Top arXiv papers

sign in to customize
  • PDF
    Quantum collision models (CMs) provide advantageous case studies for investigating major issues in open quantum systems theory, and especially quantum non-Markovianity. After reviewing their general definition and distinctive features, we illustrate the emergence of a CM in a familiar quantum optics scenario. This task is carried out by highlighting the close connection between the well-known input-output formalism and CMs. Within this quantum optics framework, usual assumptions in the CMs' literature - such as considering a bath of non-interacting yet initially correlated ancillas - have a clear physical origin.
  • PDF
    Fox conjectured the Alexander polynomial of an alternating knot is trapezoidal, i.e. the coefficients first increase, then stabilize and finally decrease in a symmetric way. Recently, Hirasawa and Murasugi further conjectured a relation between the number of the stable coefficients in the Alexander polynomial and the signature invariant. In this paper we prove the Hirasawa-Murasugi conjecture for two-bridge knots.
  • Dec 15 2017 hep-th gr-qc arXiv:1712.04992v1
    PDF
    In this presentation, I review recent work with Mike Appels and David Kubiznak on thermodynamics of accelerating black holes. I start by reviewing the geometry of accelerating black holes, focussing on the conical deficit responsible for the 'force' causing the black hole to accelerate. Then I discuss black hole thermodynamics with conical deficits, showing how to include the tension of the deficit as a thermodynamic variable, and introducing a canonically conjugate \it thermodynamic length. Finally, I describe the thermodynamics of the slowly accelerating black hole in anti-de Sitter spacetime.
  • PDF
    This manuscript is a revision of our previous work that develops the three layer model for the surface second-harmonic generation yield; here, we add the necessary algebra to derive expressions that include elliptically polarized incoming fields. This allows yet another degree of flexibility to the previous work, as elliptical polarization is the most general polarization case possible. The three layer model considers that the SH conversion takes place in a thin layer just below the surface of a material. This layer lies under the vacuum region, and above any bulk material that is not SHG active. The inherent flexibility of this model makes it an excellent choice for thin films and 2D materials.
  • PDF
    In this paper, we show that the price of an European call option, whose underlying asset price is driven by the space-time fractional diffusion, can be expressed in terms of rapidly convergent double-series. The series formula can be obtained from the Mellin-Barnes representation of the option price with help of residue summation in $\mathbb{C}^2$. We also derive the series representation for the associated risk-neutral factors, obtained by Esscher transform of the space-time fractional Green functions.
  • PDF
    The advent of non-volatile memory (NVM) technologies like PCM, STT, memristors and Fe-RAM is believed to enhance the system performance by getting rid of the traditional memory hierarchy by reducing the gap between memory and storage. This memory technology is considered to have the performance like that of DRAM and persistence like that of disks. Thus, it would also provide significant performance benefits for big data applications by allowing in-memory processing of large data with the lowest latency to persistence. Leveraging the performance benefits of this memory-centric computing technology through traditional memory programming is not trivial and the challenges aggravate for parallel/concurrent applications. To this end, several programming abstractions have been proposed like NVthreads, Mnemosyne and intel's NVML. However, deciding upon a programming abstraction which is easier to program and at the same time ensures the consistency and balances various software and architectural trade-offs is openly debatable and active area of research for NVM community. We study the NVthreads, Mnemosyne and NVML libraries by building a concurrent and persistent set and open addressed hash-table data structure application. In this process, we explore and report various tradeoffs and hidden costs involved in building concurrent applications for persistence in terms of achieving efficiency, consistency and ease of programming with these NVM programming abstractions. Eventually, we evaluate the performance of the set and hash-table data structure applications. We observe that NVML is easiest to program with but is least efficient and Mnemosyne is most performance friendly but involves significant programming efforts to build concurrent and persistent applications.
  • PDF
    The MAJORANA Collaboration is searching for the neutrinoless double-beta decay of the nucleus Ge-76. The MAJORANA DEMONSTRATOR is an array of germanium detectors deployed with the aim of implementing background reduction techniques suitable for a tonne scale Ge-76-based search (the LEGEND collaboration). In the DEMONSTRATOR, germanium detectors operate in an ultra-pure vacuum cryostat at 80 K. One special challenge of an ultra-pure environment is to develop reliable cables, connectors, and electronics that do not significantly contribute to the radioactive background of the experiment. This paper highlights the experimental requirements and how these requirements were met for the MAJORANA DEMONSTRATOR, including plans to upgrade the wiring for higher reliability in the summer of 2018. Also described are requirements for LEGEND R&D efforts underway to meet these additional requirements.
  • PDF
    Recent detection of suborbital gamma-ray variability of Flat Spectrum Radio Quasar (FSRQ) 3C 279 by Fermi Large Area Telescope (LAT) is in severe conflict with established models of blazar emission. This paper presents the results of suborbital analysis of the Fermi/LAT data for the brightest gamma-ray flare of another FSRQ blazar 3C 454.3 in November 2010 (MJD 55516-22). Gamma-ray light curves are calculated for characteristic time bin lengths as short as 3 min. The measured variations of the 0.1-10 GeV photon flux are tested against the hypothesis of steady intraorbit flux. In addition, the structure function is calculated for absolute photon flux differences and for their significances. Significant gamma-ray flux variations are measured only over time scales longer than ~5h, which is consistent with the standard blazar models.
  • PDF
    The study of heavy-light meson masses should provide a way to determine renormalized quark masses and other properties of heavy-light mesons. In the context of lattice QCD, for example, it is possible to calculate hadronic quantities for arbitrary values of the quark masses. In this paper, we address two aspects relating heavy-light meson masses to the quark masses. First, we introduce a definition of the renormalized quark mass that is free of both scale dependence and renormalon ambiguities, and discuss its relation to more familiar definitions of the quark mass. We then show how this definition enters a merger of the descriptions of heavy-light masses in heavy-quark effective theory and in chiral perturbation theory ($\chi$PT). For practical implementations of this merger, we extend the one-loop $\chi$PT corrections to lattice gauge theory with heavy-light mesons composed of staggered fermions for both quarks. Putting everything together, we obtain a practical formula to describe all-staggered heavy-light meson masses in terms of quark masses as well as some lattice artifacts related to staggered fermions. In a companion paper, we use this function to analyze lattice-QCD data and extract quark masses and some matrix elements defined in heavy-quark effective theory.
