Lift-and-project ranks of the stable set polytope of joined a-perfect graphs

In this paper we study lift-and-project polyhedral operators defined by Lov?asz and Schrijver and Balas, Ceria and Cornu?ejols on the clique relaxation of the stable set polytope of web graphs. We compute the disjunctive rank of all webs and consequently of antiweb graphs. We also obtain the disjunctive rank of the antiweb constraints for which the complexity of the separation problem is still unknown. Finally, we use our results to provide bounds of the disjunctive rank of larger classes of graphs as joined a-perfect graphs, where near-bipartite graphs belong

Graphs for Pattern Recognition

This monograph deals with mathematical constructions that are foundational in such an important area of data mining as pattern recognition. By using combinatorial and graph theoretic techniques, a closer look is taken at infeasible systems of linear inequalities, whose generalized solutions act as building blocks of geometric decision rules for pattern recognition. Infeasible systems of linear inequalities prove to be a key object in pattern recognition problems described in geometric terms thanks to the committee method. Such infeasible systems of inequalities represent an important special subclass of infeasible systems of constraints with a monotonicity property – systems whose multi-indices of feasible subsystems form abstract simplicial complexes (independence systems), which are fundamental objects of combinatorial topology. The methods of data mining and machine learning discussed in this monograph form the foundation of technologies like big data and deep learning, which play a growing role in many areas of human-technology interaction and help to find solutions, better solutions and excellent solutions

Optimization Methods in Electric Power Systems: Global Solutions for Optimal Power Flow and Algorithms for Resilient Design under Geomagnetic Disturbances

An electric power system is a network of various components that generates and delivers power to end users. Since 1881, U.S. electric utilities have supplied power to billions of industrial, commercial, public, and residential customers continuously. Given the rapid growth of power utilities, power system optimization has evolved with developments in computing and optimization theory. In this dissertation, we focus on two optimization problems associated with power system planning: the AC optimal power flow (ACOPF) problem and the optimal transmission line switching (OTS) problem under geomagnetic disturbances (GMDs). The former problem is formulated as a nonlinear, non-convex network optimization problem, while the latter is the network design version of the ACOPF problem that allows topology reconfiguration and considers space weather-induced effects on power systems. Overall, the goal of this research includes: (1) developing computationally efficient approaches for the ACOPF problem in order to improve power dispatch efficiency and (2) identifying an optimal topology configuration to help ISO operate power systems reliably and efficiently under geomagnetic disturbances. Chapter 1 introduces the problems we are studying and motivates the proposed research. We present the ACOPF problem and the state-of-the-art solution methods developed in recent years. Next, we introduce geomagnetic disturbances and describe how they can impact electrical power systems. In Chapter 2, we revisit the polar power-voltage formulation of the ACOPF problem and focus on convex relaxation methods to develop lower bounds on the problem objective. Based on these approaches, we propose an adaptive, multivariate partitioning algorithm with bound tightening and heuristic branching strategies that progressively improves these relaxations and, given sufficient time, converges to the globally optimal solution. Computational results show that our methodology provides a computationally tractable approach to obtain tight relaxation bounds for hard ACOPF cases from the literature. In Chapter 3, we focus on the impact that extreme GMD events could potentially have on the ability of a power system to deliver power reliably. We develop a mixed-integer, nonlinear model which captures and mitigates GMD effects through line switching, generator dispatch, and load shedding. In addition, we present a heuristic algorithm that provides high-quality solutions quickly. Our work demonstrates that line switching is an effective way to mitigate GIC impacts. In Chapter 4, we extend the preliminary study presented in Chapter 3 and further consider the uncertain nature of GMD events. We propose a two-stage distributionally robust (DR) optimization model that captures geo-electric fields induced by uncertain GMDs. Additionally, we present a reformulation of a two-stage DRO that creates a decomposition framework for solving our problem. Computational results show that our DRO approach provides solutions that are robust to errors in GMD event predictions. Finally, in Chapter 5, we summarize the research contributions of our work and provide directions for future research

Exploiting Local Optimality and Strong Inequalities for Solving Bilevel Combinatorial and Submodular Optimization Problems

