A learning-based algorithm to quickly compute good primal solutions for Stochastic Integer Programs

We propose a novel approach using supervised learning to obtain near-optimal primal solutions for two-stage stochastic integer programming (2SIP) problems with constraints in the first and second stages. The goal of the algorithm is to predict a "representative scenario" (RS) for the problem such that, deterministically solving the 2SIP with the random realization equal to the RS, gives a near-optimal solution to the original 2SIP. Predicting an RS, instead of directly predicting a solution ensures first-stage feasibility of the solution. If the problem is known to have complete recourse, second-stage feasibility is also guaranteed. For computational testing, we learn to find an RS for a two-stage stochastic facility location problem with integer variables and linear constraints in both stages and consistently provide near-optimal solutions. Our computing times are very competitive with those of general-purpose integer programming solvers to achieve a similar solution quality

Orthonormal sequences in L2(Rd)L^2(R^d) and time frequency localization

We study uncertainty principles for orthonormal bases and sequences in $L^2(\R^d)$. As in the classical Heisenberg inequality we focus on the product of the dispersions of a function and its Fourier transform. In particular we prove that there is no orthonormal basis for $L^2(\R)$ for which the time and frequency means as well as the product of dispersions are uniformly bounded. The problem is related to recent results of J. Benedetto, A. Powell, and Ph. Jaming. Our main tool is a time frequency localization inequality for orthonormal sequences in $L^2(\R^d)$. It has various other applications.Comment: 18 page

Mirror-Descent Methods in Mixed-Integer Convex Optimization

In this paper, we address the problem of minimizing a convex function f over a convex set, with the extra constraint that some variables must be integer. This problem, even when f is a piecewise linear function, is NP-hard. We study an algorithmic approach to this problem, postponing its hardness to the realization of an oracle. If this oracle can be realized in polynomial time, then the problem can be solved in polynomial time as well. For problems with two integer variables, we show that the oracle can be implemented efficiently, that is, in O(ln(B)) approximate minimizations of f over the continuous variables, where B is a known bound on the absolute value of the integer variables.Our algorithm can be adapted to find the second best point of a purely integer convex optimization problem in two dimensions, and more generally its k-th best point. This observation allows us to formulate a finite-time algorithm for mixed-integer convex optimization

Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

Socialist Dandies International: East Europe, 1946-1959

This article maps the looks and lifestyle choices of small groups of young, like-minded people who emerged in the postwar Soviet Union and East Europe in the background of huge political, social, and cultural changes. With their androgynous bodies wrapped in drape jackets and narrow trousers, and their love of jazz and swing, these young men stood in a sharp contrast to the official ideology that promoted socialism as a new, pure, and highly rationalized project, its ideal robust and strong man, and its mass culture that insisted on educational and restrained forms of entertainment. Through the categories of dress, body, and big city, the article investigates the clashes, and the eventual truce, between the socialist streamlined and rationalized master narrative and the young dandies' fragmented and disordered narrative. The article argues that the socialist dandies were not politically minded, and that their challenge to the officially proclaimed values was informed by their adolescent recklessness and a general postwar desolation. They were declared state enemies because the socialist regimes did not allow for alternative types of modernity. Consequently, the authorities condemned the young dandies' looks and interests as cosmopolitan, because they originated in the West, and as artificial, since they belonged to the culture that had preceded a new socialist world

High-dimensional analysis reveals distinct endotypes in patients with idiopathic inflammatory myopathies

The idiopathic inflammatory myopathies (IIM) are a rare clinically heterogeneous group of conditions affecting the skin, muscle, joint, and lung in various combinations. While myositis specific autoantibodies are well described, we postulate that broader immune endotypes exist in IIM spanning B cell, T cell, and monocyte compartments. This study aims to identify immune endotypes through detailed immunophenotyping of peripheral blood mononuclear cells (PBMCs) in IIM patients compared to healthy controls. We collected PBMCs from 17 patients with a clinical diagnosis of inflammatory myositis and characterized the B, T, and myeloid cell subsets using mass cytometry by time of flight (CyTOF). Data were analyzed using a combination of the dimensionality reduction algorithm t-distributed stochastic neighbor embedding (t-SNE), cluster identification, characterization, and regression (CITRUS), and marker enrichment modeling (MEM); supervised biaxial gating validated populations identified by these methods to be differentially abundant between groups. Using these approaches, we identified shared immunologic features across all IIM patients, despite different clinical features, as well as two distinct immune endotypes. All IIM patients had decreased surface expression of RP105/CD180 on B cells and a reduction in circulating CD3+CXCR3+ subsets relative to healthy controls. One IIM endotype featured CXCR4 upregulation across all cellular compartments. The second endotype was hallmarked by an increased frequency of CD19+CD21loCD11c+ and CD3+CD4+PD1+ subsets. The experimental and analytical methods we describe here are broadly applicable to studying other immune-mediated diseases (e.g., autoimmunity, immunodeficiency) or protective immune responses (e.g., infection, vaccination)

GraphCombEx: A Software Tool for Exploration of Combinatorial Optimisation Properties of Large Graphs

