Top arXiv papers

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    We construct an effective commutative Schrödinger equation in Moyal space-time in $(1+1)$-dimension where both $t$ and $x$ are operator-valued and satisfy $\left[ \hat{t}, \hat{x} \right] = i \theta$. Beginning with a time-reparametrised form of an action we identify the actions of various space-time coordinates and their conjugate momenta on quantum states, represented by Hilbert-Schmidt operators. Since time is also regarded as a configuration space variable, we show how an `induced' inner product can be extracted, so that an appropriate quantum mechanical interpretation is obtained. We then discuss several other applications of the formalism developed so far.
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    In search of new prospects for thermoelectric materials, using ab-initio calculations and semi-classical Boltzmann theory, we have systematically investigated the electronic structure and transport properties of 18-valence electron count cobalt based half-Heusler alloys with prime focus on CoVSn, CoNbSn, CoTaSn, CoMoIn, and CoWIn. The effect of doping on transport properties has been studied under the rigid band approximation. The maximum power factor, S$^2\sigma$, for all systems is obtained on hole doping and is comparable to the existing thermoelectric material CoTiSb. The stability of all the systems is verified by phonon calculations. Based on our calculations, we suggest that CoVSn, CoNbSn, CoTaSn, CoMoIn and CoWIn could be potential candidates for high temperature thermoelectric materials.
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    The highest pressure form of the major Earth-forming mantle silicate is MgSiO3 post-perovskite (PPv). Understanding the fate of PPv at TPa pressures is the first step for understanding the mineralogy of super-Earths-type exoplanets, arguably the most interesting for their similarities with Earth. Modeling their internal structure requires knowledge of stable mineral phases, their properties under compression, and major element abundances. Several studies of PPv under extreme pressures support the notion that a sequence of pressure induced dissociation transitions produce the elementary oxides SiO2 and MgO as the ultimate aggregation form at ~3 TPa. However, none of these studies have addressed the problem of mantle composition, particularly major element abundances usually expressed in terms of three main variables, the Mg/Si and Fe/Si ratios and the Mg#, as in the Earth. Here we show that the critical compositional parameter, the Mg/Si ratio, whose value in the Earth's mantle is still debated, is a vital ingredient for modeling phase transitions and internal structure of super-Earth mantles. Specifically, we have identified new sequences of phase transformations, including new recombination reactions that depend decisively on this ratio. This is a new level of complexity that has not been previously addressed, but proves essential for modeling the nature and number of internal layers in these rocky mantles.
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    Two-dimensional (2D) semiconductors isoelectronic to phosphorene has been drawing much attention recently due to their promising applications for next-generation (opt)electronics. This family of 2D materials contains more than 400 members, including (a) elemental group-V materials, (b) binary III-VII and IV-VI compounds, (c) ternary III-VI-VII and IV-V-VII compounds, making materials design with targeted functionality unprecedentedly rich and extremely challenging. To shed light on rational functionality design with this family of materials, we systemically explore their fundamental band gaps and alignments using hybrid density functional theory (DFT) in combination with machine learning. First, GGA-PBE and HSE calculations are performed as a reference. We find this family of materials share similar crystalline structures, but possess largely distributed band-gap values ranging approximately from 0 to 8 eV. Then, we apply machine learning methods, including Linear Regression (LR), Random Forest Regression (RFR), and Support Vector Machine Regression (SVR), to build models for prediction of electronic properties. Among these models, SVR is found to have the best performance, yielding the root mean square error (RMSE) less than 0.15 eV for predicted band gaps, VBMs, and CBMs when both PBE results and elemental information are used as features. Thus, we demonstrate machine learning models are universally suitable for screening 2D isoelectronic systems with targeted functionality and especially valuable for the design of alloys and heterogeneous systems.
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    Sparse Subspace Clustering (SSC) is a state-of-the-art method for clustering high-dimensional data points lying in a union of low-dimensional subspaces. However, while $\ell_1$ optimization-based SSC algorithms suffer from high computational complexity, other variants of SSC, such as Orthogonal Matching Pursuit-based SSC (OMP-SSC), lose clustering accuracy in pursuit of improving time efficiency. In this letter, we propose a novel Active OMP-SSC, which improves clustering accuracy of OMP-SSC by adaptively updating data points and randomly dropping data points in the OMP process, while still enjoying the low computational complexity of greedy pursuit algorithms. We provide heuristic analysis of our approach, and explain how these two active steps achieve a better tradeoff between connectivity and separation. Numerical results on both synthetic data and real-world data validate our analyses and show the advantages of the proposed active algorithm.
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    We study a switching synchronization phenomenon taking place in one-dimensional memristive networks when the memristors switch from the high to low resistance state. It is assumed that the distributions of threshold voltages and switching rates of memristors are arbitrary. Using the Laplace transform, a set of non-linear equations describing the memristors dynamics is solved exactly, without any approximations. The time dependencies of memristances are found and it is shown that the voltage falls across memristors are proportional to their threshold voltages. A compact expression for the network switching time is derived.
