Extended Formulations in Mixed-integer Convex Programming

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable with standard symmetric and nonsymmetric cones. Conic reformulations are shown to be effective extended formulations themselves because they encode separability structure. For mixed-integer conic-representable problems, we provide the first outer approximation algorithm with finite-time convergence guarantees, opening a path for the use of conic solvers for continuous relaxations. We then connect the popular modeling framework of disciplined convex programming (DCP) to the existence of extended formulations independent of conic representability. We present evidence that our approach can yield significant gains in practice, with the solution of a number of open instances from the MINLPLIB2 benchmark library.Comment: To be presented at IPCO 201

Abelian Chern-Simons Vortices and Holomorphic Burgers' Hierarchy

The Abelian Chern-Simons Gauge Field Theory in 2+1 dimensions and its relation with holomorphic Burgers' Hierarchy is considered. It is shown that the relation between complex potential and the complex gauge field as in incompressible and irrotational hydrodynamics, has meaning of the analytic Cole-Hopf transformation, linearizing the Burgers Hierarchy in terms of the holomorphic Schr\"odinger Hierarchy. Then the motion of planar vortices in Chern-Simons theory, appearing as pole singularities of the gauge field, corresponds to motion of zeroes of the hierarchy. Using boost transformations of the complex Galilean group of the hierarchy, a rich set of exact solutions, describing integrable dynamics of planar vortices and vortex lattices in terms of the generalized Kampe de Feriet and Hermite polynomials is constructed. The results are applied to the holomorphic reduction of the Ishimori model and the corresponding hierarchy, describing dynamics of magnetic vortices and corresponding lattices in terms of complexified Calogero-Moser models. Corrections on two vortex dynamics from the Moyal space-time non-commutativity in terms of Airy functions are found.Comment: 15 pages, talk presented in Workshop `Nonlinear Physics IV: Theory and Experiment`, 22-30 June 2006, Gallipoli, Ital

B Quiet: Autoantigen-Specific Strategies to Silence Raucous B Lymphocytes and Halt Cross-Talk with T Cells in Type 1 Diabetes

Islet autoantibodies are the primary biomarkers used to predict type 1 diabetes (T1D) disease risk. They signal immune tolerance breach by islet autoantigen-specific B lymphocytes. T-B lymphocyte interactions that lead to expansion of pathogenic T cells underlie T1D development. Promising strategies to broadly prevent this T-B crosstalk include T cell elimination (anti-CD3, teplizumab), B cell elimination (anti-CD20, rituximab), and disruption of T cell costimulation/activation (CTLA-4/Fc fusion, abatacept). However, global disruption or depletion of immune cell subsets is associated with significant risk, particularly in children. Therefore, antigen-specific therapy is an area of active investigation for T1D prevention. We provide an overview of strategies to eliminate antigen-specific B lymphocytes as a means to limit pathogenic T cell expansion to prevent beta cell attack in T1D. Such approaches could be used to prevent T1D in at-risk individuals. Patients with established T1D would also benefit from such targeted therapies if endogenous beta cell function can be recovered or islet transplant becomes clinically feasible for T1D treatment

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

Exact Solution Methods for the kk-item Quadratic Knapsack Problem

The purpose of this paper is to solve the 0-1 $k$-item quadratic knapsack problem $(kQKP)$, a problem of maximizing a quadratic function subject to two linear constraints. We propose an exact method based on semidefinite optimization. The semidefinite relaxation used in our approach includes simple rank one constraints, which can be handled efficiently by interior point methods. Furthermore, we strengthen the relaxation by polyhedral constraints and obtain approximate solutions to this semidefinite problem by applying a bundle method. We review other exact solution methods and compare all these approaches by experimenting with instances of various sizes and densities.Comment: 12 page

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

Bruton\u27s tyrosine kinase supports gut mucosal immunity and commensal microbiome recognition in autoimmune arthritis

Bruton\u27s tyrosine kinase

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)

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

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