Top arXiv papers

sign in to customize
  • PDF
    Span programs are a model of computation that have been used to design quantum algorithms, mainly in the query model. For any decision problem, there exists a span program that leads to an algorithm with optimal quantum query complexity, but finding such an algorithm is generally challenging. We consider new ways of designing quantum algorithms using span programs. We show how any span program that decides a problem $f$ can also be used to decide "property testing" versions of $f$, or more generally, approximate the span program witness size, a property of the input related to $f$. For example, using our techniques, the span program for OR, which can be used to design an optimal algorithm for the OR function, can also be used to design optimal algorithms for: threshold functions, in which we want to decide if the Hamming weight of a string is above a threshold or far below, given the promise that one of these is true; and approximate counting, in which we want to estimate the Hamming weight of the input. We achieve these results by relaxing the requirement that 1-inputs hit some target exactly in the span program, which could make design of span programs easier. We also give an exposition of span program structure, which increases the understanding of this important model. One implication is alternative algorithms for estimating the witness size when the phase gap of a certain unitary can be lower bounded. We show how to lower bound this phase gap in some cases. As applications, we give the first upper bounds in the adjacency query model on the quantum time complexity of estimating the effective resistance between $s$ and $t$, $R_{s,t}(G)$, of $\tilde O(\frac{1}{\epsilon^{3/2}}n\sqrt{R_{s,t}(G)})$, and, when $\mu$ is a lower bound on $\lambda_2(G)$, by our phase gap lower bound, we can obtain $\tilde O(\frac{1}{\epsilon}n\sqrt{R_{s,t}(G)/\mu})$, both using $O(\log n)$ space.
  • PDF
    In this article we propose a stroboscopic approach to complex vector reconstruction in the context of quantum tomography. There are two underlying assumptions behind our reasoning. The first one claims that the evolution of a d-level pure quantum system is given by the Schrödinger equation with a time-independent Hamiltonian and the other states that the knowledge about the quantum state is provided from projective measurements, also called intensity measurements. The problem of quantum state reconstruction is connected with the notion known as phase retrieval - recovering a complex vector from modulus of inner product with frame vectors. We believe that the stroboscopic approach can significantly improve the effectiveness of the vector reconstruction as it aims to decrease the number of distinct projectors by taking advantage of the knowledge about the evolution. General conditions and observations are applied to a specific unitary model.
  • Jul 03 2015 quant-ph arXiv:1507.00423v1
    PDF
    We show that the particle number distribution of diamond modes, modes that are localised in a finite space-time region, are thermal for the Minkowski vacuum state of a massless scalar field, an analogue to the Unruh effect. The temperature of the diamond is inversely proportional to its size. An inertial observer can detect this thermal radiation by coupling to the diamond modes using an appropriate energy scaled detector. We further investigate the correlations between various diamonds and find that entanglement between adjacent diamonds dominates.
  • PDF
    Based on homodyne detection, we discuss how the presence of an event horizon affects quantum communication between an inertial partner, Alice, and a uniformly accelerated partner, Rob. We show that there exists a low frequency cutoff for Rob's homodyne detector that maximizes the signal to noise ratio and it approximately corresponds to the Unruh frequency. In addition, the low frequency cutoff which minimizes the conditional variance between Alice's input state and Rob's output state is also approximately equal to the Unruh frequency. Thus the Unruh frequency provides a natural low frequency cutoff in order to optimize quantum communication of both classical and quantum information between Alice and Rob.
  • PDF
    Given a directed acyclic graph $G,$ and a set of values $y$ on the vertices, the Isotonic Regression of $y$ is a vector $x$ that respects the partial order described by $G,$ and minimizes $||x-y||,$ for a specified norm. This paper gives improved algorithms for computing the Isotonic Regression for all weighted $\ell_{p}$-norms with rigorous performance guarantees. Our algorithms are quite practical, and their variants can be implemented to run fast in practice.
  • PDF
    We inverse engineer realizable time-dependent semiclassical pulses to invert or manipulate a two- level system faster than adiabatically when the rotating-wave approximation cannot be applied. Different inversion routes, based on a counterdiabatic approach or invariants, lead quite generally to singular fields. Making use of the relation between the invariants of motion and the Hamiltonian, and canceling the troublesome singularities, an inversion scheme is put forward for the regime in which the pulse spans few oscillations. For many oscillations an alternative numerical minimization method is proposed and demonstrated.
  • PDF
    We study a general family of quantum protocols for position verification and present a new class of attacks based on the Clifford hierarchy. These attacks outperform current strategies based on port-based teleportation for a large class of practical protocols. We then introduce the Interleaved Product protocol, a new scheme for position verification involving only the preparation and measurement of single-qubit states for which the best available attacks have a complexity exponential in the number of classical bits transmitted.
