- Prime number (Prime number)

by Wilson Yu04 Feb 2019 03:47 - Lower and upper (Lower and upper)

by Dr. Wei Wang28 Dec 2018 02:32 - Electrical conductivity (Electrical conductivity)

by Dr. Farhad Daneshvar20 Nov 2018 19:00 - On Measurement Assessment and Division Matrices (On Measurement Assessment and Division Matrices)

by Prof. Hasan Keleş01 Aug 2018 11:58 - Pauli matrices (Pauli matrices)

by Prof. Hasan Keleş16 Feb 2018 07:45 - Full counting statistics (Full counting statistics)

by Dr. Dmitri Ivanov28 Nov 2011 09:44 - Grey-body radiation (Grey-body radiation)

by Prof. Carlo Beenakker08 Jan 2011 20:36 - Minimal Dark Matter (Minimal Dark Matter)

by Dr. Marco Cirelli05 Dec 2010 22:13 - Universal Conductance Fluctuations (Universal Conductance Fluctuations)

by Prof. Carlo Beenakker08 Dec 2010 13:33 - Wigner transform (Wigner transform)

by Dr. Claude Becker06 Apr 2011 14:04

- Avoiding bottleneck situations in crowds is critical for the safety and comfort of people at large events or in public transportation. Based on the work of Lagrangian motion analysis we propose a novel video-based bottleneckdetector by identifying characteristic stowage patterns in crowd-movements captured by optical flow fields. The Lagrangian framework allows to assess complex timedependent crowd-motion dynamics at large temporal scales near the bottleneck by two dimensional Lagrangian fields. In particular we propose long-term temporal filtered Finite Time Lyapunov Exponents (FTLE) fields that provide towards a more global segmentation of the crowd movements and allows to capture its deformations when a crowd is passing a bottleneck. Finally, these deformations are used for an automatic spatio-temporal detection of such situations. The performance of the proposed approach is shown in extensive evaluations on the existing J\"ulich and AGORASET datasets, that we have updated with ground truth data for spatio-temporal bottleneck analysis.Ground truthFluid dynamicsRegion of interestPedestrian fluxConvex hullEuclidean distanceConstrictionSuperpositionImage ProcessingLarge radius...
- In crowd counting datasets, each person is annotated by a point, which is usually the center of the head. And the task is to estimate the total count in a crowd scene. Most of the state-of-the-art methods are based on density map estimation, which convert the sparse point annotations into a "ground truth" density map through a Gaussian kernel, and then use it as the learning target to train a density map estimator. However, such a "ground-truth" density map is imperfect due to occlusions, perspective effects, variations in object shapes, etc. On the contrary, we propose \emph{Bayesian loss}, a novel loss function which constructs a density contribution probability model from the point annotations. Instead of constraining the value at every pixel in the density map, the proposed training loss adopts a more reliable supervision on the count expectation at each annotated point. Without bells and whistles, the loss function makes substantial improvements over the baseline loss on all tested datasets. Moreover, our proposed loss function equipped with a standard backbone network, without using any external detectors or multi-scale architectures, plays favourably against the state of the arts. Our method outperforms previous best approaches by a large margin on the latest and largest UCF-QNRF dataset. The source code is available at \url{https://github.com/ZhihengCV/Baysian-Crowd-Counting}.Ground truthCountingUniversal Conductance FluctuationsConvolutional neural networkBayesianSparsityRegressionStatistical estimatorArchitectureTraining Image...
- One of the most surprising predictions of modern quantum theory is that the vacuum of space is not empty. In fact, quantum theory predicts that it teems with virtual particles flitting in and out of existence. While initially a curiosity, it was quickly realized that these vacuum fluctuations had measurable consequences, for instance producing the Lamb shift of atomic spectra and modifying the magnetic moment for the electron. This type of renormalization due to vacuum fluctuations is now central to our understanding of nature. However, these effects provide indirect evidence for the existence of vacuum fluctuations. From early on, it was discussed if it might instead be possible to more directly observe the virtual particles that compose the quantum vacuum. 40 years ago, Moore suggested that a mirror undergoing relativistic motion could convert virtual photons into directly observable real photons. This effect was later named the dynamical Casimir effect (DCE). Using a superconducting circuit, we have observed the DCE for the first time. The circuit consists of a coplanar transmission line with an electrical length that can be changed at a few percent of the speed of light. The length is changed by modulating the inductance of a superconducting quantum interference device (SQUID) at high frequencies (~11 GHz). In addition to observing the creation of real photons, we observe two-mode squeezing of the emitted radiation, which is a signature of the quantum character of the generation process.SQUIDCasimir effectVirtual particleLamb shiftRenormalizationVacuum stateCreation and annihilation operatorsTwo-point correlation functionNetwork theoryRadiation damping...
- We show that, without any extra physical degree introduced, the Standard Model can be readily reformulated as a Double Field Theory. Consequently, the Standard Model can couple to an arbitrary stringy gravitational background in an $\mathbf{O}(4,4)$ T-duality covariant manner and manifest two independent local Lorentz symmetries, $\mathbf{Spin}(1,3)\times\mathbf{Spin}(3,1)$. While the diagonal gauge fixing of the twofold spin groups leads to the conventional formulation on the flat Minkowskian background, the enhanced symmetry makes the Standard Model more rigid, and also stringy, than it appeared. The CP violating $\theta$-term may no longer be allowed by the symmetry, and hence the strong CP problem is solved. There are now stronger constraints imposed on the possible higher order corrections. We speculate that the quarks and the leptons may possibly belong to the two different spin classes.Standard ModelCovarianceField theorySpin groupDiffeomorphismTetradGauge symmetryT-dualityStrong CP-problemDilaton...
- A method is suggested for obtaining the Plancherel measure for Affine Hecke Algebras as a limit of integral-type formulas for inner products in the polynomial and related modules of Double Affine Hecke Algebras. The analytic continuation necessary here is a generalization of "picking up residues" due to Arthur, Heckman, Opdam and others, which can be traced back to Hermann Weyl. Generally, it is a finite sum of integrals over double affine residual subtori; a complete formula is presented for $A_1$ in the spherical case.Root systemAffine Hecke algebraChandra X-ray ObservatoryWeyl groupHarmonic analysisWeyl algebraLaurent polynomialHypergeometric functionAnalytic continuationMacdonald polynomial...
- Let G be a real reductive Lie group with maximal compact sub- group K. We generalize the usual notion of Dirac index to a twisted version, which is nontrivial even in case G and K do not have equal rank. We compute ordinary and twisted indices of standard modules. As applications, we study extensions of Harish-Chandra modules and twisted characters.Cartan subgroupRankAutomorphismConjugacy classCohomologySubgroupInfinitesimal characterWeyl groupVector spaceCartan decomposition...