  • PDF
    Secure and reliable transmission over communication channels is first characterized by Wyner's wiretap channel (WTC) model. In recent years, the WTC with noiseless feedback (WTC-NF) attracts a lot attention, and it has been shown that the legal receiver's feedback enlarges the secrecy capacity of the WTC. Even so, the current feedback strategy for the WTC mainly focuses on generating key used for encrypting the transmitted message, and this strategy does not achieve the secrecy capacity of the WTC-NF. In this paper, a new coding strategy for the WTC-NF is presented. Besides used for generating key, the legal receiver's feedback of this new strategy is also used to produced a help information which helps the legal receiver to ameliorate his decoding performance. For the WTC-NF, the proposed new feedback strategy is shown to be better than the already existing one, and a binary example is given to further explain these results.
  • PDF
    With the fast development of Internet of things (IoT), the fifth generation (5G) wireless networks need to provide massive connectivity of IoT devices and meet the demand for low latency. To satisfy these requirements, Non-Orthogonal Multiple Access (NOMA) has been recognized as a promising solution for 5G networks to significantly improve the network capacity. In parallel with the development of NOMA techniques, Mobile Edge Computing (MEC) is becoming one of the key emerging technologies to reduce the latency and improve the Quality of Service (QoS) for 5G networks. In order to capture the potential gains of NOMA in the context of MEC, this paper proposes an edge computing aware NOMA technique which can enjoy the benefits of uplink NOMA in reducing MEC users' uplink energy consumption. To this end, we formulate a NOMA based optimization framework which minimizes the energy consumption of MEC users via optimizing the user clustering, computing and communication resource allocation, and transmit powers. In particular, similar to frequency Resource Blocks (RBs), we divide the computing capacity available at the cloudlet to computing RBs. Accordingly, we explore the joint allocation of the frequency and computing RBs to the users that are assigned to different order indices within the NOMA clusters. We also design an efficient heuristic algorithm for user clustering and RBs allocation, and formulate a convex optimization problem for the power control to be solved independently per NOMA cluster. The performance of the proposed NOMA scheme is evaluated via simulations.
  • PDF
    We present a flavor and energy inference analysis for each high-energy neutrino event observed by the IceCube observatory during six years of data taking. Our goal is to obtain, for the first time, an estimate of the posterior probability distribution for the most relevant properties, such as the neutrino energy and flavor, of the neutrino-nucleon interactions producing shower and track events in the IceCube detector. For each event the main observables in the IceCube detector are the deposited energy and the event topology (showers or tracks) produced by the Cherenkov light by the transit through a medium of charged particles created in neutrino interactions. It is crucial to reconstruct from these observables the properties of the neutrino which generated such event. Here we describe how to achieve this goal using Bayesian inference and Markov chain Monte Carlo methods.
  • PDF
    In this paper, we propose a trajectory optimization for computing smooth collision free trajectories for nonholonomic curvature bounded vehicles among static and dynamic obstacles. One of the key novelties of our formulation is a hierarchal optimization routine which alternately operates in the space of angular accelerations and linear velocities. That is, the optimization has a two layer structure wherein angular accelerations are optimized keeping the linear velocities fixed and vice versa. If the vehicle/obstacles are modeled as circles than the velocity optimization layer can be shown to have the computationally efficient difference of convex structure commonly observed for linear systems. This leads to a less conservative approximation as compared to that obtained by approximating each polygon individually through its circumscribing circle. On the other hand, it leads to optimization problem with less number of constraints as compared to that obtained when approximating polygons as multiple overlapping circles. We use the proposed trajectory optimization as the basis for constructing a Model Predictive Control framework for navigating an autonomous car in complex scenarios like overtaking, lane changing and merging. Moreover, we also highlight the advantages provided by the alternating optimization routine. Specifically, we show it produces trajectories which have comparable arc lengths and smoothness as compared to those produced with joint simultaneous optimization in the space of angular accelerations and linear velocities. However, importantly, the alternating optimization provides some gain in computational time.
  • PDF
    The complete theory of electrical conductivity of graphene at arbitrary temperature is developed with taken into account mass-gap parameter and chemical potential. Both the in-plane and out-of-plane conductivities of graphene are expressed via the components of the polarization tensor in (2+1)-dimensional space-time analytically continued to the real frequency axis. Simple analytic expressions for both the real and imaginary parts of the conductivity of graphene are obtained at zero and nonzero temperature. They demonstrate an interesting interplay depending on the values of mass gap and chemical potential. In the local limit, several results obtained earlier using various approximate and phenomenological approaches are reproduced, refined and generalized. The numerical computations of both the real and imaginary parts of the conductivity of graphene are performed to illustrate the obtained results. The analytic expressions for the conductivity of graphene obtained in this paper can serve as a guide in the comparison between different theoretical approaches and between experiment and theory.
  • PDF
    We introduce a class of (0,2) superconformal field theories based on hybrid geometries, generalizing various known constructions. We develop techniques for the computation of the complete massless spectrum when the theory can be interpreted as determining a perturbative heterotic string compactification. We provide evidence for surprising properties regarding RG flows and IR accidental symmetries in (0,2) hybrid CFTs. We also study the conditions for embedding a hybrid theory in a particular class of gauged linear sigma models. This perspective suggests that our construction generates models which cannot be realized or analyzed by previously known methods.
  • PDF
