scholarly journals The Witness Set Constraint

2016 ◽  
pp. ffw009
Author(s):  
Jordi Fortuny
Keyword(s):  
Witness Set

On the role of Ramsey quantifiers in first order arithmetic

1982 ◽  
Vol 47 (2) ◽  
pp. 423-435 ◽  
Author(s):  
James H. Schmerl ◽  
Stephen G. Simpson
Keyword(s):  
Formal System ◽  
Intended Meaning ◽  
Completeness Proof ◽  
First Order ◽  
Uncountable Cardinal ◽  
Consistent Extension ◽  
Witness Set ◽  
Order Arithmetic ◽  
Infinite Set

The purpose of this paper is to study a formal system PA(Q2) of first order Peano arithmetic, PA, augmented by a Ramsey quantifier Q2 which binds two free variables. The intended meaning of Q2xx′φ(x, x′) is that there exists an infinite set X of natural numbers such that φ(a, a′) holds for all a, a′ Є X such that a ≠ a′. Such an X is called a witness set for Q2xx′φ(x, x′). Our results would not be affected by the addition of further Ramsey quantifiers Q3, Q4, …, Here of course the intended meaning of Qkx1 … xkφ(x1,…xk) is that there exists an infinite set X such that φ(a1…, ak) holds for all k-element subsets {a1, … ak} of X.Ramsey quantifiers were first introduced in a general model theoretic setting by Magidor and Malitz [13]. The system PA{Q2), or rather, a system essentially equivalent to it, was first defined and studied by Macintyre [12]. Some of Macintyre's results were obtained independently by Morgenstern [15]. The present paper is essentially self-contained, but all of our results have been directly inspired by those of Macintyre [12].After some preliminaries in §1, we begin in §2 by giving a new completeness proof for PA(Q2). A by-product of our proof is that for every regular uncountable cardinal k, every consistent extension of PA(Q2) has a k-like model in which all classes are definable. (By a class we mean a subset of the universe of the model, every initial segment of which is finite in the sense of the model.)

Numerical irreducible decomposition over a number field

2018 ◽  
Vol 17 (10) ◽  
pp. 1850195
Author(s):  
Timothy M. McCoy ◽  
Chris Peterson ◽  
Andrew J. Sommese
Keyword(s):  
Algebraic Geometry ◽  
Number Field ◽  
Polynomial System ◽  
Field Extension ◽  
General Point ◽  
Numerical Algebraic Geometry ◽  
Irreducible Decomposition ◽  
Algebraic Set ◽  
Field Of Definition ◽  
Witness Set

Let [Formula: see text] be a set of elements in the polynomial ring [Formula: see text], let [Formula: see text] denote the ideal generated by the elements of [Formula: see text], and let [Formula: see text] denote the radical of [Formula: see text]. There is a unique decomposition [Formula: see text] with each [Formula: see text] a prime ideal corresponding to a minimal associated prime of [Formula: see text] over [Formula: see text]. Let [Formula: see text] denote the reduced algebraic set corresponding to the common zeroes of the elements of [Formula: see text]. Techniques from numerical algebraic geometry can be used to determine the numerical irreducible decomposition of [Formula: see text] over [Formula: see text]. This corresponds to producing a witness set for [Formula: see text] for each [Formula: see text] together with the degree and dimension of [Formula: see text] (a point in a witness set for [Formula: see text] can be considered as a numerical approximation for a general point on [Formula: see text]). The purpose of this paper is to show how to extend these results taking into account the field of definition for the polynomial system. In particular, let [Formula: see text] be a number field (i.e. a finite field extension of [Formula: see text]) and let [Formula: see text] be a set of elements in [Formula: see text]. We show how to extend techniques from numerical algebraic geometry to determine the numerical irreducible decomposition of [Formula: see text] over [Formula: see text].

