• Quantum Probes of Spacetime Singularitiesver. 3

It is shown that there are static spacetimes with timelike curvature singularities which appear completely nonsingular when probed with quantum test particles. Examples include extreme dilatonic black holes and the fundamental string solution. In these spacetimes, the dynamics of quantum particles is well defined and uniquely determined.
• Entanglement entropy in free quantum field theoryver. 3

In this review we first introduce the general methods to calculate the entanglement entropy for free fields, within the Euclidean and the real time formalisms. Then we describe the particular examples which have been worked out explicitly in two, three and more dimensions.
EntropyEntanglement entropyGreen's functionQuantum field theoryPartition functionDirac fieldDensity matrixHamiltonianHelmholtz equationDegree of freedom...
• Holistically-Nested Edge Detectionver. 2

We develop a new edge detection algorithm that tackles two important issues in this long-standing vision problem: (1) holistic image training and prediction; and (2) multi-scale and multi-level feature learning. Our proposed method, holistically-nested edge detection (HED), performs image-to-image prediction by means of a deep learning model that leverages fully convolutional neural networks and deeply-supervised nets. HED automatically learns rich hierarchical representations (guided by deep supervision on side responses) that are important in order to approach the human ability resolve the challenging ambiguity in edge and object boundary detection. We significantly advance the state-of-the-art on the BSD500 dataset (ODS F-score of .782) and the NYU Depth dataset (ODS F-score of .746), and do so with an improved speed (0.4 second per image) that is orders of magnitude faster than some recent CNN-based edge detection algorithms.
ArchitectureConvolutional neural networkDeep learningClassificationHyperparameterBackpropagationDeep Neural NetworksImage ProcessingTraining setNeural network...
• The approach to thermal equilibrium in quantized chaotic systemsver. 2

We consider many-body quantum systems that exhibit quantum chaos, in the sense that the observables of interest act on energy eigenstates like banded random matrices. We study the time-dependent expectation values of these observables, assuming that the system is in a definite (but arbitrary) pure quantum state. We induce a probability distribution for the expectation values by treating the zero of time as a uniformly distributed random variable. We show explicitly that if an observable has a nonequilibrium expectation value at some particular moment, then it is overwhelmingly likely to move towards equilibrium, both forwards and backwards in time. For deviations from equilibrium that are not much larger than a typical quantum or thermal fluctuation, we find that the time dependence of the move towards equilibrium is given by the Kubo correlation function, in agreement with Onsager's postulate. These results are independent of the details of the system's quantum state.
ThermalisationExpectation ValueQuantizationUniform distributionTwo-point correlation functionQuantum chaosProbabilityEnergyFluctuation...
• Equivariant categories from categorical group actions on monoidal categories

G-equivariant modular categories provide the input for a standard method to construct 3d homotopy field theories. Virelizier constructed a G-equivariant category from the action of a group G on a Hopf algebra H by Hopf algebra automorphisms. The neutral component of his category is the Drinfeld center of the category of H-modules. We generalize this construction to weak actions of a group G on an arbitrary monoidal category C by (possibly non-strict) monoidal auto-equivalences and obtain a G-equivariant category with neutral component the Drinfeld center of C.
MonoidHopf algebraAutomorphismGroup actionField theoryIsomorphismGauge transformationModularityHomomorphismGroup homomorphism...
• Lieb-Liniger model: emergence of dark solitons in the course of measurements of particle positionsver. 3

Lieb-Liniger model describes bosons with contact interactions in one-dimensional space. In the limit of weak repulsive particle interactions, there are two types of low lying excitation spectrum. The first is reproduced by the Bogoliubov dispersion relation, the other is believed to correspond to dark soliton excitations. While there are various evidences that the type II spectrum is related to dark solitons, it has not been shown that measurements of positions of particles reveal dark soliton density profiles. Here, we employ the Bethe ansatz approach and show that dark solitons emerge in the measurement process if the system is prepared in an eigenstate corresponding to the type II spectrum. We analyze single and double dark solitons as well as weak and strong interaction regime.
SolitonMean fieldWeak interactionStrong interactionsWavefunctionBethe ansatzForm factorHamiltonianPeriodic boundary conditionsComputational science...
• Stability and Hamiltonian formulation of higher derivative theoriesver. 2

We analyze the presumptions which lead to instabilities in theories of order higher than second. That type of fourth order gravity which leads to an inflationary (quasi de Sitter) period of cosmic evolution by inclusion of one curvature squared term (i.e. the Starobinsky model) is used as an example. The corresponding Hamiltonian formulation (which is necessary for deducing the Wheeler de Witt equation) is found both in the Ostrogradski approach and in another form. As an example, a closed form solution of the Wheeler de Witt equation for a spatially flat Friedmann model and L=R\sp 2 is found. The method proposed by Simon to bring fourth order gravity to second order can be (if suitably generalized) applied to bring sixth order gravity to second order. In the Erratum we show that a spatially flat Friedmann model need not be geodesically complete even if the scale factor a(t) is positive and smooth for all real values of the synchronized time t.
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics

We show that the proper inclusion of soft reparameterization modes in the Sachdev-Ye-Kitaev model of $N$ randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantum mechanics. As a result, all zero temperature correlation functions decay with the universal exponent $\propto \tau^{-3/2}$ for times larger than the inverse single particle level spacing $\tau\gg N\ln N$. In the particular case of the single particle Green function this behavior is manifestation of the zero-bias anomaly, or scaling in energy as $\epsilon^{1/2}$. We also present exact diagonalization study supporting our conclusions.
Two-point correlation functionQuantum mechanicsGreen's functionMajorana fermionManifoldMean fieldGoldstone bosonPath integralExpectation ValueSaddle point...
• Weyl Anomaly and Initial Singularity Crossingver. 2

