Top arXiv papers

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    To realize long-distance quantum communication and quantum network, it is required to have multiplexed quantum memory with many memory cells. Each memory cell needs to be individually addressable and independently accessible. Here we report an experiment that realizes a multiplexed DLCZ-type quantum memory with 225 individually accessible memory cells in a macroscopic atomic ensemble. As a key element for quantum repeaters, we demonstrate that entanglement with flying optical qubits can be stored into any neighboring memory cells and read out after a programmable time with high fidelity. Experimental realization of a multiplexed quantum memory with many individually accessible memory cells and programmable control of its addressing and readout makes an important step for its application in quantum information technology.
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    Radio interferometers designed to measure the cosmological 21 cm power spectrum require high sensitivity. Several modern low-frequency interferometers feature drift-scan antennas placed on a regular grid to maximize the number of instantaneously coherent (redundant) measurements. However, even for such maximum-redundancy arrays, significant sensitivity comes through partial coherence between baselines. Current visibility-based power spectrum pipelines, though shown to ease control of systematics, lack the ability to make use of this partial redundancy. We introduce a method to leverage partial redundancy in such power spectrum pipelines for drift-scan arrays. Our method cross-multiplies baseline pairs at a time lag and quantifies the sensitivity contributions of each pair of baselines. Using the configurations and beams of the 128-element Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER-128) and staged deployments of the Hydrogen Epoch of Reionization Array (HERA), we illustrate how our method applies to different arrays and predict the sensitivity improvements associated with pairing partially coherent baselines. As the number of antennas increases, we find partial redundancy to be of increasing importance in unlocking the full sensitivity of upcoming arrays.
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    We extensively study the evolution and distinct signatures of cosmological models, in which dark energy interacts directly with dark matter. We first focus on the imprints of these coupled models on the cosmic microwave background temperature power spectrum, in which we discuss the multipole peak separation together with the integrated Sachs-Wolfe effect. We also address the growth of matter perturbations, and disentangle the interacting dark energy models using the expansion history together with the growth history. We find that a disformal coupling between dark matter and dark energy induces intermediate-scales and time-dependent damped oscillatory features in the matter growth rate function, a unique characteristic of this coupling. Apart from the disformal coupling, we also consider conformally coupled models, together with models which simultaneously make use of both couplings.
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    Recently LHCb discovered the first doubly-charmed baryon $\Xi_{cc}^{++} = ccu$ at $3621.40 \pm 0.78$ MeV, very close to our theoretical prediction. We use the same methods to predict a doubly-bottom tetraquark $Tq(bb\bar u\bar d)$ with $J^P{=}1^+$ at $10,389\pm 12$ MeV, 215 MeV below the $BB^*$ threshold. $Tq(bb\bar u\bar d)$ is therefore stable under strong and EM interactions and can only decay weakly, the first exotic hadron with such a property. On the other hand, the mass of $Tq(cc\bar u\bar d)$ with $J^P{=}1^+$ is predicted to be $3882\pm12$ MeV, 7 MeV above the $D^0 D^{*+}$ threshold. $Tq(bc\bar u\bar d)$ with $J^P{=}0^+$ is predicted at $7134\pm13$ MeV, 11 MeV below the $\bar B^0 D^0$ threshold. Our precision is not sufficient to determine whether $cc\bar u\bar d$ and $bb\bar u\bar d$ are actually above or below the threshold. They could manifest themselves as narrow resonances just at threshold.
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    For $A$ a gentle algebra, and $X$ and $Y$ string modules, we construct a combinatorial basis for Hom($X,\tau Y$). We use this to describe support $\tau$-tilting modules for $A$. We give a combinatorial realization of maps in both directions realizing the bijection between support $\tau$-tilting modules and functorially finite torsion classes. We give an explicit basis of Ext$^1(Y,X)$ as short exact sequences.
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    We consider two sharp next order asymptotics problems, namely the asymptotics for the minimum energy for optimal point configurations and the asymptotics for the many-marginals Optimal Transport, in both cases with Riesz costs with inverse power-law long range interactions. The first problem describes the ground state of a Coulomb or Riesz gas, while the second appears as a semiclassical limit of the Density Functional Theory energy modelling a quantum version of the same system. Recently the second-order term in these expansions was precisely described, and corresponds respectively to a Jellium and to a Uniform Electron Gas model. The present work shows that for inverse-power-law interactions with power $s\in]d-2,d[$ in $d$ dimensions, the two problems have the same minimum. We also show that on the whole range $s\in]0,d[$ the Uniform Electron Gas optimal constant is continuous in $s$.
