A combined first and second order variational approach for image reconstruction

In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a non-smooth second order regulariser. It combines convex functions of the total variation and the total variation of the first derivatives. In what follows, we prove existence and uniqueness of minimisers of the combined model and present the numerical solution of the corresponding discretised problem by employing the split Bregman method. The paper is furnished with applications of our model to image denoising, deblurring as well as image inpainting. The obtained numerical results are compared with results obtained from total generalised variation (TGV), infimal convolution and Euler's elastica, three other state of the art higher-order models. The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images -- a known disadvantage of the ROF model -- while being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure

Long-term trends in tropical cyclone tracks around Korea and Japan in late summer and early fall

This study investigates long-term trends in tropical cyclones (TCs) over the extratropical western North Pacific (WNP) over a period of 35 years (1982-2016). The area analyzed extended across 30-45 degrees N and 120-150 degrees E, including the regions of Korea and Japan that were seriously affected by TCs. The northward migration of TCs over the WNP to the mid-latitudes showed a sharp increase in early fall. In addition, the duration of TCs over the WNP that migrated northwards showed an increase, specifically in early to mid-September. Therefore, more recently, TC tracks have been observed to significantly extend into the mid-latitudes. The recent northward extension of TC tracks over the WNP in early fall was observed to be associated with changes in environmental conditions that were favorable for TC activities, including an increase in sea surface temperature (SST), decrease in vertical wind shear, expansion of subtropical highs, strong easterly steering winds, and an increase in relative vorticity. In contrast, northward migrations of TCs to Korea and Japan showed a decline in late August, because of the presence of unfavorable environmental conditions for TC activities. These changes in environmental conditions, such as SST and vertical wind shear, can be partially associated with the Pacific decadal oscillation

Iterative algorithms for total variation-like reconstructions in seismic tomography

A qualitative comparison of total variation like penalties (total variation, Huber variant of total variation, total generalized variation, ...) is made in the context of global seismic tomography. Both penalized and constrained formulations of seismic recovery problems are treated. A number of simple iterative recovery algorithms applicable to these problems are described. The convergence speed of these algorithms is compared numerically in this setting. For the constrained formulation a new algorithm is proposed and its convergence is proven.Comment: 28 pages, 8 figures. Corrected sign errors in formula (25

Non-Abelian dynamics and heavy multiquarks, Steiner-tree confinement in hadron spectroscopy

A brief review is first presented of attempts to predict stable multiquark states within current models of hadron spectroscopy. Then a model combining flip-flop and connected Steiner trees is introduced and shown to lead to stable multiquarks, in particular for some configurations involving several heavy quarks and bearing exotic quantum numbers.Comment: 8 pages, 5 figures, Invited talk at the 21st European Conference on Few-Body Problems in Physics, Salamanca, Spain, August 29th--September 3rd, 2010, to appear in the Proceedings, ed.~A.~Valcarce et al., to appear in Few-Body Syste

Star Models with Dark Energy

We have constructed star models consisting of four parts: (i) a homogeneous inner core with anisotropic pressure (ii) an infinitesimal thin shell separating the core and the envelope; (iii) an envelope of inhomogeneous density and isotropic pressure; (iv) an infinitesimal thin shell matching the envelope boundary and the exterior Schwarzschild spacetime. We have analyzed all the energy conditions for the core, envelope and the two thin shells. We have found that, in order to have static solutions, at least one of the regions must be constituted by dark energy. The results show that there is no physical reason to have a superior limit for the mass of these objects but for the ratio of mass and radius.Comment: 20 pages, 1 figure, references and some comments added, typos corrected, in press GR

