Exotic dynamics in a firing rate model of neural tissue with threshold accommodation

Many of the equations describing the dynamics of neural systems are written in terms of firing rate functions, which themselves are often taken to be threshold functions of synaptic activity. Dating back to work by Hill in 1936 it has been recognized that more realistic models of neural tissue can be obtained with the introduction of state-dependent dynamic thresholds. In this paper we treat a specific phenomenological model of threshold accommodation that mimics many of the properties originally described by Hill. Importantly we explore the consequences of this dynamic threshold at the tissue level, by modifying a standard neural field model of Wilson-Cowan type. As in the case without threshold accommodation classical Mexican-Hat connectivity is shown to allow for the existence of spatially localized states (bumps) in both one and two dimensions. Importantly an analysis of bump stability in one dimension, using recent Evans function techniques, shows that bumps may undergo instabilities leading to the emergence of both breathers and traveling waves. Moreover, a similar analysis for traveling pulses leads to the conditions necessary to observe a stable traveling breather. In the regime where a bump solution does not exist direct numerical simulations show the possibility of self-replicating bumps via a form of bump splitting. Simulations in two space dimensions show analogous localized and traveling solutions to those seen in one dimension. Indeed dynamical behavior in this neural model appears reminiscent of that seen in other dissipative systems that support localized structures, and in particular those of coupled cubic complex Ginzburg-Landau equations. Further numerical explorations illustrate that the traveling pulses in this model exhibit particle like properties, similar to those of dispersive solitons observed in some three component reaction-diffusion systems. A preliminary account of this work first appeared in S Coombes and M R Owen, Bumps, breathers, and waves in a neural network with spike frequency adaptation, Physical Review Letters 94 (2005), 148102(1-4).

Regional differences of outpatient physician supply as a theoretical economic and empirical generalized linear model

BACKGROUND: Regional differences in physician supply can be found in many health care systems, regardless of their organizational and financial structure. A theoretical model is developed for the physicians' decision on office allocation, covering demand-side factors and a consumption time function. METHODS: To test the propositions following the theoretical model, generalized linear models were estimated to explain differences in 412 German districts. Various factors found in the literature were included to control for physicians' regional preferences. RESULTS: Evidence in favor of the first three propositions of the theoretical model could be found. Specialists show a stronger association to higher populated districts than GPs. Although indicators for regional preferences are significantly correlated with physician density, their coefficients are not as high as population density. CONCLUSIONS: If regional disparities should be addressed by political actions, the focus should be to counteract those parameters representing physicians' preferences in over- and undersupplied regions.

Power spectrum model of visual masking: simulations and empirical data

In the study of the spatial characteristics of the visual channels, the power spectrum model of visual masking is one of the most widely used. When the task is to detect a signal masked by visual noise, this classical model assumes that the signal and the noise are previously processed by a bank of linear channels and that the power of the signal at threshold is proportional to the power of the noise passing through the visual channel that mediates detection. The model also assumes that this visual channel will have the highest ratio of signal power to noise power at its output. According to this, there are masking conditions where the highest signal-to-noise ratio (SNR) occurs in a channel centered in a spatial frequency different from the spatial frequency of the signal (off-frequency looking). Under these conditions the channel mediating detection could vary with the type of noise used in the masking experiment and this could affect the estimation of the shape and the bandwidth of the visual channels. It is generally believed that notched noise, white noise and double bandpass noise prevent off-frequency looking, and high-pass, low-pass and bandpass noises can promote it independently of the channel's shape. In this study, by means of a procedure that finds the channel that maximizes the SNR at its output, we performed numerical simulations using the power spectrum model to study the characteristics of masking caused by six types of one-dimensional noise (white, high-pass, low-pass, bandpass, notched, and double bandpass) for two types of channel's shape (symmetric and asymmetric). Our simulations confirm that (1) high-pass, low-pass, and bandpass noises do not prevent the off-frequency looking, (2) white noise satisfactorily prevents the off-frequency looking independently of the shape and bandwidth of the visual channel, and interestingly we proved for the first time that (3) notched and double bandpass noises prevent off-frequency looking only when the noise cutoffs around the spatial frequency of the signal match the shape of the visual channel (symmetric or asymmetric) involved in the detection. In order to test the explanatory power of the model with empirical data, we performed six visual masking experiments. We show that this model, with only two free parameters, fits the empirical masking data with high precision. Finally, we provide equations of the power spectrum model for six masking noises used in the simulations and in the experiments.

