Convex Hulls under Uncertainty

We study the convex-hull problem in a probabilistic setting, motivated by the need to handle data uncertainty inherent in many applications, including sensor databases, location-based services and computer vision. In our framework, the uncertainty of each input site is described by a probability distribution over a finite number of possible locations including a \emph{null} location to account for non-existence of the point. Our results include both exact and approximation algorithms for computing the probability of a query point lying inside the convex hull of the input, time-space tradeoffs for the membership queries, a connection between Tukey depth and membership queries, as well as a new notion of \some-hull that may be a useful representation of uncertain hulls

Computation of Robust Control Invariant Sets with Predefined Complexity for Uncertain Systems

This paper presents an algorithm that computes polytopic robust control-invariant (RCI) sets for rationally parameter-dependent systems with additive disturbances. By means of novel LMI feasibility conditions for invariance along with a newly developed method for volume maximization, an iterative algorithm is proposed for the computation of RCI sets with maximized volumes. The obtained RCI sets are symmetric around the origin by construction and have a user-defined level of complexity. Unlike many similar approaches, fixed state feedback structure is not imposed. In fact, a specific control input is obtained from the LMI problem for each extreme point of the RCI set. The outcomes of the proposed algorithm can be used to construct a piecewise-affine controller based on offline computations

Continuous and Optimally Complete Description of Chemical Environments Using Spherical Bessel Descriptors

Recently, machine learning potentials have been advanced as candidates to combine the high-accuracy of quantum mechanical simulations with the speed of classical interatomic potentials. A crucial component of a machine learning potential is the description of local atomic environments by some set of descriptors. These should ideally be continuous throughout the specified local atomic environment, twice-differentiable with respect to atomic positions and complete in the sense of containing all possible information about the neighborhood. An updated version of the recently proposed Spherical Bessel descriptors satisfies all three of these properties, and moreover is optimally complete in the sense of encoding all configurational information with the smallest possible number of descriptors. The Smooth Overlap of Atomic Position descriptors that are frequently visited in the literature and the Zernike descriptors that are built upon a similar basis are included into the discussion as being the natural counterparts of the Spherical Bessel descriptors, and shown to be incapable of satisfying the full list of core requirements for an accurate description. Aside being mathematically and physically superior, the Spherical Bessel descriptors have also the advantage of allowing machine learning potentials of comparable accuracy that require roughly an order of magnitude less computation time per evaluation than the Smooth Overlap of Atomic Position descriptors, which appear to be the common choice of descriptors in recent studies.Comment: 15 pages, 5 figures, under review for Journal of Chemical Physic

A Novel Approach to Describe Chemical Environments in High Dimensional Neural Network Potentials

A central concern of molecular dynamics simulations are the potential energy surfaces that govern atomic interactions. These hypersurfaces define the potential energy of the system, and have generally been calculated using either predefined analytical formulas (classical) or quantum mechanical simulations (ab initio). The former can accurately reproduce only a selection of material properties, whereas the latter is restricted to short simulation times and small systems. Machine learning potentials have recently emerged as a third approach to model atomic interactions, and are purported to offer the accuracy of ab initio simulations with the speed of classical potentials. However, the performance of machine learning potentials depends crucially on the description of a local atomic environment. A set of invariant, orthogonal and differentiable descriptors for an atomic environment is proposed, implemented in a neural network potential for solid-state silicon, and tested in molecular dynamics simulations. Neural networks using the proposed descriptors are found to outperform ones using the Behler Parinello and SOAP descriptors currently in the literature.Comment: 23 Pages, 5 figures, 2 tables, journal articl

Energies and wave functions for a soft-core Coulomb potential

For the family of model soft Coulomb potentials represented by V(r) = -\frac{Z}{(r^q+\beta^q)^{\frac{1}{q}}}, with the parameters Z>0, \beta>0, q \ge 1, it is shown analytically that the potentials and eigenvalues, E_{\nu\ell}, are monotonic in each parameter. The potential envelope method is applied to obtain approximate analytic estimates in terms of the known exact spectra for pure power potentials. For the case q =1, the Asymptotic Iteration Method is used to find exact analytic results for the eigenvalues E_{\nu\ell} and corresponding wave functions, expressed in terms of Z and \beta. A proof is presented establishing the general concavity of the scaled electron density near the nucleus resulting from the truncated potentials for all q. Based on an analysis of extensive numerical calculations, it is conjectured that the crossing between the pair of states [(\nu,\ell),(\nu',\ell')], is given by the condition \nu'\geq (\nu+1) and \ell' \geq (\ell+3). The significance of these results for the interaction of an intense laser field with an atom is pointed out. Differences in the observed level-crossing effects between the soft potentials and the hydrogen atom confined inside an impenetrable sphere are discussed.Comment: 13 pages, 5 figures, title change, minor revision

Joint Deep Image Restoration and Unsupervised Quality Assessment

Deep learning techniques have revolutionized the fields of image restoration and image quality assessment in recent years. While image restoration methods typically utilize synthetically distorted training data for training, deep quality assessment models often require expensive labeled subjective data. However, recent studies have shown that activations of deep neural networks trained for visual modeling tasks can also be used for perceptual quality assessment of images. Following this intuition, we propose a novel attention-based convolutional neural network capable of simultaneously performing both image restoration and quality assessment. We achieve this by training a JPEG deblocking network augmented with "quality attention" maps and demonstrating state-of-the-art deblocking accuracy, achieving a high correlation of predicted quality with human opinion scores.Comment: 4 Pages, 2 figures, 3 table

Artefactos de hueso como testigos de continuidad cultural en Tatarlı Höyük

This paper is a preliminary evaluation of the bone artifacts from Tatarlı Höyük in Adana, Turkey. It is a site that holds an important place in the settlement history of Cilicia and shows a continuous, characteristic settlement until the Early Roman Period. In addition to personal ornaments such as beads and pendants, tools used in different economic activities in the daily life of Tatarlı Höyük, especially weaving, such as spatulas, spindle whorls, needles, pointed tools and handles are found in the bone assemblage. Majority of textile tools in these bone assemblage can be assumed as the evidence of economic importance and continuity of the weaving industry at Tatarlı Höyük.Este artículo es una evaluación preliminar de un conjunto de artefactos de hueso procedentes de Tatarlı Höyük, en Adana, Turquía. Este yacimiento ocupa un lugar importante en la historia de los asentamientos en Cilicia y muestra una ocupación continuada y característica hasta los inicios de la dominación romana. Además de los ornamentos personales, tales como cuentas y colgantes, se han documentado herramientas empleadas en diferentes actividades cotidianas en Tatarlı Höyük, especialmente relacionadas con el tejido, tales como espátulas, ruedas de huso, agujas, útiles apuntados y mangos, los cuales componen parte del conjunto óseo trabajado. La mayoría de las herramientas de la actividad textil en este conjunto de hueso son asumidas como evidencia de la importancia económica y continuidad que la industria del tejido ocupó en Tatarlı Höyük

The Effects of Material Properties on Building Performance

In recent earthquakes during the last two decades, severe damages have been occurred on the existing buildings in Turkey. Destructive earthquakes revealed that the existing building stock in urban regions is significantly vulnerable to seismic hazard. A large number of residential buildings located in regions of high seismicity require performance evaluation before the next big earthquake hits the region. In many earthquake resistant codes, several procedures are proposed to determine the building performance. The investigations on the damaged buildings show that material strengths are very important parameters on the building performance. In this study, material strengths’ effects on the building performance were investigated by using a nonlinear elastic analysis method