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- The magnetic anisotropy and exchange coupling between spins localized at the positions of 3d transition metal atoms forming two-dimensional metal-organic coordination networks (MOCNs) grown on the Au(111) metal surface are studied. In particular, we consider MOCNs made of Ni or Mn metal centers linked by TCNQ (7,7,8,8-tetracyanoquinodimethane) organic ligands, which form rectangular networks with 1:1 stoichiometry. Based on the analysis of X-ray magnetic circular dichroism (XMCD) data taken at T= 2.5 K, we find that Ni atoms in the Ni-TCNQ MOCNs are coupled ferromagnetically and do not show any significant magnetic anisotropy, while Mn atoms in the Mn-TCNQ MOCNs are coupled antiferromagnetically and do show a weak magnetic anisotropy with in-planemagnetization. We explain these observations using both amodelHamiltonian based on mean-fieldWeiss theory and density functional theory calculations that include spin-orbit coupling. Our main conclusion is that the antiferromagnetic coupling between Mn spins and the in-plane magnetization of the Mn spins can be explained neglecting effects due to the presence of the Au(111) surface, while for Ni-TCNQ the metal surface plays a role in determining the absence of magnetic anisotropy in the system.
- We present methods for bounding infinite-time averages in dynamical systems governed by nonlinear PDEs. The methods rely on auxiliary functionals, which are similar to Lyapunov functionals but satisfy different inequalities. The inequalities are enforced by requiring certain expressions to be sums of squares of polynomials, and the optimal choice of auxiliary functional is posed as a semidefinite program (SDP) that can be solved computationally. To formulate these SDPs we approximate the PDE by truncated systems of ODEs and proceed in one of two ways. The first approach is to compute bounds for the ODE systems, increasing the truncation order until bounds converge numerically. The second approach incorporates the ODE systems with analytical estimates on their deviation from the PDE, thereby using finite truncations to produce bounds for the full PDE. We apply both methods to the Kuramoto-Sivashinsky equation. In particular, we compute upper bounds on the spatiotemporal average of energy by employing polynomial auxiliary functionals up to degree six. The first approach is used for most computations, but a subset of results are checked using the second approach, and the results agree to high precision. These bounds apply to all odd solutions of period $2\pi L$, where $L$ is varied. Sharp bounds are obtained for $L\le10$, and trends suggest that more expensive computations would yield sharp bounds at larger $L$ also. The bounds are known to be sharp (to within 0.1% numerical error) because they are saturated by the simplest nonzero steady states, which apparently have the largest mean energy among all odd solutions. Prior authors have conjectured that mean energy remains $O(1)$ for $L\gg1$ since no particular solutions with larger energy have been found. Our bounds constitute the first positive evidence for this conjecture, albeit up to finite $L$, and offer guidance for analytical proofs.
- Feb 23 2018 physics.flu-dyn arXiv:1802.08226v1When investigating particle suspensions, for example in the Stokesian dynamics simulation technique, it is sometimes necessary to use near-field asymptotic forms of scalar resistance functions for two unequal rigid spheres, commonly notated $X^A_{11}$, $X^A_{12}$, $Y^A_{11}$, etc. The required expressions for generating these scalars were initially published in Jeffrey & Onishi (J. Fluid Mech., 1984) and Jeffrey (Phys. Fluids A, 1992). These important papers suffer from a number of small errors. This short article comprehensively corrects the errors in these papers, and adds formulae which were originally omitted, so that the reader can verify independently their correctness. The corrected expressions are shown to match to the mid-field values of these scalars, which are calculated through an alternative method.
- Understanding hydrodynamization in microscopic models of heavy-ion collisions has been an important topic in current research. Many lessons obtained within the strongly-coupled (holographic) models originate from the properties of transient excitations of equilibrium encapsulated by short-lived quasinormal modes of black holes. The aim of this paper is to develop similar intuition for expanding plasma systems described by, perhaps, the simplest model from the weakly-coupled domain, i.e. the Boltzmann equation in the relaxation time approximation. We show that in this kinetic theory setup there are infinitely many transient modes carrying at late times the vast majority of information about the initial distribution function. They all have the same exponential damping set by the relaxation time but are distinguished by different power-law suppressions and different frequencies of very slow, logarithmic in proper time, oscillations. Finally, we analyze the resurgent interplay between the hydrodynamics and transients. In particular, show that there are choices of relaxation time dependence on temperature for which the asymptotics of the divergent hydrodynamic series is dominated not be the least damped transient, but rather by an unphysical exponential correction having to do with non-analyticities of the equation of motion in complexified time variable.
- We study combinatorial connectivity for two models of random geometric complexes. These two models - Čech and Vietoris-Rips complexes - are built on a homogeneous Poisson point process of intensity $n$ on a $d$-dimensional torus using balls of radius $r_n$. In the former, the $k$-simplices/faces are formed by subsets of $(k+1)$ Poisson points such that the balls of radius $r_n$ centred at these points have a mutual interesection and in the latter, we require only a pairwise intersection of the balls. Given a (simplicial) complex (i.e., a collection of $k$-simplices for all $k \geq 1$), we can connect $k$-simplices via $(k+1)$-simplices (`up-connectivity') or via $(k-1)$-simplices (`down-connectivity). Our interest is to understand these two combinatorial notions of connectivity for the random Čech and Vietoris-Rips complexes asymptically as $n \to \infty$. In particular, we analyse in detail the threshold radius for vanishing of isolated $k$-faces for up and down connectivity of both types of random geometric complexes. Though it is expected that the threshold radius $r_n = \Theta((\frac{\log n}{n})^{1/d})$ in coarse scale, our results give tighter bounds on the constants in the logarithmic scale as well as shed light on the possible second-order correction factors. Further, they also reveal interesting differences between the phase transition in the Čech and Vietoris-Rips cases. The analysis is interesting due to the non-monotonicity of the number of isolated $k$-faces (as a function of the radius) and leads one to consider `monotonic' vanishing of isolated $k$-faces. The latter coincides with the vanishing threshold mentioned above at a coarse scale (i.e., $\log n$ scale) but differs in the $\log \log n$ scale for the Čech complex with $k = 1$ in the up-connected case.
- We study the problem of private function retrieval (PFR) in a distributed storage system. In PFR the user wishes to retrieve a linear combination of $M$ messages stored in non-colluding $(N,K)$ MDS coded databases while revealing no information about the coefficients of the intended linear combination to any of the individual databases. We present an achievable scheme for MDS coded PFR with a rate that matches the capacity for coded private information retrieval derived recently, $R=(1+R_c+R_c^2+\dots+R_c^{M-1})^{-1}=\frac{1-R_c}{1-R_c^M}$, where $R_c=\frac{K}{N}$ is the rate of the MDS code. This achievable rate is tight in some special cases.
