Topic

# Expression (mathematics)

About: Expression (mathematics) is a(n) research topic. Over the lifetime, 3851 publication(s) have been published within this topic receiving 77505 citation(s). The topic is also known as: mathematical expressions & expressions.

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TL;DR: The results lend empirical support for the validity and reliability of this set of facial expressions as determined by accurate identification of expressions and high intra-participant agreement across two testing sessions, respectively.

Abstract: A set of face stimuli called the NimStim Set of Facial Expressions is described. The goal in creating this set was to provide facial expressions that untrained individuals, characteristic of research participants, would recognize. This set is large in number, multiracial, and available to the scientific community online. The results of psychometric evaluations of these stimuli are presented. The results lend empirical support for the validity and reliability of this set of facial expressions as determined by accurate identification of expressions and high intra-participant agreement across two testing sessions, respectively.

2,692 citations

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IBM

^{1}TL;DR: A new class of computing systems uses the functional programming style both in its programming language and in its state transition rules; these systems have semantics loosely coupled to states—only one state transition occurs per major computation.

Abstract: Conventional programming languages are growing ever more enormous, but not stronger. Inherent defects at the most basic level cause them to be both fat and weak: their primitive word-at-a-time style of programming inherited from their common ancestor—the von Neumann computer, their close coupling of semantics to state transitions, their division of programming into a world of expressions and a world of statements, their inability to effectively use powerful combining forms for building new programs from existing ones, and their lack of useful mathematical properties for reasoning about programs.An alternative functional style of programming is founded on the use of combining forms for creating programs. Functional programs deal with structured data, are often nonrepetitive and nonrecursive, are hierarchically constructed, do not name their arguments, and do not require the complex machinery of procedure declarations to become generally applicable. Combining forms can use high level programs to build still higher level ones in a style not possible in conventional languages.Associated with the functional style of programming is an algebra of programs whose variables range over programs and whose operations are combining forms. This algebra can be used to transform programs and to solve equations whose “unknowns” are programs in much the same way one transforms equations in high school algebra. These transformations are given by algebraic laws and are carried out in the same language in which programs are written. Combining forms are chosen not only for their programming power but also for the power of their associated algebraic laws. General theorems of the algebra give the detailed behavior and termination conditions for large classes of programs.A new class of computing systems uses the functional programming style both in its programming language and in its state transition rules. Unlike von Neumann languages, these systems have semantics loosely coupled to states—only one state transition occurs per major computation.

2,510 citations

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TL;DR: The capability of the human visual system with respect to these problems is discussed, and it is meant to serve as an ultimate goal and a guide for determining recommendations for development of an automatic facial expression analyzer.

Abstract: Humans detect and interpret faces and facial expressions in a scene with little or no effort. Still, development of an automated system that accomplishes this task is rather difficult. There are several related problems: detection of an image segment as a face, extraction of the facial expression information, and classification of the expression (e.g., in emotion categories). A system that performs these operations accurately and in real time would form a big step in achieving a human-like interaction between man and machine. The paper surveys the past work in solving these problems. The capability of the human visual system with respect to these problems is discussed, too. It is meant to serve as an ultimate goal and a guide for determining recommendations for development of an automatic facial expression analyzer.

1,809 citations

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Abstract: We present several new simple and accurate expressions for the DC inductance of square, hexagonal, octagonal, and circular spiral inductors. We evaluate the accuracy of our expressions, as well as several previously published inductance expressions, in two ways: by comparison with three-dimensional field solver predictions and by comparison with our own measurements, and also previously published measurements. Our simple expression matches the field solver inductance values typically within around 3%, about an order of magnitude better than the previously published expressions, which have typical errors ground 20% (or more). Comparison with measured values gives similar results: our expressions (and, indeed, the field solver results) match within around 5%, compared to errors of around 20% for the previously published expressions. (We believe most of the additional errors in the comparison to published measured values is due to the variety of experimental conditions under which the inductance was measured.) Our simple expressions are accurate enough for design and optimization of inductors or of circuits incorporating inductors. Indeed, since inductor tolerance is typically on the order of several percent, "more accurate" expressions are not really needed in practice.

1,346 citations

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TL;DR: This paper is an attempt to formalize in Boolean terms genetic situations, from simple concepts like recessitivity and cis-dominance, to models describing complex control circuits, to describe in compact and unambiguous way, systems which become more and more difficult to describe as their complexity is being unravelled.

Abstract: This paper is an attempt to formalize in Boolean terms genetic situations, from simple concepts like recessitivity and cis-dominance, to models describing complex control circuits.
A primary objective was to provide a language describing in a compact and unambiguous way, systems which become more and more difficult to describe as their complexity is being unravelled. Expression of a gene is given as a binary function of binary variables of three types:
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“genetic” variables, which describe the state (so-called normal, or mutated in various ways) of genes or recognition sites (promoters, operators, terminators, etc….);
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“environmental” variables such as a temperature shift or the presence of a substance above a threshold concentration;
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“internal” variables used for memorizing previous states of the system. Circuit engineers use, for memorization, pairs internal functions (Yt) and variables (yt) such that the value of the variable at time t is the same as that of the associated function at time t — Δt; the value of a variable thus serves as a memory of the value of the associated function in the proceeding period (see Florine, 1964). It was realized during this work that concepts like the expression of a gene and the presence of its product are related to each other essentially in the same way as the internal functions Yt and variables yt.
Tabulation of the logic equations as Veitch matrices greatly helps in reducing the algebraic expressions (and, hence, the corresponding verbal expressions) to their simplest form. But the main interest of the Veitch tabulation of the equations is that it gives a clear and exhaustive view of all the states of the system as predicted by the model. This is especially useful for sequential problems; the matrices show which states are stable ones, and how the system proceeds from state to state. The logic equations can also be wired up for simulation, using appropriate delays between switching on or off an internal function and its memorization variable.
The language proposed is now currently used by the author for clarification of complex models (e.g. in regulation of bacteriophage λ).

898 citations