相关论文: Derivation of Fitts' law from the Task Dynamics mo…

Fitts' law is a fundamental tool in measuring the capacity of the human motor system. However, it is, by definition, limited to aimed movements toward spatially expanded targets. We revisit its information-theoretic basis with the goal of…

Taking as a hypothesis a form of the labour theory of value, and $without$ $assuming$ $equilibrium$, we derive an equation that yields the profit-rate $\pi$ as a function of time. For a mature economy, $\pi(t)$ reduces to the product of two…

Trajectories in human aimed movements are inherently variable. Using the concept of positional variance profiles, such trajectories are shown to be decomposable into two phases: In a first phase, the variance of the limb position over many…

The article introduces corrections to Zipf's and Heaps' laws based on systematic models of the proportion of hapaxes, i.e., words that occur once. The derivation rests on two assumptions: The first one is the standard urn model which…

The task of text segmentation may be undertaken at many levels in text analysis---paragraphs, sentences, words, or even letters. Here, we focus on a relatively fine scale of segmentation, hypothesizing it to be in accord with a stochastic…

Here we sketch a new derivation of Zipf's law for word frequencies based on optimal coding. The structure of the derivation is reminiscent of Mandelbrot's random typing model but it has multiple advantages over random typing: (1) it starts…

Zipf's law predicts a power-law relationship between word rank and frequency in language communication systems and has been widely reported in a variety of natural language processing applications. However, the emergence of natural language…

A fundamental challenge in the cognitive sciences is discovering the dynamics that govern behaviour. Take the example of spoken language, which is characterised by a highly variable and complex set of physical movements that map onto the…

We investigate the origin of Zipf's law for words in written texts by means of a stochastic dynamical model for text generation. The model incorporates both features related to the general structure of languages and memory effects inherent…

We introduce a logic, called LT, to express properties of transductions, i.e. binary relations from input to output (finite) words. In LT, the input/output dependencies are modelled via an origin function which associates to any position of…

The cause of the speed-accuracy tradeoff (typically quantified via Fitts' Law) is a debated topic of interest in motor neuroscience, and is commonly studied using tools from control theory. Two prominent theories involve the presence of…

We analyse the dynamics of the Warsaw Stock Exchange index WIG at a daily time horizon before and after its well defined local maxima of the cusp-like shape decorated with oscillations. The rising and falling paths of the index peaks can be…

Zipf's law has been found in many human-related fields, including language, where the frequency of a word is persistently found as a power law function of its frequency rank, known as Zipf's law. However, there is much dispute whether it is…

Zipf's law is a hallmark of several complex systems with a modular structure, such as books composed by words or genomes composed by genes. In these component systems, Zipf's law describes the empirical power law distribution of component…

Phonetic production bias is the external force most commonly invoked in computational models of sound change, despite the fact that it is not responsible for all, or even most, sound changes. Furthermore, the existence of production bias…

Language models must capture statistical dependencies between words at timescales ranging from very short to very long. Earlier work has demonstrated that dependencies in natural language tend to decay with distance between words according…

Understanding the properties of response time distributions is a long-standing problem in cognitive science. We provide a tutorial overview of several contemporary models that assume power law scaling is a plausible description of the…

Zipf's law, which states that the probability of an observation is inversely proportional to its rank, has been observed in many domains. While there are models that explain Zipf's law in each of them, those explanations are typically…

Taylor's law describes the fluctuation characteristics underlying a system in which the variance of an event within a time span grows by a power law with respect to the mean. Although Taylor's law has been applied in many natural and social…

Languages across the world exhibit Zipf's law of abbreviation, namely more frequent words tend to be shorter. The generalized version of the law - an inverse relationship between the frequency of a unit and its magnitude - holds also for…