- Feb 23 2018 cond-mat.quant-gas quant-ph arXiv:1802.08222v1Magnetic monopole, a hypothetical elementary particle with isolated magnetic pole, is crucial for the quantization of electric charge. In recent years, analogues of magnetic monopoles, represented by topological defects in parameter spaces, have been studied in a wide range of physical systems. These works mainly focused on Abelian Dirac monopoles in spin-1/2 or non-Abelian Yang monopoles in spin-3/2 systems. Here we propose to realize three types of spin-1 topological monopoles and study their geometric properties using the parameter space formed by three hyperfine states of ultracold atoms coupled by radio-frequency fields. These spin-1 monopoles, characterized by different monopole charges, possess distinct Berry curvature fields and spin textures, which are directly measurable in experiments. The topological phase transitions between different monopoles are accompanied by the emergence of spin "vortex", and can be intuitively visualized using Majorana's stellar representation. We show how to determine the Berry curvature, hence the geometric phase and monopole charge from dynamical effects. Our scheme provides a simple and highly tunable platform for observing and manipulating spin-1 topological monopoles, paving the way for exploring new topological quantum matter.
- Feb 23 2018 cond-mat.str-el arXiv:1802.08221v1The Fermi surface topology of a Weyl semimetal (WSM) depends strongly on the position of the chemical potential. If it resides close to the band touching points (Weyl nodes), as it does in TaAs, separate Fermi surfaces of opposite chirality emerge, leading to novel phenomena such as the chiral magnetic effect. If the chemical potential lies too far from the nodes, however, the chiral Fermi surfaces merge into a single large Fermi surface with no net chirality. This is realized in the WSM NbP, where the Weyl nodes lie far below the Fermi energy and where the transport properties in low magnetic fields show no evidence of chiral Fermi surfaces. Here we show that the behavior of NbP in high magnetic fields is nonetheless dominated by the presence of the Weyl nodes. Torque magnetometry up to 60 tesla reveals a change in the slope of $\tau/B$ at the quantum limit B$^\star$ ($\approx 32\,\rm{T}$), where the chemical potential enters the $n=0$ Landau level. Numerical simulations show that this behaviour results from the magnetic field pulling the chemical potential to the chiral $n=0$ Landau level belonging to the Weyl nodes. These results show that high magnetic fields can uncover topological singularities in the underlying band structure of a potential WSM, and can recover topologically non-trivial experimental properties, even when the position of the chemical potential precludes their observation in zero magnetic field.
- Feb 23 2018 cond-mat.mtrl-sci arXiv:1802.08220v1Graphene layers grown by chemical vapour deposition (CVD) method and transferred from Cu-foils to the oxidized Si-substrates were investigated by spectroscopic ellipsometry (SE), Raman and X-Ray Photoelectron Spectroscopy (XPS) methods. The optical properties of transferred CVD graphene layers do not always correspond to the ones of the exfoliated graphene due to the contamination from the chemicals used in the transfer process. However, the real thickness and the mean properties of the transferred CVD graphene layers can be found using ellipsometry if a real thickness of the SiO2 layer is taken into account. The pulsed layer deposition (PLD) and atomic layer deposition (ALD) methods were used to grow dielectric layers on the transferred graphene and the obtained structures were characterized using optical methods. The approach demonstrated in this work could be useful for the characterization of various materials grown on graphene.
- The standard state space model is widely believed to account for the cerebellar computation in motor adaptation tasks [1]. Here we show that several recent experiments [2-4] where the visual feedback is irrelevant to the motor response challenge the standard model. Furthermore, we propose a new model that accounts for the the results presented in [2-4]. According to this new model, learning and forgetting are coupled and are error size dependent. We also show that under reasonable assumptions, our proposed model is the only model that accounts for both the classical adaptation paradigm as well as the recent experiments [2-4].
- Mark T. Graham, Michele Cappellari, Hongyu Li, Shude Mao, Matthew Bershady, Dmitry Bizyaev, Jonathan Brinkmann, Joel R. Brownstein, Kevin Bundy, Niv Drory, David R. Law, Kaike Pan, Daniel Thomas, David A. Wake, Anne-Marie Weijmans, Kyle B. Westfall, Renbin YanFeb 23 2018 astro-ph.GA arXiv:1802.08213v1We measure $\lambda_{R_e}$, a proxy for galaxy specific stellar angular momentum within one effective radius, and the ellipticity, $\epsilon$, for about 2300 galaxies of all morphological types observed with integral field spectroscopy as part of the MaNGA survey, the largest such sample to date. We use the $(\lambda_{R_e}, \epsilon)$ diagram to separate early-type galaxies into fast and slow rotators. We also visually classify each galaxy according to its optical morphology and two-dimensional stellar velocity field. Comparing these classifications to quantitative $\lambda_{R_e}$ measurements reveals tight relationships between angular momentum and galaxy structure. In order to account for atmospheric seeing, we use realistic models of galaxy kinematics to derive a general approximate analytic correction for $\lambda_{R_e}$. Thanks to the size of the sample and the large number of massive galaxies, we unambiguously detect a clear bimodality in the $(\lambda_{R_e}, \epsilon)$ diagram which may result from fundamental differences in galaxy assembly history. There is a sharp secondary density peak inside the region of the diagram with low $\lambda_{R_e}$ and $\epsilon < 0.4$, previously suggested as the definition for slow rotators. Most of these galaxies are visually classified as non-regular rotators and have high velocity dispersion. The intrinsic bimodality must be stronger, as it tends to be smoothed by noise and inclination. The large sample of slow rotators allows us for the first time to unveil a secondary peak at +/-90 degrees in their distribution of the misalignments between the photometric and kinematic position angles. We confirm that genuine slow rotators start appearing above a stellar mass of 2\times10^11 M_⊙$ where a significant number of high-mass fast rotators also exist.
- We propose to measure the yields of $^4{\rm He}$ and $^4{\rm Li}$ in relativistic heavy-ion collisions to clarify a mechanism of light nuclei production. Since the masses of $^4{\rm He}$ and $^4{\rm Li}$ are almost equal, the yield of $^4{\rm Li}$ predicted by the thermal model is 5 times bigger than that of $^4{\rm He}$ which reflects the different numbers of internal degrees of freedom of the two nuclides. Their internal structure is, however, very different: the alpha particle is well bound and compact while $^4{\rm Li}$ is weakly bound and loose. Within the coalescence model the ratio of yields of $^4{\rm Li}$ to $^4{\rm He}$ is shown to be significantly smaller than that in the thermal model and the ratio decreases fast from central to peripheral collisions of relativistic heavy-ion collisions because the coalescence rate strongly depends on the nucleon source radius.
- Unusual behavior of quantum materials commonly arises from their effective low-dimensional physics, which reflects the underlying anisotropy in the spin and charge degrees of freedom. Torque magnetometry is a highly sensitive technique to directly quantify the anisotropy in quantum materials, such as the layered high-T$_c$ superconductors, anisotropic quantum spin-liquids, and the surface states of topological insulators. Here we introduce the magnetotropic coefficient $k=\partial^2 F/\partial \theta^2$, the second derivative of the free energy F with respect to the angle $\theta$ between the sample and the applied magnetic field, and report a simple and effective method to experimentally detect it. A sub-$\mu$g crystallite is placed at the tip of a commercially available atomic force microscopy cantilever, and we show that $k$ can be quantitatively inferred from a shift in the resonant frequency under magnetic field. While related to the magnetic torque $\tau=\partial F/\partial \theta$, $k$ takes the role of torque susceptibility, and thus provides distinct insights into anisotropic materials akin to the difference between magnetization and magnetic susceptibility. The thermodynamic coefficient $k$ is discontinuous at second-order phase transitions and subject to Ehrenfest relations with the specific heat and magnetic susceptibility. We apply this simple yet quantitative method on the exemplary cases of the Weyl-semimetal NbP and the spin-liquid candidate RuCl$_3$, yet it is broadly applicable in quantum materials research.
