Parameters estimation for spatio-temporal maximum entropy distributions: application to neural spike trains

We propose a numerical method to learn Maximum Entropy (MaxEnt) distributions with spatio-temporal constraints from experimental spike trains. This is an extension of two papers [10] and [4] who proposed the estimation of parameters where only spatial constraints were taken into account. The extension we propose allows to properly handle memory effects in spike statistics, for large sized neural networks.Comment: 34 pages, 33 figure

Spatio-temporal spike trains analysis for large scale networks using maximum entropy principle and Monte-Carlo method

Understanding the dynamics of neural networks is a major challenge in experimental neuroscience. For that purpose, a modelling of the recorded activity that reproduces the main statistics of the data is required. In a first part, we present a review on recent results dealing with spike train statistics analysis using maximum entropy models (MaxEnt). Most of these studies have been focusing on modelling synchronous spike patterns, leaving aside the temporal dynamics of the neural activity. However, the maximum entropy principle can be generalized to the temporal case, leading to Markovian models where memory effects and time correlations in the dynamics are properly taken into account. In a second part, we present a new method based on Monte-Carlo sampling which is suited for the fitting of large-scale spatio-temporal MaxEnt models. The formalism and the tools presented here will be essential to fit MaxEnt spatio-temporal models to large neural ensembles.Comment: 41 pages, 10 figure

Spike trains statistics in Integrate and Fire Models: exact results

We briefly review and highlight the consequences of rigorous and exact results obtained in \cite{cessac:10}, characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where neurons are subject to noise, without restriction on the synaptic weights connectivity. The main result is that spike trains statistics are characterized by a Gibbs distribution, whose potential is explicitly computable. This establishes, on one hand, a rigorous ground for the current investigations attempting to characterize real spike trains data with Gibbs distributions, such as the Ising-like distribution, using the maximal entropy principle. However, it transpires from the present analysis that the Ising model might be a rather weak approximation. Indeed, the Gibbs potential (the formal "Hamiltonian") is the log of the so-called "conditional intensity" (the probability that a neuron fires given the past of the whole network). But, in the present example, this probability has an infinite memory, and the corresponding process is non-Markovian (resp. the Gibbs potential has infinite range). Moreover, causality implies that the conditional intensity does not depend on the state of the neurons at the \textit{same time}, ruling out the Ising model as a candidate for an exact characterization of spike trains statistics. However, Markovian approximations can be proposed whose degree of approximation can be rigorously controlled. In this setting, Ising model appears as the "next step" after the Bernoulli model (independent neurons) since it introduces spatial pairwise correlations, but not time correlations. The range of validity of this approximation is discussed together with possible approaches allowing to introduce time correlations, with algorithmic extensions.Comment: 6 pages, submitted to conference NeuroComp2010 http://2010.neurocomp.fr/; Bruno Cessac http://www-sop.inria.fr/neuromathcomp

In vitro evaluation of iron-deficiency tolerance in an endemic putative apple rootstock

In most species of fruit trees, iron deficiency-induced chlorosis causes severaleconomic damages. Recently, in vitro culture techniques have been used to assessrootstocks for susceptibility to iron deficiency-induced chlorosis. In the present study, thein vitro shoots of three apple genotypes including Malus baccata, MM.106 and Gami-Almasi, a native putative apple rootstock, were evaluated on MS medium supplementedwith four concentrations of Fe (0, 9, 18, 36 mg/L) from Fe-NaEDTA and the concentration ofFe in MS medium as the control. Visual chlorosis index, leaf chlorophyll index, leaf area,fresh weight increment and dry weight of shoots were determined 26 days after culture.Iron concentrations affected the visual chlorosis index of M. baccata and MM.106.However, there were no chlorosis symptoms in Gami-Almasi. Leaf chlorophyll index wereaffected significantly by genotypes and Fe concentration. Leaf area and fresh weightincrement differed significantly in various genotypes; nevertheless, the effect of Feconcentration was not significant. Leaf area and fresh weight were recorded the highest inM. baccata compared to the other two genotypes. Genotypes and Fe concentrationtreatments were not affected dry weight of the shoots

Conformal mapping of unbounded multiply connected regions onto canonical slit regions

We present a boundary integral equation method for conformal mapping of unbounded multiply connected regions onto five types of canonical slit regions. For each canonical region, three linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on an unboundedmultiply connected region. The integral equations are uniquely solvable. The kernels involved in these integral equations are the modified Neumann kernels and the adjoint generalized Neumann kernels

Techno-Economics of Hybrid NF/FO with Thermal Desalination Plants

Hybrid desalination technology is defined as any combination of thermal and membrane processes in seawater desalination systems. So far, the two technologies have evolved rather independently with some degree of competition. Traditionally, in co-generation market applications, thermal desalination has succeeded in establishing a stronghold where large capacities are needed, energy costs are low, and seawater quality is challenging. However, in recent years, membrane systems have also succeeded in grabbing a larger share of the world seawater desalination market, mainly as a result of progress made in membrane and energy recovery technologies. Realizing the potential benefits and challenges faced by both technologies on their own, designers have been looking for ways to synergize and combine the two technologies in optimum configurations, which promise to further reduce the total cost of seawater desalination

Towards affordable water supply

Kaduna State of Nigeria has a 1991 population of 4.1 million of which 58 per cent is served with water supply by Kaduna State Water Board. A State-Wide Water Resources Masterplan is being developed to improve coverage to more than 70 per cent covering a projected population of 7.1 million by the year 2020

Bedform effect on the bed-load transport rate using a comparison between two bedform (flat and standing bedform)

In this research, the impact of bedform on the bed - load transport rate was studied through experiments. The experiments were conducted on two cases, one when the bedform was flat, and the other when the bedform was standing wave. The arrival time is the time of bed - load reaches a reference surface at the end of the flume. Noted that the arrival time of the bed - load to the end flume when the bedform as flat differs from the arrival time when the bedform as standing wave, It was found that the arrival time in the case of flat bedform is less comparing to the case when the bedform is standing wave. Index form factor (L*/L) was proposed to distinguish between the flat bedform and the standing wave bedform, this factor was introduced in dimensional analysis with the other variables affecting the prediction of bed - load transport rate formula. Linear regression was found to predict formula for index form factor L*/L and also prediction formula for computed the bed - load transport rate (qs) with high R-square. The results from predicted formula were verified by comparing them with other researchers’ formal’s using statistical measures. At long last, it was found that the amount of the bed - load transport rate when the bedform was a flat is greater than the amount of the bed - load transport rate when the bedform was standing wave. Since the value of the bed - load transport rate has to do with the decision to maintain the unlined channels and thus it affects the cost of maintenance of the unlined channels