An ADMM Algorithm for a Class of Total Variation Regularized Estimation Problems

We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second that is separable in the difference between consecutive variable blocks. Examples of such problems include Fused Lasso estimation, total variation denoising, and multi-period portfolio optimization with transaction costs. In each iteration of our method, the first step involves separately optimizing over each variable block, which can be carried out in parallel. The second step is not separable in the variables, but can be carried out very efficiently. We apply the algorithm to segmentation of data based on changes inmean (l_1 mean filtering) or changes in variance (l_1 variance filtering). In a numerical example, we show that our implementation is around 10000 times faster compared with the generic optimization solver SDPT3

Efficient infrared upconversion via a ladder-type atomic configuration

We have demonstrated experimentally that infrared light at 1529.4nm can be converted into the visible at 780nm with 54% efficiency through a ladder-type atomic configuration in 85Rb. Specifically we theoretically analyze that high efficiency is due to the large nonlinear dispersion of the index of refraction from the off-resonant enhancement in a four-wave mixing (FWM) process. By using two perpendicular polarized pump fields, the coherence of two FWM processes in this configuration is verified.Comment: The new version is published in Journal of Modern Optic

Direct numerical simulation of compressible interfacial multiphase flows using a mass-momentum-energy consistent volume-of-fluid method

Compressible interfacial multiphase flows (CIMF) are essential to different applications, such as liquid fuel injection in supersonic propulsion systems. Since high-level details in CIMF are often difficult to measure in experiments, numerical simulation is an important alternative to shed light on the unclear physics. A direct numerical simulation (DNS) of CIMF will need to rigorously resolve the shock waves, the interfaces, and the interaction between the two. A novel numerical method has been developed and implemented in the present study. The geometric volume-of-fluid (VOF) method is employed to resolve the sharp interfaces between the two phases. The advection of the density, momentum, and energy is carried out consistently with VOF advection. To suppress spurious oscillations near shocks, numerical diffusion is introduced based on the Kurganov-Tadmor method in the region away from the interface. The contribution of pressure is incorporated using the projection method and the pressure is obtained by solving the Poisson-Helmholtz equation, which allows the present method to handle flows with all Mach numbers. The present method is tested by a sequence of CIMF problems. The simulation results are validated against theories, experiments, and other simulations, and excellent agreement has been achieved. In particular, the linear single-mode Richtmyer-Meshkov instabilities with finite Weber and Reynolds numbers are simulated. The simulation results agree very well with the linear stability theory, which affirms the capability of the present method in capturing the viscous and capillary effects on shock-interface interaction

Periodic Bouncing Modes for Two Uniformly Magnetized Spheres. I. Trajectories

We consider a uniformly magnetized sphere that moves without friction in a plane in response to the field of a second, identical, fixed sphere, making elastic hard-sphere collisions with this sphere. We seek periodic solutions to the associated nonlinear equations of motion. We find closed-form mathematical solutions for small-amplitude modes and use these to characterize and validate our large-amplitude modes, which we find numerically. Our Runge-Kutta integration approach allows us to find 1243 distinct periodic modes with the free sphere located initially at its stable equilibrium position. Each of these modes bifurcates from the finite-amplitude radial bouncing mode with infinitesimal-amplitude angular motion and supports a family of states with increasing amounts of angular motion. These states offer a rich variety of behaviors and beautiful, symmetric trajectories, including states with up to 157 collisions and 580 angular oscillations per period. A vibrant online learning community shares information about building beautiful sculptures from collections of small neodymium magnet spheres, with YouTube tutorial videos attracting over a hundred million views.1,2 These spheres offer engaging hands-on exposure to principles of magnetism and are used both in and out of the classroom to teach principles of mathematics, physics, chemistry, biology, and engineering.3 We showed recently that the forces and torques between two uniformly magnetized spheres are identical to the forces and torques between two point magnetic dipoles. In this paper, we exploit this equivalence to study the conservative nonlinear dynamics of a uniformly magnetized sphere subject to the magnetic forces and torques produced by a second, fixed, uniformly magnetized sphere, assuming frictionless hard-sphere elastic collisions between them. Our search for periodic states uncovers a wide variety of periodic modes, some of which are highly complex and beautiful

