We consider growing networks with algebraic preferential attachment and address two questions: (1) what is the effect of temporal fluctuations in the number of new links acquired by the network? and (2) what is the network tolerance against random failures and intentional attacks? We find that the fluctuations generally have little effect on the network properties, although they lead to a plate...

Ladies and gentlemen, Today I am going to tell you the story of how a chapter of mathematics has been closed and a new chapter is beginning. Let me begin with some elementary observations. A major purpose of Geometry is to describe and classify geometric structures of interest. We see many such interesting structures in our day to day life. Let us begin with topological structures of a two dime...

Quadratic divergencies which lead to the usual fine–tuning or hierarchy problem are discussed in top condensation models. As in the Standard Model a cancellation of quadratic divergencies is not possible without the boson contributions in the radiative corrections which are absent in lowest order of an 1/Nc-expansion. To deal with the cancellation of quadratic divergencies we propose therefore ...

Theoretical arguments are given in favour of existence of gluonic degrees of freedom at the constituent level. Models for hybrid mesons are discussed, and the predictions are compared with the data on me-son spectroscopy in the light quark sector. It is demonstrated that the q ¯ qg content might be responsible for the properties of some recently found mesonic states.

The set of space-time short-distance structures which can be described through linear operators is limited to a few basic cases. These are continua, lattices and a further short-distance structure which implies an ultraviolet cut-off. Under certain conditions, these cut-off degrees of freedom can reappear as internal degrees of freedom. We review the current status of the classification and pre...

Hundred twenty years after the fundamental work of Poincaré, the statistics of Poincaré recurrences in Hamiltonian systems with a few degrees of freedom is studied by numerical simulations. The obtained results show that in a regime, where the measure of stability islands is significant, the decay of recurrences is characterized by a power law at asymptotically large times. The exponent of this...

Many analyses at the collider utilize the hadronic jets that are the footprints of QCD partons. These are used both to study the QCD processes themselves and increasingly as tools to study other physics, for example top mass reconstruction. However, jets are not fundamental degrees of freedom in the theory, so we need an operational jet definition and reliable methods to calculate their propert...

The canonical model in economics considers people to be rational and self-regarding. However, much evidence challenges this view, raising the question of when "Economic Man" dominates the outcome of social interactions, and when bounded rationality or other-regarding preferences dominate. Here we show that strategic incentives are the key to answering this question. A minority of self-regarding...

This paper did a survey in the area of degrees of freedom (DoF) in wireless network. We give the definitions of degrees of freedom in different areas first. Then we introduce some methods used to determine the degrees of freedom in different scenario. In section IV, we discuss the applications of the degrees of freedom. We state some interesting open questions in the end of this survey.

We show that the density of energy levels of a wide class of finite-dimensional quantum systems tends to a Gaussian distribution as the number of degrees of freedom increases. Our result is based on a variant of the central limit theorem which is especially suited to models whose partition function is explicitly known. In particular, we provide a theoretical explanation of the fact that the lev...