  • PDF
    We consider two entangled accelerating qubits coupled with real scalar fields, each described by the Unruh-Wald model. It is demonstrated that because of the Unruh effect, the bipartite entanglement of the two qubits suddenly dies when the acceleration of one or more qubits are large enough. We also consider three entangled accelerating qubits in GHZ state and in W state, with equal acceleration-frequency ratio, and found that in either state, the tripartite entanglement suddenly dies at a certain value of acceleration-frequency ratio. The equivalence between the Rindler metric and the Schwarzchild metric in the vicinity of the horizon of a black hole implies that for the two entangled qubits outside a black hole, the entanglement suddenly dies when one or both of the qubits are close enough to the horizon, while for the three entangled qubits in GHZ or W state, the tripartite entanglement suddenly dies when these qubits are close enough to the horizon.
  • PDF
    Anonymous Veto (AV) and Dining cryptographers (DC) are two basic primitives for the cryptographic problems that can hide the identity of the sender(s) of classical information. They can be achieved by classical methods and the security is based on computational hardness or requires pairwise shared private keys. In this regard, we present a secure quantum protocol for both DC and AV problems by exploiting the GHZ correlation. We first solve a generalized version of the DC problem with the help of multiparty GHZ state. This allow us to provide a secure quantum protocol for the AV problem. Security of both the protocols rely on some novel and fundamental features of the GHZ correlation known as GHZ paradox.
  • PDF
    The continuous quantum phase transition between noninteracting, time-reversal symmetric topological and trivial insulators in three dimensions is described by a massless Dirac fermion. We address the stability of this quantum critical point against short range electronic interactions by using renormalization group analysis and mean field theory. For sufficiently weak interactions, we show that the nature of the direct transition remains unchanged. Beyond a critical strength of interactions we find that either (i) there is a direct first order transition between two time reversal symmetric insulators or (ii) the direct transition is eliminated by an intervening time reversal and inversion odd "axionic" insulator. We also demostrate the existence of an interaction driven first order quantum phase transition between topological and trivial gapped states in lower dimensions.
  • PDF
    We use Hubble Space Telescope Wide-Field Camera 3 (HST/WFC3) rest-frame optical imaging to select a pilot sample of star-forming galaxies in the redshift range z = 2.00-2.65 whose multi-component morphologies are consistent with expectations for major mergers. We follow up this sample of major merger candidates with Keck/NIRSPEC longslit spectroscopy obtained in excellent seeing conditions (FWHM ~ 0.5 arcsec) to obtain Halpha-based redshifts of each of the morphological components in order to distinguish spectroscopic pairs from false pairs created by projection along the line of sight. Of six pair candidates observed, companions (estimated mass ratios 5:1 and 7:1) are detected for two galaxies down to a 3sigma limiting emission-line flux of ~ 10^-17 erg/s/cm2. This detection rate is consistent with a ~ 50% false pair fraction at such angular separations (1-2 arcsec), and with recent claims that the star-formation rate (SFR) can differ by an order of magnitude between the components in such mergers. The two spectroscopic pairs identified have total SFR, SFR surface densities, and stellar masses consistent on average with the overall z ~ 2 star forming galaxy population.
  • PDF
    We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric models are usually built from completely random measures, a Poisson-process based construction in which the atom weights are independent. Completely random measures imply strong independence assumptions in the corresponding hierarchical model, and these assumptions are often misplaced in real-world settings. Correlated random measures address this limitation. They model correlation within the measure by using a Gaussian process in concert with the Poisson process. With correlated random measures, for example, we can develop a latent feature model for which we can infer both the properties of the latent features and their dependency pattern. We develop several other examples as well. We study a correlated random measure model of pairwise count data. We derive an efficient variational inference algorithm and show improved predictive performance on large data sets of documents, web clicks, and electronic health records.
  • PDF
    Liouville quantum gravity (LQG) and the Brownian map (TBM) are two distinct models of measure-endowed random surfaces. LQG is defined in terms of a real parameter $\gamma$, and it has long been believed that when $\gamma = \sqrt{8/3}$, the LQG sphere should be equivalent (in some sense) to TBM. However, the LQG sphere comes equipped with a conformal structure, and TBM comes equipped with a metric space structure, and endowing either one with the other's structure has been an open problem for some time. This paper is the first in a three-part series that unifies LQG and TBM by endowing each object with the other's structure and showing that the resulting laws agree. The present work uses a form of the quantum Loewner evolution (QLE) to construct a metric on a dense subset of a $\sqrt{8/3}$-LQG sphere and to establish certain facts about the law of this metric, which are in agreement with similar facts known for TBM. The subsequent papers will show that this metric extends uniquely and continuously to the entire $\sqrt{8/3}$-LQG surface and that the resulting measure-endowed metric space is TBM.
