218,798 research outputs found
Extraordinary variability and sharp transitions in a maximally frustrated dynamic network
Using Monte Carlo and analytic techniques, we study a minimal dynamic network
involving two populations of nodes, characterized by different preferred
degrees. Reminiscent of introverts and extroverts in a population, one set of
nodes, labeled \textit{introverts} (), prefers fewer contacts (a lower
degree) than the other, labeled \textit{extroverts} (). As a starting point,
we consider an \textit{extreme} case, in which an simply cuts one of its
links at random when chosen for updating, while an adds a link to a random
unconnected individual (node). The model has only two control parameters,
namely, the number of nodes in each group, and ). In the steady
state, only the number of crosslinks between the two groups fluctuates, with
remarkable properties: Its average () remains very close to 0 for all
or near its maximum () if
. At the transition (), the fraction
wanders across a substantial part of , much like a pure random walk.
Mapping this system to an Ising model with spin-flip dynamics and unusual
long-range interactions, we note that such fluctuations are far greater than
those displayed in either first or second order transitions of the latter.
Thus, we refer to the case here as an `extraordinary transition.' Thanks to the
restoration of detailed balance and the existence of a `Hamiltonian,' several
qualitative aspects of these remarkable phenomena can be understood
analytically.Comment: 6 pages, 3 figures, accepted for publication in EP
Quantum Kaleidoscopes and Bell's theorem
A quantum kaleidoscope is defined as a set of observables, or states,
consisting of many different subsets that provide closely related proofs of the
Bell-Kochen-Specker (BKS) and Bell nonlocality theorems. The kaleidoscopes
prove the BKS theorem through a simple parity argument, which also doubles as a
proof of Bell's nonlocality theorem if use is made of the right sort of
entanglement. Three closely related kaleidoscopes are introduced and discussed
in this paper: a 15-observable kaleidoscope, a 24-state kaleidoscope and a
60-state kaleidoscope. The close relationship of these kaleidoscopes to a
configuration of 12 points and 16 lines known as Reye's configuration is
pointed out. The "rotations" needed to make each kaleidoscope yield all its
apparitions are laid out. The 60-state kaleidoscope, whose underlying
geometrical structure is that of ten interlinked Reye's configurations
(together with their duals), possesses a total of 1120 apparitions that provide
proofs of the two Bell theorems. Some applications of these kaleidoscopes to
problems in quantum tomography and quantum state estimation are discussed.Comment: Two new references (No. 21 and 22) to related work have been adde
Extreme Thouless effect in a minimal model of dynamic social networks
In common descriptions of phase transitions, first order transitions are
characterized by discontinuous jumps in the order parameter and normal
fluctuations, while second order transitions are associated with no jumps and
anomalous fluctuations. Outside this paradigm are systems exhibiting `mixed
order transitions' displaying a mixture of these characteristics. When the jump
is maximal and the fluctuations range over the entire range of allowed values,
the behavior has been coined an `extreme Thouless effect'. Here, we report
findings of such a phenomenon, in the context of dynamic, social networks.
Defined by minimal rules of evolution, it describes a population of extreme
introverts and extroverts, who prefer to have contacts with, respectively, no
one or everyone. From the dynamics, we derive an exact distribution of
microstates in the stationary state. With only two control parameters,
(the number of each subgroup), we study collective variables of
interest, e.g., , the total number of - links and the degree
distributions. Using simulations and mean-field theory, we provide evidence
that this system displays an extreme Thouless effect. Specifically, the
fraction jumps from to (in the
thermodynamic limit) when crosses , while all values appear with
equal probability at .Comment: arXiv admin note: substantial text overlap with arXiv:1408.542
Bounding the Greedy Strategy in Finite-Horizon String Optimization
We consider an optimization problem where the decision variable is a string
of bounded length. For some time there has been an interest in bounding the
performance of the greedy strategy for this problem. Here, we provide weakened
sufficient conditions for the greedy strategy to be bounded by a factor of
, where is the optimization horizon length. Specifically, we
introduce the notions of -submodularity and -GO-concavity, which together
are sufficient for this bound to hold. By introducing a notion of
\emph{curvature} , we prove an even tighter bound with the factor
. Finally, we illustrate the strength of our results by
considering two example applications. We show that our results provide weaker
conditions on parameter values in these applications than in previous results.Comment: This paper has been accepted by 2015 IEEE CD
Two-stage Turing model for generating pigment patterns on the leopard and the jaguar
Based on the results of phylogenetic analysis, which showed that flecks are the primitive pattern of the felid family and all other patterns including rosettes and blotches develop from it, we construct a Turing reaction-diffusion model which generates spot patterns initially. Starting from this spotted pattern, we successfully generate patterns of adult leopards and jaguars by tuning parameters of the model in the subsequent phase of patterning
Oscillatory Turing Patterns in a Simple Reaction-Diffusion System
Turing suggested that, under certain conditions, chemicals can react and diffuse in such a way as to produce steady-state inhomogeneous spatial patterns of chemical concentrations. We consider a simple two-variable reaction-diffusion system and find there is a spatio-temporally oscillating solution (STOS) in parameter regions where linear analysis predicts a pure Turing instability and no Hopf instability. We compute the boundary of the STOS and spatially non-uniform solution (SSNS) regions and investigate what features control its behavior
Critical point of QCD from lattice simulations in the canonical ensemble
A canonical ensemble algorithm is employed to study the phase diagram of QCD using lattice simulations. We lock in the desired quark number sector
using an exact Fourier transform of the fermion determinant. We scan the phase
space below and look for an S-shape structure in the chemical potential,
which signals the coexistence phase of a first order phase transition in finite
volume. Applying Maxwell construction, we determine the boundaries of the
coexistence phase at three temperatures and extrapolate them to locate the
critical point. Using an improved gauge action and improved Wilson fermions on
lattices with a spatial extent of 1.8 \fm and quark masses close to that of
the strange, we find the critical point at and baryon
chemical potential .Comment: 5 pages, 7 figures, references added, published versio
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