An Input‐Output Model of Extended Producer Responsibility

Under an extended producer responsibility (EPR) system, when a producer delivers a product to the market it must also pay a takeback fee, which is used to cover the costs of end‐of‐life disposal. EPR systems are currently used in Europe and beyond to manage a variety of products, including packaging and used tires. In this article we develop an input‐output (IO) model that is able to assess the impacts of an EPR system, and is based on the waste IO (WIO) model. The WIO model is itself a hybrid‐unit model extension of the Leontief model that is able to capture the substitution effect between recycled/recovered material/energy from waste treatment and their non‐waste cognates. The resulting EPRIO model, besides the conventional direct and indirect effects of the Leontief model and the substitution effects of the WIO model, is able to capture the opportunity costs of financing the EPR system, and additionally requires the specification of an alternative waste management policy, with its own opportunity costs. The impact of an EPR policy is thus the difference between the impacts of the reference EPR and the alternative waste treament policies. The resulting model is illustrated with a simple example of a used tire management EPR system.     

Tracking the contribution of inductive bias to individualised internal models

Internal models capture the regularities of the environment and are central to understanding how humans adapt to environmental statistics. In general, the correct internal model is unknown to observers, instead they rely on an approximate model that is continually adapted throughout learning. However, experimenters assume an ideal observer model, which captures stimulus structure but ignores the diverging hypotheses that humans form during learning. We combine non-parametric Bayesian methods and probabilistic programming to infer rich and dynamic individualised internal models from response times. We demonstrate that the approach is capable of characterizing the discrepancy between the internal model maintained by individuals and the ideal observer model and to track the evolution of the contribution of the ideal observer model to the internal model throughout training. In particular, in an implicit visuomotor sequence learning task the identified discrepancy revealed an inductive bias that was consistent across individuals but varied in strength and persistence.     

Interactions of small nonpolar molecules with biological membranes: an exactly solvable model

An exactly solvable model of the interaction of small nonpolar molecules with biological membranes is developed. This model, which is based upon a “decorated dimer model” extension of Nagle's membrane model, is demonstrated to qualitatively reproduce many of the changes in the order-disorder phase transition seen when biological membranes are exposed to anesthetic gases. The decorated dimer model is itself interesting because it provides an example of an exactly solvable monomer-dimer model in which phase transitions can occur in the presence of monomers.     

Age-dependent predation is not a simple process. II. Wolves,ungulates, and a discrete time model for predation on juveniles with a stabilizing tail

A discrete time model for a predator-prey model, where the predator eats only juvenile prey is developed. The model is developed to capture some of the behavior of wolf-ungulate systems. Age-dependent predation is shown to be a stabilizing influence. The behavior of the model depends critically on the age of senescence of the prey—an extremely small number of old prey individuals represent a very powerful stabilizing factor. The model behaves in a similar fashion to, but is less stable than, an age structured Ricker model.     

Balanced Sparse Model for Tight Frames in Compressed Sensing Magnetic Resonance Imaging

Compressed sensing has shown to be promising to accelerate magnetic resonance imaging. In this new technology, magnetic resonance images are usually reconstructed by enforcing its sparsity in sparse image reconstruction models, including both synthesis and analysis models. The synthesis model assumes that an image is a sparse combination of atom signals while the analysis model assumes that an image is sparse after the application of an analysis operator. Balanced model is a new sparse model that bridges analysis and synthesis models by introducing a penalty term on the distance of frame coefficients to the range of the analysis operator. In this paper, we study the performance of the balanced model in tight frame based compressed sensing magnetic resonance imaging and propose a new efficient numerical algorithm to solve the optimization problem. By tuning the balancing parameter, the new model achieves solutions of three models. It is found that the balanced model has a comparable performance with the analysis model. Besides, both of them achieve better results than the synthesis model no matter what value the balancing parameter is. Experiment shows that our proposed numerical algorithm constrained split augmented Lagrangian shrinkage algorithm for balanced model (C-SALSA-B) converges faster than previously proposed algorithms accelerated proximal algorithm (APG) and alternating directional method of multipliers for balanced model (ADMM-B).     