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    We use determinant Quantum Monte Carlo (DQMC), in combination with the principal component analysis (PCA) approach to unsupervised learning, to extract information about phase transitions in several of the most fundamental Hamiltonians describing strongly correlated materials. We first explore the zero temperature antiferromagnet to singlet transition in the Periodic Anderson Model, the Mott insulating transition in the Hubbard model on a honeycomb lattice, and the magnetic transition in the 1/6-filled Lieb lattice. We then discuss the prospects for learning finite temperature superconducting transitions in the attractive Hubbard model, for which there is no sign problem. Finally, we investigate finite temperature CDW transitions in the Holstein model, where the electrons are coupled to phonon degrees of freedom. We examine the different behaviors associated with providing Hubbard-Stratonovich auxiliary fields configurations on both the entire space-time lattice and on a single imaginary time slice, or other quantities, such as equal-time Green's and pair-pair correlation functions.
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    The behavior of a massive charged test Dirac field in the background of a Reissner-Nordström black hole is investigated. Especially, we obtain the frequencies of quasibound states by solving the Dirac equation numerically both in time and frequency domain. Our results suggest that although the absence of superradiance excludes the existence of stationary solutions for massive Dirac fields, it is still possible to find arbitrarily long-lived solutions.
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    Let $k$ be a field and $G \subseteq Gl_n(k)$ be a finite group with $|G|^{-1} \in k$. Let $G$ act linearly on $A = k[X_1, \ldots, X_n]$ and let $A^G$ be the ring of invariant's. Suppose there does not exist any non-trivial one-dimensional representation of $G$ over $k$. Then we show that if $Q$ is a $G$-invariant homogeneous ideal of $A$ such that $A/Q$ is a Gorenstein ring then $A^G/Q^G$ is also a Gorenstein ring.
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    We prove a Plancherel theorem for a nonlinear Fourier transform in two dimensions arising in the Inverse-Scattering method for the defocusing Davey-Stewartson II equation. We then use it to prove global well-posedness and scattering in $L^2$ for defocusing DSII. This Plancherel theorem also implies global uniqueness in the inverse boundary value problem of Calderón in dimension $2$, for conductivities $\sigma>0$ with $\log \sigma \in \dot H^1$. The proof of the nonlinear Plancherel theorem includes new estimates on fractional integrals in Sobolev spaces, as well as a new result on $L^2$- boundedness of pseudo-differential equations with non-smooth symbols, valid in all dimensions.
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    We analyze the energy configuration of a charged black hole in the Teleparallel Framework of General Relativity. We obtain the energy-momentum tensor of the gravitational field in a stationary frame, and we calculate its contribution to the total energy of the system. We study the same gravitational field measured by an accelerated frame and we analyze how the energy-momentum tensor is transformed. We found that in the accelerated frame, a Poyinting-like flux appears for the gravitational field but not for the electromagnetic field.
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    We describe studies on the nanoscale transport dynamics of carriers in strained AlN/GaN/AlN quantum wells: an electron-hole bilayer charge system with large difference in transport properties between the two charge layers. From electronic band diagram analysis, the presence of spatially separated two-dimensional electron and hole charge layers is predicted at opposite interfaces. Since these charge layers exhibit distinct spectral signatures at terahertz frequencies, a combination of terahertz and far-infrared spectroscopy enables us to extract (a) individual contributions to the total conductivity, as well as (b) effective scattering rates for charge-carriers in each layer. Furthermore, by comparing direct-current and terahertz extracted conductivity levels, we are able to determine the extent to which structural defects affect charge transport. Our results evidence that (i) a non-unity Hall-factor and (ii) the considerable contribution of holes to the overall conductivity, lead to a lower apparent mobility in Hall-effect measurements. Overall, our work demonstrates that terahertz spectroscopy is a suitable technique for the study of bilayer charge systems with large differences in transport properties between layers, such as quantum wells in III-Nitride semiconductors.
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    This paper considers coordinated linear precoding in downlink multicell multiuser orthogonal frequency-division multiple access (OFDMA) network. A less-complex, fast and provably convergent algorithm that maximizes the weighted sum-rate with per base station (BS) transmit power constraint is formulated. We approximate the nonconvex weighted sum- rate maximization (WSRM) problem with a solvable convex form by means of sequential parametric convex approximation (SPCA) approach. The second order cone program (SOCP) formulations of the objective function and constraints of the optimization problem are derived through proper change of vari- ables, first order linear approximation and hyperbolic constraints transformation, etc. The algorithm converges to the suboptimal solution taking fewer number of iterations in comparison to other known iterative WSRM algorithms. Finally, numerical results are presented to justify the effectiveness and superiority of the proposed algorithm.
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    Relationship-based access control (ReBAC) provides a high level of expressiveness and flexibility that promotes security and information sharing. We formulate ReBAC as an object-oriented extension of attribute-based access control (ABAC) in which relationships are expressed using fields that refer to other objects, and path expressions are used to follow chains of relationships between objects. ReBAC policy mining algorithms have potential to significantly reduce the cost of migration from legacy access control systems to ReBAC, by partially automating the development of a ReBAC policy from an existing access control policy and attribute data. This paper presents an algorithm for mining ReBAC policies from access control lists (ACLs) and attribute data represented as an object model, and an evaluation of the algorithm on four sample policies and two large case studies. Our algorithm can be adapted to mine ReBAC policies from access logs and object models. It is the first algorithm for these problems.
