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Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…
Elementary cellular automata deterministically map a binary sequence to another using simple local rules. Visualizing the structure of this mapping is difficult because the number of nodes (i.e. possible binary sequences) grows…
We investigate the complexity of bilevel combinatorial optimization with uncertainty in the follower's objective, in a robust optimization approach. We show that the robust counterpart of the bilevel problem under interval uncertainty can…
In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.
Jaberi [7] presented approximation algorithms for the problem of computing a minimum size 2-vertex strongly biconnected subgraph in directed graphs. We have implemented approximation algorithms presented in [7] and we have tested the…
Let $k\ge 2$. We prove that the characteristic sequence of a regular language over a $k$-letter alphabet is $k$-automatic. More generally, if $t\ge 2$ and $t,k$ are multiplicatively dependent, we show that the characteristic sequence of a…
The natural order in the space of binary sequences permits to recover the $U$-sequence. Also the scaling laws of the period-doubling cascade and the intermittency route to chaos defined in that ordered set are explained. These arise as…
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…
Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…
Binary sequences with minimal autocorrelations have applications in communication engineering, mathematics and computer science. In statistical physics they appear as groundstates of the Bernasconi model. Finding these sequences is a…
The binary neural network, largely saving the storage and computation, serves as a promising technique for deploying deep models on resource-limited devices. However, the binarization inevitably causes severe information loss, and even…
In `A survey of two-graphs' \cite{Sei}, J.J. Seidel lays out the connections between simple graphs, two-graphs, equiangular lines and strongly regular graph. It is well known that there is a one-to-one correspondence between regular…
We investigate the large values of class numbers of cubic fields, showing that one can find arbitrary long sequences of "close" abelian cubic number fields with class numbers as large as possible. We also give a first step toward an…
We introduce the new concept of joint nonlinear complexity for multisequences over finite fields and we analyze the joint nonlinear complexity of two families of explicit inversive multisequences. We also establish a probabilistic result on…
We consider the problem of finding response curves for a class of binary two-dimensional cellular automata with $L$-shaped neighbourhood. We show that the dependence of the density of ones after an arbitrary number of iterations, on the…
We first introduce a family of binary $pq^2$-periodic sequences based on the Euler quotients modulo $pq$, where $p$ and $q$ are two distinct odd primes and $p$ divides $q-1$. The minimal polynomials and linear complexities are determined…
Diagram-chasing arguments frequently lead to "magical" relations between distant points of diagrams: exactness implications, connecting morphisms, etc.. These long connections are usually composites of short "unmagical" connections, but the…
In classification problems, especially those that categorize data into a large number of classes, the classes often naturally follow a hierarchical structure. That is, some classes are likely to share similar structures and features. Those…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here…