- For a finite Lie algebra $G_N$ of rank N, the Weyl orbits $W(\Lambda^{++})$ of strictly dominant weights $\Lambda^{++}$ contain $dimW(G_N)$ number of weights where $dimW(G_N)$ is the dimension of its Weyl group $W(G_N)$. For any $W(\Lambda^{++})$, there is a very peculiar subset $\wp(\Lambda^{++})$ for which we always have $$ dim\wp(\Lambda^{++})=dimW(G_N)/dimW(A_{N-1}) . $$ For any dominant weight $ \Lambda^+ $, the elements of $\wp(\Lambda^+)$ are called {\bf Permutation Weights}. It is shown that there is a one-to-one correspondence between elements of $\wp(\Lambda^{++})$ and $\wp(\rho)$ where $\rho$ is the Weyl vector of $G_N$. The concept of signature factor which enters in Weyl character formula can be relaxed in such a way that signatures are preserved under this one-to-one correspondence in the sense that corresponding permutation weights have the same signature. Once the permutation weights and their signatures are specified for a dominant $\Lambda^+$, calculation of the character $ChR(\Lambda^+)$ for irreducible representation $R(\Lambda^+)$ will then be provided by $A_N$ multiplicity rules governing generalized Schur functions. The main idea is again to express everything in terms of the so-called {\bf Fundamental Weights} with which we obtain a quite relevant specialization in applications of Weyl character formula.PermutationWeyl character formulaRankIrreducible representationWeyl groupDimensionsOrbitVectorLie algebra...
- We establish upper bounds for the decay rate of the energy of the damped fractional wave equation when the averages of the damping coefficient on all intervals of a fixed length are bounded below. If the power of the fractional Laplacian, $s$, is between 0 and 2, the decay is polynomial. For $s \ge 2$, the decay is exponential. Second, we show that our assumption on the damping is necessary for the energy to decay exponentially.Wave equationDecay rateFractional LaplacianUnitary operatorUncertainty principleGeodesicEnergyPolynomialHilbert spaceTheory...
- We construct the general effective field theory of gravity coupled to the Standard Model of particle physics, which we name GRSMEFT. Our method allows the systematic derivation of a non-redundant set of operators of arbitrary dimension with generic field content and gravity. We explicitly determine the pure gravity EFT up to dimension ten, the EFT of a shift-symmetric scalar coupled to gravity up to dimension eight, and the operator basis for the GRSMEFT up to dimension eight. Extensions to all orders are straightforward.SpurionTensor productWeyl tensorGeneral relativityCurvature tensorScaling dimensionTheories of gravityGauge fieldEffective field theoryUnitarity...
- In this paper, we are interested in analyzing the asymptotic profiles of solutions to the Cauchy problem for linear structurally damped $\sigma$-evolution equations in $L^2$-sense. Depending on the parameters $\sigma$ and $\delta$ we would like to not only indicate approximation formula of solutions but also recognize the optimality of their decay rates as well in the distinct cases of parabolic like damping and $\sigma$-evolution like damping. Moreover, such results are also discussed when we mix these two kinds of damping terms in a $\sigma$-evolution equation to investigate how each of them affects the asymptotic profile of solutions.Evolution equationDecay rateCauchy problemSmall dataAttentionNonnegativeModified Bessel FunctionClassificationWave equationDiffusion equation...
- The solar atmosphere is dominated by loops of magnetic flux which connect the multi-million-degree corona to the much cooler chromosphere. The temperature and density structure of quasi-static loops is determined by the continuous flow of energy from the hot corona to the lower solar atmosphere. Loop scaling laws provide relationships between global properties of the loop (such as peak temperature, pressure, and length); they follow from the physical variable dependencies of various terms in the energy equation, and hence the form of the loop scaling law provides insight into the key physics that controls the loop structure. Traditionally, scaling laws have been derived under the assumption of collision-dominated thermal conduction. Here we examine the impact of different regimes of thermal conduction -- collision-dominated, turbulence-dominated, and free-streaming -- on the form of the scaling laws relating the loop temperature and heating rate to its pressure and half-length. We show that the scaling laws for turbulence-dominated conduction are fundamentally different than those for collision-dominated and free-streaming conduction, inasmuch as the form of the scaling laws now depend primarily on conditions at the low-temperature, rather than high-temperature, part of the loop. We also establish regimes in temperature and density space in which each of the applicable scaling laws prevail.Scaling lawTurbulenceCoronal loopCoronaFree streaming of particlesSolar atmosphereChromosphereMean free pathApexHard X-ray...
- One of the key problems in solar flare physics is the determination of the low-energy cut-off; the value that determines the energy of nonthermal electrons and hence flare energetics. We discuss different approaches to determine the low-energy cut-off in the spectrum of accelerated electrons: (i) the total electron number model, (ii) the time-of-flight model (based on the equivalence of the time-of-flight and the collisional deflection time); (iii) the warm target model of Kontar et al.~(2015), and (iv) the model of the spectral cross-over between thermal and nonthermal components. We find that the first three models are consistent with a low-energy cutoff with a mean value of $\approx 10$ keV, while the cross-over model provides an upper limit for the low-energy cutoff with a mean value of $ \approx 21$ keV. Combining the first three models we find that the ratio of the nonthermal energy to the dissipated magnetic energy in solar flares has a mean value of $q_E=0.57\pm0.08$, which is consistent with an earlier study based on the simplified approximation of the warm target model alone ($q_E=0.51\pm0.17$). This study corroborates the self-consistency between three different low-energy cutoff models in the calculation of nonthermal flare energies.Time-of-flightSolar flareHard X-rayEmission measureRamaty High Energy Solar Spectroscopic ImagerSpectral index of power spectrumMagnetic energyObservational errorX-ray spectrumFilling fraction...
- We present a Bayesian hierarchical inference formalism (Basilisk) to constrain the galaxy-halo connection using satellite kinematics. Unlike traditional methods, Basilisk does not resort to stacking the kinematics of satellite galaxies in bins of central luminosity, and does not make use of summary statistics, such as satellite velocity dispersion. Rather, Basilisk leaves the data in its raw form and computes the corresponding likelihood. In addition, Basilisk can be applied to flux-limited, rather than volume-limited samples, greatly enhancing the quantity and dynamic range of the data. And finally, Basilisk is the only available method that simultaneously solves for halo mass and orbital anisotropy of the satellite galaxies, while properly accounting for scatter in the galaxy-halo connection. Basilisk uses the conditional luminosity function to model halo occupation statistics, and assumes that satellite galaxies are a relaxed tracer population of the host halo's potential with kinematics that obey the spherical Jeans equation. We test and validate Basilisk using mocks of varying complexity, and demonstrate that it yields unbiased constraints on the galaxy-halo connection and at a precision that rivals galaxy-galaxy lensing. In particular, Basilisk accurately recovers the full PDF of the relation between halo mass and central galaxy luminosity, and simultaneously constrains the orbital anisotropy of the satellite galaxies. Basilisk's inference is not affected by potential velocity bias of the central galaxies, or by slight errors in the inferred, radial profile of satellite galaxies that arise as a consequence of interlopers and sample impurity.GalaxySatellite galaxyVirial massLuminosityKinematicsMilky WayAnisotropyGalactic haloInferenceVelocity dispersion...