Equilibrium existence in the circle model with linear quadratic transport cost

We treat the problem of existence of a location-then-price equilibrium in the circle model with a linear quadratic type of transportation cost function which can be either convex or concave. We show the existence of a unique perfect equilibrium for the concave case when the linear and quadratic terms are equal and of a unique perfect equilibrium for the convex case when the linear term is equal to zero. Aside from these two cases, there are feasible locations by the firms for which no equilibrium in the price subgame exists. Finally, we provide a full taxonomy of the price equilibrium regions in terms of weights of the linear and quadratic terms in the cost function.

Linear and nonlinear thermal instability of Newtonian and non-Newtonian fluid saturated porous media

The present work aims to investigate the influence of different aspects, such as non-standard steady solutions, complex fluid rheologies and non-standard porous-channel geometries, on the stability of a Darcy-Bénard system. In order to do so, both linear and nonlinear stability theories are considered. A linear analysis focuses on studying the dynamics of the single disturbance wave present in the system, while its nonlinear counterpart takes into consideration the interactions among the single modes. The scope of the stability analysis is to obtain information regarding the transition from an equilibrium solution to another one, and also information regarding the transition nature and the emergent solution after the transition. The disturbance governing equations are solved analytically, whenever possible, and numerical by considering different approaches. Among other important results, it is found that a cylinder cross-section does not affect the thermal instability threshold, but just the linear pattern selection for dilatant and pseudoplastic fluid saturated porous media. A new rheological model is proposed as a solution for singular issues involving the power-law model. Also, a generalised class of one parameter basic solutions is proposed as an alternative description of the isoflux Darcy--Bénard problem. Its stability is investigated.

Censored Linear Regression Models For Irregularly Observed Longitudinal Data Using The Multivariate-t Distribution.

In acquired immunodeficiency syndrome (AIDS) studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. For such data structures, we propose a robust structure for a censored linear model based on the multivariate Student's t-distribution. To compensate for the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient expectation maximization type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by-product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step that rely on formulas for the mean and variance of a truncated multivariate Student's t-distribution. The methodology is illustrated through an application to an Human Immunodeficiency Virus-AIDS (HIV-AIDS) study and several simulation studies.

Determination Of Detergent And Dispensant Additives In Gasoline By Ring-oven And Near Infrared Hypespectral Imaging.

A method using the ring-oven technique for pre-concentration in filter paper discs and near infrared hyperspectral imaging is proposed to identify four detergent and dispersant additives, and to determine their concentration in gasoline. Different approaches were used to select the best image data processing in order to gather the relevant spectral information. This was attained by selecting the pixels of the region of interest (ROI), using a pre-calculated threshold value of the PCA scores arranged as histograms, to select the spectra set; summing up the selected spectra to achieve representativeness; and compensating for the superimposed filter paper spectral information, also supported by scores histograms for each individual sample. The best classification model was achieved using linear discriminant analysis and genetic algorithm (LDA/GA), whose correct classification rate in the external validation set was 92%. Previous classification of the type of additive present in the gasoline is necessary to define the PLS model required for its quantitative determination. Considering that two of the additives studied present high spectral similarity, a PLS regression model was constructed to predict their content in gasoline, while two additional models were used for the remaining additives. The results for the external validation of these regression models showed a mean percentage error of prediction varying from 5 to 15%.