  • PDF
    We study the predictions for structure formation in an induced gravity dark energy model with a quartic potential. By developing a dedicated Einstein-Boltzmann code, we study self-consistently the dynamics of homogeneous cosmology and of linear perturbations without using any parametrization. By evolving linear perturbations with initial conditions in the radiation era, we accurately recover the quasi-static analytic approximation in the matter dominated era. We use Planck 2013 data and a compilation of baryonic acoustic oscillation (BAO) data to constrain the coupling $\gamma$ to the Ricci curvature and the other cosmological parameters. By connecting the gravitational constant in the Einstein equation to the one measured in a Cavendish-like experiment, we find $\gamma < 0.0012$ at 95% CL with Planck 2013 and BAO data. This is the tightest cosmological constraint on $\gamma$ and on the corresponding derived post-Newtonian parameters. Because of a degeneracy between $\gamma$ and the Hubble constant $H_0$, we show how larger values for $\gamma$ are allowed, but not preferred at a significant statistical level, when local measurements of $H_0$ are combined in the analysis with Planck 2013 data.
  • PDF
    Image scoring sustains cooperation in the repeated two-player prisoner's dilemma through indirect reciprocity, even though defection is the uniquely dominant selfish behaviour in the one-shot game. Many real-world dilemma situations, however, firstly, take place in groups and, secondly, lack the necessary transparency to inform subjects reliably of others' individual past actions. Instead, there is revelation of information regarding groups, which allows for `group scoring' but not for image scoring. Here, we study how sensitive the positive results related to image scoring are to information based on group scoring. We combine analytic results and computer simulations to specify the conditions for the emergence of cooperation. We show that under pure group scoring, that is, under the complete absence of image-scoring information, cooperation is unsustainable. Away from this extreme case, however, the necessary degree of image scoring relative to group scoring depends on the population size and is generally very small. We thus conclude that the positive results based on image scoring apply to a much broader range of informational settings that are relevant in the real world than previously assumed.
  • PDF
    Acanthamoebae are free-living protists and human pathogens, whose cellular functions and pathogenicity strongly depend on the transport of intracellular vesicles and granules through the cytosol. Using high-speed live cell imaging in combination with single-particle tracking analysis, we show here that the motion of endogenous intracellular particles in the size range from a few hundred nanometers to several micrometers in Acanthamoeba castellanii is strongly superdiffusive and influenced by cell locomotion, cytoskeletal elements, and myosin II. We demonstrate that cell locomotion significantly contributes to intracellular particle motion, but is clearly not the only origin of superdiffusivity. By analyzing the contribution of microtubules, actin, and myosin II motors we show that myosin II is a major driving force of intracellular motion in A. castellanii. The cytoplasm of A. castellanii is supercrowded with intracellular vesicles and granules, such that significant intracellular motion can only be achieved by actively driven motion, while purely thermally driven diffusion is negligible.
  • PDF
    We give a sufficient condition for the simplex of invariant measures for a hereditary system to be Poulsen. In particular, we show that this simplex is Poulsen in case of positive entropy $\mathscr{B}$-free systems. We also give an example of a positive entropy hereditary system whose simplex of invariant measures is not Poulsen.
  • PDF
    Using the cosmological smoothed particle hydrodynamical code GADGET-3 we make a realistic assessment of the technique of using constant cumulative number density as a tracer of galaxy evolution at high redshift. We find that over a redshift range of $3\leq z \leq7$ one can on average track the growth of the stellar mass of a population of galaxies selected from the same cumulative number density bin to within $\sim 0.20$ dex. Over the stellar mass range we probe ($10^{10.39}\leq M_s/M_\odot \leq 10^{10.75}$ at $z =$ 3 and $10^{8.48}\leq M_s/M_\odot \leq 10^{9.55}$ at $z =$ 7) one can reduce this bias by selecting galaxies based on an evolving cumulative number density. We find the cumulative number density evolution exhibits a trend towards higher values which can be quantified by simple linear formulations going as $-0.10\Delta z$ for descendants and $0.12\Delta z$ for progenitors. Utilizing such an evolving cumulative number density increases the accuracy of descendant/progenitor tracking by a factor of $\sim2$. This result is in excellent agreement, within $0.10$ dex, with abundance matching results over the same redshift range. However, we find that our more realistic cosmological hydrodynamic simulations produce a much larger scatter in descendant/progenitor stellar masses than previous studies, particularly when tracking progenitors. This large scatter makes the application of either the constant cumulative number density or evolving cumulative number density technique limited to average stellar masses of populations only, as the diverse mass assembly histories caused by stochastic physical processes such as gas accretion, mergers, and star formation of individual galaxies will lead to a larger scatter in other physical properties such as metallicity and star-formation rate.
  • PDF
    This article proposes the use of pseudorandom decimal sequences that have gone through an additional random mapping for the design of cryptographic keys. These sequences are generated by starting with inverse prime expansions in base 3 and then replacing 2 in the expansion with either the string 01 or 10 based on the preceding bit, which represents a general mapping. We show that the resulting pseudorandom sequences have excellent autocorrelation properties. Such a method can be extended to inverse prime expansions to any base.
  • PDF
    We discuss the history of the monodromy theorem, starting from Weierstraß, and the concept of monodromy group. From this viewpoint we compare then the Weierstraß, the Legendre and other normal forms for elliptic curves, explaining their geometric meaning and distinguishing them by their stabilizer in P SL(2,Z) and their monodromy. Then we focus on the birth of the concept of the Jacobian variety, and the geometrization of the theory of Abelian functions and integrals. We end illustrating the methods of complex analysis in the simplest issue, the difference equation $f(z) = g(z+1) - g(z)$ on $\mathbb C$.
