Related papers: The Main Problem of Block Theory: Picky Elements a…

We use the theory of blocks of cyclic defect to prove that under a certain condition on the principal p-block of a finite group G the normalized unit group of the integral group ring of G contains an element of order pq if and only if so…

We prove, for primes $p\ge5$, two inequalities between the fundamental invariants of Brauer $p$-blocks of finite quasi-simple groups: the number of characters in the block, the number of modular characters, the number of height zero…

(Block-)coordinate minimization is an iterative optimization method which in every iteration finds a global minimum of the objective over a variable or a subset of variables, while keeping the remaining variables constant. While for some…

We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive…

Block spin renormalization group is the main tool used in our program to see symmetry breaking in a weakly interacting many Boson system on a three dimensional lattice at low temperature. In this paper, we discuss some of its purely…

We present first-order perturbation analysis of a simple eigenvalue and the corresponding right and left eigenvectors of a general square matrix, not assumed to be Hermitian or normal. The eigenvalue result is well known to a broad…

Stanley decompositions are used in invariant theory and the theory of normal forms for dynamical systems to provide a unique way of writing each invariant as a polynomial in the Hilbert basis elements. Since the required Stanley…

Conventional particle theories such as the Standard Model have a number of freely adjustable coupling constants and mass parameters, depending on the symmetry algebra of the local gauge group and the representations chosen for the spinor…

If a finite group $A$ acts coprimely as automorphisms on a finite group $G$, then the $A$-invariant Brauer $p$-blocks of $G$ are exactly those that contain $A$-invariant irreducible characters.

We attempt to generalize the $p$-modular representation theory of finite groups to finite transporter categories, which are regarded as generalized groups. We shall carry on our tasks through modules of transporter category algebras, a type…

Minimal linear codes are algebraic objects which gained interest in the last twenty years, due to their link with Massey's secret sharing schemes. In this context, Ashikhmin and Barg provided a useful and a quite easy to handle sufficient…

Blocking semiovals and the determination of their (minimum) sizes constitute one of the central research topics in finite projective geometry. In this article we introduce the concept of blocking set with the $r_\infty$-property in a finite…

Let $k$ be an algebraically closed field of characteristic $p$, and let $\mathcal{O}$ be either $k$ or its ring of Witt vectors $W(k)$. Let $G$ a finite group and $B$ a block of $\mathcal{O}G$ with normal abelian defect group and abelian…

We develop a mathematical framework to address a broad class of metric and preference learning problems within a Hilbert space. We obtain a novel representer theorem for the simultaneous task of metric and preference learning. Our key…

In this note we give applications of recent results coming mostly from the third paper of this series. It is shown that the number of irreducible characters in a $p$-block of a finite group with abelian defect group $D$ is bounded by $|D|$…

We define the block neighborhood of a reversible CA, which is related both to its decomposition into a product of block permutations and to quantum computing. We give a purely combinatorial characterization of the block neighborhood, which…

The stochastic block model is able to generate different network partitions, ranging from traditional assortative communities to disassortative structures. Since the degree-corrected stochastic block model does not specify which mixing…

What property of the data distribution determines the excess risk of principal component analysis? In this paper, we provide a precise answer to this question. We establish a central limit theorem for the error of the principal subspace…

Conjecture A of \cite{EM14} predicts the equality between the smallest positive height of the irreducible characters in a $p$-block of a finite group and the smallest positive height of the irreducible characters in its defect group. Hence,…

In this article, we investigate different parsimony-based approaches towards finding recombination breakpoints in a multiple sequence alignment. This recombination detection task is crucial in order to avoid errors in evolutionary analyses…