How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include heavy tails for in- and out-degree distributions, communities, small-world phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time. Here we study a wide range of real graphs, and we observe some surprising phenomena. First, most of these graphs densify over time, with the number of edges growing superlinearly in the number of nodes. Second, the average distance between nodes often shrinks over time, in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes (like O(log n) orO(log(log n)). Existing graph generation models do not exhibit these types of behavior, even at a qualitative level. We provide a new graph generator, based on a “forest fire” spreading process, that has a simple, intuitive justification, requires very few parameters (like the “flammability” of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study.

own. The Widening Academic Achievement Gap Between the Rich and the Poor:

Induction of hyperammonia in irradiated hepatoma cells: a

I n s t i t u t e: Sub-station,

Evidence from positional augmentation

At rst glance, we would expect that the more choices we have, the happier we will be. Experiments show, however, then when the number of choices increases, customers become less happy. In this paper, we provide a possible explanation for this paradox. 1 Formulation of the Problem Intuitively

Quantum entanglement of pair of particles is now an established fact as described in [1]. But its theoretical explanation is yet to be found. So this letter attempts to propose one possible explanation, based on this author‟s previous works. In a paper titled: “Some conjectures on the nature

ABSTRACT: I tentatively suggest that the superposition principle of quantum mechanics is explicable in a mathematically natural way if it is possible to understand probability amplitudes as complex-valued logarithms. This notion is inspired by the fact that the quantum state may be interpreted as a

be used as a base for some future model or theory is formulated. In the framework of this hypothesis, experiments which demonstrate parity violation or CP-violation do not contradict MRS or TRS conservation. The hypothesis of possible parity violation was suggested in 1956 by Lee and Yang [1

of measurements as a function of n is observed instead of a single peak. The positions of the peaks are not random and the patterns depend on position and time varying periodically in time scales possibly assignable to Earth-Sun and Earth-Moon gravitational interaction. These observations suggest a modification