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    Recently, in the paper "The Schwarz alternating method in solid mechanics" by Alejandro Mota, Irina Tezaur and Coleman Alleman [Comput. Methods Appl. Mech. Engrg. 319 (2017) 1951] the authors extended the well known Schwarz alternating method from linear to finite-deformation solid mechanics. They developed and introduced four variants of the Schwarz alternating method, presented proof of geometric convergence of the method and prepared parallel implementation applied to some examples. Unfortunately, the work contains serious errors, both from the point of view of finite-deformation solid mechanics as well as mathematical elasticity.
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    Development of novel materials may often require a rational use of high price components, like noble metals, in combination with the possibility to tune their properties in a desirable way. Here we present a theoretical DFT study of Au and Pd single atoms supported by doped MgO(001). By introducing B, C and N impurities into the MgO(001) surface, the interaction between the surface and the supported metal adatoms can be adjusted. Impurity atoms act as strong binding sites for Au and Pd adatoms and can help to produce highly dispersed metal particles. The reactivity of metal atoms supported by doped MgO(001), as probed by CO, is altered compared to their counterparts on pristine MgO(001). We find that Pd atoms on doped MgO(001) are less reactive than on perfect MgO(001). In contrast, Au adatoms bind CO much stronger when placed on doped MgO(001). In the case of Au on N-doped MgO(001) we find that charge redistribution between the metal atom and impurity takes place even when not in direct contact, which enhances the interaction of Au with CO. The presented results suggest possible ways for optimizing the reactivity of oxide supported metal catalysts through impurity engineering.
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    Aiming to address the fast multi-object tracking for dense small object in the cluster background, we review track orientated multi-hypothesis tracking(TOMHT) with consideration of batch optimization. Employing autocorrelation based motion score test and staged hypotheses merging approach, we build our homologous hypothesis generation and management method. A new one-to-many constraint is proposed and applied to tackle the track exclusions during complex occlusions. Besides, to achieve better results, we develop a multi-appearance segmentation for detection, which exploits tree-like topological information and realizes one threshold for one object. Experimental results verify the strength of our methods, indicating speed and performance advantages of our tracker.
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    In this corrigendum, an error in the proof of a theorem in [Linear Algebra and its Applications 509 (2016) 82--113] is pointed out. This theorem states that every graph $T_n$ consisting of $n-2$ triangles sharing a common base is SPN. An alternative proof is given here for the case $n=5$, but for all $n>5$ it remains open whether $T_n$ is SPN. As a result, the question whether $K_{2,n}$, $n>4$, is SPN also remains open.
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    This paper proposes a novel and efficient method to build a Computer-Aided Diagnoses (CAD) system for lung nodule detection based on Computed Tomography (CT). This task was treated as an Object Detection on Video (VID) problem by imitating how a radiologist reads CT scans. A lung nodule detector was trained to automatically learn nodule features from still images to detect lung nodule candidates with both high recall and accuracy. Unlike previous work which used 3-dimensional information around the nodule to reduce false positives, we propose two simple but efficient methods, Multi-slice propagation (MSP) and Motionless-guide suppression (MLGS), which analyze sequence information of CT scans to reduce false negatives and suppress false positives. We evaluated our method in open-source LUNA16 dataset which contains 888 CT scans, and obtained state-of-the-art result (Free-Response Receiver Operating Characteristic score of 0.892) with detection speed (end to end within 20 seconds per patient on a single NVidia GTX 1080) much higher than existing methods.
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    The properties of cuprate high-temperature superconductors are largely shaped by competing phases whose nature is often a mystery. Chiefly among them is the pseudogap phase, which sets in at a doping $p^*$ that is material-dependent. What determines $p^*$ is currently an open question. Here we show that the pseudogap cannot open on an electron-like Fermi surface, and can only exist below the doping $p_{FS}$ at which the large Fermi surface goes from hole-like to electron-like, so that $p^*$ $\leq$ $p_{FS}$. We derive this result from high-magnetic-field transport measurements in La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ under pressure, which reveal a large and unexpected shift of $p^*$ with pressure, driven by a corresponding shift in $p_{FS}$. This necessary condition for pseudogap formation, imposed by details of the Fermi surface, is a strong constraint for theories of the pseudogap phase. Our finding that $p^*$ can be tuned with a modest pressure opens a new route for experimental studies of the pseudogap.
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    We investigate the ground-state phases of a mixture of spin-1 and spin-2 Bose-Einstein condensates at zero magnetic field. In addition to the intra-spin interactions, two spin-dependent interaction coefficients are introduced to describe the inter-spin interaction. We systematically explore the wide parameter space, and obtain phase diagrams containing a rich variety of phases. For example, there exists a phase in which the spin-1 and spin-2 vectors are tilted relative to each other breaking the axial symmetry.
