Anomaly Detection for Data with Spatial Attributes

The problem of detecting spatially-coherent groups of data that exhibit anomalous behavior has started to attract attention due to applications across areas such as epidemic analysis and weather forecasting. Earlier efforts from the data mining community have largely focused on finding outliers, individual data objects that display deviant behavior. Such point-based methods are not easy to extend to find groups of data that exhibit anomalous behavior. Scan Statistics are methods from the statistics community that have considered the problem of identifying regions where data objects exhibit a behavior that is atypical of the general dataset. The spatial scan statistic and methods that build upon it mostly adopt the framework of defining a character for regions (e.g., circular or elliptical) of objects and repeatedly sampling regions of such character followed by applying a statistical test for anomaly detection. In the past decade, there have been efforts from the statistics community to enhance efficiency of scan statstics as well as to enable discovery of arbitrarily shaped anomalous regions. On the other hand, the data mining community has started to look at determining anomalous regions that have behavior divergent from their neighborhood.In this chapter,we survey the space of techniques for detecting anomalous regions on spatial data from across the data mining and statistics communities while outlining connections to well-studied problems in clustering and image segmentation. We analyze the techniques systematically by categorizing them appropriately to provide a structured birds eye view of the work on anomalous region detection;we hope that this would encourage better cross-pollination of ideas across communities to help advance the frontier in anomaly detection.

Simple approach to determine resonant frequencies of microstrip antennas

A simple approach for accurate determination of the resonant frequencies of microstrip antennas of regular geometries is developed and presented. In this approach, a generalised empirical formula for the computation of effective dielectric permittivity is given which takes into account the ratio of the fringing area to the area of the patch. A correction to the equivalent side length of an equilateral triangular patch, previously published, is modified and a new formula is given. A correction to the effective dimensions of an elliptical microstrip antenna is also carried out. Numerical results obtained for the resonant frequencies of elliptical, circular, rectangular and equilateral-triangular microstrip antennas are in good agreement with the available theoretical and experimental results reported by others. The present approach is more efficient, simpler and more accurate

Field on Poincare Group and Quantum Description of Orientable Objects

We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner`s ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with the help of two reference frames (space-fixed and body-fixed). A technical realization of this generalization (for instance, in 3+1 dimensions) amounts to introducing wave functions that depend on elements of the Poincar, group G. A complete set of transformations that test the symmetries of an orientable object and of the embedding space belongs to the group I =GxG. All such transformations can be studied by considering a generalized regular representation of G in the space of scalar functions on the group, f(x,z), that depend on the Minkowski space points xaG/Spin(3,1) as well as on the orientation variables given by the elements z of a matrix ZaSpin(3,1). In particular, the field f(x,z) is a generating function of the usual spin-tensor multi-component fields. In the theory under consideration, there are four different types of spinors, and an orientable object is characterized by ten quantum numbers. We study the corresponding relativistic wave equations and their symmetry properties.

Highly accurate quantum chemistry : spin-orbit splittings via multireference coupled-cluster methods and applications in heavy-atom main-group chemistry

Diese Dissertation demonstriert und verbessert die Vorhersagekraft der Coupled-Cluster-Theorie im Hinblick auf die hochgenaue Berechnung von Moleküleigenschaften. Die Demonstration erfolgt mittels Extrapolations- und Additivitätstechniken in der Single-Referenz-Coupled-Cluster-Theorie, mit deren Hilfe die Existenz und Struktur von bisher unbekannten Molekülen mit schweren Hauptgruppenelementen vorhergesagt wird. Vor allem am Beispiel von cyclischem SiS_2, einem dreiatomigen Molekül mit 16 Valenzelektronen, wird deutlich, dass die Vorhersagekraft der Theorie sich heutzutage auf Augenhöhe mit dem Experiment befindet: Theoretische Überlegungen initiierten eine experimentelle Suche nach diesem Molekül, was schließlich zu dessen Detektion und Charakterisierung mittels Rotationsspektroskopie führte. Die Vorhersagekraft der Coupled-Cluster-Theorie wird verbessert, indem eine Multireferenz-Coupled-Cluster-Methode für die Berechnung von Spin-Bahn-Aufspaltungen erster Ordnung in 2^Pi-Zuständen entwickelt wird. Der Fokus hierbei liegt auf Mukherjee's Variante der Multireferenz-Coupled-Cluster-Theorie, aber prinzipiell ist das vorgeschlagene Berechnungsschema auf alle Varianten anwendbar. Die erwünschte Genauigkeit beträgt 10 cm^-1. Sie wird mit der neuen Methode erreicht, wenn Ein- und Zweielektroneneffekte und bei schweren Elementen auch skalarrelativistische Effekte berücksichtigt werden. Die Methode eignet sich daher in Kombination mit Coupled-Cluster-basierten Extrapolations-und Additivitätsschemata dafür, hochgenaue thermochemische Daten zu berechnen.

