Are the input parameters of white-noise-driven integrate-and-fire neurons uniquely determined by rate and CV?

Integrate-and-fire (IF) neurons have found widespread applications in computational neuroscience. Particularly important are stochastic versions of these models where the driving consists of a synaptic input modeled as white Gaussian noise with mean $\mu$ and noise intensity $D$. Different IF models have been proposed, the firing statistics of which depends nontrivially on the input parameters $\mu$ and $D$. In order to compare these models among each other, one must first specify the correspondence between their parameters. This can be done by determining which set of parameters ($\mu$, $D$) of each model is associated to a given set of basic firing statistics as, for instance, the firing rate and the coefficient of variation (CV) of the interspike interval (ISI). However, it is not clear {\em a priori} whether for a given firing rate and CV there is only one unique choice of input parameters for each model. Here we review the dependence of rate and CV on input parameters for the perfect, leaky, and quadratic IF neuron models and show analytically that indeed in these three models the firing rate and the CV uniquely determine the input parameters

Can aerosols be trapped in open flows?

The fate of aerosols in open flows is relevant in a variety of physical contexts. Previous results are consistent with the assumption that such finite-size particles always escape in open chaotic advection. Here we show that a different behavior is possible. We analyze the dynamics of aerosols both in the absence and presence of gravitational effects, and both when the dynamics of the fluid particles is hyperbolic and nonhyperbolic. Permanent trapping of aerosols much heavier than the advecting fluid is shown to occur in all these cases. This phenomenon is determined by the occurrence of multiple vortices in the flow and is predicted to happen for realistic particle-fluid density ratios.Comment: Animation available at http://www.pks.mpg.de/~rdvilela/leapfrogging.htm

Aggregation and fragmentation dynamics of inertial particles in chaotic flows

Inertial particles advected in chaotic flows often accumulate in strange attractors. While moving in these fractal sets they usually approach each other and collide. Here we consider inertial particles aggregating upon collision. The new particles formed in this process are larger and follow the equation of motion with a new parameter. These particles can in turn fragment when they reach a certain size or shear forces become sufficiently large. The resulting system consists of a large set of coexisting dynamical systems with a varying number of particles. We find that the combination of aggregation and fragmentation leads to an asymptotic steady state. The asymptotic particle size distribution depends on the mechanism of fragmentation. The size distributions resulting from this model are consistent with those found in rain drop statistics and in stirring tank experiments.Comment: 4 pages, 4 figure

A comparative study of different integrate-and-fire neurons: spontaneous activity, dynamical response, and stimulus-induced correlation

Stochastic integrate-and-fire (IF) neuron models have found widespread applications in computational neuroscience. Here we present results on the white-noise-driven perfect, leaky, and quadratic IF models, focusing on the spectral statistics (power spectra, cross spectra, and coherence functions) in different dynamical regimes (noise-induced and tonic firing regimes with low or moderate noise). We make the models comparable by tuning parameters such that the mean value and the coefficient of variation of the interspike interval match for all of them. We find that, under these conditions, the power spectrum under white-noise stimulation is often very similar while the response characteristics, described by the cross spectrum between a fraction of the input noise and the output spike train, can differ drastically. We also investigate how the spike trains of two neurons of the same kind (e.g. two leaky IF neurons) correlate if they share a common noise input. We show that, depending on the dynamical regime, either two quadratic IF models or two leaky IFs are more strongly correlated. Our results suggest that, when choosing among simple IF models for network simulations, the details of the model have a strong effect on correlation and regularity of the output.Comment: 12 page

GLUT1 expression in malignant tumors and its use as an immunodiagnostic marker

OBJECTIVE: To analyze glucose transporter 1 expression patterns in malignant tumors of various cell types and evaluate their diagnostic value by immunohistochemistry. INTRODUCTION: Glucose is the major source of energy for cells, and glucose transporter 1 is the most common glucose transporter in humans. Glucose transporter 1 is aberrantly expressed in several tumor types. Studies have implicated glucose transporter 1 expression as a prognostic and diagnostic marker in tumors, primarily in conjunction with positron emission tomography scan data. METHODS: Immunohistochemistry for glucose transporter 1 was performed in tissue microarray slides, comprising 1955 samples of malignant neoplasm from different cell types. RESULTS: Sarcomas, lymphomas, melanomas and hepatoblastomas did not express glucose transporter 1. Fortyseven per cent of prostate adenocarcinomas were positive, as were 29% of thyroid, 10% of gastric and 5% of breast adenocarcinomas. Thirty-six per cent of squamous cell carcinomas of the head and neck were positive, as were 42% of uterine cervix squamous cell carcinomas. Glioblastomas and retinoblastomas showed membranous glucose transporter 1 staining in 18.6% and 9.4% of all cases, respectively. Squamous cell carcinomas displayed membranous expression, whereas adenocarcinomas showed cytoplasmic glucose transporter 1 expression. CONCLUSION: Glucose transporter 1 showed variable expression in various tumor types. Its absence in sarcomas, melanomas, hepatoblastomas and lymphomas suggests that other glucose transporters mediate the glycolytic pathway in these tumors. The data suggest that glucose transporter 1 is a valuable immunohistochemical marker that can be used to identify patients for evaluation by positron emission tomography scan. The function of cytoplasmic glucose transporter 1 in adenocarcinomas must be further examined

Coagulation and fragmentation dynamics of inertial particles

Inertial particles suspended in many natural and industrial flows undergo coagulation upon collisions and fragmentation if their size becomes too large or if they experience large shear. Here we study this coagulation-fragmentation process in time-periodic incompressible flows. We find that this process approaches an asymptotic, dynamical steady state where the average number of particles of each size is roughly constant. We compare the steady-state size distributions corresponding to two fragmentation mechanisms and for different flows and find that the steady state is mostly independent of the coagulation process. While collision rates determine the transient behavior, fragmentation determines the steady state. For example, for fragmentation due to shear, flows that have very different local particle concentrations can result in similar particle size distributions if the temporal or spatial variation of shear forces is similar.Comment: 8 pages, 7 figure