7,925 research outputs found
Hodge numbers for the cohomology of Calabi-Yau type local systems
We use Higgs cohomology to determine the Hodge numbers of the first
intersection cohomology group of a local system V arising from the third direct
image of a family of Calabi-Yau 3-folds over a smooth, quasi-projective curve.
We give applications to Rhode's families of Calabi-Yau 3-folds without MUM.Comment: Some signs corrected. This article draws heavily from arXiv:0911.027
Representation of Markov chains by random maps: existence and regularity conditions
We systematically investigate the problem of representing Markov chains by
families of random maps, and which regularity of these maps can be achieved
depending on the properties of the probability measures. Our key idea is to use
techniques from optimal transport to select optimal such maps. Optimal
transport theory also tells us how convexity properties of the supports of the
measures translate into regularity properties of the maps via Legendre
transforms. Thus, from this scheme, we cannot only deduce the representation by
measurable random maps, but we can also obtain conditions for the
representation by continuous random maps. Finally, we present conditions for
the representation of Markov chain by random diffeomorphisms.Comment: 22 pages, several changes from the previous version including
extended discussion of many detail
Optimal Topological Test for Degeneracies of Real Hamiltonians
We consider adiabatic transport of eigenstates of real Hamiltonians around
loops in parameter space. It is demonstrated that loops that map to nontrivial
loops in the space of eigenbases must encircle degeneracies. Examples from
Jahn-Teller theory are presented to illustrate the test. We show furthermore
that the proposed test is optimal.Comment: Minor corrections, accepted in Phys. Rev. Let
Transport and thermoelectric properties of the LaAlO/SrTiO interface
The transport and thermoelectric properties of the interface between
SrTiO and a 26-monolayer thick LaAlO-layer grown at high
oxygen-pressure have been investigated at temperatures from 4.2 K to 100 K and
in magnetic fields up to 18 T. For 4.2 K, two different electron-like
charge carriers originating from two electron channels which contribute to
transport are observed. We probe the contributions of a degenerate and a
non-degenerate band to the thermoelectric power and develop a consistent model
to describe the temperature dependence of the thermoelectric tensor. Anomalies
in the data point to an additional magnetic field dependent scattering.Comment: 7 pages, 4 figure
Hamiltonian equation of motion and depinning phase transition in two-dimensional magnets
Based on the Hamiltonian equation of motion of the theory with
quenched disorder, we investigate the depinning phase transition of the
domain-wall motion in two-dimensional magnets. With the short-time dynamic
approach, we numerically determine the transition field, and the static and
dynamic critical exponents. The results show that the fundamental Hamiltonian
equation of motion belongs to a universality class very different from those
effective equations of motion.Comment: 6 pages, 7 figures, have been accept by EP
Spectral plots and the representation and interpretation of biological data
It is basic question in biology and other fields to identify the char-
acteristic properties that on one hand are shared by structures from a
particular realm, like gene regulation, protein-protein interaction or neu- ral
networks or foodwebs, and that on the other hand distinguish them from other
structures. We introduce and apply a general method, based on the spectrum of
the normalized graph Laplacian, that yields repre- sentations, the spectral
plots, that allow us to find and visualize such properties systematically. We
present such visualizations for a wide range of biological networks and compare
them with those for networks derived from theoretical schemes. The differences
that we find are quite striking and suggest that the search for universal
properties of biological networks should be complemented by an understanding of
more specific features of biological organization principles at different
scales.Comment: 15 pages, 7 figure
Robust synchronization of a class of coupled delayed networks with multiple stochastic disturbances: The continuous-time case
In this paper, the robust synchronization problem is investigated for a new class of continuous-time complex networks that involve parameter uncertainties, time-varying delays, constant and delayed couplings, as well as multiple stochastic
disturbances. The norm-bounded uncertainties exist in all the network parameters after decoupling, and the stochastic disturbances are assumed to be Brownian motions that act on the constant coupling term, the delayed coupling term as well as the overall network dynamics. Such multiple stochastic disturbances could reflect more realistic dynamical behaviors of the coupled complex network presented within a noisy environment. By using a combination of the Lyapunov functional method, the robust analysis tool, the stochastic analysis techniques and the properties of Kronecker product, we derive several delay-dependent sufficient conditions that ensure the coupled complex network to be globally robustly synchronized in the mean square for all admissible parameter uncertainties. The criteria obtained in this paper are in the form of linear matrix inequalities (LMIs) whose solution can be easily calculated by using the standard numerical software. The main results are shown to be general enough to cover many existing ones reported in the literature. Simulation examples are presented to demonstrate the feasibility and applicability of the proposed results
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