Models for Minimax Stochastic Linear Optimization Problems with Risk Aversion

We propose a semidefinite optimization (SDP) model for the class of minimax two-stage stochastic linear optimization problems with risk aversion. The distribution of second-stage random variables belongs to a set of multivariate distributions with known first and second moments. For the minimax stochastic problem with random objective, we provide a tight SDP formulation. The problem with random right-hand side is NP-hard in general. In a special case, the problem can be solved in polynomial time. Explicit constructions of the worst-case distributions are provided. Applications in a production-transportation problem and a single facility minimax distance problem are provided to demonstrate our approach. In our experiments, the performance of minimax solutions is close to that of data-driven solutions under the multivariate normal distribution and better under extremal distributions. The minimax solutions thus guarantee to hedge against these worst possible distributions and provide a natural distribution to stress test stochastic optimization problems under distributional ambiguity.Singapore-MIT Alliance for Research and TechnologyNational University of Singapore. Dept. of Mathematic

Using Synchronic and Diachronic Relations for Summarizing Multiple Documents Describing Evolving Events

In this paper we present a fresh look at the problem of summarizing evolving events from multiple sources. After a discussion concerning the nature of evolving events we introduce a distinction between linearly and non-linearly evolving events. We present then a general methodology for the automatic creation of summaries from evolving events. At its heart lie the notions of Synchronic and Diachronic cross-document Relations (SDRs), whose aim is the identification of similarities and differences between sources, from a synchronical and diachronical perspective. SDRs do not connect documents or textual elements found therein, but structures one might call messages. Applying this methodology will yield a set of messages and relations, SDRs, connecting them, that is a graph which we call grid. We will show how such a grid can be considered as the starting point of a Natural Language Generation System. The methodology is evaluated in two case-studies, one for linearly evolving events (descriptions of football matches) and another one for non-linearly evolving events (terrorist incidents involving hostages). In both cases we evaluate the results produced by our computational systems.Comment: 45 pages, 6 figures. To appear in the Journal of Intelligent Information System

Overcoming the Challenges Associated with Image-based Mapping of Small Bodies in Preparation for the OSIRIS-REx Mission to (101955) Bennu

The OSIRIS-REx Asteroid Sample Return Mission is the third mission in NASA's New Frontiers Program and is the first U.S. mission to return samples from an asteroid to Earth. The most important decision ahead of the OSIRIS-REx team is the selection of a prime sample-site on the surface of asteroid (101955) Bennu. Mission success hinges on identifying a site that is safe and has regolith that can readily be ingested by the spacecraft's sampling mechanism. To inform this mission-critical decision, the surface of Bennu is mapped using the OSIRIS-REx Camera Suite and the images are used to develop several foundational data products. Acquiring the necessary inputs to these data products requires observational strategies that are defined specifically to overcome the challenges associated with mapping a small irregular body. We present these strategies in the context of assessing candidate sample-sites at Bennu according to a framework of decisions regarding the relative safety, sampleability, and scientific value across the asteroid's surface. To create data products that aid these assessments, we describe the best practices developed by the OSIRIS-REx team for image-based mapping of irregular small bodies. We emphasize the importance of using 3D shape models and the ability to work in body-fixed rectangular coordinates when dealing with planetary surfaces that cannot be uniquely addressed by body-fixed latitude and longitude.Comment: 31 pages, 10 figures, 2 table

Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media

We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the collapse of finite-size beams, and the formation and interaction of spatial solitons.Comment: Review article, will be published in Journal of Optics B, special issue on Optical Solitons, 6 figure

A framework for the local information dynamics of distributed computation in complex systems

The nature of distributed computation has often been described in terms of the component operations of universal computation: information storage, transfer and modification. We review the first complete framework that quantifies each of these individual information dynamics on a local scale within a system, and describes the manner in which they interact to create non-trivial computation where "the whole is greater than the sum of the parts". We describe the application of the framework to cellular automata, a simple yet powerful model of distributed computation. This is an important application, because the framework is the first to provide quantitative evidence for several important conjectures about distributed computation in cellular automata: that blinkers embody information storage, particles are information transfer agents, and particle collisions are information modification events. The framework is also shown to contrast the computations conducted by several well-known cellular automata, highlighting the importance of information coherence in complex computation. The results reviewed here provide important quantitative insights into the fundamental nature of distributed computation and the dynamics of complex systems, as well as impetus for the framework to be applied to the analysis and design of other systems.Comment: 44 pages, 8 figure