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    On a Weinstein manifold, we define a constructible co/sheaf of categories on the skeleton. The construction works with arbitrary coefficients, and depends only on the homotopy class of a section of the Lagrangian Grassmannian of the stable symplectic normal bundle. The definition is as follows. Take any, possibly high codimension, exact embedding into a cosphere bundle. Thicken to a hypersurface, and consider the Kashiwara-Schapira stack along the thickened skeleton. Pull back along the inclusion of the original skeleton. Gromov's h-principle for contact embeddings guarantees existence and uniqueness up to isotopy of such an embedding. Invariance of microlocal sheaves along such isotopy is well known. We expect, but do not prove here, invariance of the global sections of this co/sheaf of categories under Liouville deformation.
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    We address the challenge of computing search paths in real-time for subsea applications where the goal is to locate an unknown number of targets on the seafloor. Our approach maximizes a formal definition of search effectiveness given finite search effort. We account for false positive measurements and variation in the performance of the search sensor due to geographic variation of the seafloor. We compare near-optimal search paths that can be computed in real-time with optimal search paths for which real-time computation is infeasible. We show how sonar data acquired for locating targets at a specific location can also be used to characterize the performance of the search sonar at that location. Our approach is illustrated with numerical experiments where search paths are planned using sonar data previously acquired from Boston Harbor.
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    A critical review on excited states of negative ions has been given recently by Buckman and Clark (1994), in a major update of the review by Schulz (1973). However, for completeness we include a summary of some known (mainly low lying) excited states. We include a brief discussion and indicate some problematic points with additional references. The observation of resonances in gas phase atomic collisions is discussed in this context. Finally we mention some very nice new results concerning the observation of these resonant states in particle surface interactions and briefly discuss the role that they can play. A table of electron affinities of atomic negative ions is provided at the end.
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    Discussion forums are an important source of information. They are often used to answer speci c questions a user might have and to discover more about a topic of interest. Discussions in these forums may evolve in intricate ways, making it di cult for users to follow the ow of ideas. We propose a novel approach for auto- matically identifying the underlying thread structure of a forum discussion. Our approach is based on a neural model that computes coherence scores of possible reconstructions and then selects the highest scoring, i.e., the most coherent one. Preliminary experi- ments demonstrate promising results outperforming a number of strong baseline methods.
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    This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each pair of nodes is able to communicate with each other directly and reliably. We consider the mobile Byzantine fault model proposed by Garay '94 -- in the model, an omniscient adversary can corrupt up to $f$ nodes in each round, and at the beginning of each round, faults may "move" in the system (i.e., different sets of nodes may become faulty in different rounds). Recent work by Bonomi et al. '16 proposed a simple iterative approximate consensus algorithm which requires at least $4f+1$ nodes. This paper proposes a novel technique of using "confession" (a mechanism to allow others to ignore past behavior) and a variant of reliable broadcast to improve the fault-tolerance level. In particular, we present an approximate consensus algorithm that requires only $\lceil 7f/2\rceil + 1$ nodes, an $\lfloor f/2 \rfloor$ improvement over the state-of-the-art algorithms. Moreover, we also show that the proposed algorithm is optimal within a family of round-based algorithms.
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    We present a quantum algorithm to compute the entanglement spectrum of arbitrary quantum states. The interesting universal part of the entanglement spectrum is typically contained in the largest eigenvalues of the density matrix which can be obtained from the lower Renyi entropies through the Newton-Girard method. Obtaining the $p$ largest eigenvalues ($\lambda_1>\lambda_2\ldots>\lambda_p$) requires a parallel circuit depth of $\mathcal{O}(p(\lambda_1/\lambda_p)^p)$ and $\mathcal{O}(p\log(N))$ qubits where up to $p$ copies of the quantum state defined on a Hilbert space of size $N$ are needed as the input. We validate this procedure for the entanglement spectrum of the topologically-ordered Laughlin wave function corresponding to the quantum Hall state at filling factor $\nu=1/3$. Our scaling analysis exposes the tradeoffs between time and number of qubits for obtaining the entanglement spectrum in the thermodynamic limit using finite-size digital quantum computers. We also illustrate the utility of the second Renyi entropy in predicting a topological phase transition and in extracting the localization length in a many-body localized system.
