Related papers: On strong alt-induced codes
Recently, Ali et al. posed several open problems concerning extremal graphs with respect to the ABS index. These problems involve characterizing graphs that attain the maximum ABS index within specific graph classes, including: connected…
We study the problem of experiment design to learn causal structures from interventional data. We consider an active learning setting in which the experimenter decides to intervene on one of the variables in the system in each step and uses…
In this survey we overview known results on the strong subgraph $k$-connectivity and strong subgraph $k$-arc-connectivity of digraphs. After an introductory section, the paper is divided into four sections: basic results, algorithms and…
A new version of a Strong Law of Large Numbers is proposed in this note for pairwise independent random variables. The main goal is to relax the assumption on a finite expectation for each term.
Fix an oriented graph H, and let G be a graph with bounded clique number and very large chromatic number. If we somehow orient its edges, must there be an induced subdigraph isomorphic to H? Kierstead and Rodl raised this question for two…
We introduce the factor complex of a neural code, and show how intervals and maximal codewords are captured by the combinatorics of factor complexes. We use these results to obtain algebraic and combinatorial characterizations of…
One of the best ways for developers to test and improve their skills in a fun and challenging way are programming challenges, offered by a plethora of websites. For the inexperienced ones, some of the problems might appear too challenging,…
A class of good integers has been introduced by P. Moree in $1997$ together with the characterization of good odd integers. Such integers have shown to have nice number theoretical properties and wide applications. In this paper, a complete…
In probabilistic programming, the inference problem asks to determine a program's posterior distribution conditioned on its "observe" instructions. Inference is challenging, especially when exact rather than approximate results are…
Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In…
In this work, two types of codes such that they both dominate and locate the vertices of a graph are studied. Those codes might be sets of detectors in a network or processors controlling a system whose set of responses should determine a…
Additive codes have attracted considerable attention for their potential to outperform linear codes. However, distinguishing strictly additive codes from those that are equivalent to linear codes remains a fundamental challenge. To resolve…
The $(\kappa,\ell)$-edge-inducibility problem asks for the maximum number of $\kappa$-subsets inducing exactly $\ell$ edges that a graph of given order $n$ can have. Using flag algebras and stability approach, we resolve this problem for…
Variable-length splittable codes are derived from encoding sequences of ordered integer pairs, where one of the pair's components is upper bounded by some constant, and the other one is any positive integer. Each pair is encoded by the…
Context: Code coverage is widely used as a software quality assurance measure. However, its effect, and specifically the advisable dose, are disputed in both the research and engineering communities. Prior work reports only correlational…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
We study whether automatically-induced prompts that effectively extract information from a language model can also be used, out-of-the-box, to probe other language models for the same information. After confirming that discrete prompts…
An integer additive set-indexer is defined as an injective function $f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G) \rightarrow 2^{\mathbb{N}_0}$ defined by $g_f (uv) = f(u)+ f(v)$ is also injective, where…
Given a finite alphabet $A$, a quasi-metric $d$ over $A^*$, and a non-negative integer $k$, we introduce the relation $\tau_{d,k}\subseteq A^*\times A^*$ such that $(x,y)\in\tau_{d,k}$ holds whenever $d(x,y)\le k$. The error detection…
We consider problems to make a given bidirected graph strongly connected with minimum cardinality of additional signs or additional arcs. For the former problem, we show the minimum number of additional signs and give a linear-time…