Related papers: Long cycles in linear thresholding systems
We present a structured neural network architecture that is inspired by linear time-varying dynamical systems. The network is designed to mimic the properties of linear dynamical systems which makes analysis and control simple. The…
The whole complex process to obtain a protein encoded by a gene is difficult to include in a mathematical model. There are many models for describing different aspects of a genetic network. Finding a better model is one of the most…
We propose a general strategy for feedback control design of complex dynamical systems exploiting the nonlinear mechanisms in a systematic unsupervised manner. These dynamical systems can have a state space of arbitrary dimension with…
Stylized models of the neurodynamics that underpin sensory motor control in animals are proposed and studied. The voluntary motions of animals are typically initiated by high level intentions created in the primary cortex through a…
A longstanding challenge for the Machine Learning community is the one of developing models that are capable of processing and learning from very long sequences of data. The outstanding results of Transformers-based networks (e.g., Large…
In 2009, two different groups independently explored the behavior of random threshold graphs. Here, we extend their techniques to find the distribution of other properties, including matching number, degeneracy, and length of the longest…
Recurrent neural policies are widely used in partially observable control and meta-RL tasks. Their abilities to maintain internal memory and adapt quickly to unseen scenarios have offered them unparalleled performance when compared to…
Long-range interacting many-body systems exhibit a number of peculiar and intriguing properties. One of those is the scaling of relaxation times with the number $N$ of particles in a system. In this paper I give a survey of results on…
Increasingly sophisticated mathematical modelling processes from Machine Learning are being used to analyse complex data. However, the performance and explainability of these models within practical critical systems requires a rigorous and…
The fields of neural computation and artificial neural networks have developed much in the last decades. Most of the works in these fields focus on implementing and/or learning discrete functions or behavior. However, technical, physical,…
The ability to effectively control brain dynamics holds great promise for the enhancement of cognitive function in humans, and the betterment of their quality of life. Yet, successfully controlling dynamics in neural systems is challenging,…
Motivation: Cell-biological processes are regulated through a complex network of interactions between genes and their products. The processes, their activating conditions, and the associated transcriptional responses are often unknown.…
The time-elapsed model for neural networks is a nonlinear age structured equationwhere the renewal term describes the network activity and influences the dischargerate, possibly with a delay due to the length of connections.We solve a long…
Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…
This work presents a control-oriented identification scheme for efficient control design and stability analysis of nonlinear systems. Neural networks are used to identify a discrete-time nonlinear state-space model to approximate…
Recent measurements of durations of non-equilibrium processes provide valuable information on microscopic mechanisms and energetics. Comprehensive theory for corresponding experiments so far is well developed for single-particle systems…
Biological systems perform an astonishing array of dynamical processes -- including development and repair, regulation, behavior and motor control, sensing and signaling, and adaptation, among others. Powered by the transduction of stored…
Self-regulatory models are common in nature, as described e.g. in (\cite{mur}), (\cite{ha}) and (\cite{Gb}).\\ Let us consider a system made up of a number of glands as a motivation. Each gland secretes a hormone that allows secretion in…
Most of animal and human behavior occurs on time scales much longer than the response times of individual neurons. In many cases, it is plausible that these long time scales emerge from the recurrent dynamics of electrical activity in…
This paper provides a set of cycling problems in linear programming. These problems should be useful for researchers to develop and test new simplex algorithms. As matter of the fact, this set of problems is used to test a recently proposed…