    Define a $\mathcal V^{(d)}$-algebra as an associative algebra with a symmetric and invariant co-inner product of degree $d$. Here, we consider $\mathcal V^{(d)}$ as a dioperad which includes operations with zero inputs. We show that the quadratic dual of $\mathcal V^{(d)}$ is $(\mathcal V^{(d)})^!=\mathcal V^{(-d)}$ and prove that $\mathcal V^{(d)}$ is Koszul. We also show that the corresponding properad is not Koszul contractible.
  • PDF
    We present a new study of the spatial distribution and ages of the star clusters in the Small Magellanic Cloud (SMC). To detect and estimate the ages of the star clusters we rely on the new fully-automated method developed by Bitsakis et al. (2017). Our code detects 1319 star clusters in the central 18 deg$^{2}$ of the SMC we surveyed (1108 of which have never been reported before). The age distribution of those clusters suggests enhanced cluster formation around 240 Myr ago. It also implies significant differences in the cluster distribution of the bar with respect to the rest of the galaxy, with the younger clusters being predominantly located in the bar. Having used the same set-up, and data from the same surveys as for our previous study of the LMC, we are able to robustly compare the cluster properties between the two galaxies. Our results suggest that the bulk of the clusters in both galaxies were formed approximately 300 Myr ago, probably during a direct collision between the two galaxies. On the other hand, the locations of the young ($\le$50 Myr) clusters in both Magellanic Clouds, found where their bars join the HI arms, suggest that cluster formation in those regions is a result of internal dynamical processes. Finally, we discuss the potential causes of the apparent outside-in quenching of cluster formation that we observe in the SMC. Our findings are consistent with an evolutionary scheme where the interactions between the Magellanic Clouds constitute the major mechanism driving their overall evolution.
  • PDF
    We present a terahertz spectroscopic study of polar ferrimagnet FeZnMo$_3$O$_8$. Our main finding is a giant high-temperature optical diode effect, or nonreciprocal directional dichroism, where the transmitted light intensity in one direction is over 100 times lower than intensity transmitted in the opposite direction. The effect takes place in the paramagnetic phase with no long-range magnetic order in the crystal, which contrasts sharply with all existing reports of the terahertz optical diode effect in other magnetoelectric materials, where the long-range magnetic ordering is a necessary prerequisite. In \fzmo, the effect occurs resonantly with a strong magnetic dipole active transition centered at 1.27 THz and assigned as electron spin resonance between the eigenstates of the single-ion anisotropy Hamiltonian. We propose that the optical diode effect in paramagnetic FeZnMo$_3$O$_8$ is driven by signle-ion terms in magnetoelectric free energy.
  • PDF
    The fractal dimension of domain walls produced by changing the boundary conditions from periodic to anti-periodic in one spatial direction is studied using both the strong-disorder renormalization group and the greedy algorithm for the Edwards-Anderson Ising spin-glass model for up to six space dimensions. We find that for five or less space dimensions, the fractal dimension is less than the space dimension. This means that interfaces are not space filling, thus implying replica symmetry breaking is absent in space dimensions fewer than six. However, the fractal dimension approaches the space dimension in six dimensions, indicating that replica symmetry breaking occurs above six dimensions. In two space dimensions, the strong-disorder renormalization group results for the fractal dimension are in good agreement with essentially exact numerical results, but the small difference is significant. We discuss the origin of this close agreement. For the greedy algorithm there is analytical expectation that the fractal dimension is equal to the space dimension in six dimensions and our numerical results are consistent with this expectation.
  • PDF
    We present the first high significance detection ($4.1\sigma$) of the Baryon Acoustic Oscillations (BAO) feature in the galaxy bispectrum of the twelfth data release (DR12) of the Baryon Oscillation Spectroscopic Survey (BOSS) CMASS sample ($0.43 \leq z \leq 0.7$). We measured the scale dilation parameter, $\alpha$, using the power spectrum, bispectrum, and both simultaneously for DR12, plus 2048 PATCHY mocks in the North and South Galactic Caps (NGC and SGC, respectively), and the volume weighted averages of those two samples (N+SGC). The fitting to the mocks validated our analysis pipeline, yielding values consistent with the mock cosmology. By fitting to the power spectrum and bispectrum separately, we tested the robustness of our results, finding consistent values from the NGC, SGC and N+SGC in all cases. We found $D_{\mathrm{V}} = 2032 \pm 24 (\mathrm{stat.}) \pm 15 (\mathrm{sys.})$ Mpc, $D_{\mathrm{V}} = 2038 \pm 55 (\mathrm{stat.}) \pm 15 (\mathrm{sys.})$ Mpc, and $D_{\mathrm{V}} = 2031 \pm 22 (\mathrm{stat.}) \pm 10 (\mathrm{sys.})$ Mpc from the N+SGC power spectrum, bispectrum and simultaneous fitting, respectively.
  • PDF
    The aim of this paper is to analyze the long-time behaviour of extended Runge--Kutta--Nyström (ERKN) integrators for highly oscillatory Hamiltonian systems. It is important to note that the well-known Gautschi-type methods of order two yield examples of ERKN integrators. To this end, we use the modulated Fourier expansion to analyze the long-time numerical energy conservation. We will show that the ERKN integrators with symmetry conditions have two almost-invariants and have a near conservation of the total and oscillatory energy over a long term.
  • PDF
    V582 Aur is an FU Ori-type young eruptive star in outburst since $\sim$1985. The eruption is currently in a relatively constant plateau phase, with photometric and spectroscopic variability superimposed. Here we will characterize the progenitor of the outbursting object, explore its environment, and analyse the temporal evolution of the eruption. We are particularly interested in the physical origin of the two deep photometric dips, one occurred in 2012, and one is ongoing since 2016. We collected archival photographic plates, and carried out new optical, infrared, and millimeter wave photometric and spectroscopic observations between 2010 and 2017, with high sampling rate during the current minimum. Beside analysing the color changes during fading, we compiled multiepoch spectral energy distributions, and fitted them with a simple accretion disk model. Based on pre-outburst data and a millimeter continuum measurement, we suggest that the progenitor of the V582 Aur outburst is a low-mass T Tauri star with average properties. The mass of an unresolved circumstellar structure, probably a disk, is 0.04 M$_{\odot}$. The optical and near-infrared spectra demonstrate the presence of hydrogen and metallic lines, show the CO bandhead in absorption, and exhibit a variable H$\alpha$ profile. The color variations strongly indicate that both the $\sim$1 year long brightness dip in 2012, and the current minimum since 2016 are caused by increased extinction along the line of sight. According to our accretion disk models, the reddening changed from $A_V$=4.5 mag to 12.5 mag, while the accretion rate remained practically constant. Similarly to the models of the UXor phenomenon of intermediate and low-mass young stars, orbiting disk structures could be responsible for the eclipses.