Bilevel combinatorial and submodular optimization problems arise in a broad range of real-life applications including price setting, network design, information gathering, viral marketing, and so on. However, the current state-of-the-art solution approaches still have difficulties to solve them exactly for many broad classes of practically relevant problems. In this dissertation, using the concepts of local optimality and strong valid inequalities, we explore the fundamental mathematical structure of these problems and boost the computational performance of exact solution methods for these two important classes of optimization problems. In our initial study, we focus on a class of bilevel spanning tree (BST) problems, motivated by a hierarchical (namely, bilevel) generalization of the classical minimum spanning tree problem. We show that depending on the type of the objective function involved at each level, BST can be solved to optimality either in polynomial time by a specialized algorithm or via a mixed-integer linear programming (MILP) model solvable by an off-the-shelf solver. The latter case corresponds to an NP-hard class of the problem. Our second study proposes a hierarchy of upper and lower bounds for the bilevel problems, where the follower’s variables are all binary. In particular, we develop a generalized bilevel framework that explores the local optimality conditions at the lower level. Submodularity and disjunctive-based approach are then exploited to derive strong MILP formulations for the resulting framework. Computational experiments indicate that the quality of our newly proposed bounds is superior to the current standard approach. Furthermore, we generalize our aforementioned results for BST and show that the proposed bounds are sharp for bilevel matroid problems. Finally, to address the computational challenges in the submodular maximization problem, we present the polyhedral study of its mixed 0–1 set. Specifically, we strengthen some existing results in the literature by finding two families of facet-defining inequalities through the lens of sequence independent lifting. We further extend the scope of this work and describe the multi-dimensional sequence independent lifting for a more complex set. The developed polyhedral results complement the classical results from the literature for the mixed0–1 knapsack and single-node flow sets

Gesture, Haltung, Ethos: The Politics of Rehearsal

Drawing on the work of Walter Benjamin, Jacques Derrida and Samuel Weber, the thesis discerns a theoretical description and demonstrative performance of theatrical iterability as the structural crisis of meaning and mastery in mediated self-relation. In this context, the concept of a politics of rehearsal imposes itself as a modality of acting, which demonstratively affirms, exposes and aggravates a constitutive breach in self-presence qua mediation. The thesis links this modality of rehearsal to a concern with the political effectiveness of bearing certain effects of virtuality, possibility and potentiality. As a repetition that maintains a simultaneous reference to the future and the past, the rehearsal is further associated with an attitude of ex-appropriation that follows the task of inheritance as a perpetual re-work of mourning. In actively resisting all limited tendencies towards closure and non-sharing in the transmission of cultural history, the politics of rehearsal becomes the model attitude of an amateur’s participatory desire. With brief recourse to Bernard Stiegler the thesis develops the figure of an “amateur” who perpetually seeks for renewed possibilities of a transforming and transformative participation in the socio-individual de-construction of a precarious ethos from within an affirmed position of limited security. It finds amateurs at work and play in the context of Benjamin’s writings on Bertolt Brecht, Franz Kafka and the German Baroque Trauerspiel, as well as the performance practices of Yvonne Rainer, Goat Island and Every house has a door. In their overt exposure of a body’s inextricable relation to the archive, these experimental theatre and dance practitioners are found to employ a method and style of appropriative restrained, which seeks to demonstratively re-launch a cultural inheritance by aggravating its future response-ability. The thesis analyses their compositional strategies of interruption, citation and virtualisation as an amateur’s appeal to the participatory coming of the negative infinity of justice as infinite perfectibility

Goya's grotesque : abjection in los Caprichos, Desastres de la Guerra, and los Disparates

