A new ADMM algorithm for the Euclidean median and its application to robust patch regression

The Euclidean Median (EM) of a set of points $\Omega$ in an Euclidean space is the point x minimizing the (weighted) sum of the Euclidean distances of x to the points in $\Omega$. While there exits no closed-form expression for the EM, it can nevertheless be computed using iterative methods such as the Wieszfeld algorithm. The EM has classically been used as a robust estimator of centrality for multivariate data. It was recently demonstrated that the EM can be used to perform robust patch-based denoising of images by generalizing the popular Non-Local Means algorithm. In this paper, we propose a novel algorithm for computing the EM (and its box-constrained counterpart) using variable splitting and the method of augmented Lagrangian. The attractive feature of this approach is that the subproblems involved in the ADMM-based optimization of the augmented Lagrangian can be resolved using simple closed-form projections. The proposed ADMM solver is used for robust patch-based image denoising and is shown to exhibit faster convergence compared to an existing solver.Comment: 5 pages, 3 figures, 1 table. To appear in Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing, April 19-24, 201

Magnetoelectric Effect and Spontaneous Polarization in HoFe3_3(BO3_3)4_4 and Ho0.5_{0.5}Nd0.5_{0.5}Fe3_3(BO3_3)4_4

The thermodynamic, magnetic, dielectric, and magnetoelectric properties of HoFe$_3$(BO$_3$)$_4$ and Ho$_{0.5}$Nd$_{0.5}$Fe$_3$(BO$_3$)$_4$ are investigated. Both compounds show a second order Ne\'{e}l transition above 30 K and a first order spin reorientation transition below 10 K. HoFe$_3$(BO$_3$)$_4$ develops a spontaneous electrical polarization below the Ne\'{e}l temperature (T$_N$) which is diminished in external magnetic fields. No magnetoelectric effect could be observed in HoFe$_3$(BO$_3$)$_4$. In contrast, the solid solution Ho$_{0.5}$Nd$_{0.5}$Fe$_3$(BO$_3$)$_4$ exhibits both, a spontaneous polarization below T$_N$ and a magnetoelectric effect at higher fields that extends to high temperatures. The superposition of spontaneous polarization, induced by the internal magnetic field in the ordered state, and the magnetoelectric polarizations due to the external field results in a complex behavior of the total polarization measured as a function of temperature and field.Comment: 12 pages, 15 figure

Theoretical analysis of neutron scattering results for quasi-two dimensional ferromagnets

A theoretical study has been carried out to analyse the available results from the inelastic neutron scattering experiment performed on a quasi-two dimensional spin-1/2 ferromagnetic material $K_2CuF_4$. Our formalism is based on a conventional semi-classical like treatment involving a model of an ideal gas of vortices/anti-vortices corresponding to an anisotropic XY Heisenberg ferromagnet on a square lattice. The results for dynamical structure functions for our model corresponding to spin-1/2, show occurrence of negative values in a large range of energy transfer even encompassing the experimental range, when convoluted with a realistic spectral window function. This result indicates failure of the conventional theoretical framework to be applicable to the experimental situation corresponding to low spin systems. A full quantum formalism seems essential for treating such systems.Comment: 16 pages, 6 figures, 1 Table Submitted for publicatio

Transport and bistable kinetics of a Brownian particle in a nonequilibrium environment

A system reservoir model, where the associated reservoir is modulated by an external colored random force, is proposed to study the transport of an overdamped Brownian particle in a periodic potential. We then derive the analytical expression for the average velocity, mobility, and diffusion rate. The bistable kinetics and escape rate from a metastable state in the overdamped region are studied consequently. By numerical simulation we then demonstrate that our analytical escape rate is in good agreement with that of numerical result.Comment: 10 pages, 2 figures, RevTex4, minor correction

Contrasting seed biology of two ornamental palms: Pygmy Date Palm (Phoenix roebelenii O’Brien) and Fishtail Palm (Caryota urens L.)