  • PDF
    1T-TiSe$_2$ is an emblematic system for it was the earliest crystal conjectured to display the elusive excitonic insulator ground state, of which the CDW and PLD would be a natural manifestation. But agreement and definitive experimental proof have not materialized. We demonstrate that, to describe with quantitative accuracy the experimental doping and temperature phase diagram related to the CDW transition, one must explicitly account for electron-electron interactions and the excitonic instability that arises from direct coupling between electron and hole pockets. Thorough and systematic calculations of the electronic and phonon spectrum based on density functional perturbation theory are shown here to predict the suppression of the CDW/PLD phase beyond a critical doping which overshoots the experimental value by about one order of magnitude. In contrast, a self-consistent many-body calculation of the excitonic order parameter and renormalized bandstructure is able to, alone, capture the experimental phase diagram in extremely good qualitative and quantitative agreement. Together with recent experiments that probed the collective excitations characteristic of the excitonic phase, our results contribute to settling the pivotal role played by electron-electron interactions in precipitating the CDW transition in TiSe$_2$.
  • PDF
    The Randall-Sundrum model with a deformed metric can generate light Kaluza-Klein (KK) Higgs modes consistent with the electroweak precision analysis for a certain range of parameters. The first KK mode of the Higgs ($h_{1}$) in such a model could lie in the mass range varying from 800 GeV to 1.3 TeV. We find that the $h_{1}$ is gaugephobic and decays dominantly into a $t\bar{t}$ pair. The search strategy for $h_{1}$ decaying to $t\bar{t}$ at the Large Hadron Collider (LHC) in this low mass range has been studies. We have used substructure tools to suppress the large QCD background associated with this channel. We find that $h_{1}$ can be probed at the LHC.
  • PDF
    We investigate the effects of AGN feedback on the cosmological evolution of an isolated elliptical galaxy by performing two-dimensional high-resolution hydrodynamical numerical simulations. The inner boundary of the simulation is chosen so that the Bondi radius is resolved, which is crucial for the determination of the mass accretion rate of the AGN. According to the theory of black hole accretion, there are two accretion modes, hot and cold, which correspond to different accretion rates and have different radiation and wind outputs. In our simulations, the two modes are discriminated and the feedback effects by radiation and wind in each mode are taken into account. The main improvement of the present work compared to previous ones is that we adopt the most updated AGN physics, including the descriptions of radiation and wind from the hot accretion flows and wind from cold accretion disks. Physical processes like star formation, Type Ia and Type II supernovae are taken into account. We study the AGN light curve, typical AGN lifetime, growth of the black hole mass, AGN duty-cycle, star formation, and the X-ray surface brightness of the galaxy. We have compared our simulation results with observations and found general consistency. Comparisons with previous simulation works find significant differences, indicating the importance of AGN physics. The respective roles of radiation and wind feedbacks are examined and it is found that they are different for different problems of interest such as AGN luminosity and star formation. We find that it is hard to neglect any of them, so we suggest to simply use the names of "cold feedback mode" and "hot feedback mode" to replace the currently used names.
  • PDF
    Electromagnetic metamaterials offer a great avenue to engineer and amplify the nonlinear response of materials. Their electric, magnetic, and magneto-electric linear and nonlinear response are related to their structure, providing unprecedented liberty to control those properties. Both the linear and the nonlinear properties of metamaterials are typically anisotropic. While the methods to retrieve the effective linear properties are well established, existing nonlinear retrieval methods have serious limitations. In the present work, we generalize a nonlinear transfer matrix approach to account for all nonlinear susceptibility terms and show how to use this approach to retrieve all effective nonlinear susceptibilities of metamaterial elements. The approach is demonstrated using sum frequency generation, but can be applied to other second order or higher order processes.
  • PDF
    We present a study of hierarchical structure in the Perseus molecular cloud, from the scale of the entire cloud ($\gtrsim$10 pc) to smaller clumps ($\sim$1 pc), cores ($\sim$0.05-0.1 pc), envelopes ($\sim$300-3000 AU) and protostellar objects ($\sim$15 AU). We use new observations from the Submillimeter Array (SMA) large project "Mass Assembly of Stellar Systems and their Evolution with the SMA (MASSES)" to probe the envelopes, and recent single-dish and interferometric observations from the literature for the remaining scales. This is the first study to analyze hierarchical structure over five scales in the same cloud complex. We compare the number of fragments with the number of Jeans masses in each scale to calculate the Jeans efficiency, or the ratio of observed to expected number of fragments. The velocity dispersion is assumed to arise either from purely thermal motions, or from combined thermal and non-thermal motions inferred from observed spectral line widths. For each scale, thermal Jeans fragmentation predicts more fragments than observed, corresponding to inefficient thermal Jeans fragmentation. For the smallest scale, thermal plus non-thermal Jeans fragmentation also predicts too many protostellar objects. However at each of the larger scales thermal plus non-thermal Jeans fragmentation predicts fewer than one fragment, corresponding to no fragmentation into envelopes, cores, and clumps. Over all scales, the results are inconsistent with complete Jeans fragmentation based on either thermal or thermal plus non-thermal motions. They are more nearly consistent with inefficient thermal Jeans fragmentation, where the thermal Jeans efficiency increases from the largest to the smallest scale.
  • PDF
    In light of a discrepancy of the direct $CP$ violation in $K\to\pi\pi$ decays, $\varepsilon'/\varepsilon_K$, we investigate gluino contributions to the electroweak penguin, where flavor violations are induced by squark trilinear couplings. Top-Yukawa contributions to $\Delta S = 2$ observables are taken into account, and vacuum stability conditions are evaluated in detail. It is found that this scenario can explain the discrepancy of $\varepsilon'/\varepsilon_K$ for the squark mass smaller than 5.6 TeV. We also show that the gluino contributions can amplify $\mathcal{B}(K \to \pi \nu \overline{\nu})$, $\mathcal{B}(K_S \to \mu^+ \mu^-)_{\rm eff}$ and $\Delta A_{\rm CP}(b\to s\gamma)$. Such large effects could be measured in future experiments.
  • PDF
