3,705 research outputs found
On the Hilbert scheme of curves in higher-dimensional projective space
In this paper we prove that, for any , there exist infinitely many
and for each of them a smooth, connected curve in such
that lies on exactly irreducible components of the Hilbert scheme
\hilb(\P^r). This is proven by reducing the problem to an analogous statement
for the moduli of surfaces of general type.Comment: latex, 12 pages, no figure
Alternating groups and moduli space lifting Invariants
Main Theorem: Spaces of r-branch point 3-cycle covers, degree n or Galois of
degree n!/2 have one (resp. two) component(s) if r=n-1 (resp. r\ge n). Improves
Fried-Serre on deciding when sphere covers with odd-order branching lift to
unramified Spin covers. We produce Hurwitz-Torelli automorphic functions on
Hurwitz spaces, and draw Inverse Galois conclusions. Example: Absolute spaces
of 3-cycle covers with +1 (resp. -1) lift invariant carry canonical even (resp.
odd) theta functions when r is even (resp. odd). For inner spaces the result is
independent of r. Another use appears in,
http://www.math.uci.edu/~mfried/paplist-mt/twoorbit.html, "Connectedness of
families of sphere covers of A_n-Type." This shows the M(odular) T(ower)s for
the prime p=2 lying over Hurwitz spaces first studied by,
http://www.math.uci.edu/~mfried/othlist-cov/hurwitzLiu-Oss.pdf, Liu and
Osserman have 2-cusps. That is sufficient to establish the Main Conjecture: (*)
High tower levels are general-type varieties and have no rational points.For
infinitely many of those MTs, the tree of cusps contains a subtree -- a spire
-- isomorphic to the tree of cusps on a modular curve tower. This makes
plausible a version of Serre's O(pen) I(mage) T(heorem) on such MTs.
Establishing these modular curve-like properties opens, to MTs, modular
curve-like thinking where modular curves have never gone before. A fuller html
description of this paper is at
http://www.math.uci.edu/~mfried/paplist-cov/hf-can0611591.html .Comment: To appear in the Israel Journal as of 1/5/09; v4 is corrected from
proof sheets, but does include some proof simplification in \S
Landau (\Gamma,\chi)-automorphic functions on \mathbb{C}^n of magnitude \nu
We investigate the spectral theory of the invariant Landau Hamiltonian
\La^\nu acting on the space of
-automotphic functions on \C^n, for given real number ,
lattice of \C^n and a map such that the
triplet satisfies a Riemann-Dirac quantization type
condition. More precisely, we show that the eigenspace
{\mathcal{E}}^\nu_{\Gamma,\chi}(\lambda)=\set{f\in
{\mathcal{F}}^\nu_{\Gamma,\chi}; \La^\nu f = \nu(2\lambda+n) f};
\lambda\in\C, is non trivial if and only if . In such
case, is a finite dimensional vector space
whose the dimension is given explicitly. We show also that the eigenspace
associated to the lowest Landau level of
\La^\nu is isomorphic to the space, {\mathcal{O}}^\nu_{\Gamma,\chi}(\C^n),
of holomorphic functions on \C^n satisfying g(z+\gamma) = \chi(\gamma)
e^{\frac \nu 2 |\gamma|^2+\nu\scal{z,\gamma}}g(z), \eqno{(*)} that we can
realize also as the null space of the differential operator
acting on
functions on \C^n satisfying .Comment: 20 pages. Minor corrections. Scheduled to appear in issue 8 (2008) of
"Journal of Mathematical Physics
The pre-WDVV ring of physics and its topology
We show how a simplicial complex arising from the WDVV
(Witten-Dijkgraaf-Verlinde-Verlinde) equations of string theory is the
Whitehouse complex. Using discrete Morse theory, we give an elementary proof
that the Whitehouse complex is homotopy equivalent to a wedge of
spheres of dimension . We also verify the Cohen-Macaulay
property. Additionally, recurrences are given for the face enumeration of the
complex and the Hilbert series of the associated pre-WDVV ring.Comment: 13 pages, 4 figures, 2 table
Semiclassical Description of Wavepacket Revival
We test the ability of semiclassical theory to describe quantitatively the
revival of quantum wavepackets --a long time phenomena-- in the one dimensional
quartic oscillator (a Kerr type Hamiltonian). Two semiclassical theories are
considered: time-dependent WKB and Van Vleck propagation. We show that both
approaches describe with impressive accuracy the autocorrelation function and
wavefunction up to times longer than the revival time. Moreover, in the Van
Vleck approach, we can show analytically that the range of agreement extends to
arbitrary long times.Comment: 10 pages, 6 figure
Tools in the orbit space approach to the study of invariant functions: rational parametrization of strata
Functions which are equivariant or invariant under the transformations of a
compact linear group acting in an euclidean space , can profitably
be studied as functions defined in the orbit space of the group. The orbit
space is the union of a finite set of strata, which are semialgebraic manifolds
formed by the -orbits with the same orbit-type. In this paper we provide a
simple recipe to obtain rational parametrizations of the strata. Our results
can be easily exploited, in many physical contexts where the study of
equivariant or invariant functions is important, for instance in the
determination of patterns of spontaneous symmetry breaking, in the analysis of
phase spaces and structural phase transitions (Landau theory), in equivariant
bifurcation theory, in crystal field theory and in most areas where use is made
of symmetry adapted functions.