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    The computational complexity of solving nonlinear support vector machine (SVM) is prohibitive on large-scale data. In particular, this issue becomes very sensitive when the data represents additional difficulties such as highly imbalanced class sizes. Typically, nonlinear kernels produce significantly higher classification quality to linear kernels but introduce extra kernel and model parameters. Thus, the parameter fitting is required to increase the quality but it reduces the performance dramatically. We introduce a generalized fast multilevel framework for SVM and discuss several versions of its algorithmic components that lead to a good trade-off between quality and time. Our framework is implemented using PETSc which allows integration with scientific computing tasks. The experimental results demonstrate significant speed up compared to the state-of-the-art SVM libraries.
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    We study the static, zero-temperature Casimir effect between two cylindrical surfaces, obtaining approximate expressions which are reliable under the assumption that the distance between those surfaces is always much smaller than the local curvature radii of the surfaces. To obtain the approximation, we apply known results about the thermal Casimir effect for a planar geometry. To that effect, we relate the time coordinate in the latter to the angular variable in the cylindrical case, as well as the temperature to the radius of the cylinders.
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    In this talk, I will summarize the present state of a long-term effort to obtain information on the high-order asymptotic behaviour of the QED perturbation series through the effective action. Starting with the constant-field case, I will discuss the Euler-Heisenberg Lagrangian in various dimensions, and up to the three-loop level. This Lagrangian holds the information on the N-photon amplitudes in the low-energy limit, and combining it with spinor helicity methods explicit all-N results can be obtained at the one-loop and, for the "all + " amplitudes, also at the two-loop level. For the imaginary part of the Euler-Heisenberg Lagrangian, an all-loop formula has been conjectured independently by Affleck, Alvarez and Manton for Scalar QED, and by Lebedev and Ritus for Spinor QED. This formula can be related through a Borel dispersion relation to the leading large-N behaviour of the N-photon amplitudes. It is analytic in the fine structure constant, which is puzzling and suggests a diagrammatic investigation of the large-N limit in perturbation theory. Preliminary results of such a study for the 1+1 dimensional case throw doubt on the validity of the conjecture.
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    In this note we describe the role of the Schur multiplier in the structure of the $p$-torsion of discrete groups. More concretely, we show how the knowledge of $H_2G$ allows to approximate many groups by colimits of copies of finite $p$-groups. Our examples include interesting families of non-commutative infinite groups, including Burnside groups, certain solvable examples and the first Grigorchuk group. We also provide a counterexample for a conjecture of E. Farjoun.
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    We study nonlinear vibrational modes of oscillations for tetrahedral configurations of particles. In the case of tetraphosphorus, the interaction of atoms is given by bond stretching and van der Waals forces. Using equivariant gradient degree, we present a full topological classification of the spatio-temporal symmetries of the periodic solutions. This procedure gives all the symmetries of the nonlinear vibrations for general force fields.
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    Let $F$ be a finite field with the characteristic $p > 2$ and let $G$ be the unitary Grassmann algebra generated by an infinite dimensional vector space $V$ over $F$. In this paper, we determine a basis for $\mathbb{Z}_{2}$-graded polynomial identities for any non-trivial $\mathbb{Z}_{2}$-grading such that its underlying vector space is homogeneous.
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    The determination of the neutrino mass ordering is currently pursued by several experiments and proposals. A very challenging one is its evaluation from reactor experiments based on the tiny interference effect between the $\Delta m^2_{31}$ and $\Delta m^2_{32}$ oscillations. Current analyses require several years of data taking and an extreme energy resolution to achieve anyhow less than 5 $\sigma$. Referring to the JUNO experimental conditions we developed a completely new technique that will allow to definitively perform a robust 5 $\sigma$ measurement in less than six years of running. Evaluation and inclusion of systematic errors and backgrounds have been performed, the most relevant among them being the addition of the two remote reactor plants 250 km away. Baselines of each contributing reactor core and its spatial resolution have been taken into account. Possible results after two years of running and the foreseen initially-reduced available reactor power have been studied, too. These results confirm the very positive perspectives for JUNO to determine the mass ordering in a vacuum-oscillation dominated region. As a side result the new technique provides a $\Delta m^2_{32(13)}$ evaluation with an unprecedented accuracy at reactors.
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    In this paper we investigate the complexity of model selection and model testing in chemical reaction networks by formulating them as Euclidean distance problems. We determine closed form expressions for the Euclidean distance degree of the steady state varieties associated to several different families of toric chemical reaction networks with arbitrarily many reaction sites. We show how our results can be used as a metric for the computational cost of solving the model testing and model selection problems.