- We present a new age-dating technique that combines gyrochronology with isochrone fitting to infer ages for FGKM main-sequence and subgiant field stars. Gyrochronology and isochrone fitting are each capable of providing relatively precise ages for field stars in certain areas of the Hertzsprung-Russell diagram: gyrochronology works optimally for cool main-sequence stars, and isochrone fitting can provide precise ages for stars near the main-sequence turnoff. Combined, these two age-dating techniques can provide precise and accurate ages for a broader range of stellar masses and evolutionary stages than either method used in isolation. We demonstrate that the position of a star on the Hertzsprung- Russell or color-magnitude diagram can be combined with its rotation period to infer a precise age via both isochrone fitting and gyrochronology simultaneously. We show that incorporating rotation periods with 5% uncertainties into stellar evolution models improves age precision for FGK stars on the main sequence, and can, on average, provide age estimates up to three times more precise than isochrone fitting alone. In addition, we provide a new gyrochronology relation, calibrated to the Praesepe cluster and the Sun, that includes a variance model to capture the rotational behavior of stars whose rotation periods do not lengthen with the square-root of time, and parts of the Hertzsprung-Russell diagram where gyrochronology has not been calibrated. This publication is accompanied by an open source Python package, stardate, for inferring the ages of main-sequence and subgiant FGKM stars from rotation periods, spectroscopic parameters and/or apparent magnitudes and parallaxes.StarMain sequence starHertzsprung-Russell diagramBeehive ClusterStellar agesSubgiantMetallicityOf starsStellar evolutionSun...
- A key prediction of the standard cosmological model -- which relies on the assumption that dark matter is cold, i.e. non-relativistic at the epoch of structure formation -- is the existence of a large number of dark matter substructures on sub-galactic scales. This assumption can be tested by studying the perturbations induced by dark matter substructures on cold stellar streams. Here, we study the prospects for discriminating cold from warm dark matter by generating mock data for upcoming astronomical surveys such as the Large Synoptic Survey Telescope (LSST), and reconstructing the properties of the dark matter particle from the perturbations induced on the stellar density profile of a stream. We discuss the statistical and systematic uncertainties, and show that the method should allow to set stringent constraints on the mass of thermal dark matter relics, and possibly to yield an actual measurement of the dark matter particle mass if it is in the $\mathcal{O}(1)$ keV range.Dark matter subhaloWarm dark matterCold dark matterDark matterStellar streamStarDark matter particleThermal WDMDark matter particle massDensity contrast...
- The stellar initial mass function (IMF) is playing a critical role in the history of our universe. We propose a theory that is based solely on local processes, namely the dust opacity limit, the tidal forces and the properties of the collapsing gas envelope. The idea is that the final mass of the central object is determined by the location of the nearest fragments, which accrete the gas located further away, preventing it to fall onto the central object. To estimate the relevant statistics in the neighbourhood of an accreting protostar, we perform high resolution numerical simulations. We also use these simulations to further test the idea that fragmentation in the vicinity of an existing protostar is determinant in setting the peak of the stellar mass spectrum. We develop an analytical model, which is based on a statistical counting of the turbulent density fluctuations, generated during the collapse, that are at least equal to the mass of the first hydrostatic core, and sufficiently important to supersede tidal and pressure forces to be self-gravitating. The analytical mass function presents a peak located at roughly 10 times the mass of the first hydrostatic core in good agreement with the numerical simulations. Since the physical processes involved are all local, i.e. occurs at scales of a few 100 AU or below, and do not depend on the gas distribution at large scale and global properties such as the mean Jeans mass, the mass spectrum is expected to be relatively universal.Astronomical UnitFragmentationHydrostaticsAccretionMach numberInitial mass functionNumerical simulationMass spectrumProtostarTidal force...
- The free-streaming length of dark matter depends on fundamental dark matter physics, and determines the abundance and central densities of dark matter halos on sub-galactic scales. Using the image positions and flux-ratios from eight quadruply-imaged quasars, we constrain the free-streaming length of dark matter, the amplitude of the subhalo mass function (SHMF), and the logarithmic slope of the SHMF. We model both main deflector subhalos and halos along the line of sight, and account for warm dark matter (WDM) free-streaming effects on both the mass function and the mass-concentration relation. By calibrating the evolution of the SHMF with host halo mass and redshift using a suite of simulated halos, we infer a global normalization for the SHMF. Our analysis accounts for finite-size background sources, and marginalizes over the mass profile of the main deflector. Parameterizing dark matter free-streaming through the half-mode mass $m_{\rm{hm}}$, we constrain dark matter warmth and the corresponding thermal relic particle mass $m_{\rm{DM}}$. At $2 \sigma$: $m_{\rm{hm}} < 10^{7.8} M_{\odot}$ ($m_{DM} > 5.2 \ \rm{keV}$). Assuming CDM, we simultaneously constrain the projected mass in substructure between $10^6 - 10^{9} M_{\odot}$ near lensed images and the logarithmic slope of the SHMF. At $2 \sigma$, we infer $1.3 - 6.6 \times 10^{7} M_{\odot} \rm{kpc^{-2}}$, corresponding to mean projected mass fractions of $\bar{f}_{\rm{sub}} = 0.034_{-0.022}^{+0.024}$, respectively. At $1 \sigma$, we constrain the logarithmic slope of the SHMF $\alpha = -1.896_{-0.014}^{+0.010}$. These results are in excellent agreement with the predictions of cold dark matter.Dark matterDark matter subhaloVirial massWarm dark matterFree streaming of particlesSubhalo mass functionHalo mass functionDark matter haloMass profileLine of sight...
- This pedagogical note revisits the concept of electromagnetic helicity in classical systems. In particular, magnetic helicity and its role in mean field dynamo theories is briefly discussed highlighting the major mathematical inconsistency in most of these theories---violation of magnetic helicity conservation. A short review of kinematic dynamo theory and its classic theorems is also presented in the Appendix.HelicityMagnetic helicityMagnetohydrodynamicsDynamo theoryTurbulenceMagnetic energyDissipationMean field dynamo theoryKinematicsElectromagnetism...
- We present a critical assessment of the SN1987A supernova cooling bound on axions and other light particles. Core-collapse simulations used in the literature to substantiate the bound omitted from the calculation the envelope exterior to the proto-neutron star (PNS). As a result, the only source of neutrinos in these simulations was, by construction, a cooling PNS. We show that if the canonical delayed neutrino mechanism failed to explode SN1987A, and if the pre-collapse star was rotating, then an accretion disk would form that could explain the late-time ($t\gtrsim5$ sec) neutrino events. Such accretion disk would be a natural feature if SN1987A was a collapse-induced thermonuclear explosion. Axions do not cool the disk and do not affect its neutrino output, provided the disk is optically-thin to neutrinos, as it naturally is. These considerations cast doubt on the supernova cooling bound.AxionNeutrinoProtoneutron starSupernova 1987ACoolingSupernovaAccretion diskAccretionNeutrino luminosityCore-collapse supernova...