  • PDF
    Recent quantum mechanical calculations of rate coefficients for collisional transfer of population between the hyperfine states of 13CN enable their population densities to be determined. We have computed the relative populations of the hyperfine states of the N = 0, 1, 2 rotational states for kinetic temperatures 5 $\le$ T $\le$ 20 K and molecular hydrogen densities 1 $\le$ n(H2) $\le$10 10 cm --3. Spontaneous and induced radiative transitions were taken into account. Our calculations show that, if the lines are optically thin, the populations of the hyperfine states, F, within a given rotational manifold are proportional to their statistical weights, (2F + 1) -- i.e. in local thermodynamic equilibrium -- over the entire range of densities. We have re-analysed IRAM 30 m telescope observations of 13CN hyperfine transitions (N = 1 $\rightarrow$ 0) in four starless cores. A comparison of these observations with our calculations confirms that the hyperfine states are statistically populated in these sources.
  • PDF
    Infrared (IR) excesses around K-type red giants (RGs) have previously been discovered using IRAS data, and past studies have suggested a link between RGs with overabundant Li and IR excesses, implying the ejection of circumstellar shells or disks. We revisit the question of IR excesses around RGs using higher spatial resolution IR data, primarily from WISE. Our goal was to elucidate the link between three unusual RG properties: fast rotation, enriched Li, and IR excess. We have 316 targets thought to be K giants, about 40% of which we take to be Li-rich. In 24 cases with previous detections of IR excess at low spatial resolution, we believe that source confusion is playing a role, in that either (a) the source that is bright in the optical is not responsible for the IR flux, or (b) there is more than one source responsible for the IR flux as measured in IRAS. We looked for IR excesses in the remaining sources, identifying 28 that have significant IR excesses by ~20 um (with possible excesses for 2 additional sources). There appears to be an intriguing correlation in that the largest IR excesses are all in Li-rich K giants, though very few Li-rich K giants have IR excesses (large or small). These largest IR excesses also tend to be found in the fastest rotators. There is no correlation of IR excess with the carbon isotopic ratio, 12C/13C. IR excesses by 20 um, though relatively rare, are at least twice as common among our sample of Li-rich K giants. If dust shell production is a common by-product of Li enrichment mechanisms, these observations suggest that the IR excess stage is very short-lived, which is supported by theoretical calculations. Conversely, the Li-enrichment mechanism may only occasionally produce dust, and an additional parameter (e.g., rotation) may control whether or not a shell is ejected.
  • PDF
    Streams of gas and dust in the inner parsec of the Galactic center form a distinct feature known as the Minispiral, which has been studied in radio waveband as well as in the infrared wavebands. A large fraction of the Minispiral gas is ionized by radiation of OB stars present in the Nuclear Star Cluster (NSC). Based on the inferred mass in the innermost parsec ($\sim 10^6$ solar masses), over $\sim 10^3$ -- $10^4$ neutron stars should move in the sphere of gravitational influence of the SMBH. We estimate that a fraction of them propagate through the denser, ionized medium concentrated mainly along the three arms of the Minispiral. Based on the properties of the gaseous medium, we discuss different interaction regimes of magnetised neutron stars passing through this region. Moreover, we sketch expected observational effects of these regimes. The simulation results may be applied to other galactic nuclei hosting NSC, where the expected distribution of the interaction regimes is different across different galaxy types.
  • PDF
    While measuring returns to scale in data envelopment analysis (DEA), the occurrence of multiple supporting hyperplanes has been perceived as a crucial issue. To deal effectively with this in weigh restrictions (WR) framework, we first precisely identify the two potential sources of its origin in the non-radial DEA setting. If the firm under evaluation P is WR-efficient, the non-full-dimensionality of its corresponding P-face-a face of minimum dimension that contains P-is the unique source of origin (problem Type I). Otherwise, the occurrence of multiple WR-projections or, correspondingly, multiple P-faces becomes the other additional source of origin (problem Type II). To the best of our knowledge, while problem Type I has been correctly addressed in the literature, the simultaneous occurrences of problems Types I and II have not effectively been coped with. Motivated by this, we first show that problem Type II can be circumvented by using a P-face containing all the P-faces. Based on this finding, we then devise a two-stage linear programming based procedure by extending a recently developed methodology by [Mehdiloozad, M., Mirdehghan, S. M., Sahoo, B. K., & Roshdi, I. (2015). On the identification of the global reference set in data envelopment analysis. European Journal of Operational Research, 245, 779-788]. Our proposed method inherits all the advantages of the recently developed method and is computationally efficient. The practical applicability of our proposed method is demonstrated through a real-world data set of 80 Iranian secondary schools.