    Bow shocks and related density enhancements produced by the winds of massive stars moving through the interstellar medium provide important information regarding the motions of the stars, the properties of their stellar winds, and the characteristics of the local medium. Since bow shocks are aspherical structures, light scattering within them produces a net polarization signal even if the region is spatially unresolved. Scattering opacity arising from free electrons and dust leads to a distribution of polarized intensity across the bow shock structure. That polarization encodes information about the shape, composition, opacity, density, and ionisation state of the material within the structure. In this paper we use the Monte Carlo radiative transfer code SLIP to investigate the polarization created when photons scatter in a bow shock-shaped region of enhanced density surrounding a stellar source. We present results assuming electron scattering, and investigate the polarization behaviour as a function of optical depth, temperature, and source of photons for two different cases: pure scattering and scattering with absorption. In both regimes we consider resolved and unresolved cases. We discuss the implication of these results as well as their possible use along with observational data to constrain the properties of observed bow shock systems. In different situations and under certain assumptions, our simulations can constrain viewing angle, optical depth and temperature of the scattering region, and the relative luminosities of the star and shock.
  • PDF
    We determine conditions for the formation of compressible stripes near the quantum Hall effect (QHE) edges of top-gated epitaxial graphene on Si-terminated SiC (G/SiC) and compare those to graphene exfoliated onto insulating substrate in the field-effect-transistor (GraFET) geometry. For G/SiC, a large density of localised surface states on SiC just underneath graphene layer and charge transfer between them lead both to doping of graphene and to screening of potential profile near its edge. This suppresses formation of compressible stripes near QHE edges in graphene, making them much narrower than the corresponding compressible stripes in GraFETs.
  • PDF
    We determine abundance ratios of 37 dwarf ellipticals (dEs) in the nearby Virgo cluster. This sample is representative of the early-type population of galaxies in the absolute magnitude range -19.0 < Mr < -16.0. We analyze their absorption line-strength indices by means of index-index diagrams and scaling relations and use the stellar population models to interpret them. We present ages, metallicities and abundance ratios obtained from these dEs within an aperture size of Re/8. We calculate [Na/Fe] from NaD, [Ca/Fe] from Ca4227 and [Mg/Fe] from Mgb. We find that [Na/Fe] is under-abundant with respect to solar while [Mg/Fe] is around solar. This is exactly opposite to what is found for giant ellipticals, but follows the trend with metallicity found previously for the Fornax dwarf NGC 1396. We discuss possible formation scenarios that can result in such elemental abundance patterns and we speculate that dEs have disk-like SFH favouring them to originate from late-type dwarfs or small spirals. Na-yields appear to be very metal-dependent, in agreement with studies of giant ellipticals, probably due to the large dependence on the neutron-excess in stars. We conclude that dEs have undergone a considerable amount of chemical evolution, they are therefore not uniformly old, but have extended SFH, similar to many of the Local Group galaxies.
  • PDF
    We present a field theoretic treatment of an adiabatic quantum motor. We explicitly discuss a motor termed Thouless motor which is based on a Thouless pump operating in reverse. When a sliding periodic potential is considered as the motor degree of freedom, a bias voltage applied to the electron channel sets the motor in motion. We investigate a Thouless motor whose electron channel is modeled as a Luttinger liquid. Interactions increase the gap opened by the periodic potential. For an infinite Luttinger liquid the coupling induced friction is enhanced by electron-electron interactions. When the LL is ultimately coupled to Fermi liquid reservoirs, the dissipation reduces to its value for a noninteracting electron system for a constant motor velocity. Our results can also be applied to a motor based on a nanomagnet coupled to a quantum spin Hall edge.
  • PDF
    The non-trivial evolution of wavefunctions in momentum space leads to novel phases and responses. As with any topological property, a key challenge lies in finding experiments that identify the non-local characteristics. Indeed, revealing this Berry curvature often requires extreme conditions and/or surface sensitive probes. These rely on measuring the Berry phase acquired through a closed loop evolution in momentum space, or through the bulk-boundary correspondence leading to new states at the surface. Alternatively, various components of the electronic structure can be detected by the bulk photovoltaic effect (BPVE) where non-linearity rectifies light to dc currents. Weyl semimetals are particularly promising, as their non-degenerate, Dirac-like, chiral states produce diverging Berry curvature. Here we report a room temperature, colossal BPVE in the Weyl semimetal TaAs, which is an order of magnitude larger than any previous measurement. By varying the polarization of light with respect to the crystal axis, we establish the collosal BPVE resulting from the non-trivial topology of Weyl fermions, i.e. the diverging Berry curvature near the Weyl nodes. The BPVE in Weyl semiemtals we uncover can be exploited for detecting electron topology, broadband detectors, and solar/thermal energy conversion.
  • PDF
    White dwarfs are often found in binary systems with orbital periods ranging from tens of minutes to hours in which they can accrete gas from their companion stars. In about 15% of these binaries, the magnetic field of the white dwarf is strong enough ($\geq 10^6$ Gauss) to channel the accreted matter along field lines onto the magnetic poles. The remaining systems are referred to as "non-magnetic", since to date there has been no evidence that they have a dynamically significant magnetic field. Here we report an analysis of archival optical observations of the "non-magnetic" accreting white dwarf in the binary system MV Lyrae (hereafter MV Lyr), whose lightcurve displayed quasi-periodic bursts of $\approx 30$ minutes duration every $\approx 2$ hours. The observations indicate the presence of an unstable magnetically-regulated accretion mode, revealing the existence of magnetically gated accretion, where disk material builds up around the magnetospheric boundary (at the co-rotation radius) and then accretes onto the white dwarf, producing bursts powered by the release of gravitational potential energy. We infer a surface magnetic field strength for the white dwarf in MV Lyr between $2 \times 10^4 \leq B \leq 10^5$ Gauss, too low to be detectable by other current methods. Our discovery provides a new way of studying the strength and evolution of magnetic fields in accreting white dwarfs and extends the connections between accretion onto white dwarfs, young stellar objects and neutron stars, for which similar magnetically gated accretion cysles have been identified.
  • PDF