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    This paper presents a path planning method for partial field coverage. We therefore propose to use a specific path planning pattern. Guiding notion is that lighter machinery with smaller storage tanks can alleviate soil compaction, but does not permit to cover a given field in a single run, for example, during a spraying application. Instead, multiple returns to a mobile or stationary depot located outside of the field are required for storage tank refilling. We therefore suggest a suitable path planning method that accounts for the limited turning radii of agricultural vehicles, satisfies repressed area minimisation constraints, and aims at overall path length minimisation. The benefits of the proposed method are illustrated by means of a comparison to a method that is based on a S-shaped planning motif. It is illustrated how the proposed path planning pattern can also be employed efficiently for single-run field coverage.
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    Magnetic induction was first proposed as a planetary heating mechanism by Sonett and Colburn in 1968, in recent years this theory has lost favor as a plausible source of heating in the early solar system. However, new models of proto-planetary disk evolution suggest that magnetic fields play an important role in solar system formation. In particular, the magneto-hydrodynamic behavior of proto-planetary disks is believed to be responsible for the net outward flow of angular momentum in the solar system. It is important to re-evaluate the plausibility of magnetic induction based on the intense magnetic field environments described by the most recent models of proto-planetary disk evolution. In order to re-evaluate electromagnetic induction theory the electrical conductivity of meteorites must be determined. To develop a technique capable of making these measurements, a time-varying magnetic field was generated to inductively heat metallic control samples. The thermal response of each sample, which depends on electrical conductivity, was monitored until a thermal steady state was achieved. The relationship between conductivity and thermal response can be exploited to estimate the electrical conductivity of unknown samples. After applying the technique to various metals it was recognized that this method is not capable of making precise electrical conductivity measurements. However, this method can constrain the product of the electrical conductivity and the square of the magnetic permeability, or ${\sigma}{{\mu}^2}$, for meteoritic and metallic samples alike. The results also illustrate that along with electrical conductivity \sigma, the magnetic permeability \mu of a substance has an important effect on induction heating phenomena for paramagnetic (\mu/\mu0 > 1) and especially ferromagnetic materials (\mu/\mu0 >> 1).
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    HI intensity mapping is a new observational technique to survey the large-scale structure of matter using the 21 cm emission line of atomic hydrogen (HI). It can be used to constrain cosmological parameters, including the dark energy equation-of-state $w$. As our experimental setups we use BINGO (BAO from Integrated Neutral Gas Observations) and the SKA (Square Kilometre Array) phase-1 dish array operating in auto-correlation mode. We find that the use of the power spectrum is potentially more powerful than the BAO wiggles alone, even in the presence of extra nuisance parameters such as the HI bias and HI amplitude. For the optimal case of BINGO with no foregrounds, we find that the combination of the HI angular power spectrum with Planck results allows $w$ to be measured with a precision of $4\%$, while the combination of the BAO acoustic scale with Planck gives a precision of $7\%$. We consider a number of potentially complicating effects, including foregrounds and redshift dependent bias, which increase the uncertainty on $w$ but not dramatically; in all cases we find the final uncertainty to be $\Delta w < 8\%$ for BINGO. For the combination of SKA-MID in auto-correlation mode with Planck, we find that $w$ can be measured with a precision of $4\%$ for band 1 $(0.35 < z < 3)$ and $2\%$ for band 2 $(0 < z < 0.49)$. Extending the model to include the sum of neutrino masses yields a $95\%$ upper limit of $\sum m_\nu < 0.24$ eV for BINGO and $\sum m_\nu < 0.08$ eV for SKA phase 1, competitive with the current best constraints in the case of BINGO and significantly better than them in the case of SKA.
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    Carrier recombination dynamics in strip silicon nano-waveguides is analyzed through time-resolved pump-and-probe experiments, revealing a complex recombination dynamics at densities ranging from ${10^{14}}$ to ${10^{17}}\,$cm$^{{-3}}$. Our results show that the carrier lifetime varies as recombination evolves, with faster decay rates at the initial stages (with lifetime of ${\sim 800}\,$ps), and much slower lifetimes at later stages (up to ${\sim 300}\,$ns). We also observe experimentally the effect of trapping, manifesting as a decay curve highly dependent on the initial carrier density. We further demonstrate that operating at high carrier density can lead to faster recombination rates. Finally, we present a theoretical discussion based on trap-assisted recombination statistics applied to nano-waveguides. Our results can impact the dynamics of several nonlinear nanophotonic devices in which free-carriers play a critical role, and open further opportunities to enhance the performance of all-optical silicon-based devices based on carrier recombination engineering.
