633 research outputs found
Gromov-Witten Gauge Theory I
We introduce a geometric completion of the stack of maps from stable marked
curves to the quotient stack [point/GL(1)], and use it to construct some
gauge-theoretic analogues of the Gromov-Witten invariants. We also indicate the
generalization of these invariants to the quotient stacks [X/GL(1)], where X is
a smooth proper complex algebraic variety.Comment: v3: Shorter, cleaner proof of main theorem. Accepted versio
Threshold Effects in Multi-channel Coupling and Spectroscopic Factors in Exotic Nuclei
In the threshold region, the cross section and the associated overlap
integral obey the Wigner threshold law that results in the Wigner-cusp
phenomenon. Due to flux conservation, a cusp anomaly in one channel manifests
itself in other open channels, even if their respective thresholds appear at a
different energy. The shape of a threshold cusp depends on the orbital angular
momentum of a scattered particle; hence, studies of Wigner anomalies in weakly
bound nuclei with several low-lying thresholds can provide valuable
spectroscopic information. In this work, we investigate the threshold behavior
of spectroscopic factors in neutron-rich drip-line nuclei using the Gamow Shell
Model, which takes into account many-body correlations and the continuum
effects. The presence of threshold anomalies is demonstrated and the
implications for spectroscopic factors are discussed.Comment: Accepted in Physical Review C Figure correcte
Feature selection by Higher Criticism thresholding: optimal phase diagram
We consider two-class linear classification in a high-dimensional, low-sample
size setting. Only a small fraction of the features are useful, the useful
features are unknown to us, and each useful feature contributes weakly to the
classification decision -- this setting was called the rare/weak model (RW
Model). We select features by thresholding feature -scores. The threshold is
set by {\it higher criticism} (HC). Let \pee_i denote the -value
associated to the -th -score and \pee_{(i)} denote the -th order
statistic of the collection of -values. The HC threshold (HCT) is the order
statistic of the -score corresponding to index maximizing (i/n -
\pee_{(i)})/\sqrt{\pee_{(i)}(1-\pee_{(i)})}. The ideal threshold optimizes the
classification error. In \cite{PNAS} we showed that HCT was numerically close
to the ideal threshold. We formalize an asymptotic framework for studying the
RW model, considering a sequence of problems with increasingly many features
and relatively fewer observations. We show that along this sequence, the
limiting performance of ideal HCT is essentially just as good as the limiting
performance of ideal thresholding. Our results describe two-dimensional {\it
phase space}, a two-dimensional diagram with coordinates quantifying "rare" and
"weak" in the RW model. Phase space can be partitioned into two regions -- one
where ideal threshold classification is successful, and one where the features
are so weak and so rare that it must fail. Surprisingly, the regions where
ideal HCT succeeds and fails make the exact same partition of the phase
diagram. Other threshold methods, such as FDR threshold selection, are
successful in a substantially smaller region of the phase space than either HCT
or Ideal thresholding.Comment: 4 figures, 24 page
Syzygies of torsion bundles and the geometry of the level l modular variety over M_g
We formulate, and in some cases prove, three statements concerning the purity
or, more generally the naturality of the resolution of various rings one can
attach to a generic curve of genus g and a torsion point of order l in its
Jacobian. These statements can be viewed an analogues of Green's Conjecture and
we verify them computationally for bounded genus. We then compute the
cohomology class of the corresponding non-vanishing locus in the moduli space
R_{g,l} of twisted level l curves of genus g and use this to derive results
about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3}
is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is
greater than or equal to 19. In the last section we explain probabilistically
the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the
statement of Prop 2.
Statistical Diagnostics of Metastatic Involvement of Regional Lymph Nodes
The method of statistical classification with indicating patients that require more detailed diagnostics is proposed and analysed
Strengthening the Cohomological Crepant Resolution Conjecture for Hilbert-Chow morphisms
Given any smooth toric surface S, we prove a SYM-HILB correspondence which
relates the 3-point, degree zero, extended Gromov-Witten invariants of the
n-fold symmetric product stack [Sym^n(S)] of S to the 3-point extremal
Gromov-Witten invariants of the Hilbert scheme Hilb^n(S) of n points on S. As
we do not specialize the values of the quantum parameters involved, this result
proves a strengthening of Ruan's Cohomological Crepant Resolution Conjecture
for the Hilbert-Chow morphism from Hilb^n(S) to Sym^n(S) and yields a method of
reconstructing the cup product for Hilb^n(S) from the orbifold invariants of
[Sym^n(S)].Comment: Revised versio
Persistent currents of noninteracting electrons
We thoroughly study the persistent current of noninteracting electrons in
one, two, and three dimensional thin rings. We find that the results for
noninteracting electrons are more relevant for individual mesoscopic rings than
hitherto appreciated. The current is averaged over all configurations of the
disorder, whose amount is varied from zero up to the diffusive limit, keeping
the product of the Fermi wave number and the ring's circumference constant.
Results are given as functions of disorder and aspect ratios of the ring. The
magnitude of the disorder-averaged current may be larger than the
root-mean-square fluctuations of the current from sample to sample even when
the mean free path is smaller, but not too small, than the circumference of the
ring. Then a measurement of the persistent current of a typical sample will be
dominated by the magnitude of the disorder averaged current.Comment: 10 pages, 4 figure
Chaotic Phenomenon in Nonlinear Gyrotropic Medium
Nonlinear gyrotropic medium is a medium, whose natural optical activity
depends on the intensity of the incident light wave. The Kuhn's model is used
to study nonlinear gyrotropic medium with great success. The Kuhn's model
presents itself a model of nonlinear coupled oscillators. This article is
devoted to the study of the Kuhn's nonlinear model. In the first paragraph of
the paper we study classical dynamics in case of weak as well as strong
nonlinearity. In case of week nonlinearity we have obtained the analytical
solutions, which are in good agreement with the numerical solutions. In case of
strong nonlinearity we have determined the values of those parameters for which
chaos is formed in the system under study. The second paragraph of the paper
refers to the question of the Kuhn's model integrability. It is shown, that at
the certain values of the interaction potential this model is exactly
integrable and under certain conditions it is reduced to so-called universal
Hamiltonian. The third paragraph of the paper is devoted to quantum-mechanical
consideration. It shows the possibility of stochastic absorption of external
field energy by nonlinear gyrotropic medium. The last forth paragraph of the
paper is devoted to generalization of the Kuhn's model for infinite chain of
interacting oscillators
- …