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    Community detection is one of the pivotal tools for discovering the structure of complex networks. Majority of community detection methods rely on optimization of certain quality functions characterizing the proposed community structure. Perhaps, the most commonly used of those quality functions is modularity. Many heuristics are claimed to be efficient in modularity maximization, which is usually justified in relative terms through comparison of their outcomes with those provided by other known algorithms. However as all the approaches are heuristics, while the complete brute-force is not feasible, there is no known way to understand if the obtained partitioning is really the optimal one. In this article we address the modularity maximization problem from the other side --- finding an upper-bound estimate for the possible modularity values within a given network, allowing to better evaluate suggested community structures. Moreover, in some cases when then upper bound estimate meets the actually obtained modularity score, it provides a proof that the suggested community structure is indeed the optimal one. We propose an efficient algorithm for building such an upper-bound estimate and illustrate its usage on the examples of well-known classical and synthetic networks, being able to prove the optimality of the existing partitioning for some of the networks including well-known Zachary's Karate Club.
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    We prove that there does not exist any real hypersurface in complex Grassmannians of rank two with semi-parallel structure Jacobi operator. With this result, the nonexistence of real hypersurface in complex Grassmannians of rank two with recurrent structure Jacobi operator is proved.
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    We discuss spontaneous supersymmetry (SUSY) breaking in a model with an anomalous $U(1)_A$ symmetry. In this model, the size of the each term in the superpotential is controlled by the $U(1)_A$ charge assignment and SUSY is spontaneously broken via the Fayet-Iliopoulos of $U(1)_A$ at the meta-stable vacuum. In the global SUSY analysis, the gaugino masses become much smaller than the sfermion masses, because an approximate R-symmetry appears at the SUSY breaking vacuum. In this paper, we show that gaugino masses can be as large as gravitino mass, taking the supergravity effect into consideration. This is because the R-symmetry is not imposed so that the constant term in the superpotential, which is irrelevant to the global SUSY analysis, largely contributes to the soft SUSY breaking terms in the supergravity. As the mediation mechanism, we introduce the contributions of the field not charged under $U(1)_A$ and the moduli field to cancel the anomaly of $U(1)_A$. We comment on the application of our SUSY breaking scenario to the GUT models.
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    We investigated how the magnetic field in solar active regions (ARs) controls flare activity, i.e., whether a confined or eruptive flare occurs. We analyzed 44 flares of GOES class M5.0 and larger that occurred during 2011--2015. We used 3D potential magnetic field models to study their location (using the flare distance from the flux-weighted AR center $d_{\mathrm{FC}}$) and the strength of the magnetic field in the corona above (via decay index $n$ and flux ratio). We also present a first systematic study of the orientation of the coronal magnetic field, using the orientation $\varphi$ of the flare-relevant polarity inversion line as a measure. We analyzed all quantities with respect to the size of the underlying dipole field, characterized by the distance between the opposite-polarity centers, $d_{\mathrm{PC}}$. Flares originating from underneath the AR dipole $(d_{\mathrm{FC}}/d_{\mathrm{PC}}<0.5$) tend to be eruptive if launched from compact ARs ($d_{\mathrm{PC}}\leq60$ Mm) and confined if launched from extended ARs. Flares ejected from the periphery of ARs ($d_{\mathrm{FC}}/d_{\mathrm{PC}}>0.5$) are predominantly eruptive. In confined events the flare-relevant field adjusts its orientation quickly to that of the underlying dipole with height ($\Delta\varphi\gtrsim40^\circ$ until the apex of the dipole field), in contrast to eruptive events where it changes more slowly with height. The critical height for torus instability, $h_{\mathrm{crit}}=h(n=1.5)$, discriminates best between confined ($h_{\mathrm{crit}}\gtrsim40$ Mm) and eruptive flares ($h_{\mathrm{crit}}\lesssim40$ Mm). It discriminates better than $\Delta\varphi$, implying that the decay of the confining field plays a stronger role than its orientation at different heights.
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    We present a first-principle computation of the mass distribution of jets which have undergone the grooming procedure known as Soft Drop. This calculation includes the resummation of the large logarithms of the jet mass over its transverse momentum, up to next-to-logarithmic accuracy, matched to exact fixed-order results at next-to-leading order. We also include non-perturbative corrections obtained from Monte-Carlo simulations and discuss analytic expressions for hadronisation and Underlying Event effects.
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    We characterize positivity preserving, translation invariant, linear operators in $L^p(\mathbb{R}^n)^m$, $p \in [1,\infty)$, $m,n \in \mathbb{N}$.
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    This paper shows a mathematical formalization, algorithms and computation software of volume optimal cycles, which are useful to understand geometric features shown in a persistence diagram. Volume optimal cycles give us concrete and optimal homologous structures, such as rings or cavities, on a given data. The key idea is the optimality on $(q + 1)$-chain complex for a $q$th homology generator. This optimality formalization is suitable for persistent homology. We can solve the optimization problem using linear programming. For an alpha filtration on $\mathbb{R}^n$, volume optimal cycles on an $(n-1)$-th persistence diagram is more efficiently computable using merge-tree algorithm. The merge-tree algorithm also gives us a tree structure on the diagram and the structure has richer information. The key mathematical idea is Alexander duality.
