Papers by Alexander Shapiro
Operations Research Letters, 2009
In this paper we discuss time consistency of multi-stage risk averse stochastic programming probl... more In this paper we discuss time consistency of multi-stage risk averse stochastic programming problems. We approach the concept of time consistency from an optimization point of view. That is, at each state of the system optimality of a decision policy should not involve states which cannot happen in the future. We also discuss a relation of this concept of time consistency to deriving dynamic programming equations. Finally, we argue that some risk averse approaches to multi-stage programming are time consistent while some others are not.
A recent paper by Shapiro and colleagues reconstructs spectral and total irradiance variations of... more A recent paper by Shapiro and colleagues reconstructs spectral and total irradiance variations of the Sun during the holocene. They derive a total and spectral solar irradiance that was substantially lower during the Maunder minimum than the one observed today. The difference is remarkably larger than other estimations published in the recent literature. In this presentation we examine the spectral reconstructions in the light of stellar data. We compare the observed and predicted solar variability with that of stars as observed by Radick et al. (1998), Lockwood et al. (2007) and Hall et al. (2009) in the b and y filters for the last 10- 20 years.
The main goal of this paper is to develop accuracy estimates for stochastic programming problems ... more The main goal of this paper is to develop accuracy estimates for stochastic programming problems by employing robust stochastic approximation (SA) type algorithms. To this end we show that while running a Robust Mirror Descent Stochastic Approximation procedure one can compute, with a small additional eort, lower and upper statistical bounds for the optimal objective value. We demonstrate that for a certain class of convex stochastic programs these bound are comparable in quality with similar bounds computed by the sample average approximation method, while their computational cost is considerably smaller.
Active regions and sunspots occur predominantly at low to mid heliographic latitudes. Hence, it s... more Active regions and sunspots occur predominantly at low to mid heliographic latitudes. Hence, it seems reasonable to assume that the radiant output of the sun is not spherically symmetrical. Due to the relatively small inclination (~7.25°) of the solar rotation axis this asphericity is difficult to detect in integrated disk data taken from an ecliptic-bound vantage point. A histogram analysis of 13 years of VIRGO TSI data revealed a slight north-south asymmetry with maximal deviations of ±4 parts in 10^5. Interestingly, the north-south asymmetry persists even after subtracting the simulated TSI data by Krivova et al. (2003) from the VIRGO TSI measurements. The Krivova time series attributes the TSI to magnetic activity patterns as observed by MDI (sunspots, faculae, and plage). The asymmetry thus seems to be of a different origin, i.e. unrelated to sunspots, faculae, or plage, although smaller magnetic structures might contribute to the asymmetry. We will also investigate a potential...
2013 IEEE SOI-3D-Subthreshold Microelectronics Technology Unified Conference (S3S), 2013
Near threshold circuits (NTC) are an attractive and promising technology that provides significan... more Near threshold circuits (NTC) are an attractive and promising technology that provides significant power savings with some delay penalty. The feasibility of NTC technology with MOS Current Mode Logic (MCML) based on a 14 nm FinFET process node is examined in this paper. A 32 bit Kogge Stone adder is chosen as a demonstration vehicle for simulation and feasibility analysis. MCML yields enhanced power efficiency when operated with a 100% activity factor above 1 GHz as compared to CMOS. Standard CMOS does not achieve frequencies above 9 GHz without a dramatic increase in power consumption. MCML is most efficient beyond 9 GHz over a wide range of activity factors. MCML also exhibits significantly lower noise levels as compared to standard CMOS. The results of the analysis demonstrate that pairing NTC and MCML is efficient when operating at high frequencies and activity factors.