  • PDF
    We have observed the Virgo Cluster spiral galaxy, NGC~4845, at 1.6 and 6 GHz using the Karl G. Jansky Very Large Array, as part of the `Continuum Halos in Nearby Galaxies -- an EVLA Survey' (CHANG-ES). The source consists of a bright unresolved core with a surrounding weak central disk (1.8 kpc diameter). The core is variable over the 6 month time scale of the CHANG-ES data and has increased by a factor of $\approx$ 6 since 1995. The wide bandwidths of CHANG-ES have allowed us to determine the spectral evolution of this core which peaks \it between 1.6 and 6 GHz (it is a GigaHertz-peaked spectrum source).We show that the spectral turnover is dominated by synchrotron self-absorption and that the spectral evolution can be explained by adiabatic expansion (outflow), likely in the form of a jet or cone. The CHANG-ES observations serendipitously overlap in time with the hard X-ray light curve obtained by Nikolajuk \& Walter (2013) which they interpret as due to a tidal disruption event (TDE) of a super-Jupiter mass object around a $10^5\, M_\odot$ black hole. We outline a standard jet model, provide an explanation for the observed circular polarization, and quantitatively suggest a link between the peak radio and peak X-ray emission via inverse Compton upscattering of the photons emitted by the relativistic electrons. We predict that it should be possible to resolve a young radio jet via VLBI as a result of this nearby TDE.
  • PDF
    A single atomic layer of black phosphorus, phosphorene, was experimentally realized in 2014. It has a puckered honeycomb lattice structure and a semiconducting electronic structure. In the first part of this paper, we use a simple LCAO model, and discuss qualitatively the electronic structure of phosphorene systems under electric and magnetic fields, especially, noting their midgap edge states. The next part is spent for the review of the research progress on phosphorene in the past one year since its appearance in 2014. Phosphorene has been a typical object to study the semiconductor physics in atomic layers.
  • PDF
    We consider Newton methods for common types of single commodity and multi-commodity network flow problems. Despite the potentially very large dimension of the problem, they can be implemented using the conjugate gradient method and low-dimensional network operations, as shown nearly thirty years ago. We revisit these methods, compare them to more recent proposals, and describe how they can be implemented in a distributed computing system. We also discuss generalizations, including the treatment of arc gains, linear side constraints, and related special structures.
  • PDF
    We consider a dense urban cellular network where the base stations (BSs) are stacked vertically as well as extending infinitely in the horizontal plane, resulting in a greater than two dimensional (2D) deployment. Using a dual-slope path loss model that is well supported empirically, we extend recent 2D coverage probability and potential throughput results to 3 dimensions. We prove that the "critical close-in path loss exponent" $\alpha_0$ where SINR eventually decays to zero is equal to the dimensionality $d$, i.e. $\alpha_0 \leq 3$ results in an eventual SINR of 0 in a 3D network. We also show that the potential (i.e. best case) aggregate throughput decays to zero for $\alpha_0 < d/2$. Both of these scaling results also hold for the more realistic case that we term ${3\rm{D}^{+}}$, where there are no BSs below the user, as in a dense urban network with the user on or near the ground.
  • PDF
    We prove that all axiomatic extensions of the full Lambek calculus with exchange can be axiomatized by formulas on the $\mathcal N_3$ level of the substructural hierarchy.
  • PDF
    The cosmetic crossing conjecture (also known as the "nugatory crossing conjecture") asserts that the only crossing changes that preserve the oriented isotopy class of a knot in the 3-sphere are nugatory. We use the Dehn surgery characterization of the unknot to prove this conjecture for knots in integer homology spheres whose branched double covers are L-spaces satisfying a homological condition. This includes as a special case all alternating and quasi-alternating knots with square-free determinant. As an application, we prove the cosmetic crossing conjecture holds for all knots with at most nine crossings and provide new examples of knots, including pretzel knots, non-arborescent knots and symmetric unions for which the conjecture holds.
  • PDF
    We show that for any finite configuration of closed curves $\Gamma\subset \mathbb{R}^2$, one can construct an explicit planar polynomial vector field that realizes $\Gamma$, up to homeomorphism, as the set of its limit cycles with prescribed periods, multiplicities and stabilities. The only obstruction given on this data is the obvious compatibility relation between the stabilities and the parity of the multiplicities. The constructed vector fields are Darboux integrable and admit a polynomial inverse integrating factor.
  • PDF
    I propose a simple and manageable method that allows for deriving coupling constants of model energy density functionals (EDFs) directly from ab initio calculations performed for finite fermion systems. A proof-of-principle application allows for linking properties of finite nuclei, determined by using the nuclear nonlocal Gogny functional, to the coupling constants of the quasilocal Skyrme functional. The method does not rely on properties of infinite fermion systems but on the ab initio calculations in finite systems. It also allows for quantifying merits of different model EDFs in describing the ab initio results.
  • PDF
    We study sufficient conditions for the belonging of random process to certain Besov space and for the Central Limit Theorem (CLT) in these spaces. We investigate also the non-asymptotic tail behavior of normed sums of centered random independent variables (vectors) with values in these spaces. Main apparatus is the theory of mixed (anisotropic) Lebesgue-Riesz spaces, in particular so-called permutation inequality.