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    The approximate nature of radiative transfer equation (RTE) leads to a bunch of considerations on the effect of "dependent scattering" in random media, especially particulate media composed of discrete scatterers, in the last a few decades, which usually indicates those deviations RTE (combined with ISA) lead to from experimental and exact numerical results due to electromagnetic wave interference. Here we theoretically and numerically demonstrate the effect of dependent scattering on absorption in disordered media consisting of highly scattering scatterers. By making comparison between the independent scattering approximation-radiative transfer equation (ISA-RTE) and the full-wave coupled dipole method (CDM), we find that deviations between the two methods increase as scatterer density in the media increases. The discrepancy also grows with optical thickness. To quantitatively take dependent scattering effect into account, we develop a theoretical model using quasi-crystalline approximation (QCA) to derive dependent-scattering corrected radiative properties, based on the path-integral diagrammatic technique in multiple scattering theory. The model results in a more reasonable agreement with numerical simulations. The present work has profound implications for the coherent scattering physics in random media with absorption, correctly modeling light absorptance in random media and interpreting the experimental observations in various applications for random media such as solar energy concentration, micro/nanofluids, structural color generation, etc.
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    We present a linearizable, non-blocking $k$-ary search tree ($k$-ST) that supports fast searches and range queries. Our algorithm uses single-word compare-and-swap (CAS) operations, and tolerates any number of crash failures. Performance experiments show that, for workloads containing small range queries, our $k$-ST significantly outperforms other algorithms which support these operations, and rivals the performance of a leading concurrent skip-list, which provides range queries that cannot always be linearized.
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    In \citeLuo, the author proved that if $L$ is a contact stationary Legendrian surface in $\mathbb{S}^5$ with the canonical Sasakian structure and the square length of its second fundamental form belongs to $[0,2]$. Then we have $L$ is either totally umbilical or is a flat minimal Legendrian torus. In this short note we further prove that if $L$ is a totally umbilical contact stationary Legendrian surface in $\mathbb{S}^5$ with the square length of its second fundamental form belongs to $[0,2]$, then $L$ is totally geodesic. This gives an affirmative positive answer to problem 1 in the apppendix of \citeLuo.
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    In this paper we prove the central limit theorem for the number of clusters formed by the particles of the Arratia flow starting from the interval $[0;n]$ as $n\to\infty$ and obtain an estimate of the Berry-Esseen type for the rate of this convergence.
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    The mechanics of crawling cells on a substrate is investigated by using a minimal model that satisfies the force-free condition. A cell is described by two subcellular elements connected by a linear actuator that changes the length of the cell cyclically in time, together with periodic alternation of adhesive characters at the interface between the cell and the substrate. Here the key model parameters are the phase shifts between the elongation of the actuator and the alternation of the adhesion of the two elements. We emphasize that the phase shifts determine not only the efficiency of the crawling motion but also its direction.
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    Silicon-based Static Random Access Memories (SRAM) and digital Boolean logic have been the workhorse of the state-of-art computing platforms. Despite tremendous strides in scaling the ubiquitous metal-oxide-semiconductor transistor, the underlying \textitvon-Neumann computing architecture has remained unchanged. The limited throughput and energy-efficiency of the state-of-art computing systems, to a large extent, results from the well-known \textitvon-Neumann bottleneck. The energy and throughput inefficiency of the von-Neumann machines have been accentuated in recent times due to the present emphasis on data-intensive applications like artificial intelligence, machine learning \textitetc. A possible approach towards mitigating the overhead associated with the von-Neumann bottleneck is to enable \textitin-memory Boolean computations. In this manuscript, we present an augmented version of the conventional SRAM bit-cells, called \textitthe X-SRAM, with the ability to perform in-memory, vector Boolean computations, in addition to the usual memory storage operations. We propose at least six different schemes for enabling in-memory vector computations including NAND, NOR, IMP (implication), XOR logic gates with respect to different bit-cell topologies $-$ the 8T cell and the 8$^+$T Differential cell. In addition, we also present a novel \textit`read-compute-store' scheme, wherein the computed Boolean function can be directly stored in the memory without the need of latching the data and carrying out a subsequent write operation. The feasibility of the proposed schemes has been verified using predictive transistor models and Monte-Carlo variation analysis.
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    We prove a compactness theorem for Kähler metrics with various bounds on Ricci curvature and the $\mathcal I$ functional. We explore applications of our result to the continuity method and the Calabi flow.
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    In this paper we construct two groupoids from morphisms of groupoids, with one from a categorical viewpoint and the other from a geometric viewpoint. We show that for each pair of groupoids, the two kinds of groupoids of morphisms are equivalent. Then we study the automorphism groupoid of a groupoid.
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    In this paper, we firstly give the definition of the coupled Hall-Littlewood function and its realization in terms of vertex operators. Then we construct the representation of the two-site generalized $q$-boson model in the algebra of coupled Hall-Littlewood functions. Finally, we find that the vertex operators which generate coupled Hall-Littlewood functions can also be used to obtain the partition function of the A-model topological string on the conifold.
