536 research outputs found
Some results on the Krein parameters of an association scheme
We consider association schemes with d classes and the underlying Bose-
Mesner algebra, A. Then, by taking into account the relationship between the
Hadamard and the Kronecker products of matrices and making use of some matrix
techniques over the idempotents of the unique basis of minimal orthogonal idempotents
of A , we prove some results over the Krein parameters of an association
scheme
Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations
Excerpt: Mathematics is a language which can describe patterns in everyday life as well as abstract concepts existing only in our minds. Patterns exist in data, functions, and sets constructed around a common theme, but the most tangible patterns are visual. Visual demonstrations can help undergraduate students connect to abstract concepts in advanced mathematical courses. The study of partial differential equations, in particular, benefits from numerical analysis and simulation
A Statistical Mechanical Problem in Schwarzschild Spacetime
We use Fermi coordinates to calculate the canonical partition function for an
ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the
validity of the results we prove theorems for limiting cases. We recover the
Newtonian gas law subject only to tidal forces in the Newtonian limit.
Additionally we recover the special relativistic gas law as the radius of the
orbit increases to infinity. We also discuss how the method can be extended to
the non ideal gas case.Comment: Corrected an equation misprint, added four references, and brief
comments on the system's center of mass and the thermodynamic limi
Gaussian quantum marginal problem
The quantum marginal problem asks what local spectra are consistent with a
given spectrum of a joint state of a composite quantum system. This setting,
also referred to as the question of the compatibility of local spectra, has
several applications in quantum information theory. Here, we introduce the
analogue of this statement for Gaussian states for any number of modes, and
solve it in generality, for pure and mixed states, both concerning necessary
and sufficient conditions. Formally, our result can be viewed as an analogue of
the Sing-Thompson Theorem (respectively Horn's Lemma), characterizing the
relationship between main diagonal elements and singular values of a complex
matrix: We find necessary and sufficient conditions for vectors (d1, ..., dn)
and (c1, ..., cn) to be the symplectic eigenvalues and symplectic main diagonal
elements of a strictly positive real matrix, respectively. More physically
speaking, this result determines what local temperatures or entropies are
consistent with a pure or mixed Gaussian state of several modes. We find that
this result implies a solution to the problem of sharing of entanglement in
pure Gaussian states and allows for estimating the global entropy of
non-Gaussian states based on local measurements. Implications to the actual
preparation of multi-mode continuous-variable entangled states are discussed.
We compare the findings with the marginal problem for qubits, the solution of
which for pure states has a strikingly similar and in fact simple form.Comment: 18 pages, 1 figure, material added, references updated, except from
figure identical with version to appear in Commun. Math. Phy
D-Theory: Field Theory via Dimensional Reduction of Discrete Variables
A new non-perturbative approach to quantum field theory --- D-theory --- is
proposed, in which continuous classical fields are replaced by discrete
quantized variables which undergo dimensional reduction. The 2-d classical O(3)
model emerges from the (2+1)-d quantum Heisenberg model formulated in terms of
quantum spins. Dimensional reduction is demonstrated explicitly by simulating
correlation lengths up to 350,000 lattice spacings using a loop cluster
algorithm. In the framework of D-theory, gauge theories are formulated in terms
of quantum links --- the gauge analogs of quantum spins. Quantum links are
parallel transporter matrices whose elements are non-commuting operators. They
can be expressed as bilinears of anticommuting fermion constituents. In quantum
link models dimensional reduction to four dimensions occurs, due to the
presence of a 5-d Coulomb phase, whose existence is confirmed by detailed
simulations using standard lattice gauge theory. Using Shamir's variant of
Kaplan's fermion proposal, in quantum link QCD quarks appear as edge states of
a 5-d slab. This naturally protects their chiral symmetries without
fine-tuning. The first efficient cluster algorithm for a gauge theory with a
continuous gauge group is formulated for the U(1) quantum link model. Improved
estimators for Wilson loops are constructed, and dimensional reduction to
ordinary lattice QED is verified numerically.Comment: 15 pages, LaTeX, including 9 encapsulated postscript figures.
