A case study in authorship attribution: The Mondrigo1

In this paper, we present authorship attribution methods applied to ¡El Mondrigo! (1968), a controversial text supposedly created by order of the Mexican Government to defame a student strike. Up to now, although the authorship of the book has been attributed to several journalists and writers, it could not be demonstrated and remains an open problem. The work aims at establishing which one of the most commonly attributed writers is the real author. To do that, we implement methods based on stylometric features using textual distance, supervised, and unsupervised learning. The distance-based methods implemented in this work are Kilgarriff and Delta of Burrows, an SVM algorithm is used as the supervised method, and the k-means algorithm as the unsupervised algorithm. The applied methods were consistent by pointing out a single author as the most likely one.

Каждая латеральная полоса является ядром положительного ортогонально аддитивного оператора

{In this paper we continue a study of relationships between the lateral partial order $\sqsubseteq$ in a vector lattice (the relation $x \sqsubseteq y$ means that $x$ is a fragment of $y$) and the theory of orthogonally additive operators on vector lattices. It was shown in~\cite{pMPP} that the concepts of lateral ideal and lateral band play the same important role in the theory of orthogonally additive operators as ideals and bands play in the theory for linear operators in vector lattices. We show that, for a vector lattice $E$ and a lateral band $G$ of~$E$, there exists a vector lattice~$F$ and a positive, disjointness preserving orthogonally additive operator $T \colon E \to F$ such that ${\rm ker} \, T = G$. As a consequence, we partially resolve the following open problem suggested in \cite{pMPP}: Are there a vector lattice~$E$ and a lateral ideal in $E$ which is not equal to the kernel of any positive orthogonally additive operator $T\colon E\to F$ for any vector lattice $F$?

Guest Column

Algebraic Natural Proofs is a recent framework which formalizes the type of reasoning used for proving most lower bounds on algebraic computational models. This concept is similar to and inspired by the famous natural proofs notion of Razborov and Rudich [RR97] for boolean circuit lower bounds, but, unlike in the boolean case, it is an open problem whether this constitutes a barrier for proving super-polynomial lower bounds for strong models of algebraic computation. From an algebraic-geometric viewpoint, it is also related to basic questions in Geometric Complexity Theory (GCT), and from a meta-complexity theoretic viewpoint, it can be seen as an algebraic version of the MCSP problem. We survey the recent work around this concept which provides some evidence both for and against the existence of an algebraic natural proofs barrier, with an emphasis on the di erent viewpoints and the connections to other areas.

Matchtigs: minimum plain text representation of kmer sets

Kmer-based methods are widely used in bioinformatics, which raises the question of what is the smallest practically usable representation (i.e. plain text) of a set of kmers. We propose a polynomial algorithm computing a minimum such representation (which was previously posed as a potentially NP-hard open problem), as well as an efficient near-minimum greedy heuristic. When compressing genomes of large model organisms, read sets thereof or bacterial pangenomes, with only a minor runtime increase, we decrease the size of the representation by up to 60% over unitigs and 27% over previous work. Additionally, the number of strings is decreased by up to 97% over unitigs and 91% over previous work. Finally we show that a small representation has advantages in downstream applications, as it speeds up queries on the popular kmer indexing tool Bifrost by 1.66x over unitigs and 1.29x over previous work.

Bypassing the Monster: A Faster and Simpler Optimal Algorithm for Contextual Bandits Under Realizability

We consider the general (stochastic) contextual bandit problem under the realizability assumption, that is, the expected reward, as a function of contexts and actions, belongs to a general function class [Formula: see text]. We design a fast and simple algorithm that achieves the statistically optimal regret with only [Formula: see text] calls to an offline regression oracle across all T rounds. The number of oracle calls can be further reduced to [Formula: see text] if T is known in advance. Our results provide the first universal and optimal reduction from contextual bandits to offline regression, solving an important open problem in the contextual bandit literature. A direct consequence of our results is that any advances in offline regression immediately translate to contextual bandits, statistically and computationally. This leads to faster algorithms and improved regret guarantees for broader classes of contextual bandit problems.

A new solution to the Rhoades’ open problem with an application

We give a new solution to the Rhoades’ open problem on the discontinuity at fixed point via the notion of an S-metric. To do this, we develop a new technique by means of the notion of a Zamfirescu mapping. Also, we consider a recent problem called the “fixed-circle problem” and propose a new solution to this problem as an application of our technique.

Higher-spin states of the superstring in an electromagnetic background

Constructing a consistent four-dimensional Lagrangian for charged massive higher-spin fields propagating in an electromagnetic background is an open problem. In 1989, Argyres and Nappi used bosonic open string field theory to construct a Lagrangian for charged massive spin-2 fields in a constant electromagnetic background. In this paper, we use the four-dimensional hybrid formalism for open superstring field theory to construct a supersymmetric Lagrangian for charged massive spin-2 and spin-3/2 fields in a constant electromagnetic background. The hybrid formalism has the advantage over the RNS formalism of manifest $$ \mathcal{N} $$ N = 1 d=4 spacetime supersymmetry so that the spin-2 and spin-3/2 fields are combined into a single superfield and there is no need for picture-changing or spin fields.

A graph operation and its applications in generating orderenergetic and equienergetic graphs

A general graph operation is defined and some of its applications are given in this paper. The adjacency spectrum of any graph generated by this operation is given. A method for generating integral graphs using this operation is discussed. Corresponding to any given graph, we can generate an infinite sequence of pair of equienergetic non-cospectral graphs using this graph operation. Given an orderenergetic graph, it is shown that we can construct two different sequences of orderenergetic graphs. A condition for generating orderenergetic graphs from non-orderenergetic graphs are also derived. This method of constructing connected orderenergetic graphs solves one of the open problem stated in the paper by Akbari et al.(2020).

New Results for Arithmetic –Geometric Mean Inequalities and Singular Values in Matrices

Matrix theory is very popular in different kind of sciences such as engineering, architecture, physics, chemistry, computer science, IT, so on as well as mathematics many theoretical results dealing with the structure of the matrices even this topic seems easy to work. That is why many scientists still consider some open problem in matrix theory. In this paper, generalizations of the arithmetic-geometric mean inequality is presented for singular values related to block matrices. Singular values are also given for sums, products and direct sums of the matrices.

Evaluation of Moisture Diffusion by IR Thermography

It is well known that IRT is among the preferred instruments in the qualitative monitoring of humidity in buildings. The evaporation of water leads to a sink of thermal energy that eventually manifests as a decreasing of the temperature. The imaging and non-contact characteristics of IRT make the monitoring of this temperature decrease particularly easy and effective. Nonetheless, the quantitative extraction of some figures that make the qualitative observation more reliable is still an open problem.