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    We show how third-party web trackers can deanonymize users of cryptocurrencies. We present two distinct but complementary attacks. On most shopping websites, third party trackers receive information about user purchases for purposes of advertising and analytics. We show that, if the user pays using a cryptocurrency, trackers typically possess enough information about the purchase to uniquely identify the transaction on the blockchain, link it to the user's cookie, and further to the user's real identity. Our second attack shows that if the tracker is able to link two purchases of the same user to the blockchain in this manner, it can identify the user's entire cluster of addresses and transactions on the blockchain, even if the user employs blockchain anonymity techniques such as CoinJoin. The attacks are passive and hence can be retroactively applied to past purchases. We discuss several mitigations, but none are perfect.
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    Diamond Si is a semiconductor with an indirect band gap that is the basis of modern semiconductor technology. Although many metastable forms of Si were observed using diamond anvil cells for compression and chemical precursors for synthesis, no metallic phase at ambient conditions has been reported thus far. Here we report the prediction of pure metallic Si allotropes with open channels at ambient pressure, unlike a cubic diamond structure in covalent bonding networks. The metallic phase termed P6/m-Si6 can be obtained by removing Na after pressure release from a novel Na-Si clathrate called P6/m-NaSi6, which is discovered through first-principles study at high pressure. We confirm that both P6/m-NaSi6 and P6/m-Si6 are stable and superconducting with the critical temperatures of about 13 and 12 K at ambient pressure, respectively. The discovery of new Na-Si and Si clathrate structures presents the possibility of exploring new exotic allotropes useful for Si-based devices.
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    Optimization problems with more than one objective consist in a very attractive topic for researchers due to its applicability in real-world situations. Over the years, the research effort in Computational Intelligence area resulted in algorithms able to achieve good results by solving problems with more than one conflicting objective. However, these techniques do not exhibit the same performance as the number of objectives increases and become greater than 3. This paper proposes an adaptation of the metaheuristic Fish School Search to solve optimization problems with many objectives. This adaptation is based on the division of the school in clusters that are specialized in solving a single-objective problem generated by the decomposition of the original problem. For this, we used concepts and ideas often found in the literature and applied in state-of-the-art algorithms, namely: (i) reference points and lines in the objectives space; (ii) clustering process; and (iii) the decomposition technique Penalty-based Boundary Intersection. The proposed algorithm was compared with two state-of-the-art bio-inspired algorithms. Results have shown competitiveness, as well as the necessity of improving the performance of the proposed technique on multi-modal many-objective problems.
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    In this paper we introduce a natural function class and prove the existence and uniqueness of both nonnegative renormalized solutions and entropy solutions for the fractional p-Laplacian parabolic problem with L^1 data. And moreover, we obtain the equivalence of renormalized solutions and entropy solutions and establish a comparison result.
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    We study hadronic molecular states in a coupled system of $J/\psi N - \Lambda_c\bar{D}^{(*)} - \Sigma_c^{(*)}\bar{D}^{(*)}$ in $I(J^P) = \frac{1}{2}(\frac{3}{2}^-)$ channel, using the complex scaling method combined with the Gaussian expansion method. We construct the potential including one pion exchange and one $D^{(*)}$ meson exchange with $S$-wave orbital angular momentum. We find that the both mass and width of the pentaquark $P_c(4380)$ can be reproduced within a reasonable parameter region, and that its main decay mode is $\Lambda_c\bar{D}^*$. We extend our analysis to a coupled system of $\Lambda_c D^{(*)} - \Sigma_c^{(*)}D^{(*)}$ in $I(J^P) = \frac{1}{2}(\frac{3}{2}^-)$ channel. We find that there exists a doubly charmed baryon of $ccqq\bar{q}$ type as a hadronic molecule, the mass and width of which are quite close to those of $P_c(4380)$.
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    We study the near-infrared properties of 690 Mira candidates in the central region of the Large Magellanic Cloud, based on time-series observations at JHKs. We use densely-sampled I-band observations from the OGLE project to generate template light curves in the near infrared and derive robust mean magnitudes at those wavelengths. We obtain near-infrared Period-Luminosity relations for Oxygen-rich Miras with a scatter as low as 0.12 mag at Ks. We study the Period-Luminosity-Color relations and the color excesses of Carbon-rich Miras, which show evidence for a substantially different reddening law.
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    A lack of understanding of human biology creates a hurdle for the development of precision medicines. To overcome this hurdle we need to better understand the potential synergy between a given investigational treatment (vs. placebo or active control) and various demographic or genetic factors, disease history and severity, etc., with the goal of identifying those patients at increased risk of exhibiting clinically meaningful treatment benefit. For this reason, we propose the VG method, which combines the idea of an individual treatment effect (ITE) from Virtual Twins (Foster, et al., 2011) with the unbiased variable selection and cutoff value determination algorithm from GUIDE (Loh, et al., 2015). Simulation results show the VG method has less variable selection bias than Virtual Twins and higher statistical power than GUIDE Interaction in the presence of prognostic variables with strong treatment effects. Type I error and predictive performance of Virtual Twins, GUIDE and VG are compared through the use of simulation studies. Results obtained after retrospectively applying VG to data from a clinical trial also are discussed.
