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    Background: Mustard aphid is a major pest of Brassica oilseeds. No source for aphid resistance is presently available in Brassica juncea . A wild crucifer, Brassica fruticulosa is known to be resistant to mustard aphid. An artificially synthesized amphiploid, AD-4 (B. fruticulosa x B. rapa var. brown sarson) was developed for use as a bridge species to transfer fruticulosa resistance to B. juncea. Using the selfed backcross we could select a large number of lines with resistance to mustard aphid. This paper reports cytogenetic stability of introgression lines, molecular evidence for alien introgression and their reaction to mustard aphid infestation. Results: Majority of introgression lines had expected euploid chromosome number(2n= 36), showed normal meiosis and high pollen grain fertility. Well-distributed and transferable simple-sequence repeats (SSR) markers for all the 18 B. juncea chromosomes helped to characterize introgression events. Average proportions of recipient and donor genome in the substitution lines were 49.72 and 35.06%, respectively. Minimum alien parent genome presence (27.29%) was observed in the introgression line, Ad3K-280 . Introgressed genotypes also varied for their resistance responses to mustard aphid infestations under artificial release conditions for two continuous seasons. Some of the test genotypes showed consistent resistant reaction. Conclusions: B.juncea-fruticulosa introgression set may prove to be a very powerful breeding tool for aphid resistance related QTL/gene discovery and fine mapping of the desired genes/QTLs to facilitate marker assisted transfer of identified gene(s) for mustard aphid resistance in the background of commercial mustard genotypes.
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    In the paper the Čech border homology and cohomology groups of closed pairs of normal spaces are constructed and investigated. These groups give intrinsic characterizations of Čech homology and cohomology groups based on finite open coverings, homological and cohomological coefficients of cyclicity, small and large cohomological dimensions of remainders of Stone-Čech compactifications of metrizable spaces.
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    A detailed thermal analysis of a Niobium (Nb) based superconducting radio frequency (SRF) cavity in a liquid helium bath is presented, taking into account the temperature and magnetic field dependence of the surface resistance and thermal conductivity in the superconducting state of the starting Nb material with different impurity levels. The drop in SRF cavity quality factor (Q_0) in the high acceleration gradient regime (before ultimate breakdown of the SRF cavity) is studied in details. It is argued that the high field Q_0-drop in SRF cavity is considerably influenced by the material parameters such as electrical conductivity, and thermal diffusivity. The detail analysis also shows that the current specification on the purity of niobium material for SRF cavity fabrication is somewhat over specified, and an optimally pure Nb material may be good enough. This information will have important implication towards the cost reduction of superconducting technology based particle accelerators for various applications.
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    A new scheme for an OAM communications system which exploits the radial component p of Laguerre Gauss modes in addition to the azimuthal component l generally used is presented. We derive a new encoding algorithm which makes use of the spatial distribution of intensity to create an alphabet dictionary for communication. We investigate the probability of error in decoding, for several detector options. A possible application could be improved communication modality for data center networks.
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    Let u be a hermitian involution, and e an orthogonal projection, acting on the same Hilbert space. We establish the exact formula, in terms of the norm of eue, for the distance from e to the set of all orthogonal projections q from the algebra generated by e,u, and such that quq=0.
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    We propose a new partial decoding algorithm for one-point Hermitian codes that can decode up to the same number of errors as the Guruswami--Sudan decoder. Simulations suggest that it has a similar failure probability as the latter one. The algorithm is based on a recent generalization of the power decoding algorithm for Reed--Solomon codes and does not require an expensive root-finding step. In addition, it promises improvements for decoding interleaved Hermitian codes.
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    The Bethe-Salpeter equation for three bosons with zero-range interaction is solved for the first time. For comparison the light-front equation is also solved. The input is the two-body scattering length and the outputs are the three-body binding energies, Bethe-Salpeter amplitudes and light-front wave functions. Three different regimes are analyzed: (\it i) For weak enough two-body interaction the three-body system is unbound. (\it ii) For stronger two-body interaction a three-body bound state appears. It provides an interesting example of a deeply bound Borromean system. (\it iii) For even stronger two-body interaction this state becomes unphysical with a negative mass squared. However, another physical (excited) state appears, found previously in light-front calculations. The Bethe-Salpeter approach implicitly incorporates three-body forces of relativistic origin, which are attractive and increase the binding energy.
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    The paper addresses the exact evaluation of the generalized Stieltjes transform $S_{\lambda}[f]=\int_0^{\infty} f(x) (\omega+x)^{-\lambda}\mathrm{d}x$ about $\omega =0$ from which the asymptotic behavior of $S_{\lambda}[f]$ for small parameters $\omega$ is directly extracted. An attempt to evaluate the integral by expanding the integrand $(\omega+x)^{-\lambda}$ about $\omega=0$ and then naively integrating the resulting infinite series term by term lead to an infinite series whose terms are divergent integrals. Assigning values to the divergent integrals, say, by analytic continuation or by Hadamard's finite parts is known to reproduce only some of the correct terms of the expansion but completely misses out a group of terms. Here we evaluate explicitly the generalized Stieltjes transform by means of finite part-integration recently introduced in [E.A. Galapon, \it Proc. Roy. Soc. A \bf 473, 20160567 (2017)]. It is shown that, when $f(x)$ does not vanish or has zero of order $m$ at the origin such that $(\lambda-m)\geq 1$, the dominant terms of $S_{\lambda}[f]$ as $\omega\rightarrow 0$ come from contributions arising from the poles and branch points of the complex valued function $f(z) (\omega+z)^{-\lambda}$. These dominant terms are precisely the terms missed out by naive term by term integration. Furthermore, it is demonstrated how finite-part integration leads to new series representations of special functions by exploiting their known Stieltjes integral representations.
