相关论文: The base-e representation of numbers and the power…
Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning…
The normal operation of power system relies on accurate state estimation that faithfully reflects the physical aspects of the electrical power grids. However, recent research shows that carefully synthesized false-data injection attacks can…
In this paper we study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction…
A generic communication model of a boolean network with transmission errors is proposed to explore the power-law scaling of states' evolution in small-world networks. In the model, the power spectrum of the population difference between…
Many complex systems--from social and communication networks to biological networks and the Internet--are thought to exhibit scale-free structure. However, prevailing explanations rely on the constant addition of new nodes, an assumption…
The citation network constituted by the SPIRES data base is investigated empirically. The probability that a given paper in the SPIRES data base has $k$ citations is well described by simple power laws, $P(k) \propto k^{-\alpha}$, with…
We consider a version of D. Price's model for the growth of a bibliographic network, where in each iteration a constant number of citations is randomly allocated according to a weighted combination of accidental (uniformly distributed) and…
In this paper, we consider the problem of distributed inference in tree based networks. In the framework considered in this paper, distributed nodes make a 1-bit local decision regarding a phenomenon before sending it to the fusion center…
Ferrers diagrams are used to visually represent integer partitions. We describe a way to use Ferrers diagrams to uniquely represent integers in terms of their prime factors. This leads to a lower bound on the number of primes less than a…
We introduce a new class of numerical schemes which allow for low regularity approximations to the expectation $ \mathbb{E}(|u_{k}(\tau, v^{\eta})|^2)$, where $u_k$ denotes the $k$-th Fourier coefficient of the solution $u$ of the…
Scale-free networks constitute a fast-developing field that has already provided us with important tools to understand natural and social phenomena. From biological systems to environmental modifications, from quantum fields to high energy…
Complex systems contain a lot of individuals and some interactions between them. The structure of interactions can be modeled to be a network: nodes represent individuals and links to be interaction between two individuals. This paper tries…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
In this short paper, following the most recent advances in complex network theory, a new approach to number theory with potential applications to other fields is proposed. The model by Garcia-Perez, Serrano and Boguna, introduces an…
The approximation of natural numbers subsets has always been one of the fundamental issues in computability theory. Computable approximation, $\Delta_2$-approximation, as well as introducing the generically computable sets have been some…
Rule-based machine translation is more data efficient than the big data-based machine translation approaches, making it appropriate for languages with low bilingual corpus resources -- i.e., minority languages. However, the rule-based…
The problem of extrapolating the series in powers of small variables to the region of large variables is addressed. Such a problem is typical of quantum theory and statistical physics. A method of extrapolation is developed based on…
It has been observed that many complex real-world networks have certain properties, such as a high clustering coefficient, a low diameter, and a power-law degree distribution. A network with a power-law degree distribution is known as…
An important question in representative democracies is how to determine the optimal parliament size of a given country. According to an old conjecture, known as the cubic root law, there is a fairly universal power-law relation, with an…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…