Related papers: Digital Convexity and Combinatorics on Words
Word clouds are a popular tool for visualizing documents, but they are not a good tool for comparing documents, because identical words are not presented consistently across different clouds. We introduce the concept of word storms, a…
Card-based cryptography is a research area to implement cryptographic procedures using a deck of physical cards. In recent years, it has been found to be related to finite group theory and algebraic combinatorics, and is becoming more and…
We consider a class of combinatorial optimization problems that emerge in a variety of domains among which: condensed matter physics, theory of financial risks, error correcting codes in information transmissions, molecular and protein…
A new geometrically-motivated algorithm for nonnegative matrix factorization is developed and applied to the discovery of latent "topics" for text and image "document" corpora. The algorithm is based on robustly finding and clustering…
Semantic word clouds visualize the semantic relatedness between the words of a text by placing pairs of related words close to each other. Formally, the problem of drawing semantic word clouds corresponds to drawing a rectangle contact…
We survey known results and open problems in abelian combinatorics on words. Abelian combinatorics on words is the extension to the commutative setting of the classical theory of combinatorics on words. The extension is based on…
We study the graph on reduced words with edges given by the Coxeter relations for the symmetric group. We define a metric on reduced words for a given permutation, analogous to Coxeter length for permutations, for which the graph becomes…
A language L is suffix-convex if for any words u, v,w, whenever w and uvw are in L, vw is in L as well. Suffix-convex languages include left ideals, suffix-closed languages, and suffix-free languages, which were studied previously. In this…
Our languages are in constant flux driven by external factors such as cultural, societal and technological changes, as well as by only partially understood internal motivations. Words acquire new meanings and lose old senses, new words are…
Online optimization covers problems such as online resource allocation, online bipartite matching, adwords (a central problem in e-commerce and advertising), and adwords with separable concave returns. We analyze the worst case competitive…
There have been many recent advances in the structure and measurement of distributed language models: those that map from words to a vector-space that is rich in information about word choice and composition. This vector-space is the…
Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This…
Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear (abstract affine) functions. The purpose of this paper is to…
This paper develops and analyzes an online distributed proximal-gradient method (DPGM) for time-varying composite convex optimization problems. Each node of the network features a local cost that includes a smooth strongly convex function…
Many words have evolved in meaning as a result of cultural and social change. Understanding such changes is crucial for modelling language and cultural evolution. Low-dimensional embedding methods have shown promise in detecting words'…
Online convex optimization is a sequential prediction framework with the goal to track and adapt to the environment through evaluating proper convex loss functions. We study efficient particle filtering methods from the perspective of such…
Word evolution refers to the changing meanings and associations of words throughout time, as a byproduct of human language evolution. By studying word evolution, we can infer social trends and language constructs over different periods of…
This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical…
We investigate inflection structure of a synthetic language using Latin as an example. We construct a bipartite graph in which one group of vertices correspond to dictionary headwords and the other group to inflected forms encountered in a…
Hybrid computation combines discrete and continuous dynamics in the form of an entangled mixture inherently present both in various natural phenomena, and in applications ranging from control theory to microbiology. The emergent behaviours…