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    The paper is devoted to studying the global dynamics of the Boltzmann equation on bounded domains. We allow a class of non-negative initial data which have arbitrary large amplitude and even contain vacuum. The result shows that the oscillation of solutions away from global Maxwellians becomes small after some positive time provided that they are initially close to each other in $L^2$. This yields the disappearance of any initial vacuum and the exponential convergence of large-amplitude solutions to equilibrium in large time. The most key ingredients in our strategy of the proof include: (i) $L^2_{x,v}$--$L^\infty_xL^1_v$--$L^\infty_{x,v}$ estimates along a bootstrap argument; (ii) Pointwise estimates on the upper bound of the gain term by the product of $L^\infty$ norm and $L^2$ norm; (iii) An iterative procedure on the nonlinear term.
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    In this note we prove the instability by blow-up of the ground state solutions for a class of fourth order Schr\"odinger equations. This extends the first rigorous results on blowing-up solutions for the biharmonic NLS due to Boulenger and Lenzmann \citeBoLe and confirm numerical conjectures from \citeBaFi, BaFiMa1, BaFiMa, FiIlPa.
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    We present a comprehensive 5-43 GHz VLBA study of the blazar 3C 273 initiated after an onset of a strong $\gamma$-ray flare in this source. We have analyzed the kinematics of new-born components, light curves, and position of the apparent core to pinpoint the location of the $\gamma$-ray emission. Estimated location of the $\gamma$-ray emission zone is close to the jet apex, 2 pc to 7 pc upstream from the observed 7 mm core. This is supported by ejection of a new component. The apparent core position was found to be inversely proportional to frequency. The brightness temperature in the 7 mm core reached values up to at least $10^{13}$ K during the flare. This supports the dominance of particle energy density over that of magnetic field in the 7 mm core. Particle density increased during the radio flare at the apparent jet base, affecting synchrotron opacity. This manifested itself as an apparent core shuttle along the jet during the 7 mm flare. It is also shown that a region where optical depth decreases from $\tau\sim1$ to $\tau<<1$ spans over several parsecs along the jet. The jet bulk flow speed estimated at the level of 12c on the basis of time lags between 7 mm light curves of stationary jet features is 1.5 times higher than that derived from VLBI apparent kinematics analysis.
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    In this paper, we study a novel approach for the estimation of quantiles when facing potential right censoring of the responses. Contrary to the existing literature on the subject, the adopted strategy of this paper is to tackle censoring at the very level of the loss function usually employed for the computation of quantiles, the so-called "check" function. For interpretation purposes, a simple comparison with the latter reveals how censoring is accounted for in the newly proposed loss function. Subsequently, when considering the inclusion of covariates for conditional quantile estimation, by defining a new general loss function, the proposed methodology opens the gate to numerous parametric, semiparametric and nonparametric modelling techniques. In order to illustrate this statement, we consider the well-studied linear regression under the usual assumption of conditional independence between the true response and the censoring variable. For practical minimization of the studied loss function, we also provide a simple algorithmic procedure shown to yield satisfactory results for the proposed estimator with respect to the existing literature in an extensive simulation study. From a more theoretical prospect, consistency of the estimator for linear regression is obtained using very recent results on non-smooth semiparametric estimation equations with an infinite-dimensional nuisance parameter, while numerical examples illustrate the adequateness of a simple bootstrap procedure for inferential purposes. Lastly, an application to a real dataset is used to further illustrate the validity and finite sample performance of the proposed estimator.
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    We analyze a similar scheme for producing light-mediated entanglement between atomic ensembles, as first realized by Julsgaard, Kozhekin and Polzik [Nature \bf 413, 400 (2001)]. In the standard approach to modeling the scheme, a Holstein-Primakoff approximation is made, where the atomic ensembles are treated as bosonic modes, and is only valid for short interaction times. In this paper, we solve the time evolution without this approximation, which extends the region of validity of the interaction time. For short entangling times, we find this produces a state with similar characteristics as a two-mode squeezed state, in agreement with standard predictions. For long entangling times, the state evolves into a non-Gaussian form, and the two-mode squeezed state characteristics start to diminish. This is attributed to more exotic types of entangled states being generated. We characterize the states by examining the Fock state probability distributions, Husimi $Q$ distributions, and non-local entanglement between the ensembles. We compare and connect several quantities obtained using the Holstein-Primakoff approach and our exact time evolution methods.
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    When Physical Unclonable Functions (PUFs) are used for cryptographic purposes, error correction in combination with a helper data scheme is an essential component due to the fuzzy nature of a PUF. All known schemes require both a code and additional helper data to recover PUF responses. Recently, Müelich and Bossert proposed a scheme that only requires a code. In this paper, we answer two open questions about the new scheme. First, we show that under certain assumptions, the code construction within the scheme is possible with high probability. Second, it is proven that after constructing the code, the security level of the scheme is known and is sufficiently large with high probability.