We consider the role of quantum effects, mainly, Weyl anomaly in modifying FLRW model singular behavior at early times. Weyl anomaly corrections to FLRW models have been considered in the past, here we reconsider this model and show the following: The singularity of this model is weak according to Tipler and Krolak, therefore, the spacetime might admit a geodesic extension. Weyl anomaly corrections changes the nature of the initial singularity from a big bang singularity to a sudden singularity. The two branches of solutions consistent with the semiclassical treatment form a disconnected manifold. Joining these two parts at the singularity provides us with a $C^1$ extension to nonspacelike geodesics and leaves the spacetime geodesically complete. Using Gauss-Codazzi equations one can derive generalized junction conditions for this higher-derivative gravity. The extended spacetime obeys Friedmann and Raychaudhuri equations and the junction conditions. The junction does not generate Dirac delta functions in matter sources which keeps the equation of state unchanged.
GeodesicWeyl anomalyFriedmann-Lemaitre-Robertson-Walker metricCosmologyFriedmann equationsGauss-Codazzi equationsSpace-time singularityEquation of stateBig BangManifold...
• An SYK-Like Model Without Disorderver. 2

Making use of known facts about "tensor models," it is possible to construct a quantum system without quenched disorder that has the same large $n$ limit for its correlation functions and thermodynamics as the SYK model. This might be useful in further probes of this approach to holographic duality.
GraphFeynman diagramsQuenchingRandom matrix theoryDualityHamiltonianPermutationManifoldSymmetry groupTwo-point correlation function...
• Physics, Topology, Logic and Computation: A Rosetta Stonever. 3

In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much like a "cobordism". Similar diagrams can be used to reason about logic, where they represent proofs, and computation, where they represent programs. With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. In this expository paper, we make some of these analogies precise using the concept of "closed symmetric monoidal category". We assume no prior knowledge of category theory, proof theory or computer science.
MorphismMonoidIsomorphismTensor productCategory theoryFeynman diagramsProgramming LanguageManifoldQuantum computationProof theory...
• Modeling BSM effects on the Higgs transverse-momentum spectrum in an EFT approach

We consider the transverse-momentum distribution of a Higgs boson produced through gluon fusion in hadron collisions. At small transverse momenta, the large logarithmic terms are resummed up to next-to-leading-logarithmic (NLL) accuracy. The resummed computation is consistently matched to the next-to-leading-order (NLO) result valid at large transverse momenta. The ensuing Standard Model prediction is supplemented by possible new-physics effects parametrised through three dimension-six operators related to the modification of the top and bottom Yukawa couplings, and to the inclusion of a point-like Higgs-gluon coupling, respectively. We present resummed transverse-momentum spectra including the effect of these operators at NLL+NLO accuracy and study their impact on the shape of the distribution. We find that such modifications, while affecting the total rate within the current uncertainties, can lead to significant distortions of the spectrum. The proper parametrization of such effects becomes increasingly important for experimental analyses in Run II of the LHC.
Higgs bosonStandard ModelTransverse momentumResummationDimension--six operatorsYukawa couplingNext-to-next-to-leading order computationRenormalizationHard thermal loopLarge Hadron Collider...
• Package-X 2.0: A Mathematica package for the analytic calculation of one-loop integrals

This arXiv post announces the public release of Package-X 2.0, a Mathematica package for the analytic calculation of one-loop integrals. Package-X 2.0 can now generate analytic expressions for arbitrarily high rank dimensionally regulated tensor integrals with up to four distinct propagators, each with arbitrary integer weight, near an arbitrary even number of spacetime dimensions, giving UV divergent, IR divergent, and finite parts at (almost) any real-valued kinematic point. Additionally, it can generate multivariable Taylor series expansions of these integrals around any non-singular kinematic point to arbitrary order. All special functions and abbreviations output by Package-X 2.0 supports Mathematica's arbitrary precision evaluation capabilities to deal with issues of numerical stability. Finally, tensor algebraic routines of Package-X have been polished and extended to support open fermion chains both on and off shell. The documentation (equivalent to over 100 printed pages) is accessed through Mathematica's Wolfram Documentation Center and contains information on all Package-X symbols, with over 300 basic usage examples, 3 project-scale tutorials, and instructions on linking to FeynCalc and LoopTools.
One-loop integralsKinematicsLoop integralGamma matricesWolfram Mathematica packagePropagatorFeynman parameterRankWolfram MathematicaInfrared divergence...
• Suppressing structure formation at dwarf galaxy scales and below: late kinetic decoupling as a compelling alternative to warm dark matterver. 3

Warm dark matter cosmologies have been widely studied as an alternative to the cold dark matter paradigm, the characteristic feature being a suppression of structure formation on small cosmological scales. A very similar situation occurs if standard cold dark matter particles are kept in local thermal equilibrium with a, possibly dark, relativistic species until the universe has cooled down to keV temperatures. We perform a systematic phenomenological study of this possibility, and classify all minimal models containing dark matter and an arbitrary radiation component that allow such a late kinetic decoupling. We recover explicit cases recently discussed in the literature and identify new classes of examples that are very interesting from a model-building point of view. In some of these models dark matter is inevitably self-interacting, which is remarkable in view of recent observational support for this possibility. Hence, dark matter models featuring late kinetic decoupling have the potential not only to alleviate the missing satellites problem but also to address other problems of the cosmological concordance model on small scales, in particular the cusp-core and too-big-too-fail problems, in some cases without invoking any additional input.
Dark matterDark RadiationKinetic decouplingDark matter particleDark matter particle massThermalisationSelf-interacting dark matterWarm dark matterScattering amplitudeLocal thermal equilibrium...
• Hunting Dark Matter in ultra-compact structures: from large scales to the solar system

