Support Vector Machines in Analysis of Top Quark Production

Multivariate data analysis techniques have the potential to improve physics analyses in many ways. The common classification problem of signal/background discrimination is one example. The Support Vector Machine learning algorithm is a relatively new way to solve pattern recognition problems and has several advantages over methods such as neural networks. The SVM approach is described and compared to a conventional analysis for the case of identifying top quark signal events in the dilepton decay channel amidst a large number of background events.Comment: 8 pages, 8 figures, to be published in the proceedings of the "Advanced Statistical Techniques in Particle Physics" conference in Durham, UK (March, 2002

Equivalence problem for the orthogonal webs on the sphere

We solve the equivalence problem for the orthogonally separable webs on the three-sphere under the action of the isometry group. This continues a classical project initiated by Olevsky in which he solved the corresponding canonical forms problem. The solution to the equivalence problem together with the results by Olevsky forms a complete solution to the problem of orthogonal separation of variables to the Hamilton-Jacobi equation defined on the three-sphere via orthogonal separation of variables. It is based on invariant properties of the characteristic Killing two-tensors in addition to properties of the corresponding algebraic curvature tensor and the associated Ricci tensor. The result is illustrated by a non-trivial application to a natural Hamiltonian defined on the three-sphere.Comment: 32 page

Fast Conical Hull Algorithms for Near-separable Non-negative Matrix Factorization

The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012) turns non-negative matrix factorization (NMF) into a tractable problem. Recently, a new class of provably-correct NMF algorithms have emerged under this assumption. In this paper, we reformulate the separable NMF problem as that of finding the extreme rays of the conical hull of a finite set of vectors. From this geometric perspective, we derive new separable NMF algorithms that are highly scalable and empirically noise robust, and have several other favorable properties in relation to existing methods. A parallel implementation of our algorithm demonstrates high scalability on shared- and distributed-memory machines.Comment: 15 pages, 6 figure

Analysis of a Custom Support Vector Machine for Photometric Redshift Estimation and the Inclusion of Galaxy Shape Information

Aims: We present a custom support vector machine classification package for photometric redshift estimation, including comparisons with other methods. We also explore the efficacy of including galaxy shape information in redshift estimation. Support vector machines, a type of machine learning, utilize optimization theory and supervised learning algorithms to construct predictive models based on the information content of data in a way that can treat different input features symmetrically. Methods: The custom support vector machine package we have developed is designated SPIDERz and made available to the community. As test data for evaluating performance and comparison with other methods, we apply SPIDERz to four distinct data sets: 1) the publicly available portion of the PHAT-1 catalog based on the GOODS-N field with spectroscopic redshifts in the range $z < 3.6$, 2) 14365 galaxies from the COSMOS bright survey with photometric band magnitudes, morphology, and spectroscopic redshifts inside $z < 1.4$, 3) 3048 galaxies from the overlap of COSMOS photometry and morphology with 3D-HST spectroscopy extending to $z < 3.9$, and 4) 2612 galaxies with five-band photometric magnitudes and morphology from the All-wavelength Extended Groth Strip International Survey and $z < 1.57$. Results: We find that SPIDER-z achieves results competitive with other empirical packages on the PHAT-1 data, and performs quite well in estimating redshifts with the COSMOS and AEGIS data, including in the cases of a large redshift range ($0 < z < 3.9$). We also determine from analyses with both the COSMOS and AEGIS data that the inclusion of morphological information does not have a statistically significant benefit for photometric redshift estimation with the techniques employed here.Comment: Submitted to A&A, 11 pages, 10 figures, 1 table, updated to version in revisio

Stringy Black Holes and the Geometry of Entanglement

Recently striking multiple relations have been found between pure state 2 and 3-qubit entanglement and extremal black holes in string theory. Here we add further mathematical similarities which can be both useful in string and quantum information theory. In particular we show that finding the frozen values of the moduli in the calculation of the macroscopic entropy in the STU model, is related to finding the canonical form for a pure three-qubit entangled state defined by the dyonic charges. In this picture the extremization of the BPS mass with respect to moduli is connected to the problem of finding the optimal local distillation protocol of a GHZ state from an arbitrary pure three-qubit state. These results and a geometric classification of STU black holes BPS and non-BPS can be described in the elegant language of twistors. Finally an interesting connection between the black hole entropy and the average real entanglement of formation is established.Comment: 34 pages, 6 figure

Support Vector Machine classification of strong gravitational lenses

The imminent advent of very large-scale optical sky surveys, such as Euclid and LSST, makes it important to find efficient ways of discovering rare objects such as strong gravitational lens systems, where a background object is multiply gravitationally imaged by a foreground mass. As well as finding the lens systems, it is important to reject false positives due to intrinsic structure in galaxies, and much work is in progress with machine learning algorithms such as neural networks in order to achieve both these aims. We present and discuss a Support Vector Machine (SVM) algorithm which makes use of a Gabor filterbank in order to provide learning criteria for separation of lenses and non-lenses, and demonstrate using blind challenges that under certain circumstances it is a particularly efficient algorithm for rejecting false positives. We compare the SVM engine with a large-scale human examination of 100000 simulated lenses in a challenge dataset, and also apply the SVM method to survey images from the Kilo-Degree Survey.Comment: Accepted by MNRA