Search results for " math"

A Time-Non-Homogeneous Double-Ended Queue with Failures and Repairs and Its Continuous Approximation

2018

We consider a time-non-homogeneous double-ended queue subject to catastrophes and repairs. The catastrophes occur according to a non-homogeneous Poisson process and lead the system into a state of failure. Instantaneously, the system is put under repair, such that repair time is governed by a time-varying intensity function. We analyze the transient and the asymptotic behavior of the queueing system. Moreover, we derive a heavy-traffic approximation that allows approximating the state of the systems by a time-non-homogeneous Wiener process subject to jumps to a spurious state (due to catastrophes) and random returns to the zero state (due to repairs). Special attention is devoted to the cas…

Single-cell analysis of population context advances RNAi screening at multiple levels

2012

Isogenic cells in culture show strong variability, which arises from dynamic adaptations to the microenvironment of individual cells. Here we study the influence of the cell population context, which determines a single cell's microenvironment, in image‐based RNAi screens. We developed a comprehensive computational approach that employs Bayesian and multivariate methods at the single‐cell level. We applied these methods to 45 RNA interference screens of various sizes, including 7 druggable genome and 2 genome‐wide screens, analysing 17 different mammalian virus infections and four related cell physiological processes. Analysing cell‐based screens at this depth reveals widespread RNAi‐induce…

Hölder regularity for stochastic processes with bounded and measurable increments

2022

We obtain an asymptotic Hölder estimate for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principle or as solutions to discretized PDEs. The result, which is also generalized to functions satisfying Pucci-type inequalities for discrete extremal operators, is a counterpart to the Krylov-Safonov regularity result in PDEs. However, the discrete step size $\varepsilon$ has some crucial effects compared to the PDE setting. The proof combines analytic and probabilistic arguments.

Response-To-Intervention in Finland and the United States: Mathematics Learning Support as an Example

2018

Response to Intervention (RTI) was accepted in the early 2000s as a new framework for identifying learning difficulties (LD) in the U.S. In Finland, a similar multi-tiered framework has existed since 2010. In the present study, these frameworks are presented from the viewpoint of the role of assessment and instruction as expressed in documents that describe the frameworks, as it seems that these two components of RTI are the most disparate between the U.S. and Finland. We present a suggestion for the Finnish framework as an example of support in mathematics learning that incorporates principles of RTI (such as systematized assessment and instruction, cyclic support, and modifiable instructi…

The link of a finitely determined map germ from R 2 to R 2

2010

Let f: (R2, 0) → (R2, 0) be a finitely determined map germ. The link of f is obtained by taking a small enough representative f: U ⊂ R2 → R2 and the intersection of its image with a small enough sphere Sε1 centered at the origin in R2. We will describe the topology of f in terms of the Gauss word associated to its link.

Some Remarks about Product Spaces

2018

Summary This article covers some technical aspects about the product topology which are usually not given much of a thought in mathematics and standard literature like [7] and [6], not even by Bourbaki in [4]. Let {Ti}i∈I be a family of topological spaces. The prebasis of the product space T = ∏ i∈I Ti is defined in [5] as the set of all π −1 i (V) with i ∈ I and V open in Ti . Here it is shown that the basis generated by this prebasis consists exactly of the sets ∏ i∈I Vi with Vi open in Ti and for all but finitely many i ∈ I holds Vi = Ti . Given I = {a} we have T ≅ Ta , given I = {a, b} with a≠ b we have T ≅ Ta ×Tb . Given another family of topological spaces {Si}i∈I such that Si ≅ Ti fo…

A survey on algebraic dilatations

2023

In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and theoretical aspects and the other applications to existing theories.

The Equiangular Compass

2012

Courbes de Bézier quadratiques et nombres complexes massiques

2017

International audience; Les courbes de Bézier quadratiques jouent un rôle fondamental pour la modélisation d'arcs de coniques. L'utili-sation de points massiques permet de modéliser des demi-coniques dans le plan affine euclidien ou des surfaces canal dans l'espace de Minkowski-Lorentz. L'utilisation des nombres complexes permet de simplifier beaucoup de raisonnements en géométrie et de simplifier l'utilisation des transformations affines planes. Dans cet article, nous définissons dans un premier temps les nombres complexes massiques et dans un second temps, nous modéli-sons des arcs de coniques en utilisant des courbes de Bézier rationnelles quadratiques avec des points complexes massiques…

Husserl's Transcendentalization of Mathematical Naturalism

2020

Abstract The paper aims to capture a form of naturalism that can be found “built-in” in phenomenology, namely the idea to take science or mathematics on its own, without postulating extraneous normative “molds” on it. The paper offers a detailed comparison of Penelope Maddy’s naturalism about mathematics and Husserl’s approach to mathematics in Formal and Transcendental Logic (1929). It argues that Maddy’s naturalized methodology is similar to the approach in the first part of the book. However, in the second part Husserl enters into a transcendental clarification of the evidences and presuppositions of the mathematicians’ work, thus “transcendentalizing” his otherwise naturalist approach t…