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    Fluorescent dipoles reflect the spatial orientation of the fluorophores, which indicates structural information of the targeted proteins. As an important super-resolution technique, Structured Illumination Microscopy (SIM) requires three different couples of linearly polarized light to generate high-contrast interferometric fringes, relating to polarization modulation, a technique to measure dipole orientations. Here we reveal the inherent connection between SIM and polarization modulation: exciting fluorescent anisotropic specimens using a linearly polarized light is a type of structured illumination in the dimension of dipole orientation, with polarization modulation varying the phases of the pattern. Further, we invented polarized SIM (pSIM) with super-resolution imaging of the fluorescent dipoles, through expanding the spatial and polarization observable region in reciprocal space. pSIM maintains all the advantages of SIM and can be performed directly on the existing commercial SIM microscopes. We believe pSIM would become a powerful and widely accessible technique in studying biological structures.
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    A high-Q silica whispering-gallery mode microresonator is an attractive platform on which to demonstrate a broad and phase-locked Raman comb in various wavelength regimes. Raman combs can be used for applications such as compact pulse laser sources, sensors, optical clocks, and coherence tomography. However, the formation dynamics of a Raman comb has not been well exploited. Here we study the dynamics of the Raman comb formation in silica rod microresonators, which have cavity free spectral ranges in microwave rates. We generated a Raman comb with a smooth spectral envelope and also observed the transition between two Raman combs located at different center wavelengths. The transition behavior was obtained when we changed the pump detuning and the coupling strength between the microresonator and fiber. We also explain these phenomena by using a simple model based on coupled mode equations.
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    We present a Bayesian and frequentist analysis of the DAMPE charged cosmic ray spectrum. The spectrum, by eye, contained a spectral break at about 1 TeV and a monochromatic excess at about 1.4 TeV. The break was supported by a Bayes factor of about $10^{10}$ and we argue that the statistical significance was resounding. We investigated whether we should attribute the excess to dark matter annihilation into electrons in a nearby subhalo. We found a local significance of about $3.6\sigma$ and a global significance of about $2.3\sigma$, including a two-dimensional look-elsewhere effect by simulating 1000 pseudo-experiments. The Bayes factor was sensitive to our choices of priors, but favoured the excess by about 2 for our choices. Thus, whilst intriguing, the evidence for a signal is not currently compelling.
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    We extend the Ax-Schanuel theorem recently proven for Shimura varieties by Mok-Pila-Tsimerman to all varieties supporting a pure polarized integral variation of Hodge structures. The essential new ingredient is a volume bound on Griffiths transverse subvarieties of period domains.
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    We investigated transient optical responses in an optimally-doped high-Tc superconductor La2-xSrxCuO4 (x=0.15) by using 800-nm optical pump and terahertz probe spectroscopy. With increasing the photoexcitation intensities, the Josephson plasma resonance shows a gradual redshift, indicating the suppression of superconductivity by the photoexcitation. With further increasing the photoexcitation intensities, a new longitudinal mode in the loss function spectrum appears and grows from the high energy side, accompanied by a new transverse mode as manifested in the conductivity spectrum. The observed spectra are described by the multilayer model with alternating interlayer Josephson couplings. The new longitudinal and transverse modes sustain much longer than several hundred picoseconds after the photoexcitation, indicating that the new metastable phase with possessing alternating interlayer Josephson couplings is induced by the strong photoexcitation.
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    The characterization of intermittent, multiscale and transient dynamics using data-driven analysis remains an open challenge. We demonstrate an application of the Dynamic Mode Decomposition (DMD) with sparse sampling for the diagnostic analysis of multiscale physics. The DMD method is an ideal spatiotemporal matrix decomposition that correlates spatial features of computational or experimental data to periodic temporal behavior. DMD can be modified into a multiresolution analysis to separate complex dynamics into a hierarchy of multiresolution timescale components, where each level of the hierarchy divides dynamics into distinct background (slow) and foreground (fast) timescales. The multiresolution DMD is capable of characterizing nonlinear dynamical systems in an equation-free manner by recursively decomposing the state of the system into low-rank spatial modes and their temporal Fourier dynamics. Moreover, these multiresolution DMD modes can be used to determined sparse sampling locations which are nearly optimal for dynamic regime classification and full state reconstruction. Specifically, optimized sensors are efficiently chosen using QR column pivots of the DMD library, thus avoiding an NP-hard selection process. We demonstrate the efficacy of the method on several examples, including global sea-surface temperature data, and show that only a small number of sensors are needed for accurate global reconstructions and classification of El Niño events.
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    Theoretical stellar evolution models are constructed and tailored to the best known, observationally derived characteristics of metal-poor ([Fe/H]$\sim-2.3$) stars representing a range of evolutionary phases: subgiant HD140283, globular cluster M92, and four single, main sequence stars with well-determined parallaxes: HIP46120, HIP54639, HIP106924, and WOLF1137. It is found that the use of a solar-calibrated value of the mixing length parameter $\alpha_{\text{MLT}}$ in models of these objects is ineffective at reproducing their observed properties. Empirically calibrated values of $\alpha_{\text{MLT}}$ are presented for each object, accounting for uncertainties in the input physics employed in the models. It is advocated that the implementation of an adaptive mixing length is necessary in order for stellar evolution models to maintain fidelity in the era of asteroseismic observations.