- Heavy neutral leptons are present in many well-motivated beyond the Standard Model theories, sometimes being accessible at present colliders. Depending on their masses and couplings they could be long-lived and lead to events with displaced vertices, and thus to promising signatures due to low Standard Model background. We revisit the potential of the LHC to discover this kind of new particles via searches for displaced vertices, which can probe masses of few GeV for mixings currently allowed by experimental constraints. We also discuss the importance of considering all the possible production channels, including the production in association with light neutrinos, in order to fully explore this region of the parameter space.Sterile neutrinoDisplaced verticesLarge Hadron ColliderStandard ModelNeutrinoCharged leptonColliderBSM physicsNeutrino massQCD jet...
- Being able to model correlations between labels is considered crucial in multi-label classification. Rule-based models enable to expose such dependencies, e.g., implications, subsumptions, or exclusions, in an interpretable and human-comprehensible manner. Albeit the number of possible label combinations increases exponentially with the number of available labels, it has been shown that rules with multiple labels in their heads, which are a natural form to model local label dependencies, can be induced efficiently by exploiting certain properties of rule evaluation measures and pruning the label search space accordingly. However, experiments have revealed that multi-label heads are unlikely to be learned by existing methods due to their restrictiveness. To overcome this limitation, we propose a plug-in approach that relaxes the search space pruning used by existing methods in order to introduce a bias towards larger multi-label heads resulting in more expressive rules. We further demonstrate the effectiveness of our approach empirically and show that it does not come with drawbacks in terms of training time or predictive performance.ClassificationTraining setCompact modelingRelaxationLearning ruleConfusion matrixMachine learningGround truthMarketRank...
- Odd-frequency superconductivity represents a truly unconventional ordered state which, in contrast to conventional superconductivity, exhibits pair correlations which are odd in relative time and, hence, inherently dynamical. In this review article we provide an overview of recent advances in the study of odd-frequency superconducting correlations in one-dimensional systems. In particular, we focus on recent developments in the study of nanowires with Rashba spin-orbit coupling and metallic edges of two-dimensional topological insulators in proximity to conventional superconductors. These systems have recently elicited a great deal of interest due to their potential for realizing one-dimensional topological superconductivity whose edges can host Majorana zero modes. We also provide a detailed discussion of the intimate relationship between Majorana zero modes and odd-frequency pairing. Throughout this review, we highlight the ways in which odd-frequency pairing provides a deeper understanding of the unconventional superconducting correlations present in each of these intriguing systems and how the study and control of these states holds the potential for future applications.Spin-orbit interactionSuperconductorNanowireSuperconductivityNormal metal/superconductor junctionNormal-superconductorTopological insulatorCooper pairOne-dimensional systemQuantum dots...
- For a simplicial complex with n sets, let W^-(x) be the set of sets in G contained in x and W^+(x) the set of sets in G containing x. An integer-valued function h on G defines for every A subset G an energy E[A]=sum_x in A h(x). The function energizes the geometry similarly as divisors do in the continuum, where the Riemann-Roch quantity chi(G)+deg(D) plays the role of the energy. Define the n times n matrices L=L^--(x,y)=E[W^-(x) cap W^-(y)] and L^++(x,y) = E[W^+(x) cap W^+(y)]. With the notation S(x,y)=1_n omega(x) =delta(x,y) (-1)dim(x) and str(A)=tr(SA) define g=S L^++ S. The results are: det(L)=det(g) = prod_x in G h(x) and E[G] = sum_x,y g(x,y) and E[G]=str(g). The number of positive eigenvalues of g is equal to the number of positive energy values of h. In special cases, more is true: A) If h(x) in -1, 1}, the matrices L=L^--,L^++ are unimodular and L^-1 = g, even if G is a set of sets. B) In the constant energy h(x)=1 case, L and g are isospectral, positive definite matrices in SL(n,Z). For any set of sets G we get so isospectral multi-graphs defined by adjacency matrices L^++ or L^-- which have identical spectral or Ihara zeta function. The positive definiteness holds for positive divisors in general. C) In the topological case h(x)=omega(x), the energy E[G]=str(L) = str(g) = sum_x,y g(x,y)=chi(G) is the Euler characteristic of G and phi(G)=prod_x omega(x), a product identity which holds for arbitrary set of sets. D) For h(x)=t^|x| with some parameter t we have E[H]=1-f_H(t) with f_H(t)=1+f_0 t + cdots + f_d t^d+1 for the f-vector of H and L(x,y) = (1-f_W^-(x) cap W^-(y)(t)) and g(x,y)=omega(x) omega(y) (1-f_W^+(x) cap W^+(y)(t)). Now, the inverse of g is g^-1(x,y) = 1-f_W^-(x) cap W^-(y)(t)/t^dim(x cap y) and E[G] = 1-f_G(t)=sum_x,y g(x,y).GraphEuler characteristicStarIhara zeta functionZeta functionRing homomorphismEllipticityManifoldDualityCurvature...
- Stars stripped of their envelopes from interaction with a binary companion emit a significant fraction of their radiation as ionizing photons. They are potentially important stellar sources of ionizing radiation, however, they are still often neglected in spectral synthesis simulations or simulations of stellar feedback. We modeled the radiative contribution from stripped stars by using detailed evolutionary and spectral models. We estimated their impact on the integrated spectra and specifically on the emission rates of HI-, HeI-, and HeII-ionizing photons from stellar populations. We find that stripped stars have the largest impact on the ionizing spectrum of a population in which star formation halted several Myr ago. In such stellar populations, stripped stars dominate the emission of ionizing photons, mimicking a younger stellar population in which massive stars are still present. Our models also suggest that stripped stars have harder ionizing spectra than massive stars. The additional ionizing radiation affects observable properties that are related to the ionizing emission from stellar populations. In co-eval stellar populations, the ionizing radiation from stripped stars increases the ionization parameter and the production efficiency of HI-ionizing photons. They also cause high values for these parameters for about ten times longer than what is predicted for massive stars. The hard ionizing radiation from stripped stars likely introduces a characteristic ionization structure of the nebula, which leads to the emission of highly ionized elements such as O$^{2+}$ and C$^{3+}$. We, therefore, expect that the presence of stripped stars affects the location in the BPT diagram and the diagnostic ratio of OIII to OII nebular emission lines. Our models are publicly available through CDS database and on the Starburst99 website.StarIonizing radiationStellar populationsMassive starsStar formationIonizationMetallicityMain sequence starLuminosityMass transfer...
