Local Guarantees in Graph Cuts and Clustering

Correlation Clustering is an elegant model that captures fundamental graph cut problems such as Min $s-t$ Cut, Multiway Cut, and Multicut, extensively studied in combinatorial optimization. Here, we are given a graph with edges labeled $+$ or $-$ and the goal is to produce a clustering that agrees with the labels as much as possible: $+$ edges within clusters and $-$ edges across clusters. The classical approach towards Correlation Clustering (and other graph cut problems) is to optimize a global objective. We depart from this and study local objectives: minimizing the maximum number of disagreements for edges incident on a single node, and the analogous max min agreements objective. This naturally gives rise to a family of basic min-max graph cut problems. A prototypical representative is Min Max $s-t$ Cut: find an $s-t$ cut minimizing the largest number of cut edges incident on any node. We present the following results: $(1)$ an $O(\sqrt{n})$-approximation for the problem of minimizing the maximum total weight of disagreement edges incident on any node (thus providing the first known approximation for the above family of min-max graph cut problems), $(2)$ a remarkably simple $7$-approximation for minimizing local disagreements in complete graphs (improving upon the previous best known approximation of $48$), and $(3)$ a $1/(2+\varepsilon)$-approximation for maximizing the minimum total weight of agreement edges incident on any node, hence improving upon the $1/(4+\varepsilon)$-approximation that follows from the study of approximate pure Nash equilibria in cut and party affiliation games

On Deterministic Sketching and Streaming for Sparse Recovery and Norm Estimation

We study classic streaming and sparse recovery problems using deterministic linear sketches, including l1/l1 and linf/l1 sparse recovery problems (the latter also being known as l1-heavy hitters), norm estimation, and approximate inner product. We focus on devising a fixed matrix A in R^{m x n} and a deterministic recovery/estimation procedure which work for all possible input vectors simultaneously. Our results improve upon existing work, the following being our main contributions: * A proof that linf/l1 sparse recovery and inner product estimation are equivalent, and that incoherent matrices can be used to solve both problems. Our upper bound for the number of measurements is m=O(eps^{-2}*min{log n, (log n / log(1/eps))^2}). We can also obtain fast sketching and recovery algorithms by making use of the Fast Johnson-Lindenstrauss transform. Both our running times and number of measurements improve upon previous work. We can also obtain better error guarantees than previous work in terms of a smaller tail of the input vector. * A new lower bound for the number of linear measurements required to solve l1/l1 sparse recovery. We show Omega(k/eps^2 + klog(n/k)/eps) measurements are required to recover an x' with |x - x'|_1 <= (1+eps)|x_{tail(k)}|_1, where x_{tail(k)} is x projected onto all but its largest k coordinates in magnitude. * A tight bound of m = Theta(eps^{-2}log(eps^2 n)) on the number of measurements required to solve deterministic norm estimation, i.e., to recover |x|_2 +/- eps|x|_1. For all the problems we study, tight bounds are already known for the randomized complexity from previous work, except in the case of l1/l1 sparse recovery, where a nearly tight bound is known. Our work thus aims to study the deterministic complexities of these problems

Rare Complications of Cervical Spine Surgery: Pseudomeningocoele.

STUDY DESIGN: This study was a retrospective, multicenter cohort study. OBJECTIVES: Rare complications of cervical spine surgery are inherently difficult to investigate. Pseudomeningocoele (PMC), an abnormal collection of cerebrospinal fluid that communicates with the subarachnoid space, is one such complication. In order to evaluate and better understand the incidence, presentation, treatment, and outcome of PMC following cervical spine surgery, we conducted a multicenter study to pool our collective experience. METHODS: This study was a retrospective, multicenter cohort study of patients who underwent cervical spine surgery at any level(s) from C2 to C7, inclusive; were over 18 years of age; and experienced a postoperative PMC. RESULTS: Thirteen patients (0.08%) developed a postoperative PMC, 6 (46.2%) of whom were female. They had an average age of 48.2 years and stayed in hospital a mean of 11.2 days. Three patients were current smokers, 3 previous smokers, 5 had never smoked, and 2 had unknown smoking status. The majority, 10 (76.9%), were associated with posterior surgery, whereas 3 (23.1%) occurred after an anterior procedure. Myelopathy was the most common indication for operations that were complicated by PMC (46%). Seven patients (53%) required a surgical procedure to address the PMC, whereas the remaining 6 were treated conservatively. All PMCs ultimately resolved or were successfully treated with no residual effects. CONCLUSIONS: PMC is a rare complication of cervical surgery with an incidence of less than 0.1%. They prolong hospital stay. PMCs occurred more frequently in association with posterior approaches. Approximately half of PMCs required surgery and all ultimately resolved without residual neurologic or other long-term effects

