Mesrob I. Ohannessian

The intertemporal utility of demand and price elasticity of consumption in power grids with shiftable loads

This paper presents a mathematical model of consumer behavior in response to stochastically-varying electricity prices, and a characterization of price elasticity of consumption induced by optimally shifting flexible demands within a fixed time window. The approach is based on deriving the optimal load-shifting policy through a finite horizon stochastic dynamic program, and the analysis is performed under both perfect and partial information about price distribution. An aggregate demand model is constructed from individual demands with random arrivals and random deadlines. Under this model, the aggregate demand becomes a function of price only, and thus allows for quantitative characterization of the utility of demand and price elasticity. While the demand for electricity is often deemed to be highly inelastic, it is shown in this paper that optimal load-shifting can create a considerable amount of price elasticity, even when the aggregate consumption over a long period remains constant.

A turbo-style algorithm for lexical baseforms estimation

In this research, an iterative and unsupervised Turbo-style algorithm is presented and implemented for the task of automatic lexical acquisition. The algorithm makes use of spoken examples of both spellings and words and fuses information from letter and subword recognizers to boost the overall lexical learning performance. The algorithm is tested on a challenging lexicon of restaurant and street names and evaluated in terms of spelling accuracy and letter error rate. Absolute improvements of 7.2% and 3% (15.5% relative improvement) are obtained in the spelling accuracy and the letter error rate respectively following only 2 iterations of the algorithm.

Canonical estimation in a rare-events regime

We propose a general methodology for performing statistical inference within a ‘rare-events regime’ that was recently suggested by Wagner, Viswanath and Kulkarni. Our approach allows one to easily establish consistent estimators for a very large class of canonical estimation problems, in a large alphabet setting. These include the problems studied in the original paper, such as entropy and probability estimation, in addition to many other interesting ones. We particularly illustrate this approach by consistently estimating the size of the alphabet and the range of the probabilities. We start by proposing an abstract methodology based on constructing a probability measure with the desired asymptotic properties. We then demonstrate two concrete constructions by casting the Good-Turing estimator as a pseudo-empirical measure, and by using the theory of mixture model estimation.

Dynamic estimation of the price-response of deadline-constrained electric loads under threshold policies

The paper presents a consistent and unbiased estimator for dynamic, one-step-ahead prediction of the aggregate response of a large number of individual loads to a common price signal, using only aggregate past response data. The price per unit of consumption is an exogenous signal which is updated at discrete time intervals. It is assumed that individual loads arrive in the system at random times with random demands and random consumption deadlines, and may defer their consumption up to the deadline in order to minimize their total cost. It is further assumed that the individual loads adopt a threshold policy in the sense that they only consume when the price is below a certain threshold. A dynamic aggregate model is constructed from models of independent individual loads. A consistent and unbiased estimator which only uses aggregate data, i.e., the price and aggregate consumption time-series is presented for estimating the aggregate consumption as a function of price.

Large alphabets: Finite, infinite, and scaling models

How can we effectively model situations with large alphabets? On a pragmatic level, any engineered system, be it for inference, communication, or encryption, requires working with a finite number of symbols. Therefore, the most straight-forward model is a finite alphabet. However, to emphasize the disproportionate size of the alphabet, one may want to compare its finite size with the length of data at hand. More generally, this gives rise to scaling models that strive to capture regimes of operation where one anticipates such imbalance. Large alphabets may also be idealized as infinite. The caveat then is that such generality strips away many of the convenient machinery of finite settings. However, some of it may be salvaged by refocusing the tasks of interest, such as by moving from sequence to pattern compression, or by minimally restricting the classes of infinite models, such as via tail properties. In this paper we present an overview of models for large alphabets, some recent results, and possible directions in this area.

Optimal Caching Router Placement for Reduction in Retransmission Delay

We analyze the use of caching of video frames at network routers for reducing average retransmission delay. We formulate an expression for the average retransmission delay using video caching routers. In turn, we use this expression to formulate a mathematical program to minimize the average retransmission delay. We find a dynamic programming solution to the resultant non-linear convex binary integer program. We compare the results obtained from the dynamic programming solution with those obtained via experimental exhaustive enumeration. The experimental results validate our models and dynamic programming solution. Finally, we use numerical analysis to quantify the retransmission delay difference between the best and worst caching router placements. Our findings show that the optimal placement of caching routers can significantly reduce cost by minimizing the number of caching routers required to meet a desired retransmission delay performance. Furthermore, our dynamic programming solution shows that such optimal placement can be efficiently determined from network parameters, without an exhaustive search.

A novel parallel architecture for local histogram equalization

Local histogram equalization is an image enhancement algorithm that has found wide application in the pre-processing stage of areas such as computer vision, pattern recognition and medical imaging. The computationally intensive nature of the procedure, however, is a main limitation when real time interactive applications are in question. This work explores the possibility of performing parallel local histogram equalization, using an array of special purpose elementary processors, through an HDL implementation that targets FPGA or ASIC platforms. A novel parallelization scheme is presented and the corresponding architecture is derived. The algorithm is reduced to pixel-level operations. Processing elements are assigned image blocks, to maintain a reasonable performance-cost ratio. To further simplify both processor and memory organizations, a bit-serial access scheme is used. A brief performance assessment is provided to illustrate and quantify the merit of the approach.