Ultra-Compact Micro Halos (UCMHs) are objects formed in the early universe that persist due to their large central density inuring them to the worst effects of later tidal stripping. Such objects are probes of many details of early universe physics, such as primordial phase-transitions, inflation, and non-Gaussianity of the primordial density perturbation field. The fact that they are also highly dark matter-dominated objects means that they are attractive objects of study in the continuing hunt for the nature of Dark Matter (DM). The local environment of our Milky-Way offers interesting perspectives for their possible detection with future radio and $\gamma$-ray telescopes. Their detection, or lack thereof, providing constraints on both cosmology and large-scale structure physics. Another reason to study such objects in the local environment of the solar system is found in the conjecture that encounters with UCMHs could induce catastrophic events on planets within our solar system, e.g. mass-extinction events on Earth. All these arguments provide compelling reasons to determine what fraction of WIMP DM could be contained in these structures, and what the consequences of its annihilation might be. In this work we studied the inter-relation of the WIMP annihilation cross-section and the maximum fraction of DM found in UCMHs using the multi-frequency consequences of DM annihilation within these objects, as well as constraints that can be further derived upon the primordial power spectrum of perturbations. Finally, we revisit the hypothesis of "volcanogenic" DM inducing mass extinction events on Earth. In so doing we cast doubts on this hypothesis but suggest that it could instead be motivated as a driver of Martian mantle de-gassing that eventually shuts down the geodynamo within the red planet.
Dark matterWeakly interacting massive particleEarthSquare Kilometre ArrayFERMI telescopeMarsMantleCherenkov Telescope ArraySolar systemPlanet...
• Measuring alignments between galaxies and the cosmic web at $z \sim 2-3$ using IGM tomography

Many galaxy formation models predict alignments between galaxy spin and the cosmic web (i.e. the directions of filaments and sheets), leading to intrinsic alignment between galaxies that creates a systematic error in weak lensing measurements. These effects are often predicted to be stronger at high-redshifts ($z\gtrsim1$) that are inaccessible to massive galaxy surveys on foreseeable instrumentation, but IGM tomography of the Ly$\alpha$ forest from closely-spaced quasars and galaxies is starting to measure the $z\sim2-3$ cosmic web with the requisite fidelity. Using mock surveys from hydrodynamical simulations, we examine the utility of this technique, in conjunction with coeval galaxy samples, to measure alignment between galaxies and the cosmic web at $z\sim2.5$. We show that IGM tomography surveys with $\lesssim5$ $h^{-1}$ Mpc sightline spacing can accurately recover the eigenvectors of the tidal tensor, which we use to define the directions of the cosmic web. For galaxy spins and shapes, we use a model parametrized by the alignment strength, $\Delta\langle\cos\theta\rangle$, with respect to the tidal tensor eigenvectors from the underlying density field, and also consider observational effects such as errors in the galaxy position angle, inclination, and redshift. Measurements using the upcoming $\sim1\,\mathrm{deg}^2$ CLAMATO tomographic survey and 600 coeval zCOSMOS-Deep galaxies should place $3\sigma$ limits on extreme alignment models with $\Delta\langle\cos\theta\rangle\sim0.1$, but much larger surveys encompassing $>10,000$ galaxies, such as Subaru PFS, will be required to constrain models with $\Delta\langle\cos\theta\rangle\sim0.03$. These measurements will constrain models of galaxy-cosmic web alignment and test tidal torque theory at $z\sim2$, improving our understanding of the redshift dependence of galaxy-cosmic web alignment and the physics of intrinsic alignments.
Cosmic webGalaxy filamentVoidIntrinsic alignmentSignal to noise ratioHydrodynamical simulationsQuasarSpiral galaxyMilky WayCovariance...
• Energy Conservation and the Chiral Magnetic Effect

We analyze the chiral magnetic effect in a neutral plasma from the point of view of energy conservation, and construct an effective potential for the growth of helical perturbations of the electromagnetic field. We show that a negative curvature at the origin of the potential, indicating instability of the plasma, is induced by a chiral asymmetry in electron Fermi energy, as opposed to number density, while the potential grows at large field value. It follows that the ground state for a plasma has zero magnetic helicity; a nonzero electron mass will allow an excited state of a plasma with nonzero helicity to relax to that ground state quickly. We conclude that a chiral plasma instability triggered by weak interactions is not a viable mechanism for explaining magnetic fields in neutron stars.
InstabilityChiral chemical potentialChiral magnetic effectHelical magnetic fieldFermi energyChiralityWeak interactionElectron massGauge fieldEffective potential...
• Mass modeling of galaxy clusters: quantifying hydrostatic bias and contribution from non-thermal pressurever. 2

Galaxy cluster mass determinations achieved using X-ray and Sunyaev-Zel'dovich data combined with the assumption of hydrostatic equilibrium are generally biased. The bias exists for two main reasons: non-thermal pressure forces are expected to contribute to the overall pressure balance and deviations from spherical symmetry and hydrostatic equilibrium can be present. In this paper, we use a sample of zoom-in hydrodynamical simulations of galaxy clusters to measure the magnitude of hydrostatic bias and the non-thermal contribution to the total pressure. We propose a new empirical model for non-thermal pressure based on our simulations that can be applied to observations. We show that our model can be successfully applied to remove most of the bias related to neglection of non-thermal pressure, which is usually not included in hydrostatic cluster mass profile reconstructions. The use of this model may significantly improve the calibration of cluster scaling relations that are a key tool for cluster cosmology.
Cluster of galaxiesHydrostatic equilibriumVirial cluster massHydrostaticsMass profilePressure profileStatistical estimatorHydrostatic massPressure supportCalibration...
• Quantized Faraday and Kerr rotation and axion electrodynamics of the surface states of three-dimensional topological insulatorsver. 3