Periodic Bouncing Modes for Two Uniformly Magnetized Spheres. II. Scaling

A uniformly magnetized sphere moves without friction in a plane in response to the field of a second, identical, fixed sphere and makes elastic hard-sphere collisions with this sphere. Numerical simulations of the threshold energies and periods of periodic finite-amplitude nonlinear bouncing modes agree with small-amplitude closed-form mathematical results, which are used to identify scaling parameters that govern the entire amplitude range, including power-law scaling at large amplitudes. Scaling parameters are combinations of the bouncing number, the rocking number, the phase, and numerical factors. Discontinuities in the scaling functions are found when viewing the threshold energy and period as separate functions of the scaling parameters, for which large-amplitude scaling exponents are obtained from fits to the data. These discontinuities disappear when the threshold energy is viewed as a function of the threshold period, for which the large-amplitude scaling exponent is obtained analytically and for which scaling applies to both in-phase and out-of-phase modes. The purpose of this work is to investigate the scaling relationships between the threshold energy, the threshold period, the bouncing number, the rocking number, and the phase of 1497 periodic modes found previously for the motion of a uniformly magnetized sphere subject to the field of a second, identical, fixed sphere. This large dataset offers the opportunity to identify scaling relationships to high precision for this highly nonlinear problem. Such scaling relationships recall techniques used in studying phase transitions and fractals and invite the search for universal scaling laws that may also apply to other systems. This work is motivated by our interest in the properties of collections of small neodymium magnet spheres that are used to create beautiful magnetic sculptures and are used both in and out of the classroom to teach principles of mathematics, physics, chemistry, biology, and engineering

High-fidelity, broadband stimulated-Brillouin-scattering-based slow light using fast noise modulation

We demonstrate a 5-GHz-broadband tunable slow-light device based on stimulated Brillouin scattering in a standard highly-nonlinear optical fiber pumped by a noise-current-modulated laser beam. The noise modulation waveform uses an optimized pseudo-random distribution of the laser drive voltage to obtain an optimal flat-topped gain profile, which minimizes the pulse distortion and maximizes pulse delay for a given pump power. Eye-diagram and signal-to-noise ratio (SNR) analysis show that this new broadband slow-light technique significantly increases the fidelity of a delayed data sequence, while maintaining the delay performance. A fractional delay of 0.81 with a SNR of 5.2 is achieved at the pump power of 350 mW using a 2-km-long highly nonlinear fiber with the fast noise-modulation method, demonstrating a 50% increase in eye-opening and a 36% increase in SNR compared to a previous slow-modulation method

The James Owens Site (41TT769) in the Sulphur River Basin of Northeast Texas

The James Owens site (41TT769) is an apparent Middle to Late Caddoan settlement that was investigated in June 2001 at the request of the landowner, Mr. James Owens of Irving, Texas. The landowner is planning on building a house here in the future, and during the course of clearing the land and constructing a gravel drive way to the future house site, he noted some archeological materials on the surface. Discussions between Mr. Owens, Bryan Boyd (Texas Archeological Steward Network), and Mark Parsons, regional archeologist for the Texas Historical Commission, led to the limited investigations reported on here. The work we conducted was designed to obtain information on the age and content of the James Owens site, and determine what further archeological steps might be necessary to preserve the site and the information it contains. The James Owens site is situated on a small and heavily overgrown natural rise near the edge of an expanse of “moundy uplands” in the Post Oak Savannah. Immediately to the south is a flat stream terrace and floodplain of White Oak Creek, a tributary of the Sulphur River, and the current channel of White Oak Creek lies about 4 km to the south of the site. At the time of the 2001 investigations, the rise had been partially cleared by the landowner, with a gravel road leading from a Farm-to-Market road to the site itself. Lithic and ceramic artifacts were visible on the surface in the clearing

Theoretical and Phenomenological Constraints on Form Factors for Radiative and Semi-Leptonic B-Meson Decays

We study transition form factors for radiative and rare semi-leptonic B-meson decays into light pseudoscalar or vector mesons, combining theoretical constraints and phenomenological information from Lattice QCD, light-cone sum rules, and dispersive bounds. We pay particular attention to form factor parameterisations which are based on the so-called series expansion, and study the related systematic uncertainties on a quantitative level. In this context, we also provide the NLO corrections to the correlation function between two flavour-changing tensor currents, which enters the unitarity constraints for the coefficients in the series expansion.Comment: 52 pages; v2: normalization error in (29ff.) corrected, conclusion about relevance of unitarity bounds modified; form factor fits unaffected; references added; v3: discussion on truncation of series expansion added, matches version to be published in JHEP; v4: corrected typos in Tables 5 and

Viable tax constitutions

Taxation is only sustainable if the general public complies with it. This observation is uncontroversial with tax practitioners but has been ignored by the public finance tradition, which has interpreted tax constitutions as binding contracts by which the power to tax is irretrievably conferred by individuals to government, which can then levy any tax it chooses. However, in the absence of an outside party enforcing contracts between members of a group, no arrangement within groups can be considered to be a binding contract, and therefore the power of tax must be sanctioned by individuals on an ongoing basis. In this paper we offer, for the first time, a theoretical analysis of this fundamental compliance problem associated with taxation, obtaining predictions that in some cases point to a re-interptretation of the theoretical constructions of the public finance tradition while in others call them into question