5,496 research outputs found
Algebraic Connectivity and Degree Sequences of Trees
We investigate the structure of trees that have minimal algebraic
connectivity among all trees with a given degree sequence. We show that such
trees are caterpillars and that the vertex degrees are non-decreasing on every
path on non-pendant vertices starting at the characteristic set of the Fiedler
vector.Comment: 8 page
Spectral Renormalization Group for the Gaussian model and theory on non-spatial networks
We implement the spectral renormalization group on different deterministic
non-spatial networks without translational invariance. We calculate the
thermodynamic critical exponents for the Gaussian model on the Cayley tree and
the diamond lattice, and find that they are functions of the spectral
dimension, . The results are shown to be consistent with those from
exact summation and finite size scaling approaches. At , the lower
critical dimension for the Ising universality class, the Gaussian fixed point
is stable with respect to a perturbation up to second order. However,
on generalized diamond lattices, non-Gaussian fixed points arise for
.Comment: 16 pages, 14 figures, 5 tables. The paper has been extended to
include a interactions and higher spectral dimension
The Conformal Penrose Limit and the Resolution of the pp-curvature Singularities
We consider the exact solutions of the supergravity theories in various
dimensions in which the space-time has the form M_{d} x S^{D-d} where M_{d} is
an Einstein space admitting a conformal Killing vector and S^{D-d} is a sphere
of an appropriate dimension. We show that, if the cosmological constant of
M_{d} is negative and the conformal Killing vector is space-like, then such
solutions will have a conformal Penrose limit: M^{(0)}_{d} x S^{D-d} where
M^{(0)}_{d} is a generalized d-dimensional AdS plane wave. We study the
properties of the limiting solutions and find that M^{(0)}_{d} has 1/4
supersymmetry as well as a Virasoro symmetry. We also describe how the
pp-curvature singularity of M^{(0)}_{d} is resolved in the particular case of
the D6-branes of D=10 type IIA supergravity theory. This distinguished case
provides an interesting generalization of the plane waves in D=11 supergravity
theory and suggests a duality between the SU(2) gauged d=8 supergravity of
Salam and Sezgin on M^{(0)}_{8} and the d=7 ungauged supergravity theory on its
pp-wave boundary.Comment: 20 pages, LaTeX; typos corrected, journal versio
Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations
We study the initial-value problem for a general class of nonlinear nonlocal
coupled wave equations. The problem involves convolution operators with kernel
functions whose Fourier transforms are nonnegative. Some well-known examples of
nonlinear wave equations, such as coupled Boussinesq-type equations arising in
elasticity and in quasi-continuum approximation of dense lattices, follow from
the present model for suitable choices of the kernel functions. We establish
local existence and sufficient conditions for finite time blow-up and as well
as global existence of solutions of the problem.Comment: 11 pages. Minor changes and added reference
Constructing Quantum Logic Gates Using q-Deformed Harmonic Oscillator Algebras
We study two-level q-deformed angular momentum states and us- ing q-deformed
harmonic oscillators, we provide a framework for con- structing qubits and
quantum gates. We also present the construction of some basic quantum gates
including CNOT, SWAP, Toffoli and Fredkin.Comment: Slightly modified version of the accepted manuscrip
Network synchronization: Spectral versus statistical properties
We consider synchronization of weighted networks, possibly with asymmetrical
connections. We show that the synchronizability of the networks cannot be
directly inferred from their statistical properties. Small local changes in the
network structure can sensitively affect the eigenvalues relevant for
synchronization, while the gross statistical network properties remain
essentially unchanged. Consequently, commonly used statistical properties,
including the degree distribution, degree homogeneity, average degree, average
distance, degree correlation, and clustering coefficient, can fail to
characterize the synchronizability of networks
The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials
This paper is concerned with the analysis of the Cauchy problem of a general
class of two-dimensional nonlinear nonlocal wave equations governing anti-plane
shear motions in nonlocal elasticity. The nonlocal nature of the problem is
reflected by a convolution integral in the space variables. The Fourier
transform of the convolution kernel is nonnegative and satisfies a certain
growth condition at infinity. For initial data in Sobolev spaces,
conditions for global existence or finite time blow-up of the solutions of the
Cauchy problem are established.Comment: 15 pages. "Section 6 The Anisotropic Case" added and minor changes.
Accepted for publication in Nonlinearit
Work and Heat Value of Bound Entanglement
Entanglement has recently been recognized as an energy resource which can
outperform classical resources if decoherence is relatively low. Multi-atom
entangled states can mutate irreversibly to so called bound entangled (BE)
states under noise. Resource value of BE states in information applications has
been under critical study and a few cases where they can be useful have been
identified. We explore the energetic value of typical BE states. Maximal work
extraction is determined in terms of ergotropy. Since the BE states are
non-thermal, extracting heat from them is less obvious. We compare single and
repeated interaction schemes to operationally define and harvest heat from BE
states. BE and free entangled (FE) states are compared in terms of their
ergotropy and maximal heat values. Distinct roles of distillability in work and
heat values of FE and BE states are pointed out. Decoherence effects in
dynamics of ergotropy and mutation of FE states into BE states are examined to
clarify significance of the work value of BE states. Thermometry of
distillability of entanglement using micromaser cavity is proposed.Comment: 22 pages, 10 figure
Symmetrized p-convexity and Related Some Integral Inequalities
In this paper, the author introduces the concept of the symmetrized p-convex
function, gives Hermite-Hadamard type inequalities for symmetrized p-convex
functions.Comment: 13 page
An Adaptive Locally Connected Neuron Model: Focusing Neuron
This paper presents a new artificial neuron model capable of learning its
receptive field in the topological domain of inputs. The model provides
adaptive and differentiable local connectivity (plasticity) applicable to any
domain. It requires no other tool than the backpropagation algorithm to learn
its parameters which control the receptive field locations and apertures. This
research explores whether this ability makes the neuron focus on informative
inputs and yields any advantage over fully connected neurons. The experiments
include tests of focusing neuron networks of one or two hidden layers on
synthetic and well-known image recognition data sets. The results demonstrated
that the focusing neurons can move their receptive fields towards more
informative inputs. In the simple two-hidden layer networks, the focusing
layers outperformed the dense layers in the classification of the 2D spatial
data sets. Moreover, the focusing networks performed better than the dense
networks even when 70 of the weights were pruned. The tests on
convolutional networks revealed that using focusing layers instead of dense
layers for the classification of convolutional features may work better in some
data sets.Comment: 45 pages, a national patent filed, submitted to Turkish Patent
Office, No: -2017/17601, Date: 09.11.201
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