The principle of optimality as the foundation of biotechnological modeling

There are many points of contact between optimization problems and modeling. On the one hand the model adjustment process itself as a process of estimation is closely connected with optimization, in that it is to produce what is in one sense the best possible model. The basic structure of the optimization problem as problem in decision making with the necessary input of an objective function is thus evident. On the other hand a model is never an end in itself but on the basis of its simulation capacity a means to an end, for example in biotechnological optimization. From this point of view the model is a product of scientific work and thus an economic value. Equally, through its intended purpose the model exhibits a utility value. A complete evaluation of the model as a condition of rational modeling must take into account both these aspects. That is possible in principle by adding the modeling expenditure to expenditure for the realization of biotechnological processes, expressing the economic consequences of model quality as an objective function, and minimizing the specific total expenditure for the product to be produced. Biotechnological practice requires that the “optimum” model is approached by means of iterative processes. Some practical examples will make the process clear, taking into account qualitative (semantic) and quantitative (accuracy) aspects of the utility value.     

Statistical Dose-Response Models with Hormetic Effects

Monotonically increasing or decreasing functions are often used to model the relationship between the response of an experimental unit and the dose of a given substance. Of late, there has been an increased interest in dose-response relationships that exhibit hormetic effects. These effects may be characterized by an increase in response at low doses instead of the expected decrease in response that is observed at higher doses. Herein, we study the statistical implications of hormesis in several ways. First, we present a broad class of parametric mathematical-statistical models, constructed from standard dose-response models, that allow the incorporation of hormetic effects in such a way that the presence of hormesis can be tested statistically. Second, we consider the impact of model misspecification on effective dose estimation, such as the ED50 and the limiting dose for stimulation, when the hormetic effect is present but ignored in the dose-response model by the researcher (model underspecification) and when an hormetic effect is not present but incorporated into the dose-response model (model overspecification). Our simulation study reveals that it is more damaging to the estimation of effective dose to ignore the hormetic effect through model underspecification than to include the hormetic effect in the model through model overspecification. Third, we develop a nonpara-metric regression technique useful as an exploratory procedure to indicate hormetic effects when present. Finally, both parametric and nonparametric methods are illustrated with an example.     

Simulation of human sleep: ultradian dynamics of electroencephalographic slow-wave activity

The typical declining trend of electroencephalographic (EEG) slow-wave activity (SWA) within a sleep period is represented in the two-process model of sleep regulation by an exponentially decaying process (Process S). The model has been further elaborated to simulate not only the global changes of SWA, but also the dynamics within non-rapid-eye-movement (non-REM) sleep episodes. In this new model, the initial intraepisodic buildup of SWA is determined by the combined action of an exponentially increasing process and a saturation process, whereas its fall at the end of an episode is due to an exponentially decreasing process. The global declining trend of SWA over consecutive episodes results from the monotonic decay of the intraepisodic saturation level. In contrast to Process S in the two-process model, this decay is not represented by an exponential function, but is proportional to the momentary level of SWA. REM sleep episodes are triggered by an external function. The model allows one to simulate the ultradian pattern of SWA for baseline nights as well as changes induced by a prolonged waking period, a daytime nap, a partial slow-wave sleep deprivation, or an antidepressant drug.     

Haplotype reconstruction from SNP fragments by minimum error correction

MOTIVATION: Haplotype reconstruction based on aligned single nucleotide polymorphism (SNP) fragments is to infer a pair of haplotypes from localized polymorphism data gathered through short genome fragment assembly. An important computational model of this problem is the minimum error correction (MEC) model, which has been mentioned in several literatures. The model retrieves a pair of haplotypes by correcting minimum number of SNPs in given genome fragments coming from an individual's DNA. RESULTS: In the first part of this paper, an exact algorithm for the MEC model is presented. Owing to the NP-hardness of the MEC model, we also design a genetic algorithm (GA). The designed GA is intended to solve large size problems and has very good performance. The strength and weakness of the MEC model are shown using experimental results on real data and simulation data. In the second part of this paper, to improve the MEC model for haplotype reconstruction, a new computational model is proposed, which simultaneously employs genotype information of an individual in the process of SNP correction, and is called MEC with genotype information (shortly, MEC/GI). Computational results on extensive datasets show that the new model has much higher accuracy in haplotype reconstruction than the pure MEC model.     