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    We consider the 3D equation $u_{yy} = u_{tx} + u_yu_{xx} - u_xu_{xy}$ and its 2D reductions: (1) $u_{yy} = (u_y+y)u_{xx}-u_xu_{xy}-2$ (which is equivalent to the Gibbons-Tsarev equation) and (2) $u_{yy} = (u_y+2x)u_{xx} + (y-u_x)u_{xy} -u_x$. Using reduction of the known Lax pair for the 3D equation, we describe nonlocal symmetries of~(1) and~(2) and show that the Lie algebras of these symmetries are isomorphic to the Witt algebra.
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    We study solutions of the focusing energy-critical nonlinear heat equation $u_t = \Delta u - |u|^2u$ in $\mathbb{R}^4.$ We show that solutions emanating from initial data with energy and $\dot{H}^1-$norm below those of the stationary solution $W$ are global and decay to zero, via the "concentration-compactness plus rigidity" strategy of Kenig-Merle. First, such global solutions are shown to dissipate to zero, using a refinement of the small data theory and the $L^2$-dissipation relation. Finite-time blow-up is then ruled out using the backwards-uniqueness of Escauriaza, Seregin and Sverak in an argument similar to that of Kenig and Koch for the Navier-Stokes equations.
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    A mathematical model of the metabolic process of atherosclerosis is constructed.
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    Sensing in complex systems requires large-scale information exchange and on-the-go communications over heterogeneous networks and integrated processing platforms. Many networked cyber-physical systems exhibit hierarchical infrastructures of information flows, which naturally leads to a multi-level tree-like information structure in which each level corresponds to a particular scale of representation. This work focuses on the multiscale fusion of data collected at multiple levels of the system. We propose a multiscale state-space model to represent multi-resolution data over the hierarchical information system and formulate a multi-stage dynamic zero-sum game to design a multi-scale $H_{\infty}$ robust filter. We present numerical experiments for one and two-dimensional signals and provide a comparative analysis of the minimax filter with the standard Kalman filter to show the improvement in signal-to-noise ratio (SNR).
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    We propose a new type of a Heisenberg-limited quantum interferometer, whose input is indistinguishably photon-subtracted twin beams. Such an interferometer can yield Heisenberg-limited performance while at the same time giving a direct fringe reading, unlike for the twin-beam input of the Holland-Burnett interferometer. We propose a feasible experimental realization, using a nondegenerate optical parametric oscillator above threshold.
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    We find large classes of injective and projective $p$-multinormed spaces. In fact, these classes are universal, in the sense that every $p$-multinormed space embeds into (is a quotient of) an injective (resp. projective) $p$-multinormed space. As a consequence, we show that any $p$-multinormed space has a canonical representation as a subspace of a quotient of a Banach lattice.
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    Using computational and theoretical approaches, we investigate the snap-through transition of buckled graphene membranes. Our main interest is related to the possibility of using the buckled membrane as a plate of capacitor with memory (memcapacitor). For this purpose, we performed molecular-dynamics (MD) simulations and elasticity theory calculations of the up-to-down and down-to-up snap-through transitions for the membranes of several sizes. We have obtained expressions for the threshold switching forces needed for both up-to-down and down-to-up transitions. Moreover, the up-to-down transition switching force was calculated using the density functional theory (DFT). Our DFT results are in general agreement with MD and analytical theory findings. Our systematic approach can be used for the description of other structures experiencing the snap-through transition, including nanomechanical and biological ones.
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    Consider a vector bundle over a Kähler manifold which admits a Hermitian Yang-Mills connection. We show that the pullback bundle on the blowup of the Kähler manifold at a collection of points also admits a Hermitian Yang-Mills connection, for Kähler classes on the blowup which make the exceptional divisors small. Our proof uses gluing techniques, and is hence asymptotically explict. This recovers, through the Hitchin-Kobayashi correspondence, algebro-geometric results due to Buchdahl and Sibley.
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    Is it possible to generally construct a dynamical system to simulate a black system without recovering the equations of motion of the latter? Here we show that this goal can be approached by a learning machine. Trained by a set of input-output responses or a segment of time series of a black system, a learning machine can be served as a copy system to mimic the dynamics of various black systems. It can not only behave as the black system at the parameter set that the training data are made, but also recur the evolution history of the black system. As a result, the learning machine provides an effective way for prediction, and enables one to probe the global dynamics of a black system. These findings have significance for practical systems whose equations of motion cannot be approached accurately. Examples of copying the dynamics of an artificial neural network, the Lorenz system, and a variable star are given. Our idea paves a possible way towards copy a living brain.
