Related papers: Firing map of an almost periodic input function
Motivated by experimental observations, we investigate a variant of the cocktail party problem: the detection of a weak periodic stimulus in the presence of fluctuations and another periodic stimulus which is stronger than the periodic…
Functional reactive programming (FRP) is a declarative programming paradigm for implementing reactive programs at a high level of abstraction. It applies functional programming principles to construct and manipulate time-varying values,…
Recently, simple dynamical systems such as the 1-d maps on the interval, gained significant attention in the context of statistical physics and complex systems. The decay of correlations in these systems, can be characterized and measured…
Starting from a spectral expansion of the Fokker-Plank equation for the membrane potential density in a network of spiking neurons, a low-dimensional dynamics of the collective firing rate is derived. As a result a $n$-order ordinary…
In the thermodynamic limit, a probabilistic cellular automaton can be approximated by a deterministic nonlinear map. Here we construct such a map for the forest fire problem. The construction is based on the results of the Monte Carlo…
The coding properties of cells with different types of receptive fields have been studied for decades. ON-type neurons fire in response to positive fluctuations of the time-dependent stimulus, whereas OFF cells are driven by negative…
The emergence of an autocatalytic network from an available set of elements is a fundamental step in early evolutionary processes, such as the origin of metabolism. Given a set of elements, the reactions between them (chemical or…
Spike time response curves (STRC's) are used to study the influence of synaptic stimuli on the firing times of a neuron oscillator without the assumption of weak coupling. They allow us to approximate the dynamics of synchronous state in…
Periodic and nonperiodic components of electrophysiological signals are modelled in terms of syncronized sequences of closed loops of firing neurons correlated in Markov chains. Single closed loops of firing neurons reproduce fundamental…
The functional relationship between an input and a sensory neuron's response can be described by the neuron's stimulus-response mapping function. A general approach for characterizing the stimulus-response mapping function is called system…
We classify the sets of natural numbers $n$ for which certain dynamical systems $(X,f)$ on a compact metric space $X$ have a periodic point of (least) period $n$. Interest in this question dates back to Sharkovskii's theorem for continuous…
Let C be a closed subset of a topological space X, and let f : C --> X. Let us assume that f is continuous and f(x) lies in C for every x in the boundary of C. How many times can one iterate f? This paper provides estimates on the number of…
Structural balance is an important characteristic of graphs/networks where edges can be positive or negative, with direct impact on the study of real-world complex systems. When a network is not structurally balanced, it is important to…
We study certain topological problems that are inspired by applications to autonomous robot manipulation. Consider a continuous map $f\colon X\to Y$, where $f$ can be a kinematic map from the configuration space $X$ to the working space $Y$…
The efficiency of the human brain in performing classification tasks has attracted considerable research interest in brain-inspired neuromorphic computing. Hardware implementations of a neuromorphic system aims to mimic the computations in…
Synchronizability of stable, output-coupled, identical, time-varying linear systems is studied. It is shown that if the observability grammian satisfies a persistence of excitation condition, then there exists a bounded, time-varying linear…
A continuum $X$ is a dendrite if it is locally connected and contains no simple closed curve, a self mapping $f$ of $X$ is called monotone if the preimage of any connected subset of $X$ is connected. If $X$ is a dendrite and $f:X\to X$ is a…
In this paper, we study abstract dynamical systems with discrete phase spaces. One example of such a system is induced by the $3 x{+}1$-map on the set of all natural numbers, also known as the Collatz map. Our main focus is on dynamical…
In a generic neuron model, we present the linear response theory for the firing rate in response to both time dependent input currents and noise amplitudes. In both cases the signal transmission is strongly attenuated for frequencies above…
In the context of data-driven control, persistence of excitation (PE) of an input sequence is defined in terms of a rank condition on the Hankel matrix of the input data. For nonlinear systems, recent results employed rank conditions…