The Supremum Norm of the Discrepancy Function: Recent Results and Connections

A great challenge in the analysis of the discrepancy function D_N is to obtain universal lower bounds on the L-infty norm of D_N in dimensions d \geq 3. It follows from the average case bound of Klaus Roth that the L-infty norm of D_N is at least (log N) ^{(d-1)/2}. It is conjectured that the L-infty bound is significantly larger, but the only definitive result is that of Wolfgang Schmidt in dimension d=2. Partial improvements of the Roth exponent (d-1)/2 in higher dimensions have been established by the authors and Armen Vagharshakyan. We survey these results, the underlying methods, and some of their connections to other subjects in probability, approximation theory, and analysis.Comment: 15 pages, 3 Figures. Reports on talks presented by the authors at the 10th international conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Sydney Australia, February 2011. v2: Comments of the referee are incorporate

Синтез нечетких систем автоматического управления генетическими алгоритмами по векторным критериям в среде MATLAB

Задачи многокритериального параметрического синтеза систем управления сведены к задачам оптимизации векторных целевых функций, решение которых позволяет удержать процесс синтеза систем в допустимой области. Для оптимизации векторных целевых функций систем автоматического управления модифицированы бинарный и непрерывный генетические алгоритмы. Показана эффективность применения модифицированных генетических алгоритмов для синтеза систем управления путем оптимизации векторных целевых функций. Рассмотрение задач синтеза линейных и нечетких ПИД регуляторов показало, что в задаче синтеза нечеткого регулятора определяется вектор переменных параметров большей размерности, а в модели системы управления вместо линейных уравнений применяются нелинейные уравнения с использованием системы нечеткого вывода

Explicit Evidence Systems with Common Knowledge

Justification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting's semantics for the Logic of Proofs LP. We show the soundness, completeness, and finite model property of our multi-agent justification logic with respect to this Kripke-style semantics. We demonstrate that our logic is a conservative extension of Yavorskaya's minimal bimodal explicit evidence logic, which is a two-agent version of LP. We discuss the relationship of our logic to the multi-agent modal logic S4 with common knowledge. Finally, we give a brief analysis of the coordinated attack problem in the newly developed language of our logic

Profil Kreativitas dan Ketrampilan Bekerja Ilmiah pada Konsep Asam, Basa, dan Garam Siswa

This study aims to analyze the creativity and scientific work skills of Grade VII students of SMP Negeri 1 Ampelgading on the concepts of acid, base and salt. This study uses a test method, the determination of the sample is class VII a number of 32 students, creativity from the category of not creative, less creative, creative and very creative respectively at 6.65%; 39.57%; 53.78%; 0.00%. In the analysis of scientific work skills data from the unskilled, less skilled, skilled and highly skilled categories respectively 4.63%; 38.52%; 55.55%; 1.3%. There is a difference in the presentation between students' creativity and scientific work skills

On the Bohr inequality

The Bohr inequality, first introduced by Harald Bohr in 1914, deals with finding the largest radius $r$, $0<r<1$, such that $\sum_{n=0}^\infty |a_n|r^n \leq 1$ holds whenever $|\sum_{n=0}^\infty a_nz^n|\leq 1$ in the unit disk $\mathbb{D}$ of the complex plane. The exact value of this largest radius, known as the \emph{Bohr radius}, has been established to be $1/3.$ This paper surveys recent advances and generalizations on the Bohr inequality. It discusses the Bohr radius for certain power series in $\mathbb{D},$ as well as for analytic functions from $\mathbb{D}$ into particular domains. These domains include the punctured unit disk, the exterior of the closed unit disk, and concave wedge-domains. The analogous Bohr radius is also studied for harmonic and starlike logharmonic mappings in $\mathbb{D}.$ The Bohr phenomenon which is described in terms of the Euclidean distance is further investigated using the spherical chordal metric and the hyperbolic metric. The exposition concludes with a discussion on the $n$-dimensional Bohr radius

Sample-based distance-approximation for subsequence-freeness

In this work, we study the problem of approximating the distance to subsequence-freeness in the sample-based distribution-free model. For a given subsequence (word) $w = w_1 \dots w_k$, a sequence (text) $T = t_1 \dots t_n$ is said to contain $w$ if there exist indices $1 \leq i_1 < \dots < i_k \leq n$ such that $t_{i_{j}} = w_j$ for every $1 \leq j \leq k$. Otherwise, $T$ is $w$-free. Ron and Rosin (ACM TOCT 2022) showed that the number of samples both necessary and sufficient for one-sided error testing of subsequence-freeness in the sample-based distribution-free model is $\Theta(k/\epsilon)$. Denoting by $\Delta(T,w,p)$ the distance of $T$ to $w$-freeness under a distribution $p :[n]\to [0,1]$, we are interested in obtaining an estimate $\widehat{\Delta}$, such that $|\widehat{\Delta} - \Delta(T,w,p)| \leq \delta$ with probability at least $2/3$, for a given distance parameter $\delta$. Our main result is an algorithm whose sample complexity is $\tilde{O}(k^2/\delta^2)$. We first present an algorithm that works when the underlying distribution $p$ is uniform, and then show how it can be modified to work for any (unknown) distribution $p$. We also show that a quadratic dependence on $1/\delta$ is necessary