相关论文: Quadratic Term Correction on Heaps' Law

A topological argument is presented concering the structure of semantic space, based on the negative correlation between polysemy and word length. The resulting graph structure is applied to the modeling of free-recall experiments,…

In a recent paper [S. Mandal et al., Phys. Rev. E 88, 022129 (2013)] the nature of spatial correlations of plasticity in hard sphere glasses was addressed both via computer simulations and in experiments. It was found that the…

Quadratic Hawkes (QHawkes) processes have proved effective at reproducing the statistics of price changes, capturing many of the stylised facts of financial markets. Motivated by the recently reported strong occurrence of endogenous…

In a matching paper (arXiv:1207.5027), I proved that Conservation of Size and Information in a discrete token based system is overwhelmingly likely to lead to a power-law component size distribution with respect to the size of its unique…

Recent works have highlighted optimization difficulties faced by gradient descent in training the first and last layers of transformer-based language models, which are overcome by optimizers such as Adam. These works suggest that the…

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…

We consider the high-dimensional heteroscedastic regression model, where the mean and the log variance are modeled as a linear combination of input variables. Existing literature on high-dimensional linear regres- sion models has largely…

We present a simple model of a stock market where a random communication structure between agents gives rise to a heavy tails in the distribution of stock price variations in the form of an exponentially truncated power-law, similar to…

Word embeddings represent language vocabularies as clouds of $d$-dimensional points. We investigate how information is conveyed by the general shape of these clouds, instead of representing the semantic meaning of each token. Specifically,…

Statistical analysis of corpora provides an approach to quantitatively investigate natural languages. This approach has revealed that several power laws consistently emerge across different corpora and languages, suggesting universal…

Quantitative linguistics has provided us with a number of empirical laws that characterise the evolution of languages and competition amongst them. In terms of language usage, one of the most influential results is Zipf's law of word…

Zipf's law is a fundamental paradigm in the statistics of written and spoken natural language as well as in other communication systems. We raise the question of the elementary units for which Zipf's law should hold in the most natural way,…

The one-loop quantum corrections to the free energy associated with scalar field in a higher dimensional static curved space-time is investigated making use of the conformal transformation method. For a space-time with bifurcate horizon,…

Logarithmic oscillations superimposed on a power-law trend appear in the behavior of various complex hierarchical systems. In this paper, we study the logarithmic oscillations of relaxation curves in p-adic diffusion models that are used to…

The quantum properties of a helix-like shaped QCD string are studied in the context of the semi-classical Lund fragmentation model. It is shown how simple quantization rules combined with the causality considerations in the string…

A coercion semantics of a programming language with subtyping is typically defined on typing derivations rather than on typing judgments. To avoid semantic ambiguity, such a semantics is expected to be coherent, i.e., independent of the…

In this article we propose a new and so-called holomorphic deformation scheme for locally convex algebras and Hopf algebras. Essentially we regard converging power series expansion of a deformed product on a locally convex algebra, thus…

Tasks that model the relation between pairs of tokens in a string are a vital part of understanding natural language. Such tasks, in general, require exhaustive pair-wise comparisons of tokens, thus having a quadratic runtime complexity in…

Logarithmic transformation of the data has been recommended by the literature in the case of highly skewed distributions such as those commonly found in information science. The purpose of the transformation is to make the data conform to…

A version of the recent functional inequality between the Hessians of the square root and the logarithm of positive functions is proven in spaces with non-zero curvature.