Related papers: Growth Functions, Rates and Classes of String-Base…
The Burrows-Wheeler transform (BWT) is a reversible transform that converts a string $w$ into another string $\mathsf{BWT}(w)$. The size of the run-length encoded BWT (RLBWT) can be interpreted as a measure of repetitiveness in the class of…
We obtain Wiman-Valiron type inequalities for random entire functions and for random analytic functions on the unit disk that improve a classical result of Erd\H{o}s and R\'enyi and recent results of Kuryliak and Skaskiv. Our results are…
These notes are about ridge functions. Recent years have witnessed a flurry of interest in these functions. Ridge functions appear in various fields and under various guises. They appear in fields as diverse as partial differential…
Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…
With the rise of large language models (LLMs) for flexibly processing information as strings, a natural application is regression, specifically by preprocessing string representations into LLM embeddings as downstream features for metric…
There is increasing interest in modeling high-dimensional longitudinal outcomes in applications such as developmental neuroimaging research. Growth curve model offers a useful tool to capture both the mean growth pattern across individuals,…
We consider a general class of preferential attachment schemes evolving by a reinforcement rule with respect to certain sublinear weights. In these schemes, which grow a random network, the sequence of degree distributions is an object of…
Diverse studies in systems neuroscience begin with extended periods of curriculum training known as `shaping' procedures. These involve progressively studying component parts of more complex tasks, and can make the difference between…
We construct entire curves in projective spaces that exhibit frequent hypercyclicity under translations along countably many prescribed directions while maintaining optimal slow growth rates. Furthermore, we establish a fundamental…
We consider the dynamics of a separable Continuous Time Random Walk (CTRW) when the random walker is biased by a velocity field in a uniformly growing domain. Concrete examples for such domains include growing biological cells or lipid…
We present a new semi-external algorithm that builds the Burrows--Wheeler transform variant of Bauer et al. (a.k.a., BCR BWT) in linear expected time. Our method uses compression techniques to reduce computational costs when the input is…
A theory for studying the dynamic scaling properties of branes and relativistic topological defect networks is presented. The theory, based on a relativistic version of the level set method, well-known in other contexts, possesses…
A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on tree like networks, and the network transports the very resource it needs to build itself. Some…
Modeling of growth (or decay) curves arises in many fields such as microbiology, epidemiology, marketing, and econometrics. Parametric forms like Logistic and Gompertz are often used for modeling such monotonic patterns. While useful for…
It has recently been realised that strings with time-dependent tensions exhibit interesting dynamics; in particular, when the tension decreases loops of string can grow and possibly percolate. We extend previous analytic studies of strings…
During grain growth in multiphase system, a convincing understanding on how the evolution kinetics of an individual phase-grains relates to the growth rate of entire microstructure is yet to be achieved. Therefore, in this work, comfortably…
Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we…
We develop a model of string dynamics with back-reaction from both scaling and non-scaling loops taken into account. The evolution of a string network is described by the distribution functions of coherence segments and kinks. We derive two…
We summarize studies of growing lengths in different aging systems. The article is structured as follows. We recall the definition of a number of observables, typically correlations and susceptibilities, that give access to dynamic and…
We revisit previously developed analytic models for defect evolution and adapt them appropriately for the study of semilocal string networks. We thus confirm the expectation (based on numerical simulations) that linear scaling evolution is…