of both the linear readout Wout (straightforward in this case using a linear regression) and the optimal parameters θ. Unlike the situation encountered in the neural networks context for which efficient training algorithms have been developed over the years  = 0) associated to (1) and the mean and variance of the input signal I(t) are designed using the input mask c so that the reservoir output remains around it and does not visit other stable equilibria or dynamical elements. In the next section we provide empirical and theoretical arguments for this claim. The performance measures that we consider in our study are the nonlinear memory capacities introduced in252627The construction of this approximated formula is based on the observation that the optimal RC performance is always obtained when the TDR is working in a I(t) so that the reservoir output remains close to it. This equilibrium point can be interpreted as an input bias that, for general RCs, is one of the most commonly optimized parameters.The estimations of the RC performance using the nonlinear memory capacity that we present later on, consist of approximating the reservoir by its partial linearization at the level of the delayed self feedback term and of respecting the nonlinearity in the input injection. This approach is only acceptable when the optimal dynamical regime that we are interested in, remains close to a given point. A natural candidate for such qualitative behavior could be obtained by initializing the reservoir at an asymptotically stable equilibrium of the autonomous system associated to (1) and by controlling the mean and the variance of the input signal echo state property, is materialized for general RCs by enforcing that the spectral radius of the internal connectivity matrix of the reservoir is smaller than one56I(t) is set to zero. This feature typically relates to gains of the feedback smaller than the Hopf threshold of the delay dynamics or, equivalently, to a sufficiently low feedback rate so that self-sustained oscillations are avoided.There is both theoretical and empirical evidence that suggests that optimal performance is obtained for the RCs that we are interested in when working in a statistically stationary regime around a stable equilibrium. Indeed, one of the defining features of RC, namely the fading memory property6Asymptotic stability is closely related with the so-called In the context of recent successful physical realizations of RC, experimental parameters are systematically chosen so that the conditions described above are satisfied. Indeed, in1414We conclude by emphasizing that, even though optimal performance is attained when working in a statistically stationary regime around a stable equilibrium for the specific time-delay RCs that we are using, this is not a general feature that applies to all RCs or other network based computational paradigms. Indeed, recent worksI(t) = 0. It can be shown using a Lyapunov-Krasovskiy-type analysis32x0 is guaranteed whenever there exists an ε > 0 and a constant Due to the central role played by stability in our discussion, we now carefully analyze various sufficient conditions that ensure that the RC is functioning in a stable regime. All the statements that follow are carefully proved in the f is differentiable at x0 then this point is stable as long as f in (1) with respect to the first argument at the point .The first condition can be used to prove the stability of equilibria exhibited by TDRs created using concave (but not necessarily differentiable) nonlinear kernels. As to the second one, it shows that if DxF, which is a N × N matrix that will be referred to as the connectivity matrix, has a spectral radius smaller than one. Since it is not possible to compute the eigenvalues of DxF for an arbitrary number of neurons N, we are hence obliged to proceed by finding estimations for the Cauchy boundρ) using either a matrix norm or the Gershgorin discsThe stability study can also be carried out by working with the discrete-time approximation (5) of the TDR which is determined by the reservoir map Notice that this remarkable result puts together the stability conditions for the continuous and discrete time systems.As an example of application of these results, consider the Mackey-Glass nonlinear kernel21γ is usually referred to as the input gain and η the feedback gain. When this prescription is used in (1) in the autonomous regime, that is, I(t) = 0, the associated dynamical system exhibits two families of equilibria x0 parametrized by η, namely, x0 = 0 and the roots of p = 2, two distinct cases arise: when η < 1 there is a unique equilibrium at the origin which is stable as long as η > 1 two other equilibria appear at x0 = ±(η − 1)1/2 which are stable whenever η < 3. These statements are proved in Corollary D.6 of the f = η sin2(x + γI + ϕ), where the parameter