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    We calculate ionization energies and fundamental vibrational transitions for H$_2^+$, D$_2^+$, and HD$^+$ molecular ions. The NRQED expansion for the energy in terms of the fine structure constant $\alpha$ is used. Previous calculations of orders $m\alpha^6$ and $m\alpha^7$ are improved by including second-order contributions due to the vibrational motion of nuclei. Furthermore, we evaluate the largest corrections at the order $m\alpha^8$. That allows to reduce the fractional uncertainty to the level of $7\cdot10^{-12}$ for fundamental transitions and to $4\cdot10^{-12}$ for the ionization energies.
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    In this paper we classify the monomial complete intersection algebras, in two variables, and of positive characteristic, which has the strong Lef- schetz property. Together with known results, this gives a complete classi- fication of the monomial complete intersections with the strong Lefschetz property.
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    The topological charge density, topological susceptibility and its slope in momentum space $\chi^{\prime}(k^2)$ at momentum $k^{2}=0$ are determined by multi-probing approximation using overlap fermions in quenched SU(3) gauge theory. Then we investigate the topological structure of the quenched QCD vacuum, and compare it with result from the all-scale topological density, the results are consistent. Random permuted topological charge density is used to check whether these structures represent underlying ordered properties. Pseudoscalar glueball mass is extracted from the two-point correlation function of the topological charge density. We study $3$ ensembles of different lattice spacing $a$ with the same lattice volume $16^{3}\times32$, the results are compatible with the results of eigenmode expansion and all-scale topological charge density.
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    A vital aspect in energy storage planning and operation is to accurately model its operational cost, which mainly comes from the battery cell degradation. Battery degradation can be viewed as a complex material fatigue process that based on stress cycles. Rainflow algorithm is a popular way for cycle identification in material fatigue process, and has been extensively used in battery degradation assessment. However, the rainflow algorithm does not have a closed form, which makes the major difficulty to include it in optimization. In this paper, we prove the rainflow cycle-based cost is convex. Convexity enables the proposed degradation model to be incorporated in different battery optimization problems and guarantees the solution quality. We provide a subgradient algorithm to solve the problem. A case study on PJM regulation market demonstrates the effectiveness of the proposed degradation model in maximizing the battery operating profits as well as extending its lifetime.
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    We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Doléans-Dade exponential formula and a uniform exponential inequality using a generic chaining argument. As applications, we obtain a upper bound for a sequence of discrete time martingales indexed by a class of functionals, and so derive the rate of convergence for nonparametric maximum likelihood estimators, which is an improvement of earlier work of van de Geer.
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    Local adaptivity and mesh refinement are key to the efficient simulation of wave phenomena in heterogeneous media or complex geometry. Locally refined meshes, however, dictate a small time-step everywhere with a crippling effect on any explicit time-marching method. In [18] a leap-frog (LF) based explicit local time-stepping (LTS) method was proposed, which overcomes the severe bottleneck due to a few small elements by taking small time-steps in the locally refined region and larger steps elsewhere. Here a rigorous convergence proof is presented for the fully-discrete LTS-LF method when combined with a standard conforming finite element method (FEM) in space. Numerical results further illustrate the usefulness of the LTS-LF Galerkin FEM in the presence of corner singularities.
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    Let $G$ be an $n$-node simple directed planar graph with nonnegative edge weights. We study the fundamental problems of computing (1) a global cut of $G$ with minimum weight and (2) a~cycle of $G$ with minimum weight. The best previously known algorithm for the former problem, running in $O(n\log^3 n)$ time, can be obtained from the algorithm of \Lacki, Nussbaum, Sankowski, and Wulff-Nilsen for single-source all-sinks maximum flows. The best previously known result for the latter problem is the $O(n\log^3 n)$-time algorithm of Wulff-Nilsen. By exploiting duality between the two problems in planar graphs, we solve both problems in $O(n\log n\log\log n)$ time via a divide-and-conquer algorithm that finds a shortest non-degenerate cycle. The kernel of our result is an $O(n\log\log n)$-time algorithm for computing noncrossing shortest paths among nodes well ordered on a common face of a directed plane graph, which is extended from the algorithm of Italiano, Nussbaum, Sankowski, and Wulff-Nilsen for an undirected plane graph.
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    This paper is devoted to study the asymptotic properties of $l^{\infty}-$valued likelihood processes. We first derive the regularity of $l^{\infty}-$valued log-likelihood processes, then we move on to prove the central limit theorem of these processes, which is the main result of this paper. In the proof of results in this paper, we not only employ the stochastic analysis techniques and empirical processes modern theory, but also use the function index Hellinger processes as auxiliary tool to complete the proof.
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    A new approach is introduced for deriving a mixed variational formulation for Kirchhoff plate bending problems with mixed boundary conditions involving clamped, simply supported, and free boundary parts. Based on a regular decomposition of an appropriate nonstandard Sobolev space for the bending moments, the fourth-order problem can be equivalently written as a system of three (consecutively to solve) second-order problems in standard Sobolev spaces. This leads to new discretization methods, which are flexible in the sense, that any existing and well-working discretization method and solution strategy for standard second-order problems can be used as a modular building block of the new method. Similar results for the first biharmonic problem have been obtained in our previous work [W. Krendl, K. Rafetseder and W. Zulehner, A decomposition result for biharmonic problems and the Hellan-Herrmann-Johnson method, ETNA, 2016]. The extension to more general boundary conditions encounters several difficulties including the construction of an appropriate nonstandard Sobolev space, the verification of Brezzi's conditions, and the adaptation of the regular decomposition.
