Inverse problems for Schrodinger equations with Yang-Mills potentials in domains with obstacles and the Aharonov-Bohm effect

We study the inverse boundary value problems for the Schr\"{o}dinger equations with Yang-Mills potentials in a bounded domain $\Omega_0\subset\R^n$ containing finite number of smooth obstacles $\Omega_j,1\leq j \leq r$. We prove that the Dirichlet-to-Neumann operator on $\partial\Omega_0$ determines the gauge equivalence class of the Yang-Mills potentials. We also prove that the metric tensor can be recovered up to a diffeomorphism that is identity on $\partial\Omega_0$.Comment: 15 page

Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow

We compute the sum of the positive Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. The computation is based on the analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and hyperbolic Laplacians when the underlying Riemann surface degenerates.Comment: Minor corrections. To appear in Publications mathematiques de l'IHE

Modeling of primary dendrite arm spacing variations in thin-slab casting of low carbon and low alloy steels

Solidification structure of a High Strength Low Alloy (HSLA) steel, in terms of dendrite arm spacing distribution across the shell thickness, is studied in a breakout shell from a thin-slab caster at Tata Steel in IJmuiden. Columnar dendrites were found to be the predominant morphology throughout the shell with size variations across the shell thickness. Primary Dendrite Arm Spacing (PDAS) increases by increasing the distance from meniscus or slab surface. Subsequently, a model is proposed to describe the variation of the PDAS with the shell thickness (the distance from slab surface) under solidifiction conditions experienced in the primary cooling zone of thin-slab casting. The proposed relationship related the PDAS to the shell thickness and, hence, can be used as a tool for predicting solidifcation structure and optimizing the thin-slab casting of low alloy steels

Circadian Organization in Hemimetabolous Insects

The circadian system of hemimetabolous insects is reviewed in respect to the locus of the circadian clock and multioscillatory organization. Because of relatively easy access to the nervous system, the neuronal organization of the clock system in hemimetabolous insects has been studied, yielding identification of the compound eye as the major photoreceptor for entrainment and the optic lobe for the circadian clock locus. The clock site within the optic lobe is inconsistent among reported species; in cockroaches the lobula was previously thought to be a most likely clock locus but accessory medulla is recently stressed to be a clock center, while more distal part of the optic lobe including the lamina and the outer medulla area for the cricket. Identification of the clock cells needs further critical studies. Although each optic lobe clock seems functionally identical, in respect to photic entrainment and generation of the rhythm, the bilaterally paired clocks form a functional unit. They interact to produce a stable time structure within individual insects by exchanging photic and temporal information through neural pathways, in which serotonin and pigment-dispersing factor (PDF) are involved as chemical messengers. The mutual interaction also plays an important role in seasonal adaptation of the rhythm

Super-CLEVR: A Virtual Benchmark to Diagnose Domain Robustness in Visual Reasoning

Visual Question Answering (VQA) models often perform poorly onout-of-distribution data and struggle on domain generalization. Due to themulti-modal nature of this task, multiple factors of variation are intertwined,making generalization difficult to analyze. This motivates us to introduce avirtual benchmark, Super-CLEVR, where different factors in VQA domain shiftscan be isolated in order that their effects can be studied independently. Fourfactors are considered: visual complexity, question redundancy, conceptdistribution and concept compositionality. With controllably generated data,Super-CLEVR enables us to test VQA methods in situations where the test datadiffers from the training data along each of these axes. We study four existingmethods, including two neural symbolic methods NSCL and NSVQA, and twonon-symbolic methods FiLM and mDETR; and our proposed method, probabilisticNSVQA (P-NSVQA), which extends NSVQA with uncertainty reasoning. P-NSVQAoutperforms other methods on three of the four domain shift factors. Ourresults suggest that disentangling reasoning and perception, combined withprobabilistic uncertainty, form a strong VQA model that is more robust todomain shifts. The dataset and code are released athttps://github.com/Lizw14/Super-CLEVR.<br

The genetic basis of host preference and resting behavior in the major African malaria vector, Anopheles arabiensis