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    Superconducting qubits are sensitive to a variety of loss mechanisms which include dielectric loss from interfaces. The calculation of participation near the key interfaces of planar designs can be accomplished through an analytical description of the electric field density based on conformal mapping. In this way, a two-dimensional approximation to coplanar waveguide and capacitor designs produces values of the participation as a function of depth from the top metallization layer as well as the volume participation within a given thickness from this surface by reducing the problem to a surface integration over the region of interest. These quantities are compared to finite element method numerical solutions, which validate the values at large distances from the coplanar metallization but diverge near the edges of the metallization features due to the singular nature of the electric fields. A simple approximation to the electric field energy at shallow depths (relative to the waveguide width) is also presented that closely replicates the numerical results based on conformal mapping. These techniques are applied to the calculation of surface participation within a transmon qubit design, where the effects due to shunting capacitors can be easily integrated with those associated with metallization comprising the local environment of the qubit junction.
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    The recent years have brought great advances in our knowledge of magnetic fields in cool giant and supergiant stars. For example, starspots have been directly imaged on the surface of an active giant star using optical interferometry, and magnetic fields have been detected in numerous slowly rotating giants and even on supergiants. Here, I review what is currently known of the magnetism in cool giant and supergiant stars, and discuss the origin of these fields and what is theoretically known about them.
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    It is well-known that in dimensions at least three semilinear wave equations with null conditions admit global solutions for small initial data. It is also known that in dimension two such result still holds for a certain class of quasi-linear wave equations with null conditions. The proofs are based on the decay mechanism of linear waves. However, in one dimension, waves do not decay. Nevertheless, we will prove that small data still lead to global solutions if the null condition is satisfied.
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    This paper establishes that the Nahm transform sending spatially periodic instantons (instantons on the product of the real line and a three-torus) to singular monopoles on the dual three-torus is indeed a bijection as suggested by the heuristic. In the process, we show how the Nahm transform intertwines to a Fourier-Mukai transform via Kobayashi-Hitchin correspondences. We also prove existence and non-existence results.
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    Advanced computing and data acquisition technologies have made possible the collection of high-dimensional data streams in many fields. Efficient online monitoring tools which can correctly identify any abnormal data stream for such data are highly sought after. However, most of the existing monitoring procedures directly apply the false discover rate (FDR) controlling procedure to the data at each time point, and the FDR at each time point (the point-wise FDR) is either specified by users or determined by the in-control (IC) average run length (ARL). If the point-wise FDR is specified by users, the resulting procedure lacks control of the global FDR and keeps users in the dark in terms of the IC-ARL. If the point-wise FDR is determined by the IC-ARL, the resulting procedure does not give users the flexibility to choose the number of false alarms (Type-I errors) they can tolerate when identifying abnormal data streams, which often makes the procedure too conservative. To address those limitations, we propose a two-stage monitoring procedure that can control both the IC-ARL and Type-I errors at the levels specified by users. As a result, the proposed procedure allows users to choose not only how often they expect any false alarms when all data streams are IC, but also how many false alarms they can tolerate when identifying abnormal data streams. With this extra flexibility, our proposed two-stage monitoring procedure is shown in the simulation study and real data analysis to outperform the exiting methods.
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    Nonparametric control charts that can detect arbitrary distributional changes are highly desirable due to their flexibility to adapt to different distributional assumptions and distributional changes. However, most of such control charts in the literature either involve some tuning parameter, which needs to be pre-specified, or involve intensive computation. In this paper, we propose a new nonparametric adaptive CUSUM chart for detecting arbitrary distributional changes. The proposed control chart does not depend on any tuning parameter and is efficient in computation. Its self-starting nature makes the proposed control chart applicable to situations where no sufficiently large reference data are available. Our proposed control chart also has a built-in post-signal diagnostics function that can identify what kind of distributional changes have occurred after an alarm. Our simulation study and real data analysis show that the proposed control chart performs well across a broad range of settings, and compares favorably with existing nonparametric control charts.