We present a prototype of a software tool for exploration of multiple combinatorial optimisation problems in large real-world and synthetic complex networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial Explorer), provides a unified framework for scalable computation and presentation of high-quality suboptimal solutions and bounds for a number of widely studied combinatorial optimisation problems. Efficient representation and applicability to large-scale graphs and complex networks are particularly considered in its design. The problems currently supported include maximum clique, graph colouring, maximum independent set, minimum vertex clique covering, minimum dominating set, as well as the longest simple cycle problem. Suboptimal solutions and intervals for optimal objective values are estimated using scalable heuristics. The tool is designed with extensibility in mind, with the view of further problems and both new fast and high-performance heuristics to be added in the future. GraphCombEx has already been successfully used as a support tool in a number of recent research studies using combinatorial optimisation to analyse complex networks, indicating its promise as a research software tool

High-Throughput Detection of Autoantigen-Specific B Cells Among Distinct Functional Subsets in Autoimmune Donors

Antigen-specific B cells (ASBCs) can drive autoimmune disease by presenting autoantigen to cognate T cells to drive their activation, proliferation, and effector cell differentiation and/or by differentiating into autoantibody-secreting cells. Autoantibodies are frequently used to predict risk and diagnose several autoimmune diseases. ASBCs can drive type 1 diabetes even when immune tolerance mechanisms block their differentiation into antibody-secreting cells. Furthermore, anti-histidyl tRNA synthetase syndrome patients have expanded IgM+ Jo-1-binding B cells, which clinically diagnostic IgG Jo-1 autoantibodies may not fully reflect. Given the potential disconnect between the pathologic function of ASBCs and autoantibody secretion, direct study of ASBCs is a necessary step towards developing better therapies for autoimmune diseases, which often have no available cure. We therefore developed a high-throughput screening pipeline to 1) phenotypically identify specific B cell subsets, 2) expand them in vitro, 3) drive them to secrete BCRs as antibody, and 4) identify wells enriched for ASBCs through ELISA detection of antibody. We tested the capacity of several B cell subset(s) to differentiate into antibody-secreting cells following this robust stimulation. IgM+ and/or IgD+, CD27- memory, memory, switched memory, and BND B cells secreted B cell receptor (BCR) as antibody following in vitro stimulation, whereas few plasmablasts responded. Bimodal responses were observed across autoimmune donors for IgM+ CD21lo and IgM- CD21lo B cells, consistent with documented heterogeneity within the CD21lo subset. Using this approach, we detected insulin-binding B cell bias towards CD27- memory and CD27+ memory subsets in pre-symptomatic type 1 diabetes donors. We took advantage of routine detection of Jo-1-binding B cells in Jo-1+ anti-histidyl tRNA synthetase syndrome patients to show that Jo-1-binding B cells and total B cells expanded 20-30-fold using this culture system. Overall, these studies highlight technology that is amenable to small numbers of cryopreserved peripheral blood mononuclear cells that enables interrogation of phenotypic and repertoire attributes of ASBCs derived from autoimmune patients

CD19 + CD21lo/neg cells are increased in systemic sclerosis-associated interstitial lung disease

Interstitial lung disease (ILD) represents a significant cause of morbidity and mortality in systemic sclerosis (SSc). The purpose of this study was to examine recirculating lymphocytes from SSc patients for potential biomarkers of interstitial lung disease (ILD). Peripheral blood mononuclear cells (PBMCs) were isolated from patients with SSc and healthy controls enrolled in the Vanderbilt University Myositis and Scleroderma Treatment Initiative Center cohort between 9/2017-6/2019. Clinical phenotyping was performed by chart abstraction. Immunophenotyping was performed using both mass cytometry and fluorescence cytometry combined with t-distributed stochastic neighbor embedding analysis and traditional biaxial gating. This study included 34 patients with SSc-ILD, 14 patients without SSc-ILD, and 25 healthy controls. CD2

Local Hardy Spaces of Musielak-Orlicz Type and Their Applications

Let \phi: \mathbb{R}^n\times[0,\fz)\rightarrow[0,\fz) be a function such that $\phi(x,\cdot)$ is an Orlicz function and $\phi(\cdot,t)\in A^{\mathop\mathrm{loc}}_{\infty}(\mathbb{R}^n)$ (the class of local weights introduced by V. S. Rychkov). In this paper, the authors introduce a local Hardy space $h_{\phi}(\mathbb{R}^n)$ of Musielak-Orlicz type by the local grand maximal function, and a local $\mathop\mathrm{BMO}$-type space $\mathop\mathrm{bmo}_{\phi}(\mathbb{R}^n)$ which is further proved to be the dual space of $h_{\phi}(\mathbb{R}^n)$. As an application, the authors prove that the class of pointwise multipliers for the local $\mathop\mathrm{BMO}$-type space $\mathop\mathrm{bmo}^{\phi}(\mathbb{R}^n)$, characterized by E. Nakai and K. Yabuta, is just the dual of L^1(\rn)+h_{\Phi_0}(\mathbb{R}^n), where $\phi$ is an increasing function on $(0,\infty)$ satisfying some additional growth conditions and $\Phi_0$ a Musielak-Orlicz function induced by $\phi$. Characterizations of $h_{\phi}(\mathbb{R}^n)$, including the atoms, the local vertical and the local nontangential maximal functions, are presented. Using the atomic characterization, the authors prove the existence of finite atomic decompositions achieving the norm in some dense subspaces of $h_{\phi}(\mathbb{R}^n)$, from which, the authors further deduce some criterions for the boundedness on $h_{\phi}(\mathbb{R}^n)$ of some sublinear operators. Finally, the authors show that the local Riesz transforms and some pseudo-differential operators are bounded on $h_{\phi}(\mathbb{R}^n)$.Comment: Sci. China Math. (to appear