Related papers: The Capacity of Some P\'olya String Models

Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a…

Cells are known to utilize biochemical noise to probabilistically switch between distinct gene expression states. We demonstrate that such noise-driven switching is dominated by tails of probability distributions and is therefore…

In this paper the Penna model is reconsidered. With computer simulations we check how the control parameters of the model influence the size of the stable population.

We develop a general method to explore how the function performed by a biological network can constrain both its structural and dynamical network properties. This approach is orthogonal to prior studies which examine the functional…

We study the spectral density of factor models of multivariate time series. By making use of the Random Matrix Theory we analytically quantify the effect of noise dressing on the spectral density due to the finiteness of the sample. We…

Detecting and measuring repetitiveness of strings is a problem that has been extensively studied in data compression and text indexing. However, when the data are structured in a non-linear way, like in the context of two-dimensional…

We initiate a study of a new model of property testing that is a hybrid of testing properties of distributions and testing properties of strings. Specifically, the new model refers to testing properties of distributions, but these are…

Complex networks theory has commonly been used for modelling and understanding the interactions taking place between the elements composing complex systems. More recently, the use of generative models has gained momentum, as they allow…

We introduce a new model of random tree that grows like a random recursive tree, except at some exceptional "doubling events" when the tree is replaced by two copies of itself attached to a new root. We prove asymptotic results for the size…

Splicing systems are generative mechanisms introduced by Tom Head in 1987 to model the biological process of DNA recombination. The computational engine of a splicing system is the "splicing operation", a cut-and-paste binary string…

Due to the redundant nature of DNA synthesis and sequencing technologies, a basic model for a DNA storage system is a multi-draw "shuffling-sampling" channel. In this model, a random number of noisy copies of each sequence is observed at…

The strong coupling limit of a quantum system is in general quite complicated, but in some cases a great simplification occurs: the strongly coupled limit is equivalent to the weakly coupled limit of some other system. In string theory…

The memory consistency model is a fundamental system property characterizing a multiprocessor. The relative merits of strict versus relaxed memory models have been widely debated in terms of their impact on performance, hardware complexity…

Recent investigations involving the decay of unstable D-branes in string theory suggest that the tree level open string theory which describes the dynamics of the D-brane already knows about the closed string states produced in the decay of…

Deep neural networks (DNN) are the state of the art on many engineering problems such as computer vision and audition. A key factor in the success of the DNN is scalability - bigger networks work better. However, the reason for this…

We study the amount of reliable information that can be stored in a DNA-based storage system composed of short DNA molecules. In this regime, Shomorony and Heckel (2022) put forward a conjecture on the scaling of the number of information…

Boolean formulae compactly encode huge, constrained search spaces. Thus, variability-intensive systems are often encoded with Boolean formulae. The search space of a variability-intensive system is usually too large to explore without…

We introduce and analyse an individual-based evolutionary model, in which a population of genetically diverse organisms compete with each other for limited resources. Through theoretical analysis and stochastic simulations, we show that the…

Beta-binomial/Poisson models have been used by many authors to model multivariate count data. Lora and Singer (Statistics in Medicine, 2008) extended such models to accommodate repeated multivariate count data with overdipersion in the…

A brief review of the status of duality symmetries in string theory is presented. The evidence is accumulating rapidly that an enormous group of duality symmetries, including perturbative T dualities and non-perturbative S-dualities,…