Topological insulators have been proposed to be best characterized as bulk magnetoelectric materials which show response functions quantized in terms of fundamental physical constants. It has been predicted that this manifests as Faraday and Kerr rotations quantized in units of the fine structure constant $\alpha=e^2/2 \epsilon_0 hc$. In this work we use a charge-transfer-doping preparation to lower the chemical potential of Bi$_2$Se$_3$ films into the bulk gap and as low as $\sim$ 30 meV above the Dirac point, and then probe their low-energy electrodynamic response with high-precision time-domain terahertz polarimetry. As a function of field, a crossover from semi-classical cyclotron resonance to a quantum regime was observed. In this regime, although the DC transport is still semi-classical, we observed quantized Faraday and Kerr rotations. A non-trivial Berry's phase offset to these values gives evidence for the long-sought axion electrodynamics and topological magnetoelectric effect. Among other aspects, the unique time structure used in these measurements allow us a direct measure of the fine structure constant based on a topological invariant of a solid-state system.
Faraday rotationQuantizationTranslational invarianceTopological insulatorAxion electrodynamicsInternational System of UnitsFine structure constantTime-reversal symmetryTerahertz time-domain spectroscopyFilling fraction...
• A Decade of WHIM Searches: Where do we Stand and Where do we Go?ver. 2

In this article we first review the past decade of efforts in detecting the missing baryons in the Warm Hot Intergalactic Medium (WHIM) and summarize the current state of the art by updating the baryon census and physical state of the detected baryons in the local Universe. We then describe observational strategies that should enable a significant step forward in the next decade, while waiting for the step-up in quality offered by future missions. In particular we design a multi-mega-second and multiple cycle XMM-Newton legacy program (which we name the Ultimate Roaming Baryon Exploration, or URBE) aimed to secure detections of the peaks in the density distribution of the Universe missing baryons over their entire predicted range of temperatures.
Warm hot intergalactic mediumXMM-NewtonLine of sightSpectrometersMissing baryonsCosmic Origins SpectrographIonizationAbsorption lineHubble Space TelescopeBlazar...
• An estimate of the DM profile in the Galactic bulge region

We present an analysis of the mass distribution in the region of the Galactic bulge, which leads to constraints on the total amount and distribution of Dark Matter (DM) therein. Our results -based on the dynamical measurement of the BRAVA collaboration- are quantitatively compatible with those of a recent analysis, and generalised to a vaste sample of observationally inferred morphologies of the stellar components in the region of the Galactic bulge. By fitting the inferred DM mass to a generalised NFW profile, we find that cores (index gamma smaller than 0.6) are forbidden only for very light configurations of the bulge, and that cusps (index gamma bigger than 1.2) are allowed, but not necessarily preferred. Interestingly, we find that the results for the bulge region are compatible with those obtained with dynamical methods (based on the rotation curve) applied to outer regions of the Milky Way, for all morphologies adopted. We find that the uncertainty on the shape of the stellar morphology heavily affects the determination of the DM distribution in the bulge region, which is gravitationally dominated by baryons, adding up to the uncertainty on its normalization. The combination of the two hinders the actual possibility to infer sound conclusions about the distribution of DM in the region of the Galactic bulge, and only future observations of the stellar census and dynamics in this region will bring us closer to a quantitatively more definite answer.
Dark matterGalactic BulgeDark Matter Density ProfileMilky WayDark matter particle massRotation CurveStellar massGalactic CenterNavarro-Frenk-White profileMass distribution...
• Density profile of dark matter haloes and galaxies in the Horizon-AGN simulation: the impact of AGN feedback

Using a suite of three large cosmological hydrodynamical simulations, Horizon-AGN, Horizon-noAGN (no AGN feedback) and Horizon-DM (no baryons), we investigate how a typical sub-grid model for AGN feedback affects the evolution of the inner density profiles of massive dark matter haloes and galaxies. Based on direct object-to-object comparisons, we find that the integrated inner mass and density slope differences between objects formed in these three simulations (hereafter, H_AGN, H_noAGN and H_DM) significantly evolve with time. More specifically, at high redshift (z~5), the mean central density profiles of H_AGN and H_noAGN dark matter haloes tend to be much steeper than their H_DM counterparts owing to the rapidly growing baryonic component and ensuing adiabatic contraction. By z~1.5, these mean halo density profiles in H_AGN have flattened, pummelled by powerful AGN activity ("quasar mode"): the integrated inner mass difference gaps with H_noAGN haloes have widened, and those with H_DM haloes have narrowed. Fast forward 9.5 billion years, down to z=0, and the trend reverses: H_AGN halo mean density profiles drift back to a more cusped shape as AGN feedback efficiency dwindles ("radio mode"), and the gaps in integrated central mass difference with H_noAGN and H_DM close and broaden respectively. On the galaxy side, the story differs noticeably. Averaged stellar profile central densities and inner slopes are monotonically reduced by AGN activity as a function of cosmic time, resulting in better agreement with local observations. As both dark matter and stellar inner density profiles respond quite sensitively to the presence of a central AGN, there is hope that future observational determinations of these quantities can be used constrain AGN feedback models.
AGN feedbackDark matter haloActive Galactic NucleiDark matterEllipticityHalo density profileMassive galaxiesVirial massHorizonBlack hole...
• Emergent phenomena and partonic structure in hadrons

Modern facilities are poised to tackle fundamental questions within the Standard Model, aiming to reveal the nature of confinement, its relationship to dynamical chiral symmetry breaking (DCSB) - the origin of visible mass - and the connection between these two, key emergent phenomena. There is strong evidence to suggest that they are intimately connected with the appearance of momentum-dependent masses for gluons and quarks in QCD, which are large in the infrared: $m_g \sim 500\,$MeV and $M_q\sim 350\,$MeV. DCSB, expressed in the dynamical generation of a dressed-quark mass, has an enormous variety of verifiable consequences, including an enigmatic result that the properties of the (almost) massless pion are the cleanest expression of the mechanism which is responsible for almost all the visible mass in the Universe. This contribution explains that these emergent phenomena are expressed with particular force in the partonic structure of hadrons, e.g. in valence-quark parton distribution amplitudes and functions, and, consequently, in numerous hadronic observables, so that we are now in a position to exhibit the consequences of confinement and DCSB in a wide range of hadron observables, opening the way to empirical verification of their expression in the Standard Model.
PionConfinementChiral limitTrace anomalyLight quarkPartonBound stateStandard ModelQuark massParton distribution function...
• Challenges in Cosmology from the Big Bang to Dark Energy, Dark Matter and Galaxy Formation

I review the current status of Big Bang Cosmology, with emphasis on current issues in dark matter, dark energy, and galaxy formation. These topics motivate many of the current goals of experimental cosmology which range from targeting the nature of dark energy and dark matter to probing the epoch of the first stars and galaxies.
Dark matterCosmologyDark energyBig BangGalaxy FormationInflationWeakly interacting massive particlePlanck missionStarSupersymmetry...
• Learning to Compare Image Patches via Convolutional Neural Networks

In this paper we show how to learn directly from image data (i.e., without resorting to manually-designed features) a general similarity function for comparing image patches, which is a task of fundamental importance for many computer vision problems. To encode such a function, we opt for a CNN-based model that is trained to account for a wide variety of changes in image appearance. To that end, we explore and study multiple neural network architectures, which are specifically adapted to this task. We show that such an approach can significantly outperform the state-of-the-art on several problems and benchmark datasets.
Convolutional neural networkEuclidean distanceArchitectureImage ProcessingTraining setReceiver operating characteristicOverfittingNeural networkIlluminanceFalse positive rate...
• Testability of evolutionary game dynamics models based on experimental economics data

In order to better understand the dynamic processes of a real game system, we need an appropriate dynamics model, so to evaluate the validity of a model is not a trivial task. Here, we demonstrate an approach, considering the dynamic patterns of angular momentum and speed as the measurement variables, for evaluating the validity of various dynamics models. Using the data in real time Rock-Paper-Scissors (RPS) games experiments, we obtain the experimental patterns, and then derive the related theoretical patterns from a series of typical dynamics models respectively. By testing the goodness-of-fit between the experimental and theoretical patterns, the validity of the models can be evaluated. One of the results is that, among all the non-parametric models tested, the best-known Replicator dynamics model performs almost worst, while the Projection dynamics model performs best. Besides providing new empirical patterns of social dynamics, we demonstrate that the approach can be an effective and rigorous method to evaluate game dynamics models.
StatisticsTime-reversal symmetryEvolutionary game theoryGame theoryTime SeriesGoodness of fitRock-paper-scissorsNash equilibriumBinomial testCoefficient of determination...
• The Effects of Communication Burstiness on Consensus Formation and Tipping Points in Social Dynamics

Current models for opinion dynamics typically utilize a Poisson process for speaker selection, making the waiting time between events exponentially distributed. Human interaction tends to be a more bursty process, though, having higher probabilities of either extremely short waiting times or long periods of silence rather than the relative regularity of Poisson selection. To quantify the effects this difference may have on the dynamics of social models, we place in competition two groups exhibiting different speakers waiting-time distributions. These competitions are implemented in the binary Naming Game and in the voter model, showing that the relevant aspect of the waiting-time distribution is the density of the head rather than that of the tail. In fact, we show that even with identical mean waiting times, a group with a higher density of short waiting times is favored in competition over the group with a less bursty distribution. This effect remains in the presence of nodes holding a single opinion that never changes, as the fraction of such committed individuals necessary for achieving consensus decreases dramatically when their waiting-time distribution has a higher head density than the waiting-time distribution of the nodes holding competing opinions.
Poisson processUniform distributionInflection pointGraphStatistical physicsHuman dynamicsNetwork scienceSocial systemsCritical valueExponential function...
• In-medium pseudoscalar $D/B$ mesons and charmonium decay width

Using QCD sum rules and chiral SU(3) model, we investigate the effect of temperature, density, strangeness fraction and isospin asymmetric parameter on the shift in masses and decay constants of the pseudoscalar $D$ and $B$ meson in hadronic medium, which consist of nucleons and hyperons. The in-medium properties of $D$ and $B$ mesons within QCD sum rule approach depend upon the quark and gluon condensates. In chiral SU(3) model, quark and gluon condensates are introduced through the explicit symmetry breaking term and the trace anomaly property of the QCD, respectively and are written in terms of scalar fields $\sigma$, $\zeta$, $\delta$ and $\chi$. Hence, through medium modification of $\sigma$, $\zeta$, $\delta$ and $\chi$ fields, we obtain the medium modified masses and decay constants of $D$ and $B$ mesons. As an application, using $^3 P_0$ model, we calculate the in-medium decay width of the higher charmonium states $\psi(3686)$, $\psi(3770)$ and $\chi(3556)$ to the $D \bar{D}$ pairs, considering the in-medium mass of $D$ mesons. These results may be important to understand the possible outcomes of high energy physics experiments, e.g., CBM and PANDA at GSI, Germany.
Decay widthIsospinQCD sum rulesStrangenessGluon condensatePseudoscalarScalar fieldHeavy ion collisionSymmetric nuclear matterQuark-gluon plasma...
• $\Lambda_c \to \Lambda \ell^+ \nu_\ell$ form factors and decay rates from lattice QCD with physical quark masses

The decays $\Lambda_c \to \Lambda \ell^+ \nu_\ell$, where $\ell=e,\mu$, are the most important baryonic $c \to s \ell^+ \nu_\ell$ transitions. These processes can be used to determine the Cabibbo-Kobayashi-Maskawa quark mixing matrix element $|V_{cs}|$, to normalize branching fraction measurements of other heavy-baryon decays, and to test theoretical methods for heavy-baryon decay form factors. Here, the first lattice QCD calculation of the form factors that govern $\Lambda_c \to \Lambda \ell^+ \nu_\ell$ decays is reported. The calculation was performed with 2+1 flavors of dynamical domain-wall fermions, using two different lattice spacings and a range of quark masses, including one ensemble with approximately physical quark masses corresponding to a pion mass of 139(2) MeV. The form factors are extrapolated to the continuum limit and are parametrized using model-independent $z$-expansions. The resulting predictions for the $\Lambda_c \to \Lambda e^+ \nu_e$ and $\Lambda_c \to \Lambda \mu^+ \nu_\mu$ decay rates divided by $|V_{cs}|^2$ are $0.2007(71)(74)\:{\rm ps}^{-1}$ and $0.1945(69)(72)\:{\rm ps}^{-1}$, respectively, where the two uncertainties are statistical and systematic. Taking $|V_{cs}|$ from a global CKM fit and the $\Lambda_c$ lifetime from experiments, this translates to branching fractions of $\mathcal{B}(\Lambda_c\to\Lambda e^+\nu_e)=0.0380(19)_{\rm LQCD\:\: }(11)_{\tau_{\Lambda_c}}$ and $\mathcal{B}(\Lambda_c\to\Lambda \mu^+\nu_\mu)=0.0369(19)_{\rm LQCD\:\: }(11)_{\tau_{\Lambda_c}}$. These results are consistent with, and two times more precise than, the measurements performed recently by the BES III Collaboration. Using instead the measured branching fractions together with the lattice calculation to determine the CKM matrix element gives $|V_{cs}|= 0.949(24)_{\rm LQCD\:\: }(14)_{\tau_{\Lambda_c}}(49)_{\mathcal{B}}$.
Form factorDecay rateBranching ratioLattice QCDQuark massCabibbo-Kobayashi-Maskawa matrixHeavy baryon decaysLattice calculationsStandard ModelElectron neutrino...
• Hints against the cold and collisionless nature of dark matter from the galaxy velocity function

The observed number of dwarf galaxies as a function of rotation velocity is significantly smaller than predicted by the $\Lambda$CDM model. This discrepancy cannot be simply solved by assuming strong baryonic processes, since they would violate the observed relation between maximum circular velocity ($v_{\rm max}$) and baryon mass of galaxies. A speculative but tantalising possibility is that the mismatch between observation and theory points towards the existence of non-cold or non-collisionless dark matter (DM). In this paper, we investigate the effects of warm, mixed (i.e warm plus cold), and self-interacting DM scenarios on the abundance of dwarf galaxies and the relation between observed HI line-width and maximum circular velocity. Both effects have the potential to alleviate the apparent mismatch between the observed and theoretical abundance of galaxies as a function of $v_{\rm max}$. For the case of warm and mixed DM, we show that the discrepancy disappears, even for luke-warm models that evade stringent bounds from the Lyman-$\alpha$ forest. Self-interacting DM scenarios can also provide a solution as long as they lead to extended ($\gtrsim 1.5$ kpc) dark matter cores in the density profiles of dwarf galaxies. Only models with velocity-dependent cross sections can yield such cores without violating other observational constraints at larger scales.
Velocity functionCold dark matterDark matterGalaxySelf-interacting dark matterWarm dark matterDwarf galaxyMixed dark matterMaximum circular velocityMilky Way...
• The Ghost in the Quantum Turing Machinever. 2

In honor of Alan Turing's hundredth birthday, I unwisely set out some thoughts about one of Turing's obsessions throughout his life, the question of physics and free will. I focus relatively narrowly on a notion that I call "Knightian freedom": a certain kind of in-principle physical unpredictability that goes beyond probabilistic unpredictability. Other, more metaphysical aspects of free will I regard as possibly outside the scope of science. I examine a viewpoint, suggested independently by Carl Hoefer, Cristi Stoica, and even Turing himself, that tries to find scope for "freedom" in the universe's boundary conditions rather than in the dynamical laws. Taking this viewpoint seriously leads to many interesting conceptual problems. I investigate how far one can go toward solving those problems, and along the way, encounter (among other things) the No-Cloning Theorem, the measurement problem, decoherence, chaos, the arrow of time, the holographic principle, Newcomb's paradox, Boltzmann brains, algorithmic information theory, and the Common Prior Assumption. I also compare the viewpoint explored here to the more radical speculations of Roger Penrose. The result of all this is an unusual perspective on time, quantum mechanics, and causation, of which I myself remain skeptical, but which has several appealing features. Among other things, it suggests interesting empirical questions in neuroscience, physics, and cosmology; and takes a millennia-old philosophical debate into some underexplored territory.
Quantum mechanicsCausalityEarthNo cloning theoremALICE experimentCosmologyBig BangQuantum computerBoltzmann brainQubit...
• Limits on Efficient Computation in the Physical Worldver. 2

More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be jettisoned in the light of modern physics, many others emerge nearly unscathed; and I use powerful tools from computational complexity theory to help determine which are which.
• Why Philosophers Should Care About Computational Complexityver. 3

One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In particular, I argue that computational complexity theory---the field that studies the resources (such as time, space, and randomness) needed to solve computational problems---leads to new perspectives on the nature of mathematical knowledge, the strong AI debate, computationalism, the problem of logical omniscience, Hume's problem of induction, Goodman's grue riddle, the foundations of quantum mechanics, economic rationality, closed timelike curves, and several other topics of philosophical interest. I end by discussing aspects of complexity theory itself that could benefit from philosophical analysis.
Computational complexity theoryFoundations of quantum mechanicsField
• Locally-orthogonal, unstructured grid-generation for general circulation modelling on the sphere

An algorithm for the generation of non-uniform, locally-orthogonal staggered unstructured grids on spheroidal geometries is described. This technique is designed to generate high-quality staggered Voronoi/Delaunay dual meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather predication. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of guaranteed-quality, unstructured spheroidal Delaunay triangulations is introduced. A locally-orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. The initial staggered Voronoi/Delaunay tessellation is iteratively improved through hill-climbing optimisation techniques. It is shown that this approach typically produces grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. Initial results are presented for a selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling. The use of user-defined mesh spacing functions to generate smoothly graded, non-uniform grids for multi-resolution type studies is discussed in detail.
Delaunay tessellationGeneral circulation modelsVoronoi tessellationDiscretizationStatisticsEdge contractionVorticityEddyLocal neighbourhoodScheduling...
• Relativistic causality and position space renormalization

The paper gives a historical survey of the causal position space renormalization with a special attention to the role of Raymond Stora in the development of this subject. Renormalization is reduced to subtracting the pole term in analytically regularized primitively divergent Feynman amplitudes. The identification of residues with "quantum periods" and their relation to recent developments in number theory are emphasized. We demonstrate the possibility of integration over internal vertices (that requires control over the infrared behavior) in the case of the massless $\varphi^4$ theory and display the dilation and the conformal anomaly.
RenormalizationGraphCausalityDilationNumber theoryTrace anomalyInfrared limitConformal invarianceMomentum spaceCERN...
• Key to Physics beyond the Standard Model: Modification of the QFTs so as to make their diagrams convergentver. 4

Motivation: We think that the physics about microscopic, small distance phenomena that underlie quantum scattering is the keystone of Physics beyond the Standard Model; and it may provide solutions to the ultraviolet divergences, the crucial QFT fault that is presently professionally declared as remedied by renormalization. Results: a) Testable theory, Regularization by replacing QFT partial differential equations with the Boltzmann integro-differential equations. b) Novel, possibly nonlinear and infinitesimal-range, fundamental forces. c) Regularization parameters are hypothetical physical constants. d) A potential framework for explaining hierarchy problems. e) Medium of the Universe with faster than light effects. Application: Usage of the present high energy facilities for gathering quantitative information about the underlying physics of QFTs by the experimental values of regularization parameters . Keywords: Standard Model; Boltzmann equation PACS numbers: 2.30.Jr, 11.10.Gh, 11.90.+t, 95.35.+d, 51.10.+
Beyond the Standard ModelRegularizationPartial differential equationKeyphraseSuperluminal motionInfinitesimalIntegro-differential equationUltraviolet divergenceTransport equationStandard Model...
• Some Mathematical and Physical Remarks on Surreal Numbers

We make a number of observations on Conway surreal number theory which may be useful, for further developments, in both in mathematics and theoretical physics. In particular, we argue that the concepts of surreal numbers and matroids can be linked. Moreover, we established a relation between the Gonshor approach on surreal numbers and tensors. We also comment about the possibility to connect surreal numbers with supesymmetry. In addition, we comment about possible relation between surreal numbers and fractal theory. Finally, we argue that the surreal structure may provide a different mathematical tools in the understanding of singularities in both high energy physics and gravitation.
Surreal numberQubitNumber theoryFractalDualityOriented matroidDivision algebraSupersymmetryRankCosmology...
• Quantum theory in real Hilbert space: How the complex Hilbert space structure emerges from Poincar\'e symmetryver. 2

As established by Sol\er, Quantum Theories may be formulated in real, complex or quaternionic Hilbert spaces only. St\"uckelberg provided physical reasons for ruling out real Hilbert spaces relying on Heisenberg principle. Focusing on this issue from another viewpoint, we argue that there is a fundamental reason why elementary quantum systems are not described in real Hilbert spaces: their symmetry group. We consider an elementary relativistic system within Wigner's approach defined as a faithful irreducible continuous unitary representation of the Poincar\'e group in a real Hilbert space. We prove that, if the squared-mass operator is non-negative, the system admits a natural, Poincar\'e invariant and unique up to sign, complex structure which commutes with the whole algebra of observables generated by the representation. All that leads to a physically equivalent formulation in a complex Hilbert space. Differently from what happens in the real picture, here all selfadjoint operators are observables in accordance with Sol\er's thesis, and the standard quantum version of Noether theorem holds. We next focus on the physical hypotheses adopted to define a quantum elementary relativistic system relaxing them and making our model physically more general. We use a physically more accurate notion of irreducibility regarding the algebra of observables only, we describe the symmetries in terms of automorphisms of the restricted lattice of elementary propositions and we adopt a notion of continuity referred to the states. Also in this case, the final result proves that there exist a unique (up to sign) Poincar\'e invariant complex structure making the theory complex and completely fitting into Sol\`er's picture. This complex structure reveals a nice interplay of Poincar\'e symmetry and the classification of the commutant of irreducible real von Neumann algebras.
Unitary representationVon Neumann algebraPolar decompositionCommutantUnitary operatorTrace classSubgroupQuantum theoryOne-parameter groupVector space...
• A review of the electronic and optical properties of strained graphene and other similar 2D materials