- The Carnegie-Chicago Hubble Program (CCHP) is building a direct path to the Hubble constant (H0) using Population II stars as the calibrator of the SN Ia-based distance scale. This path to calibrate the SN Ia is independent of the systematics in the traditional Cepheid-based technique. In this paper, we present the distance to M101, the host to SN2011fe, using the I-band tip of the red giant branch (TRGB) based on observations from the ACS/WFC instrument on the Hubble Space Telescope. The CCHP targets the halo of M101 where there is little to no host-galaxy dust, the red giant branch is isolated from nearly all other stellar populations, and there is virtually no source confusion or crowding at the magnitude of the tip. Applying the standard procedure for the TRGB method from the other works in the CCHP series, we find a foreground-extinction-corrected M101 distance modulus of {\mu_0}=29.07+/-0.04(stat)+/-0.05(sys) mag, which corresponds to a distance of D=6.52+/-0.12(stat)+/-0.15(sys) Mpc. This result is consistent with several recent Cepheid-based determinations, suggesting agreement between Population I and II distance scales for this nearby SN Ia-host galaxy. We further analyze four archival datasets for M101 that have targeted its outer disk to argue that targeting in the stellar halo provides much more reliable distance measurements from the TRGB method due to the combination of multiple structural components and heavily population contamination. Application of the TRGB in complex regions will have sources of uncertainty not accounted for in commonly used uncertainty measurement techniques.Tip of the red giant branchPinwheel GalaxyLuminosity functionExtinctionPhotometryStellar populationsCepheidStarHost galaxyReddening...
- The gluing formula of the zeta-determinant of a Laplacian given by Burghelea, Friedlander and Kappeler contains an unknown constant. In this paper we compute this constant to complete the formula under the assumption of the product structure near boundary. As applications of this result,we prove the adiabatic decomposition theorems of the zeta-determinant of a Laplacian with respect to the Dirichlet and Neumann boundary conditions and of the analytic torsion with respect to the absolute and relative boundary conditions.Analytic torsionNeumann boundary condition
- We evaluate the spectral determinant for the damped wave equation on an interval of length $T$ with Dirichlet boundary conditions, proving that it does not depend on the damping. This is achieved by analysing the square of the damped wave operator using the general result by Burghelea, Friedlander, and Kappeler on the determinant for a differential operator with matrix coefficients.Wave equationZeta functionDirichlet boundary conditionCauchy problemUpper half-planeAttentionMobilityWave propagationGraphSturm-Liouville operator...
- Perhaps the most abundant form of waste energy in our surrounding is the parasitic magnetic noise arising from electrical power transmission system. In this work, a flexible and rollable magneto-mechano-electric nanogenerator (MMENG) based wireless IoT sensor has been demonstrated in order to capture and utilize the magnetic noise. Free standing magnetoelectric (ME) composites are fabricated by combining magnetostrictive nickel ferrite nanoparticles and piezoelectric polyvinylidene-co-trifluoroethylene polymer. The magnetoelectric 0-3 type nanocomposites possess maximum ME co-efficient of 11.43 mV/cm-Oe. Even, without magnetic bias field 99 % of the maximum ME co-efficient value is observed due to self-bias effect. As a result, the MMENG generates sufficient peak-to-peak open circuit voltage, output power density and successfully operates commercial capacitor under the weak and low frequency stray magnetic field arising from the power cable of home appliances such as, electric kettle. Finally, the harvested electrical signal has been wirelessly transmitted to a smart phone in order to demonstrate the possibility of position monitoring system construction. This cost effective and easy to integrate approach with tailored size and shape of device configuration is expected to be explored in next-generation self-powered IoT sensors including implantable biomedical devices and human health monitoring sensory systems.MagnetoelectricInternet of ThingsNanogeneratorCapacitorNanoparticleNanocompositePolymersEnergyMagnetic fieldFrequency...
- Recent explainability related studies have shown that state-of-the-art DNNs do not always adopt correct evidences to make decisions. It not only hampers their generalization but also makes them less likely to be trusted by end-users. In pursuit of developing more credible DNNs, in this paper we propose CREX, which encourages DNN models to focus more on evidences that actually matter for the task at hand, and to avoid overfitting to data-dependent bias and artifacts. Specifically, CREX regularizes the training process of DNNs with rationales, i.e., a subset of features highlighted by domain experts as justifications for predictions, to enforce DNNs to generate local explanations that conform with expert rationales. Even when rationales are not available, CREX still could be useful by requiring the generated explanations to be sparse. Experimental results on two text classification datasets demonstrate the increased credibility of DNNs trained with CREX. Comprehensive analysis further shows that while CREX does not always improve prediction accuracy on the held-out test set, it significantly increases DNN accuracy on new and previously unseen data beyond test set, highlighting the advantage of the increased credibility.AttentionConvolutional neural networkSparsityTraining setText ClassificationArchitectureRegularizationDeep Neural NetworksLong short term memoryOverfitting...
- This paper focuses on "tracing player knowledge" in educational games. Specifically, given a set of concepts or skills required to master a game, the goal is to estimate the likelihood with which the current player has mastery of each of those concepts or skills. The main contribution of the paper is an approach that integrates machine learning and domain knowledge rules to find when the player applied a certain skill and either succeeded or failed. This is then given as input to a standard knowledge tracing module (such as those from Intelligent Tutoring Systems) to perform knowledge tracing. We evaluate our approach in the context of an educational game called "Parallel" to teach parallel and concurrent programming with data collected from real users, showing our approach can predict students skills with a low mean-squared error.Machine learningGround truthMean squared errorClassificationLogistic regressionFeature vectorTraining setSchedulingMultilayer perceptronExpectation maximization...
- Person re-identification (person Re-Id) aims to retrieve the pedestrian images of a same person that captured by disjoint and non-overlapping cameras. Lots of researchers recently focuse on this hot issue and propose deep learning based methods to enhance the recognition rate in a supervised or unsupervised manner. However, two limitations that cannot be ignored: firstly, compared with other image retrieval benchmarks, the size of existing person Re-Id datasets are far from meeting the requirement, which cannot provide sufficient pedestrian samples for the training of deep model; secondly, the samples in existing datasets do not have sufficient human motions or postures coverage to provide more priori knowledges for learning. In this paper, we introduce a novel unsupervised pose augmentation cross-view person Re-Id scheme called PAC-GAN to overcome these limitations. We firstly present the formal definition of cross-view pose augmentation and then propose the framework of PAC-GAN that is a novel conditional generative adversarial network (CGAN) based approach to improve the performance of unsupervised corss-view person Re-Id. Specifically, The pose generation model in PAC-GAN called CPG-Net is to generate enough quantity of pose-rich samples from original image and skeleton samples. The pose augmentation dataset is produced by combining the synthesized pose-rich samples with the original samples, which is fed into the corss-view person Re-Id model named Cross-GAN. Besides, we use weight-sharing strategy in the CPG-Net to improve the quality of new generated samples. To the best of our knowledge, we are the first try to enhance the unsupervised cross-view person Re-Id by pose augmentation, and the results of extensive experiments show that the proposed scheme can combat the state-of-the-arts.Generative Adversarial NetRankMarketConvolutional neural networkLatent variableArchitectureGenerative modelDeep learningImage ProcessingAutoencoder...