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    In this paper, we address the challenging problem of optimal experimental design (OED) of constrained inverse problems. We consider two OED formulations that allow reducing the experimental costs by minimizing the number of measurements. The first formulation assumes a fine discretization of the design parameter space and uses sparsity promoting regularization to obtain an efficient design. The second formulation parameterizes the design and seeks optimal placement for these measurements by solving a small-dimensional optimization problem. We consider both problems in a Bayes risk as well as an empirical Bayes risk minimization framework. For the unconstrained inverse state problem, we exploit the closed form solution for the inner problem to efficiently compute derivatives for the outer OED problem. The empirical formulation does not require an explicit solution of the inverse problem and therefore allows to integrate constraints efficiently. A key contribution is an efficient optimization method for solving the resulting, typically high-dimensional, bilevel optimization problem using derivative-based methods. To overcome the lack of non-differentiability in active set methods for inequality constraints problems, we use a relaxed interior point method. To address the growing computational complexity of empirical Bayes OED, we parallelize the computation over the training models. Numerical examples and illustrations from tomographic reconstruction, for various data sets and under different constraints, demonstrate the impact of constraints on the optimal design and highlight the importance of OED for constrained problems.
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    In this paper we introduce a natural realization space for a polytope that arises as the positive part of an algebraic variety. The variety is determined by the slack ideal of the polytope, a saturated determinantal ideal that encodes the combinatorics of the polytope. The slack ideal offers an effective computational framework for several classical questions about polytopes such as rational realizability, projective uniqueness, non-prescribability of faces, and realizability of combinatorial polytopes. The simplest slack ideals are toric. We identify the toric ideals that arise from projectively unique polytopes as the toric ideal of the bipartite graph given by the vertex-facet non-incidences of the polytope. Several new and classical examples illuminate the relationships between projective uniqueness and toric slack ideals
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    We study the electroweak phase transition in three scalar extension models beyond the Standard Model. Assuming new scalars are decoupled at some heavy scale, we use the covariant derivative expansion method to derive all of the dimension-6 effective operators, whose coefficients are highly correlated in a specific model. We provide bounds to the complete set of dimension-6 operators by including the electroweak precision test and recent Higgs measurements. We find that the parameter space of strong first-order phase transition (induced by the $|H|^6$ operator) can be greatly probed in the $Zh$ production at future electron-positron colliders.
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    We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirectional coupling case. The unidirectional coupling has the advantage of easily obtaining global amplitude death in a ring of coupled oscillators with randomly distributed natural frequency. Finally, we explain the results using the eigenvalue analysis of Jacobian matrix at the origin and also discuss the transition of dynamical behavior coming from connection structure as coupling strength increases.
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    This paper presents a new class of magneto acoustic spin Hall (MASH) oscillators that combine the tunability of standard spin torque nano oscillators (STNO) with the high quality factor (Q) of high overtone bulk acoustic wave resonators (HBAR), integrating both reference and tunable oscillators on the same chip with CMOS. In MASH oscillators, voltage oscillations across the magnetic tunnel junction (MTJ) are shaped by the transmission response of the HBAR that acts as a multiple peakbandpass filter and a delay element due to its large time constant, providing delayed feedback. The filtered voltage oscillations can be fed back to the MTJ via a) strain, b) current, or c) magnetic field. We develop a SPICE-based circuit model by combining experimentally benchmarked models including the stochastic Landau-Lifshitz-Gilbert (sLLG) equation for magnetization dynamics and the Butterworth Van Dyke (BVD) circuit for the HBAR. Using the self-consistent model, we project up to ~50X enhancement in the oscillator linewidth with Q reaching up to 36500 at 3 GHz, while preserving the tunability by locking the STNO to the nearest high Q peak of the HBAR. We expect that our results will inspire NEMS-based solutions to spintronic devices by combining attractive features of both fields for a variety of applications.
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    Hydrogen bond networks play vital roles in biological functions ranging from protein folding to enzyme catalysis. Here we combine electronic structure calculations and ab initio path integral molecular dynamics simulations, which incorporate both nuclear and electronic quantum effects, to show why the network of short hydrogen bonds in the active site of ketosteroid isomerase is remarkably robust to mutations along the network and how this gives rise to large local electric fields. We demonstrate that these properties arise from the network's ability to respond to a perturbation by shifting proton positions and redistributing electronic charge density. This flexibility leads to small changes in properties such as the partial ionization of residues and $pK_a$ isotope effects upon mutation of the residues, consistent with recent experiments. This proton flexibility is further enhanced when an extended hydrogen bond network forms in the presence of an intermediate analog, which allows us to explain the chemical origins of the large electric fields in the enzyme's active site observed in recent experiments.
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    In this paper, we first prove the global well-posedness of 3-D anisotropic Navier-Stokes system provided that the vertical component of the initial velocity is sufficiently small in the anisotropic Sobolev space $H^{f12,0}$ and the vertical viscosity coefficient of the system is large enough. As an application, we shall prove the global well-posedness of the classical 3-D Navier-Stokes system with the initial data varying fast enough in one direction.
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    We prove an isoperimetric inequality for groups. As an application, we obtain lower bound on Følner functions in various nilpotent-by-cyclic groups. Under a regularity assumption, we obtain a characterization of Følner functions of these groups. As another application, we evaluate the asymptotics of the Følner function of $Sym(\mathbb{Z})\rtimes {\mathbb{Z}}$. We construct new examples of groups with Shalom's property $H_{\mathrm{FD}}$, in particular among nilpotent-by-cyclic and lacunary hyperbolic groups. Among these examples we find groups with property $H_{\mathrm{FD}}$, which are direct products of lacunary hyperbolic groups and have arbitrarily large Følner functions.
