Phase Diagram of Spiking Neural Networks

In computer simulations of spiking neural networks, often it is assumed that every two neurons of the network are connected by a probability of 2\%, 20\% of neurons are inhibitory and 80\% are excitatory. These common values are based on experiments, observations, and trials and errors, but here, I take a different perspective, inspired by evolution, I systematically simulate many networks, each with a different set of parameters, and then I try to figure out what makes the common values desirable. I stimulate networks with pulses and then measure their: dynamic range, dominant frequency of population activities, total duration of activities, maximum rate of population and the occurrence time of maximum rate. The results are organized in phase diagram. This phase diagram gives an insight into the space of parameters -- excitatory to inhibitory ratio, sparseness of connections and synaptic weights. This phase diagram can be used to decide the parameters of a model. The phase diagrams show that networks which are configured according to the common values, have a good dynamic range in response to an impulse and their dynamic range is robust in respect to synaptic weights, and for some synaptic weights they oscillate in $\alpha$ or $\beta$ frequencies, even in absence of external stimuli.Comment: oscillations are studied in this versio

Finite size scaling approach to dynamic storage allocation problem

It is demonstrated how dynamic storage allocation algorithms can be analyzed in terms of finite size scaling. The method is illustrated in the three simple cases of the it first-fit, next-fit and it best-fit algorithms, and the system works at full capacity. The analysis is done from two different points of view - running speed and employed memory. In both cases, and for all algorithms, it is shown that a simple scaling function exists and the relevant exponents are calculated. The method can be applied on similar problems as well.Comment: 9 pages, 4 figures, will apear in Physica

Three Bead Rotating Chain model shows universality in the stretching of proteins

We introduce a model of proteins in which all of the key atoms in the protein backbone are accounted for, thus extending the Freely Rotating Chain model. We use average bond lengths and average angles from the Protein Databank as input parameters, leaving the number of residues as a single variable. The model is used to study the stretching of proteins in the entropic regime. The results of our Monte Carlo simulations are found to agree well with experimental data, suggesting that the force extension plot is universal and does not depend on the side chains or primary structure of proteins

Scale-free networks with an exponent less than two

We study scale free simple graphs with an exponent of the degree distribution $\gamma$ less than two. Generically one expects such extremely skewed networks -- which occur very frequently in systems of virtually or logically connected units -- to have different properties than those of scale free networks with $\gamma>2$: The number of links grows faster than the number of nodes and they naturally posses the small world property, because the diameter increases by the logarithm of the size of the network and the clustering coefficient is finite. We discuss a simple prototype model of such networks, inspired by real world phenomena, which exhibits these properties and allows for a detailed analytical investigation

Simulation of Droplet Trains in Microfluidic Networks

In this work we show that in a microfluidic network and in low Reynolds numbers a system can be irreversible because of hysteresis effects.The network, which is employed in our simulations, is taken from recent experiments. The network consists of one loop connected to input and output pipes. A train of droplets enter the system at a uniform rate, but they may leave it in different patterns, e.g. periodic or even chaotic. The out put pattern depends on the time interval among the incoming droplets as well as the network geometry and for some parameters the system is not reversible