Homology class of a Lagrangian Klein bottle

It is shown that an embedded Lagrangian Klein bottle represents a non-trivial mod 2 homology class in a compact symplectic four-manifold $(X,\omega)$ with $c_1(X)\cdot[\omega]>0$. (In versions 1 and 2, the last assumption was missing. A counterexample to this general claim and the first proof of the corrected result have been found by Vsevolod Shevchishin.) As a corollary one obtains that the Klein bottle does not admit a Lagrangian embedding into the standard symplectic four-space.Comment: Version 3 - completely rewritten to correct a mistake; Version 4 - minor edits, added references; AMSLaTeX, 6 page

On Verifiable Sufficient Conditions for Sparse Signal Recovery via ℓ1\ell_1 Minimization

We propose novel necessary and sufficient conditions for a sensing matrix to be "$s$-good" - to allow for exact $\ell_1$-recovery of sparse signals with $s$ nonzero entries when no measurement noise is present. Then we express the error bounds for imperfect $\ell_1$-recovery (nonzero measurement noise, nearly $s$-sparse signal, near-optimal solution of the optimization problem yielding the $\ell_1$-recovery) in terms of the characteristics underlying these conditions. Further, we demonstrate (and this is the principal result of the paper) that these characteristics, although difficult to evaluate, lead to verifiable sufficient conditions for exact sparse $\ell_1$-recovery and to efficiently computable upper bounds on those $s$ for which a given sensing matrix is $s$-good. We establish also instructive links between our approach and the basic concepts of the Compressed Sensing theory, like Restricted Isometry or Restricted Eigenvalue properties

Data Integration Driven Ontology Design, Case Study Smart City

Methods to design of formal ontologies have been in focus of research since the early nineties when their importance and conceivable practical application in engineering sciences had been understood. However, often significant customization of generic methodologies is required when they are applied in tangible scenarios. In this paper, we present a methodology for ontology design developed in the context of data integration. In this scenario, a targeting ontology is applied as a mediator for distinct schemas of individual data sources and, furthermore, as a reference schema for federated data queries. The methodology has been used and evaluated in a case study aiming at integration of buildings' energy and carbon emission related data. We claim that we have made the design process much more efficient and that there is a high potential to reuse the methodology

Verifiable conditions of ℓ1\ell_1-recovery of sparse signals with sign restrictions

We propose necessary and sufficient conditions for a sensing matrix to be "s-semigood" -- to allow for exact $\ell_1$-recovery of sparse signals with at most $s$ nonzero entries under sign restrictions on part of the entries. We express the error bounds for imperfect $\ell_1$-recovery in terms of the characteristics underlying these conditions. Furthermore, we demonstrate that these characteristics, although difficult to evaluate, lead to verifiable sufficient conditions for exact sparse $\ell_1$-recovery and to efficiently computable upper bounds on those $s$ for which a given sensing matrix is $s$-semigood. We concentrate on the properties of proposed verifiable sufficient conditions of $s$-semigoodness and describe their limits of performance

Mirror Descent and Convex Optimization Problems With Non-Smooth Inequality Constraints

We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective function; convex or strongly convex objective and constraint; deterministic or randomized information about the objective and constraint. We hope that it is convenient for a reader to have all the methods for different settings in one place. Described methods are based on Mirror Descent algorithm and switching subgradient scheme. One of our focus is to propose, for the listed different settings, a Mirror Descent with adaptive stepsizes and adaptive stopping rule. This means that neither stepsize nor stopping rule require to know the Lipschitz constant of the objective or constraint. We also construct Mirror Descent for problems with objective function, which is not Lipschitz continuous, e.g. is a quadratic function. Besides that, we address the problem of recovering the solution of the dual problem

Cosmic censorship of smooth structures

It is observed that on many 4-manifolds there is a unique smooth structure underlying a globally hyperbolic Lorentz metric. For instance, every contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric is diffeomorphic to the standard $\R^4$. Similarly, a smooth 4-manifold homeomorphic to the product of a closed oriented 3-manifold $N$ and $\R$ and admitting a globally hyperbolic Lorentz metric is in fact diffeomorphic to $N\times \R$. Thus one may speak of a censorship imposed by the global hyperbolicty assumption on the possible smooth structures on $(3+1)$-dimensional spacetimes.Comment: 5 pages; V.2 - title changed, minor edits, references adde

Detailed Studies of Pixelated CZT Detectors Grown with the Modified Horizontal Bridgman Method

The detector material Cadmium Zinc Telluride (CZT), known for its high resolution over a broad energy range, is produced mainly by two methods: the Modified High-Pressure Bridgman (MHB) and the High-Pressure Bridgman (HPB) process. This study is based on MHB CZT substrates from the company Orbotech Medical Solutions Ltd. with a detector size of 2.0x2.0x0.5 cm^3, 8x8 pixels and a pitch of 2.46 mm. Former studies have emphasized only on the cathode material showing that high-work-function improve the energy resolution at lower energies. Therfore, we studied the influence of the anode material while keeping the cathode material constant. We used four different materials: Indium, Titanium, Chromium and Gold with work-functions between 4.1 eV and 5.1 eV. The low work-function materials Indium and Titanium achieved the best performance with energy resolutions: 2.0 keV (at 59 keV) and 1.9 keV (at 122 keV) for Titanium; 2.1 keV (at 59 keV) and 2.9 keV (at 122 keV) for Indium. These detectors are very competitive compared with the more expensive ones based on HPB material if one takes the large pixel pitch of 2.46 mm into account. We present a detailed comparison of our detector response with 3-D simulations, from which we determined the mobility-lifetime-products for electrons and holes. Finally, we evaluated the temperature dependency of the detector performance and mobility-lifetime-products, which is important for many applications. With decreasing temperature down to -30C the breakdown voltage increases and the electron mobility-lifetime-product decreases by about 30% over a range from 20C to -30C. This causes the energy resolution to deteriorate, but the concomitantly increasing breakdown voltage makes it possible to increase the applied bias voltage and restore the full performance.Comment: Accepted for publication in Astroparticle Physics, 25 pages, 13 figure

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

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