Limiar ventilatorio e comportamento do sinal eletromiografico durante exercicio incremental no cicloergometro

Universidade Estadual de Campinas . Faculdade de Educação Física

Stress distribution in the cervical region of an upper central incisor in a 3D finite element model

The aim of this study was to evaluate the stress distribution in the cervical region of a sound upper central incisor in two clinical situations, standard and maximum masticatory forces, by means of a 3D model with the highest possible level of fidelity to the anatomic dimensions. Two models with 331,887 linear tetrahedral elements that represent a sound upper central incisor with periodontal ligament, cortical and trabecular bones were loaded at 45º in relation to the tooth's long axis. All structures were considered to be homogeneous and isotropic, with the exception of the enamel (anisotropic). A standard masticatory force (100 N) was simulated on one of the models, while on the other one a maximum masticatory force was simulated (235.9 N). The software used were: PATRAN for pre- and post-processing and Nastran for processing. In the cementoenamel junction area, tensile forces reached 14.7 MPa in the 100 N model, and 40.2 MPa in the 235.9 N model, exceeding the enamel's tensile strength (16.7 MPa). The fact that the stress concentration in the amelodentinal junction exceeded the enamel's tensile strength under simulated conditions of maximum masticatory force suggests the possibility of the occurrence of non-carious cervical lesions such as abfractions.

A positional FEM Formulation for geometrical non-linear analysis of shells

This work presents a fully non-linear finite element formulation for shell analysis comprising linear strain variation along the thickness of the shell and geometrically exact description for curved triangular elements. The developed formulation assumes positions and generalized unconstrained vectors as the variables of the problem, not displacements and finite rotations. The full 3D Saint-Venant-Kirchhoff constitutive relation is adopted and, to avoid locking, the rate of thickness variation enhancement is introduced. As a consequence, the second Piola-Kirchhoff stress tensor and the Green strain measure are employed to derive the specific strain energy potential. Curved triangular elements with cubic approximation are adopted using simple notation. Selected numerical simulations illustrate and confirm the objectivity, accuracy, path independence and applicability of the proposed technique.

Modelo de programação linear para otimização econômica do projeto de irrigação Baixo Acaraú - CE

The present work had as objective uses a model of lineal programming algorithm to optimize the use of the water in the District of Irrigation Baixo Acarau-CE proposing the best combination of crop types and areas established of 8,0 ha. The model aim maximize the net benefit of small farmer, incorporating the constraints in water and land availability, and constraints on the market. Considering crop types and the constraints, the study lead to the following conclusions: 1. The water availability in the District was not a limiting resources, while all available land was assigned in six of the seven cultivation plans analyzed. Furthermore, water availability was a restrictive factor as compared with land only when its availability was made to reduce to 60% of its actual value; 2. The combination of soursop and melon plants was the one that presented the largest net benefit, corresponding to R$ 5,250.00/ha/yr. The planting area for each crop made up to 50% of the area of the plot; 3. The plan that suggests the substitution of the cultivation of the soursop, since a decrease in annual net revenue of 5.87%. However, the plan that contemplates the simultaneous substitution of both soursop and melon produced the lowest liquid revenue, with reduction of 33.8%.

Determination of Threshold Dose of Photodynamic Therapy to Measure Superficial Necrosis

Background Data: Photodynamic therapy (PDT) involves the photoinduction of cytotoxicity using a photosensitizer agent, a light source of the proper wavelength, and the presence of molecular oxygen. A model for tissue response to PDT based on the photodynamic threshold dose (Dth) has been widely used. In this model cells exposed to doses below Dth survive while at doses above the Dth necrosis takes place. Objective: This study evaluated the light Dth values by using two different methods of determination. One model concerns the depth of necrosis and the other the width of superficial necrosis. Materials and Methods: Using normal rat liver we investigated the depth and width of necrosis induced by PDT when a laser with a gaussian intensity profile is used. Different light doses, photosensitizers (Photogem, Photofrin, Photosan, Foscan, Photodithazine, and Radachlorin), and concentrations were employed. Each experiment was performed on five animals and the average and standard deviations were calculated. Results: A simple depth and width of necrosis model analysis allows us to determine the threshold dose by measuring both depth and surface data. Comparison shows that both measurements provide the same value within the degree of experimental error. Conclusion: This work demonstrates that by knowing the extent of the superficial necrotic area of a target tissue irradiated by a gaussian light beam, it is possible to estimate the threshold dose. This technique may find application where the determination of Dth must be done without cutting the tissue.

