Related papers: What is Cost?
This summarizes the study of the financial and economic crisis in Europe. The starting questions were: 1) Why do we have a crisis? Unde venis? 2) What will be the outcome? Quo vadis? Here is the reasoning which touches many areas, ranging…
(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable permutations with a word problem which is a universal…
We look at equivalence relations on the set of models of a theory -- MERs, for short -- such that the class of equivalent pairs is itself an elementary class, in a language appropriate for pairs of models. We provide many examples of…
This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems…
We investigate computability in the lattice of equivalence relations on the natural numbers. We mostly investigate whether the subsets of appropriately defined subrecursive equivalence relations -for example the set of all polynomial-time…
This document is both a synthesis of current notions about complex systems, and a practical approach description. A disambiguation is proposed and exposes possible reasons for controversies related to causation and emergence. Theoretical…
Mutual information is commonly used as a measure of similarity between competing labelings of a given set of objects, for example to quantify performance in classification and community detection tasks. As argued recently, however, the…
These are the notes from my courses on the arithmetic of quadratic forms.
We present a methodology combining surface NLP and Machine Learning techniques for ranking asbtracts and generating summaries based on annotated corpora. The corpora were annotated with meta-semantic tags indicating the category of…
Academic publishers claim that they add value to scholarly communications by coordinating reviews and contributing and enhancing text during publication. These contributions come at a considerable cost: U.S. academic libraries paid $1.7…
This chapter is divided into two parts. The first part is a survey of some recent results on nests and the orderability problem. The second part consists of results, partial results and open questions, all viewed in the light of nests. From…
These notes form an introduction to Lie algebras and group theory. Most of the material can be found in many works by various authors given in the list of references. The reader is referred to such works for more detail.
The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…
We aim to renew interest in a particular multi-document summarization (MDS) task which we call AgreeSum: agreement-oriented multi-document summarization. Given a cluster of articles, the goal is to provide abstractive summaries that…
This note studies the existence of quotients by finite set theoretic equivalence relations. May 18: Substantial revisions with a new appendix by C. Raicu
This is an introduction to The Theme Issue on "Free Boundary Problems and Related Topics", which consists of 14 survey/review articles on the topics, of Philosophical Transactions of the Royal Society A: Physical, Mathematical and…
This is a survey article on classical groups (over arbitrary division rings) and their geometries.
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
There are a number of papers dedicated to the description of free particles and antiparticles with zero mass and spin 1/2. A great many equations with different C, P, T properties have been proposed and the impression could be formed that…
In this paper we have investigated enumeration orders of elements of r.e. sets enumerated by means of Turing machines. We have defined a reducibility based on enumeration orders named "Enumeration Order Reducibility" on computable functions…