  • PDF
    Many of the systems that are traditionally analyzed as complex networks have natural interpretations as multiplex structures. While these formulations retain more information than standard network models, there is not yet a fully developed theory for computing network metrics and statistics on these objects. As many of the structural representations associated to these models can distort the underlying characteristics of dynamical process, we introduce an algebraic method for modeling arbitrary dynamics on multiplex networks. Since several network metrics are based on generalized notions of dynamical transfer, we can use this framework to extend many of the standard network metrics to multiplex structures in a consistent fashion.
  • PDF
    We study the global existence of solutions to a one-dimensional drift-diffusion equation with logistic term, generalizing the classical parabolic-elliptic Keller-Segel aggregation equation arising in mathematical biology. In particular, we prove that there exists a global weak solution, if the order of the fractional diffusion $\alpha \in (1-c_1, 2]$, where $c_1>0$ is an explicit constant depending on the physical parameters present in the problem (chemosensitivity and strength of logistic damping). Furthermore, in the range $1-c_2<\alpha\leq 2$ with $0<c_2<c_1$, the solution is globally smooth. Let us emphasize that when $1-c<\alpha<1$ the diffusion is in the supercritical regime.
  • PDF
    When nodes can repeatedly update their behavior (as in agent-based models or repeated-game play settings) the problem of optimal network seeding becomes very complex. For the popular model of binary-behavior updating based on thresholds of adoption among neighbors, we consider several planning problems in the design of \textitSticky Interventions: when adoption decisions are reversible, the planner aims to find a Seed Set where temporary intervention leads to long-term behavior change. We prove that completely converting a network at minimum cost is $\Omega(\ln (OPT) )$-hard to approximate and that maximizing conversion subject to a budget is $(1-\frac{1}{e})$-hard to approximate. Optimization heuristics which rely on many objective function evaluations may still be practical, particularly in relatively-sparse networks: we prove that the long-term impact of a Seed Set can be evaluated in $O(|E|^2)$ operations. For a more descriptive model variant in which some neighbors may be more influential than others, we show that under integer edge weights from $\{0,1,2,...,k\}$ objective function evaluation requires only $O(k|E|^2)$ operations. These operation bounds are based on improvements we give for bounds on time-steps-to-convergence under discrete-time reversible-threshold updates in networks.
  • PDF
    Based on self-consistent T-matrix approximation (SCTMA), the Mott insulator - Bose-glass phase transition of one-dimensional noninteracting bosons subject to binary disorder is considered. The results obtained differ essentially from the conventional case of box distribution of the disorder. The Mott insulator - Bose-glass transition is found to exist at arbitrary strength of the impurities. The single particle density of states is calculated within the frame of SCTMA, numerically, and (for infinite disorder strength) analytically. A good agreement is reported between all three methods. We speculate that certain types of the interaction may lead to the Bose-glass - superfluid transition absent in our theory.
  • PDF
    We prove a closed formula for the integrals of the top Segre classes of tautological bundles over the Hilbert schemes of points of a K3 surface X. We derive relations among the Segre classes via equivariant localization of the virtual fundamental classes of Quot schemes on X. The resulting recursions are then solved explicitly. The formula proves the K-trivial case of a conjecture of M. Lehn from 1999. The relations determining the Segre classes fit into a much wider theory. By localizing the virtual classes of certain relative Quot schemes on surfaces, we obtain new systems of relations among tautological classes on moduli spaces of surfaces and their relative Hilbert schemes of points. For the moduli of K3 sufaces, we produce relations intertwining the kappa classes and the Noether-Lefschetz loci. Conjectures are proposed.
  • PDF
    Fast algorithms for matrix multiplication, or those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Aside from Strassen's original algorithm, few fast algorithms have been efficiently implemented or used in practical applications. However, there exist many practical alternatives to Strassen's algorithm with varying performance and numerical properties. While fast algorithms are known to be numerically stable, their error bounds are slightly weaker than the classical algorithm. We argue in this paper that the numerical sacrifice of fast algorithms, particularly for the typical use cases of practical algorithms, is not prohibitive, and we explore ways to improve the accuracy both theoretically and empirically. The numerical accuracy of fast matrix multiplication depends on properties of the algorithm and of the input matrices, and we consider both contributions independently. We generalize and tighten previous error analyses of fast algorithms, compare the properties among the class of known practical fast algorithms, and discuss algorithmic techniques for improving the error guarantees. We also present means for reducing the numerical inaccuracies generated by anomalous input matrices using diagonal scaling matrices. Finally, we include empirical results that test the various improvement techniques, in terms of both their numerical accuracy and their performance.