- Macdonald processes are measures on sequences of integer partitions built using the Cauchy summation identity for Macdonald symmetric functions. These measures are a useful tool to uncover the integrability of many probabilistic systems, including the Kardar-Parisi-Zhang (KPZ) equation and a number of other models in its universality class. In this paper we develop the structural theory behind half-space variants of these models and the corresponding half-space Macdonald processes. These processes are built using a Littlewood summation identity instead of the Cauchy identity, and their analysis is considerably harder than their full-space counterparts. We compute moments and Laplace transforms of observables for general half-space Macdonald measures. Introducing new dynamics preserving this class of measures, we relate them to various stochastic processes, in particular the log-gamma polymer in a half-quadrant (they are also related to the stochastic six-vertex model in a half-quadrant and the half-space ASEP). For the polymer model, we provide explicit integral formulas for the Laplace transform of the partition function. Non-rigorous saddle point asymptotics yield convergence of the directed polymer free energy to either the Tracy-Widom GOE, GSE or the Gaussian distribution depending on the average size of weights on the boundary.
- Feb 23 2018 cond-mat.mtrl-sci arXiv:1802.08208v1Materials exhibiting controllable magnetic phase transitions are currently in demand for many spintronics applications. Here we investigate from first principles the electronic structure and intrinsic anomalous Hall, spin Hall and anomalous Nernst response properties of the FeRh metallic alloy which undergoes a thermally driven antiferromagnetic-to-ferromagnetic phase transition. We show that the energy band structures and underlying Berry curvatures have important signatures in the various Hall effects. Specifically, the suppression of the anomalous Hall and Nernst effects in the AFM state and a sign change in the spin Hall conductivity across the transition are found. It is suggested that the FeRh can be used a spin current detector capable of differentiating the spin Hall effect from other anomalous transverse effects. The implications of this material and its thermally driven phases as a spin current detection scheme are also discussed.
- Feb 23 2018 math.NT arXiv:1802.08207v1The Asai (or twisted tensor) $L$-function of a Bianchi modular form $\Psi$ is the $L$-function attached to the tensor induction to $\mathbb{Q}$ of its associated Galois representation. In this paper, when $\Psi$ is ordinary at $p$ we construct a $p$-adic analogue of this $L$-function: that is, a $p$-adic measure on $\mathbb{Z}_p^\times$ that interpolates the critical values of the Asai $L$-function twisted by Dirichlet characters of $p$-power conductor. The construction uses techniques analogous to those used by Lei, Zerbes and the first author in order to construct an Euler system attached to the Asai representation of a quadratic Hilbert modular form.
- Feb 23 2018 astro-ph.CO hep-ph arXiv:1802.08206v1We explore the possible spectrum of binary mergers of sub-solar mass black holes formed out of dark matter particles interacting via a dark electromagnetism. We estimate the properties of these dark black holes by assuming that their formation process is parallel to Population-III star formation; except that dark molecular cooling can yield smaller opacity limit. We estimate the binary coalescence rates for the Advanced LIGO and Einstein telescope, and find that scenarios compatible with all current constraints could produce dark black holes at rates high enough for detection by Advanced LIGO.
- Feb 23 2018 astro-ph.HE arXiv:1802.08205v1AX J0049.4-7323 is a Be/X-ray binary in the Small Magellanic Cloud hosting a ~750 s pulsar which has been observed over the last ~17 years by several X-ray telescopes. Despite numerous observations, little is known about its X-ray behaviour. Therefore, we coherently analysed archival Swift, Chandra, XMM-Newton, RXTE, and INTEGRAL data, and we compared them with already published ASCA data, to study its X-ray long-term spectral and flux variability. AX J0049.4-7323 shows a high X-ray variability, spanning more than three orders of magnitudes, from L ~ 1.6E37 erg/s (0.3-8 keV, d=62 kpc) down to L ~ 8E33 erg/s. RXTE, Chandra, Swift, and ASCA observed, in addition to the expected enhancement of X-ray luminosity at periastron, flux variations by a factor of ~ 270 with peak luminosities of ~2.1E36 erg/s far from periastron. These properties are difficult to reconcile with the typical long-term variability of Be/XRBs, traditionally interpreted in terms of type I and type II outbursts. The study of AX J0049.4-7323 is complemented with a spectral analysis of Swift, Chandra, and XMM-Newton data which showed a softening trend when the emission becomes fainter, and an analysis of optical/UV data collected by the UVOT telescope on board Swift. In addition, we measured a secular spin-up rate of $\dot{P}=(-3.00\pm0.12)\times 10^{-3}$ s day$^{-1}$, which suggests that the pulsar has not yet achieved its equilibrium period. Assuming spherical accretion, we estimated an upper limit for the magnetic field strength of the pulsar of ~3E12 G.
- According to the Grothendieck-Lefschetz theorem from SGA 2, there are no nontrivial line bundles on the punctured spectrum $U_R$ of a local ring $R$ that is a complete intersection of dimension $\ge 4$. Dao conjectured a generalization for vector bundles $\mathscr{V}$ of arbitrary rank on $U_R$: such a $\mathscr{V}$ is free if and only if $\mathrm{depth}_R(\mathrm{End}_R(\Gamma(U_R, \mathscr{V}))) \ge 4$. We use deformation theoretic techniques to settle Dao's conjecture. We also present examples showing that its assumptions are sharp.
- A Polynomial Time Subsumption Algorithm for Nominal Safe $\mathcal{ELO}_\bot$ under Rational ClosureFeb 23 2018 cs.AI arXiv:1802.08201v1Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe $\mathcal{ELO}_\bot$, a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe $\mathcal{ELO}_\bot$ under RC that relies entirely on a series of classical, monotonic $\mathcal{EL}_\bot$ subsumption tests. Therefore, any existing classical monotonic $\mathcal{EL}_\bot$ reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability.
- We study the nonperturbative quantum evolution of the interacting O(N) vector model at large-N, formulated on a spatial two-sphere, with time dependent couplings which diverge at finite time. This model - the so-called "E-frame" theory, is related via a conformal transformation to the interacting O(N) model in three dimensional global de Sitter spacetime with time independent couplings. We show that with a purely quartic, relevant deformation the quantum evolution of the E-frame model is regular even when the classical theory is rendered singular at the end of time by the diverging coupling. Time evolution drives the E-frame theory to the large-N Wilson-Fisher fixed point when the classical coupling diverges. We study the quantum evolution numerically for a variety of initial conditions and demonstrate the finiteness of the energy at the classical "end of time". With an additional (time dependent) mass deformation, quantum backreaction lowers the mass, with a putative smooth time evolution only possible in the limit of infinite quartic coupling. We discuss the relevance of these results for the resolution of crunch singularities in AdS geometries dual to E-frame theories with a classical gravity dual.