Knowledge-based energy functions for computational studies of proteins

This chapter discusses theoretical framework and methods for developing knowledge-based potential functions essential for protein structure prediction, protein-protein interaction, and protein sequence design. We discuss in some details about the Miyazawa-Jernigan contact statistical potential, distance-dependent statistical potentials, as well as geometric statistical potentials. We also describe a geometric model for developing both linear and non-linear potential functions by optimization. Applications of knowledge-based potential functions in protein-decoy discrimination, in protein-protein interactions, and in protein design are then described. Several issues of knowledge-based potential functions are finally discussed.Comment: 57 pages, 6 figures. To be published in a book by Springe

Spectral quark model and low-energy hadron phenomenology

We propose a spectral quark model which can be applied to low energy hadronic physics. The approach is based on a generalization of the Lehmann representation of the quark propagator. We work at the one-quark-loop level. Electromagnetic and chiral invariance are ensured with help of the gauge technique which provides particular solutions to the Ward-Takahashi identities. General conditions on the quark spectral function follow from natural physical requirements. In particular, the function is normalized, its all positive moments must vanish, while the physical observables depend on negative moments and the so-called log-moments. As a consequence, the model is made finite, dispersion relations hold, chiral anomalies are preserved, and the twist expansion is free from logarithmic scaling violations, as requested of a low-energy model. We study a variety of processes and show that the framework is very simple and practical. Finally, incorporating the idea of vector-meson dominance, we present an explicit construction of the quark spectral function which satisfies all the requirements. The corresponding momentum representation of the resulting quark propagator exhibits only cuts on the physical axis, with no poles present anywhere in the complex momentum space. The momentum-dependent quark mass compares very well to recent lattice calculations. A large number of predictions and relations can be deduced from our approach for such quantities as the pion light-cone wave function, non-local quark condensate, pion transition form factor, pion valence parton distribution function, etc.Comment: revtex, 24 pages, 3 figure

Low Energy Chiral Lagrangian in Curved Space-Time from the Spectral Quark Model

We analyze the recently proposed Spectral Quark Model in the light of Chiral Perturbation Theory in curved space-time. In particular, we calculate the chiral coefficients $L_1, ..., L_{10}$, as well as the coefficients $L_{11}$, $L_{12}$, and $L_{13}$, appearing when the model is coupled to gravity. The analysis is carried for the SU(3) case. We analyze the pattern of chiral symmetry breaking as well as elaborate on the fulfillment of anomalies. Matching the model results to resonance meson exchange yields the relation between the masses of the scalar, tensor and vector mesons, $M_{f_0}=M_{f_2}=\sqrt{2} M_V= 4 \sqrt{3 /N_c} \pi f_\pi$. Finally, the large-$N_c$ limit suggests the dual relations in the vector and scalar channels, $M_V=M_S= 2 \sqrt{6 /N_c} \pi f_\pi$ and $^{1/2}_S = < r^2 >^{1/2}_V = 2 \sqrt{N_c} / f_\pi = 0.59 {\rm fm}$.Comment: 18 pages, no figure

Astroparticle Physics with a Customized Low-Background Broad Energy Germanium Detector

The MAJORANA Collaboration is building the MAJORANA DEMONSTRATOR, a 60 kg array of high purity germanium detectors housed in an ultra-low background shield at the Sanford Underground Laboratory in Lead, SD. The MAJORANA DEMONSTRATOR will search for neutrinoless double-beta decay of 76Ge while demonstrating the feasibility of a tonne-scale experiment. It may also carry out a dark matter search in the 1-10 GeV/c^2 mass range. We have found that customized Broad Energy Germanium (BEGe) detectors produced by Canberra have several desirable features for a neutrinoless double-beta decay experiment, including low electronic noise, excellent pulse shape analysis capabilities, and simple fabrication. We have deployed a customized BEGe, the MAJORANA Low-Background BEGe at Kimballton (MALBEK), in a low-background cryostat and shield at the Kimballton Underground Research Facility in Virginia. This paper will focus on the detector characteristics and measurements that can be performed with such a radiation detector in a low-background environment.Comment: Submitted to NIMA Proceedings, SORMA XII. 9 pages, 4 figure