Nonlinear Gluon Evolution in the Color Glass Condensate: I

We consider a nonlinear evolution equation recently proposed to describe the small-$x$ hadronic physics in the regime of very high gluon density. This is a functional Fokker-Planck equation in terms of a classical random color source, which represents the color charge density of the partons with large $x$. In the saturation regime of interest, the coefficients of this equation must be known to all orders in the source strength. In this first paper of a series of two, we carefully derive the evolution equation, via a matching between classical and quantum correlations, and set up the framework for the exact background source calculation of its coefficients. We address and clarify many of the subtleties and ambiguities which have plagued past attempts at an explicit construction of this equation. We also introduce the physical interpretation of the saturation regime at small $x$ as a Color Glass Condensate. In the second paper we shall evaluate the expressions derived here, and compare them to known results in various limits.Comment: 67 pages, 7 eps figure

Adaptive robust optimization with applications in inventory and revenue management

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2010.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from PDF version of thesis.Includes bibliographical references (p. 201-213).In this thesis, we examine a recent paradigm for solving dynamic optimization problems under uncertainty, whereby one considers decisions that depend directly on the sequence of observed disturbances. The resulting policies, called recourse decision rules, originated in Stochastic Programming, and have been widely adopted in recent works in Robust Control and Robust Optimization; the specific subclass of affine policies has been found to be tractable and to deliver excellent empirical performance in several relevant models and applications. In the first chapter of the thesis, using ideas from polyhedral geometry, we prove that disturbance-affine policies are optimal in the context of a one-dimensional, constrained dynamical system. Our approach leads to policies that can be computed by solving a single linear program, and which bear an interesting decomposition property, which we explore in connection with a classical inventory management problem. The result also underscores a fundamental distinction between robust and stochastic models for dynamic optimization, with the former resulting in qualitatively simpler problems than the latter. In the second chapter, we introduce a hierarchy of polynomial policies that are also directly parameterized in the observed uncertainties, and that can be efficiently computed using semidefinite optimization methods. The hierarchy is asymptotically optimal and guaranteed to improve over affine policies for a large class of relevant problems. To test our framework, we consider two problem instances arising in inventory management, for which we find that quadratic policies considerably improve over affine ones, while cubic policies essentially close the optimality gap. In the final chapter, we examine the problem of dynamically pricing inventories in multiple items, in order to maximize revenues. For a linear demand function, we propose a distributionally robust uncertainty model, argue how it can be constructed from limited historical data, and show how pricing policies depending on the observed model mis-specifications can be computed by solving second-order conic or semidefinite optimization problems. We calibrate and test our model using both synthetic data, as well as real data from a large US retailer. Extensive Monte-Carlo simulations show 3 that adaptive robust policies considerably improve over open-loop formulations, and are competitive with popular heuristics in the literature.by Dan Andrei Iancu.Ph.D

Geometric Approach to Digital Quantum Information. Quantum Entanglement. -Senior Project

Abstract The purpose of the project was to attempt an interpretation of the nature of digital quantum information from a geometrical perspective. This lead to designing an algorithm for building the equivalents of Platonic solids in a 2 n dimensional Hilbert space, structures called uniform Hilbertian polytopes. The long-term goal was to better understand quantum entanglement, and possibly find a measure for its degree in a given state

A Hierarchy of Near-Optimal Policies for Multistage Adaptive Optimization

In this paper, we propose a new tractable framework for dealing with linear dynamical systems affected by uncertainty, applicable to multistage robust optimization and stochastic programming. We introduce a hierarchy of near-optimal polynomial disturbance-feedback control policies, and show how these can be computed by solving a single semidefinite programming problem. The approach yields a hierarchy parameterized by a single variable (the degree of the polynomial policies), which controls the trade-off between the optimality gap and the computational requirements. We evaluate our framework in the context of three classical applications-two in inventory management, and one in robust regulation of an active suspension system-in which very strong numerical performance is exhibited, at relatively modest computational expense.National Science Foundation (U.S.) (Grant EFRI-0735905)National Science Foundation (U.S.) (Grant DMI-0556106)United States. Air Force Office of Scientific Research (Grant FA9550-06-1-0303