N = 20, d = 0.2581, η = 1.2443, γ = 1.4762, and ϕ = 0.1161. The equilibria of the associated autonomous system are given by the points x0 where the curves y = x and y = η sin2(x + ϕ) intersect. With this parameter values, intersections take place at x0 = 0.0244, x0 = 0.9075, and x0 = 1.063, which makes multi modality possible. As it can be shown with the results in the x0 = 0.0244 when we present to it a quadratic memory task. More specifically, we inject in a TDR an independent and identically normally distributed signal z(t) with mean zero and variance 10−4 and we then train a linear readout Wout  in order to recover the quadratic function z(t − 1)2 + z(t − 2)2 + z(t − 3)2 out of the reservoir output. The top left panel in c. It is clear that by modifying any of these two parameters we control how far the reservoir dynamics separates from the stable equilibrium, which we quantitatively evaluate in the two bottom panels by representing the RC performance in terms of the mean and the variance of the resulting reservoir output. Both panels depict how the injection of a signal slightly shifted in mean or with a sufficiently high variance results in reservoir outputs that separate from the stable equilibrium and in a severely degraded performance. An important factor in this deterioration seems to be the multi modality, that is, if the shifting in mean or the input signal variance are large enough then the reservoir output visits the stability basin of the other stable point placed at x0 = 1.063; in the top right and bottom panels we have marked with red color the values for which bimodality has occurred so that the negative effect of this phenomenon is noticeable. In the In order to confirm these theoretical and experimental arguments, we have carried out several numerical simulations in which we studied the RC performance in terms of the dynamical regime of the reservoir at the time of carrying out various nonlinear memory tasks. More specifically, we construct a reservoir using the Ikeda nonlinear kernel with N-dimensional (N is the number of neurons) vector autoregressive stochastic process of order oneθ and the input mask c.The findings just presented have major consequences in the theoretical tools available for the evaluation of the RC performance. Indeed, since we now know that optimal operation is attained when the TDR functions in a unimodal fashion around an asymptotically stable steady state, we can approximate it by its partial linearization with respect to the delayed self feedback term at that point and keeping the nonlinearity for the input injection. For statistically independent input signals of the type used to compute nonlinear memory capacities of the type introduced inx0 with respect to the delayed self feedback and by the R-order Taylor series expansion of the functional that describes the signal injection, we obtain an expression of the form:Consider a stable equilibrium ε(t) is given by:where withith order partial derivative of the nonlinear kernel f with respect to the second argument I(t), evaluated at the point .and z(t) independent and identically distributed random variables with mean 0 and variance N-dimensional vector autoregressive model of order 1 (VAR(1)). Indeed, it is easy to see that the assumption N-dimensional independent and identically distributed random variables with mean με and covariance matrix If we now use as input signal qR is the same as in (10) and where we use the convention that the powers where the polynomial μz, and the second one is made out of the multiplication of the evaluation of the two polynomials.where the first summand stands for the multiplication of the polynomials f satisfies the generic condition that the polynomial in u given by Using these observations, we can consider (8) as the prescription of a VAR(1) model driven by the independent noise and an also time independent autocovariance function k) = AΓ(k − 1) and the identity Γ(−k) = Γ(k)⊤. As we explain in the following paragraphs, the moments (11), (13), and (14) are all that is needed in order to characterize the memory capacities of the RC.which determines the higher order autocovariances via the relation Γ function Wout adapted to the memory task H is given by the solution of a ridge linear regression problem with regularization parameter y(t)} of the memory task function. The H-memory capacity CH of the TDR computer under consideration characterized by a nonlinear kernel f with parameters θ, an input mask c, and a regularizing ridge parameter λ is defined as one minus the normalized mean square error committed at the time of accomplishing the memory task H. When the reservoir is approximated by a VAR(1) process, then the corresponding H-memory capacity is given byA The developments leading to this expression are contained in the y(t), x(t)) and var (y(t)) need to be computed