The Arecaceae family includes palm trees of economic importance both as a source of agricultural produce and asornamental components in landscaping projects. Pygmy date palm (Phoenix roebelenii) and solitary fishtail palm (Caryotaurens) are well known landscaping plants today. Both species have their origin in Southeast Asia and, especially C. urens iswidespread in peninsular India and Sri Lanka. They are multipurpose species with a variety of applications and thus veryheavily utilized. Knowledge of palm seed storage biology will improve their conservation prospects. In present studies, freshseed moisture content in P. roebelenii was recorded to be 30% with germinability of 98%. After desiccation to 8% moisturegerminability was reduced to 90% and the seeds survived cryo-exposure. Fresh seeds of C. urens, with initial moisturecontent of 34% and 95% germinability could be desiccated to lowest level of only 29% moisture content, with complete lossof germinability. Fresh as well as desiccated seeds of this species did not survive cryo-exposure. While the seeds of C. urensstored at room temperature lost their germinability by 110 days, seeds of P. roebelenii could germinate even after 9 monthsof storage. P. roebelenii is proven to exhibit orthodox seed storage behaviour while C. urens is found to exhibit recalcitrantseed storage behaviour. Long-term ex situ cryo-conservation in the form of seed gene banks would be suitable for seedpropagated orthodox palm species and a few germplasm centres may be established for recalcitrant Indian palms in suitablebio-geographic regions as a complimentary ex situ conservation

Magnetic Field resulting from non-linear electrical transport in single crystals of charge-ordered Pr0.63_{0.63} Ca0.37_{0.37} MnO3_{3}}

In this letter we report that the current induced destabilization of the charge ordered (CO) state in a rare-earth manganite gives rise to regions with ferromagnetic correlation. We did this experiment by measurement of the I-V curves in single crystal of the CO system Pr$_{0.63}$Ca$_{0.37}$MnO$_{3}$ and simultanously measuring the magnetization of the current carrying conductor using a high T$_c$ SQUID working at T = 77K. We have found that the current induced destabilization of the CO state leads to a regime of negative differential resistance which leads to a small enhancement of the magnetization of the sample, indicating ferromagnetically aligned moments.Comment: 4 pages LateX, 4 eps figure

EFX Allocations: Simplifications and Improvements

The existence of EFX allocations is a fundamental open problem in discretefair division. Given a set of agents and indivisible goods, the goal is todetermine the existence of an allocation where no agent envies anotherfollowing the removal of any single good from the other agent's bundle. Sincethe general problem has been illusive, progress is made on two fronts: $(i)$proving existence when the number of agents is small, $(ii)$ proving existenceof relaxations of EFX. In this paper, we improve results on both fronts (andsimplify in one of the cases). We prove the existence of EFX allocations with three agents, restricting onlyone agent to have an MMS-feasible valuation function (a strict generalizationof nice-cancelable valuation functions introduced by Berger et al. whichsubsumes additive, budget-additive and unit demand valuation functions). Theother agents may have any monotone valuation functions. Our proof technique issignificantly simpler and shorter than the proof by Chaudhury et al. onexistence of EFX allocations when there are three agents with additivevaluation functions and therefore more accessible. Secondly, we consider relaxations of EFX allocations, namely, approximate-EFXallocations and EFX allocations with few unallocated goods (charity). Chaudhuryet al. showed the existence of $(1-\epsilon)$-EFX allocation with$O((n/\epsilon)^{\frac{4}{5}})$ charity by establishing a connection to aproblem in extremal combinatorics. We improve their result and prove theexistence of $(1-\epsilon)$-EFX allocations with $\tilde{O}((n/\epsilon)^{\frac{1}{2}})$ charity. In fact, some of our techniques can be usedto prove improved upper-bounds on a problem in zero-sum combinatoricsintroduced by Alon and Krivelevich.<br

Optical Flow Estimation in the Deep Learning Age

Akin to many subareas of computer vision, the recent advances in deep learning have also significantly influenced the literature on optical flow. Previously, the literature had been dominated by classical energy-based models, which formulate optical flow estimation as an energy minimization problem. However, as the practical benefits of Convolutional Neural Networks (CNNs) over conventional methods have become apparent in numerous areas of computer vision and beyond, they have also seen increased adoption in the context of motion estimation to the point where the current state of the art in terms of accuracy is set by CNN approaches. We first review this transition as well as the developments from early work to the current state of CNNs for optical flow estimation. Alongside, we discuss some of their technical details and compare them to recapitulate which technical contribution led to the most significant accuracy improvements. Then we provide an overview of the various optical flow approaches introduced in the deep learning age, including those based on alternative learning paradigms (e.g., unsupervised and semi-supervised methods) as well as the extension to the multi-frame case, which is able to yield further accuracy improvements.Comment: To appear as a book chapter in Modelling Human Motion, N. Noceti, A. Sciutti and F. Rea, Eds., Springer, 202