We study the large-scale topological and dynamical properties of real Internet maps at the autonomous system level, collected in a 3-yr time interval. We find that the connectivity structure of the Internet presents statistical distributions settled in a well-defined stationary state. The large-scale properties are characterized by a scale-free topology consistent with previous observations. Co...

We present a simple explanation for the occurrence of power-law tails in statistical distributions by showing that if stochastic processes with exponential growth in expectation are killed (or observed) randomly, the distribution of the killed or observed state exhibits power-law behavior in one or both tails. This simple mechanism can explain power-law tails in the distributions of the sizes o...

The methods of Maximum Entropy have been deployed for some years to address the problem of species abundance distributions. In this approach, it is important to identify the correct weighting factors, or priors, to be applied before maximising the entropy function subject to constraints. The forms of such priors depend not only on the exact problem but can also depend on the way it is set up; p...

We consider the statistical distribution of zeros of random meromorphic functions whose poles are independent random variables. It is demonstrated that correlation functions of these zeros can be computed analytically, and explicit calculations are performed for the two-point correlation function. This problem naturally appears in, e.g., rank-1 perturbation of an integrable Hamiltonian and, in ...

In this paper we consider a location model based on the threshold concept. We find the best location such that the probability of revenues falling short of the threshold is minimized. This objective is appropriate when a firm will not survive if its revenues fall below a known threshold. A new store is to be located. Demand is not deterministic but rather has a statistical distribution. We seek...

A theory is presented that establishes a dominance hierarchy of potential distinctions (order relations) between two distributions. It is proposed that it is worthwhile for researchers to ascertain the strongest possible distinction, because all weaker distinctions are logically implied. Implications of the theory for hypothesis testing, theory construction, and scales of measurement are consid...

There is considerable variation in the prosodic phrasing of speech between different speakers and speech styles. Due to the time and cost of obtaining large quantities of data to train a model for every variation, it is desirable to develop models that can be adapted to new conditions with a limited amount of training data. We describe a technique for adapting HMMbased phrase boundary predictio...

Our native language has a lifelong effect on how we perceive speech sounds. Behaviorally, this is manifested as categorical perception, but the neural mechanisms underlying this phenomenon are still unknown. Here, we constructed a computational model of categorical perception, following principles consistent with infant speech learning. A self-organizing network was exposed to a statistical dis...

It is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of many physical, natural, and social events (earthquake size, species abundance, income and wealth, as well as file, city, and firm sizes) display this structure. We present a test for the occurrence of power-law tails ...

We analyzed the statistical distribution of intra-specific local abundances for a set North American breeding bird species. We constructed frequency plots for every species and found that they showed long-tail power-law behavior, truncated at an upper abundance cut-off value. Based on finite size scaling arguments, we investigated whether frequency curves may be considered scaled copies of each...