Related papers: BDDs Naturally Represent Boolean Functions, and ZD…
A toral algebraic set $A$ is an algebraic set in $\C^n$ whose intersection with $\T^n$ is sufficiently large to determine the holomorphic functions on $A$. We develop the theory of these sets, and give a number of applications to function…
In two papers we noted that in common practice many algebraic constructions are defined only `up to isomorphism' rather than explicitly. We mentioned some questions raised by this fact, and we gave some partial answers. The present paper…
Several structure learning algorithms have been proposed towards discovering causal or Bayesian Network (BN) graphs. The validity of these algorithms tends to be evaluated by assessing the relationship between the learnt and the ground…
We introduce topological differential testing (TDT), an approach to extracting the consensus behavior of a set of programs on a corpus of inputs. TDT uses the topological notion of a simplicial complex (and implicitly draws on richer…
There is a strong interest in studying the correspondence between Euclidean quantum fields and neural networks. This correspondence takes different forms depending on the type of networks considered. In this work, we study this…
Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…
A complete classification of the computational complexity of the fixed-point existence problem for boolean dynamical systems, i.e., finite discrete dynamical systems over the domain {0, 1}, is presented. For function classes F and graph…
In a recent paper by Jonasson and Steif, definitions to describe the volatility of sequences of Boolean functions, \( f_n \colon \{ -1,1 \}^n \to \{ -1,1 \} \) were introduced. We continue their study of how these definitions relate to…
Zero-Shot Learning (ZSL) seeks to recognize a sample from either seen or unseen domain by projecting the image data and semantic labels into a joint embedding space. However, most existing methods directly adapt a well-trained projection…
We present a layered Boltzmann machine (BM) that can better exploit the advantages of a distributed representation. It is widely believed that deep BMs (DBMs) have far greater representational power than its shallow counterpart, restricted…
We study the properties of linear and non-linear determining functionals for dissipative dynamical systems generated by PDEs. The main attention is payed to the lower bounds for the number of such functionals. In contradiction to the common…
A doodle is a collection of immersed circles without triple intersections in the $2$-sphere. It was shown by the second author and P.~Tayler that doodles induce commutator identities (identities amongst commutators) in a free group. In this…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
Let F(x_1,...,x_m) = u_1 x_1 + ... + u_m x_m be a linear form with nonzero, relatively prime integer coefficients u_1,..., u_m. For any set A of integers, let F(A) = {F(a_1,...,a_m) : a_i in A for i=1,...,m}. The representation function…
Zero-shot learning (ZSL) makes object recognition in images possible in absence of visual training data for a part of the classes from a dataset. When the number of classes is large, classes are usually represented by semantic class…
Benders' decomposition (BD) is a framework for solving optimization problems by removing some variables and modeling their contribution to the original problem via so-called Benders cuts. While many advanced optimization techniques can be…
Boolean function bi-decomposition is ubiquitous in logic synthesis. It entails the decomposition of a Boolean function using two-input simple logic gates. Existing solutions for bi-decomposition are often based on BDDs and, more recently,…
Submodular functions, defined on continuous or discrete domains, arise in numerous applications. We study the minimization of the difference of two submodular (DS) functions, over both domains, extending prior work restricted to set…
Stern's diatomic sequence is a well-studied and simply defined sequence with many fascinating characteristics. The binary signed-digit (BSD) representation of integers is used widely in efficient computation, coding theory and other…
We consider complete graphs with edge weights and/or node weights taking values in some set. In the first part of this paper, we show that a large number of graphs are completely determined, up to isomorphism, by the distribution of their…