- Astrometric and spectroscopic monitoring of individual stars orbiting the supermassive black hole in the Galactic Center offer a promising way to detect general relativistic effects. While low-order effects are expected to be detected following the periastron passage of S2 in Spring 2018, detecting higher-order effects due to black hole spin will require the discovery of closer stars. In this paper, we set out to determine the requirements such a star would have to satisfy to allow the detection of black hole spin. We focus on the instrument GRAVITY, which saw first light in 2016 and which is expected to achieve astrometric accuracies $10-100 \mu$as. For an observing campaign with duration $T$ years, $N_{obs}$ total observations, astrometric precision $\sigma_x$ and normalized black hole spin $\chi$, we find that $a_{orb}(1-e^2)^{3/4} \lesssim 300 R_S \sqrt{\frac{T}{4 \text{years}}} \left(\frac{N_{obs}}{120}\right)^{0.25} \sqrt{\frac{10 \mu as}{\sigma_x}} \sqrt{\frac{\chi}{0.9}}$ is needed. For $\chi=0.9$ and a potential observing campaign with $\sigma_x = 10 \mu$as, 30 observations/year and duration 4-10 years, we expect $\sim 0.1$ star with $K<19$ satisfying this constraint based on the current knowledge about the stellar population in the central 1". We also propose a method through which GRAVITY could potentially measure radial velocities with precision $\sim 50$ km/s. If the astrometric precision can be maintained, adding radial velocity information increases the expected number of stars by roughly a factor of two. While we focus on GRAVITY, the results can also be scaled to parameters relevant for future extremely large telescopes.
- We uncover a remarkable quantum scattering phenomenon in two-dimensional Dirac material systems where the manifestations of both classically integrable and chaotic dynamics emerge simultaneously and are electrically controllable. The distinct relativistic quantum fingerprints associated with different electron spin states are due to a physical mechanism analogous to chiroptical effect in the presence of degeneracy breaking. The phenomenon mimics a chimera state in classical complex dynamical systems but here in a relativistic quantum setting - henceforth the term "Dirac quantum chimera," associated with which are physical phenomena with potentially significant applications such as enhancement of spin polarization, unusual coexisting quasibound states for distinct spin configurations, and spin selective caustics. Experimental observations of these phenomena are possible through, e.g., optical realizations of ballistic Dirac fermion systems.
- Feb 23 2018 cond-mat.supr-con arXiv:1802.08196v1The trilayer and pentalayer spin valve structures are revisited to determine the behavior of pair correlations and Josephson current when the magnetic layers are canted at arbitrary angle. The two systems display markedly different behaviors in the center magnetic layer. While the trilayer generates a triplet component that is weakly affected by canting, the pentalayer tunes in singlet pair correlations depending heavily on canting. We also show that a minimum with depleted $m=\pm1$ triplet components, rather than a $0-\pi$ transition, may be observed in the current profile $I_c(d_F)$ of a trilayer spin valve. The depleted-triplet minimum (DTM) is directly attributable to a decrease of $m=\pm1$ triplet correlations with increased thickness of the central ferromagnet, accompanied by a hidden, simultaneous sign change of the Gor'kov functions contributed from the left and right superconductors. We introduce a toy model for superconducting-magnetic proximity systems to better illuminate the behavior of individual components of the Gor'kov function and compare with a full numerical calculation.
- This paper assesses the empirical content of one of the most prevalent assumptions in the economics of networks literature, namely the assumption that decision makers have full knowledge about the networks they interact on. Using network data from 75 villages, we ask 4,554 individuals to assess whether five randomly chosen pairs of households in their village are linked through financial, social, and informational relationships. We find that network knowledge is low and highly localized, declining steeply with the pair's network distance to the respondent. 46% of respondents are not even able to offer a guess about the status of a potential link between a given pair of individuals. Even when willing to offer a guess, respondents can only correctly identify the links 37% of the time. We also find that a one-step increase in the social distance to the pair corresponds to a 10pp increase in the probability of misidentifying the link. We then investigate the theoretical implications of this assumption by showing that the predictions of various models change substantially if agents behave under the more realistic assumption of incomplete knowledge about the network. Taken together, our results suggest that the assumption of full network knowledge (i) may serve as a poor approximation to the real world and (ii) is not innocuous: allowing for incomplete network knowledge may have first-order implications for a range of qualitative and quantitative results in various contexts.
- We outline the theory of reflections for prederivators, derivators and stable derivators. In order to parallel the classical theory valid for categories, we outline how reflections can be equivalently described as categories of fractions, reflective factorization systems, and categories of algebras for idempotent monads. This is a further development of the theory of monads and factorization systems for derivators.
- We extend the weak universality of KPZ in [Hairer-Quastel] to weakly asymmetric interface models with general growth mechanisms beyond polynomials. A key new ingredient is a pointwise bound on correlations of trigonometric functions of Gaussians in terms of their polynomial counterparts. This enables us to reduce the problem of a general nonlinearity with sufficient regularity to that of a polynomial.
- We construct solutions of non-uniform black strings in dimensions from $D \approx 9$ all the way up to $D = \infty$, and investigate their thermodynamics and dynamical stability. Our approach employs the large-$D$ perturbative expansion beyond the leading order, including corrections up to $1/D^4$. Combining both analytical techniques and relatively simple numerical solution of ODEs, we map out the ranges of parameters in which non-uniform black strings exist in each dimension and compute their thermodynamics and quasinormal modes with accuracy. We establish with very good precision the existence of Sorkin's critical dimension and we prove that not only the thermodynamic stability, but also the dynamic stability of the solutions changes at it. We perform time evolutions of unstable black strings by numerically solving two-dimensional PDEs. Depending on the mass of the string, the evolution either (i) ends on a stable non-uniform black string; or (ii) it quickly proceeds to a singular pinch-off; or (iii) it can pass through a long-lived, metastable non-uniform phase before heading towards pinch-off.
- Feb 23 2018 cond-mat.dis-nn arXiv:1802.08190v1Amorphous silicon (a-Si) models are analyzed for structural, electronic and vibrational characteristics. Several models of various sizes have been computationally fabricated for this analysis. It is shown that a recently developed structural modeling algorithm known as force-enhanced atomic refinement (FEAR) provides results in agreement with experimental neutron and x-ray diffraction data while producing a total energy below conventional schemes. We also show that a large model (500 atoms) and a complete basis is necessary to properly describe vibrational and thermal properties. We compute the density for a-Si, and compare with experimental results.