    The recent 'Planet Nine' hypothesis has led to many observational and archival searches for this giant planet proposed to orbit the Sun at hundreds of astronomical units. While trans-Neptunian object searches are typically conducted in the optical, models suggest Planet Nine could be self-luminous and potentially bright enough at ~3-5 microns to be detected by the Wide-field Infrared Survey Explorer (WISE). We have previously demonstrated a Planet Nine search methodology based on time-resolved WISE coadds, allowing us to detect moving objects much fainter than would be possible using single-frame extractions. In the present work, we extend our 3.4 micron (W1) search to cover more than three quarters of the sky and incorporate four years of WISE observations spanning a seven year time period. This represents the deepest and widest-area WISE search for Planet Nine to date. We characterize the spatial variation of our survey's sensitivity and rule out the presence of Planet Nine in the parameter space searched at W1 < 16.7 in high Galactic latitude regions (90% completeness).
  • PDF
    The enigmatic star KIC 8462852, informally known as "Boyajian's Star", has exhibited unexplained variability from both short timescale (days) dimming events, and years-long fading in the Kepler mission. No single physical mechanism has successfully explained these observations to date. Here we investigate the ultraviolet variability of KIC 8462852 on a range of timescales using data from the GALEX mission that occurred contemporaneously with the Kepler mission. The wide wavelength baseline between the Kepler and GALEX data provides a unique constraint on the nature of the variability. Using 1600 seconds of photon-counting data from four GALEX visits spread over 70 days in 2011, we find no coherent NUV variability in the system on 10-100 second or months timescales. Comparing the integrated flux from these 2011 visits to the 2012 NUV flux published in the GALEX-CAUSE Kepler survey, we find a 3% decrease in brightness for KIC 8462852. We find this level of variability is significant, but not necessarily unusual for stars of similar spectral type in the GALEX data. This decrease coincides with the secular optical fading reported by Montet & Simon (2016). We find the multi-wavelength variability is somewhat inconsistent with typical interstellar dust absorption, but instead favors a R$_V$ = 5.0 $\pm$ 0.9 reddening law potentially from circumstellar dust.
  • PDF
    Galactic winds regulate star formation in disk galaxies and help to enrich the circum-galactic medium. They are therefore crucial for galaxy formation, but their driving mechanism is still poorly understood. Recent studies have demonstrated that cosmic rays (CRs) can drive outflows if active CR transport is taken into account. Using hydrodynamical simulations of isolated galaxies with virial masses between $10^{10}$ and $10^{13}\mathrm{~M_\odot}$, we study how the properties of CR-driven winds depend on halo mass. CRs are treated in a two-fluid approximation and their transport is modelled through isotropic or anisotropic diffusion. We find that CRs are only able to drive mass-loaded winds beyond the virial radius in haloes with masses below $10^{12}\mathrm{~M_\odot}$. For our lowest examined halo mass, the wind is roughly spherical and has velocities of $\sim20\mathrm{~km\;s^{-1}}$. With increasing halo mass, the wind becomes biconical and can reach ten times higher velocities. The mass loading factor drops rapidly with virial mass, a dependence that approximately follows a power-law with a slope between $-1$ and $-2$. This scaling is slightly steeper than observational inferences, and also steeper than commonly used prescriptions for wind feedback in cosmological simulations. The slope is quite robust to variations of the CR injection efficiency or the CR diffusion coefficient. In contrast to the mass loading, the energy loading shows no significant dependence on halo mass. While these scalings are close to successful heuristic models of wind feedback, the CR-driven winds in our present models are not yet powerful enough to fully account for the required feedback strength.
  • PDF
    The Hypatia Catalog Database (www.hypatiacatalog.com) is the largest database of high resolution stellar abundances for stars within the solar neighborhood. It currently offers 72 elements and species within 5,986 stars, 347 of which host planets. The Hypatia Catalog Database features an interactive table and multiple plotting interfaces that allow easy access and exploration of stellar abundance data and properties within the Hypatia Catalog (Hinkel et al. 2014, 2016, 2017). The Hypatia Catalog is a multidimensional, amalgamate dataset comprised of stellar abundance measurements for FGKM-type stars within 150 pc of the Sun from carefully culled literature sources, currently totaling 161 datasets, that measured both [Fe/H] and at least one other element. In addition to abundances, stellar properties and planetary properties, where applicable, have been made available within the online Hypatia Catalog Database. Data and plots can also be downloaded through the website for use in personal code or presentations, respectively. The Hypatia Catalog and Hypatia Catalog Database will continue to be routinely updated in order to incorporate the most recent stellar abundance data published within the literature.
  • PDF
    The free streaming length of the dark matter particle, and its possible interactions, imprint a measurable signature on the density profiles and abundance of structure on sub-galactic scales. We present a statistical technique for probing dark matter via substructure through a joint analysis of samples of strong lens systems with four multiple images (quads). Our method is amenable to any parameterization of the subhalo mass function and density profile for individual substructures. As an example, we apply it to a mass function of a warm dark matter particle characterized by a normalization $A_0$, and a free streaming length parameterized by the half-mode mass $m_{\rm{hm}}$. We demonstrate that limits on $m_{\rm{hm}}$ deteriorate rapidly with increasing uncertainty in image fluxes, highlighting the importance of precisely measuring them, and controlling for external sources of error. We omit subhalos outside of the lens plane, which are believed to boost the signal, so our results can be interpreted as conservative constraints. We forecast bounds on dark matter warmth for samples of 180 quads, attainable with upcoming surveys such as Euclid, LSST, and WFIRST. Assuming a cold dark matter scenario, we forecast $2\sigma$ bounds of $m_{\rm{hm}}<10^{6.4} M_{\odot}$, $10^{7.5} M_{\odot}$, $10^{8} M_{\odot}$, and $10^{8.4} M_{\odot}$ for flux errors of 0$\%$, $2\%$, $4\%$, and $8\%$, corresponding to thermal relic masses of 13.9 keV, 6.4 keV, 4.6 keV, and 3.3 keV, respectively.
  • PDF
    We prove a formula for the Hodge numbers of square-free divisors of Calabi-Yau threefold hypersurfaces in toric varieties. Euclidean branes wrapping divisors affect the vacuum structure of Calabi-Yau compactifications of type IIB string theory, M-theory, and F-theory. Determining the nonperturbative couplings due to Euclidean branes on a divisor $D$ requires counting fermion zero modes, which depend on the Hodge numbers $h^i({\cal{O}}_D)$. Suppose that $X$ is a smooth Calabi-Yau threefold hypersurface in a toric variety $V$, and let $D$ be the restriction to $X$ of a square-free divisor of $V$. We give a formula for $h^i({\cal{O}}_D)$ in terms of combinatorial data. Moreover, we construct a CW complex $\mathscr{P}_D$ such that $h^i({\cal{O}}_D)=h_i(\mathscr{P}_D)$. We describe an efficient algorithm that makes possible for the first time the computation of sheaf cohomology for such divisors at large $h^{1,1}$. As an illustration we compute the Hodge numbers of a class of divisors in a threefold with $h^{1,1}=491$. Our results are a step toward a systematic computation of Euclidean brane superpotentials in Calabi-Yau hypersurfaces.