- Generative Adversarial Networks (GAN) have gained a lot of popularity from their introduction in 2014 till present. Research on GAN is rapidly growing and there are many variants of the original GAN focusing on various aspects of deep learning. GAN are perceived as the most impactful direction of machine learning in the last decade. This paper focuses on the application of GAN in autonomous driving including topics such as advanced data augmentation, loss function learning, semi-supervised learning, etc. We formalize and review key applications of adversarial techniques and discuss challenges and open problems to be addressed.Generative Adversarial NetAutonomous drivingMachine learningSemi-supervised learningAdversarial examplesImage ProcessingGenerative modelDeep learningOptimizationClassification...
#### Wasserstein GANver. 3

We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches. Furthermore, we show that the corresponding optimization problem is sound, and provide extensive theoretical work highlighting the deep connections to other distances between distributions.Generative Adversarial NetTotal-Variation regularizationArchitectureManifoldOptimizationNeural networkHyperparameterCompletenessGenerative modelDuality...- Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training instability. The recently proposed Wasserstein GAN (WGAN) makes progress toward stable training of GANs, but sometimes can still generate only low-quality samples or fail to converge. We find that these problems are often due to the use of weight clipping in WGAN to enforce a Lipschitz constraint on the critic, which can lead to undesired behavior. We propose an alternative to clipping weights: penalize the norm of gradient of the critic with respect to its input. Our proposed method performs better than standard WGAN and enables stable training of a wide variety of GAN architectures with almost no hyperparameter tuning, including 101-layer ResNets and language models over discrete data. We also achieve high quality generations on CIFAR-10 and LSUN bedrooms.Generative Adversarial NetArchitectureHyperparameterInstabilityGenerative modelLanguageNetworks...
- Traditional generative adversarial networks (GAN) and many of its variants are trained by minimizing the KL or JS-divergence loss that measures how close the generated data distribution is from the true data distribution. A recent advance called the WGAN based on Wasserstein distance can improve on the KL and JS-divergence based GANs, and alleviate the gradient vanishing, instability, and mode collapse issues that are common in the GAN training. In this work, we aim at improving on the WGAN by first generalizing its discriminator loss to a margin-based one, which leads to a better discriminator, and in turn a better generator, and then carrying out a progressive training paradigm involving multiple GANs to contribute to the maximum margin ranking loss so that the GAN at later stages will improve upon early stages. We call this method Gang of GANs (GoGAN). We have shown theoretically that the proposed GoGAN can reduce the gap between the true data distribution and the generated data distribution by at least half in an optimally trained WGAN. We have also proposed a new way of measuring GAN quality which is based on image completion tasks. We have evaluated our method on four visual datasets: CelebA, LSUN Bedroom, CIFAR-10, and 50K-SSFF, and have seen both visual and quantitative improvement over baseline WGAN.Generative Adversarial NetRankingGenerative modelManifoldGround truthArchitectureInstabilityMutual informationOptimizationMinimax...
- Generative adversarial networks (GANs) have received a tremendous amount of attention in the past few years, and have inspired applications addressing a wide range of problems. Despite its great potential, GANs are difficult to train. Recently, a series of papers (Arjovsky & Bottou, 2017a; Arjovsky et al. 2017b; and Gulrajani et al. 2017) proposed using Wasserstein distance as the training objective and promised easy, stable GAN training across architectures with minimal hyperparameter tuning. In this paper, we compare the performance of Wasserstein distance with other training objectives on a variety of GAN architectures in the context of single image super-resolution. Our results agree that Wasserstein GAN with gradient penalty (WGAN-GP) provides stable and converging GAN training and that Wasserstein distance is an effective metric to gauge training progress.Generative Adversarial NetArchitectureHyperparameterConvolutional neural networkGenerative modelDeep learningInverse Reinforcement LearningSecurityGlassActivation function...
- Predicting and understanding human motion dynamics has many applications, such as motion synthesis, augmented reality, security, and autonomous vehicles. Due to the recent success of generative adversarial networks (GAN), there has been much interest in probabilistic estimation and synthetic data generation using deep neural network architectures and learning algorithms. We propose a novel sequence-to-sequence model for probabilistic human motion prediction, trained with a modified version of improved Wasserstein generative adversarial networks (WGAN-GP), in which we use a custom loss function designed for human motion prediction. Our model, which we call HP-GAN, learns a probability density function of future human poses conditioned on previous poses. It predicts multiple sequences of possible future human poses, each from the same input sequence but a different vector z drawn from a random distribution. Furthermore, to quantify the quality of the non-deterministic predictions, we simultaneously train a motion-quality-assessment model that learns the probability that a given skeleton sequence is a real human motion. We test our algorithm on two of the largest skeleton datasets: NTURGB-D and Human3.6M. We train our model on both single and multiple action types. Its predictive power for long-term motion estimation is demonstrated by generating multiple plausible futures of more than 30 frames from just 10 frames of input. We show that most sequences generated from the same input have more than 50\% probabilities of being judged as a real human sequence. We will release all the code used in this paper to Github.Generative Adversarial NetRecurrent neural networkGround truthArchitectureDeep Neural NetworksLong short term memoryGaussian mixture modelSecurityMotion estimationGraph...
- Unsupervised learning with generative adversarial networks (GANs) has proven to be hugely successful. Regular GANs hypothesize the discriminator as a classifier with the sigmoid cross entropy loss function. However, we found that this loss function may lead to the vanishing gradients problem during the learning process. To overcome such a problem, we propose in this paper the Least Squares Generative Adversarial Networks (LSGANs) which adopt the least squares loss for both the discriminator and the generator. We show that minimizing the objective function of LSGAN yields minimizing the Pearson $\chi^2$ divergence. We also show that the derived objective function that yields minimizing the Pearson $\chi^2$ divergence performs better than the classical one of using least squares for classification. There are two benefits of LSGANs over regular GANs. First, LSGANs are able to generate higher quality images than regular GANs. Second, LSGANs perform more stably during the learning process. For evaluating the image quality, we conduct both qualitative and quantitative experiments, and the experimental results show that LSGANs can generate higher quality images than regular GANs. Furthermore, we evaluate the stability of LSGANs in two groups. One is to compare between LSGANs and regular GANs without gradient penalty. We conduct three experiments, including Gaussian mixture distribution, difficult architectures, and a newly proposed method --- datasets with small variability, to illustrate the stability of LSGANs. The other one is to compare between LSGANs with gradient penalty (LSGANs-GP) and WGANs with gradient penalty (WGANs-GP). The experimental results show that LSGANs-GP succeed in training for all the difficult architectures used in WGANs-GP, including 101-layer ResNet.Generative Adversarial NetArchitectureLeast squaresClassificationMinimaxInferenceGenerative modelEntropyDeep Boltzmann machineUnsupervised learning...