- Feb 23 2018 cs.DM arXiv:1802.08189v1In the Directed Steiner Network problem we are given an arc-weighted digraph $G$, a set of terminals $T \subseteq V(G)$, and an (unweighted) directed request graph $R$ with $V(R)=T$. Our task is to output a subgraph $G' \subseteq G$ of the minimum cost such that there is a directed path from $s$ to $t$ in $G'$ for all $st \in A(R)$. It is known that the problem can be solved in time $|V(G)|^{O(|A(R)|)}$ [Feldman&Ruhl, SIAM J. Comput. 2006] and cannot be solved in time $|V(G)|^{o(|A(R)|)}$ even if $G$ is planar, unless Exponential-Time Hypothesis (ETH) fails [Chitnis et al., SODA 2014]. However, as this reduction (and other reductions showing hardness of the problem) only shows that the problem cannot be solved in time $|V(G)|^{o(|T|)}$ unless ETH fails, there is a significant gap in the complexity with respect to $|T|$ in the exponent. We show that Directed Steiner Network is solvable in time $f(R)\cdot |V(G)|^{O(c_g \cdot |T|)}$, where $c_g$ is a constant depending solely on the genus of $G$ and $f$ is a computable function. We complement this result by showing that there is no $f(R)\cdot |V(G)|^{o(|T|^2/ \log |T|)}$ algorithm for any function $f$ for the problem on general graphs, unless ETH fails.
- Feb 23 2018 math.PR arXiv:1802.08188v1We are interested in populations in which the fitness of different genetic types fluctuates in time and space, driven by temporal and spatial fluctuations in the environment. For simplicity, our population is assumed to be composed of just two genetic types. Short bursts of selection acting in opposing directions drive to maintain both types at intermediate frequencies, while the fluctuations due to 'genetic drift' work to eliminate variation in the population. We consider first a population with no spatial structure, modelled by an adaptation of the Lambda (or generalised) Fleming-Viot process, and derive a stochastic differential equation as a scaling limit. This amounts to a limit result for a Lambda-Fleming-Viot process in a rapidly fluctuating random environment. We then extend to a population that is distributed across a spatial continuum, which we model through a modification of the spatial Lambda-Fleming-Viot process with selection. In this setting we show that the scaling limit is a stochastic partial differential equation. As is usual with spatially distributed populations, in dimensions greater than one, the 'genetic drift' disappears in the scaling limit, but here we retain some stochasticity due to the fluctuations in the environment, resulting in a stochastic p.d.e. driven by a noise that is white in time but coloured in space. We discuss the (rather limited) situations under which there is a duality with a system of branching and annihilating particles. We also write down a system of equations that captures the frequency of descendants of particular subsets of the population and use this same idea of 'tracers', which we learned from Hallatschek and Nelson (2008) and Durrett and Fan (2016), in numerical experiments with a closely related model based on the classical Moran model.
- Feb 23 2018 math.LO arXiv:1802.08187v1We propose a new contact relation between polytopes. Intuitively, we say that two polytopes are in strong contact if a small enough object can pass from one of them to the other while remaining in their union. In the first half of the paper we prove that this relation is indeed a contact relation between polytopes, which turns out not to be the case for arbitrary regular closed in Euclidean spaces sets. In the second half we study the universal fragments of the logics of the resultant contact algebras. We prove that they all coincide with the set of theorems of a standard quantifier-free formal system for connected contact algebras, which also coincides with the universal fragments of the logics of a variety of (classes of) contact algebras of interest.
- We study the properties of the quasienergy states of a quantum system driven by a classical dynamical systems. The quasienergies are defined in a same manner as in light-matter interaction but where the Floquet approach is generalized by the use of the Koopman approach of dynamical systems. We show how the properties of the classical flow (fixed and cyclic points, ergodicity, chaos) influence the driven quantum system. This approach of the Schrödinger-Koopman quasienergies can be applied to quantum control, quantum information in presence of noises, and dynamics of mixed classical-quantum systems. We treat the example of a spin ensemble kicked following discrete classical flow as the Arnold's cat map and the Chirikov standard map.
- Feb 23 2018 math.NT arXiv:1802.08185v1Let p and q be two positive primes. In this paper we obtain a complete characterization of quaternion division algebras H_K(p,q) over quadratic and biquadratic number fields K.
- Online optimization has been a successful framework for solving large-scale problems under computational constraints and partial information. Current methods for online convex optimization require either a projection or exact gradient computation at each step, both of which can be prohibitively expensive for large-scale applications. At the same time, there is a growing trend of non-convex optimization in machine learning community and a need for online methods. Continuous submodular functions, which exhibit a natural diminishing returns condition, have recently been proposed as a broad class of non-convex functions which may be efficiently optimized. Although online methods have been introduced, they suffer from similar problems. In this work, we propose Meta-Frank-Wolfe, the first online projectionfree algorithm that uses stochastic gradient estimates. The algorithm relies on a careful sampling of gradients in each round and achieves the optimal $O(\sqrt{T})$ adversarial regret bounds for convex and continuous submodular optimization. We also propose One-Shot Frank-Wolfe, a simpler algorithm which requires only a single stochastic gradient estimate in each round and achieves a $O(T^{2/3})$ stochastic regret bound for convex and continuous submodular optimization. We apply our methods to develop a novel "lifting" framework for the online discrete submodular maximization and also see that they outperform current state of the art techniques on an extensive set of experiments.
- Feb 23 2018 cs.HC arXiv:1802.08182v1Despite the increasing presence of Internet of Things (IoT) devices inside the home, we know little about how users feel about their privacy living with Internet-connected devices that continuously monitor and collect data in their homes. To gain insight into this state of affairs, we conducted eleven semi-structured interviews with owners of smart homes, investigating privacy values and expectations. In this paper, we present the findings that emerged from our study: First, users prioritize the convenience and connectedness of their smart homes, and these values dictate their privacy opinions and behaviors. Second, user opinions about who should have access to their smart home data depend on the perceived benefit. Third, users assume their privacy is protected because they trust the manufacturers of their IoT devices. Our findings bring up several implications for IoT privacy, which include the need for design for privacy and evaluation standards.
- A. Nucara, M. Corasaniti, A. Kalaboukhov, M. Ortolani, E. Falsetti, A. Sambri, F. Miletto Granozio, F. Capitani, J.-B. Brubach, P. Roy, U. Schade, P. CalvaniFeb 23 2018 cond-mat.mtrl-sci arXiv:1802.08181v1We have used grazing-angle infrared spectroscopy to detect the Berreman effect (BE) in the quasi-two-dimensional electron system (q-2DES) which forms spontaneously at the interface between SrTiO$_{3}$ (STO) and a thin film of LaAlO$_3$ (LAO). From the BE, which allows one to study longitudinal optical excitations in ultrathin films like the q-2DES, we have extracted at different temperatures its thickness, the charge density and mobility of the carriers under crystalline LAO (sample A), and the charge density under amorphous LAO (sample B). This quantity turns out to be higher than in sample A, but a comparison with Hall measurements shows that under amorphous LAO the charges are partly localized at low $T$ with a low activation energy (about 190 K in $k_B$ units), and are thermally activated according to a model for large polarons. The thickness of the q-2DES extracted from our spectra turns out to be 4 $\pm 1$ nm for crystalline LAO, 7 $\pm 2$ nm for amorphous LAO.