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    Let $(R,\fm)$ be a $d$-dimensional Cohen-Macaulay local ring, $I$ an $\fm$-primary ideal of $R$ and $J=(x_1,...,x_d)$ a minimal reduction of $I$. We show that if $J_{d-1}=(x_1,...,x_{d-1})$ and $\sum\limits_{n=1}^\infty\lambda{({{I^{n+1}}\cap J_{d-1}})/({J{I^n} \cap J_{d-1}})=i}$ where i=0,1, then $\depth G(I)\geq{d-i-1}$. Moreover, we prove that if ${e_2}(I)=\sum\limits_{n = 2}^\infty{(n-1)\lambda({{I^{n }}}/{J{I^{n-1}}})}-2;$ or if $I$ is integrally closed and\\ ${e_2}(I)=\sum\limits_{n=2}^\infty{(n-1)\lambda({{I^{n}}}/{J{I^{n-1}}})}-i$ where $i=3,4$, then ${e_1}(I)=\sum\limits_{n=1}^\infty{\lambda({{I^{n }}}/{J{I^{n-1}}})}-1.$ In addition, we show that $r(I)$ is independent. Furthermore, we study the independence of $r(I)$ with some other conditions.
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    This paper presents a distributed algorithm for controlling the deployment of a team of mobile agents in formations whose shapes can be characterized by a broad class of polygons, including regular ones, where each agent occupies a corner of the polygon. The algorithm shares the appealing properties of the popular distance-based rigid formation control, but with the additional advantage of requiring the control of fewer pairs of neighboring agents. Furthermore, the scale of the polygon can be controlled by only one pair of neighboring agents. We also exploit the exponential stability of the controlled formation in order to steer the formation as a whole with translations and rotations in a prescribed way. We provide both theoretical analysis and illustrative simulations.
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    We revisit the rapidity dependence of the average transverse momentum $\left\langle p_{T}\right\rangle$ in a $pp$ and $pA$ collision, using the High Energy Factorization (HEF). We update previous predictions for the $\left\langle p_{T}\right\rangle$ both in central and forward rapidity region using parton densities following from extended BK and BFKL evolution equations to account for corrections of higher orders as well as one obtained by Sudakov resummation. Furthermore, we demonstrate that in the mid rapidity region the saturation based formalisms predict increase of the transversal momentum while in the forward rapidity region the $\left\langle p_{T}(y)\right\rangle$ decreases.
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    A tunable, all-optical, coupling method has been realized for a high-\textitQ silica microsphere and an optical waveguide. By means of a novel optical nanopositioning method, induced thermal expansion of an asymmetric microsphere stem for laser powers up to 171~mW has been observed and used to fine tune the microsphere-waveguide coupling. Microcavity displacements ranging from (0.612~$\pm$~0.13) -- (1.5 $\pm$ 0.13) $\mu$m and nanometer scale sensitivities varying from (2.81 $\pm$ 0.08) -- (7.39 $\pm$ 0.17) nm/mW, with an apparent linear dependency of coupling distance on stem laser heating, were obtained. Using this method, the coupling was altered such that different coupling regimes could be explored for particular samples. This tunable coupling method, in principle, could be incorporated into lab-on-a-chip microresonator systems, photonic molecule systems, and other nanopositioning frameworks.
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    Usual Structure-from-Motion (SfM) techniques require at least trifocal overlaps to calibrate cameras and reconstruct a scene. We consider here scenarios of reduced image sets with little overlap, possibly as low as two images at most seeing the same part of the scene. We propose a new method, based on line coplanarity hypotheses, for estimating the relative scale of two independent bifocal calibrations sharing a camera, without the need of any trifocal information or Manhattan-world assumption. We use it to compute SfM in a chain of up-to-scale relative motions. For accuracy, we however also make use of trifocal information for line and/or point features, when present, relaxing usual trifocal constraints. For robustness to wrong assumptions and mismatches, we embed all constraints in a parameterless RANSAC-like approach. Experiments show that we can calibrate datasets that previously could not, and that this wider applicability does not come at the cost of inaccuracy.
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    We introduce a new local symmetry into the fermion sector of a gauge invariant Lagrangian which may or may not contain a scalar or spontaneous symmetry breaking. The standard model in the unitary gauge and QCD are particular cases where this symmetry may apply. We determine the associated vector and axial vector currents and their conservation laws. We show that a single current conservation law may lead to multiple Ward-Takahashi identities. Our results can potentially have important consequences for the construction of the tetraquark states in a generalized linear sigma model with two chiral nonets and may give useful clues about the hadron structure in general.
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    In this paper we study coupled dynamical systems and establish several invariance principles relating to the dimensions of the subspace spanned by solutions of each individual system. We consider two types of coupled systems, one with scalar couplings and the other with matrix couplings. Via the rank-preserving flow theory, we prove that scalar-coupled dynamical systems possess the dimensional-invariance principles, in that the dimension of the subspace spanned by the individual systems' solutions remains invariant. For coupled dynamical systems with matrix coefficients/couplings, necessary and sufficient conditions are given to characterize dimensional-invariance principles. The established invariance principles provide additional characterizations and insights to analyze the transient behaviors and solution evolution for a large family of coupled systems, such as multi-agent consensus dynamics, distributed coordination systems, formation control systems, among others.