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    A two-dimensional double-metal oxide MnCoO4 was predicted to be an intrinsic ferromagnetic semiconductor by using density functional theory. The low cleavage energy 0.36 Jm-2, which is similar to that of graphene, indicates that it can be easily exfoliated. The bulk structure has an antiferromagnetic ground state while the ferromagnetic configuration is the ground state against two antiferromagnetic and three ferrimagnetic configurations in the two-dimensional structure. The spin flip gaps for valence and conduction bands are 0.41 and 0.10 eV calculated with the HSE06 density functional, which are much larger than the thermal energy at room temperature. The Curie temperature obtained from the Monte Carlo simulation is 40 K. Under 9% tensile strain, the spin flip gaps increase largely so that the spin flip can be suppressed. The direct antiferromagnetic coupling between the Mn and Co atoms reduces largely while the indirect ferromagnetic couplings between two Mn or two Co atoms mediated by the O atoms do not decrease much in the stretched structure. The Curie temperature increases to 230 K, higher than the dry ice temperature. Moreover, phonon dispersion indicates that the MnCoO4 is also stable under the tensile stain. Therefore, two-dimensional MnCoO4 could be a good candidate for low-dimensional spintronics.
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    It is important to investigate the relationships between the power sources and the chemical compositions of galaxies for understanding the scenario of galaxy evolution. We carried out an unbiased molecular line survey towards AGN host galaxy NGC1068, and prototypical starburst galaxies, NGC 253 and IC 342, with the Nobeyama 45-m telescope in the 3-mm band. The advantage of this line survey is that the obtained spectra have the highest angular resolution ever obtained with single-dish telescopes. In particular, the beam size of this telescope is ~15"--19", which is able to spatially separate the nuclear molecular emission from that of the starburst ring (d~30") in NGC 1068. We successfully detected approximately 23 molecular species in each galaxy, and calculated rotation temperatures and column densities. We estimate the molecular fractional abundances with respect to 13CO and CS molecules and compare them among three galaxies in order to investigate the chemical signatures of an AGN environment. As a result, we found clear trends on the abundances of molecules surrounding the AGN on 1 kpc scale. HCN, H13CN, CN, 13CN, and HC3N are more abundant, and CH3CCH is deficient in NGC 1068 compared with the starburst galaxies. High abundances of HCN, H13CN, and HC3N suggest that the circumnuclear disk in NGC 1068 is in a high-temperature environment. The reason for the non-detection of CH3CCH is likely to be dissociation by high energy radiation or less sublimation of a precursor of CH3CCH from grains.
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    Ground states of quadratic Hamiltonians for fermionic systems can be characterized in terms of orthogonal complex structures. The standard way in which such Hamiltonians are diagonalized makes use of a certain "doubling" of the Hilbert space. In this work we show that this redundancy in the Hilbert space can be completely lifted if the relevant orthogonal structure is taken into account. Such an approach allows for a treatment of Majorana fermions which is both physically and mathematically transparent. Furthermore, an explicit connection between orthogonal complex structures and the topological $\mathbb Z_2$-invariant is given.
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    We investigate the quantum vacuum and find the fluctuations can lead to the inhomogeneous quantum vacuum. We find that the vacuum fluctuations can significantly influence the cosmological inhomogeneity, which is different from what previously expected. By introducing the modified Green's function, we reach a new inflationary scenario which can explain why the Universe is still expanding without slowing down. We also calculate the tunneling amplitude of the Universe based on the inhomogeneous vacuum. We find that the inhomogeneity can lead to the penetration of the universe over the potential barrier faster than previously thought.
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    Fully connected multilayer perceptrons are used for obtaining numerical solutions of partial differential equations in various dimensions. Independent variables are fed into the input layer, and the output is considered as solution's value. To train such a network one can use square of equation's residual as a cost function and minimize it with respect to weights by gradient descent. Following previously developed method, derivatives of the equation's residual along random directions in space of independent variables are also added to cost function. Similar procedure is known to produce nearly machine precision results using less than 8 grid points per dimension for 2D case. The same effect is observed here for higher dimensions: solutions are obtained on low density grids, but maintain their precision in the entire region. Boundary value problems for linear and nonlinear Poisson equations are solved inside 2, 3, 4, and 5 dimensional balls. Grids for linear cases have 40, 159, 512 and 1536 points and for nonlinear 64, 350, 1536 and 6528 points respectively. In all cases maximum error is less than $8.8\cdot10^{-6}$, and median error is less than $2.4\cdot10^{-6}$. Very weak grid requirements enable neural networks to obtain solution of 5D linear problem within 22 minutes, whereas projected solving time for finite differences on the same hardware is 50 minutes. Method is applied to second order equation, but requires little to none modifications to solve systems or higher order PDEs.
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    In this article, we study the problem of parameter estimation for a discrete Ornstein - Uhlenbeck model driven by Poisson fractional noise. Based on random walk approximation for the noise, we study least squares and maximum likelihood estimators. Thus, asymptotic behaviours of the estimator is carried out, and a simulation study is shown to illustrate our results.
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    Let $\phi$ be an $L^2$-normalized spherical vector in an everywhere unramified cuspidal automorphic representation of $\mathrm{PGL}_n$ over $\mathbb{Q}$ with Laplace eigenvalue $\lambda_{\phi}$. We establish explicit estimates for various quantities related with $\phi$ that are uniform in $\lambda_{\phi}$. This includes uniforms bounds for spherical Whittaker functions on $\mathrm{GL}_n(\mathbb{R})$, uniform bounds for the global sup-norm of $\phi$, and uniform bounds for the "essential support" of $\phi$, i.e. the region outside which it decays exponentially. The proofs combine analytic and arithmetic tools.