Risk assessment for quantitative responses using a mixture model

A problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment than others. A mixture model has traditionally been proposed to describe the distribution of responses in treatment groups for such experiments. Using a mixture dose-response model, we derive an upper confidence limit on additional risk, defined as the excess risk over the background risk due to an added dose. Our focus will be on experiments with continuous responses for which risk is the probability of an adverse effect defined as an event that is extremely rare in controls. The asymptotic distribution of the likelihood ratio statistic is used to obtain the upper confidence limit on additional risk. The method can also be used to derive a benchmark dose corresponding to a specified level of increased risk. The EM algorithm is utilized to find the maximum likelihood estimates of model parameters and an extension of the algorithm is proposed to derive the estimates when the model is subject to a specified level of added risk. An example is used to demonstrate the results, and it is shown that by using the mixture model a more accurate measure of added risk is obtained.     

Modeling zero‐inflated count data when exposure varies: With an application to tumor counts

This paper is concerned with the analysis of zero‐inflated count data when time of exposure varies. It proposes a modified zero‐inflated count data model where the probability of an extra zero is derived from an underlying duration model with Weibull hazard rate. The new model is compared to the standard Poisson model with logit zero inflation in an application to the effect of treatment with thiotepa on the number of new bladder tumors.     

An Engineered Membrane to Measure Electroporation: Effect of Tethers and Bioelectronic Interface

This article reports on the construction and predictive models for a platform comprised of an engineered tethered membrane. The platform provides a controllable and physiologically relevant environment for the study of the electroporation process. The mixed self-assembled membrane is formed via a rapid solvent exchange technique. The membrane is tethered to the gold electrode and includes an ionic reservoir separating the membrane and gold surface. Above the membrane, there is an electrolyte solution, and a gold counterelectrode. A voltage is applied between the gold electrodes and the current measured. The current is dependent on the energy required to form aqueous pores and the conductance of each pore. A two-level predictive model, consisting of a macroscopic and a continuum model, is developed to relate the pore dynamics to the measured current. The macroscopic model consists of an equivalent circuit model of the tethered membrane, and asymptotic approximations to the Smoluchowski-Einstein equation of electroporation that is dependent on the pore conductance and the energy required to form aqueous pores. The continuum model is a generalized Poisson-Nernst-Planck (GPNP) system where an activity coefficient to account for steric effects of ions is added to the standard PNP system. The GPNP is used to evaluate the conductance of aqueous pores, and the electrical energy required to form the pores. As an outcome of the setup of the device and the two-level model, biologically important variables can be estimated from experimental measurements. To validate the accuracy of the two-level model, the predicted current is compared with experimentally measured current for different tethering densities.     

Closed loop identification of transfer function model for unstable bioreactors for tuning PID controllers

Closed loop identification of transfer function model for an unstable bioreactor is proposed based on an optimization method using either a step or a pulse response of PI/PID controlled bioreactor. A simple method is proposed for the initial guesses of the parameters of the first order plus time delay (FOPTD) transfer function model. A PID controller is designed for the identified model. Simulation study on the nonlinear model equations of an unstable bioreactor exhibiting multiple steady-states shows that the PID controller designed on the identified FOPTD model gives a good closed loop response similar to the one designed based on the linearized model from the nonlinear model equations.     

全错位排列问题的一种改进的表面DNA计算模型

文章提出全错位排列问题的一种改进的表面计算模型,通过巧妙的编码,不但继承了表面计算的诸多优点,而且摆脱了以往模型难以推广的不足.同时,设计中采用了荧光淬灭的有关技术,利用观察荧光淬灭来确定问题的非解,这种读解方法简单有效,算法是有效可行的.     

Two-phase model of the kinetics of growth of Rhizopus oligosporus in membrane culture

An empirical model was developed to describe a growth profile occurring in solid-state fermentation (SSF), namely that consisting of an initial period of rapid acceleration followed by an extended period of deceleration. This kinetic profile is not adequately described by the logistic model. The empirical model is based on the concept of active and nonactive hyphal segments. Exponential and deceleration growth phases are modeled. The model parameters can be determined directly from the dry-weight profile and they depend on the growth medium present. The model suggests that, at the instant the culture enters the deceleration phase, there is a 71% to 86% decrease in the number of actively extending hyphal tips and that, during the deceleration phase, there is an exponential decay in the number of active hyphal segments, with a first-order decay constant of 0.042 to 0.072 h(-1).     