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    The superconductor-insulator transition (SIT) is considered an excellent example of a quantum phase transition which is driven by quantum fluctuations at zero temperature. The quantum critical point is characterized by a diverging correlation length and a vanishing energy scale. Low energy fluctuations near quantum criticality may be experimentally detected by specific heat, $c_{\rm p}$, measurements. Here, we use a unique highly sensitive experiment to measure $c_{\rm p}$ of two-dimensional granular Pb films through the SIT. The specific heat shows the usual jump at the mean field superconducting transition temperature $T_{\rm c}^{\rm {mf}}$ marking the onset of Cooper pairs formation. As the film thickness is tuned toward the SIT, $T_{\rm c}^{\rm {mf}}$ is relatively unchanged, while the magnitude of the jump and low temperature specific heat increase significantly. This behaviour is taken as the thermodynamic fingerprint of quantum criticality in the vicinity of a quantum phase transition.
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    We give explicit Fredholm conditions for classes of pseudodifferential operators on suitable singular and non-compact spaces. In particular, we include a "user's guide" to Fredholm conditions on particular classes of manifolds including asymptotically hyperbolic manifolds, asymptotically Euclidean (or conic) manifolds, and manifolds with poly-cylindrical ends. The reader interested in applications should be able read right away the results related to those examples, beginning with Section 5. Our general, theoretical results are that an operator adapted to the geometry is Fredholm if, and only if, it is elliptic and all its limit operators, in a sense to be made precise, are invertible. Central to our theoretical results is the concept of a Fredholm groupoid, which is the class of groupoids for which this characterization of the Fredholm condition is valid. We use the notions of exhaustive and strictly spectral families of representations to obtain a general characterization of Fredholm groupoids. In particular, we introduce the class of the so-called groupoids with Exel's property as the groupoids for which the regular representations are exhaustive. We show that the class of "stratified submersion groupoids" has Exel's property, where stratified submersion groupoids are defined by glueing fibered pull-backs of bundles of Lie groups. We prove that a stratified submersion groupoid is Fredholm whenever its isotropy groups are amenable. Many groupoids, and hence many pseudodifferential operators appearing in practice, fit into this framework. This fact is explored to yield Fredholm conditions not only in the above mentioned classes, but also on manifolds that are obtained by desingularization or by blow-up of singular sets.
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    This work addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction which employs the $\ell_1$-norm as the loss function for the residual error and utilizes a generalized nonconvex penalty for sparsity inducing. The $\ell_1$-loss is less sensitive to outliers in the measurements than the popular $\ell_2$-loss, while the nonconvex penalty has the capability of ameliorating the bias problem of the popular convex LASSO penalty and thus can yield more accurate recovery. To solve this nonconvex and nonsmooth minimization formulation efficiently, we propose a first-order algorithm based on alternating direction method of multipliers (ADMM). A smoothing strategy on the $\ell_1$-loss function has been used in deriving the new algorithm to make it convergent. Further, a sufficient condition for the convergence of the new algorithm has been provided for generalized nonconvex regularization. In comparison with several state-of-the-art algorithms, the new algorithm showed better performance in numerical experiments in recovering sparse signals and compressible images. The new algorithm scales well for large-scale problems, as often encountered in image processing.
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    Zagier in [4] discusses a construction of a function $F_{k,D}(x)$ defined for an even integer $k \geq 2$, and a positive discriminant $D$. This construction is intimately related to half-integral weight modular forms. In particular, the average value of this function is a constant multiple of the $D$-th Fourier coefficient of weight $k+1/2$ Eisenstein series constructed by H. Cohen in \citeCohen. In this note we consider a construction which works both for even and odd positive integers $k$. Our function $F_{k,D,d}(x)$ depends on two discriminants $d$ and $D$ with signs sign$(d)=$ sign$(D)=(-1)^k$, degenerates to Zagier's function when $d=1$, namely, \[ F_k,D,1(x)=F_k,D(x), \]and has very similar properties. In particular, we prove that the average value of $F_{k,D,d}(x)$ is again a Fourier coefficient of H. Cohen's Eisenstein series of weight $k+1/2$, while now the integer $k \geq 2$ is allowed to be both even and odd.
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    In 2003 Dinur and Nissim showed an impossibility result for privacy that if the amount of noise is $o(\sqrt{n})$, then privacy is impossible to achieve (where the output space is binary "Yes" or "No"). $\Omega({\sqrt{n}})$ noise must be added to have at least weak notions of privacy. However, the question has remained open as to whether $O(n)$ noise is able to preserve accuracy in elementary private data operations such as aggregation and averaging in addition to protecting privacy both before and after data aggregation. In this paper, we introduce the family of Anonymized Local Privacy mechanisms. These mechanisms have an output space of three values "Yes", "No", or "$\perp$" (not participating) and leverage the law of large numbers to generate linear noise in the number of data owners to protect privacy both before and after aggregation yet preserve accuracy. In addition, Anonymized Local Privacy satisfies the Haystack Privacy mechanism whereby each data owner blends with, and is indistinguishable from, at least $c$ crowds, where each crowd is composed of at least $k$ indistinguishable data owners, essentially "hiding in a haystack". We show the optimal mechanism which satisfies Anonymized Local Privacy. We describe the suitability in a distributed on-demand network and show that we preserve accuracy, even when the number of data owners to protect is less than 0.002\% of the total population.
