Related papers: On non-negative solutions to large systems of rand…

A perceptron with N random weights can store of the order of N patterns by removing a fraction of the weights without changing their strengths. The critical storage capacity as a function of the concentration of the remaining bonds for…

We consider linear elimination of variables in steady state equations of a chemical reaction network. Particular subsets of variables corresponding to sets of so-called reactant-noninteracting species, are introduced. The steady state…

We study non-variational degenerate elliptic equations with high order singular structures. No boundary data are imposed and singularities occur along an {\it a priori} unknown interior region. We prove that positive solutions have a…

We study the binary perceptron, a random constraint satisfaction problem that asks to find a Boolean vector in the intersection of independently chosen random halfspaces. A striking feature of this model is that at every positive constraint…

There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…

In this paper we revisit random linear under-determined systems with sparse solutions. We consider $\ell_1$ optimization heuristic known to work very well when used to solve these systems. A collection of fundamental results that relate to…

In this paper, we consider the systems with trajectories originating in the nonnegative orthant becoming nonnegative after some finite time transient. First we consider dynamical systems (i.e., fully observable systems with no inputs),…

The aim of this paper is to investigate the dynamics of a higher order system of rational difference equations. Our concentration is on boundedness character, the oscillatory, the existence of unbounded solutions and the global behavior of…

For a large class of linear neutral type systems the problem of eigenvalues and eigenvectors assignment is investigated, i.e. finding the system which has the given spectrum and almost all, in some sense, eigenvectors.

This paper studies binary linear programming problems in the presence of uncertainties that may cause solution values to change during implementation. This type of uncertainty, termed implementation uncertainty, is modeled explicitly…

We present a deep transformation model for probabilistic regression. Deep learning is known for outstandingly accurate predictions on complex data but in regression tasks, it is predominantly used to just predict a single number. This…

We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…

While many physical processes are non-equilibrium in nature, the theory and modeling of such phenomena lag behind theoretical treatments of equilibrium systems. The diversity of powerful theoretical tools available to describe equilibrium…

We want to select the best systems out of a given set of systems (or rank them) with respect to their expected performance. The systems allow random observations only and we assume that the joint observation of the systems has a…

The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…

In this paper we look at a class of random optimization problems. We discuss ways that can help determine typical behavior of their solutions. When the dimensions of the optimization problems are large such an information often can be…

We expand the class of linear symmetric equations for which large sets with no non-trivial solutions are known. Our idea is based on first finding a small set with no solutions and then enlarging it to arbitrary size using a…

For massive and heterogeneous modern datasets, it is of fundamental interest to provide guarantees on the accuracy of estimation when computational resources are limited. In the application of learning to rank, we provide a hierarchy of…

Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…

The prediction of complex nonlinear dynamical systems with the help of machine learning techniques has become increasingly popular. In particular, reservoir computing turned out to be a very promising approach especially for the…