Contribution to Lattice 97 by 5 authors, to appear in Nuclear Physics B
(Proceeding Supplements). Requires psfig.tex and espcrc2.st
Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises
Dynamics of an ensemble of -unit FitzHugh-Nagumo (FN) neurons subject to
white noises has been studied by using a semi-analytical dynamical mean-field
(DMF) theory in which the original -dimensional {\it stochastic}
differential equations are replaced by 8-dimensional {\it deterministic}
differential equations expressed in terms of moments of local and global
variables. Our DMF theory, which assumes weak noises and the Gaussian
distribution of state variables, goes beyond weak couplings among constituent
neurons. By using the expression for the firing probability due to an applied
single spike, we have discussed effects of noises, synaptic couplings and the
size of the ensemble on the spike timing precision, which is shown to be
improved by increasing the size of the neuron ensemble, even when there are no
couplings among neurons. When the coupling is introduced, neurons in ensembles
respond to an input spike with a partial synchronization. DMF theory is
extended to a large cluster which can be divided into multiple sub-clusters
according to their functions. A model calculation has shown that when the noise
intensity is moderate, the spike propagation with a fairly precise timing is
possible among noisy sub-clusters with feed-forward couplings, as in the
synfire chain. Results calculated by our DMF theory are nicely compared to
those obtained by direct simulations. A comparison of DMF theory with the
conventional moment method is also discussed.Comment: 29 pages, 2 figures; augmented the text and added Appendice
An allele-selective inter-chromosomal protein bridge supports monogenic antigen expression in the African trypanosome
UPF1-like helicases play roles in telomeric heterochromatin formation and X-chromosome inactivation, and also in monogenic variant surface glycoprotein (VSG) expression via VSG exclusion-factor-2 (VEX2), a UPF1-related protein in the African trypanosome. We show that VEX2 associates with chromatin specifically at the single active VSG expression site on chromosome 6, forming an allele-selective connection, via VEX1, to the trans-splicing locus on chromosome 9, physically bridging two chromosomes and the VSG transcription and splicing compartments. We further show that the VEX-complex is multimeric and self-regulates turnover to tightly control its abundance. Using single cell transcriptomics following VEX2-depletion, we observed simultaneous derepression of many other telomeric VSGs and multi-allelic VSG expression in individual cells. Thus, an allele-selective, inter-chromosomal, and self-limiting VEX1-2 bridge supports monogenic VSG expression and multi-allelic VSG exclusion
Light-cone QCD Sum Rules for the Baryon Electromagnetic Form Factors and its magnetic moment
We present the light-cone QCD sum rules up to twist 6 for the electromagnetic
form factors of the baryon. To estimate the magnetic moment of the
baryon, the magnetic form factor is fitted by the dipole formula. The numerical
value of our estimation is , which is in
accordance with the experimental data and the existing theoretical results. We
find that it is twist 4 but not the leading twist distribution amplitudes that
dominate the results.Comment: 13 page, 7 figures, accepted for publication in Euro. Phys. J.
Photoproduction of pions and properties of baryon resonances from a Bonn-Gatchina partial wave analysis
Masses, widths and photocouplings of baryon resonances are determined in a
coupled-channel partial wave analysis of a large variety of data. The
Bonn-Gatchina partial wave formalism is extended to include a decomposition of
t- and u-exchange amplitudes into individual partial waves. The multipole
transition amplitudes for and are
given and compared to results from other analyses.Comment: 18 pages, 14 figure
P-wave excited baryons from pion- and photo-induced hyperon production
We report evidence for , , ,
, , and , and find
indications that might have a companion state at 1970\,MeV. The
controversial is not seen. The evidence is derived from a
study of data on pion- and photo-induced hyperon production, but other data are
included as well. Most of the resonances reported here were found in the
Karlsruhe-Helsinki (KH84) and the Carnegie-Mellon (CM) analyses but were
challenged recently by the Data Analysis Center at GWU. Our analysis is
constrained by the energy independent scattering amplitudes from either
KH84 or GWU. The two amplitudes from KH84 or GWU, respectively, lead to
slightly different branching ratios of contributing resonances but the
debated resonances are required in both series of fits.Comment: 22 pages, 28 figures. Some additional sets of data are adde
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