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    We study quantitative periodic homogenization of integral functionals in the context of non-linear elasticity. Under suitable assumptions on the energy densities (in particular frame indifference; minimality, non-degeneracy and smoothness at the identity; $p\geq d$-growth from below; and regularity of the microstructure), we show that in a neighborhood of the set of rotations, the multi-cell homogenization formula of non-convex homogenization reduces to a single-cell formula. The latter can be expressed with help of correctors. We prove that the homogenized integrand admits a quadratic Taylor expansion in an open neighborhood of the rotations -- a result that can be interpreted as the fact that homogenization and linearization commute close to the rotations. Moreover, for small applied loads, we provide an estimate on the homogenization error in terms of a quantitative two-scale expansion.
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    This paper builds on new results concerning the polytopic set of possible states of a linear discrete-time SISO system subject to bounded disturbances from measurements corrupted by bounded noise. We construct an algorithm which, for the special case of a plant with a lag, recursively updates these polytopic sets when new measurements arrive. In an example we use the algorithm to investigate how the complexity of the polytopes changes with time.
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    We report a large linear magnetoresistance in Cu$_{2-x}$Te, reaching $\Delta\rho/\rho(0)$ = 250\% at 2 K in a 9 T field. This is observed for samples with $x$ in the range 0.13 to 0.22, and the results are comparable to the effects observed in Ag$_2 X$ materials, although in this case the results appear for a much wider range of bulk carrier density. Examining the magnitude vs. crossover field from low-field quadratic to high-field linear behavior, we show that models based on classical transport behavior best explain the observed results. The effects are traced to misdirected currents due to topologically inverted behavior in this system, such that stable surface states provide the high mobility transport channels. The resistivity also crosses over to a $T^2$ dependence in the temperature range where the large linear MR appears, an indicator of electron-electron interaction effects within the surface states. Thus this is an example of a system in which these interactions dominate the low-temperature behavior of the surface states.
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    In 1997, Serre proved that the eigenvalues of normalised $p$-th Hecke operator $T^{'}_p$ acting on the space of cusp forms of weight $k$ and level $N$ are equidistributed in $[-2,2]$ with respect to a measure that converge to the Sato-Tate measure, whenever $N+k \to \infty$. In 2009, Murty and Sinha proved the effective version of Serre's theorem. In 2011, using Kuznetsov trace formula, Lau and Wang derived the effective joint distribution of eigenvalues of normalized Hecke operators acting on the space of primitive cusp forms of weight $k$ and level $1$. In this paper, we extend the result of Lau and Wang to space of cusp forms of higher level. Here we use Eichler-Selberg trace formula instead of Kuznetsov trace formula to deduce our result.
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    In this paper, we define the notion of reconstruction that maps the dynamic model of a mass action chemical reaction network (CRN) to another system through a positive diagonal matrix. These two network systems will share some common properties, including the set of equilibria and stability behavior (if some moderate conditions also hold). We prove that for those mass action systems having complex balanced reconstructions, the local asymptotic stability of equilibrium points can be reached if the initial state is selected judiciously and the generalized Gibbs' free energy is defined acting as the Lyapunov function. To facilitate applications, we further provide systematic methods for computing reconstructions and complex balanced reconstructions. Some examples and simulations are presented to exhibit the validity of reconstruction strategy.
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    (This is a recompiled version of $Chin. J. of Phys., Vol. 26, No. 4, 180$ since the previous available electronic document on web was unreadable) We impose a permutation symmetry S3 upon the two Higgs doublet extension of the SU(2) x U( 1) standard model, and then break S3 symmetry spontaneously. A mass relation is obtained from which the mass of the top quark is predicted to be 39 Gev at 1 Gev renormalization scale, if the relative strength between the coupling of the first Higgs field with the up-type quarks is assumed to be the same as that with the down-type quarks. We find that in our model the flavor changing neutral currents vanish automatically.
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    A third order real tensor is called a piezoelectric-type tensor if it is partially symmetric with respect to its last two indices. The piezoelectric tensor is a piezoelectric-type tensor of dimension three. We introduce C-eigenvalues and C-eigenvectors for piezoelectric-type tensors. Here, "C" names after Curie brothers, who first discovered the piezoelectric effect. We show that C-eigenvalues always exist, they are invariant under orthonormal transformations, and for a piezoelectric-type tensor, the largest C-eigenvalue and its C-eigenvectors form the best rank-one piezoelectric-type approximation of that tensor. This means that for the piezoelectric tensor, its largest C-eigenvalue determines the highest piezoelectric coupling constant. We further show that for the piezoelectric tensor, the largest C-eigenvalue corresponds to the electric displacement vector with the largest $2$-norm in the piezoelectric effect under unit uniaxial stress, and the strain tensor with the largest $2$-norm in the converse piezoelectric effect under unit electric field vector. Thus, C-eigenvalues and C-eigenvectors have concrete physical meanings in piezoelectric effect and converse piezoelectric effect. Finally, we apply C-eigenvalues and associated C-eigenvectors for various piezoelectric crystals with different symmetries.
  • PDF