User-friendly tail bounds for sums of random matrices

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for the norm of a sum of random rectangular matrices follow as an immediate corollary. The proof techniques also yield some information about matrix-valued martingales. In other words, this paper provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid. The matrix inequalities promise the same diversity of application, ease of use, and strength of conclusion that have made the scalar inequalities so valuable.Comment: Current paper is the version of record. The material on Freedman's inequality has been moved to a separate note; other martingale bounds are described in Caltech ACM Report 2011-0

Jean Briggs's Never in Anger as an Ethnography of Experience

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66542/2/10.1177_0308275X9301300406.pd

Boundary work: An interpretive ethnographic perspective on negotiating and leveraging cross-cultural identity

The complexity of global organizations highlights the importance of members’ ability to span diverse boundaries that may be defined by organization structures, national borders, and/or a variety of cultures associated with organization, nation-based societal and work cultures, industries, and/or professions. Based on ethnographic research in a Japan–US binational firm, the paper describes and analyzes the boundary role performance of the firm\u27s Japanese members. It contributes toward theory on boundary spanning by introducing a “cultural identity negotiation” conceptual framework. We show boundary spanning as a process shaped through the interplay of the contextual issues that make a boundary problematic; an individual\u27s multiple repertoires of cultural knowledge; and the individual boundary spanner\u27s “negotiation”, through interaction with others, of his/her cultural identities – the sense of “who I am” as a cultural being that is fundamental to an individual\u27s self-concept. At the same time, we make transparent the epistemological and methodological foundations of an interpretive ethnographic approach, demonstrating its value for understanding complex organizational processes. Research findings have practical implications for the selection and training of an organization\u27s employees, particularly of persons who may be considered “bicultural”

How managed a market? Modes of commissioning in England and Germany

Background: In quasi-markets governance over healthcare providers is mediated by commissioners. Different commissioners apply different combinations of six methods of control (’media of power’) for exercising governance: managerial performance, negotiation, discursive control, incentives, competition and juridical control. This paper compares how English and German healthcare commissioners do so. Methods: Systematic comparison of observational national-level case studies in terms of six media of power, using data from multiple sources. Results: The comparison exposes and contrasts two basic generic modes of commissioning: 1. Surrogate planning (English NHS), in which a negotiated order involving micro-commissioning, provider competition, financial incentives and penalties are the dominant media of commissioner power over providers. 2. Case-mix commissioning (Germany), in which managerial performance, an ‘episode based’ negotiated order and juridical controls appear the dominant media of commissioner power. Conclusions: Governments do not necessarily maximise commissioners’ power over providers by implementing as many media of power as possible because these media interact, some complementing and others inhibiting each other. In particular, patient choice of provider inhibits commissioners’ use of provider competition as a means of control

Conceptualizing and measuring distance in international business research:Recurring questions and best practice guidelines

Distance is a central concept in international business research, yet there is debate about the construct as well as its operationalization. In this editorial, we address three of the most important recurring questions posed by authors, editors, and reviewers by examining the theory, methods, and data of distance research. We discuss (1) how to theorize on distance, and (2) what method and (3) what data to use when constructing a distance index. We develop practical recommendations grounded in theory, illustrating and supporting them by calculating cross-country distance indices for all available country pairs and two of the most used distance indices: cultural and institutional. We show that, whereas a specific method to calculate distance may matter to some extent, the choice for a specific cultural or institutional framework to measure cultural or institutional distance has a major impact on country-pair distances. Overall, this editorial highlights the importance of matching data and method to the theoretical argument.</p

A new research agenda for managing socio-cultural integration

Post-acquisition socio-cultural integration has received increasing attention from both scholars and practitioners since the early 1990s. During the past decade, research has increasingly focused on emotions and identity in mergers and acquisitions. This chapter introduces the reader to the vibrant research field and its relevance. This section sets the scene for the book, which provides a deeper understanding of how emotions—both positive and negative—as well as values and identity enable a deeper socio-cultural integration after a merger or acquisition, and how leadership plays a crucial role in making it all happen. This chapter also highlights how the Nordic approach to post-acquisition socio-cultural integration refers to a large community of Nordic academics focusing on the softer social and human side of acquisition, often relying on a huge variety of qualitative methods, and to Nordic companies that are not afraid of adopting a more collaborative approach to post-acquisition integration