1,661 research outputs found
Asymmetric diffusion and the energy gap above the 111 ground state of the quantum XXZ model
We consider the anisotropic three dimensional XXZ Heisenberg ferromagnet in a
cylinder with axis along the 111 direction and boundary conditions that induce
ground states describing an interface orthogonal to the cylinder axis. Let
be the linear size of the basis of the cylinder. Because of the breaking of the
continuous symmetry around the axis, the Goldstone theorem implies
that the spectral gap above such ground states must tend to zero as . In \cite{BCNS} it was proved that, by perturbing in a sub--cylinder
with basis of linear size the interface ground state, it is possible
to construct excited states whose energy gap shrinks as . Here we prove
that, uniformly in the height of the cylinder and in the location of the
interface, the energy gap above the interface ground state is bounded from
below by . We prove the result by first mapping the
problem into an asymmetric simple exclusion process on and then by
adapting to the latter the recursive analysis to estimate from below the
spectral gap of the associated Markov generator developed in \cite{CancMart}.
Along the way we improve some bounds on the equivalence of ensembles already
discussed in \cite{BCNS} and we establish an upper bound on the density of
states close to the bottom of the spectrum.Comment: 48 pages, latex2e fil
Phase ordering after a deep quench: the stochastic Ising and hard core gas models on a tree
Consider a low temperature stochastic Ising model in the phase coexistence
regime with Markov semigroup . A fundamental and still largely open
problem is the understanding of the long time behavior of \d_\h P_t when the
initial configuration \h is sampled from a highly disordered state
(e.g. a product Bernoulli measure or a high temperature Gibbs measure).
Exploiting recent progresses in the analysis of the mixing time of Monte Carlo
Markov chains for discrete spin models on a regular -ary tree \Tree^b, we
tackle the above problem for the Ising and hard core gas (independent sets)
models on \Tree^b. If is a biased product Bernoulli law then, under
various assumptions on the bias and on the thermodynamic parameters, we prove
-almost sure weak convergence of \d_\h P_t to an extremal Gibbs measure
(pure phase) and show that the limit is approached at least as fast as a
stretched exponential of the time . In the context of randomized algorithms
and if one considers the Glauber dynamics on a large, finite tree, our results
prove fast local relaxation to equilibrium on time scales much smaller than the
true mixing time, provided that the starting point of the chain is not taken as
the worst one but it is rather sampled from a suitable distribution.Comment: 35 page
On the probability of staying above a wall for the (2+1)-dimensional SOS model at low temperature
We obtain sharp asymptotics for the probability that the (2+1)-dimensional
discrete SOS interface at low temperature is positive in a large region. For a
square region , both under the infinite volume measure and under the
measure with zero boundary conditions around , this probability turns
out to behave like , with the
surface tension at zero tilt, also called step free energy, and the box
side. This behavior is qualitatively different from the one found for
continuous height massless gradient interface models.Comment: 21 pages, 6 figure
Random lattice triangulations: Structure and algorithms
The paper concerns lattice triangulations, that is, triangulations of the
integer points in a polygon in whose vertices are also integer
points. Lattice triangulations have been studied extensively both as geometric
objects in their own right and by virtue of applications in algebraic geometry.
Our focus is on random triangulations in which a triangulation has
weight , where is a positive real parameter, and
is the total length of the edges in . Empirically, this
model exhibits a "phase transition" at (corresponding to the
uniform distribution): for distant edges behave essentially
independently, while for very large regions of aligned edges
appear. We substantiate this picture as follows. For sufficiently
small, we show that correlations between edges decay exponentially with
distance (suitably defined), and also that the Glauber dynamics (a local Markov
chain based on flipping edges) is rapidly mixing (in time polynomial in the
number of edges in the triangulation). This dynamics has been proposed by
several authors as an algorithm for generating random triangulations. By
contrast, for we show that the mixing time is exponential. These
are apparently the first rigorous quantitative results on the structure and
dynamics of random lattice triangulations.Comment: Published at http://dx.doi.org/10.1214/14-AAP1033 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Dynamics of Lattice Triangulations on Thin Rectangles
We consider random lattice triangulations of rectangular regions
with weight where is a parameter and
denotes the total edge length of the triangulation. When
and is fixed, we prove a tight upper bound of order
for the mixing time of the edge-flip Glauber dynamics. Combined with the
previously known lower bound of order for [3],
this establishes the existence of a dynamical phase transition for thin
rectangles with critical point at
From source to target and back: symmetric bi-directional adaptive GAN
The effectiveness of generative adversarial approaches in producing images
according to a specific style or visual domain has recently opened new
directions to solve the unsupervised domain adaptation problem. It has been
shown that source labeled images can be modified to mimic target samples making
it possible to train directly a classifier in the target domain, despite the
original lack of annotated data. Inverse mappings from the target to the source
domain have also been evaluated but only passing through adapted feature
spaces, thus without new image generation. In this paper we propose to better
exploit the potential of generative adversarial networks for adaptation by
introducing a novel symmetric mapping among domains. We jointly optimize
bi-directional image transformations combining them with target self-labeling.
Moreover we define a new class consistency loss that aligns the generators in
the two directions imposing to conserve the class identity of an image passing
through both domain mappings. A detailed qualitative and quantitative analysis
of the reconstructed images confirm the power of our approach. By integrating
the two domain specific classifiers obtained with our bi-directional network we
exceed previous state-of-the-art unsupervised adaptation results on four
different benchmark datasets
Bridging Between Computer and Robot Vision Through Data Augmentation: A Case Study on Object Recognition
Despite the impressive progress brought by deep network in visual object recognition, robot vision is still far from being a solved problem. The most successful convolutional architectures are developed starting from ImageNet, a large scale collection of images of object categories downloaded from the Web. This kind of images is very different from the situated and embodied visual experience of robots deployed in unconstrained settings. To reduce the gap between these two visual experiences, this paper proposes a simple yet effective data augmentation layer that zooms on the object of interest and simulates the object detection outcome of a robot vision system. The layer, that can be used with any convolutional deep architecture, brings to an increase in object recognition performance of up to 7{\%}, in experiments performed over three different benchmark databases. An implementation of our robot data augmentation layer has been made publicly available
Domain Generalization by Solving Jigsaw Puzzles
Human adaptability relies crucially on the ability to learn and merge
knowledge both from supervised and unsupervised learning: the parents point out
few important concepts, but then the children fill in the gaps on their own.
This is particularly effective, because supervised learning can never be
exhaustive and thus learning autonomously allows to discover invariances and
regularities that help to generalize. In this paper we propose to apply a
similar approach to the task of object recognition across domains: our model
learns the semantic labels in a supervised fashion, and broadens its
understanding of the data by learning from self-supervised signals how to solve
a jigsaw puzzle on the same images. This secondary task helps the network to
learn the concepts of spatial correlation while acting as a regularizer for the
classification task. Multiple experiments on the PACS, VLCS, Office-Home and
digits datasets confirm our intuition and show that this simple method
outperforms previous domain generalization and adaptation solutions. An
ablation study further illustrates the inner workings of our approach.Comment: Accepted at CVPR 2019 (oral
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