Search

The Automatic Quasi-clique Merger algorithm is a new algorithm adapted from early work published under the name QCM “introduced by Ou and Zhang (JIMO 2007)”. The AQCM algorithm performs hierarchical clustering in any data set for which there is an associated similarity measure quantifying the similarity of any data i and data j. Importantly, the method exhibits two valuable performance properties: (1) the ability to automatically return either a larger or smaller number of clusters depending on the inherent properties of the data rather than on a parameter. (2) the ability to return a very large number of relatively small clusters automatically when such clusters are reasonably well defined in a data set. In this work we present the general idea of a quasi-clique agglomerative approach, provide the full details of the mathematical steps of the AQCM algorithm, and explain some of the motivation behind the new methodology. The main achievement of the new methodology is that the agglomerative process now unfolds adaptively according to the inherent structure unique to a given data set, and this happens without the time-costly parameter adjustment that drove the previous QCM algorithm. For this reason we call the new algorithm automatic. We provide a demonstration of the algorithm’s performance at the task of community detection in a social media network of 22,900 nodes.

This article aims at revisiting, with the aid of simple and neat numerical examples, some of the basic features of macroscopic irreversibility, and, thus, of the mechanical foundation of the second principle of thermodynamics as drawn by Boltzmann. Emphasis will be put on the fact that, in systems characterized by a very large number of degrees of freedom, irreversibility is already manifest at a single-trajectory level for the vast majority of the far-from-equilibrium initial conditions - a property often referred to as typicality. We also discuss the importance of the interaction among the microscopic constituents of the system and the irrelevance of chaos to irreversibility, showing that the same irreversible behaviours can be observed both in chaotic and non-chaotic systems., Comment: 21 pages, 6 figures, accepted for publication in Physica A

A first characterization of the spectral properties of the Apollonian network is presented. Results are based on the numerically evaluated eigenvalue spectra of adjacency matrices for the first nine generations of the network. The main features refer to the presence of several gaps on the eigenvalue axis and a very large number of degenerated eigenvalues. The increase in the degeneracy of a family of eigenvalues is found to obey a very simple empirical relation.

It is known that by performing dense measurement, that is, by repeating the same measurement a very large number of times in a finite time we can preserve and maintain an initial quantum state. We show here the same effect applying even for the case of the quantum coherent states. Moreover, by taking the complete system of (measured system + measuring system) we prove the Zeno effect not only for the measured system, but also for the complete system. That is, we include here, in our optical treatment of the Zeno effect, the relevant equations of the detecting device, so as to show that the general system (of observed system + observing system) demonstrates the same behaviour under dense measurement as it is regularly demonstrated by the observed system. But unlike the case for noncoherent states where the Zeno effect is proved by applying approximate calculations, here we prove this effect rigorously without any approximation whatsoever. We prove it first for the crosscorrelation case where two points are involved: the point source, and the point of observation where a point detector is located. Then we generalize it to the more realistic case of an extended light source emanating light from more than one spot which is detected by more than one detector.

We show that the Multinomial Logit model of bounded rational choice can be derived in the same way as the Gibbs–Boltzmann distribution in statistical physics. In particular, this model describes the behavior of a thermodynamic agent (which is an agent whose utility function depends on a very large number of variables) with respect to a small subset of variables “weakly interacting” with the others. We also show that the same model is obtained if entropic control costs or information costs are introduced, in which case the temperature like parameter can be considered as the price of (negative) entropy.