    Coupled metronomes serve as a paradigmatic model for exploring the collective behaviors of complex dynamical systems, as well as a classical setup for classroom demonstrations of synchronization phenomena. Whereas previous studies of metronome synchronization have been concentrating on symmetric coupling schemes, here we consider the asymmetric case by adopting the scheme of layered metronomes. Specifically, we place two metronomes on each layer, and couple two layers by placing one on top of the other. By varying the initial conditions of the metronomes and adjusting the friction between the two layers, a variety of synchronous patterns are observed in experiment, including the splay synchronization (SS) state, the generalized splay synchronization (GSS) state , the anti-phase synchronization (APS) state, the in-phase delay synchronization (IPDS) state, and the in-phase synchronization (IPS) state. In particular, the IPDS state, in which the metronomes on each layer are synchronized in phase but are of a constant phase delay to metronomes on the other layer, is observed for the first time. In addition, a new technique based on audio signals is proposed for pattern detection, which is more convenient and easier to apply than the existing acquisition techniques. Furthermore, a theoretical model is developed to explain the experimental observations, and is employed to explore the dynamical properties of the patterns, including the basin distributions and the pattern transitions. Our study sheds new lights on the collective behaviors of coupled metronomes, and the developed setup can be used in the classroom for demonstration purposes.
  • PDF
    We present a new method for torque magnetometry by using a commercially available membrane-type surface-stress sensor (MSS). This sensor has a silicon membrane supported by four beams in which piezoresistive paths are integrated. Although originally developed as a gas sensor, it can be used for torque measurement by modifying its on-chip wiring. We demonstrate the magnetic-torque measurement of submillimeter-sized crystals at a low temperature and in strong magnetic fields. This MSS can observe de-Haas-van-Alphen oscillation, which confirms that it can be an alternative tool for self-sensitive microcantilevers.
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    In this paper we present a method for the addition of integral action to non-passive outputs of a class of port-Hamiltonian systems. The proposed integral controller is a dynamic extension, constructed from the open loop system, such that the closed loop preserves the port-Hamiltonian form. It is shown that the controller is able to reject the effects of both matched and unmatched disturbances, preserving the regulation of the non-passive outputs. Previous solutions to this problem have relied on a change of coordinates whereas the presented solution is developed using the original state vector and, therefore, retains its physical interpretation. In addition, the resulting closed loop dynamics have a natural interpretation as a Control by Interconnection scheme.
  • PDF
    Speeding up adiabatic method has attracted much attention with the wide applications in quantum information processing. In this paper, two kinds of methods, Lewis-Riesenfeld invariant-based inverse engineering and transitionless quantum driving are applied to implement speeding up adiabatic state conversion in optomechanical system. The perfect population transfer can be achieved within a short time. At last, the energetic cost is analysed for the transitionless quantum driving.
  • PDF
    Poor diet and nutrition in the United States has immense financial and health costs, and development of new tools for diet planning could help families better balance their financial and temporal constraints with the quality of their diet and meals. This paper formulates a novel model for dietary planning that incorporates two types of temporal constraints (i.e., dynamics on the perishability of raw ingredients over time, and constraints on the time required to prepare meals) by explicitly incorporating the relationship between raw ingredients and selected food recipes. Our formulation is a model predictive control (MPC) with integer-valued decision variables, and so we study the problem of designing approximation algorithms (i.e, algorithms with polynomial-time computation and guarantees on the quality of the computed solution) for our dietary model. We develop a deterministic approximation algorithm that is based on a deterministic variant of randomized rounding, and then evaluate our deterministic approximation algorithm with numerical experiments of dietary planning using a database of about 2000 food recipes and 150 raw ingredients.
  • PDF
    We have resolved for the first time the radial and vertical structure of the almost edge-on envelope/disk system of the low-mass Class 0 protostar L1527. For that, we have used ALMA observations with a spatial resolution of 0.25$^{\prime\prime}$$\times$0.13$^{\prime\prime}$ and 0.37$^{\prime\prime}$$\times$0.23$^{\prime\prime}$ at 0.8 mm and 1.2 mm, respectively. The L1527 dust continuum emission has a deconvolved size of 78 au $\times$ 21 au, and shows a flared disk-like structure. A thin infalling-rotating envelope is seen in the CCH emission outward of about 150 au, and its thickness is increased by a factor of 2 inward of it. This radius lies between the centrifugal radius (200 au) and the centrifugal barrier of the infalling-rotating envelope (100 au). The gas stagnates in front of the centrifugal barrier and moves toward vertical directions. SO emission is concentrated around and inside the centrifugal barrier. The rotation speed of the SO emitting gas is found to be decelerated around the centrifugal barrier. A part of the angular momentum could be extracted by the gas which moves away from the mid-plane around the centrifugal barrier. If this is the case, the centrifugal barrier would be related to the launching mechanism of low velocity outflows, such as disk winds.
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    Let $\mathbb{F}_p$ be the finite field of prime order $p$. For any function $f \colon \mathbb{F}_p{}^n \to \mathbb{F}_p$, there exists a unique polynomial over $\mathbb{F}_p$ having degree at most $p-1$ with respect to each variable which coincides with $f$. We call it the minimal polynomial of $f$. It is in general a non-trivial task to find a concrete expression of the minimal polynomial of a given function, which has only been worked out for limited classes of functions in the literature. In this paper, we study minimal polynomial expressions of several functions that are closely related to some practically important procedures such as auction and voting.
  • PDF
    We calculate the collective excitations of a dipolar Bose-Einstein condensate in the regime where it self-binds into droplets stabilized by quantum fluctuations. We show that the filament-shaped droplets act as a quasi-one-dimensional waveguide along which low angular momentum phonons propagate. The evaporation (unbinding) threshold occurring as the atom number $N$ is reduced to the critical value $N_c$ is associated with a monopole-like excitation going soft as $\epsilon_0\sim(N-N_c)^{1/4}$. Considering the system in the presence of a trapping potential, we quantify the crossover from a trap-bound condensate to a self-bound droplet.