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    Some viruses, such as human immunodeficiency virus, can infect several types of cell populations. The age of infection can also affect the dynamics of infected cells and production of viral particles. In this work, we study a virus model with infection-age and different types of target cells which takes into account the saturation effect in antibody immune response and a general non-linear infection rate. We construct suitable Lyapunov functionals to show that the global dynamics of the model is completely determined by two critical values: the basic reproduction number of virus and the reproductive number of antibody response.
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    We present an analysis of the role of the charge within the self-complete quantum gravity paradigm. By studying the classicalization of generic ultraviolet improved charged black hole solutions around the Planck scale, we showed that the charge introduces important differences with respect to the neutral case. First, there exists a family of black hole parameters fulfilling the particle-black hole condition. Second, there is no extremal particle-black hole solution but quasi extremal charged particle-black holes at the best. We showed that the Hawking emission disrupts the condition of particle-black hole. By analyzing the Schwinger pair production mechanism, the charge is quickly shed and the particle-black hole condition can ultimately be restored in a cooling down phase towards a zero temperature configuration, provided non-classical effects are taken into account.
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    Cooperative adsorption of gases by porous frameworks permits more efficient uptake and removal than does the more usual non-cooperative (Langmuir-type) adsorption. Cooperativity, signaled by a step-like isotherm, is usually attributed to a phase transition of the framework. However, the class of metal-organic frameworks mmen-M$_2$(dobpdc) exhibit cooperative adsorption of CO2 but show no evidence of a phase transition. Here we show how cooperativity emerges in these frameworks in the absence of a phase transition. We use a combination of quantum and statistical mechanics to show that cooperativity results from a sharp but finite increase, with pressure, of the mean length of chains of CO2 molecules that polymerize within the framework. Our study provides microscopic understanding of the emergent features of cooperative binding, including the position, slope and height of the isotherm step, and indicates how to optimize gas storage and separation in these materials.
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    Cosmic superstrings of string theory differ from conventional cosmic strings of field theory. We review how the physical and cosmological properties of the macroscopic string loops influence experimental searches for these relics from the epoch of inflation. The universe's average density of cosmic superstrings can easily exceed that of conventional cosmic strings having the same tension by two or more orders of magnitude. The cosmological behavior of the remnant superstring loops is qualitatively distinct because the string tension is exponentially smaller than the string scale in flux compactifications in string theory. Low tension superstring loops live longer, experience less recoil (rocket effect from the emission of gravitational radiation) and tend to cluster like dark matter in galaxies. Clustering enhances the string loop density with respect to the cosmological average in collapsed structures in the universe. The enhancement at the Sun's position is $\sim 10^5$. We develop a model encapsulating the leading order string theory effects, the current understanding of the string network loop production and the influence of cosmological structure formation suitable for forecasting the detection of superstring loops via optical microlensing, gravitational wave bursts and fast radio bursts. We evaluate the detection rate of bursts from cusps and kinks by LIGO- and LISA-like experiments. Clustering dominates rates for $G \mu < 10^{-11.9}$ (LIGO cusp), $G \mu<10^{-11.2}$ (LISA cusp), $G \mu < 10^{-10.6}$ (LISA kink); we forecast experimentally accessible gravitational wave bursts for $G \mu>10^{-14.2}$ (LIGO cusp), $G \mu>10^{-15}$ (LISA cusp) and $G \mu>10^{- 14.1}$ (LISA kink).
  • PDF
    Empirical evidence reveals that a contagion process often occurs with mixing simple and complex contagion, meaning that while some agents follow simple contagion, the others follow complex contagion. Inspired by this observation, we propose a generalized model of contagion dynamics unifying both simple and complex contagion with heterogeneous adoptability of agents. We illustrate a phase diagram with respect to the transmission probability and the fraction of nodes with complex contagion. We find that our generalized contagion model exhibits a rich variety of phase transitions such as continuous, discontinuous, and hybrid phase transitions, criticality, tricriticality, and double transitions. Especially, we find a double phase transition showing continuous transition and following discontinuous transition in the density of adopted nodes with respect to a transmission probability. We show that the double transition occurs with an intermediate phase in which nodes following simple contagion become adopted but nodes with complex contagion remain susceptible.
  • PDF
    In this paper, we study the notion of Johnson pseudo-contractibility for certain Banach algebras. For a bicyclic semigroup $S$, we show that $\ell^{1}(S)$ is not Johnson pseudo-contractible. Also for a Johnson pseudo-contractible Banach algebra $A$, we show that $A$ has no non-zero approximately complemented closed nilpotent ideal.
  • PDF
    Let $\Sigma_g$ denote the closed orientable surface of genus $g$ and fix an arbitrary simplicial triangulation of $\Sigma_g$. We construct and study a natural surjective group homomorphism from the surface braid group on $n$ strands on $\Sigma_g$ to the first singular homology group of $\Sigma_g$ with integral coefficients. In particular, we show that the kernel of this homomorphism is generated by canonical braids which arise from the triangulation of $\Sigma_g$. This provides a simple description of natural subgroups of surface braid groups which are closely tied to the homology groups of the surfaces $\Sigma_g$.

