1,206 research outputs found
Stably reflexive modules and a lemma of Knudsen
In his fundamental work on the stack of stable n-pointed genus g curves, Finn
F. Knudsen introduced the concept of a stably reflexive module in order to
prove a key technical lemma. We propose an alternative definition and
generalise the results in the appendix to his article. Then we give a
`coordinate free' generalisation of his lemma, generalise a construction used
in Knudsen's proof concerning versal families of pointed algebras, and show
that Knudsen's stabilisation construction works for plane curve singularities.
In addition we prove approximation theorems generalising Cohen-Macaulay
approximation with stably reflexive modules in flat families. The
generalisation is not covered (even in the closed fibres) by the
Auslander-Buchweitz axioms.Comment: 27 pages. The statement in Thm. 6.1 (iv) has been corrected. Many
proofs have been expanded. A few minor changes in some of the statements.
Comments and an example added. To appear in J. Algebr
Static intervortex forces
A point particle approximation to the classical dynamics of well separated
vortices of the abelian Higgs model is developed. A static vortex is
asymptotically identical to a solution of the linearized field theory (a
Klein-Gordon/Proca theory) in the presence of a singular point source at the
vortex centre. It is shown that this source is a composite scalar monopole and
magnetic dipole, and the respective charges are determined numerically for
various values of the coupling constant. The interaction potential of two well
separated vortices is computed by calculating the interaction Lagrangian of two
such point sources in the linear theory. The potential is used to model type II
vortex scattering.Comment: Much shorter (10 pages) published version, new titl
The normative underpinnings of population-level alcohol use: An individual-level simulation model
Background. By defining what is “normal,” appropriate, expected, and unacceptable, social norms shape human behavior. However, the individual-level mechanisms through which social norms impact population-level trends in health-relevant behaviors are not well understood. Aims. To test the ability of social norms mechanisms to predict changes in population-level drinking patterns. Method. An individual-level model was developed to simulate dynamic normative mechanisms and behavioral rules underlying drinking behavior over time. The model encompassed descriptive and injunctive drinking norms and their impact on frequency and quantity of alcohol use. A microsynthesis initialized in 1979 was used as a demographically representative synthetic U.S. population. Three experiments were performed in order to test the modelled normative mechanisms. Results. Overall, the experiments showed limited influence of normative interventions on population-level alcohol use. An increase in the desire to drink led to the most meaningful changes in the population’s drinking behavior. The findings of the experiments underline the importance of autonomy, that is, the degree to which an individual is susceptible to normative influence. Conclusion. The model was able to predict theoretically plausible changes in drinking patterns at the population level through the impact of social mechanisms. Future applications of the model could be used to plan norms interventions pertaining to alcohol use as well as other health behaviors
Strong coupling constants of heavy spin--3/2 baryons with light pseudoscalar mesons
The strong coupling constants among members of the heavy spin--3/2 baryons
containing single heavy quark with light pseudoscalar mesons are calculated in
the framework of the light cone QCD sum rules. Using symmetry arguments, the
structure independent relations among different correlation functions are
obtained. It is shown that all possible transitions can be described in terms
of one universal invariant function whose explicit expression is Lorenz
structure dependent.Comment: 16 Pages, 1 figure and 1 Tabl
Entanglement in the quantum Ising model
We study the asymptotic scaling of the entanglement of a block of spins for
the ground state of the one-dimensional quantum Ising model with transverse
field. When the field is sufficiently strong, the entanglement grows at most
logarithmically in the number of spins. The proof utilises a transformation to
a model of classical probability called the continuum random-cluster model, and
is based on a property of the latter model termed ratio weak-mixing. Our proof
applies equally to a large class of disordered interactions
All Inequalities for the Relative Entropy
The relative entropy of two n-party quantum states is an important quantity
exhibiting, for example, the extent to which the two states are different. The
relative entropy of the states formed by reducing two n-party to a smaller
number of parties is always less than or equal to the relative entropy of
the two original n-party states. This is the monotonicity of relative entropy.