since the autocovariance Γ(0) is fully determined by (14) once the reservoir and the equilibrium x0 around which we operate have been chosen. As an example, we provide the expressions corresponding to the two most basic information processing routines, namely the linear and the quadratic memory tasks. Details on how to obtain the following equalities are contained in the Notice that in order to evaluate (15) for a specific memory task, only Cov opens the door to the theoretical treatment of many RC design related questions that so far were addressed using a trial and error approach. In particular, the availability of a closed form formula of the type (15) for the memory capacity of the RC is extremely convenient to determine the optimal reservoir architecture to carry out a given task. Nevertheless, it is obviously very important to assess the quality of the VAR(1) approximation underlying it and of the consequences that result from it. Indeed, we recall that the expression (15) was obtained via the partial linearization of the reservoir at a stable equilibrium in which it is initialized and kept in stationary operation. Despite the good theoretical and experimental reasons to proceed in this fashion provided above, we have confirmed their pertinence by explicitly comparing the reservoir memory capacity surfaces obtained empirically with those coming from the analytical expression (15). We have carried this comparison out for various tasks and have constructed the memory capacity surfaces as a function of different design parameters.p = 2, γ = 0.796, and twenty neurons. We present to it the 6-lag quadratic memory task H corresponding to choosing in (17) a seven dimensional diagonal matrix Q with the diagonal entries given by the vector . The first element, corresponding to the 0-lag memory (quadratic nowcasting), is set to zero in order to keep the difficulty of the task high enough. We then vary the value d of the distance between neurons between 0 and 1 and the feedback gain parameter η between 1 and 3. As we already discussed, the TDR in autonomous regime exhibits for these parameter values two stable equilibria placed at ±(η − 1)1/2; for this experiment we will always work with the positive equilibria by initializing the TDRs at those points. R = 8 in (9)). The points in the surfaces of the middle and right panels are the result of Monte Carlo evaluations  of the NMSE exhibited by the discrete and continuous time TDRs, respectively. The time-evolution of the time-delay differential equation (continuous time model) was simulated using a Runge-Kutta fourth-order method with a discretization step equal to d/5. A quick inspection of We first consider a RC constructed using the Mackey-Glass nonlinear kernel (7) with η0 = 1.0781 and we vary the input gain γ and the distance between neurons d. The quadratic memory task is reduced this time to 3-lags. We emphasize that in this setup the stable operation point is always the same and equal to (η0 − 1)1/2. γ adjusts the input gain but leaves unchanged the operation point. Additionally, the moderate difficulty of the task makes possible attaining lower optimal error rates with the same number of neurons. In order to ensure the robustness of these results with respect to the choice of nonlinear kernel, we have included in the In order to show that these statements are robust with respect to the choice of task and varying parameters, we have carried out a similar experiment with a RC in which we fix the feedback gain c in the performance of a Mackey-Glass kernel based reservoir in a 3-lag quadratic memory task. The figure shows, for each number of neurons, the performance obtained by a RC in which the reservoir parameters θ and the input mask c have been chosen so that the memory capacity CH in (15) is maximized; we have subsequently kept the optimal parameters θ and we have randomly constructed one thousand input masks c with entries belonging to the interval . The box plots in Once the adequacy of the memory capacity evaluation formula (15) has been established, we can use this result to investigate the influence of other architecture parameters in the reservoir performance. In In conclusion, the construction of approximating models for the reservoir as well as the availability of performance evaluation formulas like (15) based on it, constitute extremely valuable analytical tools whose existence should prove very beneficial in the fast and efficient extension and customization of RC type techniques to tasks far more sophisticated than the ones we considered in this paper. This specific point is the subject of ongoing research on which we will report in a forthcoming publication.How to cite this article: Grigoryeva, L. et al. Optimal nonlinear information processing capacity in delay-based reservoir computers. Sci. Rep.5, 12858; doi: 10.1038/srep12858 (2015).