The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide variety of algorithms — among them sum-product, cluster variational methods, expectation-propagation, mean field methods, max-product and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.

/pdf/graphical-models-exponential-families-and-variational-3i6dwlfta1.pdf

Graphical Models, Exponential Families, and Variational Inference

The Smart Grid, regarded as the next generation power grid, uses two-way flows of electricity and information to create a widely distributed automated energy delivery network. In this article, we survey the literature till 2011 on the enabling technologies for the Smart Grid. We explore three major systems, namely the smart infrastructure system, the smart management system, and the smart protection system. We also propose possible future directions in each system. colorred{Specifically, for the smart infrastructure system, we explore the smart energy subsystem, the smart information subsystem, and the smart communication subsystem.} For the smart management system, we explore various management objectives, such as improving energy efficiency, profiling demand, maximizing utility, reducing cost, and controlling emission. We also explore various management methods to achieve these objectives. For the smart protection system, we explore various failure protection mechanisms which improve the reliability of the Smart Grid, and explore the security and privacy issues in the Smart Grid.

/pdf/smart-grid-the-new-and-improved-power-grid-a-survey-4jypbbgv3j.pdf

Smart Grid — The New and Improved Power Grid: A Survey

Information Theory and Reliable Communication

Smart Grid - The New and Improved Power Grid:

Jets, ie collimated streams of matter, occur from the microscale up to the large-scale structure of the universe Our focus will be mostly on surface tension effects, which result from the cohesive properties of liquids Paradoxically, cohesive forces promote the breakup of jets, widely encountered in nature, technology and basic science, for example in nuclear fission, DNA sampling, medical diagnostics, sprays, agricultural irrigation and jet engine technology Liquid jets thus serve as a paradigm for free-surface motion, hydrodynamic instability and singularity formation leading to drop breakup In addition to their practical usefulness, jets are an ideal probe for liquid properties, such as surface tension, viscosity or non-Newtonian rheology They also arise from the last but one topology change of liquid masses bursting into sprays Jet dynamics are sensitive to the turbulent or thermal excitation of the fluid, as well as to the surrounding gas or fluid medium The aim of this review is to provide a unified description of the fundamental and the technological aspects of these subjects

Physics of liquid jets

Vapour condensation in cloud cores produces small droplets that are close to one another in size. Droplets are believed to grow to raindrop size by coalescence due to collision. Air turbulence is thought to be the main cause for collisions of similar-sized droplets exceeding radii of a few micrometres, and therefore rain prediction requires a quantitative description of droplet collision in turbulence. Turbulent vortices act as small centrifuges that spin heavy droplets out, creating concentration inhomogeneities and jets of droplets, both of which increase the mean collision rate. Here we derive a formula for the collision rate of small heavy particles in a turbulent flow, using a recently developed formalism for tracing random trajectories. We describe an enhancement of inertial effects by turbulence intermittency and an interplay between turbulence and gravity that determines the collision rate. We present a new mechanism, the 'sling effect', for collisions due to jets of droplets that become detached from the air flow. We conclude that air turbulence can substantially accelerate the appearance of large droplets that trigger rain.

https://math.arizona.edu/~stepanov/papers/pdf/2002_N_FFS.pdf

Acceleration of rain initiation by cloud turbulence

Here we develop an approach to predict power grid weak points, and specifically to efficiently identify the most probable failure modes in static load distribution for a given power network. This approach is applied to two examples: Guam's power system and also the IEEE RTS-96 system, both modeled within the static dc power flow model. Our algorithm is a power network adaption of the worst configuration heuristics, originally developed to study low probability events in physics and failures in error-correction. One finding is that, if the normal operational mode of the grid is sufficiently healthy, the failure modes, also called instantons, are sufficiently sparse, i.e., the failures are caused by load fluctuations at only a few buses. The technique is useful for discovering weak links which are saturated at the instantons. It can also identify generators working at the capacity and generators under capacity, thus providing predictive capability for improving the reliability of any power network.

Predicting Failures in Power Grids: The Case of Static Overloads

We consider one-dimensional Burgers equation driven by large-scale white-in-time random force. The tails of the velocity gradients probability distribution function (PDF) are analyzed by saddle point approximation in the path integral describing the velocity statistics. The structure of the saddle-point (instanton), that is, the velocity field configuration realizing the maximum of probability, is studied numerically in details. The numerical results allow us to find analytical solution for the long-time part of the instanton. Its careful analysis confirms the result of Balkovsky et al. [Phys. Rev. Lett. $78,$ 1452 (1997)] based on short-time estimations that the left tail of PDF has the form $\mathrm{ln}\mathcal{P}{(u}_{x})\ensuremath{\propto}\ensuremath{-}|{u}_{x}{|}^{3/2}.$

https://math.arizona.edu/~stepanov/papers/pdf/2001_PRE_CS.pdf

Large negative velocity gradients in Burgers turbulence.

In linear programming (LP) decoding of a low-density parity-check (LDPC) code one minimizes a linear functional, with coefficients related to log-likelihood ratios, over a relaxation of the polytope spanned by the codewords. In order to quantify LP decoding it is important to study vertexes of the relaxed polytope, so-called pseudocodewords. We propose a technique to heuristcally create a list of pseudocodewords close to the zero codeword and their distances. Our pseudocodeword-search algorithm starts by randomly choosing configuration of the noise. The configuration is modified through a discrete number of steps. Each step consists of two substeps: one applies an LP decoder to the noise-configuration deriving a pseudocodeword, and then finds configuration of the noise equidistant from the pseudocodeword and the zero codeword. The resulting noise configuration is used as an entry for the next step. The iterations converge rapidly to a pseudocodeword neighboring the zero codeword. Repeated many times, this procedure is characterized by the distribution function of the pseudocodeword effective distance. The efficiency of the procedure is demonstrated on examples of the Tanner code and Margulis codes operating over an additive white Gaussian noise (AWGN) channel.

/pdf/an-efficient-pseudocodeword-search-algorithm-for-linear-493q60h1oq.pdf

An Efficient Pseudocodeword Search Algorithm for Linear Programming Decoding of LDPC Codes

One of the main obstacles to the wider use of the modern error-correction codes is that, due to the complex behavior of their decoding algorithms, no systematic method which would allow characterization of the bit-error-rate (BER) is known. This is especially true at the weak noise where many systems operate and where coding performance is difficult to estimate because of the diminishingly small number of errors. We show how the instanton method of physics allows one to solve the problem of BER analysis in the weak noise range by recasting it as a computationally tractable minimization problem.

/pdf/diagnosis-of-weaknesses-in-modern-error-correction-codes-a-4p9fdjd111.pdf

Mikhail Stepanov

Papers

Acceleration of rain initiation by cloud turbulence

Predicting Failures in Power Grids: The Case of Static Overloads

Large negative velocity gradients in Burgers turbulence.

An Efficient Pseudocodeword Search Algorithm for Linear Programming Decoding of LDPC Codes

Diagnosis of Weaknesses in Modern Error Correction Codes: A Physics Approach