Thesis (Ph.D.)--University of the Witwatersrand, Arts Faculty (Fine Arts), 1999My basic premise in this study is, if abjection is a psychosocial phenomenon, even a kind of waste category and mechanism, it should be discernible and analysable as an underlying structure in the form, iconography and purpose of works of art. Certain modes of art will manifest or express it more lucidly and abundantly than others. Satire and the Grotesque, which Goya adopts in his graphic Work, are especially fruitful in this regard. In both, one can find processes and states of degradation and vitiation that accord with the two facets of abjection Hal Foster (1996) so pragmatically terms the operation to abject and the condition to be abject. Satire, with its inclination to criticise political, social and ecclesiastical figures, can chiefly be interpreted in terms of the operation to abject (to lower, cast down, depose, sideline), while the Grotesque, displaying the distorted, monstrous, 'freakish', hybrid, impossible, relates more to tire condition to be abject. This conjunction between satire/the Grotesque and abjection guides my interpretation of Los Caprichos and Los Disparates. Los Caprichos, in which Goya took it upon himself to "censure" and "ridicule" "human errors and vices", are marked by a quite strict use of satire to criticise, mock and marginalise certain social groups (prostitutes, nobles and corrupt clerics, in particular). Since society, or the Symbolic that undergirds it, cannot do without the abject, either in its role as midden or as oppositional determinant or defining other, the satirical project cannot banish or destroy the abject; it can, however, bid and lobby for some degree of social reclamation and rejuvenation. The satirist depicts the grotesque, sordid, obscene, deviant, abandoned and licentious to indicate to the viewer/reader what s/h e must laugh off to live a decent, obedient, constructive and law-fearing life. Goya takes this aapproach in Los Caprichos. After all, in at least one letter to his friend Martin Zapater he hinted that he feared the "witches, goblins, phantoms, arrogant giants, knaves" and "scoundrels" of his society, and evidently felt a need to part from them. How deep this need ran one cannot say; many of his images suggest a degree of equivocation (he vacillates between being on the side of the law and on the side of Ms own more incorruptible conscience, from which he upbraids the law) and ambivalence (on the one hand, he scolds his objects of attack and appears to be repelled by them; on the other, he seems to relish depicting them in grotesque and blighted shapes, as if the satirical purpose is secondary to the opportunity his art provides to invent forms and get close to the forbidden, the anti-social, the rotten, the abject). In Los Disparates equivocation and ambivalence come more to the fore. Goya often appears most aggressively satirical in the Disparates when he questions corruption in social institutions such as tire Church and the law. Some images, notably Folhj of the Mass, juxtapose a wrathful figure with a mass of social ills, foibles and depravities, and seem characteristically satirical, but the majority of the etchings are striking in their lack of closure, as if a "state of unresolved tension", to quote Michael Steig, adequately rewarded Goya for the labour of production. Man xoandering among Phantoms, for example, is ambiguous and seems to sum up Goya's relationsMp to the abject toward the end of his life: through the surrogate of an old man, Goya appears to have struck a deal with the abject; submerged in it, corrupted by it, impure, but nevertheless sufficiently single-minded to find an identity separate from it. Complicit, but differentiated: all subjects stand in this way to the abject. In Los Desastres, especially given that I do not deal with the Caprichos Enfdticos section of the series, my interpretation is determined less by satire than by the question of how an antagonistic nation uses war as a mechanism of conclusive abjection to extend military, political and, ultimately. Symbolic influence - by means of sanctioned murder, execution, even rape - over another nation, w ith the aim of making that nation succumb to the abjection of surrender and the imposition of a foreign Symbolic. War also produces heaps of corpses and, in the occupied cities, ill and starving destitutes: those reduced to conditions of permanent or near-permanent abjection by war's ballistic exacerbation of the operation to abject. Contact with abjection through art strengthens, weakens and expands the self. It carries the threat of immersion in the repressed and the promise of risque pleasure - both from the diminution of unpleasure through the making or viewing of art, and the more positive pleasure of jouissance. Contact with abjection allows, further, for the complicated experience of being liminal, grotesque and abject oneself while caught between the poles of the Symbolic and tire abject. Whether we, as makers an d /o r viewers, criticise or joy in it, abjection holds out the alluring prospect of catharsis and temporary relief both from its own hazards and the rigours and inhibitions of social life. Goya, it would appear, found this intervenient condition compelling enough to return to it - if he ever truly left it - over a period of almost three decades through the medium of the three graphic series I explore in this dissertation

Art as a Political Witness

The book explores the concept of artistic witnessing as political activity. In which ways may art and artists bear witness to political events? The Contributors engage with dance, film, photography, performance, poetry and theatre and explore artistic witnessing as political activity in a wide variety of case studies

Losing Utopia? a study of British and Japanese Utopian novels in the face of postmodern consciousness

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