13,835 research outputs found
On the characters of the Sylow p-subgroups of untwisted Chevalley groups Y_n(p^a)
Let be a Sylow p-subgroup of an untwisted Chevalley group
of rank n defined over where q is a power of a prime p. We
partition the set of irreducible characters of into
families indexed by antichains of positive roots of the root system of type
. We focus our attention on the families of characters of which
are indexed by antichains of length 1. Then for each positive root we
establish a one to one correspondence between the minimal degree members of the
family indexed by and the linear characters of a certain subquotient
of . For our single root character
construction recovers amongst other things the elementary supercharacters of
these groups. Most importantly though this paper lays the groundwork for our
classification of the elements of , and
Relative entropy and variational properties of generalized Gibbsian measures
We study the relative entropy density for generalized Gibbs measures. We
first show its existence and obtain a familiar expression in terms of entropy
and relative energy for a class of ``almost Gibbsian measures'' (almost sure
continuity of conditional probabilities). For quasilocal measures, we obtain a
full variational principle. For the joint measures of the random field Ising
model, we show that the weak Gibbs property holds, with an almost surely
rapidly decaying translation-invariant potential. For these measures we show
that the variational principle fails as soon as the measures lose the almost
Gibbs property. These examples suggest that the class of weakly Gibbsian
measures is too broad from the perspective of a reasonable thermodynamic
formalism.Comment: Published by the Institute of Mathematical Statistics
(http://www.imstat.org) in the Annals of Probability
(http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000034
Particle Acceleration and the Formation of Relativistic Outflows in Viscous Accretion Disks with Shocks
In this Letter, we present a new self-consistent theory for the production of
the relativistic outflows observed from radio-loud black hole candidates and
active galaxies as a result of particle acceleration in hot, viscous accretion
disks containing standing, centrifugally-supported isothermal shocks. This is
the first work to obtain the structure of such disks for a relatively large
value of the Shakura-Sunyaev viscosity parameter (), and to
consider the implications of the shock for the acceleration of relativistic
particles in viscous disks. In our approach, the hydrodynamics and the particle
acceleration are coupled and the solutions are obtained self-consistently based
on a rigorous mathematical method. We find that particle acceleration in the
vicinity of the shock can provide enough energy to power the observed
relativistic jet in M87.Comment: published in ApJ
Using Synthetic Data to Train Neural Networks is Model-Based Reasoning
We draw a formal connection between using synthetic training data to optimize
neural network parameters and approximate, Bayesian, model-based reasoning. In
particular, training a neural network using synthetic data can be viewed as
learning a proposal distribution generator for approximate inference in the
synthetic-data generative model. We demonstrate this connection in a
recognition task where we develop a novel Captcha-breaking architecture and
train it using synthetic data, demonstrating both state-of-the-art performance
and a way of computing task-specific posterior uncertainty. Using a neural
network trained this way, we also demonstrate successful breaking of real-world
Captchas currently used by Facebook and Wikipedia. Reasoning from these
empirical results and drawing connections with Bayesian modeling, we discuss
the robustness of synthetic data results and suggest important considerations
for ensuring good neural network generalization when training with synthetic
data.Comment: 8 pages, 4 figure
Rice monitoring using ENVISAT-ASAR data: preliminary results of a case study in the Mekong River Delta, Vietnam
Vietnam is one of the world’s largest rice exporting countries, and the fertile Mekong River Delta at the southern tip of Vietnam accounts for more than half of the country’s rice production. Unfortunately, a large part of rice crop growing time coincides with a rainy season, resulting in a limited number of cloud-free optical remote sensing images for rice monitoring. Synthetic aperture radar (SAR) data allows for observations independent of weather conditions and solar illumination, and is potentially well suited for rice crop monitoring.
The aim of the study was to apply new generation Envisat ASAR data with dual polarization (HH and VV) to rice cropping system mapping and monitoring in An Giang province, Mekong River Delta. Several sample areas were established on the ground, where selected rice parameters (e.g. rice height and biomass) are periodically being measured over a period of 12 months. A correlation analysis of rice parameters and radar imagery values is then being conducted to determine the significance and magnitude of the relationships.
This paper describes a review of the previous research studies on rice monitoring using SAR data, the context of this on-going study, and some preliminary results that provide insights on how ASAR imagery could be useful for rice crop monitoring. More work is being done to develop algorithms for mapping and monitoring rice cropping systems, and to validate a rice yield prediction model for one year cycle using time-series SAR imagery
Arbitrage, Equilibrium, and Nonsatiation
In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (Econometrica, 1987) proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner's existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations. Why do unbounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. We make two main contributions to the theory of arbitrage and competitive equilibrium. First, we show that, in general, in unbounded exchange economies (for example, asset exchange economies allowing short sales), even if some agents' preferences are satiated, the absence of arbitrage is sufficient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades - that is, as long as agents' preferences satisfy weak nonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation - a condition considerably weaker than local or global nonsatiation - that makes possible this transformation. Moreover, as we show via examples, without weak nonsatiation, existence fails.Arbitrage, Asset market equilibrium, Nonsatiation, Recession cones
Deep Variational Reinforcement Learning for POMDPs
Many real-world sequential decision making problems are partially observable
by nature, and the environment model is typically unknown. Consequently, there
is great need for reinforcement learning methods that can tackle such problems
given only a stream of incomplete and noisy observations. In this paper, we
propose deep variational reinforcement learning (DVRL), which introduces an
inductive bias that allows an agent to learn a generative model of the
environment and perform inference in that model to effectively aggregate the
available information. We develop an n-step approximation to the evidence lower
bound (ELBO), allowing the model to be trained jointly with the policy. This
ensures that the latent state representation is suitable for the control task.
In experiments on Mountain Hike and flickering Atari we show that our method
outperforms previous approaches relying on recurrent neural networks to encode
the past
Auto-Encoding Sequential Monte Carlo
We build on auto-encoding sequential Monte Carlo (AESMC): a method for model
and proposal learning based on maximizing the lower bound to the log marginal
likelihood in a broad family of structured probabilistic models. Our approach
relies on the efficiency of sequential Monte Carlo (SMC) for performing
inference in structured probabilistic models and the flexibility of deep neural
networks to model complex conditional probability distributions. We develop
additional theoretical insights and introduce a new training procedure which
improves both model and proposal learning. We demonstrate that our approach
provides a fast, easy-to-implement and scalable means for simultaneous model
learning and proposal adaptation in deep generative models
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