On the role of reinfection in the transmission of infectious diseases

We introduce a spatial stochastic model for the spread of tuberculosis. After a primary infection, an individual may become sick (and infectious) through an endogenous reinfection or through an exogenous reinfection. We show that even in the absence of endogenous reinfection an epidemic is possible if the exogenous reinfection parameter is high enough. This is in sharp contrast with what happens for a mean field model corresponding to our spatial stochastic model.     

An Engineered Membrane to Measure Electroporation: Effect of Tethers and Bioelectronic Interface

This article reports on the construction and predictive models for a platform comprised of an engineered tethered membrane. The platform provides a controllable and physiologically relevant environment for the study of the electroporation process. The mixed self-assembled membrane is formed via a rapid solvent exchange technique. The membrane is tethered to the gold electrode and includes an ionic reservoir separating the membrane and gold surface. Above the membrane, there is an electrolyte solution, and a gold counterelectrode. A voltage is applied between the gold electrodes and the current measured. The current is dependent on the energy required to form aqueous pores and the conductance of each pore. A two-level predictive model, consisting of a macroscopic and a continuum model, is developed to relate the pore dynamics to the measured current. The macroscopic model consists of an equivalent circuit model of the tethered membrane, and asymptotic approximations to the Smoluchowski-Einstein equation of electroporation that is dependent on the pore conductance and the energy required to form aqueous pores. The continuum model is a generalized Poisson-Nernst-Planck (GPNP) system where an activity coefficient to account for steric effects of ions is added to the standard PNP system. The GPNP is used to evaluate the conductance of aqueous pores, and the electrical energy required to form the pores. As an outcome of the setup of the device and the two-level model, biologically important variables can be estimated from experimental measurements. To validate the accuracy of the two-level model, the predicted current is compared with experimentally measured current for different tethering densities.     

Development of a constructed subsurface-flow wetland simulation model

This paper presents a mechanistic, compartmental simulation model of subsurface-flow constructed wetlands. The model consists of six submodels, including the nitrogen and carbon cycles, both autotrophic and heterotrophic bacteria growth and metabolism, and water and oxygen balances. Data from an existing constructed wetland in Maryland were used to calibrate the model. Model results reproduced seasonal trends well. Interactions between the carbon, nitrogen, and oxygen cycles were evident in model output. In general, effluent biochemical oxygen demand, organic nitrogen, ammonium and nitrate concentrations were predicted well. Because little is known about rootzone aeration by wetland plants, oxygen predictions were fair. The model is generally insensitive to changes in individual parameters. This is due to the complexity of the ecosystem and the model, as well as the numerous feedback mechanisms. The model is most sensitive to changes in parameters that affect microbial growth and substrate use directly. This dynamic, compartmental, simulation model is an effective tool for evaluating the performance of subsurface-flow constructed wetlands. The model provided insights into treatment problems at an existing constructed wetland. With further evaluation and refinement, the model will be a useful design tool for subsurface-flow constructed wetlands.     

Reducing model complexity of the general Markov model of evolution

The selection of an optimal model for data analysis is an important component of model-based molecular phylogenetic studies. Owing to the large number of Markov models that can be used for data analysis, model selection is a combinatorial problem that cannot be solved by performing an exhaustive search of all possible models. Currently, model selection is based on a small subset of the available Markov models, namely those that assume the evolutionary process to be globally stationary, reversible, and homogeneous. This forces the optimal model to be time reversible even though the actual data may not satisfy these assumptions. This problem can be alleviated by including more complex models during the model selection. We present a novel heuristic that evaluates a small fraction of these complex models and identifies the optimal model.     

On the spread of epidemics in a closed heterogeneous population

Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptible-infective-removed) model is formulated and analyzed when susceptibility to or infectivity of a particular disease is distributed. It is shown that a heterogeneous model can be reduced to a homogeneous model with a nonlinear transmission function, which is given in explicit form. The widely used power transmission function is deduced from the model with distributed susceptibility and infectivity with the initial gamma-distribution of the disease parameters. Therefore, a mechanistic derivation of the phenomenological model, which is believed to mimic reality with high accuracy, is provided. The equation for the final size of an epidemic for an arbitrary initial distribution of susceptibility is found. The implications of population heterogeneity are discussed, in particular, it is pointed out that usual moment-closure methods can lead to erroneous conclusions if applied for the study of the long-term behavior of the models.