xER: An Explainable Model for Entity Resolution using an Efficient Solution for the Clique Partitioning Problem

In this paper, we propose a global, self- explainable solution to solve a prominent NLP problem: Entity Resolution (ER). We formu- late ER as a graph partitioning problem. Every mention of a real-world entity is represented by a node in the graph, and the pairwise sim- ilarity scores between the mentions are used to associate these nodes to exactly one clique, which represents a real-world entity in the ER domain. In this paper, we use Clique Partition- ing Problem (CPP), which is an Integer Pro- gram (IP) to formulate ER as a graph partition- ing problem and then highlight the explainable nature of this method. Since CPP is NP-Hard, we introduce an efficient solution procedure, the xER algorithm, to solve CPP as a combi- nation of finding maximal cliques in the graph and then performing generalized set packing using a novel formulation. We discuss the advantages of using xER over the traditional methods and provide the computational exper- iments and results of applying this method to ER data sets.

Gender Bias in Natural Language Processing Across Human Languages

Natural Language Processing (NLP) systems are at the heart of many critical automated decision-making systems making crucial recommendations about our future world. Gender bias in NLP has been well studied in English, but has been less studied in other languages. In this paper, a team including speakers of 9 languages - Chinese, Spanish, English, Arabic, German, French, Farsi, Urdu, and Wolof - reports and analyzes measurements of gender bias in the Wikipedia corpora for these 9 languages. We develop extensions to profession-level and corpus-level gender bias metric calculations originally designed for English and apply them to 8 other languages, including languages that have grammatically gendered nouns including different feminine, masculine, and neuter profession words. We discuss future work that would benefit immensely from a computational linguistics perspective.

حل بعض مسائل التحليل الرياضي باستخدام أنواع من الزمر

يرتبط الإطار الرياضي لميكانيك الكم ارتباطاً وثيقاً بما يصفه علماء الرياضيات بنظريةتمثيل الزمر , درسنا في بحثنا هذا هذه الفكرة ببعض التفصيل

Using Schur rings to find the automorphism group of Cayley graph of order p.q where p ¹ q are prime numbers

In this paper we determine the automorphism group of Cayley graph over the group where p ¹ q are prime numbers, by building the corresponding Schur ring which is generated by Q , and determine the automorphism group of this ring which is the automorphism group of this graph.

الأغلفة الخطية الأربعة المتقاطعة بأربعة مستقيمات

في هذا العمل دراسة تناظر السطوح الجبرية اللامتغيرة بالنسبة لزمرة التناظرات التامة وغير المنتيهة G في الفضاء الإقليدي Em

on some properties of Lie groups and Fuzzy Lie groups for solution some of problems

The aim of this paper is to use some properties of Lie groups and fuzzy Lie groups in many statements to prove on some open problems, so we can prove on the lemma(1) and (2).

On some of properties of Lie groups and Fuzzy Lie groups

Our aim of this paper is to study some properties of Lie groups and fuzzy Lie groups in many statements. So we can determine some properties of Lie groups and we prove on its by the Topological spaces constructing on the Lie groups as the Zero- dimensional space and connected space. In fuzzy Lie groups, we can also get some results and we prove on its in this paper.

A study in the resolution of singularity on a field with characteristic ≠ 2

Singularities in general are considered to be one of the important issues in algebraic geometry and applied mathematics, among them the ADE or simple singularities which drew attention since they have appeared separately in various areas of scientific applications. The name comes from three graphs characterized by letters A, D and E denoting types of Lie groups. Arnold stated them in a direct manner. Many people gave studies about the subject like Roczen.M who presented the canonical resolution in dimension 3 and Char ≠ 2. giving an equivalent non-singular variety is what meant by resolution, Canonical resolution adds a description of the exceptional loci.

On the inverse limit of finite dimensional lie algebras

We extend the well Known Levi-Malcev decomposition theorem of finite dimensional Lie algebras to the case of pro-finite dimensional Lie algebras L = limLn (n ∈ N). We also prove that every finite dimensional homomorphic image of the Cartesian product of finite dimensional nilpotent Lie algebras is also nilpotent.

New Properties for Inductive Isomorphisms of Groups

تتضمن الورقة العلمية نتائج مهمة تتكون من خواص جديدة للتماثلات الاستقرائية للزمر. وتتجلى الخواص الرئيسة الجديدة في نصوص كل من المبرهنة ( 6) و المبرهنة (7) و النتيجة (8) التي تم إثبات صحتها في هذا البحث، حيث تمت الإجابة عن أسئلة مفتوحة حول الجداء نصف المباشر و حول التماثل و حول مشتق الزمرة كخواص للتماثل الاستقرائي لزمرتين.