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    We use orthogonally polarized two-colour (OTC) laser pulses to separate quantum paths in multiphoton ionization of Ar atoms. Our OTC pulses consist of 400~nm and 800~nm light at a relative intensity ratio of 10:1. We find a hitherto unobserved interference in the photoelectron momentum distribution, which exhibits a strong dependence on the relative phase of the OTC pulse. Analysis of model calculations reveal that the interference is caused by quantum pathways from non-adjacent quarter cycles.
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    To assist the design of novel, highly efficient molecular junctions, a deep understanding of the precise charge transport mechanisms through these devices is of prime importance. In the present contribution, we describe a procedure to investigate spatially-resolved electron transport through a nanojunction from first principles, at the example of a nitro-substituted oligo-(phenylene ethynylene) covalently bound to graphene nanoribbon leads. Recently, we demonstrated that the conductivity of this single-molecule-graphene-nanoribbon junction can be switched quantitatively and reversibly upon application of a static electric field in a top gate position, in the spirit of a traditional field effect transistor [J. Phys. Chem. C, 2016, 120, 28808-28819]. The propensity of the central oligomer unit to align with the external field was found to induce a damped rotational motion and to cause an interruption of the conjugated $\pi$-system, thereby drastically reducing the conductance through the nanojunction. In the current work, we use the driven Liouville-von-Neumann (DLvN) approach for time-dependent electronic transport calculations to simulate the electronic current dynamics under time-dependent potential biases for the two logical states of the nanojunction. Our quantum dynamical simulations rely on a novel localization procedure using an orthonormal set of molecular orbitals obtained from a standard density functional theory calculation to generate a localized representation for the different parts of the molecular junction. The transparent DLvN formalism allows us to directly access the density matrix and to reconstruct the time-dependent electronic current density, unraveling unique mechanistic details of the electron transport.
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    Gravitational microlensing is the only method capable of exploring the entire population of free-floating planets down to Mars-mass objects, because the microlensing signal does not depend on the brightness of the lensing object. A characteristic timescale of microlensing events depends on the mass of the lens: the less massive the lens, the shorter the microlensing event. A previous analysis of 474 microlensing events found an excess of very short events (1-2 days) - more than known stellar populations would suggest - indicating the existence of a large population of unbound or wide-orbit Jupiter-mass planets (reported to be almost twice as common as main-sequence stars). These results, however, do not match predictions of planet formation theories and are in conflict with surveys of young clusters. Here we report the analysis of a six times larger sample of microlensing events discovered during the years 2010-2015. Although our survey has very high sensitivity (detection efficiency) to short-timescale (1--2 days) microlensing events, we found no excess of events with timescales in this range, with a 95% upper limit on the frequency of Jupiter-mass free-floating or wide-orbit planets of 0.25 planet per main-sequence star. We detected a few possible ultrashort-timescale events (with timescales of less than 0.5 day), which may indicate the existence of Earth- and super-Earth-mass free-floating planets, as predicted by planet-formation theories. [abridged]
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    Chen, Faudree, Gould, Jacobson, and Lesniak determined the minimum degree threshold for which a balanced $k$-partite graph has a Hamiltonian cycle. When $k\geq 3$, however, a Hamiltonian $k$-partite graph is not necessarily balanced. We give an asymptotic minimum degree threshold for Hamiltonian cycles in a broader class of not-necessarily-balanced $k$-partite graphs. In particular our result asymptotically implies the result of Chen et al.\ for balanced $k$-partite graphs. We prove that any graph meeting the degree condition is either a robust-expander or else contains a Hamiltonian cycle directly.
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    We consider dynamical percolation on the $d$-dimensional discrete torus of side length $n$, $\mathbb{Z}_n^d$, where each edge refreshes its status at rate $\mu=\mu_n\le 1/2$ to be open with probability $p$. We study random walk on the torus, where the walker moves at rate $1/(2d)$ along each open edge. In earlier work of two of the authors with A. Stauffer, it was shown that in the subcritical case $p<p_c(\mathbb{Z}^d)$, the (annealed) mixing time of the walk is $\Theta(n^2/\mu)$, and it was conjectured that in the supercritical case $p>p_c(\mathbb{Z}^d)$, the mixing time is $\Theta(n^2+1/\mu)$; here the implied constants depend only on $d$ and $p$. We prove a quenched (and hence annealed) version of this conjecture up to a poly-logarithmic factor under the assumption $\theta(p)>1/2$. Our proof is based on percolation results (e.g., the Grimmett-Marstrand Theorem) and an analysis of the volume-biased evolving set process; the key point is that typically, the evolving set has a substantial intersection with the giant percolation cluster at many times. This allows us to use precise isoperimetric properties of the cluster (due to G. Pete) to infer rapid growth of the evolving set, which in turn yields the upper bound on the mixing time.