Recent comments

gae spedalieri Mar 13 2017 14:13 UTC

1) Sorry but this is false.

1a) That analysis is specifically for reducing QECC protocol to an entanglement distillation protocol over certain class of discrete variable channels. Exactly as in BDSW96. Task of the protocol is changed in the reduction.

1b) The simulation is not via a general LOCC b

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Siddhartha Das Mar 13 2017 13:22 UTC

We feel that we have cited and credited previous works appropriately in our paper. To clarify:

1) The LOCC simulation of a channel and the corresponding adaptive reduction can be found worked out in full generality in the 2012 Master's thesis of Muller-Hermes. We have cited the original paper BD

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gae spedalieri Mar 13 2017 08:56 UTC

This is one of those papers where the contribution of previous literature is omitted and not fairly represented.

1- the LOCC simulation of quantum channels (not necessarily teleportation based) and the corresponding general reduction of adaptive protocols was developed in PLOB15 (https://arxiv.org/

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Noon van der Silk Mar 08 2017 04:45 UTC

I feel that while the proliferation of GUNs is unquestionable a good idea, there are many unsupervised networks out there that might use this technology in dangerous ways. Do you think Indifferential-Privacy networks are the answer? Also I fear that the extremist binary networks should be banned ent

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Qian Wang Mar 07 2017 17:21 UTC

"To get the videos and their labels, we used a YouTube video annotation system, which labels videos with their main topics."
Can anyone explain a bit about this?

Christopher Chamberland Mar 02 2017 18:48 UTC

A good paper for learning about exRec's is this one https://arxiv.org/abs/quant-ph/0504218. Also, rigorous threshold lower bounds are obtained using an adversarial noise model approach.

Anirudh Krishna Mar 02 2017 18:40 UTC

Here's a link to a lecture from Dan Gottesman's course at PI about exRecs.
http://pirsa.org/displayFlash.php?id=07020028

You can find all the lectures here:
http://www.perimeterinstitute.ca/personal/dgottesman/QECC2007/index.html

Ben Criger Mar 02 2017 08:58 UTC

Good point, I wish I knew more about ExRecs.

Robin Blume-Kohout Feb 28 2017 09:55 UTC

I totally agree -- that part is confusing. It's not clear whether "arbitrary good precision ... using a limited amount of hardware" is supposed to mean that arbitrarily low error rates can be achieved with codes of fixed size (clearly wrong) or just that the resources required to achieve arbitraril

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James Wootton Feb 28 2017 08:54 UTC

I think I was mostly reacting to where he tries to sell the importance of the work.

>Fault tolerant theorems show that an arbitrary good precision can be obtained using a limited amount of hardware...we unveil the role of an implicit assumption made in these mathematical theorems: the ability to

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