A Stochastic Algorithm Based on Reverse Sampling Technique to Fight Against the Cyberbullying

2021 ◽  
Vol 15 (4) ◽  
pp. 1-22
Author(s):  
Ruidong Yan ◽  
Yi Li ◽  
Deying Li ◽  
Yongcai Wang ◽  
Yuqing Zhu ◽  
...  
Keyword(s):  
Sampling Technique ◽  
Stochastic Approach ◽  
Positive Influence ◽  
Constant Factor ◽  
Stochastic Algorithm ◽  
Optimal Value ◽  
Target Set ◽  
Witness Set ◽  
The Relationship ◽  
Np Hardness

Cyberbullying has caused serious consequences especially for social network users in recent years. However, the challenge is how to fight against the cyberbullying effectively from the algorithmic perspective. In this article, we study the fighting against the cyberbullying problem, i.e., identify an initial witness set with a budget to spread the positive influence to protect the users in a specific target set such that the number of cybervictim users in the target set being activated by the seed set of cyberbullying is minimized. We first formulate this problem and show its NP-hardness. We further prove that the objective function is submodular with respect to the size of witnesses set when we convert the original problem into the maximal version. Then we propose a stochastic approach to solve this maximal version problem based on the Reverse Sampling Technique with a constant factor guarantee. In addition, we provide theoretical analysis and discuss the relationship between the optimal value and the value returned by the proposed algorithm. To evaluate the proposed approach, we implement extensive experiments on synthetic and real datasets. The experimental results show our approach is superior to the comparison methods.

In Defense of a Quantificational Account of Definite DPs

2006 ◽  
Vol 37 (2) ◽  
pp. 275-288 ◽  
Author(s):  
Daniela Isac
Keyword(s):  
Weak Crossover ◽  
Narrow Scope ◽  
Crossover Effects ◽  
Witness Set

Two types of arguments support a quantificational view of definite DPs. First, definite DPs share properties with other quantified expressions. In particular, they pattern together in antecedent-contained deletion constructions, they show weak crossover effects, and at least some of them interact scopally with other quantified expressions. Second, the apparent failure of (some) definite DPs to interact scopally with other quantified expressions and to exhibit island effects stems from two properties of definite DPs: they are all principal filters, and the witness set of singular definite DPs is a singleton. These two properties have the effect of rendering the wide and narrow scope readings of definite DPs indistinguishable.

scholarly journals The socio-rhetorical force of ‘truth talk’ and lies: The case of 1 John

2011 ◽  
Vol 67 (1) ◽  
Author(s):  
Dietmar Neufeld
Keyword(s):  
New Testament ◽  
Gospel Of John ◽  
Communal Identity ◽  
The New Testament ◽  
1 John ◽  
Truth Claims ◽  
Witness Set ◽  
Roman Antiquity ◽  
Rhetorical Force

This article canvassed Greek and Roman sources for discussions concerning truth talk and lies. It has investigated what social historians and/or anthropologists are saying about truth talking and lying and has developed a model that will examine the issue of truth and lying in socio-religious terms as defined by the Graeco-Roman sources. The article tracked down the socio-rhetorical force of truth talk and lies, in terms of how they are strategically deployed to negotiate authority, to exert epistemic control, to define a personal and communal identity and to defend innovation in the midst of competing truth claims. It focused on the New Testament writing (1 John) and demonstrated that the author, in his desire to establish and defend his vision of truth, resorts to a style of truth talk endemic to the literary habits of Graeco-Roman antiquity. In so doing, the author established himself as a credible witness, set himself apart from those propounding falsehoods and, to some extent, distanced himself from the vision of truth propounded in the Gospel of John.

scholarly journals The Witness Set Constraint

2017 ◽  
Vol 34 (2) ◽  
pp. e2-e2 ◽  
Author(s):  
Jordi Fortuny
Keyword(s):  
Witness Set

scholarly journals GUARDING ART GALLERIES BY GUARDING WITNESSES

2006 ◽  
Vol 16 (02n03) ◽  
pp. 205-226 ◽  
Author(s):  
KYUNG-YONG CHWA ◽  
BYUNG-CHEOL JO ◽  
CHRISTIAN KNAUER ◽  
ESTHER MOET ◽  
RENÉ VAN OOSTRUM ◽  
...  
Keyword(s):  
Minimum Size ◽  
Art Galleries ◽  
Witness Set ◽  
Set Of Points ◽  
Time Bounds

Let P be a polygon, possibly with holes. We define a witness set W to be a set of points in P such that if any (prospective) guard set G guards W, then it is guaranteed that G guards P. Not all polygons admit a finite witness set. If a finite minimal witness set exists, then it cannot contain any witness in the interior of P, all witnesses must lie on the boundary of P, and there can be at most one witness in the interior of every edge. We give an algorithm to compute a minimum size witness set for P in O(n2 log n) time, if such a set exists, or to report the non-existence within the same time bounds. We also outline two algorithms that use a witness set for P to test whether a (prospective) guard set sees all points in P.

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