  • PDF
    We demonstrate that n-doped resistive heaters in silicon waveguides show photoconductive effects having responsivities as high as 271 mA/W. These photoconductive heaters, integrated into microring resonator (MRR)-based filters, were used to automatically tune and stabilize the filter's resonance wavelength to the input laser's wavelength. This is achieved without requiring dedicated defect implantations, additional material depositions, dedicated photodetectors, or optical power tap-outs. Automatic wavelength stabilization of first-order MRR and second-order series-coupled MRR filters is experimentally demonstrated. Open eye diagrams were obtained for data transmission at 12.5 Gb/s while the temperature was varied by 5 C at a rate of 0.28 C/s. We theoretically show that series-coupled MRR-based filters of any order can be automatically tuned by using photoconductive heaters to monitor the light intensity in each MRR, and sequentially aligning the resonance of each MRR to the laser's wavelength.
  • PDF
    We survey some of the AGT relations between N=2 gauge theories in four dimensions and geometric representations of symmetry algebras of two-dimensional conformal field theory on the equivariant cohomology of their instanton moduli spaces. We treat the cases of gauge theories on both flat space and ALE spaces in some detail, and with emphasis on the implications arising from embedding them into supersymmetric theories in six dimensions. Along the way we construct new toric noncommutative ALE spaces using the general theory of complex algebraic deformations of toric varieties, and indicate how to generalise the construction of instanton moduli spaces. We also compute the equivariant partition functions of topologically twisted six-dimensional Yang-Mills theory with maximal supersymmetry in a general Omega-background, and use the construction to obtain novel reductions to theories in four dimensions.
  • PDF
    Following Ribet's seminal 1976 paper there have been many results employing congruences between stable cuspforms and lifted forms to construct non-split extensions of Galois representations. We show how this strategy can be extended to construct elements in the Bloch-Kato Selmer groups of general +/--Asai (or tensor induction) representations. We demonstrate that suitable congruences between polarized automorphic forms over a CM field always produce elements in the Selmer group for exactly the Asai representation (+ or -) that is critical in the sense of Deligne. For this we relate the oddness of the associated polarized Galois representations (in the sense of the Bellaiche-Chenevier sign being +1) to the parity condition for criticality. We further outline a strategy using an orthogonal-symplectic theta correspondence to prove the existence of such congruences for the Asai representations associated to Bianchi modular forms and explain why we expect these congruences to be governed by the divisibility of the near-central critical value of the Asai L-function, in accordance with the Bloch-Kato conjecture.
  • PDF
    Future climate change impacts depend on temperatures not only through changes in their means but also through changes in their variability. General circulation models (GCMs) predict changes in both means and variability; however, GCM output should not be used directly as simulations for impacts assessments because GCMs do not fully reproduce present-day temperature distributions. This paper addresses an ensuing need for simulations of future temperatures that combine both the observational record and GCM projections of changes in means and temporal covariances. Our perspective is that such simulations should be based on transforming observations to account for GCM projected changes, in contrast to methods that transform GCM output to account for discrepancies with observations. Our methodology is designed for simulating transient (non-stationary) climates, which are evolving in response to changes in CO$_2$ concentrations (as is the Earth at present). This work builds on previously described methods for simulating equilibrium (stationary) climates. Since the proposed simulation relies on GCM projected changes in covariance, we describe a statistical model for the evolution of temporal covariances in a GCM under future forcing scenarios, and apply this model to an ensemble of runs from one GCM, CCSM3. We find that, at least in CCSM3, changes in the local covariance structure can be explained as a function of the regional mean change in temperature and the rate of change of warming. This feature means that the statistical model can be used to emulate the evolving covariance structure of GCM temperatures under scenarios for which the GCM has not been run. When combined with an emulator for mean temperature, our methodology can simulate evolving temperatures under such scenarios, in a way that accounts for projections of changes while still retaining fidelity with the observational record.
  • PDF
    Let $S$ be the (minimal) Enriques surface obtained from the symmetric quartic surface $(\sum_{i<j}x_ix_j)^2=kx_1x_2x_3x_4$ in $\mathbb{P}^3$ with $k\neq 0,4,36$, by taking quotient of the Cremona action $(x_i) \mapsto (1/x_i)$. The automorphism group of $S$ is a semi-direct product of a free product $\mathcal{F}$ of four involutions and the symmetric group $\mathfrak{S}_4$. Up to action of $\mathcal{F}$, there are exactly $29$ elliptic pencils on $S$.
  • PDF
    For each $n\geq 2$ we construct a new closed embedded mean curvature self-shrinking hypersurface in $\mathbb{R}^{2n}$. These self-shrinkers are diffeomorphic to $S^{n-1}\times S^{n-1}\times S^1$ and are $SO(n)\times SO(n)$ invariant. The method is inspired by constructions of Hsiang and these surfaces generalize self-shrinking "tori" diffeomorphic to $S^{n-1}\times S^1$ constructed by Angenent.