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    We develop the theoretical foundations of a network distance that has recently been applied to various subfields of topological data analysis, namely persistent homology and hierarchical clustering. While this network distance has previously appeared in the context of finite networks, we extend the setting to that of compact networks. The main challenge in this new setting is the lack of an easy notion of sampling from compact networks; we solve this problem in the process of obtaining our results. The generality of our setting means that we automatically establish results for exotic objects such as directed metric spaces and Finsler manifolds. We identify readily computable network invariants and establish their quantitative stability under this network distance. We also discuss the computational complexity involved in precisely computing this distance, and develop easily-computable lower bounds by using the identified invariants. By constructing a wide range of explicit examples, we show that these lower bounds are effective in distinguishing between networks. Finally, we provide a simple algorithm that computes a lower bound on the distance between two networks in polynomial time and illustrate our metric and invariant constructions on a database of random networks and a database of simulated hippocampal networks.
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    Biometrics have a long-held hope of replacing passwords by establishing a non-repudiated identity and providing authentication with convenience. Convenience drives consumers toward biometrics-based access management solutions. Unlike passwords, biometrics cannot be script-injected; however, biometric data is considered highly sensitive due to its personal nature and unique association with users. Biometrics differ from passwords in that compromised passwords may be reset. Compromised biometrics offer no such relief. A compromised biometric offers unlimited risk in privacy (anyone can view the biometric) and authentication (anyone may use the biometric). Standards such as the Biometric Open Protocol Standard (BOPS) (IEEE 2410-2016) provide a detailed mechanism to authenticate biometrics based on pre-enrolled devices and a previous identity by storing the biometric in encrypted form. This paper describes a biometric-agnostic approach that addresses the privacy concerns of biometrics through the implementation of BOPS. Specifically, two novel concepts are introduced. First, a biometric is applied to a neural network to create a feature vector. This neural network alone can be used for one-to-one matching (authentication), but would require a search in linear time for the one-to-many case (identity lookup). The classifying algorithm described in this paper addresses this concern by producing normalized floating-point values for each feature vector. This allows authentication lookup to occur in up to polynomial time, allowing for search in encrypted biometric databases with speed, accuracy and privacy.
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    The large volume of scientific publications is likely to have hidden knowledge which can be discovered dealing with the massive information altogether using a system which can cover the huge amount of data. We propose a method for generating hypotheses in the field of physics using the massive publications of physics journals. We convert the text data of titles and abstracts in publications to a bipartite graph extracting words of matter and keywords and suggest methods for predicting links between matter and keywords node. Those links generate hypotheses for research by suggesting the new possible relationship between some matter and phenomena or properties. Suggested methods have better performance than existed methods for link prediction in the bipartite graph. The experiments also show the detail application of our system for specific purpose: suggesting new matter which will be related with the concept of antiferromagnetism, superconductor and NMR spectroscopy.
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    The realization of multimessenger astrophysics will open new vistas upon the most energetic events in the universe. Messenger particles of all four of nature's fundamental forces, recorded by detectors on the ground and satellites in space, enable coincidence searches for multimessenger phenomena that will allow us to discover, observe, and explore these sources. The Astrophysical Multimessenger Observatory Network (AMON) links multiple high-energy neutrino, cosmic ray, and gamma-ray observatories as well as gravitational wave facilities into a single virtual system, enabling near real-time coincidence searches for multimessenger astrophysical transients and their electromagnetic counterparts, and providing alerts to follow-up observatories. The science case, design elements, partner observatories, and status of the AMON project are presented, followed by recent results from AMON real-time and archival analyses.
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    In the minimum planarization problem, given some $n$-vertex graph, the goal is to find a set of vertices of minimum cardinality whose removal leaves a planar graph. This is a fundamental problem in topological graph theory. We present a $\log^{O(1)} n$-approximation algorithm for this problem on general graphs with running time $n^{O(\log n/\log\log n)}$. We also obtain a $O(n^\varepsilon)$-approximation with running time $n^{O(1/\varepsilon)}$ for any arbitrarily small constant $\varepsilon > 0$. Prior to our work, no non-trivial algorithm was known for this problem on general graphs, and the best known result even on graphs of bounded degree was a $n^{\Omega(1)}$-approximation [Chekuri and Sidiropoulos 2013]. As an immediate corollary, we also obtain improved approximation algorithms for the crossing number problem on graphs of bounded degree. Specifically, we obtain $O(n^{1/2+\varepsilon})$-approximation and $n^{1/2} \log^{O(1)} n$-approximation algorithms in time $n^{O(1/\varepsilon)}$ and $n^{O(\log n/\log\log n)}$ respectively. The previously best-known result was a polynomial-time $n^{9/10}\log^{O(1)} n$-approximation algorithm [Chuzhoy 2011]. Our algorithm introduces several new tools including an efficient grid-minor construction for apex graphs, and a new method for computing irrelevant vertices. Analogues of these tools were previously available only for exact algorithms. Our work gives efficient implementations of these ideas in the setting of approximation algorithms, which could be of independent interest.
