Related papers: Joint Realizability of Monotone Boolean functions
A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…
The concept of a nested canalizing Boolean function has been studied over the course of the last decade in the context of understanding the regulatory logic of molecular interaction networks, such as gene regulatory networks. Such functions…
We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a collection of partial functions closed under relative…
We consider the Stochastic Boolean Function Evaluation (SBFE) problem where the task is to efficiently evaluate a known Boolean function $f$ on an unknown bit string $x$ of length $n$. We determine $f(x)$ by sequentially testing the…
Model-based deep learning (MoDL) algorithms that rely on unrolling are emerging as powerful tools for image recovery. In this work, we introduce a novel monotone operator learning framework to overcome some of the challenges associated with…
This paper focuses on the study of certain classes of Boolean functions that have appeared in several different contexts. Nested canalyzing functions have been studied recently in the context of Boolean network models of gene regulatory…
Monotone Boolean functions are a structurally important class of Boolean functions, but their restricted form imposes strong limitations on achievable nonlinearity. In this paper, we investigate whether evolutionary computation can evolve…
We consider integrative modeling of multiple gene networks and diverse genomic data, including protein-DNA binding, gene expression and DNA sequence data, to accurately identify the regulatory target genes of a transcription factor (TF).…
We improve both upper and lower bounds for the distribution-free testing of monotone conjunctions. Given oracle access to an unknown Boolean function $f:\{0,1\}^n \rightarrow \{0,1\}$ and sampling oracle access to an unknown distribution…
We study a stochastic variant of monotone submodular maximization problem as follows. We are given a monotone submodular function as an objective function and a feasible domain defined on a finite set, and our goal is to find a feasible…
A classical question of propositional logic is one of the shortest proof of a tautology. A related fundamental problem is to determine the relative efficiency of standard proof systems, where the relative complexity is measured using the…
In this work, the synchronization problem of a master-slave system of autonomous ordinary differential equations (ODEs) is considered. Here, the systems are, chaotic with a nonlinearity represented by a piecewise linear function,…
Boolean networks model finite discrete dynamical systems with complex behaviours. The state of each component is determined by a Boolean function of the state of (a subset of) the components of the network. This paper addresses the…
According to the method, suggested in our previous work (nlin/0509012) and based on the consideration of the specially coupled systems, the possibility of physical realization of the phenomena of complex analytic dynamics (such as…
Let $\mathbb{A}_n^m$ be an arbitrary $n$-dimensional commutative associative algebra over the field of complex numbers with $m$ idempotents. Let $e_1=1,e_2,\ldots,e_k$ with $2\leq k\leq 2n$ be elements of $\mathbb{A}_n^m$ which are linearly…
This paper studies a class of mean-field control (MFC) problems with singular controls under general dynamic state-control-law constraints. We first propose a customized relaxed control formulation to cope with the dynamic mixed constraints…
Recent experimental advances in biology allow researchers to obtain gene expression profiles at single-cell resolution over hundreds, or even thousands of cells at once. These single-cell measurements provide snapshots of the states of the…
Random Boolean networks have been used widely to explore aspects of gene regulatory networks. A modified form of the model through which to systematically explore the effects of increasing the number of gene states has previously been…
We define a measure for the complexity of Boolean functions related to their implementation in neural networks, and in particular close related to the generalization ability that could be obtained through the learning process. The measure…
This paper is a contribution to the study of a quasi-order on the set $\Omega$ of Boolean functions, the \emph{simple minor} quasi-order. We look at the join-irreducible members of the resulting poset $\tilde{\Omega}$. Using a two-way…