We present the ambitions of the SWUSV (Space Weather and Ultraviolet Solar Variability) Microsate... more We present the ambitions of the SWUSV (Space Weather and Ultraviolet Solar Variability) Microsatellite Mission that encompasses three major scientific objectives: (1) Space Weather including the prediction and detection of major eruptions and coronal mass ejections (Lyman-Alpha and Herzberg continuum imaging); (2) solar forcing on the climate through radiation and their interactions with the local stratosphere (UV spectral irradiance from 180 to 400 nm by bands of 20 nm, plus Lyman-Alpha and the CN bandhead); (3) simultaneous radiative budget of the Earth, UV to IR, with an accuracy better than 1% in differential. The paper briefly outlines the mission and describes the five proposed instruments of the model payload: SUAVE (Solar Ultraviolet Advanced Variability Experiment), an optimized telescope for FUV (Lyman-Alpha) and MUV (200-220 nm Herzberg continuum) imaging (sources of variability); UPR (Ultraviolet Passband Radiometers), with 64 UV filter radiometers; a vector magnetometer; thermal plasma measurements and Langmuir probes; and a total and spectral solar irradiance and Earth radiative budget ensemble
SPE EUROPEC/EAGE Annual Conference and Exhibition, 2010
Microbial enhanced oil recovery (MEOR) utilizes the activity of microorganisms, where microorgani... more Microbial enhanced oil recovery (MEOR) utilizes the activity of microorganisms, where microorganisms simultaneously grow in a reservoir and convert substrate into recovery enhancing products (usually, surfactants). In order to predict the performance of a MEOR process, a simulation tool is required, with all the relevant physical processes included. We have developed a mathematical model describing the process of MEOR, where reactive transport is combined with a simple compositional approach. The model describes the displacement of oil by water containing bacteria, substrate, and the produced metabolite, surfactant. The metabolite is allowed to partition between the oil and water phases according to a distribution coefficient. Production of surfactant decreases the oil/water interfacial tension, reduces the residual oil saturation, and provides additional oil recovery. In this work, we have implemented our MEOR model into a compositional streamline simulator based on the standard IM...
Transport in Porous Media, 2014
ABSTRACT Physico-chemical interactions between the fluid and reservoir rock due to the presence o... more ABSTRACT Physico-chemical interactions between the fluid and reservoir rock due to the presence of active components in the injected brine produce changes within the reservoir and can significantly impact the fluid flow. We have developed a 1D numerical model for waterflooding accounting for dissolution and precipitation of the components. Extending previous studies, we consider an arbitrary chemical non-equilibrium reaction-induced dissolution. We account for different individual volumes that a component has when precipitated or dissolved. This volume non-additivity also affects the pressure and the flow rate. An equation of state is used to account for brine density variation with regard to pressure and composition. We present a numerical study of the evolution of the reservoir parameters in the framework of the developed model. It is demonstrated that the systems characterized by large Damkohler numbers (fast reaction rates) may exhibit rapid increase of porosity and permeability near the inlet probably indicating a formation of high permeable channels (wormholes). Water saturation in the zone of dissolution increases due to an increase in the bulk volume accessible for the injected fluid. Volumetric non-additivity is found to be responsible for insignificant change in the velocity of the displacement front.
Review of Financial Studies, 2007
Society winter meetings for their comments. Special thanks to Martijn Cremers. Pavitra Kumar, Dmi... more Society winter meetings for their comments. Special thanks to Martijn Cremers. Pavitra Kumar, Dmitry Makarov, Juha Valkama, and Jialan Wang provided excellent research assistance. Parts of this work are drawn from the paper that was previously circulated under the title "Offsetting the Incentives: Risk Shifting and Benefits of Benchmarking in Money Management" (2005, CEPR DP 5006). Research support from the Q Group is gratefully acknowledged. We are indebted to Will Goetzmann, Geert Rouwenhorst, and the International Center for Finance at Yale SOM for kindly providing the data. All errors are solely our responsibility.
SIAM Review, 1998
This paper presents an overview of some recent, and significant, progress in the theory of optimi... more This paper presents an overview of some recent, and significant, progress in the theory of optimization problems with perturbations. We put the emphasis on methods based on upper and lower estimates of the objective function of the perturbed problems. These methods allow one to compute expansions of the optimal value function and approximate optimal solutions in situations where the set of Lagrange multipliers is not a singleton, may be unbounded, or is even empty. We give rather complete results for nonlinear programming problems and describe some extensions of the method to more general problems. We illustrate the results by computing the equilibrium position of a chain that is almost vertical or horizontal.
Psychometrika, 1982
This paper considers some mathematical aspects of minimum trace factor analysis (MTFA). The uniqu... more This paper considers some mathematical aspects of minimum trace factor analysis (MTFA). The uniqueness of an optimal point of MTFA is proved and necessary and sufficient conditions for a point x to be optimal are established. Finally, some results about the connection between MTFA and the classical minimum rank factor analysis will be presented.
Operations Research Letters, 1999
We introduce Stochastic Mathematical Programs with Equilibrium Constraints (SMPEC), which general... more We introduce Stochastic Mathematical Programs with Equilibrium Constraints (SMPEC), which generalize MPEC models by explicitly incorporating possible uncertainties in the problem data to obtain robust solutions to hierarchical problems. For this problem, we establish results on the existence of solutions, and on the convexity and directional di erentiability of the implicit upper-level objective function, both for continuously and discretely distributed probability distributions. In so doing, we establish links between SMPEC models and two-stage stochastic programs with recourse. We also discuss basic parallel iterative algorithms for discretely distributed SMPEC problems.
