相关论文: Translating Equality Downwards
We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…
A permutation $\sigma=\sigma_1 \sigma_2 \cdots \sigma_n$ has a descent at $i$ if $\sigma_i>\sigma_{i+1}$. A descent $i$ is called a peak if $i>1$ and $i-1$ is not a descent. The size of the set of all permutations of $n$ with a given…
A notion of balanced pairs in an extriangulated category with a negative first extension is defined in this article. We prove that there exists a bijective correspondence between balanced pairs and proper classes $\xi$ with enough…
The field of machine translation has progressed tremendously in recent years. Even though the translation quality has improved significantly, current systems are still unable to produce uniformly acceptable machine translations for the…
In this paper, we study various classes of partition functions such as those related to the parity of the number of parts, to differences of partition numbers, and to partitions with a repeated smallest part. We establish identities…
We give a general method for proving quantum lower bounds for problems with small range. Namely, we show that, for any symmetric problem defined on functions $f:\{1, ..., N\}\to\{1, ..., M\}$, its polynomial degree is the same for all…
This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…
The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…
In this survey we consider polynomial optimization problems, asking to minimize a polynomial function over a compact semialgebraic set, defined by polynomial inequalities. This models a great variety of (in general, nonlinear nonconvex)…
Recent advancements in machine learning and deep learning have brought algorithmic fairness into sharp focus, illuminating concerns over discriminatory decision making that negatively impacts certain individuals or groups. These concerns…
The contraction is applied to obtaining of integrable systems associated with nonsemisimple algebras. The effect of contraction is splitting off some components from initial system without loss of integrability.
Reconciling the tension between inductive learning and deductive reasoning in first-order relational domains is a longstanding challenge in AI. We study the problem of answering queries in a first-order relational probabilistic logic…
A higher order difference equation may be generally defined in an arbitrary nonempty set S as: \[ f_{n}(x_{n},x_{n-1},...,x_{n-k})=g_{n}(x_{n},x_{n-1},...,x_{n-k}) \] where $f_{n},g_{n} :S^{k+1}\rightarrow S$ are given functions for…
Translated texts exhibit systematic linguistic differences compared to original texts in the same language, and these differences are referred to as translationese. Translationese has effects on various cross-lingual natural language…
We investigate the structure of quantum proof systems by establishing collapse results that reveal simplifications in their complexity landscape. By extending classical theorems such as the Karp-Lipton theorem to quantum settings and…
It is widely claimed that the quantile function is equivariant under increasing transformations. We show by a counterexample that this is not true (even for strictly increasing transformations). However, we show that the quantile function…
In this work, we investigate methods for the challenging task of translating between low-resource language pairs that exhibit some level of similarity. In particular, we consider the utility of transfer learning for translating between…
Gradual semantics with abstract argumentation provide each argument with a score reflecting its acceptability, i.e. how "much" it is attacked by other arguments. Many different gradual semantics have been proposed in the literature, each…
Classical-realistic analysis of entangled systems have lead to retrodiction paradoxes, which ordinarily have been dismissed on the grounds of counter-factuality. Instead, we claim that such paradoxes point to a deeper logical structure…
The concept of a clone is central to many branches of mathematics, such as universal algebra, algebraic logic, and lambda calculus. Abstractly a clone is a category with two objects such that one is a countably infinite power of the other.…