Character (mathematics)

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

The Rate of Change of a Character Correlated with Fitness

Abstract: An extended form of Fisher's Fundamental Theorem of Natural Selection gives the rate of change of the mean value, [Formula: see text], of a measured character. For a character determined by multiple alleles at two loci, this is [Formula: see text] where the Newtonian superior dot means the time derivative and the circle is the time derivative of the logarithm. Covg (m, γ) is the genic (additive genetic) covariance of the character and fitness. Specifically, it is the covariance of the average excess of an allele for fitness and its average effect on the character. [Formula: see text] is the average rate of change of the value of the character for individual genotypes, weighted by their frequencies. The value could be nonzero because of changing environments or change in the age distribution of the population. The third term on the right is the average over all pairs of alleles at both loci of the product of the dominance deviation and the rate of change of ln θ(n), where θ(n) is a measure of departure from random proportions. The last term is a similar expression for epistatic interactions. If selection is much weaker than recombination, after several generations, the last two terms are much smaller than the first. When the measured character is fitness, our result reduces to Kimura's generalization of Fisher's Fundamental Theorem of Natural Selection.

Method and apparatus for preparing customized reading material

Abstract: A presentation of textual material is provided in a “role-play” reading format which has text corresponding to the dialogue of a plurality of characters in order to facilitate reading aloud in a group. The text for the dialogue of a plurality of characters is presented in a different indicia throughout substantially all the presentation. Preferably the indicia is color so the dialogue for each character is in a different color. The text for each character is also selected and presented at a level corresponding to the reading level of the reader selecting or assigned to read each character. The text is preferably selected from among a plurality of texts pre-written at substantially different reading levels. The reading material can be presented on paper, or on media suitable for display on an electronic screen. The text for each character is in a size and font suitable for the reading level of the reader selecting or assigned to read the dialogue for the character. A legend on each page of the reading material correlates the identity of each reader with the character or characters selected or assigned to be read by each reader, and with the indicia applied to the dialogue for each character.

Tracking representationalism and the painfulness of pain

Abstract: When you look at the red mug on the desk in front of you, you have an experience with a distinctive phenomenal character. In virtue of what does your experience have this phenomenal character? A popular answer to this question is that given by representationalism, the thesis (at a minimum) that the phenomenal character of an experience supervenes on its representational content. According to representationalism, your experience of the red mug on your desk has its distinctive phenomenal character in virtue of the way it represents the world as being-i.e., in virtue of its representational content.

Representation Theory of the W1+∞ Algebra

Abstract: We review the recent development in the representation theory of the $W_{1+\infty}$ algebra. The topics that we concern are, Quasifinite representation, Free field realizations, (Super) Matrix Generalization, Structure of subalgebras such as $W_\infty$ algebra, Determinant formula, Character formula. (Invited talk at ``Quantum Field Theory, Integrable Models and Beyond", YITP, 14-17 February 1994. To appear in Progress of Theoretical Physics Proceedings Supplement.)

Virtual keyboard input for international languages

Abstract: In one example, a computing device includes at least one processor configured to output for display, a graphical keyboard. The at least one processor may also be configured to model, in a first lattice, a plurality of candidate character strings that include symbols of a first alphabet. The first lattice may indicate spatial probabilities of the plurality of candidate character strings. The at least one processor may be configured to determine, using a second lattice that indicates probabilities of one or more words of a second language based at least in part on the spatial probabilities of the plurality of candidate character strings, a probability that the at least one of the plurality of candidate character strings corresponds to at least one word included in the second language. The at least one processor may be configured to output for display, the one or more symbols representing at least one word.