Tumor slices as a model to evaluate doxorubicin in vitro treatment and expression of trios of genes PRSS11, MTSS1, CLPTM1 and PRSS11, MTSS1, SMYD2 in canine mammary gland cancer

Background: In women with breast cancer submitted to neoadjuvant chemotherapy based in doxorubicin, tumor expression of groups of three genes (PRSS11, MTSS1, CLPTM1 and PRSS11, MTSS1, SMYD2) have classified them as responsive or resistant. We have investigated whether expression of these trios of genes could predict mammary carcinoma response in dogs and whether tumor slices, which maintain epithelial-mesenchymal interactions, could be used to evaluate drug response in vitro. Methods: Tumors from 38 dogs were sliced and cultured with or without doxorubicin 1 mu M for 24 h. Tumor cells were counted by two observers to establish a percentage variation in cell number, between slices. Based on these results, a reduction in cell number between treated and control samples >= 21.7%, arbitrarily classified samples, as drug responsive. Tumor expression of PRSS11, MTSS1, CLPTM1 and SMYD2, was evaluated by real time PCR. Relative expression results were then transformed to their natural logarithm values, which were spatially disposed according to the expression of trios of genes, comprising PRSS11, MTSS1, CLPTM1 and PRSS11, MTSS1, SMYD2. Fisher linear discrimination test was used to generate a separation plane between responsive and non-responsive tumors. Results: Culture of tumor slices for 24 h was feasible. Nine samples were considered responsive and 29 non-responsive to doxorubicin, considering the pre-established cut-off value of cell number reduction = 21.7%, between doxorubicin treated and control samples. Relative gene expression was evaluated and tumor samples were then spatially distributed according to the expression of the trios of genes: PRSS11, MTSS1, CLPTM1 and PRSS11, MTSS1, SMYD2. A separation plane was generated. However, no clear separation between responsive and non-responsive samples could be observed. Conclusion: Three-dimensional distribution of samples according to the expression of the trios of genes PRSS11, MTSS1, CLPTM1 and PRSS11, MTSS1, SMYD2 could not predict doxorubicin in vitro responsiveness. Short term culture of mammary gland cancer slices may be an interesting model to evaluate chemotherapy activity.

Beyond the Fragmentation Threshold Hypothesis: Regime Shifts in Biodiversity Across Fragmented Landscapes

Ecological systems are vulnerable to irreversible change when key system properties are pushed over thresholds, resulting in the loss of resilience and the precipitation of a regime shift. Perhaps the most important of such properties in human-modified landscapes is the total amount of remnant native vegetation. In a seminal study Andren proposed the existence of a fragmentation threshold in the total amount of remnant vegetation, below which landscape-scale connectivity is eroded and local species richness and abundance become dependent on patch size. Despite the fact that species patch-area effects have been a mainstay of conservation science there has yet to be a robust empirical evaluation of this hypothesis. Here we present and test a new conceptual model describing the mechanisms and consequences of biodiversity change in fragmented landscapes, identifying the fragmentation threshold as a first step in a positive feedback mechanism that has the capacity to impair ecological resilience, and drive a regime shift in biodiversity. The model considers that local extinction risk is defined by patch size, and immigration rates by landscape vegetation cover, and that the recovery from local species losses depends upon the landscape species pool. Using a unique dataset on the distribution of non-volant small mammals across replicate landscapes in the Atlantic forest of Brazil, we found strong evidence for our model predictions - that patch-area effects are evident only at intermediate levels of total forest cover, where landscape diversity is still high and opportunities for enhancing biodiversity through local management are greatest. Furthermore, high levels of forest loss can push native biota through an extinction filter, and result in the abrupt, landscape-wide loss of forest-specialist taxa, ecological resilience and management effectiveness. The proposed model links hitherto distinct theoretical approaches within a single framework, providing a powerful tool for analysing the potential effectiveness of management interventions.