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    It has been shown that increasing model depth improves the quality of neural machine translation. However, different architectural variants to increase model depth have been proposed, and so far, there has been no thorough comparative study. In this work, we describe and evaluate several existing approaches to introduce depth in neural machine translation. Additionally, we explore novel architectural variants, including deep transition RNNs, and we vary how attention is used in the deep decoder. We introduce a novel "BiDeep" RNN architecture that combines deep transition RNNs and stacked RNNs. Our evaluation is carried out on the English to German WMT news translation dataset, using a single-GPU machine for both training and inference. We find that several of our proposed architectures improve upon existing approaches in terms of speed and translation quality. We obtain best improvements with a BiDeep RNN of combined depth 8, obtaining an average improvement of 1.5 BLEU over a strong shallow baseline. We release our code for ease of adoption.
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    The MICROSCOPE space mission aims to test the Equivalence Principle with an accuracy of $10^{-15}$. The drag-free micro-satellite will orbit around the Earth and embark a differential electrostatic accelerometer including two cylindrical test masses submitted to the same gravitational field and made of different materials. The experience consists in testing the equality of the electrostatic acceleration applied to the masses to maintain them relatively motionless. The accuracy of the measurements exploited for the test of the Equivalence Principle is limited by our a priori knowledge of several physical parameters of the instrument. These parameters are partially estimated on-ground, but with an insufficient accuracy, and an in-orbit calibration is therefore required to correct the measurements. The calibration procedures have been defined and their analytical performances have been evaluated. In addition, a simulator software including the dynamics model of the instrument, the satellite drag-free system and the perturbing environment has been developed to numerically validate the analytical results. After an overall presentation of the MICROSCOPE mission, this paper will describe the calibration procedures and focus on the simulator. Such an in-flight calibration is mandatory for similar space missions taking advantage of a drag-free system.
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    In this paper we deal with a non-linear Diophantine equation which arises from the determinant computation of an integer matrix. We show how to find a solution, when it exists. We define an equivalence relation and show how the set of all the solutions can be partitioned in a finite set of equivalence classes and find a set of solutions, one for each of these classes. We find a formula to express all the solutions and a formula to compute the cardinality of the set of fundamental solutions. An algorithm to compute the solutions is proposed and clarified with some examples.
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    There have been some works that learn a lexicon together with the corpus to improve the word embeddings. However, they either model the lexicon separately but update the neural networks for both the corpus and the lexicon by the same likelihood, or minimize the distance between all of the synonym pairs in the lexicon. Such methods do not consider the relatedness and difference of the corpus and the lexicon, and may not be the best optimized. In this paper, we propose a novel method that considers the relatedness and difference of the corpus and the lexicon. It trains word embeddings by learning the corpus to predicate a word and its corresponding synonym under the context at the same time. For polysemous words, we use a word sense disambiguation filter to eliminate the synonyms that have different meanings for the context. To evaluate the proposed method, we compare the performance of the word embeddings trained by our proposed model, the control groups without the filter or the lexicon, and the prior works in the word similarity tasks and text classification task. The experimental results show that the proposed model provides better embeddings for polysemous words and improves the performance for text classification.
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    The Paper actually concerns a toy model, not physical Casimir cavities made of conducting plates, but the results are taken implicitly to apply in general. We question on general physical grounds one basic assumption and the results of a renormalization procedure. Then, for physical systems, i) considering condensed matter theory/experiments, we find strong evidence against the conclusive claims concerning a putative and dominating surface energy present individually on the plates, and ii) we propose two experiments with physical Casimir cavities to show in detail that the results of the renormalization in this case look somewhat paradoxical. In any case the proposed experiments appear to be feasible and thus it could be tested if the putative self-energies of the plates are indeed there in a physical Casimir cavity, or if the toy model of the Paper has by contrast no connection with physical reality. However at the moment the authors are not legitimate to issue as conclusive claims statements like- refute the claim sometimes attributed to Feynman that virtual photons do not gravitate -
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Recent comments