  • PDF
    The method pioneered by Ruffini and Bonazzola (RB) to describe boson stars involves an expansion of the boson field which is linear in creation and annihilation operators. This expansion constitutes an exact solution to a non-interacting field theory, and has been used as a reasonable ansatz for an interacting one. In this work, we show how one can go beyond the RB ansatz towards an exact solution of the interacting operator Klein-Gordon equation, which can be solved iteratively to ever higher precision. Our Generalized Ruffini-Bonazzola approach takes into account contributions from nontrivial harmonic dependence of the wavefunction, using a sum of terms with energy $k\,E_0$, where $k\geq1$ and $E_0$ is the chemical potential of a single bound axion. The method critically depends on an expansion in a parameter $\Delta \equiv \sqrt{1-E_0{}^2/m^2}<1$, where $m$ is the mass of the boson. In the case of the axion potential, we calculate corrections which are relevant for axion stars in the transition or dense branches. We find with high precision the local minimum of the mass, $M_{min}\approx 463\,f^2/m$, at $\Delta\approx0.27$, where $f$ is the axion decay constant. This point marks the crossover from transition to dense branches of solutions, and a corresponding crossover from structural instability to stability.
  • PDF
    Superuniversality is the sharing of the same critical exponents among distinct critical points. This surprising behavior is observed at phase transitions between various quantum Hall states found in the two-dimensional electron gas. Motivated by the theoretical challenge posed by superuniversality, we introduce a new effective description that has an emergent $U(N)$ gauge symmetry with $N > 1$ for a quantum phase transition between an integer quantum Hall state and an insulator. We use modular transformations to generate from this theory new effective descriptions for quantum phase transitions between a large class of fractional quantum Hall states whose quasiparticle excitations have abelian statistics. In the 't Hooft large $N$ limit, the correlation length and dynamical critical exponents are independent of the particular transition in the absence of disorder. We argue that this conclusion survives away from the large $N$ limit using recent duality conjectures and, thereby, provide theoretical support for the phenomenon of superuniversality found at distinct quantum Hall critical points.
  • PDF
    A quantum system of particles can exist in a localized phase, exhibiting ergodicity breaking and maintaining forever a local memory of its initial conditions. We generalize this concept to a system of extended objects, such as strings and membranes, arguing that such a system can also exhibit localization in the presence of sufficiently strong disorder (randomness) in the Hamiltonian. We show that localization of large extended objects can be mapped to a lower-dimensional many-body localization problem. For example, motion of a string involves propagation of point-like signals down its length to keep the different segments in causal contact. For sufficiently strong disorder, all such internal modes will exhibit many-body localization, resulting in the localization of the entire string. The eigenstates of the system can then be constructed perturbatively through a convergent 'string locator expansion.' We propose a type of out-of-time-order string correlator as a diagnostic of such a string localized phase. Localization of other higher-dimensional objects, such as membranes, can also be studied through a hierarchical construction by mapping onto localization of lower-dimensional objects. Our arguments are 'asymptotic' (i.e. valid up to rare regions) but they extend the notion of localization (and localization protected order) to a host of settings where such ideas previously did not apply. These include high-dimensional ferromagnets with domain wall excitations, three-dimensional topological phases with loop-like excitations, and three-dimensional type-II superconductors with flux line excitations. In type-II superconductors, localization of flux lines could stabilize superconductivity at energy densities where a normal state would arise in thermal equilibrium.
  • PDF
    We present results from a systematic selection of tidal disruption events (TDEs) in a wide area (4800 deg$^2$) $g+R$ band experiment by the Intermediate Palomar Transient Factory (iPTF) with a rolling cadence of 1 and 3 days. We use photometric selection criteria to down select from a total of 493 nuclear transients detected during the experiment to a sample of 26 blue ($g-r < 0$ mag) nuclear transients in red host galaxies. Using Swift follow-up UV and X-ray imaging, and ground-based optical spectroscopy, we classify 14 Type Ia supernovae (SNe Ia), 9 highly variable active galactic nuclei (AGNs), 2 confirmed TDEs, and 1 potential core-collapse supernova. From our study, we measure a TDE per galaxy rate of 1.7 $^{+2.85}_{-1.27}$ $\times$10$^{-4}$ gal$^{-1}$ yr$^{-1}$ (90% CL in Poisson statistics) using a galaxy number density estimated from the SDSS luminosity function. We find that it is possible to filter out AGNs by employing a more stringent transient color cut ($g-r <$ $-$0.2 mag). The UV is an important discriminator for filtering out SN contamination, since in the optical, SNe Ia can appear as blue as TDEs in their early phases. However, the contamination from SN Ia drops significantly with a more stringent spatial offset cut, suggesting higher precision in astrometry is essential for separating TDEs from SNe Ia in the optical. Our most stringent optical photometric selection criteria yields a contamination rate of 4.5:1, allowing for a manageable number of TDE candidates for complete spectroscopic follow-up and real-time classification in the ZTF era.
  • PDF
    We present models of realistic globular clusters with post-Newtonian dynamics for black holes. By modeling the relativistic accelerations and gravitational-wave emission in isolated binaries and during three- and four-body encounters, we find that nearly half of all binary black hole mergers occur inside the cluster, with about 10% of those mergers entering the LIGO/Virgo band with eccentricities greater than 0.1. In-cluster mergers lead to the birth of a second generation of black holes with larger masses and high spins, which, depending on the black hole natal spins, can sometimes be retained in the cluster and merge again. As a result, globular clusters can produce merging binaries with detectable spins regardless of the birth spins of black holes formed from massive stars. These second-generation black holes would also populate any upper mass gap created by pair-instability supernovae.
  • PDF
