Oscillatory Tunnel Splittings in Spin Systems: A Discrete Wentzel-Kramers-Brillouin Approach

Certain spin Hamiltonians that give rise to tunnel splittings that are viewed in terms of interfering instanton trajectories, are restudied using a discrete WKB method, that is more elementary, and also yields wavefunctions and preexponential factors for the splittings. A novel turning point inside the classically forbidden region is analysed, and a general formula is obtained for the splittings. The result is appled to the \Fe8 system. A previous result for the oscillation of the ground state splitting with external magnetic field is extended to higher levels.Comment: RevTex, one ps figur

Efficient algorithms for tensor scaling, quantum marginals and moment polytopes

We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our algorithm provides an efficient weak membership oracle for the associated moment polytopes, an important family of implicitly-defined convex polytopes with exponentially many facets and a wide range of applications. These include the entanglement polytopes from quantum information theory (in particular, we obtain an efficient solution to the notorious one-body quantum marginal problem) and the Kronecker polytopes from representation theory (which capture the asymptotic support of Kronecker coefficients). Our algorithm can be applied to succinct descriptions of the input tensor whenever the marginals can be efficiently computed, as in the important case of matrix product states or tensor-train decompositions, widely used in computational physics and numerical mathematics. We strengthen and generalize the alternating minimization approach of previous papers by introducing the theory of highest weight vectors from representation theory into the numerical optimization framework. We show that highest weight vectors are natural potential functions for scaling algorithms and prove new bounds on their evaluations to obtain polynomial-time convergence. Our techniques are general and we believe that they will be instrumental to obtain efficient algorithms for moment polytopes beyond the ones consider here, and more broadly, for other optimization problems possessing natural symmetries

Humoral and cytokine response elicited during immunisation with recombinant Immune Mapped protein-1 (EtIMP-1) and oocysts of Eimeria tenella

Eimeria tenella, the causative agent of caecal coccidiosis, is a pathogenic gut dwelling protozoan which can cause severe morbidity and mortality in farmed chickens. Immune mapped protein-1 (IMP-1) has been identified as an anticoccidial vaccine candidate; in the present study allelic polymorphism was assessed across the IMP-1 coding sequence in E. tenella isolates from four countries and compared with the UK reference Houghton strain. Nucleotide diversity was low, limited to expansion/contraction of a CAG triplet repeat and five substitutions, three of which were non-synonymous. The EtIMP-1 coding sequence from a cloned Indian E. tenella isolate was expressed in E. coli and purified as a His-tagged thioredoxin fusion protein. An in-vivo vaccination and challenge trial was conducted to test the vaccine potential of recombinant EtIMP-1 (rEtIMP-1) and to compare post-vaccination immune responses of chickens to those stimulated by live oocyst infection. Following challenge, parasite replication measured using quantitative PCR was significantly reduced in chickens that had been vaccinated with rEtIMP-1 (rIC group; 67% reduction compared to UC or unimmunised controls; 79% reduction compared to rTC group or recombinant thioredoxin mock-immunised controls, p < 0.05), or the birds vaccinated by infection with oocysts (OC group, 90% compared to unimmunised controls). Chickens vaccinated with oocysts (OC) had significantly higher levels of interferon gamma in their serum post-challenge, compared to rEtIMP-1 vaccinated birds (rIC). Conversely rEtIMP-1 (rIC) vaccinated birds had significantly higher antigen specific serum IgY responses, correlating with higher serum IL-4 (both p < 0.05)

Evaluation of CNN-based Single-Image Depth Estimation Methods

While an increasing interest in deep models for single-image depth estimation methods can be observed, established schemes for their evaluation are still limited. We propose a set of novel quality criteria, allowing for a more detailed analysis by focusing on specific characteristics of depth maps. In particular, we address the preservation of edges and planar regions, depth consistency, and absolute distance accuracy. In order to employ these metrics to evaluate and compare state-of-the-art single-image depth estimation approaches, we provide a new high-quality RGB-D dataset. We used a DSLR camera together with a laser scanner to acquire high-resolution images and highly accurate depth maps. Experimental results show the validity of our proposed evaluation protocol

Spin Tunneling in Magnetic Molecules: Quasisingular Perturbations and Discontinuous SU(2) Instantons

Spin coherent state path integrals with discontinuous semiclassical paths are investigated with special reference to a realistic model for the magnetic degrees of freedom in the Fe8 molecular solid. It is shown that such paths are essential to a proper understanding of the phenomenon of quenched spin tunneling in these molecules. In the Fe8 problem, such paths are shown to arise as soon as a fourth order anisotropy term in the energy is turned on, making this term a singular perturbation from the semiclassical point of view. The instanton approximation is shown to quantitatively explain the magnetic field dependence of the tunnel splitting, as well as agree with general rules for the number of quenching points allowed for a given value of spin. An accurate approximate formula for the spacing between quenching points is derived

Solvent Extraction & Spectrophotometric Determination of Ru(III), Rh(III) & Pd(II) using 1-(2' -Pyridylazo)-2-phenanthrol

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