A Survey on Graph Kernels

Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We describe and categorize graph kernels based on properties inherent to their design, such as the nature of their extracted graph features, their method of computation and their applicability to problems in practice. In an extensive experimental evaluation, we study the classification accuracy of a large suite of graph kernels on established benchmarks as well as new datasets. We compare the performance of popular kernels with several baseline methods and study the effect of applying a Gaussian RBF kernel to the metric induced by a graph kernel. In doing so, we find that simple baselines become competitive after this transformation on some datasets. Moreover, we study the extent to which existing graph kernels agree in their predictions (and prediction errors) and obtain a data-driven categorization of kernels as result. Finally, based on our experimental results, we derive a practitioner's guide to kernel-based graph classification

Optical Versus Mid-Infrared Spectroscopic Classification of Ultraluminous Infrared Galaxies

The origin of huge infrared luminosities of ultraluminous infrared galaxies (ULIGs) is still in question. Recently, Genzel et al. made mid-infrared (MIR) spectroscopy of a large number of ULIGs and found that the major energy source in them is massive stars formed in the recent starburst activity; i.e., $\sim$ 70% -- 80% of the sample are predominantly powered by the starburst. However, it is known that previous optical spectroscopic observations showed that the majority of ULIGs are classified as Seyferts or LINERs (low-ionization nuclear emission-line regions). In order to reconcile this difference, we compare types of emission-line activity for a sample of ULIGs which have been observed in both optical and MIR. We confirm the results of previous studies that the majority of ULIGs classified as LINERs based on the optical emission-line diagnostics turn to be starburst-dominated galaxies based on the MIR ones. Since the MIR spectroscopy can probe more heavily-reddened, inner parts of the ULIGs, it is quite unlikely that the inner parts are powered by the starburst while the outer parts are powered by non-stellar ionization sources. The most probable resolution of this dilemma is that the optical emission-line nebulae with the LINER properties are powered predominantly by shock heating driven by the superwind activity; i.e., a blast wave driven by a collective effect of a large number of supernovae in the central region of galaxy mergers.Comment: 15 pages, 2 tables, and 3 eps figures. The Astrophysical Journal (Part 1), in pres

Non-adiabatic holonomic quantum computation

We develop a non-adiabatic generalization of holonomic quantum computation in which high-speed universal quantum gates can be realized by using non-Abelian geometric phases. We show how a set of non-adiabatic holonomic one- and two-qubit gates can be implemented by utilizing optical transitions in a generic three-level $\Lambda$ configuration. Our scheme opens up for universal holonomic quantum computation on qubits characterized by short coherence times.Comment: Some changes, journal reference adde

Iterative solutions to the steady state density matrix for optomechanical systems

We present a sparse matrix permutation from graph theory that gives stable incomplete Lower-Upper (LU) preconditioners necessary for iterative solutions to the steady state density matrix for quantum optomechanical systems. This reordering is efficient, adding little overhead to the computation, and results in a marked reduction in both memory and runtime requirements compared to other solution methods, with performance gains increasing with system size. Either of these benchmarks can be tuned via the preconditioner accuracy and solution tolerance. This reordering optimizes the condition number of the approximate inverse, and is the only method found to be stable at large Hilbert space dimensions. This allows for steady state solutions to otherwise intractable quantum optomechanical systems.Comment: 10 pages, 5 figure

On the stability of quantum holonomic gates

We provide a unified geometrical description for analyzing the stability of holonomic quantum gates in the presence of imprecise driving controls (parametric noise). We consider the situation in which these fluctuations do not affect the adiabatic evolution but can reduce the logical gate performance. Using the intrinsic geometric properties of the holonomic gates, we show under which conditions on noise's correlation time and strength, the fluctuations in the driving field cancel out. In this way, we provide theoretical support to previous numerical simulations. We also briefly comment on the error due to the mismatch between real and nominal time of the period of the driving fields and show that it can be reduced by suitably increasing the adiabatic time.Comment: 7 page

Stochastic Transition Model for Discrete Agent Movements

We propose a calibrated two-dimensional cellular automaton model to simulate pedestrian motion behavior. It is a v=4 (3) model with exclusion statistics and random shuffled dynamics. The underlying regular grid structure results in a direction-dependent behavior, which has in particular not been considered within previous approaches. We efficiently compensate these grid-caused deficiencies on model level.Comment: 8 pages, 4 figure

Internally Electrodynamic Particle Model: Its Experimental Basis and Its Predictions

The internally electrodynamic (IED) particle model was derived based on overall experimental observations, with the IED process itself being built directly on three experimental facts, a) electric charges present with all material particles, b) an accelerated charge generates electromagnetic waves according to Maxwell's equations and Planck energy equation and c) source motion produces Doppler effect. A set of well-known basic particle equations and properties become predictable based on first principles solutions for the IED process; several key solutions achieved are outlined, including the de Broglie phase wave, de Broglie relations, Schr\"odinger equation, mass, Einstein mass-energy relation, Newton's law of gravity, single particle self interference, and electromagnetic radiation and absorption; these equations and properties have long been broadly experimentally validated or demonstrated. A specific solution also predicts the Doebner-Goldin equation which emerges to represent a form of long-sought quantum wave equation including gravity. A critical review of the key experiments is given which suggests that the IED process underlies the basic particle equations and properties not just sufficiently but also necessarily.Comment: Presentation at the 27th Int Colloq on Group Theo Meth in Phys, 200

Enhanced spin accumulation in a superconductor

A lateral array of ferromagnetic tunnel junctions is used to inject and detect non-equilibrium quasi-particle spin distribution in a superconducting strip made of Al. The strip width and thickness is kept below the quasi particle spin diffusion length in Al. Non-local measurements in multiple parallel and antiparallel magnetic states of the detectors are used to in-situ determine the quasi-particle spin diffusion length. A very large increase in the spin accumulation in the superconducting state compared to that in the normal state is observed and is attributed to a diminishing of the quasi-particle population by opening of the gap below the transition temperature.Comment: 6 pages, 4 figures; accepted for publication in Journal of Applied Physic

Crystal-field effects in the first-order valence transition in YbInCu4 induced by an external magnetic field

As it was shown earlier [Dzero, Gor'kov, and Zvezdin, J. Phys.:Condens. Matter 12, L711 (2000)] the properties of the first-order valence phase transition in YbInCu4 in the wide range of magnetic fields and temperatures are perfectly described in terms of a simple entropy transition for free Yb ions. Within this approach, the crystal field effects have been taken into account and we show that the phase diagram in the $B-T$ plane acquires some anisotropy with respect to the direction of an external magnetic field.Comment: 4 pages, 3 eps figures; minor changes; to be piblished in J. of Physics: Cond. Ma