An analysis of mixed integer linear sets based on lattice point free convex sets

Split cuts are cutting planes for mixed integer programs whose validity is derived from maximal lattice point free polyhedra of the form $S:=\{x : \pi_0 \leq \pi^T x \leq \pi_0+1 \}$ called split sets. The set obtained by adding all split cuts is called the split closure, and the split closure is known to be a polyhedron. A split set $S$ has max-facet-width equal to one in the sense that $\max\{\pi^T x : x \in S \}-\min\{\pi^T x : x \in S \} \leq 1$. In this paper we consider using general lattice point free rational polyhedra to derive valid cuts for mixed integer linear sets. We say that lattice point free polyhedra with max-facet-width equal to $w$ have width size $w$. A split cut of width size $w$ is then a valid inequality whose validity follows from a lattice point free rational polyhedron of width size $w$. The $w$-th split closure is the set obtained by adding all valid inequalities of width size at most $w$. Our main result is a sufficient condition for the addition of a family of rational inequalities to result in a polyhedral relaxation. We then show that a corollary is that the $w$-th split closure is a polyhedron. Given this result, a natural question is which width size $w^*$ is required to design a finite cutting plane proof for the validity of an inequality. Specifically, for this value $w^*$, a finite cutting plane proof exists that uses lattice point free rational polyhedra of width size at most $w^*$, but no finite cutting plane proof that only uses lattice point free rational polyhedra of width size smaller than $w^*$. We characterize $w^*$ based on the faces of the linear relaxation

Stress and Exercise in Undergraduate Health Professions Students

Background: Stress is prevalent among undergraduate students, especially students in health professions majors. Exercise as a health promoting behavior decreases stress. At the same time, increased stress may decrease exercise. This study described exercise and stress among undergraduate health professions students. More specifically this study described the intensity and duration of each exercise and the frequency of exercise during a typical week of the semester for students in health professions majors. Theoretical framework: Pender’s Health Promotion Model guided this study. Design: Cross-sectional, descriptive survey. Methods: A convenience sample of 437 undergraduate students in a college of health professions (N =2,700) at a Midwest public university completed an electronic survey and reported stress and exercise during one typical week (a regular academic week without mid-term exams, final exams, or breaks) of the semester. Data analysis plan: Descriptive statistics described the sample, exercise habits, and presence of stress. Keywords: stress, exercise, undergraduate student, Health Professions Research Question: What are the stress and exercise habits in undergraduate health professions students during one typical week of the semester

Integer Polynomial Optimization in Fixed Dimension

We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an integer polynomial over the lattice points of a convex polytope, we show an algorithm to compute lower and upper bounds for the optimal value. For polynomials that are non-negative over the polytope, these sequences of bounds lead to a fully polynomial-time approximation scheme for the optimization problem.Comment: In this revised version we include a stronger complexity bound on our algorithm. Our algorithm is in fact an FPTAS (fully polynomial-time approximation scheme) to maximize a non-negative integer polynomial over the lattice points of a polytop

A polynomial oracle-time algorithm for convex integer minimization

In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex $N$-fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex $N$-fold integer minimization problems for which our approach provides polynomial time solution algorithms.Comment: 19 pages, 1 figur

"Now he walks and walks, as if he didn't have a home where he could eat": food, healing, and hunger in Quechua narratives of madness

In the Quechua-speaking peasant communities of southern Peru, mental disorder is understood less as individualized pathology and more as a disturbance in family and social relationships. For many Andeans, food and feeding are ontologically fundamental to such relationships. This paper uses data from interviews and participant observation in a rural province of Cuzco to explore the significance of food and hunger in local discussions of madness. Carers’ narratives, explanatory models, and theories of healing all draw heavily from idioms of food sharing and consumption in making sense of affliction, and these concepts structure understandings of madness that differ significantly from those assumed by formal mental health services. Greater awareness of the salience of these themes could strengthen the input of psychiatric and psychological care with this population and enhance knowledge of the alternative treatments that they use. Moreover, this case provides lessons for the global mental health movement on the importance of openness to the ways in which indigenous cultures may construct health, madness, and sociality. Such local meanings should be considered by mental health workers delivering services in order to provide care that can adjust to the alternative ontologies of sufferers and carers

Introduction to “Binary Binds”: Deconstructing Sex and Gender Dichotomies in Archaeological Practice

YesGender archaeology has made significant strides toward deconstructing the hegemony of binary categorizations. Challenging dichotomies such as man/woman, sex/gender, and biology/culture, approaches informed by poststructuralist, feminist, and queer theories have moved beyond essentialist and universalist identity constructs to more nuanced configurations. Despite the theoretical emphasis on context, multiplicity, and fluidity, binary starting points continue to streamline the spectrum of variability that is recognized, often reproducing normative assumptions in the evidence. The contributors to this special issue confront how sex, gender, and sexuality categories condition analytical visibility, aiming to develop approaches that respond to the complexity of theory in archaeological practice. The papers push the ontological and epistemological boundaries of bodies, personhood, and archaeological possibility, challenging a priori assumptions that contain how sex, gender, and sexuality categories are constituted and related to each other. Foregrounding intersectional approaches that engage with ambiguity, variability, and difference, this special issue seeks to “de-contain” categories, assumptions, and practices from “binding” our analytical gaze toward only certain kinds of persons and knowledges, in interpretations of the past and practices in the present

Broker Fixed: The Racialized Social Structure and the Subjugation of Indigenous Populations in the Andes

Responding to calls to return racial analysis to indigenous Latin America, this article moves beyond the prejudicial attitudes of dominant groups to specify how native subordination gets perpetuated as a normal outcome of the organization of society. I argue that a naturalized system of indirect rule racially subordinates native populations through creating the position of mestizo “authoritarian intermediary.” Natives must depend on these cultural brokers for their personhood, while maintaining this privileged position requires facilitating indigenous exploitation. Institutional structures combine with cultural practices to generate a vicious cycle in which increased village intermediary success increases native marginalization. This racialized social structure explains my ethnographic findings that indigenous villagers continued to support the same coterie of mestizos despite their regular and sometimes extreme acts of peculation. My findings about the primacy of race suggest new directions for research into indigenous studies, ethnic mobilizations, and the global dimensions of racial domination

Integrating Signals from the T-Cell Receptor and the Interleukin-2 Receptor

T cells orchestrate the adaptive immune response, making them targets for immunotherapy. Although immunosuppressive therapies prevent disease progression, they also leave patients susceptible to opportunistic infections. To identify novel drug targets, we established a logical model describing T-cell receptor (TCR) signaling. However, to have a model that is able to predict new therapeutic approaches, the current drug targets must be included. Therefore, as a next step we generated the interleukin-2 receptor (IL-2R) signaling network and developed a tool to merge logical models. For IL-2R signaling, we show that STAT activation is independent of both Src- and PI3-kinases, while ERK activation depends upon both kinases and additionally requires novel PKCs. In addition, our merged model correctly predicted TCR-induced STAT activation. The combined network also allows information transfer from one receptor to add detail to another, thereby predicting that LAT mediates JNK activation in IL-2R signaling. In summary, the merged model not only enables us to unravel potential cross-talk, but it also suggests new experimental designs and provides a critical step towards designing strategies to reprogram T cells