Related papers: A solution manual for Polchinski's "String Theory"
This paper addresses the online exact string matching problem which consists in finding all occurrences of a given pattern p in a text t. It is an extensively studied problem in computer science, mainly due to its direct applications to…
The book gives a detailed exposition of basic concepts and results of a theory of processes. The presentation of theoretical concepts and results is accompanied with illustrations of their application to solving various problems of…
This is the written version of a set of introductory lectures on string theory.
It is shown that the problem of computing the Strahler number of a binary tree given as a term is complete for the circuit complexity class uniform $\mathsf{NC}^1$. For several variants, where the binary tree is given by a pointer structure…
In this book we describe an approach through toric geometry to the following problem: "estimate the number (counted with appropriate multiplicity) of isolated solutions of n polynomial equations in n variables over an algebraically closed…
The aim of the paper is to demonstrate the use of the Galerkin method for some kind of Volterra equations, determininistic and stochastic as well. The paper consists of two parts: the theoretical and numerical one. In the first part we…
This text contains over three hundred specific open questions on various topics in additive combinatorics, each placed in context by reviewing all relevant results. While the primary purpose is to provide an ample supply of problems for…
The problem of finding a center string that is `close' to every given string arises and has many applications in computational biology and coding theory. This problem has two versions: the Closest String problem and the Closest Substring…
Computing the real solutions to a system of polynomial equations is a challenging problem, particularly verifying that all solutions have been computed. We describe an approach that combines numerical algebraic geometry and sums of squares…
Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…
We provide a detailed analysis of the problems and prospects of superstring theory c. 1986, anticipating much of the progress of the decades to follow.
Drummond had proposed four actions for Polchinski-Strominger effective string theories at order $R^{-6}$, where $2\pi R$ is the length of the (closed) string >. In \cite{covariant} it had been shown, based on covariance arguments, that only…
A solution of Problem 184 from the Scottish Book is presented.
These notes are based on lectures given by Michael Green during Part III of the Mathematics Tripos (the Certificate for Advanced Study in Mathematics) in the Spring of 2003. The course provided an introduction to string theory, focussing on…
We present a short survey of the literature on indexing and retrieval of mathematical knowledge, with pointers to 72 papers and tentative taxonomies of both retrieval problems and recurring techniques.
What does it mean today to study a problem from a computational point of view? We focus on parameterized complexity and on Column 16 "Graph Restrictions and Their Effect" of D. S. Johnson's Ongoing guide, where several puzzles were proposed…
String theory is the most promising candidate theory for a unified description of all fundamental forces exist in the nature. It provides a mathematical framework that combine quantum theory with Einstein's general theory of relativity. But…
The paper deals with continuous solutions of a Schilling's problem.
This is an introduction to the physics of D-branes. Topics covered include Polchinski's original calculation, a critical assessment of some duality checks, D-brane scattering, and effective worldvolume actions.
We introduce string2string, an open-source library that offers a comprehensive suite of efficient algorithms for a broad range of string-to-string problems. It includes traditional algorithmic solutions as well as recent advanced neural…