- Recent neural networks such as WaveNet and sampleRNN that learn directly from speech waveform samples have achieved very high-quality synthetic speech in terms of both naturalness and speaker similarity even in multi-speaker text-to-speech synthesis systems. Such neural networks are being used as an alternative to vocoders and hence they are often called neural vocoders. The neural vocoder uses acoustic features as local condition parameters, and these parameters need to be accurately predicted by another acoustic model. However, it is not yet clear how to train this acoustic model, which is problematic because the final quality of synthetic speech is significantly affected by the performance of the acoustic model. Significant degradation happens, especially when predicted acoustic features have mismatched characteristics compared to natural ones. In order to reduce the mismatched characteristics between natural and generated acoustic features, we propose frameworks that incorporate either a conditional generative adversarial network (GAN) or its variant, Wasserstein GAN with gradient penalty (WGAN-GP), into multi-speaker speech synthesis that uses the WaveNet vocoder. We also extend the GAN frameworks and use the discretized mixture logistic loss of a well-trained WaveNet in addition to mean squared error and adversarial losses as parts of objective functions. Experimental results show that acoustic models trained using the WGAN-GP framework using back-propagated discretized-mixture-of-logistics (DML) loss achieves the highest subjective evaluation scores in terms of both quality and speaker similarity.Generative Adversarial NetArchitectureRecurrent neural networkNeural networkOptimizationTTSNaturalnessDeep Neural NetworksLong short term memoryActivation function...
- Scribble colors based line art colorization is a challenging computer vision problem since neither greyscale values nor semantic information is presented in line arts, and the lack of authentic illustration-line art training pairs also increases difficulty of model generalization. Recently, several Generative Adversarial Nets (GANs) based methods have achieved great success. They can generate colorized illustrations conditioned on given line art and color hints. However, these methods fail to capture the authentic illustration distributions and are hence perceptually unsatisfying in the sense that they often lack accurate shading. To address these challenges, we propose a novel deep conditional adversarial architecture for scribble based anime line art colorization. Specifically, we integrate the conditional framework with WGAN-GP criteria as well as the perceptual loss to enable us to robustly train a deep network that makes the synthesized images more natural and real. We also introduce a local features network that is independent of synthetic data. With GANs conditioned on features from such network, we notably increase the generalization capability over "in the wild" line arts. Furthermore, we collect two datasets that provide high-quality colorful illustrations and authentic line arts for training and benchmarking. With the proposed model trained on our illustration dataset, we demonstrate that images synthesized by the presented approach are considerably more realistic and precise than alternative approaches.Generative Adversarial NetArchitectureGround truthImage ProcessingOverfittingConvolutional neural networkHyperparameterDilationNeural networkSub-pixel...
- We present a new stage-wise learning paradigm for training generative adversarial networks (GANs). The goal of our work is to progressively strengthen the discriminator and thus, the generators, with each subsequent stage without changing the network architecture. We call this proposed method the RankGAN. We first propose a margin-based loss for the GAN discriminator. We then extend it to a margin-based ranking loss to train the multiple stages of RankGAN. We focus on face images from the CelebA dataset in our work and show visual as well as quantitative improvements in face generation and completion tasks over other GAN approaches, including WGAN and LSGAN.Generative Adversarial NetRankingArchitectureRankManifoldGenerative modelEntropyLeast squaresMinimaxLatent variable...
- In this paper, we study the convergence of generative adversarial networks (GANs) from the perspective of the informativeness of the gradient of the optimal discriminative function. We show that GANs without restriction on the discriminative function space commonly suffer from the problem that the gradient produced by the discriminator is uninformative to guide the generator. By contrast, Wasserstein GAN (WGAN), where the discriminative function is restricted to 1-Lipschitz, does not suffer from such a gradient uninformativeness problem. We further show in the paper that the model with a compact dual form of Wasserstein distance, where the Lipschitz condition is relaxed, may also theoretically suffer from this issue. This implies the importance of Lipschitz condition and motivates us to study the general formulation of GANs with Lipschitz constraint, which leads to a new family of GANs that we call Lipschitz GANs (LGANs). We show that LGANs guarantee the existence and uniqueness of the optimal discriminative function as well as the existence of a unique Nash equilibrium. We prove that LGANs are generally capable of eliminating the gradient uninformativeness problem. According to our empirical analysis, LGANs are more stable and generate consistently higher quality samples compared with WGAN.Generative Adversarial NetNash equilibriumLipschitz continuitySpectral normalizationRegularizationLeast squaresOptimal transportDualityArchitectureEuclidean distance...
- Generating mocks for future sky surveys requires large volumes and high resolutions, which is computationally expensive even for fast simulations. In this work we try to develop numerical schemes to calibrate various halo and matter statistics in fast low resolution simulations compared to high resolution N-body and hydrodynamic simulations. For the halos, we improve the initial condition accuracy and develop a halo finder "relaxed-FOF", where we allow different linking length for different halo mass and velocity dispersions. We show that our relaxed-FoF halo finder improves the common statistics, such as halo bias, halo mass function, halo auto power spectrum in real space and in redshift space, cross correlation coefficient with the reference halo catalog, and halo-matter cross power spectrum. We also incorporate the potential gradient descent (PGD) method into fast simulations to improve the matter distribution at nonlinear scale. By building a lightcone output, we show that the PGD method significantly improves the weak lensing convergence tomographic power spectrum. With these improvements FastPM is comparable to the high resolution full N-body simulation of the same mass resolution, with two orders of magnitude fewer time steps. These techniques can be used to improve the halo and matter statistics of FastPM simulations for mock catalogs of future surveys such as DESI and LSST.Friends of friends algorithmStatisticsN-body simulationHalo finding algorithmsLight conesVirial massWeak lensingCross-correlationVelocity dispersionHalo mass function...
- The most metal-poor, high redshift damped Lyman-alpha systems (DLAs) provide a window to study some of the first few generations of stars. In this paper, we present a novel model to investigate the chemical enrichment of the near-pristine DLA population. This model accounts for the mass distribution of the enriching stellar population, the typical explosion energy of their supernovae, and the average number of stars that contribute to the enrichment of these DLAs. We conduct a maximum likelihood analysis of these model parameters using the observed relative element abundances ([C/O], [Si/O], and [Fe/O]) of the 11 most metal-poor DLAs currently known. We find that the mass distribution of the stars that have enriched this sample of metal-poor DLAs can be well-described by a Salpeter-like IMF slope at M > 10 M_sun and that a typical metal-poor DLA has been enriched by < 72 massive stars (95 per cent confidence), with masses < 40 M_sun. The inferred typical explosion energy (E_exp = 1.8^{+0.3}_{-0.2}x10^51 erg) is somewhat lower than that found by recent works that model the enrichment of metal-poor halo stars. These constraints suggest that some of the metal-poor DLAs in our sample may have been enriched by Population II stars. Using our enrichment model, we also infer some of the typical physical properties of the most metal-poor DLAs. We estimate that the total stellar mass content is log10(M_*/M_sun) = 3.5^{+0.3}_{-0.4} and the total gas mass is log10(M_gas/M_sun) = 7.0^{+0.3}_{-0.4} for systems with a relative oxygen abundance [O/H] ~ -3.0.StarPopulation IIISupernovaAbundance ratioAbundanceOf starsChemical enrichmentMassive starsPopulation IIMass distribution...
