Related papers: Stability of Boolean function classes with respect…
Regulatory dynamics in biology is often described by continuous rate equations for continuously varying chemical concentrations. Binary discretization of state space and time leads to Boolean dynamics. In the latter, the dynamics has been…
We investigate how classifiers for Boolean networks (BNs) can be constructed and modified under constraints. A typical constraint is to observe only states in attractors or even more specifically steady states of BNs. Steady states of BNs…
The stability of the recently discovered compacton solutions is studied by means of both linear stability analysis as well as Lyapunov stability criteria. From the results obtained it follows that, unlike solitons, all the allowed compacton…
We propose local versions of monotonicity for Boolean and pseudo-Boolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if none of its partial derivatives changes in sign on tuples which differ in less than p…
We characterize stability under composition of ultradifferentiable classes defined by weight sequences $M$, by weight functions $\omega$, and, more generally, by weight matrices $\mathfrak{M}$, and investigate continuity of composition…
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
It is shown that monotone Boolean functions on the Boolean cube capture the expected number of primes, under he usual identification by binary expansion. This answers a question posed by G.Kalai.
We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In…
Boolean networks constitute relevant mathematical models to study the behaviours of genetic and signalling networks. These networks define regulatory influences between molecular nodes, each being associated to a Boolean variable and a…
Computational models of biological processes provide one of the most powerful methods for a detailed analysis of the mechanisms that drive the behavior of complex systems. Logic-based modeling has enhanced our understanding and…
We prove a motivic stabilization result for the cohomology of the local systems on configuration spaces of varieties over $\mathbb{C}$ attached to character polynomials. Our approach interprets the stabilization as a probabilistic…
Recent work has unveiled a theory for reasoning about the decisions made by binary classifiers: a classifier describes a Boolean function, and the reasons behind an instance being classified as positive are the prime-implicants of the…
We present a characterization of short-term stability of random Boolean networks under \emph{arbitrary} distributions of transfer functions. Given any distribution of transfer functions for a random Boolean network, we present a formula…
We introduce a basis of rational polynomial-like functions $P_0,\ldots,P_{n-1}$ for the free module of functions $Z/nZ\to Z/mZ$. We then characterize the subfamily of congruence preserving functions as the set of linear combinations of the…
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…
This article establishes the existence of Lyapunov functions for analyzing the stability of a class of state-constrained systems, and it describes algorithms for their numerical computation. The system model consists of a differential…
Dillon-like Boolean functions are known, in the literature, to be those trace polynomial functions from $\mathbb{F}_{2^{2n}}$ to $\mathbb{F}_{2}$, with all the exponents being multiples of $2^n-1$ often called Dillon-like exponents. This…
First, we construct a class of functions with good local avalanche characteristics, but bad global avalanche characteristics. We also derive some bounds for the nonlinearity of such functions. It improves upon the results of Son et al., and…
We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.
We discuss technical results on learning function approximations using piecewise-linear basis functions, and analyze their stability and convergence using nonlinear contraction theory.