Operations Research, 2013
In this paper we discuss multistage programming with the data process subject to uncertainty. We ... more In this paper we discuss multistage programming with the data process subject to uncertainty. We consider a situation where the data process can be naturally separated into two components: one can be modeled as a random process, with a specified probability distribution, and the other one can be treated from a robust (worst-case) point of view. We formulate this in a time consistent way and derive the corresponding dynamic programming equations. To solve the obtained multistage problem, we develop a variant of the stochastic dual dynamic programming method. We give a general description of the algorithm and present computational studies related to planning of the Brazilian interconnected power system.
Nature Communications, 2013
Social behaviour has a key role in animal survival across species, ranging from insects to primat... more Social behaviour has a key role in animal survival across species, ranging from insects to primates and humans. However, the biological mechanisms driving natural interactions between multiple animals, over long-term periods, are poorly studied and remain elusive. Rigorous and objective quantification of behavioural parameters within a group poses a major challenge as it requires simultaneous monitoring of the positions of several individuals and comprehensive consideration of many complex factors. Automatic tracking and phenotyping of interacting animals could thus overcome the limitations of manual tracking methods. Here we report a broadly applicable system that automatically tracks the locations of multiple, uniquely identified animals, such as mice, within a semi-natural setting. The system combines video and radio frequency identified tracking data to obtain detailed behavioural profiles of both individuals and groups. We demonstrate the usefulness of these data in characterizing individual phenotypes, interactions between pairs and the collective social organization of groups.
Mathematics of Operations Research, 2006
We consider optimization problems involving convex risk functions. By employing techniques of con... more We consider optimization problems involving convex risk functions. By employing techniques of convex analysis and optimization theory in vector spaces of measurable functions, we develop new representation theorems for risk models, and optimality and duality theory for problems with convex risk functions.
Mathematics and Computers in Simulation, 1990
In this paper we show how an optimization problem involving the expected performance of a stochas... more In this paper we show how an optimization problem involving the expected performance of a stochastic system can be estimated using a single simulation experiment. The proposed method is based on a probability measure transformation and generation of a stochastic counterpart to the deterministic optimization program. Statistical properties of the derived estimators are discussed and examples are given.
Mathematical Programming, 1998
In this paper we consider stochastic programming problems where the objective function is given a... more In this paper we consider stochastic programming problems where the objective function is given as an expected value function. We discuss Monte Carlo simulation based approaches to a numerical solution of such problems. In particular, we discuss in detail and present numerical results for two-stage stochastic programming with recourse where the random data have a continuous (multivariate normal) distribution. We think that the novelty of the numerical approach developed in this paper is twofold. First, various variance reduction techniques are applied in order to enhance the rate of convergence. Successful application of those techniques is what makes the whole approach numerically feasible. Second, a statistical inference is developed and applied to estimation of the error, validation of optimality of a calculated solution and statistically based stopping criteria for an iterative alogrithm.
Mathematical Programming, 2002
In this paper we consider stochastic programming problems where the objective function is given a... more In this paper we consider stochastic programming problems where the objective function is given as an expected value of a convex piecewise linear random function. With an optimal solution of such a problem we associate a condition number which characterizes well or ill conditioning of the problem. Using theory of Large Deviations we show that the sample size needed to calculate the optimal solution of such problem with a given probability is approximately proportional to the condition number.
Mathematical Programming, 2011
The main goal of this paper is to develop accuracy estimates for stochastic programming problems ... more The main goal of this paper is to develop accuracy estimates for stochastic programming problems by employing stochastic approximation (SA) type algorithms. To this end we show that while running a Mirror Descent Stochastic Approximation procedure one can compute, with a small additional effort, lower and upper statistical bounds for the optimal objective value. We demonstrate that for a certain class of convex stochastic programs these bounds are comparable in quality with similar bounds computed by the sample average approximation method, while their computational cost is considerably smaller.
Mathematical Methods of Operations Research (ZOR), 2003
We discuss in this paper statistical inference of sample average approximations of multistage sto... more We discuss in this paper statistical inference of sample average approximations of multistage stochastic programming problems. We show that any random sampling scheme provides a valid statistical lower bound for the optimal (minimum) value of the true problem. However, in order for such lower bound to be consistent one needs to employ the conditional sampling procedure. We also indicate that fixing a feasible first-stage solution and then solving the sampling approximation of the corresponding ðT À 1Þ-stage problem, does not give a valid statistical upper bound for the optimal value of the true problem.
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Papers by Alexander Shapiro