Related papers: "Fractal Expression" in Chinese Calligraphy
Chinese Spelling Correction (CSC) is a critical task in natural language processing, aimed at detecting and correcting spelling errors in Chinese text. This survey provides a comprehensive overview of CSC, tracing its evolution from…
Automatic analysis for modern Chinese has greatly improved the accuracy of text mining in related fields, but the study of ancient Chinese is still relatively rare. Ancient text division and lexical annotation are important parts of…
Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are…
A RAC-drawing of a graph is a straight-line drawing in which every crossing occurs at a right-angle. We show that deciding whether a graph has a RAC-drawing is as hard as the existential theory of the reals, even if we know that every edge…
The automatic recognition of facial expressions has been an active research topic since the early nineties. There have been several advances in the past few years in terms of face detection and tracking, feature extraction mechanisms and…
We theoretically and numerically demonstrate that completely integrable scattering processes may exhibit fractal transmission fluctuations, due to typical spectral properties of integrable systems. Similar properties also occur with…
The fractional and circular chromatic numbers are the two most studied non-integral refinements of the chromatic number of a graph. Starting from the definition of a coloring base of a graph, which originated in work related to ergodic…
Fractional graph isomorphism is the linear relaxation of an integer programming formulation of graph isomorphism. It preserves some invariants of graphs, like degree sequences and equitable partitions, but it does not preserve others like…
The Liouville theorem states that classical time evolution is an incompressible flow in phase space. We investigate two formulations of classical mechanics in which this property is manifested. First, the traditional Hamilton-Jacobi theory…
This paper summarizes efforts to computationally model two transitions in the evolution of human creativity: its origins about two million years ago, and the 'big bang' of creativity about 50,000 years ago. Using a computational model of…
In this text I present some problems which led to the introduction of special kinds of graphs as tools for studying singular points of algebraic surfaces. I explain how such graphs were first described using words, and how several…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
Despite the extensive amount of scholarly work done on Indian mathematics in the last 200 years, the conditions under which it originated and evolved is still not clear. Often, one reads the ancient texts with the present concepts and…
Fractals and multifractals and their associated scaling laws provide a quantification of the complexity of a variety of scale invariant complex systems. Here, we focus on lattice multifractals which exhibit complex exponents associated with…
Cartesian products of graphs have been studied extensively since the 1960s. They make it possible to decrease the algorithmic complexity of problems by using the factorization of the product. Hypergraphs were introduced as a generalization…
Computation can be considered by taking into account two dimensions: extensional versus intensional, and sequential versus concurrent. Traditionally sequential extensional computation can be captured by the lambda-calculus. However, recent…
This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. In particular, details and many results and references are…
Fractional calculus, in allowing integrals and derivatives of any positive order (the term "fractional" kept only for historical reasons), can be considered a branch of mathematical physics which mainly deals with integro-differential…
While reading ancient texts one has to be cognizant of the assumptions made about the past. One has to ask: Are these assumptions valid? Are we projecting the present views into the past? A case in point is the dating of Vedanga Jyotisa.…
Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral…