Recently bookmarked papers

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  • In a quantum many-body system where the Hamiltonian and the order operator do not commute, it often happens that the unique ground state of a finite system exhibits long-range order (LRO) but does not show spontaneous symmetry breaking (SSB). Typical examples include antiferromagnetic quantum spin systems with Neel order, and lattice boson systems which exhibits Bose-Einstein condensation. By extending and improving previous results by Horsch and von der Linden and by Koma and Tasaki, we here develop a fully rigorous and almost complete theory about the relation between LRO and SSB in the ground state of a finite system with continuous symmetry. We show that a ground state with LRO but without SSB is inevitably accompanied by a series of energy eigenstates, known as the "tower" of states, which have extremely low excitation energies. More importantly, we also prove that one gets a physically realistic "ground state" by taking a superposition of these low energy excited states. The present paper is written in a self-contained manner, and does not require any knowledge about the previous works on the subject.
    Spontaneous symmetry breakingSymmetry breakingHamiltonianOrder operatorExpectation ValueAntiferromagneticExcited stateIsing modelContinuous symmetryAntiferromagnet...
  • In spite of flourishing studies on the topology of spin waves, a generic framework to classify and compute magnon band topology in non-collinear magnets is still missing. In this work we provide such a theory framework, by mapping an arbitrary linear spin wave into a local free-fermion Hamiltonian with exactly the same spectrum, symmetry implementation and band topology, which allows for a full classification and calculation on any topological properties of magnon bands. We apply this fermionization approach to honeycomb Kitaev magnet $\alpha$-RuCl$_3$, and show the existence of topologically protected magnon band crossings, and field-induced magnon Chern bands under small magnetic fields.
    MagnonClassificationSpin waveHamiltonianFree fermionsTopologyMagnetSpinTheorySymmetry...
  • Memristors, resistors with memory whose outputs depend on the history of their inputs, have been used with success in neuromorphic architectures, particularly as synapses or non-volatile memories. A neural network based on memristors could show advantages in terms of energy conservation and open up possibilities for other learning systems to be adapted to a memristor-based paradigm, both in the classical and quantum learning realms. No model for such a network has been proposed so far. Therefore, in order to fill this gap, we introduce models for single and multilayer perceptrons based on memristors. We adapt the delta rule to the memristor-based single-layer perceptron and the backpropagation algorithm to the memristor-based multilayer perceptron. We ran simulations of both the models and the training algorithms. These showed that both of them perform well and in accordance with Minsky-Papert's theorem, which motivates the possibility of building memristor-based hardware for a physical neural network.
    PerceptronMultilayer perceptronHidden layerNeural networkBackpropagationDelta ruleActivation functionResistorArchitectureVolatiles...
  • In this article, we investigate strategic information transmission over a noisy channel. This problem has been widely investigated in Economics, when the communication channel is perfect. Unlike in Information Theory, both encoder and decoder have distinct objectives and choose their encoding and decoding strategies accordingly. This approach radically differs from the conventional Communication paradigm, which assumes transmitters are of two types: either they have a common goal, or they act as opponent, e.g. jammer, eavesdropper. We formulate a point-to-point source-channel coding problem with state information, in which the encoder and the decoder choose their respective encoding and decoding strategies in order to maximize their long-run utility functions. This strategic coding problem is at the interplay between Wyner-Ziv's scenario and the Bayesian persuasion game of Kamenica-Gentzkow. We characterize a single-letter solution and we relate it to the previous results by using the concavification method. This confirms the benefit of sending encoded data bits even if the decoding process is not supervised, e.g. when the decoder is an autonomous device. Our solution has two interesting features: it might be optimal not to use all channel resources; the informational content impacts the encoding process, since utility functions capture preferences on source symbols.
    EntropyMarkov chainBayesianInformation theoryMutual informationPoint sourceOptimizationBayes' ruleInternet of ThingsNash equilibrium...
  • In this paper, we study the codes over the matrix ring over $\mathbb{Z}_4$, which is perhaps the first time the ring structure $M_2(\mathbb{Z}_4)$ is considered as a code alphabet. This ring is isomorphic to $\mathbb{Z}_4[w]+U\mathbb{Z}_4[w]$, where $w$ is a root of the irreducible polynomial $x^2+x+1 \in \mathbb{Z}_2[x]$ and $U\equiv$ ${11}\choose{11}$. We first discuss the structure of the ring $M_2(\mathbb{Z}_4)$ and then focus on algebraic structure of cyclic codes and self-dual cyclic codes over $M_2(\mathbb{Z}_4)$. We obtain the generators of the cyclic codes and their dual codes. Few examples are given at the end of the paper.
    Matrix ringCommutative ringCoprimeFinite ringPairwise coprimePolynomial ringQuotient ringIsomorphismPolynomialUnits...
  • In this work we offer a framework for reasoning about a wide class of existing objectives in machine learning. We develop a formal correspondence between this work and thermodynamics and discuss its implications.
    Machine learningThermodynamicsObjective
  • It has been numerically found that the particle systems interacting with power-law repulsive force can show a rigid-body like behavior in one-dimensional setting when the power-law exponent is sufficiently small (Sekimoto, Phys. Rev. Lett. 104, 124302 (2010)). Its experimental implementation or theoretical basis, however, were unknown. We here demonstrate an experimental realization with simple and robust construction of "particles." Theoretically, the new concept of rigid-body behavior is based on the transfer of momentum from the impacting particle to the rigid-body like cluster mediated by an evanescent mode of displacement without exciting propagating waves. The similarity is evoked to the M\"ossbauer's recoilless absorption/emission of photons.
    Mode couplingPhononArchitectureMossbauer effectSoftwareParticle-Particle interactionParticle massStripe phasesBlinkingNumerical simulation...
  • Robots assisting the disabled or elderly must perform complex manipulation tasks and must adapt to the home environment and preferences of their user. Learning from demonstration is a promising choice, that would allow the non-technical user to teach the robot different tasks. However, collecting demonstrations in the home environment of a disabled user is time consuming, disruptive to the comfort of the user, and presents safety challenges. It would be desirable to perform the demonstrations in a virtual environment. In this paper we describe a solution to the challenging problem of behavior transfer from virtual demonstration to a physical robot. The virtual demonstrations are used to train a deep neural network based controller, which is using a Long Short Term Memory (LSTM) recurrent neural network to generate trajectories. The training process uses a Mixture Density Network (MDN) to calculate an error signal suitable for the multimodal nature of demonstrations. The controller learned in the virtual environment is transferred to a physical robot (a Rethink Robotics Baxter). An off-the-shelf vision component is used to substitute for geometric knowledge available in the simulation and an inverse kinematics module is used to allow the Baxter to enact the trajectory. Our experimental studies validate the three contributions of the paper: (1) the controller learned from virtual demonstrations can be used to successfully perform the manipulation tasks on a physical robot, (2) the LSTM+MDN architectural choice outperforms other choices, such as the use of feedforward networks and mean-squared error based training signals and (3) allowing imperfect demonstrations in the training set also allows the controller to learn how to correct its manipulation mistakes.
    Long short term memoryRoboticsDeep Neural NetworksArchitectureKinematicsMean squared errorRecurrent neural networkNeural networkElderlyConvolutional neural network...
  • Hash tables are one of the most fundamental data structures for effectively storing and accessing sparse data, with widespread usage in domains ranging from computer graphics to machine learning. This study surveys the state-of-the-art research on data-parallel hashing techniques for emerging massively-parallel, many-core GPU architectures. Key factors affecting the performance of different hashing schemes are discovered and used to suggest best practices and pinpoint areas for further research.
    Multidimensional ArrayData structuresArchitectureArtificial neural networkNearest-neighbor siteArithmeticComputer graphicsMachine learningParallel AlgorithmScheduling...
  • We consider the regular subgroups of the automorphism group of the linear Hadamard code. These subgroups correspond to the regular subgroups of $GA(r,2)$, w.t.r action on the vectors of $F_2^{r}$, where $n=2^r-1 $ is the length of the Hamadard code. We show that the dihedral group $D_{2^{r-1}}$ is a regular subgroup of $GA(r,2)$ only when $r=3$. Following the approach of \cite{M} we study the regular subgroups of the Hamming code obtained from the regular subgroups of the automorphism group of the Hadamard code of length 15.
    SubgroupAutomorphismDihedralIsomorphismConjugacy classAffine groupPermutationSymmetry groupBit arrayVector space...
  • We extend the multi-pass streaming model to sliding window problems, and address the problem of computing order statistics on fixed-size sliding windows, in the multi-pass streaming model as well as the closely related communication complexity model. In the $2$-pass streaming model, we show that on input of length $N$ with values in range $[0,R]$ and a window of length $K$, sliding window minimums can be computed in $\widetilde{O}(\sqrt{N})$. We show that this is nearly optimal (for any constant number of passes) when $R \geq K$, but can be improved when $R = o(K)$ to $\widetilde{O}(\sqrt{NR/K})$. Furthermore, we show that there is an $(l+1)$-pass streaming algorithm which computes $l^\text{th}$-smallest elements in $\widetilde{O}(l^{3/2} \sqrt{N})$ space. In the communication complexity model, we describe a simple $\widetilde{O}(pN^{1/p})$ algorithm to compute minimums in $p$ rounds of communication for odd $p$, and a more involved algorithm which computes the $l^\text{th}$-smallest elements in $\widetilde{O}(pl^2 N^{1/(p-2l-1)})$ space. Finally, we prove that the majority statistic on boolean streams cannot be computed in sublinear space, implying that $l^\text{th}$-smallest elements cannot be computed in space both sublinear in $N$ and independent of $l$.
    RankCommunication complexityStatisticsMultidimensional ArrayOrder statisticCommunication modelData structuresAlice and BobOptimizationNonnegative...
  • We present recent ALMA observations of the CO(1-0) and CO(3-2) emission lines in the brightest cluster galaxy of RXCJ1504.1$-$0248, which is one of the most extreme cool core clusters known. The central galaxy contains $1.9\times 10^{10}~M_{\odot}$ of molecular gas. The molecular gas morphology is complex and disturbed, showing no evidence for a rotationally-supported structure in equilibrium. $80\%$ of the gas is situated within the central 5 kpc of the galactic center, while the remaining gas is located in a 20 kpc long filament. The cold gas has likely condensed out of the hot atmosphere. The filament is oriented along the edge of a putative X-ray cavity, suggesting that AGN activity has stimulated condensation. This is enegetically feasible, although the morphology is not as conclusive as systems whose molecular filaments trail directly behind buoyant radio bubbles. The velocity gradient along the filament is smooth and shallow. It is only consistent with free-fall if it lies within $20^{\circ}$ of the plane of the sky. The abundance of clusters with comparably low velocities suggests that the filament is not free-falling. Both the central and filamentary gas are coincident with bright UV emission from ongoing star formation. Star formation near the cluster core is consistent with the Kennicutt-Schmidt law. The filament exhibits increased star formation surface densities, possibly resulting from either the consumption of a finite molecular gas supply or spatial variations in the CO-to-H$_2$ conversion factor.
    Brightest cluster galaxyStar formation rateStar formationAtacama Large Millimeter ArrayGalaxyActive Galactic NucleiX-ray cavitiesMolecular cloudCluster coreCool core galaxy cluster...
  • Conceptualizing planetary habitability depends on understanding how living organisms originated and what features of environments are essential to foster abiogenesis. Estimates of the abundance of life's building blocks are confounded by incomplete knowledge of the role of chirality and racemization in organic compounds in the origination of living organisms. Chirality is an essential feature of enzymes as well as many lock-and-key type structures. There are four known processes that can act on complex organic molecules to promote racemization for abiogenesis: quantum-tunneling effects; selection via interaction with circularly polarized light (CPL); templating processes; and interactions with electrical and magnetic (EM) fields. These occur in different places, respectively: cold interstellar space; regions of space with energetic photons, dust and/or magnetic fields; and mineral surfaces (for both templating and EM fields). Chirality as a feature of terrestrial life suggests neither a special place for local development of homochirality nor for extra-terrestrial enrichment and delivery. The presence of these molecules in three competing scenarios for life's origin - chemical gardens, geothermal fields, and ice substrates - relies on a framework of hypothesis and estimation. An easily-modified worksheet is included in the supplemental material that allows a user to generate different scenarios and data related to the distribution of chiral organic molecules as building blocks for living organisms within the galaxy. A simple hypothetical mechanism for planetary magnetic field reversals, based on a high-density plasma inner core, is also presented as a means to aid in estimating field polarity and hence the orientation of racemization processes based on planetary magnetic fields.
    ChiralityOrganic moleculeAsteroidsCometComplex Organic MoleculeOptical isomerOptical activityAbundanceOrientationMagnetic field reversal...
  • Using numerical bootstrap method, we determine the critical exponents of the minimal three-dimensional $\mathcal{N}=1$ superconformal field theory (SCFT) to be $\eta_{\sigma}=0.168888(60)$ and $\omega=0.882(9)$. The model was argued in arXiv:1301.7449 to describe a quantum critical point (QCP) at the boundary a $3+1$D topological superconductor. More interestingly, the QCP can be reached by tuning a single parameter, where supersymmetry (SUSY) is realised as an emergent symmetry. By imposing emergent SUSY in numerical bootstrap, we find that the conformal scaling dimension of the real scalar operator $\sigma$ is highly restricted. If we further assume the SCFT to have only two time-reversal parity odd relevant operators, $\sigma$ and $\sigma'$, we find that allowed region for $\Delta_{\sigma}$ and $\Delta_{\sigma'}$ becomes an isolated island. The result is obtained by considering not only the four point correlator $\langle \sigma \sigma \sigma \sigma \rangle$, but also $\langle \sigma \epsilon \sigma \epsilon \rangle$ and $\langle \epsilon \epsilon\epsilon \epsilon \rangle$, with $\epsilon \sim \sigma ^2$ being the superconformal descendant of $\sigma$.
    Superconformal field theoryCritical exponentConformal BootstrapQuantum critical pointScaling dimensionOperator product expansionSuperfieldTime-reversal symmetrySupersymmetryOPE coefficients...
  • Anomaly detection is a classical problem in computer vision, namely the determination of the normal from the abnormal when datasets are highly biased towards one class (normal) due to the insufficient sample size of the other class (abnormal). While this can be addressed as a supervised learning problem, a significantly more challenging problem is that of detecting the unknown/unseen anomaly case that takes us instead into the space of a one-class, semi-supervised learning paradigm. We introduce such a novel anomaly detection model, by using a conditional generative adversarial network that jointly learns the generation of high-dimensional image space and the inference of latent space. Employing encoder-decoder-encoder sub-networks in the generator network enables the model to map the input image to a lower dimension vector, which is then used to reconstruct the generated output image. The use of the additional encoder network maps this generated image to its latent representation. Minimizing the distance between these images and the latent vectors during training aids in learning the data distribution for the normal samples. As a result, a larger distance metric from this learned data distribution at inference time is indicative of an outlier from that distribution - an anomaly. Experimentation over several benchmark datasets, from varying domains, shows the model efficacy and superiority over previous state-of-the-art approaches.
    Anomaly detectionGenerative Adversarial NetInferenceAutoencoderArchitectureVector spaceSecurityImage ProcessingMNIST datasetMultigraph...
  • We present a wormhole solution in four dimensions. It is a solution of an Einstein Maxwell theory plus charged massless fermions. The fermions give rise to a negative Casimir-like energy, which makes the wormhole possible. It is a long wormhole that does not lead to causality violations in the ambient space. It can be viewed as a pair of entangled near extremal black holes with an interaction term generated by the exchange of fermion fields. The solution can be embedded in the Standard Model by making its overall size small compared to the electroweak scale.
    WormholeBlack holeGauge fieldEinstein field equationsCasimir energyChiralityExtremal black holeTrace anomalyHorizonElectroweak scale...
  • Thermal relics lighter than an MeV contribute to the energy density of the universe at the time of nucleosynthesis and recombination. Constraints on extra radiation degrees of freedom typically exclude even the simplest of such dark sectors. We explore the possibility that a sub-MeV dark sector entered equilibrium with the Standard Model after neutrino-photon decoupling, which significantly weakens these constraints and naturally arises in the context of neutrino mass generation through the spontaneous breaking of lepton number. Acquiring an adequate dark matter abundance independently motivates the MeV-scale in these models through the coincidence of gravitational, matter-radiation equality, and neutrino mass scales, $(m_\text{Pl} / T^\text{MRE})^{1/4} \, m_\nu \sim \text{MeV}$. This class of scenarios will be decisively tested by future measurements of the cosmic microwave background and matter structure of the universe. While the dark sector dominantly interacts with Standard Model neutrinos, large couplings to nucleons are possible in principle, leading to observable signals at proposed low-threshold direct detection experiments.
    NeutrinoDark matterStandard ModelRecombinationMajoronNeutrino massCosmic microwave backgroundFreeze-outSterile neutrinoNucleosynthesis...
  • Abelian and non-Abelian topological phases exhibiting protected chiral edge modes are ubiquitous in the realm of the Fractional Quantum Hall (FQH) effect. Here, we investigate a spin-1 Hamiltonian on the square lattice which could, potentially, host the spin liquid analog of the (bosonic) non-Abelian Moore-Read FQH state, as suggested by Exact Diagonalisation of small clusters. Using families of fully SU(2)-spin symmetric and translationally invariant chiral Projected Entangled Pair States (PEPS), variational energy optimization is performed using infinite-PEPS methods, providing good agreement with Density Matrix Renormalisation Group (DMRG) results. A careful analysis of the bulk spin-spin and dimer-dimer correlation functions in the optimized spin liquid suggests that they exhibit long-range "gossamer tails". We argue these tails are finite-$D$ artifacts of the chiral PEPS, which become irrelevant when the PEPS bond dimension $D$ is increased. From the investigation of the entanglement spectrum, we observe sharply defined chiral edge modes following the prediction of the SU(2)$_2$ Wess-Zumino-Witten theory and exhibiting a conformal field theory (CFT) central charge $c=3/2$, as expected for a Moore-Read chiral spin liquid. We conclude that the PEPS formalism offers an unbiased and efficient method to investigate non-Abelian chiral spin liquids in quantum antiferromagnets.
    Chiral spin liquidAntiferromagnetConformal field theorySpin liquidOptimizationFractional quantum Hall stateHamiltonianEntanglement spectrumCentral chargeTwo-point correlation function...
  • Recovering an unknown Hamiltonian from measurements is an increasingly important task for certification of noisy quantum devices and simulators. Recent works have succeeded in recovering the Hamiltonian of an isolated quantum system with local interactions from long-ranged correlators of a single eigenstate. Here, we show that such Hamiltonians can be recovered from local observables alone, using computational and measurement resources scaling linearly with the system size. In fact, to recover the Hamiltonian acting on each finite spatial domain, only observables within that domain are required. The observables can be measured in a Gibbs state as well as a single eigenstate; furthermore, they can be measured in a state evolved by the Hamiltonian for a long time, allowing to recover a large family of time-dependent Hamiltonians. We derive an estimate for the statistical recovery error due to approximation of expectation values using a finite number of samples, which agrees well with numerical simulations.
    HamiltonianGibbs stateTime-dependent HamiltonianExpectation ValueQuantum devicesSteady stateMixed statesNumerical simulationQuantum simulatorsReduced density matrix...
  • For an autonomous agent to fulfill a wide range of user-specified goals at test time, it must be able to learn broadly applicable and general-purpose skill repertoires. Furthermore, to provide the requisite level of generality, these skills must handle raw sensory input such as images. In this paper, we propose an algorithm that acquires such general-purpose skills by combining unsupervised representation learning and reinforcement learning of goal-conditioned policies. Since the particular goals that might be required at test-time are not known in advance, the agent performs a self-supervised "practice" phase where it imagines goals and attempts to achieve them. We learn a visual representation with three distinct purposes: sampling goals for self-supervised practice, providing a structured transformation of raw sensory inputs, and computing a reward signal for goal reaching. We also propose a retroactive goal relabeling scheme to further improve the sample-efficiency of our method. Our off-policy algorithm is efficient enough to learn policies that operate on raw image observations and goals for a real-world robotic system, and substantially outperforms prior techniques.
    Reinforcement learningRoboticsAutoencoderQ-functionLatent variableGround truthPrecisionHyperparameterMean squared errorEuclidean distance...
  • Gibbsian statistical mechanics (GSM) is the most widely used version of statistical mechanics among working physicists. Yet a closer look at GSM reveals that it is unclear what the theory actually says and how it bears on experimental practice. The root cause of the difficulties is the status of the Averaging Principle, the proposition that what we observe in an experiment is the ensemble average of a phase function. We review different stances toward this principle, and eventually present a coherent interpretation of GSM that provides an account of the status and scope of the principle.
    Statistical mechanicsErgodicityRelaxation timeErgodic theoryPhase spaceMultidimensional ArrayChaosStatisticsMicrocanonical ensembleCanonical ensemble...
  • The motion of a handle spinning in space has an odd behavior. It seems to unexpectedly flip back and forth in a periodic manner as seen in a popular YouTube video. As an asymmetrical top, its motion is completely described by the Euler equations and the equations of motion have been known for more than a century. However, recent concepts of the geometric phase have allowed a new perspective on this classical problem. Here we explicitly use the equations of motion to find a closed form expression for the geometric phase of the asymmetric force-free top and explore some consequences of this formula with the particular example of the spinning handle for demonstration purposes. As one of the simplest dynamical systems, the asymmetric top should be a canonical example to explore the classical analogy of the Berry phase.
    Berry phaseEuler anglesEuler equationsClosed-form expressionElliptic integralYouTubeOrientationQuantizationAbsolute magnitudeVelocity function...
  • We publicly release a new sample of $34$ medium resolution quasar spectra at $5.77\leq z_{\rm em}\leq6.54$ observed with the Echellette Spectrograph and Imager (ESI) on the Keck telescope. This quasar sample represents an ideal laboratory to study the intergalactic medium (IGM) during the end stages of the epoch of reionization, and constrain the timing and morphology of the phase transition. For a subset of $23$ of our highest signal-to-noise ratio spectra (S/N$>7$, per $10\,{\rm km\,s^{-1}}$ pixel), we present a new measurement of the Lyman-$\alpha$ (Ly$\alpha$) forest opacity spanning the redshift range $4.8\lesssim z\lesssim6.3$. We carefully eliminate spectral regions that could be causing biases in our measurements due to additional transmitted flux in the proximity zone of the quasars, or extra absorption caused by strong intervening absorption systems along the line of sight. We compare the observed evolution of the IGM opacity with redshift to predictions from a hydrodynamical simulation with uniform ultraviolet background (UVB) radiation, as well as two semi-numerical patchy reionization models, one with a fluctuating UVB and another with a fluctuating temperature field. Our measurements show a steep rise in opacity at $z\gtrsim5.0$ and an increased scatter and thus support the picture of a spatially inhomogeneous reionization process, consistent with previous work. However, we measure significantly higher optical depths at $5.3\lesssim z\lesssim5.7$ than previous studies, which reduces the contrast between the highest opacity Gunn-Peterson troughs and the average opacity trend of the IGM, which may relieve some of the previously noted tension between these measurements and reionization models.
    QuasarOpacityIntergalactic mediumMean transmitted fluxCumulative distribution functionsReionizationUniform ultraviolet backgroundEpoch of reionizationSignal to noise ratioHydrodynamical simulations...
  • We present the first simulations of the high-redshift Ly$\alpha$ intensity field that account for scattering in the intergalactic medium (IGM). Using a 3D Monte Carlo radiative transfer code, we find that Ly$\alpha$ scattering smooths spatial fluctuations in the Ly$\alpha$ intensity on small scales and that the spatial dependence of this smoothing depends strongly on the mean neutral fraction of the IGM. Our simulations find a strong effect of reionization on $k=0.1-1~{\rm Mpc^{-1}}$, with $P_{\rm Ly\alpha}\propto k^{-1.75}$ for $\bar{x}_{\rm HI} = 0.63$ and $P_{\rm Ly\alpha} \propto k^{-2.2}$ for $\bar{x}_{\rm HI} = 0.86$ in contrast to $P_{\rm Ly\alpha}\propto k^{-1.5}$ after reionization. At wavenumbers of $k>1 ~ {\rm Mpc^{-1}}$, we find that the signal is sensitive to the emergent Ly$\alpha$ line profiles from galaxies. We also demonstrate that the cross-correlation between a Ly$\alpha$ intensity map and a future galaxy redshift survey could be detected on large scales by an instrument similar to SPHEREx, and over a wide range of scales by a hypothetical intensity mapping instrument in the vein of CDIM.
    Line intensity mappingIntergalactic mediumReionizationGalaxyIntensity21cmFASTIntergalactic gasNeutral IGMLine of sightCross-correlation...
  • We show how Newtonian cosmological simulations can be employed to investigate the non-linear evolution of two particle species in a relativistic context. We discuss the application for massive neutrinos and other multi-species systems such as Cold Dark Matter (CDM) plus baryons or Warm Dark Matter (WDM). We propose a method that allows us to perform simulations including massive neutrinos and general relativistic effects at almost the same computational cost as ordinary CDM only N-body simulations, employing tailor-made initial conditions and a dictionary for the interpretation of the simulation output.
    Cold dark matterNeutrinoWarm dark matterMassive neutrinoCosmologyN-body simulationGauge conditionBoltzmann codeMetric perturbationPerturbation theory...
  • It is well known that the quadratic-cost optimal transportation problem is formally equivalent to the second boundary value problem for the Monge-Amp\`ere equation. Viscosity solutions are a powerful tool for analysing and approximating fully nonlinear elliptic equations. However, we demonstrate that this nonlinear elliptic equation does not satisfy a comparison principle and thus existing theory of viscosity solutions is not valid. We introduce an alternative PDE that couples the usual Monge-Amp\`ere equation to a Hamilton-Jacobi equation that restricts the transportation of mass. We propose a new interpretation of the optimal transport problem in terms of viscosity subsolutions of this PDE. Equivalence of these two problems is established. This leads to a framework for proving convergence of a class of approximation schemes for the optimal transport problem.
    ViscosityBoundary value problemOptimal transport problemDiscretizationConvex setHamilton-Jacobi equationWeak solutionOptimal transportDirichlet problemExtreme point...
  • Vela X is a nearby pulsar wind nebula (PWN) powered by a $\sim 10^4$ year old pulsar. Modeling of the spectral energy distribution of the Vela X PWN has shown that accelerated electrons have largely escaped from the confinement, which is likely due to the disruption of the initially confined PWN by the SNR reverse shock. The escaped electrons propagate to the earth and contribute to the measured local cosmic-ray (CR) electron spectrum. We find that the escaped CR electrons from Vela X would hugely exceed the measured flux by HESS at $\sim 10$ TeV if the standard diffusion coefficient for the interstellar medium is used. We propose that the diffusion may be highly inefficient around Vela X and find that a spatially-dependent diffusion can lead to CR flux consistent with the HESS measurement. Using a two-zone model for the diffusion around Vela X, we find that the diffusion coefficient in the inner region of a few tens of parsecs should be $<10^{28}{\rm cm^2 s^{-1}}$ for $\sim10$ TeV CR electrons, which is about two orders of magnitude lower than the standard value for ISM. Such inefficient diffusion around PWN resembles the case of the Geminga and Monogem PWNe, suggesting that inefficient diffusion may be common in the vicinity of PWNe spanning a wide range of ages.
    Vela XCosmic rayDiffusion coefficientPulsar wind nebulaHESS telescopeEarthInterstellar mediumCosmic ray fluxPulsarGeminga...
  • With the increase in complexity of robotic systems and the rise in non-expert users, it can be assumed that a constraint in a task is not explicitly known. In tasks where avoiding singularity is critical to its success, this paper provides an approach, especially for non-expert users, for the system to learn the constraints contained in a set of demonstrations, such that they can be used to optimise an autonomous controller to avoid singularity, and thereby unpredictable behaviour when carrying out the task, without having to explicitly know the tasks constraint. The proposed approach avoids singularity by maximising task manipulability throughout the motion of the constrained system, and is not limited to kinematic systems. Its benefits are demonstrated through comparisons with other control policies.
    AttractorKinematicsGround truthRoboticsDegree of freedomAutonomous systemInverse problemsInterferenceTrajectoryPolynomial...
  • We present measurements of the X-ray observables of the intra-cluster medium (ICM), including luminosity $L_X$, ICM mass $M_{ICM}$, emission-weighted mean temperature $T_X$, and integrated pressure $Y_X$, that are derived from XMM-Newton X-ray observations of a Sunyaev-Zel'dovich Effect (SZE) selected sample of 59 galaxy clusters from the South Pole Telescope SPT-SZ survey that span the redshift range $0.20 < z < 1.5$. We constrain the best-fit power law scaling relations between X-ray observables, redshift, and halo mass. The halo masses are estimated based on previously published SZE observable to mass scaling relations, calibrated using information that includes the halo mass function. Employing SZE-based masses in this sample enables us to constrain these scaling relations for massive galaxy clusters ($M_{500}\geq 3 \times10^{14}$ $M_\odot$) to the highest redshifts where these clusters exist without concern for X-ray selection biases. We find that the mass trends are steeper than self-similarity in all cases, and with $\geq 2.5{\sigma}$ significance in the case of $L_X$ and $M_{ICM}$. The redshift trends are consistent with the self-similar expectation in all cases, but the uncertainties remain large. Core-included scaling relations tend to have steeper mass trends for $L_X$. There is no convincing evidence for a redshift-dependent mass trend in any observable. The log-normal intrinsic scatter in the observable at fixed halo mass varies from $\sim$0.10 for $M_{ICM}$ and core-excised $Y_X$ to $\sim$0.27 for core-included bolometric $L_X$. The constraints on the amplitudes of the fitted scaling relations are currently limited by the systematic uncertainties on the SZE-based halo masses, but the redshift and mass trends are limited by the X-ray sample size and the measurement uncertainties of the X-ray observables (abridged).
    Scaling lawSunyaev-Zel'dovich effectVirial massIntra-cluster mediumIntrinsic scatterLuminosityVirial cluster massCalibrationCluster of galaxiesCluster sampling...
  • AXIS is a probe-class concept under study for submission to the 2020 Decadal Survey. AXIS will extend and enhance the science of high angular resolution X-ray imaging and spectroscopy in the next decade with $\sim 0.4''$ resolution over a 24$' \times 24'$ field of view, with 0.3$"$ in the central 14$' \times 14'$, and ~10x more collecting area than Chandra. These capabilities are made possible by precision-polished lightweight single-crystal silicon optics achieving both high angular resolution and large collecting area, and next generation small-pixel silicon detectors adequately sampling the point spread function and allowing timing science and preventing pile up with high read-out rate. We have selected a low earth orbit to enable rapid target of opportunity response, similar to Swift, with a high observing efficiency, low detector background and long detector life. The combination opens a wide variety of new and exciting science such as: (1) measuring the event horizon scale structure in AGN accretion disks and the spins of supermassive black holes through observations of gravitationally-microlensed quasars; (ii) determining AGN and starburst feedback in galaxies and galaxy clusters through direct imaging of winds and interaction of jets and via spatially resolved imaging of galaxies at high-z; (iii) fueling of AGN by probing the Bondi radius of over 20 nearby galaxies; (iv) hierarchical structure formation and the SMBH merger rate through measurement of the occurrence rate of dual AGN and occupation fraction of SMBHs; (v) advancing SNR physics and galaxy ecology through large detailed samples of SNR in nearby galaxies; (vi) measuring the Cosmic Web through its connection to cluster outskirts; (vii) a wide variety of time domain science including rapid response to ToOs. With a nominal 2028 launch, AXIS benefits from natural synergies with the ELTs, LSST, ALMA, WFIRST and ATHENA.
    Chandra X-ray ObservatoryActive Galactic NucleiGalaxySupermassive black holeBlack holeHigh angular resolutionIntergalactic mediumCluster of galaxiesNearby galaxiesSupernova...
  • In this work we revisit the concept of chemical potential $\mu$ in both classical and quantum gases from a perspective of Equilibrium Statistical Mechanics (ESM). Two new results regarding the equation of state $\mu=\mu(n,T)$, where $n$ is the particle density and $T$ the absolute temperature, are given for the classical interacting gas and for the weakly-interacting quantum Bose gas. In order to make this review self-contained and adequate for a general reader we provide all the basic elements in an advanced-undergraduate or graduate statistical mechanics course required to follow all the calculations. We start by presenting a calculation of $\mu(n,T)$ for the classical ideal gas in the canonical ensemble. After this, we consider the interactions between particles and compute the effects of them on $\mu(n,T)$ for the van der Waals gas. For quantum gases we present an alternative approach to calculate the Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. We show that this scheme can be straightforwardly generalized to determine what we have called Intermediate Quantum Statistics (IQS) which deal with ideal quantum systems where a single-particle energy can be occupied by at most $j$ particles with $0 \leqslant j \leqslant N$ with $N$ the total number of particles. In the final part we address general considerations that underlie the theory of weakly interacting quantum gases. In the case of the weakly interacting Bose gas, we focus our attention to the equation of state $\mu=\mu(n,T)$ in the Hartree-Fock mean-field approximation (HF) and the implications of such results in the elucidation of the order of the phase transitions involved in the BEC phase for non-ideal Bose gases.
    Bose gasBose-Einstein condensateHartree-Fock approximationFermi gasHamiltonianEntropyEquilibrium statistical mechanicsCanonical ensemblePartition functionPhase transitions...
  • Several Monte Carlo algorithms and applications that are useful for understanding the concepts of temperature and chemical potential are discussed. We then introduce a generalization of the demon algorithm that measures the chemical potential and is suitable for simulating systems with variable particle number.
  • Naturalness is an extra-empirical quality that aims to assess plausibility of a theory. Finetuning measures are one way to quantify the task. However, knowing statistical distributions on parameters appears necessary for rigor. Such meta-theories are not known yet. A critical discussion of these issues is presented, including their possible resolutions in fixed points. Skepticism of naturalness's utility remains credible, as is skepticism to any extra-empirical theory assessment (SEETA) that claims to identify "more correct" theories that are equally empirically adequate. Specifically to naturalness, SEETA implies that one must accept all concordant theory points as a priori equally plausible, with the practical implication that a theory can never have its plausibility status diminished by even a "massive reduction" of its viable parameter space as long as a single theory point still survives. A second implication of SEETA suggests that only falsifiable theories allow their plausibility status to change, but only after discovery or after null experiments with total theory coverage. And a third implication of SEETA is that theory preference then becomes not about what theory is more correct but what theory is practically more advantageous, such as fewer parameters, easier to calculate, or has new experimental signatures to pursue.
    NaturalnessGauge coupling constantSupersymmetryRenormalisation group flowGrand unification theorySupersymmetricLarge Hadron ColliderGUT scaleInfrared fixed pointHiggs boson...
  • Fine-tuning criteria are frequently used to place upper limits on the masses of superpartners in supersymmetric extensions of the standard model. However, commonly used prescriptions for quantifying naturalness have some important shortcomings. Motivated by this, we propose new criteria for quantifying fine tuning that can be used to place upper limits on superpartner masses with greater fidelity. In addition, our analysis attempts to make explicit the assumptions implicit in quantifications of naturalness. We apply our criteria to the minimal supersymmetric extension of the standard model, and we find that the scale of supersymmetry breaking can be larger than previous methods indicate.
    NaturalnessMinimal supersymmetric Standard ModelElectroweak scaleSupersymmetricSupersymmetry breakingSupersymmetrySuperpartner massesElectroweak symmetry breakingSuperpartnerExtensions of the standard model...
  • We critically analyze the rationale of arguments from finetuning and naturalness in particle physics and cosmology. Some other numerological coincidences are also discussed.
    NaturalnessStandard ModelTechnical NaturalnessCosmological constantFoundation of PhysicsHiggs bosonCosmologyGauge coupling constantNaturalness problemHiggs boson mass...
  • The basic load balancing scenario involves a single dispatcher where tasks arrive that must immediately be forwarded to one of $N$ single-server queues. We discuss recent advances on scalable load balancing schemes which provide favorable delay performance when $N$ grows large, and yet only require minimal implementation overhead. Join-the-Shortest-Queue (JSQ) yields vanishing delays as $N$ grows large, as in a centralized queueing arrangement, but involves a prohibitive communication burden. In contrast, power-of-$d$ or JSQ($d$) schemes that assign an incoming task to a server with the shortest queue among $d$ servers selected uniformly at random require little communication, but lead to constant delays. In order to examine this fundamental trade-off between delay performance and implementation overhead, we consider JSQ($d(N)$) schemes where the diversity parameter $d(N)$ depends on $N$ and investigate what growth rate of $d(N)$ is required to asymptotically match the optimal JSQ performance on fluid and diffusion scale. Stochastic coupling techniques and stochastic-process limits play an instrumental role in establishing the asymptotic optimality. We demonstrate how this methodology carries over to infinite-server settings, finite buffers, multiple dispatchers, servers arranged on graph topologies, and token-based load balancing including the popular Join-the-Idle-Queue (JIQ) scheme. In this way we provide a broad overview of the many recent advances in the field. This survey extends the short review presented at ICM 2018 (arXiv:1712.08555).
    GraphSteady stateConjunctionBrownian motionDiffusion processMajorizationRandom graphPoisson processData centerStationary distribution...
  • This paper deals with the two fundamental problems concerning the handling of large n-gram language models: indexing, that is compressing the n-gram strings and associated satellite data without compromising their retrieval speed; and estimation, that is computing the probability distribution of the strings from a large textual source. Regarding the problem of indexing, we describe compressed, exact and lossless data structures that achieve, at the same time, high space reductions and no time degradation with respect to state-of-the-art solutions and related software packages. In particular, we present a compressed trie data structure in which each word following a context of fixed length k, i.e., its preceding k words, is encoded as an integer whose value is proportional to the number of words that follow such context. Since the number of words following a given context is typically very small in natural languages, we lower the space of representation to compression levels that were never achieved before. Despite the significant savings in space, our technique introduces a negligible penalty at query time. Regarding the problem of estimation, we present a novel algorithm for estimating modified Kneser-Ney language models, that have emerged as the de-facto choice for language modeling in both academia and industry, thanks to their relatively low perplexity performance. Estimating such models from large textual sources poses the challenge of devising algorithms that make a parsimonious use of the disk. The state-of-the- art algorithm uses three sorting steps in external memory: we show an improved construction that requires only one sorting step thanks to exploiting the properties of the extracted n-gram strings. With an extensive experimental analysis performed on billions of n-grams, we show an average improvement of 4.5X on the total running time of the state-of-the-art approach.
    Data structuresMultidimensional ArrayCountingRankOptimizationStatisticsQuantizationSoftwareMachine translationNatural language...
  • Accurate face recognition techniques make a series of critical applications possible: policemen could employ it to retrieve criminals' faces from surveillance video streams; cross boarder travelers could pass a face authentication inspection line without the involvement of officers. Nonetheless, when public security heavily relies on such intelligent systems, the designers should deliberately consider the emerging attacks aiming at misleading those systems employing face recognition. We propose a kind of brand new attack against face recognition systems, which is realized by illuminating the subject using infrared according to the adversarial examples worked out by our algorithm, thus face recognition systems can be bypassed or misled while simultaneously the infrared perturbations cannot be observed by raw eyes. Through launching this kind of attack, an attacker not only can dodge surveillance cameras. More importantly, he can impersonate his target victim and pass the face authentication system, if only the victim's photo is acquired by the attacker. Again, the attack is totally unobservable by nearby people, because not only the light is invisible, but also the device we made to launch the attack is small enough. According to our study on a large dataset, attackers have a very high success rate with a over 70\% success rate for finding such an adversarial example that can be implemented by infrared. To the best of our knowledge, our work is the first one to shed light on the severity of threat resulted from infrared adversarial examples against face recognition.
    EmbeddingFaraday rotationCalibrationOptimizationMountingDeep Neural NetworksSecurityFeature vectorMachine learningPhoton Wave Mechanics...
  • The twin paradox, which evokes from the the idea that two twins may age differently because of their relative motion, has been studied and explained ever since it was first described in 1906, the year after special relativity was invented. The question can be asked: "Is there anything more to say?" It seems evident that acceleration has a role to play, however this role has largely been brushed aside since it is not required in calculating, in a preferred reference frame, the relative age difference of the twins. Indeed, if one tries to calculate the age difference from the point of the view of the twin that undergoes the acceleration, then the role of the acceleration is crucial and cannot be dismissed. In the resolution of the twin paradox, the role of the acceleration has been denigrated to the extent that it has been treated as a red-herring. This is a mistake and shows a clear misunderstanding of the twin paradox.
    Proper timeTwin ParadoxSpecial relativityGeneral relativityLorentz invariantInfinitesimalLorentz transformationTime-reversal symmetryTime dilationDiffeomorphism invariance...
  • The Aharonov-Bohm effect including spin-noncommutative effects is considered. At linear order in $\theta$, the magnetic field is gauge invariant although spatially strongly anisotropic. Despite this anisotropy, the Schr\"odinger-Pauli equation is separable through successive unitary transformations and the exact solution is found. The scattering amplitude is calculated and compared with the usual case. In the noncommutative Aharonov-Bohm case the differential cross section is independent of $\theta$.
  • We propose a class of models in which a stable inflaton is produced as a thermal relic in the early universe and constitutes the dark matter. We show that inflaton annihilations can efficiently reheat the universe, and identify several examples of inflationary potentials that can accommodate all cosmic microwave background observables and in which the inflaton dark matter candidate has a weak scale mass. As a simple example, we consider annihilations that take place through a Higgs portal interaction, leading to encouraging prospects for future direct detection experiments.
    InflatonDark matterInflationReheatingStandard ModelHiggs portalCosmic microwave backgroundDark matter candidateHiggs bosonRelic abundance...
  • An extension of the Standard Model with Majorana singlet fermions in the 1-100 GeV range can give rise to a baryon asymmetry at freeze-in via the CP-violating oscillations of these neutrinos: this is the well known ARS mechanism. In this paper we consider possible extensions of the minimal ARS scenario that can account not only for successful leptogenesis but also explain other open problems such as dark matter. We find that an extension in the form of a weakly coupled B-L gauge boson, an invisible QCD axion model, and the singlet majoron model can simultaneously account for dark matter and the baryon asymmetry.
    Sterile neutrinoLeptogenesisMajoronDark matterBaryon asymmetry of the UniverseNeutrinoAxionFreeze-inFlavourYukawa coupling...
  • Context: In a series of papers, we study the major merger of two disk galaxies in order to establish whether or not such a merger can produce a disc galaxy. Aims: Our aim here is to describe in detail the technical aspects of our numerical experiments. Methods: We discuss the initial conditions of our major merger, which consist of two protogalaxies on a collision orbit. We show that such merger simulations can produce a non-realistic central mass concentration, and we propose simple, parametric, AGN-like feedback as a solution to this problem. Our AGN-like feedback algorithm is very simple: at each time-step we take all particles whose local volume density is above a given threshold value and increase their temperature to a preset value. We also compare the GADGET3 and GIZMO codes, by applying both of them to the same initial conditions. Results: We show that the evolution of isolated protogalaxies resembles the evolution of disk galaxies, thus arguing that our protogalaxies are well suited for our merger simulations. We demonstrate that the problem with the unphysical central mass concentration in our merger simulations is further aggravated when we increase the resolution. We show that our AGN-like feedback removes this non-physical central mass concentration, and thus allows the formation of realistic bars. Note that our AGN-like feedback mainly affects the central region of a model, without significantly modifying the rest of the galaxy. We demonstrate that, in the context of our kind of simulation, GADGET3 gives results which are very similar to those obtained with the PSPH (density independent SPH) flavor of GIZMO. Moreover, in the examples we tried, the differences between the results of the two flavors of GIZMO, namely PSPH, and MFM (mesh-less algorithm) are similar to and, in some comparisons, larger than the differences between the results of GADGET3 and PSPH.
    Active Galactic NucleiEddington limitProtogalaxyDisk galaxyCircular velocityConcentration-mass relationStarAccretionBumpingBlack hole...
  • What is the first prime? It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the first prime, we must also know what the first positive integer is. Surprisingly, with the definitions used at various times throughout history, one was often not the first positive integer (some started with two, and a few with three). In this article, we survey the history of the primality of one, from the ancient Greeks to modern times. We will discuss some of the reasons definitions changed, and provide several examples. We will also discuss the last significant mathematicians to list the number one as prime.
    Prime numberEuclid missionFundamental theorem of arithmeticComposite numberDeityCountingPerfect numberClassificationTetradAmicable number...
  • In 1947 Mills proved that there exists a constant $A$ such that $\lfloor A^{3^n} \rfloor$ is a prime for every positive integer $n$. Determining $A$ requires determining an effective Hoheisel type result on the primes in short intervals - though most books ignore this difficulty. Under the Riemann Hypothesis, we show that there exists at least one prime between every pair of consecutive cubes and determine (given RH) that the least possible value of Mills' constant $A$ does begin with 1.3063778838. We calculate this value to 6850 decimal places by determining the associated primes to over 6000 digits and probable primes (PRPs) to over 60000 digits. We also apply the Cram\'er-Granville Conjecture to Honaker's problem in a related context.
    Riemann hypothesisPrime numberElliptic curveZeta functionStatisticsComputer programmingPrimary star in a binary systemRelaxationProbabilityReal numbers...
  • The Radial Acceleration Relation confirms that a nontrivial acceleration scale can be found in the average internal dynamics of galaxies. The existence of such a scale is not obvious as far as the standard cosmological model is concerned, and it has been interpreted as a possible sign of modified gravity. The implications could be profound: it could in principle explain galactic dynamics without large amounts of yet-undetected dark matter and address issues that the standard cosmological model faces at galactic scales. Here, we consider 193 disk galaxies from the SPARC and THINGS databases and, using Bayesian inference, we show that the probability of existence of a fundamental acceleration that is common to all the galaxies is essentially zero: the $p$-value is smaller than $10^{-20}$ or, equivalently, the null hypothesis is rejected at more than 10$\sigma$. We conclude that the acceleration scale unveiled by the Radial Acceleration Relation is of emergent nature, possibly caused by a complex interplay between baryons and dark matter. In particular, the MOND theory, or any other theory that behaves like it at galactic scales, is ruled out as a fundamental theory for galaxies at more than 10$\sigma$.
    GalaxyModified Newtonian DynamicsSpitzer Photometry and Accurate Rotation CurvesMilky WayDark matterBayesian approachTHINGS surveyRotation CurveMass to light ratioStandard cosmological model...
  • We present a model-independent bound on $R(J/\psi) \! \equiv \! \mathcal{BR} (B_c^+ \rightarrow J/\psi \, \tau^+\nu_\tau)/ \mathcal{BR} (B_c^+ \rightarrow J/\psi \, \mu^+\nu_\mu)$. This bound is constructed by constraining the form factors through a combination of dispersive relations, heavy-quark relations at zero-recoil, and the limited existing determinations from lattice QCD. The resulting 95\% confidence-level bound, $0.20\leq R(J/\psi)\leq0.39$, agrees with the recent LHCb result at $1.3 \, \sigma$, and rules out some previously suggested model form factors.
    Form factorHeavy quarkLHCbLattice QCDMomentum transferStandard ModelMeson decaysBranch pointTransition form factorSystematic error...
  • We extend our previous analysis on the mass of the recently discovered $\Omega(2012)$ state by investigation of its strong decays and calculation of its width employing the method of light cone QCD sum rule. Considering two possibilities for the quantum numbers of $\Omega(2012)$ state, namely $1P$ orbital excitation with $J^P=\frac{3}{2}^-$ and $2S$ radial excitation with $J^P=\frac{3}{2}^+$, we obtain the strong coupling constants defining the $\Omega(1P/2S)\rightarrow\Xi K$ decays. The results of the coupling constants are then used to calculate the decay width corresponding to each possibility. Comparison of the obtained results on the width in this work with the experimental value and taking into account the results of our previous mass prediction on the $\Omega(2012)$ state, we conclude that this state is $1P$ orbital excitation of the ground state $\Omega$ baryon, whose quantum numbers are $J^P=\frac{3}{2}^-$.
    Coupling constantDecay widthQCD sum rulesExcited stateTwo-point correlation functionLight conesStrong coupling constantLight-cone sum rulesBorel parameterPropagator...
  • While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example problems, there is scope for machine learning tools like Support Vector Machines to improve the performance of Computer Algebra Systems. We survey the authors own work and similar applications for other mathematical software. It may seem that the inherently probabilistic nature of machine learning tools would invalidate the exact results prized by mathematical software. However, algorithms and implementations often come with a range of choices which have no effect on the mathematical correctness of the end result but a great effect on the resources required to find it, and thus here, machine learning can have a significant impact.
    Machine learningSoftwareComputer algebra systemComputational linguisticsSupport vector machineOptimisation problemPortfolioClassificationFeature selectionOverfitting...
  • The generic matrix-matrix multiplication (GEMM) is arguably the most popular computational kernel of the 20th century. Yet, surprisingly, no common methodology for evaluating GEMM performance has been established over the many decades of using GEMM for comparing architectures, compilers and ninja-class programmers. We introduce GEMMbench, a framework and methodology for evaluating performance of GEMM implementations. GEMMbench is implemented on top of Collective Knowledge (CK), a lightweight framework for reproducible and collaborative R&D in computer systems. Using CK allows the R&D community to crowdsource hand-written and compiler-generated GEMM implementations and to study their performance across multiple platforms, data sizes and data types. Our initial implementation supports hand-written OpenCL kernels operating on matrices consisting of single- and double-precision floating-point values, and producing single or multiple output elements per work-item (via thread coarsening and vectorization).
    ArchitectureCrowdsourcingOptimizationCompilersVectorTranspose of a matrixEnergyDimensionsMeasurementScalar...