Using techniques from convex geometry, we prove that monotonicity under
restrictions is the only general inequality satisfied by relative entropies. In
doing so we make a connection to secret sharing schemes with general access
structures.
A suprising outcome is that the structure of allowed relative entropy values
of subsets of multiparty states is much simpler than the structure of allowed
entropy values. And the structure of allowed relative entropy values (unlike
that of entropies) is the same for classical probability distributions and
quantum states.Comment: 15 pages, 3 embedded eps figure
Bregman Voronoi Diagrams: Properties, Algorithms and Applications
The Voronoi diagram of a finite set of objects is a fundamental geometric
structure that subdivides the embedding space into regions, each region
consisting of the points that are closer to a given object than to the others.
We may define many variants of Voronoi diagrams depending on the class of
objects, the distance functions and the embedding space. In this paper, we
investigate a framework for defining and building Voronoi diagrams for a broad
class of distance functions called Bregman divergences. Bregman divergences
include not only the traditional (squared) Euclidean distance but also various
divergence measures based on entropic functions. Accordingly, Bregman Voronoi
diagrams allow to define information-theoretic Voronoi diagrams in statistical
parametric spaces based on the relative entropy of distributions. We define
several types of Bregman diagrams, establish correspondences between those
diagrams (using the Legendre transformation), and show how to compute them
efficiently. We also introduce extensions of these diagrams, e.g. k-order and
k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set
of points and their connexion with Bregman Voronoi diagrams. We show that these
triangulations capture many of the properties of the celebrated Delaunay
triangulation. Finally, we give some applications of Bregman Voronoi diagrams
which are of interest in the context of computational geometry and machine
learning.Comment: Extend the proceedings abstract of SODA 2007 (46 pages, 15 figures
The Cenozoic Song Hong and Beibuwan Basins, Vietnam
The Vietnamese offshore margin holds a substantially underexplored petroleum potential. The key to unravelling this potential lies in understanding the tectono-stratigraphic framework of the region including the Cenozoic mechanisms governing syn-rift and source rock deposition. This is essential for prediction of, for instance the presence and nature of source rocks in South-East Asia and possible reservoir intervals in the syn-rift packages. The Vietnamese part of the Song Hong and Beibuwan Basins (Fig. 1) differs from other basins along the western margin of the South China Sea in that the Palaeogene syn-rift succession is sporadically exposed due to uplift and inversion. These exposures provide a unique glimpse into the Cenozoic syn-rift succession of the basin
Achievable rates for the Gaussian quantum channel
We study the properties of quantum stabilizer codes that embed a
finite-dimensional protected code space in an infinite-dimensional Hilbert
space. The stabilizer group of such a code is associated with a symplectically
integral lattice in the phase space of 2N canonical variables. From the
existence of symplectically integral lattices with suitable properties, we
infer a lower bound on the quantum capacity of the Gaussian quantum channel
that matches the one-shot coherent information optimized over Gaussian input
states.Comment: 12 pages, 4 eps figures, REVTe
Advice coins for classical and quantum computation
We study the power of classical and quantum algorithms equipped with nonuniform advice, in the form of a coin whose bias encodes useful information. This question takes on particular importance in the quantum case, due to a surprising result that we prove: a quantum finite automaton with just two states can be sensitive to arbitrarily small changes in a coin’s bias. This contrasts with classical probabilistic finite automata, whose sensitivity to changes in a coin’s bias is bounded by a classic 1970 result of Hellman and Cover.
Despite this finding, we are able to bound the power of advice coins for space-bounded classical and quantum computation. We define the classes BPPSPACE/coin and BQPSPACE/coin, of languages decidable by classical and quantum polynomial-space machines with advice coins. Our main theorem is that both classes coincide with PSPACE/poly. Proving this result turns out to require substantial machinery. We use an algorithm due to Neff for finding roots of polynomials in NC; a result from algebraic geometry that lower-bounds the separation of a polynomial’s roots; and a result on fixed-points of superoperators due to Aaronson and Watrous, originally proved in the context of quantum computing with closed timelike curves
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