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Weakly Modular Graphs and Nonpositive Curvature
This article investigates structural, geometrical, and topological characterizations and properties of weakly modular graphs and of
cell complexes derived from them. The unifying themes of our investigation are various “nonpositive curvature\" and “local-to-global”
properties and characterizations of weakly modular graphs and their subclasses. Weakly modular graphs have been introduced as a
far-reaching common generalization of median graphs (and more generally, of modular and orientable modular graphs), Helly graphs,
bridged graphs, and dual polar graphs occurring under different disguises (
We give a local-to-global characterization of weakly modular graphs and their subclasses in terms of simple
connectedness of associated triangle-square complexes and specific local combinatorial conditions. In particular, we revisit
characterizations of dual polar graphs by Cameron and by Brouwer-Cohen. We also show that (disk-)Helly graphs are precisely the
clique-Helly graphs with simply connected clique complexes. With
eBook
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied, in the area of robust optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying prominent theoretical results of RO, we also present some recent results linking RO to adaptable models for multistage decision-making problems. Finally, we highlight applications of RO across a wide spectrum of domains, including finance, statistics, learning, and various areas of engineering.
Journal Article
Robust portfolio optimization: a categorized bibliographic review
Robust portfolio optimization refers to finding an asset allocation strategy whose behavior under the worst possible realizations of the uncertain inputs, e.g., returns and covariances, is optimized. The robust approach is in contrast to the classical approach, where one estimates the inputs to a portfolio allocation problem and then treats them as certain and accurate. In this paper we provide a categorized bibliography on the application of robust mathematical programming to the portfolio selection problem. With no similar surveys available, one of the aims of this review is to provide quick access for those interested, but maybe not yet in the area, so they know what the area is about, what has been accomplished and where everything can be found. Toward this end, a total of 148 references have been compiled and classified in various ways. Additionally, the number of Scopus© citations by contribution and journal is recorded. Finally, a brief discussion of the review’s major findings is provided and some solid leads on future directions are given.
Journal Article
Mechanism design : a linear programming approach
\"Mechanism design is an analytical framework for thinking clearly and carefully about what exactly a given institution can achieve when the information necessary to make decisions is dispersed and privately held. This analysis provides an account of the underlying mathematics of mechanism design based on linear programming. Three advantages characterize the approach. The first is simplicity: arguments based on linear programming are both elementary and transparent. The second is unity: the machinery of linear programming provides a way to unify results from disparate areas of mechanism design. The third is reach: the technique offers the ability to solve problems that appear to be beyond solutions offered by traditional methods. No claim is made that the approach advocated should supplant traditional mathematical machinery. Rather, the approach represents an addition to the tools of the economic theorist who proposes to understand economic phenomena through the lens of mechanism design\"-- Provided by publisher.
Book
A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method
We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited by the interior-point method, allowing the (either exact or inexact) efficient solution of large instances. The consequences of different modeling conditions and problem specifications on the computational performance are also investigated both theoretically and empirically, providing a deeper understanding of the significant factors influencing the overall efficiency of the cutting-plane method. The methodology proposed allowed the solution of instances of up to 200 potential locations, one million customers and three periods, resulting in mixed integer linear optimization problems of up to 600 binary and 600 millions of continuous variables. Those problems were solved by the specialized approach in less than one hour and a half, outperforming other state-of-the-art methods, which exhausted the (144 GB of) available memory in the largest instances.
Journal Article
The golden ticket : P, NP, and the search for the impossible
\"The P-NP problem is the most important open problem in computer science, if not all of mathematics. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. But difficulty also has its advantages. Hard problems allow us to safely conduct electronic commerce and maintain privacy in our online lives.The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of the P-NP problem\"-- Provided by publisher.
Book
In Vivo, Non-Invasive Characterization of Human Bone by Hybrid Broadband (600-1200 nm) Diffuse Optical and Correlation Spectroscopies
Non-invasive in vivo diffuse optical characterization of human bone opens a new possibility of diagnosing bone related pathologies. We present an in vivo characterization performed on seventeen healthy subjects at six different superficial bone locations: radius distal, radius proximal, ulna distal, ulna proximal, trochanter and calcaneus. A tailored diffuse optical protocol for high penetration depth combined with the rather superficial nature of considered tissues ensured the effective probing of the bone tissue. Measurements were performed using a broadband system for Time-Resolved Diffuse Optical Spectroscopy (TRS) to assess mean absorption and reduced scattering spectra in the 600-1200 nm range and Diffuse Correlation Spectroscopy (DCS) to monitor microvascular blood flow. Significant variations among tissue constituents were found between different locations; with radius distal rich of collagen, suggesting it as a prominent location for bone related measurements, and calcaneus bone having highest blood flow among the body locations being considered. By using TRS and DCS together, we are able to probe the perfusion and oxygen consumption of the tissue without any contrast agents. Therefore, we predict that these methods will be able to evaluate the impairment of the oxygen metabolism of the bone at the point-of-care.
Journal Article