ELL and LLL, both introduced in [Gir98], are two logical systems which characterize respectively the class of Kalmar elementary functions and the class of deterministic polytime functions. Their syntactical formulation (both in the sequent calculus and proof-net framework) is quite different from that of “traditional” linear logic, namely because of the presence of blocks and discharged formula...

A binary code is called a superimposed cover-free $(s,\ell)$-code if the code is identified by the incidence matrix of a family of finite sets in which no intersection of $\ell$ sets is covered by the union of $s$ others. A binary code is called a superimposed list-decoding $s_L$-code if the code is identified by the incidence matrix of a family of finite sets in which the union of any $s$ sets...

A graph class $\mathcal{F}$ has the induced Erd\H{o}s-P\'osa property if there exists a function $f$ such that for every graph $G$ and every positive integer $k$, $G$ contains either $k$ pairwise vertex-disjoint induced subgraphs that belong to $\mathcal{F}$, or a vertex set of size at most $f(k)$ hitting all induced copies of graphs in $\mathcal{F}$. Kim and Kwon (SODA'18) showed that for a cy...

Oscillatory and burst discharge is recognized as a key element of signal processing from the level of receptor to cortical output cells in most sensory systems. The relevance of this activity for electrosensory processing has become increasingly apparent for cells in the electrosensory lateral line lobe (ELL) of gymnotiform weakly electric fish. Burst discharge by ELL pyramidal cells can be rec...

We study the change detection problem in general HMMs, when change parameters are unknown and the change could be gradual (slow) or sudden (drastic). Drastic changes can be detected easily using the increase in tracking error or the negative log of the observation likelihood conditioned on past observations (OL). But slow changes usually get missed. We propose a statistic for slow change detect...

Abstract Let $X$ be an abelian variety over algebraically closed field $\textbf{k}$ and $f$ a quasi-unipotent automorphism of $X$. When is the complex numbers, Lin, Oguiso, D.-Q. Zhang provide explicit formula for polynomial volume growth (or equivalently, Gelfand–Kirillov dimension twisted homogeneous coordinate ring associated with) pair $(X, f)$, by analytic argument. We give algebraic proof...

Let $\mathcal{C}_n =\left [\chi_{\lambda}(\mu)\right]_{\lambda, \mu}$ be the character table for $S_n,$ where indices $\lambda$ and $\mu$ run over $p(n)$ many integer partitions of $n.$ In this note we study $Z_{\ell}(n),$ number zero entries $\chi_{\lambda}(\mu)$ in $\mathcal{C}_n,$ is an $\ell$-core partition For every prime $\ell\geq 5,$ prove asymptotic formula form $$ Z_{\ell}(n)\sim \alph...