相关论文: Information-theoretic View of Sequence Organizatio…

We present a general approach to the problem of determining the asymptotic order of the variance of the optimal score between two independent random sequences defined over an arbitrary finite alphabet. Our general approach is based on…

Collective temporal organization in complex systems is commonly attributed to synchronization, resonance, or proximity to dynamical instabilities. Here we identify a distinct mechanism by which coherent, synchronization-like behavior can…

We study the role of finiteness and fluctuations about average quantities for basic structural properties of growing networks. We first determine the exact degree distribution of finite networks by generating function approaches. The…

The Dissertation is focused on the studies of associations between functional elements in human genome and their nucleotide structure. The asymmetry in nucleotide content (skew, bias) was chosen as the main feature for nucleotide structure.…

We study how the recurrence and transience of space-time sets for a branching random walk on a graph depends on the offspring distribution. Here, we say that a space-time set $A$ is recurrent if it is visited infinitely often almost surely…

Life uses non-equilibrium mechanisms to create ordered structures not attainable at equilibrium; the resulting order is assumed to provide functional benefits that outweigh costs of time and energy needed by these mechanisms. Here, we show…

The third-generation long reads sequencing technologies, such as PacBio and Nanopore, have great advantages over second-generation Illumina sequencing in de novo assembly studies. However, due to the inherent low base accuracy,…

Biological organisms are open, adaptve systems that can respond to changes in environment in specific ways. Adaptation and response can be posed as an optimization problem, with a tradeoff between the benefit obtained from a response and…

The orientational ordering transition is investigated in the quantum generalization of the anisotropic-planar-rotor model in the low temperature regime. The phase diagram of the model is first analyzed within the mean-field approximation.…

Background. The large-scale pattern of distribution of genes on the chromosomes in the known animal genomes is not well characterized. We hypothesized that individual genes will be distributed on chromosomes in a mathematically ordered…

We give a new explanation for why some biological systems can stay quantum coherent for long times at room temperatures, one of the fundamental puzzles of quantum biology. We show that systems with the right level of complexity between…

Extracting higher-order structures from multivariate data has become an area of intensive study in complex systems science, as these multipartite interactions can reveal insights into fundamental features of complex systems like emergent…

Every k entries in a permutation can have one of k! different relative orders, called patterns. How many times does each pattern occur in a large random permutation of size n? The distribution of this k!-dimensional vector of pattern…

We consider a branching population where individuals live and reproduce independently. Their lifetimes are i.i.d. and they give birth at a constant rate b. The genealogical tree spanned by this process is called a splitting tree, and the…

This work develops tools to understand how quantum information spreads, scrambles, and is reshaped by measurements in many-body systems. First, I study scrambling and pseudorandomness in the Brownian Sachdev-Ye-Kitaev (SYK) model,…

In the context of the genome rearrangement problem, we analyze two well known models, namely the block transposition and the prefix block transposition models, by exploiting the connection with the notion of permutation pattern. More…

Composition schemes are ubiquitous in combinatorics, statistical mechanics and probability theory. We give a unifying explanation to various phenomena observed in the combinatorial and statistical physics literature in the context…

Rumor and information spreading are natural processes that emerge from human-to-human interaction. Mathematically, this was explored in the popular Maki-Thompson model, where a phase transition was thought to be absent. Here, we show that a…

In molecular phylogeny, relationships among organisms are reconstructed using DNA or protein sequences and are displayed as trees. A linear increase in the number of sequences results in an exponential increase of possible trees. Thus,…

We develop techniques to analyse the statistics of completion times of non-deterministic elements in quantum entanglement generation, and how they affect the overall performance as measured by the secret key rate. By considering such…