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Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations
, 2005
"... 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 hea ..."
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Cited by 534 (48 self)
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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 outdegree distributions, communities, smallworld 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.
New Evidence and Possible Explanations
, 2011
"... own. The Widening Academic Achievement Gap Between the Rich and the Poor: ..."
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own. The Widening Academic Achievement Gap Between the Rich and the Poor:
recapitulation and possible explanation of the phenomenon
, 2004
"... Induction of hyperammonia in irradiated hepatoma cells: a ..."
Paradox of Choice: A Possible Explanation
"... 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, the mo ..."
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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
1 Possible Explanation for the Quantum Entanglement
"... 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 of ener ..."
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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
A Possible Explanation for the Vacuum Catastrophe
, 2014
"... The discrepancy of 120 orders of magnitude between the observed energy density of the vacuum and that predicted from manipulations of quantum assumptions has been considered as the “worst prediction in physics”. By employing abbreviated quantum “natural units ” the predicted density is 2.9 × 10120 g ..."
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The discrepancy of 120 orders of magnitude between the observed energy density of the vacuum and that predicted from manipulations of quantum assumptions has been considered as the “worst prediction in physics”. By employing abbreviated quantum “natural units ” the predicted density is 2.9 × 10120 greater than the ~10−9 J/m3 estimated by current measurements. However a comparable order of magnitude discrepancy for energy, 6 × 10120, emerges when the total calculated force within the universe is distributed across its width. The energy density within the vacuum should be ~10111 J/m3. Because the emergence of the total force value required the square of the cut off frequency for Zero Point Fluctuations, the discrepancy could be considered as an artifact of temporal sampling, that is, the implicit temporal increments from which the estimates were derived. The identity of the predicted vacuum energy density from counting modes and energy density from quantum theory and that obtained from Newtonian Force applied across the universe could be a considered example of ∑n = n, which is one condition for a holographic state.
A Possible Explanation of the Superposition Principle
, 2002
"... 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 complexvalued logarithms. This notion is inspired by the fact that the quantum state may be interpreted as a ..."
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Cited by 1 (0 self)
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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 complexvalued logarithms. This notion is inspired by the fact that the quantum state may be interpreted as a
A Possible Explanation of the CP Puzzle
, 2008
"... The problem of mirrorreflection symmetry (MRS) and timereversal symmetry (TRS) in our world is discussed. The opinion is expressed, that wellknown experiments on parity violation and CPviolation can be treated as signals of some new, yet unknown, level of matter. An hypothesis, which can be used ..."
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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 CPviolation do not contradict MRS or TRS conservation. The hypothesis of possible parity violation was suggested in 1956 by Lee and Yang [1
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