Recent comments

Andrew W Simmons Dec 14 2017 11:40 UTC

Hi Māris, you might well be right! Stabiliser QM with more qubits, I think, is also a good candidate for further investigation to see if we can close the gap a bit more between the analytical upper bound and the example-based lower bound.

Planat Dec 14 2017 08:43 UTC

Interesting work. You don't require that the polar space has to be symplectic. In ordinary quantum mechanics the commutation of n-qudit observables is ruled by a symplectic polar space. For two qubits, it is the generalized quadrangle GQ(2,2). Incidently, in https://arxiv.org/abs/1601.04865 this pro

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Māris Ozols Dec 12 2017 19:41 UTC

$E_7$ also has some nice properties in this regard (in fact, it might be even better than $E_8$). See https://arxiv.org/abs/1009.1195.

Danial Dervovic Dec 10 2017 15:25 UTC

Thank you for the insightful observations, Simon.

In response to the first point, there is a very short comment in the Discussion section to this effect. I felt an explicit dependence on $T$ as opposed to the diameter would make the implications of the result more clear. Namely, lifting can mix

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Simon Apers Dec 09 2017 07:54 UTC

Thanks for the comment, Simone. A couple of observations:

- We noticed that Danial's result can in fact be proved more directly using the theorem that is used from ([arXiv:1705.08253][1]): by choosing the quantum walk Cesaro average as the goal distribution, it can be attained with a lifted Markov

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Simone Severini Dec 07 2017 02:51 UTC

Closely related to

Simon Apers, Alain Sarlette, Francesco Ticozzi, Simulation of Quantum Walks and Fast Mixing with Classical Processes, https://scirate.com/arxiv/1712.01609

In my opinion, lifting is a good opportunity to put on a rigorous footing the relationship between classical and quantu

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Mark Everitt Dec 05 2017 07:50 UTC

Thank you for the helpful feedback.

Yes these are 14 pairs of graphs [This is an edit - I previously mistakenly posted that it was 7 pairs] that share the same equal angle slice. We have only just started looking at the properties of these graphs. Thank you for the link - that is a really useful r

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Simone Severini Dec 05 2017 01:13 UTC

When looking at matrix spectra as graph invariants, it is easy to see that the spectrum of the adjacency matrix or the Laplacian fails for 4 vertices. Also, the spectrum of the adjacency matrix together with the spectrum of the adjacency matrix of the complement fail for 7 vertices. So, the algorith

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Mark Everitt Dec 04 2017 17:52 UTC

Thank you for this - its the sort of feedback we were after.

We have found 14 examples of 8 node graphs (of the possible 12,346) that break our conjecture.

We are looking into this now to get some understanding and see if we can overcome this issue. We will check to see if the failure of our algo

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Dave Bacon Dec 02 2017 00:08 UTC

A couple of comments:

1. To be a complete algorithm I think you need to specify how many of the equal angles you need to sample from (i.e. how many Euler angles)? And also maybe what "experimental accuracy means"? If those are exponential in order to work that's bad (but still very interesting

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