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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gae Jul 21 2017 17:58 UTC

Dear Marco, indeed the description in those two papers is very general because they treat both DV and CV channels. However, things become "easier" and more specific if you restrict things to DVs. In this regard, let me point you at this paper https://arxiv.org/pdf/1706.05384.pdf , in particular to

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Marco Piani Jul 21 2017 16:33 UTC

Is it really the case for the general definition of teleportation-covariant channel given in https://arxiv.org/abs/1609.02160 or https://arxiv.org/abs/1510.08863 ? I understand that there special classes of teleportation-covariant channels are considered where what you say holds (that is, for pairs

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gae Jul 21 2017 15:51 UTC

If two channels are teleportation-covariant and between Hilbert spaces with the same dimension, then the correction unitaries are exactly the same. For instance, for any pair of Pauli channels (not just a Pauli and the identity), the corrections are Pauli operators.

Marco Piani Jul 21 2017 15:36 UTC

Is it more precisely that the result holds for any pair of *jointly* teleportation-covariant channels? The definition of teleportation-covariant channel (according to what I see in https://arxiv.org/abs/1609.02160 ) is such that the covariance can be achieved with a unitary at the output that depend

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gae Jul 21 2017 14:01 UTC

Thx Steve for pointing out this paper too, which is relevant as well. Let me just remark that the PRL mentioned in my previous comment [PRL 118, 100502 (2017), https://arxiv.org/abs/1609.02160 ] finds the result for any pair of teleportation-covariant channels (not just between a Pauli channel and t

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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!

gae Jul 21 2017 09:00 UTC

In relation with the discussion at page 21 of this paper. Consider depolarizing channels (including the trivial case of the identity channel) which are teleportation covariant as in the definition Eq. (9) of https://arxiv.org/abs/1510.08863 [Nature Communications 8, 15043 (2017)]. The diamond norm b

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Chris Ferrie Jul 18 2017 02:32 UTC

Since arXiv now supports supplementary material, we did not host the source externally. The easiest way to view the code is using https://nbviewer.jupyter.org: https://nbviewer.jupyter.org/urls/arxiv.org/src/1707.05088v1/anc/specdens-est.ipynb.

By the way, if you are having difficulty navigating

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