  • PDF
    Among various strong-curvature extensions to General Relativity, Einstein-Dilaton-Gauss-Bonnet gravity stands out as the only nontrivial theory containing quadratic curvature corrections while being free from the Ostrogradsky instability to any order in the coupling parameter. We derive an approximate stationary and axisymmetric black-hole solution of this gravitational theory in closed form, which is quadratic in the black-hole spin angular momentum and of seventh order in the coupling parameter of the theory. This extends previous work that obtained the corrections to the metric only at the leading order in the coupling parameter, and allows us to consider values of the coupling parameter close to the maximum permitted by theoretical constraints. We compute some geometrical properties of this solution, such as the dilaton charge, the moment of inertia and the quadrupole moment, and its geodesic structure, including the innermost-stable circular orbit and the epicyclic frequencies for massive particles. The latter represent a valuable tool to test General Relativity against strong-curvature corrections through observations of the electromagnetic spectrum of accreting black holes.
  • PDF
    Recent results in the construction of anomaly-free models of loop quantum gravity have shown obstacles when local physical degrees of freedom are present. Here, a set of no-go properties is derived in polarized Gowdy models, raising the question whether these systems can be covariant beyond a background treatment. As a side product, it is shown that normal deformations in classical polarized Gowdy models can be Abelianized.
  • PDF
    We present results concerning when the joint distribution of an exchangeable sequence is determined by the marginal distributions of its partial sums. The question of whether or not this determination occurs was posed by David Aldous. We then consider related uniqueness problems, including a continuous time analog to the Aldous problem and a randomized univariate moment problem.
  • PDF
    We propose a novel regularization technique for supervised and semi-supervised training of large models like deep neural network. By including into objective function the local smoothness of predictive distribution around each training data point, not only were we able to extend the Adversarial training to the setting of semi-supervised training, we were also able to eclipse current state of the art supervised and semi-supervised methods on the permutation invariant MNIST classification task.
  • PDF
    The "Wide Area VISTA Extra-galactic Survey" (WAVES) is a 4MOST Consortium Design Reference Survey which will use the VISTA/4MOST facility to spectroscopically survey ~2million galaxies to $r_{\rm AB} < 22$ mag. WAVES consists of two interlocking galaxy surveys ("WAVES-Deep" and "WAVES-Wide"), providing the next two steps beyond the highly successful 1M galaxy Sloan Digital Sky Survey and the 250k Galaxy And Mass Assembly survey. WAVES will enable an unprecedented study of the distribution and evolution of mass, energy, and structures extending from 1-kpc dwarf galaxies in the local void to the morphologies of 200-Mpc filaments at $z\sim1$. A key aim of both surveys will be to compare comprehensive empirical observations of the spatial properties of galaxies, groups, and filaments, against state-of-the-art numerical simulations to distinguish between various Dark Matter models.

Recent comments

Cedric Yen-Yu Lin Jun 29 2015 06:24 UTC
Wow, impressive. Very impressive.&#13; &#13; I like the word FORANDLATION: it's a corruption of a corruption of the word &quot;correlation&quot;.
Māris Ozols Jun 26 2015 14:19 UTC
Interesting comment at the bottom of page 9... :)
Artur Jun 22 2015 20:37 UTC
This article contains new results concerning the stroboscopic tomography, the aim of which is to reconstruct the initial density matrix on the basis of the least possible amount of data. The author proposes one complete quantum tomography model, which shows how step by step you can obtain the formul ...(continued)
Marco Tomamichel May 31 2015 22:07 UTC
Thanks for the comment! This is a good idea, I will do that in the next arXiv version.
Patrick Hayden May 28 2015 17:31 UTC
Wonderful! I've been waiting for a book like this for a while now! Thanks, Marco.&#13; &#13; I do have one trivial comment from a 30 second preliminary scan, though: please consider typesetting the proofs with a font size matching the main text. If us readers are already squinting hard trying to understand ...(continued)
lucy.vanderwende May 07 2015 16:13 UTC
The authors will want to look at work that Simone Teufel has done, in particular her Argumentative Zoning, which discusses the stance that the paper author takes with respect to the citations in that paper.
Jonathan Oppenehim May 06 2015 14:29 UTC
This article has generated a fair bit of discussion. But I found a few of the statements puzzling (Edgar Lozano also). Take for example, Theorem 1 (ii) (reversibility) which appears to contradict a number of previous results. Should we understand your work function as &quot;work in the paradigm where we ...(continued)
Ashley Apr 21 2015 18:42 UTC
Thanks for the further comments and spotting the new typos. To reply straight away to the other points:&#13; &#13; First, the resulting states might as well stay in the same bin (even though, as you rightly note, the bins no longer correspond to the same bit-strings as before). All that matters is that the ...(continued)
Perplexed Platypus Apr 21 2015 14:55 UTC
Thanks for updating the paper so promptly. The updated version addresses all my concerns so far. However I noticed a few extra (minor) things while reading through it.&#13; &#13; On page 15, last step of 2(b): if $|\psi_r\rangle$ and $|\psi_t\rangle$ were in the same bin but the combination operation failed ...(continued)
Ashley Apr 20 2015 16:27 UTC
Thank you for these very detailed and helpful comments. I have uploaded a new version of the paper to the arXiv to address them, which should appear tomorrow. I will reply to the comments in more detail (and justify the cases where I didn't modify the paper as suggested) when I receive them through ...(continued)