Monitoring international migration flows in Europe. Towards a statistical data base combining data from different sources

The paper reviews techniques developed in demography, geography and statistics that are useful for bridging the gap between available data on international migration flows and the information required for policy making and research. The basic idea of the paper is as follows: to establish a coherent and consistent data base that contains sufficiently detailed, up-to-date and accurate information, data from several sources should be combined. That raises issues of definition and measurement, and of how to combine data from different origins properly. The issues may be tackled more easily if the statistics that are being compiled are viewed as different outcomes or manifestations of underlying stochastic processes governing migration. The link between the processes and their outcomes is described by models, the parameters of which must be estimated from the available data. That may be done within the context of socio-demographic accounting. The paper discusses the experience of the U.S. Bureau of the Census in combining migration data from several sources. It also summarizes the many efforts in Europe to establish a coherent and consistent data base on international migration. The paper was written at IIASA. It is part of the Migration Estimation Study, which is a collaborative IIASA-University of Groningen project, funded by the Netherlands Organization for Scientific Research (NWO). The project aims at developing techniques to obtain improved estimates of international migration flows by country of origin and country of destination

Towards Machine Wald

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed \emph{by humans} because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page

Stable spinning optical solitons in three dimensions

We introduce spatiotemporal spinning solitons (vortex tori) of the three-dimensional nonlinear Schrodinger equation with focusing cubic and defocusing quintic nonlinearities. The first ever found completely stable spatiotemporal vortex solitons are demonstrated. A general conclusion is that stable spinning solitons are possible as a result of competition between focusing and defocusing nonlinearities.Comment: 4 pages, 6 figures, accepted to Phys. Rev. Let

Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity

We consider solutions to the second-harmonic generation equations in two-and three-dimensional dispersive media in the form of solitons localized in space and time. As is known, collapse does not take place in these models, which is why the solitons may be stable. The general solution is obtained in an approximate analytical form by means of a variational approach, which also allows the stability of the solutions to be predicted. Then, we directly simulate the two-dimensional case, taking the initial configuration as suggested by the variational approximation. We thus demonstrate that spatiotemporal solitons indeed exist and are stable. Furthermore, they are not, in the general case, equivalent to the previously known cylindrical spatial solitons. Direct simulations generate solitons with some internal oscillations. However, these oscillations neither grow nor do they exhibit any significant radiative damping. Numerical solutions of the stationary version of the equations produce the same solitons in their unperturbed form, i.e., without internal oscillations. Strictly stable solitons exist only if the system has anomalous dispersion at both the fundamental harmonic and second harmonic (SH), including the case of zero dispersion at SH. Quasistationary solitons, decaying extremely slowly into radiation, are found in the presence of weak normal dispersion at the second-harmonic frequency

Diagnosis and Management of Iliac Artery Endofibrosis: Results of a Delphi Consensus Study

Objective Iliac endofibrosis is a rare condition that may result in a reduction of blood flow to the lower extremity in young, otherwise healthy individuals. The data to inform everyday clinical management are weak and therefore a Delphi consensus methodology was used to explore areas of consensus and disagreement concerning the diagnosis and management of patients with suspected iliac endofibrosis. Methods A three-round Delphi questionnaire approach was used among vascular surgeons, sports physicians, sports scientists, radiologists, and clinical vascular scientists with experience of treating this condition to explore diagnosis and clinical management issues for patients with suspected iliac artery endofibrosis. Analysis is based on 18 responses to round 2 and 14 responses to round 3, with agreement reported when 70% of respondents were in agreement. Results Initially there was agreement on the typical symptoms at presentation and the need for an exercise test in the diagnosis. Round 3 clarified that duplex ultrasound was a useful tool in the diagnosis of endofibrosis. There was consensus on the most appropriate type of surgery (endarterectomy and vein patch) and that endovascular interventions were inadvisable. The final round helped to inform aspects of the natural history and post-operative surveillance. Progression of the disease was likely with continued exercise but cessation may prevent progression. Surveillance after surgery is generally recommended yearly with at least a clinical assessment. Conclusions There is broad agreement about the presenting symptoms and the investigations required to confirm (or exclude) the diagnosis of iliac endofibrosis. There was consensus on the surgical approach to repair. Disagreement existed about the specific diagnostic criteria that should be applied during non-invasive testing and about post-operative care and resumption of exercise