- We present a global construction of a so-called D-bracket appearing in the physics literature of Double Field Theory (DFT) and show that if certain integrability criteria are satisfied, it can be seen as a sum of two Courant algebroid brackets. In particular, we show that the local picture of the extended space-time used in DFT fits naturally in the geometrical framework of the para-Hermitian manifolds and that the data of an (almost) para-Hermitian manifold is sufficient to construct the D-bracket. Moreover, the twists of the bracket appearing in DFT can be interpreted in this framework geometrically as a consequence of certain deformations of the underlying para-Hermitian structure.
- Feb 23 2018 stat.ME arXiv:1802.08178v1Background: The development of classification methods for personalized medicine is highly dependent on the identification of predictive genetic markers. In survival analysis it is often necessary to discriminate between influential and non-influential markers. Usually, the first step is to perform a univariate screening step that ranks the markers according to their associations with the outcome. It is common to perform screening using Cox scores, which quantify the associations between survival and each of the markers individually. Since Cox scores do not account for dependencies between the markers, their use is suboptimal in the presence highly correlated markers. Methods: As an alternative to the Cox score, we propose the correlation-adjusted regression survival (CARS) score for right-censored survival outcomes. By removing the correlations between the markers, the CARS score quantifies the associations between the outcome and the set of "de-correlated" marker values. Estimation of the scores is based on inverse probability weighting, which is applied to log-transformed event times. For high-dimensional data, estimation is based on shrinkage techniques. Results: The consistency of the CARS score is proven under mild regularity conditions. In simulations, survival models based on CARS score rankings achieved higher areas under the precision-recall curve than competing methods. Two example applications on prostate and breast cancer confirmed these results. CARS scores are implemented in the R package carSurv. Conclusions: In research applications involving high-dimensional genetic data, the use of CARS scores for marker selection is a favorable alternative to Cox scores even when correlations between covariates are low. Having a straightforward interpretation and low computational requirements, CARS scores are an easy-to-use screening tool in personalized medicine research.
- Sarah E. I. Bosman, Xiaohui Fan, Linhua Jiang, Sophie L. Reed, Yoshiki Matsuoka, George D. Becker, Martin G. HaehneltFeb 23 2018 astro-ph.GA astro-ph.CO arXiv:1802.08177v1We present measurements of the mean and scatter of the IGM Lyman-\alpha opacity at 4.9 < z < 6.1 along the lines of sight of 62 quasars at z > 5.7, the largest sample assembled at these redshifts to date by a factor of two. The sample size enables us to sample cosmic variance at these redshifts more robustly than ever before. The spectra used here were obtained by the SDSS, DES-VHS and SHELLQs collaborations, drawn from the ESI and X-Shooter archives, reused from previous studies or observed specifically for this work. We measure the effective optical depth of Lyman-\alpha in bins of 10, 30, 50 and 70 cMpc h-1, construct cumulative distribution functions under two treatments of upper limits on flux and explore an empirical analytic fit to residual Lyman-\alpha transmission. We verify the consistency of our results with those of previous studies via bootstrap re-sampling and confirm the existence of tails towards high values in the opacity distributions, which may persist down to z = 5.2. Comparing our results with predictions from cosmological simulations, we find further strong evidence against models that include a spatially uniform ionizing background and temperature-density relation. We also compare to IGM models that include either a fluctuating UVB dominated by rare quasars or temperature fluctuations due to patchy reionization. Although both models produce better agreement with the observations, neither fully captures the observed scatter in IGM opacity. Our sample of 62 z > 5.7 quasar spectra opens many avenues for future study of the reionisation epoch.
- Let G be a finite group, let N be a normal subgroup of G, and let theta in Irr(N) be a G-invariant character. We fix a prime p, and we introduce a canonical partition of Irr(G|theta) relative to p. We call each member B_theta of this partition a theta-block, and to each theta-block B_theta we naturally associate a conjugacy class of p-subgroups of G/N, which we call the theta-defect groups of B_theta. If N is trivial, then the theta-blocks are the Brauer p-blocks. Using theta-blocks, we can unify the Gluck-Wolf-Navarro-Tiep theorem and Brauer's Height Zero conjecture in a single statement, which, after work of B. Sambale, turns out to be equivalent to the the Height Zero conjecture. We also prove that the k(B)-conjecture is true if and only if every theta-block B_theta has size less than or equal the size of any of its theta-defect groups, hence bringing normal subgroups to the k(B)-conjecture.
- Feb 23 2018 cond-mat.mtrl-sci arXiv:1802.08172v1Rheometric measurements on assemblies of wet polystyrene bead assemblies, in steady uniform quasistatic shear flow, for varying liquid content within the small saturation (pendular) range of isolated liquid bridges, are supplemented with a systematic study by discrete numerical simulations. Numerical results and experimental ones agree quantitatively is the intergranular friction coefficient is set to 0.09, suitable for the dry material. Shear resistance and solid fraction are recorded as functions of the reduced pressure p, comparing normal stress to capillary bridge tensile strength. The Mohr-Coulomb relation with p-independent cohesion c applies for p above 2. The assumption that contact force contributions to stress act as effective stresses predicts shear strength quite well throughout the numerically investigated range of parameters.. A generalized Mohr-Coulomb cohesion c is defined, which relates to the dry material internal friction, coordination numbers and capillary force network anisotropy. The Rumpf formula approximation, ignoring capillary shear stress is correct for the larger saturation range within the pendular regime, but fails to describe its decrease for small liquid contents.
- In this paper we try to generalize the Haefliger theorem on completly solvable Lie foliations. We prove that: every completely solvable Lie foliation on a compact manifold is the inverse image of a homogenus foliation. Every manifold in this paper is compact and our Lie group G is connexe and simply connexe.
- Feb 23 2018 hep-ex arXiv:1802.08168v1The performance of the missing transverse momentum (E$_{T}^{miss}$) reconstruction with the ATLAS detector is evaluated using data collected in proton-proton collisions at the LHC at a center-of-mass energy of 13 TeV in 2015. To reconstruct E$_{T}^{miss}$, fully calibrated electrons, muons, photons, hadronically decaying $\tau$-leptons, and jets reconstructed from calorimeter energy deposits and charged-particle tracks are used. These are combined with the soft hadronic activity measured by reconstructed charged-particle tracks not associated with the hard objects. Possible double counting of contributions from reconstructed charged-particle tracks from the inner detector, energy deposits in the calorimeter, and reconstructed muons from the muon spectrometer is avoided by applying a signal ambiguity resolution procedure which rejects already used signals when combining the various E$_{T}^{miss}$ contributions. The individual terms as well as the overall reconstructed E$_{T}^{miss}$ are evaluated with various performance metrics for scale (linearity), resolution, and sensitivity to the data-taking conditions. The method developed to determine the systematic uncertainties of the E$_{T}^{miss}$ scale and resolution is discussed. Results are shown based on the full 2015 data sample corresponding to an integrated luminosity of 3.2 fb$^{-1}$.