    The Milky Way (MW) and Andromeda (M31) galaxies possess rotating planes of satellites. Their formation has not been explained satisfactorily yet. It was suggested that the MW and M31 satellites are ancient tidal dwarf galaxies, which could explain their configuration. This suggestion gained support by an analytic backward calculation of the relative MW-M31 orbit in the MOND modified dynamics paradigm by Zhao et al. (2013) implying their close flyby 7-11 Gyr ago. Here we explore the Local Group history in MOND in more detail using a simplified first-ever self-consistent simulation. We note the features induced by the encounter in the simulation and identify their possible real counterparts. The simulation was set to approximately reproduce the observed MW and M31 masses, effective radii, separation, relative velocity and disk inclinations. We used the publicly available adaptive-mesh-refinement code Phantom of RAMSES. In the simulation, matter was transferred from the MW to M31 along a tidal tail. The encounter induced formation of several structures resembling the peculiarities of the Local Group. Most notably: 1) A rotating planar structure formed around M31 from the transferred material. It had a size similar to the observed satellite plane and was oriented edge-on to the simulated MW, just as the real one. 2) The same structure also resembled the tidal features observed around M31 by its size and morphology. 3) A warp in the MW developed with an amplitude and orientation similar to that observed. Moreover, a cloud of particles formed around the simulated MW, with the extent of the actual MW satellite system. The encounter did not end by merging in a Hubble time. The simulation thus demonstrated that MOND can possibly explain many peculiarities of the Local Group. Future more elaborate simulations should verify and expand our conclusions. (abridged)
  • PDF
    In previous work, we identified an anomalous number of events in the LHC jets+MET searches characterized by low jet multiplicity and low-to-moderate transverse energy variables. Here, we update this analysis with results from a new ATLAS search in the monojet channel which also shows a consistent excess. As before, we find that this "monojet excess" is well-described by the resonant production of a heavy colored state decaying to a quark and a massive invisible particle. In the combined ATLAS and CMS data, we now find a local (global) preference of 3.3$\sigma$ (2.5$\sigma$) for the new physics model over the Standard Model-only hypothesis. As the signal regions containing the excess are systematics-limited, we consider additional cuts to enhance the signal-to-background ratio. We show that binning finer in $H_T$ and requiring the jets to be more central can increase $S/B$ by a factor of ${\sim} 1.5$.
  • PDF
    It has been conjectured that the critical density of the Activated Random Walk model is strictly less than one for any value of the sleeping rate. We prove this conjecture on $\mathbb{Z}^d$ when $d \geq 3$ and, more generally, on graphs where the random walk is transient. Moreover, we establish the occurrence of a phase transition on non-amenable graphs, extending previous results which require that the graph is amenable or a regular tree.
  • PDF
    We propose a grand unified SU(5)$\times$U(1)$_X$ model, where the standard SU(5) grand unified theory is supplemented by minimal seesaw and a right-handed neutrino dark matter with an introduction of a global $Z_2$-parity. In the presence of three right-handed neutrinos (RHNs), the model is free from all gauge and mixed-gravitational anomalies. The SU(5) symmetry is broken into the Standard Model (SM) gauge group at $M_{\rm GUT} \simeq 4 \times 10^{16}$ GeV in the standard manner, while the U(1)$_X$ symmetry breaking occurs at the TeV scale, which generates the TeV-scale mass of the U(1)$_X$ gauge boson ($Z^\prime$ boson) and the three Majorana RHNs. A unique $Z_2$-odd RHN is stable and serves as the dark matter (DM) in the present Universe, while the remaining two RHNs work to generate the SM neutrino masses through the minimal seesaw. We investigate the $Z^\prime$-portal RHN DM scenario in this model context, and find that the constraints from the DM relic abundance and the search results for a $Z^\prime$ boson resonance at the Large Hadron Collider (LHC) are complementary to narrow down the allowed parameter region, which will be fully covered by the future LHC experiments (for the $Z^\prime$ boson mass $<$ 5 TeV). We also briefly discuss the successful implementation of Baryogenesis and cosmological inflation scenarios in the present model.
  • PDF
    Resting state electroencephalogram (EEG) abnormalities in clinically high-risk individuals (CHR), clinically stable first-episode patients with schizophrenia (FES), healthy controls (HC) suggest alterations in neural oscillatory activity. However, few studies directly compare these anomalies among each types. Therefore, this study investigated whether these electrophysiological characteristics differentiate clinical populations from one another, and from non-psychiatric controls. To address this question, resting EEG power and coherence were assessed in 40 clinically high-risk individuals (CHR), 40 first-episode patients with schizophrenia (FES), and 40 healthy controls (HC). These findings suggest that resting EEG can be a sensitive measure for differentiating between clinical disorders.This paper proposes a novel data-driven supervised learning method to obtain identification of the patients mental status in schizophrenia research. According to Marchenko-Pastur Law, the distribution of the eigenvalues of EEG data is divided into signal subspace and noise subspace. A test statistic named LES that embodies the characteristics of all eigenvalues is adopted. different classifier and different feature(LES test function) are selected for experiments, we have shown that using von Neumann Entropy as LES test function combine with SVM classifier could obtain the best average classification accuracy during three classification among HC, FES and CHR of Schizophrenia group with EEG signal. It is worth noting that the result of LES feature extraction with the highest classification accuracy is around 90% in two classification(HC compare with FES) and around 70% in three classification. Where the classification accuracy higher than 70% could be used to assist clinical diagnosis.

Recent comments

Andrew W Simmons Dec 14 2017 11:40 UTC

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

Planat Dec 14 2017 08:43 UTC

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

...(continued)
Māris Ozols Dec 12 2017 19:41 UTC

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

Danial Dervovic Dec 10 2017 15:25 UTC

Thank you for the insightful observations, Simon.

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

...(continued)
Simon Apers Dec 09 2017 07:54 UTC

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

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

...(continued)
Simone Severini Dec 07 2017 02:51 UTC

Closely related to

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

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

...(continued)
Mark Everitt Dec 05 2017 07:50 UTC

Thank you for the helpful feedback.

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

...(continued)
Simone Severini Dec 05 2017 01:13 UTC

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

...(continued)
Mark Everitt Dec 04 2017 17:52 UTC

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

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

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

...(continued)
Dave Bacon Dec 02 2017 00:08 UTC

A couple of comments:

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

...(continued)