Character (mathematics)

About: Character (mathematics) is a research topic. Over the lifetime, 46723 publications have been published within this topic receiving 411412 citations.

Character input apparatus and method and computer readable storage medium

Abstract: A character input apparatus, includes a detection unit configured to detect coordinate data of handwriting, a handwriting display unit configured to sequentially display styled handwriting obtained by styling the handwriting during handwriting operation in accordance with a designated text style and the coordinate data, a recognition unit configured to recognize a character corresponding to the handwriting, and a character display unit configured to display a styled character obtained by styling the recognized character in accordance with the text style and the coordinate data.

What size test set gives good error rate estimates

Abstract: We address the problem of determining what size test set guarantees statistically significant results in a character recognition task, as a function of the expected error rate. We provide a statistical analysis showing that if, for example, the expected character error rate is around 1 percent, then, with a test set of at least 10,000 statistically independent handwritten characters (which could be obtained by taking 100 characters from each of 100 different writers), we guarantee, with 95 percent confidence, that: (1) the expected value of the character error rate is not worse than 1.25 E, where E is the empirical character error rate of the best recognizer, calculated on the test set; and (2) a difference of 0.3 E between the error rates of two recognizers is significant. We developed this framework with character recognition applications in mind, but it applies as well to speech recognition and to other pattern recognition problems.

Hidden Markov Model Based Handwriting/Calligraphy Generation

Abstract: An exemplary method for handwritten character generation includes receiving one or more characters and, for the one or more received characters, generating handwritten characters using Hidden Markov Models trained for generating handwritten characters. In such a method the trained Hidden Markov Models can be adapted using a technique such as a maximum a posterior technique, a maximum likelihood linear regression technique or an Eigen-space technique.

Generalized kazakov-migdal-kontsevich model: group theory aspects

Abstract: The Kazakov-Migdal model, if considered as a functional of external fields, can always be represented as an expansion over characters of the GL group The integration over “matter fields” can be interpreted as going over the model (the space of all highest weight representations) of GL In the case of compact unitary groups the integrals should be substituted by discrete sums over the weight lattice The D=0 version of the model is the generalized Kontsevich integral, which in the above-mentioned unitary (discrete) situation coincides with the partition function of 2D Yang-Mills theory with the target space of genus g=0 and m=0, 1, 2 holes This particular quantity is always a bilinear combination of characters and appears to be a Toda lattice τ function (This is a generalization of the classical statement that individual GL characters are always singular KP τ functions) The corresponding element of the universal Grassmannian is very simple and somewhat similar to the one arising in investigations of the c=1 string models However, in certain circumstances the formal sum over representations should be evaluated by the steepest descent method, and this procedure leads to some more-complicated elements of the Grassmannian This “Kontsevich phase,” as opposed to the simple “character phase,” deserves further investigation