- Feb 23 2018 stat.ML arXiv:1802.08167v1We present the Causal Gaussian Process Convolution Model (CGPCM), a doubly nonparametric model for causal, spectrally complex dynamical phenomena. The CGPCM is a generative model in which white noise is passed through a causal, nonparametric-window moving-average filter, a construction that we show to be equivalent to a Gaussian process with a nonparametric kernel that is biased towards causally-generated signals. We develop enhanced variational inference and learning schemes for the CGPCM and its previous acausal variant, the GPCM (Tobar et al., 2015b), that significantly improve statistical accuracy. These modelling and inferential contributions are demonstrated on a range of synthetic and real-world signals.
- Feb 23 2018 hep-ph arXiv:1802.08166v1We show that, in the saturation/Color Glass Condensate framework, odd azimuthal harmonics of the two-gluon correlation function with a long-range separation in rapidity are generated by the higher-order saturation corrections in the interactions with the projectile and the target. At the very least, the odd harmonics require three scatterings in the projectile and three scatterings in the target. We derive the leading-order expression for the two-gluon production cross section which generates odd harmonics: the expression includes all-order interactions with the target and three interactions with the projectile. We evaluate the obtained expression both analytically and numerically, confirming that the odd-harmonics contribution to the two-gluon production in the saturation framework is non-zero.
- C. F. Turley, D. B. Fox, A. Keivani, J. J. DeLaunay, D. F. Cowen, M. Mostafa, H. A. Ayala Solares, K. MuraseFeb 23 2018 astro-ph.HE arXiv:1802.08165v1We present results of an archival coincidence analysis between Fermi LAT gamma-ray data and public neutrino data from the IceCube neutrino observatory's 40-string (IC40) and 59-string (IC59) observing runs. Our analysis has the potential to detect either a statistical excess of neutrino + gamma-ray ($\nu$+$\gamma$) emitting transients or, alternatively, individual high gamma-multiplicity events, as might be produced by a neutrino observed by IceCube coinciding with a LAT-detected gamma-ray burst. Dividing the neutrino data into three datasets by hemisphere (IC40, IC59-North, and IC59-South), we construct uncorrelated null distributions by Monte Carlo scrambling of the neutrino datasets. We carry out signal-injection studies against these null distributions, demonstrating sensitivity to individual $\nu$+$\gamma$ events of sufficient gamma-ray multiplicity, and to $\nu$+$\gamma$ transient populations responsible for $>$14\% (IC40), $>$9\% (IC59-North), or $>$8\% (IC59-South) of the gamma-coincident neutrinos observed in these datasets, respectively. Analyzing the unscrambled neutrino data, we identify no individual high-significance neutrino + high gamma-multiplicity events, and no significant deviations from the test statistic null distributions. However, we observe a similar and unexpected pattern in the IC59-North and IC59-South residual distributions that we conclude reflects a possible correlation ($p=7.0\%$) between IC59 neutrino positions and persistently bright portions of the Fermi gamma-ray sky. This possible correlation should be readily testable using eight years of further data already collected by IceCube. We are currently working with Astrophysical Multimessenger Observatory Network (AMON) partner facilities to generate low-latency $\nu$+$\gamma$ alerts from Fermi LAT gamma-ray, IceCube and ANTARES neutrino data and distribute these in real time to AMON follow-up partners.
- We consider multi-armed bandit problems in social groups wherein each individual has bounded memory and shares the common goal of learning the best arm/option. We say an individual learns the best option if eventually (as $t \to \infty$) it pulls only the arm with the highest average reward. While this goal is provably impossible for an isolated individual, we show that, in social groups, this goal can be achieved easily with the aid of social persuasion, i.e., communication. Specifically, we study the learning dynamics wherein an individual sequentially decides on which arm to pull next based on not only its private reward feedback but also the suggestions provided by randomly chosen peers. Our learning dynamics are hard to analyze via explicit probabilistic calculations due to the stochastic dependency induced by social interaction. Instead, we employ the mean-field approximation method from statistical physics and we show: (1) With probability $\to 1$ as the social group size $N \to \infty $, every individual in the social group learns the best option. (2) Over an arbitrary finite time horizon $[0, T]$, with high probability (in $N$), the fraction of individuals that prefer the best option grows to 1 exponentially fast as $t$ increases ($t\in [0, T]$). A major innovation of our mean-filed analysis is a simple yet powerful technique to deal with absorbing states in the interchange of limits $N \to \infty$ and $t \to \infty $. The mean-field approximation method allows us to approximate the probabilistic sample paths of our learning dynamics by a deterministic and smooth trajectory that corresponds to the unique solution of a well-behaved system of ordinary differential equations (ODEs). Such an approximation is desired because the analysis of a system of ODEs is relatively easier than that of the original stochastic system.
- Feb 23 2018 physics.acc-ph arXiv:1802.08158v1Multi-GeV-class laser plasma accelerating modules are key components of laser plasma accelerators, because they can be used as a booster of an upstream plasma or conventional injector or as modular acceleration sections of a multi-staged high energy plasma linac. Such a plasma module, operating in the quasi-linear regime, has been designed for the 5 GeV laser plasma accelerator stage (LPAS) of the EuPRAXIA project. The laser pulse ($\sim$150 TW, $\sim$ 15 J) is quasi-matched into a plasma channel ($n_{\rm p} = 1.5\times 10^{17}$ cm$^{-3}$, $L\sim$ 30 cm) and the bi-Gaussian electron beam is externally injected into the wakefield. The beam emittance is preserved through the acceleration by matching the beam size to the transverse focusing fields. And a final energy spread of $<$1\% has been achieved by optimizing the beam loading effect. Several methods have been proposed to reduce the slice energy spread and are found to be effective. The simulations were conducted with the 3D PIC code Warp in the Lorentz boosted frame.
- Feb 23 2018 cs.CE physics.acc-ph arXiv:1802.08157v1Magnetic quadrupoles are essential components of particle accelerators like the Large Hadron Collider. In order to study numerically the stability of the particle beam crossing a quadrupole, a large number of particle revolutions in the accelerator must be simulated, thus leading to the necessity to preserve numerically invariants of motion over a long time interval and to a substantial computational cost, mostly related to the repeated evaluation of the magnetic vector potential. In this paper, in order to reduce this cost, we first consider a specific gauge transformation that allows to reduce significantly the number of vector potential evaluations. We then analyze the sensitivity of the numerical solution to the interpolation procedure required to compute magnetic vector potential data from gridded precomputed values at the locations required by high order time integration methods. Finally, we compare several high order integration techniques, in order to assess their accuracy and efficiency for these long term simulations. Explicit high order Lie methods are considered, along with implicit high order symplectic integrators and conventional explicit Runge Kutta methods. Among symplectic methods, high order Lie integrators yield optimal results in terms of cost/accuracy ratios, but non symplectic Runge Kutta methods perform remarkably well even in very long term simulations. Furthermore, the accuracy of the field reconstruction and interpolation techniques are shown to be limiting factors for the accuracy of the particle tracking procedures.

