16,126 research outputs found
Parametrizations of canonical bases and irreducible components of nilpotent varieties
It is known that the set of irreducible components of nilpotent varieties
provides a geometric realization of the crystal basis for quantum groups. For
each reduced expression of a Weyl group element, Gei{\ss}, Leclerc and
Schr\"{o}er has recently given a parametrization of irreducible components of
nilpotent varieties in studying cluster algebras. In this paper we show that
their parametrization coincides with Lusztig's parametrization of the canonical
basis.Comment: revised version, 11 page
A note on the Moment of Complex Wiener-Ito Integrals
For a sequence of complex Wiener-Ito multiple integrals, the equivalence
between the convergence of the symmetrized contraction norms and that of the
non-symmetrized contraction norms is shown directly by means of a new version
of complex Mallivian calculus using the Wirtinger derivatives of complex-valued
functions.Comment: 8 page
Does the time horizon of the return predictive effect of investor sentiment vary with stock characteristics? A Granger causality analysis in the frequency domain
Behavioral theories posit that investor sentiment exhibits predictive power
for stock returns, whereas there is little study have investigated the
relationship between the time horizon of the predictive effect of investor
sentiment and the firm characteristics. To this end, by using a Granger
causality analysis in the frequency domain proposed by Lemmens et al. (2008),
this paper examine whether the time horizon of the predictive effect of
investor sentiment on the U.S. returns of stocks vary with different firm
characteristics (e.g., firm size (Size), book-to-market equity (B/M) rate,
operating profitability (OP) and investment (Inv)). The empirical results
indicate that investor sentiment has a long-term (more than 12 months) or
short-term (less than 12 months) predictive effect on stock returns with
different firm characteristics. Specifically, the investor sentiment has strong
predictability in the stock returns for smaller Size stocks, lower B/M stocks
and lower OP stocks, both in the short term and long term, but only has a
short-term predictability for higher quantile ones. The investor sentiment
merely has predictability for the returns of smaller Inv stocks in the short
term, but has a strong short-term and long-term predictability for larger Inv
stocks. These results have important implications for the investors for the
planning of the short and the long run stock investment strategy
An insight into the description of the crystal structure for Mirkovi\'c-Vilonen polytopes
We study the description of the crystal structure on the set of
Mirkovi\'c-Vilonen polytopes. Anderson and Mirkovi\'c defined an operator and
conjectured that it coincides with the Kashiwara operator. Kamnitzer proved the
conjecture for type A and gave an counterexample for type C_{3}. He also gave
an explicit formula to calculate the Kashiwara operator for type A. In this
paper we prove that a part of the AM conjecture still holds in general,
answering an open question of Kamnitzer (2007). Moreover, we show that although
the formula given by Kamnitzer does not hold in general, it is still valid in
many cases regardless of the type. The main tool is the connection between MV
polytopes and preprojective algebras developed by Baumann and Kamnitzer.Comment: 21 pages, version 2, to appear in Trans. Amer. Math. So
Spin Dynamics of t-J Model on Triangular Lattice
We study the spin dynamics of t-J model on triangular lattice in the
Slave-Boson-RPA scheme in light of the newly discovered superconductor
NaCoO. We find resonant peak in the dynamic spin susceptibility in
the -wave superconducting state for both hole and electron
doping in large doping range. We find the geometrical frustration inherent of
the triangular lattice provide us a unique opportunity to discriminate the
SO(5) and RPA-like intepretation of the origin of the resonant peak.Comment: 9 pages, 4 figure
The temperature dependence of the decuplet baryon masses from thermal QCD sum rules
In the present work, the masses of the decuplet baryons at finite temperature
are investigated using thermal QCD sum rules. Making use of the quark
propagator at finite temperature, we calculate the spectral functions to
order, and find that there are no contributions to the spectral
functions at order and the temperature corrections mainly come from
that containing ones. The calculations show very little temperature
dependence of the masses below . While above that value, the
masses decrease with increasing temperature. The results indicate that the
hadron-quark phase transition temperature may be for the
decuplet bayons.Comment: 11 pages, 4 figure
Existence of strong solutions to the steady Navier-Stokes equations for a compressible heat-conductive fluid with large forces
We prove that there exists a strong solution to the Dirichlet boundary value
problem for the steady Navier-Stokes equations of a compressible
heat-conductive fluid with large external forces in a bounded domain , provided that the Mach number is appropriately small. At the same time,
the low Mach number limit is rigorously verified. The basic idea in the proof
is to split the equations into two parts, one of which is similar to the steady
incompressible Navier-Stokes equations with large forces, while another part
corresponds to the steady compressible heat-conductive Navier-Stokes equations
with small forces. The existence is then established by dealing with these two
parts separately, establishing uniform in the Mach number a priori estimates
and exploiting the known results on the steady incompressible Navier-Stokes
equations.Comment: 32 page
Maximally coherent states and coherence-preserving operations
We investigate the maximally coherent states to provide a refinement in
quantifying coherence and give a measure-independent definition of the
coherence-preserving operations. A maximally coherent state can be considered
as the resource to create arbitrary quantum states of the same dimension by
merely incoherent operations. We propose that only the maximally coherent
states should achieve the maximal value for a coherence measure and use this
condition as an additional criterion for coherence measures to obtain a
refinement in quantifying coherence which excludes the invalid and inefficient
coherence measures. Under this new criterion, we then give a
measure-independent definition of the coherence-preserving operations, which
play a similar role in quantifying coherence as that played by the local
unitary operations in the scenario of studying entanglement.Comment: 7 pages, 2 figure, close to published versio
Maximum A Posteriori Inference in Sum-Product Networks
Sum-product networks (SPNs) are a class of probabilistic graphical models
that allow tractable marginal inference. However, the maximum a posteriori
(MAP) inference in SPNs is NP-hard. We investigate MAP inference in SPNs from
both theoretical and algorithmic perspectives. For the theoretical part, we
reduce general MAP inference to its special case without evidence and hidden
variables; we also show that it is NP-hard to approximate the MAP problem to
for fixed , where is the input size.
For the algorithmic part, we first present an exact MAP solver that runs
reasonably fast and could handle SPNs with up to 1k variables and 150k arcs in
our experiments. We then present a new approximate MAP solver with a good
balance between speed and accuracy, and our comprehensive experiments on
real-world datasets show that it has better overall performance than existing
approximate solvers
Inexact Proximal Cubic Regularized Newton Methods for Convex Optimization
In this paper, we use Proximal Cubic regularized Newton Methods (PCNM) to
optimize the sum of a smooth convex function and a non-smooth convex function,
where we use inexact gradient and Hessian, and an inexact subsolver for the
cubic regularized second-order subproblem. We propose inexact variants of PCNM
and accelerated PCNM respectively, and show that both variants can achieve the
same convergence rate as in the exact case, provided that the errors in the
inexact gradient, Hessian and subsolver decrease at appropriate rates.
Meanwhile, in the online stochastic setting where data comes endlessly, we give
the overall complexity of the proposed algorithms and show that they are as
competitive as the stochastic gradient descent. Moreover, we give the overall
complexity of the proposed algorithms in the finite-sum setting and show that
it is as competitive as the state of the art variance reduced algorithms.
Finally, we propose an efficient algorithm for the cubic regularized
second-order subproblem, which can converge to an enough small neighborhood of
the optimal solution in a superlinear rate.Comment: 27 page
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