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    The problem of detecting changes with multiple sensors has received significant attention in the literature. In many practical applications such as critical infrastructure monitoring and modeling of disease spread, a useful change propagation model is one where change eventually happens at all sensors, but where not all sensors witness change at the same time-instant. While prior work considered the case of known change propagation dynamics, this paper studies a more general setting of unknown change propagation dynamics. A Bayesian formulation of the problem in both centralized and decentralized settings is studied with the goal of detecting the first time-instant at which any sensor witnesses a change. Using the dynamic programming framework, the optimal solution structure is derived and in the rare change regime, several more practical change detection algorithms are proposed. Under certain conditions, the first-order asymptotic optimality of a proposed algorithm called multichart test is shown as the false alarm probability vanishes. Numerical studies illustrate that the proposed detection techniques offer near-optimal performance. Further, in the decentralized setting, it is shown that if sensors use a novel event-triggered sampling scheme called level-crossing sampling with hysteresis instead of the conventional uniform-in-time sampling scheme, the detection performance can be significantly improved using the same amount of communication resources.
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    We report on the growth and characterization of ultrathin YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) films on MgO (110) substrates, which exhibit superconducting properties at thicknesses down to 3 nm. YBCO nanowires, with thicknesses down to 10 nm and widths down to 65 nm, have been also successfully fabricated. The nanowires protected by a Au capping layer show superconducting properties close to the as-grown films, and critical current densities, which are only limited by vortex dynamics. The 10 nm thick YBCO nanowires without the Au capping present hysteretic current voltage characteristics, characterized by a voltage switch which drives the nanowires directly from the superconducting to the normal state. Such bistability is associated in NbN nanowires to the presence of localized normal domains within the superconductor. The presence of the voltage switch, in ultrathin nanostructures characterized by high sheet resistance values, though preserving high quality superconducting properties, make our nanowires very attractive devices to engineer single photon detectors.
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    In this paper we consider a class of Einstein warped product semi-Riemannian manifolds $\widehat{M} = M^{n}\times_{f}N^{m}$ with $n\geq 3$ and $m\geq 2$. For $\widehat{M}$ with compact base and Ricci-flat fiber, we prove that $\widehat{M}$ is simply a Riemannian product space. Then, when the base $M$ is conformal to a pseudo-Euclidean space which is invariant under the action of a $(n-1)$-dimensional translation group, we classify all such spaces. Furthermore, we get new examples of complete Einstein warped products Riemannian manifolds.
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    The Cygnus region of the galaxy is one of the richest regions of gas and star formation and is the brightest region of diffuse GeV emission in the northern sky. VERITAS has conducted deep observations (approximately 300 hours) in the direction of Cygnus region, reaching an average sensitivity of a few percent of the Crab nebula flux. We present the results of these observations and an analysis of over seven years of Fermi-LAT data above 1 GeV. In addition to a search for new sources in the region, we present updated spectra and morphologies of the known TeV gamma-ray sources and a study of their relationship with the GeV emission from the region. These results are discussed in their multiwavelength context including the recently published HAWC observatory gamma-ray catalog. A comparison is also made to the H.E.S.S. galactic plane survey.
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    PSR J2032+4127 has recently been identified as being in a long period (45-50 years) binary in a highly eccentric orbit with the Be star MT91 213. Periastron is due to occur in November 2017 and this rare occurrence has prompted a multiwavelength monitoring campaign to determine if the system is a gamma-ray binary, and, if so, to study what would be only the second gamma-ray binary with a known compact object. In the same direction as TeV J2032+4130, gamma-ray emission from this binary system could be related to the extended very high energy gamma-ray emission from that region. As part of this monitoring, observations are being conducted by Swift, Fermi-LAT and VERITAS. We present the status of those observations, preliminary results and the plan for continued monitoring through periastron.
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    Fast radio bursts are bright, unresolved and short flashes of radio emission originating from outside the Milky Way. The origin of these mysterious outbursts is unknown, but their high luminosity and short duration has prompted much speculation. The discovery that FRB 121102 repeats has enabled multiwavelength follow up, which has identified the host galaxy. VERITAS has observed the location of FRB 121102, including coincident observations with Arecibo. We present the results of a search for steady very high energy gamma-ray emission and the methodology for searching for short timescale, transient optical and very high energy gamma-ray emission.
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    This paper develops a novel power harvesting system to harvest ambient RF energy to power a wireless sensor. Harvesting ambient RF energy is a very difficult task as the power levels are extremely weak. Simulation results show zero threshold MOSFETs are essential in the RF to DC conversion process. 0.5VDC at the output of the RF to DC conversion stage is the minimum voltage which must be achieved for the micro-power sensor circuitry to operate. The weakest power level the proposed system can successfully harvest is -37dBm. The measured available power from the FM band has been measured to fluctuate between -33 to -43dBm using a ribbon FM dipole antenna. Ambient RF energy would best be used in conjunction with other forms of harvested ambient energy to increase diversity and dependability. The potential economic and environmental benefits make such endeavors truly worthwhile.