- We address the issue of numerical convergence in cosmological smoothed particle hydrodynamics simulations using a suite of runs drawn from the EAGLE project. Our simulations adopt subgrid models that produce realistic galaxy populations at a fiducial mass and force resolution, but systematically vary the latter in order to study their impact on galaxy properties. We provide several analytic criteria that help guide the selection of gravitational softening for hydrodynamical simulations, and present results from runs that both adhere to and deviate from them. Unlike dark matter-only simulations, hydrodynamical simulations exhibit a strong sensitivity to gravitational softening, and care must be taken when selecting numerical parameters. Our results--which focus mainly on star formation histories, galaxy stellar mass functions and sizes--illuminate three main considerations. First, softening imposes a minimum resolved escape speed, $v_\epsilon$, due to the binding energy between gas particles. Runs that adopt such small softening lengths that $v_\epsilon \gt 10\,{\rm km s^{-1}}$ (the sound speed in ionised $\sim 10^4\,{\rm K}$ gas) suffer from reduced effects of photo-heating. Second, feedback from stars or active galactic nuclei may suffer from numerical over-cooling if the gravitational softening length is chosen below a critical value, $\epsilon_{\rm eFB}$. Third, we note that small softening lengths exacerbate the segregation of stars and dark matter particles in halo centres, often leading to the counter-intuitive result that galaxy sizes {\em increase} as softening is reduced. The structure of dark matter haloes in hydrodynamical runs respond to softening in a way that reflects the sensitivity of their galaxy populations to numerical parameters.Softening lengthGalaxyDark matterStar formationDark matter haloGalactic stellar mass functionGalaxy FormationStar formation historiesSubgrid modelHydrodynamical simulations...
- We present a new, falsifiable, quantum theory of gravity, which we name Non-commutative Matter-Gravity. The commutative limit of the theory is classical general relativity. In the first two papers of this series, we have introduced the concept of an atom of space-time-matter [STM], which is described by the spectral action in non-commutative geometry, corresponding to a classical theory of gravity. We used the Connes time parameter, along with the spectral action, to incorporate gravity into trace dynamics. We then derived the spectral equation of motion for the gravity part of the STM atom, which turns out to be the Dirac equation on a non-commutative space. In the present work, we propose how to include the matter (fermionic) part and give a simple action principle for the STM atom. This leads to the equations for a quantum theory of gravity, and also to an explanation for the origin of spontaneous localisation from quantum gravity. We use spontaneous localisation to arrive at the action for classical general relativity [including matter sources] from the action for STM atoms.General relativityTheories of gravityQuantum theoryBlack holeHamiltonianDirac operatorQuantum gravityCompton wavelengthQuantum field theoryPlanck scale...
- We study decay rates for the energy of solutions of the damped wave equation on the torus. We consider dampings invariant in one direction and bounded above and below by multiples of $x^{\beta}$ near the boundary of the support and show decay at rate $1/t^{\frac{\beta+2}{\beta+3}}$. In the case where $W$ vanishes exactly like $x^{\beta}$ this result is optimal by work of the second author. The proof uses a version of the Morawetz multiplier method.Decay rateTorusWave equationGeodesicNonnegativeManifoldDilute magnetic semiconductorsStarPolynomialEnergy...
- We explore the generation of the baryon asymmetry in an extension of the Standard Model where the lepton number is promoted to a $U(1)_\ell$ gauge symmetry with an associated $Z^\prime$ gauge boson. This is based on a novel electroweak baryogenesis mechanism first proposed by us in Ref.~\cite{Carena:2018cjh}. Extra fermionic degrees of freedom - including a fermionic dark matter $\chi$ - are introduced in the dark sector for anomaly cancellation. Lepton number is spontaneously broken at high scale and the effective theory, containing the Standard Model, the $Z^\prime$, the fermionic dark matter, and an additional complex scalar field $S$, violates CP in the dark sector. The complex scalar field couples to the Higgs portal and is essential in enabling a strong first order phase transition. Dark CP violation is diffused in front of the bubble walls and creates a chiral asymmetry for $\chi$, which in turn creates a chemical potential for the Standard Model leptons. Weak sphalerons are then in charge of transforming the net lepton charge asymmetry into net baryon number. We explore the model phenomenology related to the leptophilic $Z^\prime$, the dark matter candidate, the Higgs boson and the additional scalar, as well as implications for electric dipole moments. We also discuss the case when baryon number $U(1)_B$ is promoted to a gauge symmetry, and discuss electroweak baryogenesis and its corresponding phenomenology.Standard ModelElectroweak baryogenesisHiggs bosonCP violationBaryogenesisDark sectorLepton numberElectric dipole momentElectroweak phase transitionBubble wall...
- Accurate pedestrian counting algorithm is critical to eliminate insecurity in the congested public scenes. However, counting pedestrians in crowded scenes often suffer from severe perspective distortion. In this paper, basing on the straight-line double region pedestrian counting method, we propose a dynamic region division algorithm to keep the completeness of counting objects. Utilizing the object bounding boxes obtained by YoloV3 and expectation division line of the scene, the boundary for nearby region and distant one is generated under the premise of retaining whole head. Ulteriorly, appropriate learning models are applied to count pedestrians in each obtained region. In the distant region, a novel inception dilated convolutional neural network is proposed to solve the problem of choosing dilation rate. In the nearby region, YoloV3 is used for detecting the pedestrian in multi-scale. Accordingly, the total number of pedestrians in each frame is obtained by fusing the result in nearby and distant regions. A typical subway pedestrian video dataset is chosen to conduct experiment in this paper. The result demonstrate that proposed algorithm is superior to existing machine learning based methods in general performance.CountingDilationConvolutional neural networkCounting methodCompletenessMachine learningGround truthRegressionInception ModulesRegion of interest...
- Recently, convolutional neural networks (CNNs) are the leading defacto method for crowd counting. However, when dealing with video datasets, CNN-based methods still process each video frame independently, thus ignoring the powerful temporal information between consecutive frames. In this work, we propose a novel architecture termed as "temporal channel-aware" (TCA) block, which achieves the capability of exploiting the temporal interdependencies among video sequences. Specifically, we incorporate 3D convolution kernels to encode local spatio-temporal features. Furthermore, the global contextual information is encoded into modulation weights which adaptively recalibrate channel-aware feature responses. With the local and global context combined, the proposed block enhances the discriminative ability of the feature representations and contributes to more precise results in diverse scenes. By stacking TCA blocks together, we obtain the deep trainable architecture called enhanced 3D convolutional networks (E3D). The experiments on three benchmark datasets show that the proposed method delivers state-of-the-art performance. To verify the generality, an extended experiment is conducted on a vehicle dataset TRANCOS and our approach beats previous methods by large margins.CountingConvolutional neural networkArchitectureRegion of interestGround truthLong short term memoryAttentionStatisticsAblationTraining set...