Black Holes and Complexity Classes

Beni Yoshida Feb 13 2018 19:53 UTCAbhinav Deshpande Feb 10 2018 15:42 UTC

...(continued)I see. Yes, the epsilon ball issue seems to be a thorny one in the prevalent definition, since the gate complexity to reach a target state from any of a fixed set of initial states depends on epsilon, and not in a very nice way (I imagine that it's all riddled with discontinuities). It would be inte

Elizabeth Crosson Feb 10 2018 05:49 UTC

...(continued)Thanks for the correction Abhinav, indeed I meant that the complexity of |psi(t)> grows linearly with t.

Producing an arbitrary state |phi> exactly is also too demanding for the circuit model, by the well-known argument that given any finite set of gates, the set of states that can be reached i

Abhinav Deshpande Feb 09 2018 20:21 UTC

...(continued)Elizabeth, interesting comment! Did you mean to say that the complexity of $U(t)$ increases linearly with $t$ as opposed to exponentially?

Also, I'm confused about your definition. First, let us assume that the initial state is well defined and is $|\psi(0)\rangle $.

If you define the complexit

Elizabeth Crosson Feb 08 2018 04:27 UTC

...(continued)The complexity of a state depends on the dynamics that one is allowed to use to generate the state. If we restrict the dynamics to be "evolving according a specific Hamiltonian H" then we immediately have that the complexity of U(t) = exp(i H t) grows exponentially with t, up until recurrences that

Danial Dervovic Feb 05 2018 15:03 UTC

...(continued)Thank you Māris for the extremely well thought-out and articulated points here.

I think this very clearly highlights the need to think explicitly about the precompute time if using the lifting to directly simulate the quantum walk, amongst other things.

I wish to give a well-considered respons

Michael A. Sherbon Feb 02 2018 15:56 UTC

...(continued)Good general review on the Golden Ratio and Fibonacci ... in physics, more examples are provided in the paper “Fine-Structure Constant from Golden Ratio Geometry,” Specifically,

$$\alpha^{-1}\simeq\frac{360}{\phi^{2}}-\frac{2}{\phi^{3}}+\frac{\mathit{A^{2}}}{K\phi^{4}}-\frac{\mathit{A^{\math

Māris Ozols Feb 01 2018 17:53 UTC

...(continued)This paper considers the problem of using "lifted" Markov chains to simulate the mixing of coined quantum walks. The Markov chain has to approximately (in the total variational distance) sample from the distribution obtained by running the quantum walk for a randomly chosen time $t \in [0,T]$ follow

Johnnie Gray Feb 01 2018 12:59 UTC

Thought I'd just comment here that we've rather significantly updated this paper.

wenling yang Jan 30 2018 19:08 UTC

off-loading is an interesting topic. Investigating the off-loading computation under the context of deep neural networks is a novel insight.

- Supported by Silverpond.