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    In this paper we derive new static phantom traversable wormholes by assuming a shape function with a quadratic dependence on the radial coordinate r. We mainly focus our study on wormholes sustained by exotic matter with positive energy density (as seen by any static observer) and a variable equation of state $p_r/\rho<-1$, dubbed phantom matter. Among phantom wormhole spacetimes extending to infinity, we show that a quadratic shape function allows us to construct static spacetimes of finite size, composed by a phantom wormhole connected to an anisotropic spherically symmetric distribution of dark energy. The wormhole part of the full spacetime does not fulfill the dominant energy condition, while the dark energy part does.
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    Neural networks are capable of learning rich, nonlinear feature representations shown to be beneficial in many predictive tasks. In this work, we use these models to explore the use of geographical features in predicting colorectal cancer survival curves for patients in the state of Iowa, spanning the years 1989 to 2012. Specifically, we compare model performance using a newly defined metric -- area between the curves (ABC) -- to assess (a) whether survival curves can be reasonably predicted for colorectal cancer patients in the state of Iowa, (b) whether geographical features improve predictive performance, and (c) whether a simple binary representation or richer, spectral clustering-based representation perform better. Our findings suggest that survival curves can be reasonably estimated on average, with predictive performance deviating at the five-year survival mark. We also find that geographical features improve predictive performance, and that the best performance is obtained using richer, spectral analysis-elicited features.
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    Until recently, the only known method of finding the roots of polynomials over prime power rings, other than fields, was brute force. One reason for this is the lack of a division algorithm, obstructing the use of greatest common divisors. Fix a prime $p \in \mathbb{Z}$ and $f \in ( \mathbb{Z}/p^n \mathbb{Z} ) [x]$ any nonzero polynomial of degree $d$ whose coefficients are not all divisible by $p$. For the case $n=2$, we prove a new efficient algorithm to count the roots of $f$ in $\mathbb{Z}/p^2\mathbb{Z}$ within time polynomial in $(d+\operatorname{size}(f)+\log{p})$, and record a concise formula for the number of roots, formulated by Cheng, Gao, Rojas, and Wan.
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    Given a graph $G$, the $G$-parking function ideal $M_G$ is an artinian monomial ideal in the polynomial ring $S$ with the property that a linear basis for $S/M_G$ is provided by the set of $G$-parking functions. It follows that the dimension of $S/M_G$ is given by the number of spanning trees of $G$, which by the Matrix Tree Theorem is equal to the determinant of the reduced Laplacian of $G$. The ideals $M_G$ and related algebras were introduced by Postnikov and Shapiro where they studied their Hilbert functions and homological properties. In previous work it was shown that a minimal resolution of $M_G$ can be constructed from the graphical hyperplane arrangement associated to $G$, providing a combinatorial interpretation for the Betti numbers. Motivated by constructions in the theory of chip-firing on graphs, we study certain `skeleton' ideals $M_G^{(k)} \subset M_G$ generated by subsets of vertices of $G$ of size at most $k+1$. We study monomial bases of $M_G^{(k)}$ and provide formulas and combinatorial interpretations for the dimensions of $S/M_G^{(1)}$ and $S/M_G^{(n-2)}$ for the case that $G = K_{n+1}$ is the complete graph. These monomial bases have connections to various combinatorial objects including Cayley trees and determinants of the signless Laplacians, and in some cases lead to new enumerative formulas. We furthermore study resolutions of $M_G^{(1)}$ and show that for certain $G$ a minimal resolution is supported on decompositions of Euclidean space coming from the theory of tropical hyperplane arrangements. This leads to combinatorial interpretations of the Betti numbers of these ideals.
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    Szpilrajn's Lemma entails that each partial order extends to a linear order. Dushnik and Miller use Szpilrajn's Lemma to show that each partial order has a relizer. Since then, many authors utilize Szpilrajn's Theorem and the Well-ordering principle to prove more general existence type theorems on extending binary relations. Nevertheless, we are often interested not only in the existence of extensions of a binary relation $R$ satisfying certain axioms of orderability, but in something more: (A) The conditions of the sets of alternatives and the properties which $R$ satisfies to be inherited when one passes to any member of a subfamily of the family of extensions of $R$ and: (B) The size of a family of ordering extensions of $R$, whose intersection is $R$, to be the smallest one. The key to addressing these kinds of problems is the szpilrajn inherited method. In this paper, we define the notion of $\Lambda(m)$-consistency, where $m$ can reach the first infinite ordinal $\omega$, and we give two general inherited type theorems on extending binary relations, a Szpilrajn type and a Dushnik-Miller type theorem, which generalize all the well known existence and inherited type extension theorems in the literature. \keywordsConsistent binary relations, Extension theorems, Intersection of binary relations.
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    Given a map $f\colon X \to Y$, we extend a Gottlieb's result to the generalized Gottlieb group $G^f(Y,f(x_0))$ and show that the canonical isomorphism $\pi_1(Y,f(x_0))\xrightarrow{\approx}\mathcal{D}(Y)$ restricts to an isomorphism $G^f(Y,f(x_0))\xrightarrow{\approx}\mathcal{D}^{\tilde{f}_0}(Y)$, where $\mathcal{D}^{\tilde{f}_0}(Y)$ is some subset of the group $\mathcal{D}(Y)$ of deck transformations of $Y$ for a fixed lifting $\tilde{f}_0$ of $f$ with respect to universal coverings of $X$ and $Y$, respectively.
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    We extend the Oprea's result $G_1(\mathbb{S}^{2n+1}/H)=\mathcal{Z}H$ to the 1st generalized Gottlieb group $G_1^f(\mathbb{S}^{2n+1}/H)$ for a map $f\colon A\to \mathbb{S}^{2n+1}/H$. Then, we compute or estimate the groups $G_m^f(\mathbb{S}^{2n+1}/H)$ and $P_m^f(\mathbb{S}^{2n+1}/H)$ for some $m>1$ and finite groups $H$.