Malaria transmission is dependent on the propensity of Anopheles mosquitoes to bite humans (anthropophily) instead of other dead end hosts. Recent increases in the usage of Long Lasting Insecticide Treated Nets (LLINs) in Africa have been associated with reductions in highly anthropophilic and endophilic vectors such as Anopheles gambiae s.s., leaving species with a broader host range, such as Anopheles arabiensis, as the most prominent remaining source of transmission in many settings. An. arabiensis appears to be more of a generalist in terms of its host choice and resting behavior, which may be due to phenotypic plasticity and/or segregating allelic variation. To investigate the genetic basis of host choice and resting behavior in An. arabiensis we sequenced the genomes of 23 human-fed and 25 cattle-fed mosquitoes collected both in-doors and out-doors in the Kilombero Valley, Tanzania. We identified a total of 4,820,851 SNPs, which were used to conduct the first genome-wide estimates of “SNP heritability”for host choice and resting behavior in this species. A genetic component was detected for host choice (human vs cow fed; permuted P = 0.002), but there was no evidence of a genetic component for resting behavior (indoors versus outside; permuted P = 0.465). A principal component analysis (PCA) segregated individuals based on genomic variation into three groups which were characterized by differences at the 2Rb and/or 3Ra paracentromeric chromosome inversions. There was a non-random distribution of cattle-fed mosquitoes between the PCA clusters, suggesting that alleles linked to the 2Rb and/or 3Ra inversions may influence host choice. Using a novel inversion genotyping assay, we detected a significant enrichment of the standard arrangement (non-inverted) of 3Ra among cattle-fed mosquitoes (N = 129) versus all non-cattle-fed individuals. Thus, tracking the frequency of the 3Ra in An. arabiensis populations may be of use to infer selection on host choice behavior within these vector populations; possibly in response to vector control. Controlled host-choice assays are needed to discern whether the observed genetic component has a direct relationship with innate host preference. A better understanding of the genetic basis for host feeding behavior in An. arabiensis may also open avenues for novel vector control strategies based on driving genes for zoophily into wild mosquito populations

Development Of Al-B-C Master Alloy Under External Fields

This study investigates the application of external fields in the development of an Al-B-C alloy, with the aim of synthesizing in situ Al3BC particles. A combination of ultrasonic cavitation and distributive mixing was applied for uniform dispersion of insoluble graphite particles in the Al melt, improving their wettability and its subsequent incorporation into the Al matrix. Lower operating temperatures facilitated the reduction in the amount of large clusters of reaction phases, with Al3BC being identified as the main phase in XRD analysis. The distribution of Al3BC particles was quantitatively evaluated. Grain refinement experiments reveal that Al-B-C alloy can act as a master alloy for Al-4Cu and AZ91D alloys, with average grain size reduction around 50% each at 1wt%Al-1.5B-2C additions

Diffractive orbits in isospectral billiards

Isospectral domains are non-isometric regions of space for which the spectra of the Laplace-Beltrami operator coincide. In the two-dimensional Euclidean space, instances of such domains have been given. It has been proved for these examples that the length spectrum, that is the set of the lengths of all periodic trajectories, coincides as well. However there is no one-to-one correspondence between the diffractive trajectories. It will be shown here how the diffractive contributions to the Green functions match nevertheless in a ''one-to-three'' correspondence.Comment: 20 pages, 6 figure

Relationship between solidification microstructure and hot cracking susceptibility for continuous casting of low-carbon and high-strength low-alloyed steels: A phase-field study

© The Minerals, Metals & Materials Society and ASM International 2013Hot cracking is one of the major defects in continuous casting of steels, frequently limiting the productivity. To understand the factors leading to this defect, microstructure formation is simulated for a low-carbon and two high-strength low-alloyed steels. 2D simulation of the initial stage of solidification is performed in a moving slice of the slab using proprietary multiphase-field software and taking into account all elements which are expected to have a relevant effect on the mechanical properties and structure formation during solidification. To account for the correct thermodynamic and kinetic properties of the multicomponent alloy grades, the simulation software is online coupled to commercial thermodynamic and mobility databases. A moving-frame boundary condition allows traveling through the entire solidification history starting from the slab surface, and tracking the morphology changes during growth of the shell. From the simulation results, significant microstructure differences between the steel grades are quantitatively evaluated and correlated with their hot cracking behavior according to the Rappaz-Drezet-Gremaud (RDG) hot cracking criterion. The possible role of the microalloying elements in hot cracking, in particular of traces of Ti, is analyzed. With the assumption that TiN precipitates trigger coalescence of the primary dendrites, quantitative evaluation of the critical strain rates leads to a full agreement with the observed hot cracking behavior. © 2013 The Minerals, Metals & Materials Society and ASM International

Convergence of measures on compactifications of locally symmetric spaces

We conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space S=Γ∖G/K is compact. More precisely, given a sequence of homogeneous probability measures on S, we expect that any weak limit is homogeneous with support contained in precisely one of the boundary components (including S itself). We introduce several tools to study this conjecture and we prove it in a number of cases, including when G=SL3(R) and Γ=SL3(Z)