A physically significant example of utilization of the recipe is given,
related to spontaneous polarization in chiral biaxial liquid crystals, where
the advantages with respect to previous heuristic approaches are shown.Comment: Figures generated through texdraw package; revised version appearing
in J. Phys. A: Math. Ge
Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
Many trial wavefunctions for fractional quantum Hall states in a single
Landau level are given by functions called conformal blocks, taken from some
conformal field theory. Also, wavefunctions for certain paired states of
fermions in two dimensions, such as p_x+ip_y states, reduce to such a form at
long distances. Here we investigate the adiabatic transport of such
many-particle trial wavefunctions using methods from two-dimensional field
theory. One context for this is to calculate the statistics of widely-separated
quasiholes, which has been predicted to be non-Abelian in a variety of cases.
The Berry phase or matrix (holonomy) resulting from adiabatic transport around
a closed loop in parameter space is the same as the effect of analytic
continuation around the same loop with the particle coordinates held fixed
(monodromy), provided the trial functions are orthonormal and holomorphic in
the parameters so that the Berry vector potential (or connection) vanishes. We
show that this is the case (up to a simple area term) for paired states
(including the Moore-Read quantum Hall state), and present general conditions
for it to hold for other trial states (such as the Read-Rezayi series). We
argue that trial states based on a non-unitary conformal field theory do not
describe a gapped topological phase, at least in many cases. By considering
adiabatic variation of the aspect ratio of the torus, we calculate the Hall
viscosity, a non-dissipative viscosity coefficient analogous to Hall
conductivity, for paired states, Laughlin states, and more general quantum Hall
states. Hall viscosity is an invariant within a topological phase, and is
generally proportional to the "conformal spin density" in the ground state.Comment: 44 pages, RevTeX; v2 minor changes; v3 typos corrected, three small
addition
Quantum response of dephasing open systems
We develop a theory of adiabatic response for open systems governed by
Lindblad evolutions. The theory determines the dependence of the response
coefficients on the dephasing rates and allows for residual dissipation even
when the ground state is protected by a spectral gap. We give quantum response
a geometric interpretation in terms of Hilbert space projections: For a two
level system and, more generally, for systems with suitable functional form of
the dephasing, the dissipative and non-dissipative parts of the response are
linked to a metric and to a symplectic form. The metric is the Fubini-Study
metric and the symplectic form is the adiabatic curvature. When the metric and
symplectic structures are compatible the non-dissipative part of the inverse
matrix of response coefficients turns out to be immune to dephasing. We give
three examples of physical systems whose quantum states induce compatible
metric and symplectic structures on control space: The qubit, coherent states
and a model of the integer quantum Hall effect.Comment: Article rewritten, two appendices added. 16 pages, 2 figure
Genome sequences of 12 isolates of the EU1 lineage of Phytophthora ramorum, a fungus-like pathogen that causes extensive damage and mortality to a wide range of trees and other plants
This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Here we present genome sequences for twelve isolates of the invasive pathogen Phytophthora ramorum EU1. The assembled genome sequences and raw sequence data are available via BioProject accession number PRJNA177509. These data will be useful in developing molecular tools for specific detection and identification of this pathogen.This work was supported in part by a grant funded jointly by the Biotechnology and Biological Sciences Research Council, the Department for Environment, Food and Rural Affairs, the Economic and Social Research Council, the Forestry Commission, the Natural Environment Research Council and the Scottish Government, under the Tree Health and Plant Biosecurity Initiative (BB/L012499/1). PAO was supported by a joint studentship from the Fera seedcorn programme and from the Defra Future-proofing Plant Health project (PH0441). We acknowledge funding for the joint studentship from the Fera seedcorn programme and from the Defra Future-proofing Plant Health project (PH0441)
A multilevel model for movement rehabilitation in Traumatic Brain Injury (TBI) using virtual environments
This paper presents a conceptual model for movement rehabilitation of traumatic brain injury (TBI) using virtual environments. This hybrid model integrates principles from ecological systems theory with recent advances in cognitive neuroscience, and supports a multilevel approach to both assessment and treatment. Performance outcomes at any stage of recovery are determined by the interplay of task, individual, and environmental/contextual factors. We argue that any system of rehabilitation should provide enough flexibility for task and context factors to be varied systematically, based on the current neuromotor and biomechanical capabilities of the performer or patient. Thus, in order to understand how treatment modalities are to be designed and implemented, there is a need to understand the function of brain systems that support learning at a given stage of recovery, and the inherent plasticity of the system. We know that virtual reality (VR) systems allow training environments to be presented in a highly automated, reliable, and scalable way. Presentation of these virtual environments (VEs) should permit movement analysis at three fundamental levels of behaviour: (i) neurocognitive bases of performance (we focus in particular on the development and use of internal models for action which support adaptive, on-line control); (ii) movement forms and patterns that describe the patients' movement signature at a given stage of recovery (i.e, kinetic and kinematic markers of movement proficiency), (iii) functional outcomes of the movement. Each level of analysis can also map quite seamlessly to different modes of treatment. At the neurocognitive level, for example, semi-immersive VEs can help retrain internal modeling processes by reinforcing the patients' sense of multimodal space (via augmented feedback), their position within it, and the ability to predict and control actions flexibly (via movement simulation and imagery training). More specifically, we derive four - key therapeutic environment concepts (or Elements) presented using VR technologies: Embodiment (simulation and imagery), Spatial Sense (augmenting position sense), Procedural (automaticity and dual-task control), and Participatory (self-initiated action). The use of tangible media/objects, force transduction, and vision-based tracking systems for the augmentation of gestures and physical presence will be discussed in this context
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