Clostridium difficile Infection Diagnosis by Biological Molecular Methods

In the past 15 years, the incidence of Clostridium difficile infection has emerged especially because of the new highly virulent strains. The classical diagnosis methods used to diagnose C. difficile infection take time and the enzyme immunoassay (EIA) test has demonstrated the lack of sensitivity. Even though new modern molecular methods have become available, the diagnosis of C. difficile in patients or healthy carriers remains a big challenge for both clinicians and laboratory staff. In the present chapter, we will list the main genotyping methods, stressing their advantages and disadvantages, as well. A brief presentation of the most useful kit (principle, sensitivity, specificity, benefits and disadvantages) to assess the impact of molecular methods in comparison with classical methods will offer support for future research in the present context of an increasing prevalence of C. difficile infection that represents worldwide, a real public health problem. To improve the patients’ quality of life, to limit hospital transmission, and to save money, we have tried to identify the best diagnosis algorithm as tool in C. difficile diagnosis and surveillance. This algorithm may differ depending on the capacities of the laboratories and on the socioeconomic level of the countries in question

Minimally invasive surgery for pancreatic tumors: laparoscopy versus robotic surgery

Chirurgia tumorilor pancreatice reprezintă un domeniu în care dezvoltarea tehnologică încearcă să aducă progrese semnificative în ceea ce privește tehnica chirurgicală, mai ales atunci când se indică un abord minim invaziv. Lucrarea de față subliniază principalele indicații, avantaje, dezavantaje și rezultate ce însoțesc tehnicile minim invazive laparoscopice și robotice, prin prisma ultimelor date din literatura de specialitate și experiența autorilor, alături de conduita intraoperatorie, în funcție de localizarea tumorală: cefalopancreatică sau corporeo-caudală pancreatică.Surgery for pancreatic tumors represents an area in which technological development to day seeks to bring significant advances in surgical technique, especially when a minimally invasive approach is indicated. The present paper emphasizes the main indications, advantages, disadvantages and results accompanying the minimally invasive laparoscopic and robotic techniques, in the light of the latest data from the specialized literature and the authors' experience, along with the intraoperative tactical aspects, according to the tumoral topography: cephalopancreatic or corporeo-caudal pancreatic

Nonlinear Gluon Evolution in the Color Glass Condensate: II

We complete the construction of the renormalization group equation (RGE) for the Color Glass Condenstate begun in Paper I. This is the equation which governs the evolution with rapidity of the statistical weight function for the color glass field. The coefficients in this equation --- one-loop real and virtual contributions --- are computed explicitly, to all orders in the color glass field. The resulting RGE can be interpreted as the imaginary-time evolution equation, with rapidity as the ``imaginary time'', for a quantum field theory in two spatial dimensions. In the weak field limit it reduces to the BFKL equation. In the general non-linear case, it is equivalent to an equation by Weigert which summarizes in functional form the evolution equations for Wilson line operators previously derived by Balitsky and Kovchegov.Comment: 52 page

Artificial Intelligence and Big Data Innovations: Navigating the Technology World of the near Future

The following is a transcript of a 2018 Federalist Society panel entitled Technology, Social Media, and Professional Ethics. The panel originally occurred on November 15, 2018 during the National Lawyers Convention in Washington, D.C. The panelists were: Hon. Andrei lancu, Under Secretary of Commerce for Intellectual Property and Director of the U.S. Patent Trademark Office; Ognian Oggie Shentov, Of Counsel, Jones Day; Hon. Michelle K. Lee, Former Under Secretary of Commerce for Intellectual Property and Director of the U.S. Patent and Trademark Office; Shawn D. Hamacher, Assistant General Counsel, Steelcase; and James C. Cooper, Deputy Director for Economic Analysis, Bureau of Consumer Protection, Federal Trade Commission. The moderator was the Honorable David J. Porter of the United States Court of Appeals for the Third Circuit