Recent comments

Māris Ozols Aug 03 2017 09:34 UTC

If I'm not mistaken, what you describe here is equivalent to the [QR decomposition][1]. The matrices $R_{ij}$ that act non-trivially only in a two-dimensional subspace are known as [Givens rotations][2]. The fact that any $n \times n$ unitary can be decomposed as a sequence of Givens rotations is ex

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gae Jul 26 2017 21:19 UTC

For those interested in the literature on teleportation simulation of quantum channels, a detailed and *comprehensive* review is provided in Supplementary Note 8 of https://images.nature.com/original/nature-assets/ncomms/2017/170426/ncomms15043/extref/ncomms15043-s1.pdf
The note describes well the t

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Maciej Malinowski Jul 26 2017 15:56 UTC

In what sense is the ground state for large detuning ordered and antiferromagnetic? I understand that there is symmetry breaking, but other than that, what is the fundamental difference between ground states for large negative and large positive detunings? It seems to be they both exhibit some order

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Stefano Pirandola Jul 26 2017 15:28 UTC

The performance of the memory assisted MDI-QKD with "quasi-EPR" sources is remarkable. It improves the key rate by 5 orders of magnitude over the PLOB bound at about 600 km (take a look at Figure 4).

Māris Ozols Jul 26 2017 11:07 UTC

Conway's list still has four other $1000 problems left:

https://oeis.org/A248380/a248380.pdf

SHUAI ZHANG Jul 26 2017 00:20 UTC

I am still working on improving this survey. If you have any suggestions, questions or find any mistakes, please do not hesitate to contact me: shuai.zhang@student.unsw.edu.au.

Alvaro M. Alhambra Jul 24 2017 16:10 UTC

This paper has just been updated and we thought it would be a good
idea to advertise it here. It was originally submitted a year ago, and
it has now been essentially rewritten, with two new authors added.

We have fixed some of the original results and now we:
-Show how some fundamental theorem

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Steve Flammia Jul 21 2017 13:43 UTC

Actually, there is even earlier work that shows this result. In [arXiv:1109.6887][1], Magesan, Gambetta, and Emerson showed that for any Pauli channel the diamond distance to the identity is equal to the trace distance between the associated Choi states. They prefer to phrase their results in terms

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Stefano Pirandola Jul 21 2017 09:43 UTC

This is very interesting. In my reading list!