An anisotropic elastic-viscoplastic damage model for bone tissue

A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain D(κ) , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.

Group 14 element-based non-centrosymmetric quantum spin hall insulators with large bulk gap

To date, a number of two-dimensional (2D) topological insulators (TIs) have been realized in Group 14 elemental honeycomb lattices, but all are inversionsymmetric. Here, based on first-principles calculations, we predict a new family of 2D inversion-asymmetric TIs with sizeable bulk gaps from 105 meV to 284 meV, in X2–GeSn (X = H, F, Cl, Br, I) monolayers, making them in principle suitable for room-temperature applications. The nontrivial topological characteristics of inverted band orders are identified in pristine X2–GeSn with X = (F, Cl, Br, I), whereas H2–GeSn undergoes a nontrivial band inversion at 8% lattice expansion. Topologically protected edge states are identified in X2–GeSn with X = (F, Cl, Br, I), as well as in strained H2–GeSn. More importantly, the edges of these systems, which exhibit single-Dirac-cone characteristics located exactly in the middle of their bulk band gaps, are ideal for dissipationless transport. Thus, Group 14 elemental honeycomb lattices provide a fascinating playground for the manipulation of quantum states.

Working group report: Quantum chromodynamics sub-group

This is the report of the QCD working sub-group at the Tenth Workshop on High Energy Physics Phenomenology (WHEPP-X).

Effect of the ratio of TMIn flow to group III flow on the properties of InGaN/GaN multiple quantum wells

Triple-axis x-ray diffraction (TXRD) and photoluminescence (PL) spectra are used to assess the influence of the ratio of TMIn flow to group III flow on structural defects, such as dislocations and interface roughness, and optical properties of multiple quantum wells(MQWs). In this paper the mean densities of edge and screw dislocations in InGaN/GaN MQWs are obtained by W scan of every satellite peak of (0002) symmetric and (1012) asymmetric diffractions. At the same time, the interface roughness is measured by the radio of the full width at half maximum of satellite peaks to the peak orders. The experimental results showed that the density of dislocation, especially of edge dislocation, and interface roughness increase with the increase of the ratio, which leads to the decrease of PL properties. It also can be concluded that the edge dislocation acts as nonradiative recombination centers in InGaN/GaN MQWs. Also noticed is that the variation of the ratio has more influence on edge dislocation than on screw dislocation.

Resonance-enhanced group delay times in an asymmetric single quantum barrier

It is shown that transmission and reflection group delay times in an asymmetric single quantum barrier are greatly enhanced by the transmission resonance when the energy of incident particles is larger than the height of the barrier. The resonant transmission group delay is of the order of the quasibound state lifetime in the barrier region. The reflection group delay can be either positive or negative, depending on the relative height of the potential energies on the two sides of the barrier. Its magnitude is much larger than the quasibound state lifetime. These predictions have been observed in microwave experiments. (c) 2005 Elsevier B.V. All rights reserved.

Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory.rnAs its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained.rnThe constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point.rnFinally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of existing computations, taking the independent running of the Euler topological term into account. Known perturbative results are reproduced in this case from the renormalization group equation, identifying however a unique non-Gaussian fixed point.rn

From quantum to classical dynamics: The relativistic O ( N ) model in the framework of the real-time functional renormalization group

We investigate the transition from unitary to dissipative dynamics in the relativistic O(N) vector model with the λ(φ2)2 interaction using the nonperturbative functional renormalization group in the real-time formalism. In thermal equilibrium, the theory is characterized by two scales, the interaction range for coherent scattering of particles and the mean free path determined by the rate of incoherent collisions with excitations in the thermal medium. Their competition determines the renormalization group flow and the effective dynamics of the model. Here we quantify the dynamic properties of the model in terms of the scale-dependent dynamic critical exponent z in the limit of large temperatures and in 2≤d≤4 spatial dimensions. We contrast our results to the behavior expected at vanishing temperature and address the question of the appropriate dynamic universality class for the given microscopic theory.

