相关论文: Why most papers on filters are really trivial (inc…

A working mathematician's summary of many results on the derived category, perverse sheaves, and vanishing cycles. This is the August 2025 version, with a completely revised section on vanishing cycles.

The goal of this communication is to propose a generalized notion of the "traditional derivative". This generalization includes the fractional derivatives such as the Riemann-Liouville, Gruenwald-Letnikov, Weyl, Riesz, Caputo, Marchaud…

We introduce and characterize various gluing constructions for residuated lattices that intersect on a common subreduct, and which are subalgebras, or appropriate subreducts, of the resulting structure. Starting from the 1-sum construction…

The aim of this paper is to study the characteristics of a general method to produce a new approximation sequence from a given one, by using suitable convex combinations.

We survey the known results about simple permutations. In particular, we present a number of recent enumerative and structural results pertaining to simple permutations, and show how simple permutations play an important role in the study…

A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…

The paper discusses the role of interpretations, understood as multifunctions that preserve and reflect logical consequence, as refinement witnesses in the general setting of pi-institutions. This leads to a smooth generalization of the…

We explore partitions that lie in the intersection of several sets of classical interest: partitions with parts indivisible by $m$, appearing fewer than $m$ times, or differing by less than $m$. We find results on their behavior and…

This is a short note with some (very elementary) remarks concerning realization theory and the choice of inputs for identifying systems. Its goal is to bring some of these facts to the attention of the systems biology community.

We give a generalized version of the Freyd conjecture and a way to think about a possible proof. The essential point is to describe an elementary formal reduction of the question that holds in any triangulated category. There are no new…

Recursive filters are treated as linear time-invariant (LTI) systems but they are not: uninitialised, they have an infinite number of outputs for any given input, while if initialised, they are not time-invariant. This short tutorial…

In this article, we introduce the notion of $\mathcal P$-triviality of topological manifolds and give a complete description of the $\mathcal P$-triviality of stunted real and complex projective spaces.

Let $X_{\bullet}$ denote a simplicial space. The purpose of this note is to record a decomposition of the suspension of the individual spaces $X_n$ occurring in $X_{\bullet}$ in case the spaces $X_n$ satisfy certain mild topological…

It is well-known that Choice and Regularity are independent of each other but have important common consequences of logical character (reflection principles, representations of classes by sets, etc.). We explain this phenomenon by isolating…

Increasing number of filters in deeper layers when feature maps are decreased is a widely adopted pattern in convolutional network design. It can be found in classical CNN architectures and in automatic discovered models. Even CNS methods…

As science advances, the academic community has published millions of research papers. Researchers devote time and effort to search relevant manuscripts when writing a paper or simply to keep up with current research. In this paper, we…

The particle filter is a powerful framework for estimating hidden states in dynamic systems where uncertainty, noise, and nonlinearity dominate. This mini-book offers a clear and structured introduction to the core ideas behind particle…

The main purpose of this paper is twofold. We first want to analyze in details the meaningful geometric aspect of the method introduced in the previous paper [12], concerning regularity of families of irreducible, nodal "curves" on a…

We compare two notions of $G$-fiber bundles and $G$-principal bundles in the literature, with an aim to clarify early results in equivariant bundle theory that are needed in current work of equivariant algebraic topology. We also give…

We make the simple, and yet deep, observation that a regular conditional distribution (rcd) almost surely trivialises the conditioning $\sigma$-algebra if and only if there exists a "measurable selection" of regular conditional…