NMR relaxation study of disorder in the mixed system BP x GPI(1-x) and the low temperature transition from classical to quantum rotation

1H NMR spin-lattice relaxation time (T1) studies have been carried out in the temperature range 100 K to 4 K, at two Larmor frequencies 11.4 and 23.3 MHz, in the mixed system of betaine phosphate and glycine phosphite (BPxGPI(1-x)), to study the effects of disorder on the proton group dynamics. Analysis of T1 data indicates the presence of a number of inequivalent methyl groups and a gradual transition from classical reorientations to quantum tunneling rotations. At lower temperatures, microstructural disorder in the local environments of the methyl groups, result in a distribution in the activation energy (Ea) and the torsional energy gap (E01). For certain values of x, the magnetisation recovery shows biexponential behaviour at lower temperatures.

Non-Abelian monopoles break color. II. Field theory and quantum mechanics

Many grand unified theories (GUT's) predict non-Abelian monopoles which are sources of non-Abelian (and Abelian) magnetic flux. In the preceding paper, we discussed in detail the topological obstructions to the global implementation of the action of the "unbroken symmetry group" H on a classical test particle in the field of such a monopole. In this paper, the existence of similar topological obstructions to the definition of H action on the fields in such a monopole sector, as well as on the states of a quantum-mechanical test particle in the presence of such fields, are shown in detail. Some subgroups of H which can be globally realized as groups of automorphisms are identified. We also discuss the application of our analysis to the SU(5) GUT and show in particular that the non-Abelian monopoles of that theory break color and electroweak symmetries.

The nonplanar peptide unit III. Quantum chemical calculations for related compounds and experimental X-ray diffraction data

The possible nonplanar distortions of the amide group in formamide, acetamide, N-methylacetamide, and N-ethylacetamide have been examined using CNDO/2 and INDO methods. The predictions from these methods are compared with the results obtained from X-ray and neutron diffraction studies on crystals of small open peptides, cyclic peptides, and amides. It is shown that the INDO results are in good agreement with observations, and that the dihedral angles N and defining the nonplanarity of the amide unit are correlated approximately by the relation N = -2, while C is small and uncorrelated with . The present study indicates that the nonplanar distortions at the nitrogen atom of the peptide unit may have to be taken into consideration, in addition to the variation in the dihedral angles (,), in working out polypeptide and protein structures.

E. C. G. Sudarshan and Symmetry in Classical Dynamics, Optics and Quantum Mechanics

We review work initiated and inspired by Sudarshan in relativistic dynamics, beam optics, partial coherence theory, Wigner distribution methods, multimode quantum optical squeezing, and geometric phases. The 1963 No Interaction Theorem using Dirac's instant form and particle World Line Conditions is recalled. Later attempts to overcome this result exploiting constrained Hamiltonian theory, reformulation of the World Line Conditions and extending Dirac's formalism, are reviewed. Dirac's front form leads to a formulation of Fourier Optics for the Maxwell field, determining the actions of First Order Systems (corresponding to matrices of Sp(2,R) and Sp(4,R)) on polarization in a consistent manner. These groups also help characterize properties and propagation of partially coherent Gaussian Schell Model beams, leading to invariant quality parameters and the new Twist phase. The higher dimensional groups Sp(2n,R) appear in the theory of Wigner distributions and in quantum optics. Elegant criteria for a Gaussian phase space function to be a Wigner distribution, expressions for multimode uncertainty principles and squeezing are described. In geometric phase theory we highlight the use of invariance properties that lead to a kinematical formulation and the important role of Bargmann invariants. Special features of these phases arising from unitary Lie group representations, and a new formulation based on the idea of Null Phase Curves, are presented.