This review presents the state of the art of strain and ripple-induced effects on electronic and optical properties of graphene. We start by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformations fields. Then we review the unique elastic properties of graphene and how strain can be produced. Thereafter, we examine various theoretical approaches used to study the electronic properties of strained graphene and discuss the advantages of each. Also we show how such approaches provide a platform for describing exotic properties such as a fractal spectrum related with quasicrystals, a mixed Dirac-Schr\"odinger behavior, emergent gravity, topological insulator states, among others. Moreover, we review the physical consequences of strain on the optical properties, with particular focus on the Raman spectrum. At the same time, we present recent advances to tune the optical conductivity of graphene by strain engineering, which has opened up new paths in device applications. Finally, we present a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and other group-IV elements, phosphorene, dichalcogenide- and monochalcogenide-monolayers, with a slight emphasis on the occurrence and effects of novel two-dimensional structural phase transitions occurring at finite temperature.
GrapheneHamiltonianPhosphoreneDirac pointUnit cellReciprocal latticeSuperlatticeBand gapCurvatureHoneycomb lattice...
• Multiple Time Series Ising Model for Financial Market Simulations

In this paper we propose an Ising model which simulates multiple financial time series. Our model introduces the interaction which couples to spins of other systems. Simulations from our model show that time series exhibit the volatility clustering that is often observed in the real financial markets. Furthermore we also find non-zero cross correlations between the volatilities from our model. Thus our model can simulate stock markets where volatilities of stocks are mutually correlated.
VolatilityTime SeriesMarketIsing modelCross-correlationStock MarketMagnetizationGaussian distributionThermalisationAgent-based model...
• Whom to befriend to influence peoplever. 2

Alice wants to join a new social network, and influence its members to adopt a new product or idea. Each person $v$ in the network has a certain threshold $t(v)$ for {\em activation}, i.e adoption of the product or idea. If $v$ has at least $t(v)$ activated neighbors, then $v$ will also become activated. If Alice wants to activate the entire social network, whom should she befriend? More generally, we study the problem of finding the minimum number of links that a set of external influencers should form to people in the network, in order to activate the entire social network. This {\em Minimum Links} Problem has applications in viral marketing and the study of epidemics. Its solution can be quite different from the related and widely studied Target Set Selection problem. We prove that the Minimum Links problem cannot be approximated to within a ratio of $O(2^{\log^{1-\epsilon} n})$, for any fixed $\epsilon>0$, unless $NP\subseteq DTIME(n^{polylog(n)})$, where $n$ is the number of nodes in the network. On the positive side, we give linear time algorithms to solve the problem for trees, cycles, and cliques, for any given set of external influencers, and give precise bounds on the number of links needed. For general graphs, we design a polynomial time algorithm to compute size-efficient link sets that can activate the entire graph.
GraphSocial networkDiffusion processGreedy algorithmOptimizationNP-hard problemNode of the graphNetwork effectVertex covering numberCounting...
• Dynamic landscape models of coevolutionary games

Players of coevolutionary games may update not only their strategies but also their networks of interaction. Based on interpreting the payoff of players as fitness, dynamic landscape models are proposed. The modeling procedure is carried out for Prisoner's Dilemma (PD) and Snowdrift (SD) games that both use either birth-death (BD) or death-birth (DB) strategy updating. With the main focus on using dynamic fitness landscapes as an alternative tool for analyzing coevolutionary games, landscape measures such as modality, ruggedness and information content are computed and analyzed. In addition, fixation properties of the games and quantifiers characterizing the network of interaction are calculated numerically. Relations are established between landscape properties expressed by landscape measures and quantifiers of coevolutionary game dynamics such as fixation probabilities, fixation times and network properties
• The Unusually High Halo Concentration of the Fossil Group NGC 6482: Evidence for Weak Adiabatic Contraction

We revisit the massive isolated elliptical galaxy / fossil group NGC 6482 for which previous X-ray studies of a modest Chandra observation obtained a very uncertain, but also possibly very high, halo concentration. We present new measurements of the hot gas surface brightness, temperature, and iron abundance using the modest Chandra observation and a previously unpublished Suzaku observation, the latter of which allows measurements of the gas properties to be extended out to ~r_2500. By constructing hydrostatic equilibrium models of the gas with separate components for the gas, BCG stellar mass, and the dark matter (DM), we measure c_200 = 32.2 +/- 7.1 and M_200 = (4.5 +/- 0.6 x 10^12 M_sun using an NFW DM profile. For a halo of this mass, c_200 exceeds the mean value (7.1) expected for relaxed LCDM halos by $3.5 \sigma$ in terms of the observational error, and by $6 \sigma$ considering the intrinsic scatter in the LCDM c-M relation, which situates NGC 6482 as the most extreme outlier known for a fossil system. We explored several variants of adiabatic contraction (AC) models and, while the AC models provide fits of the same quality as the un-contracted models, they do have the following advantages: (1) smaller c_200 that is less of an outlier in the LCDM c-M relation, and (2) baryon fractions that agree better with the mean cosmic value. While the standard AC prescriptions yield a BCG stellar mass that is uncomfortably small compared to results from stellar population synthesis (SPS) models, a weaker AC variant that artificially shuts off cooling and star formation at z=2 yields the same stellar mass as the un-contracted models. For these reasons, we believe our X-ray analysis prefers this weaker AC variant applied to either an NFW or Einasto DM halo. Finally, the BCG stellar mass strongly favors SPS models with a Chabrier or Kroupa IMF over a Salpeter IMF. (Abridged)
Navarro-Frenk-White profileDark matterStellar massMass profileSystematic errorHydrostatic equilibriumHydrostaticsStellar population synthesisHalo concentrationsElliptical galaxy...
• The universal rotation curve of dwarf disk galaxiesver. 2

We use the concept of the spiral rotation curves universality (see Persic et al. 1996) to investigate the luminous and dark matter properties of the dwarf disk galaxies in the local volume (size $\sim11$ Mpc). Our sample includes 36 objects with rotation curves carefully selected from the literature. We find that, despite the large variations of our sample in luminosities ($\sim$ 2 of dex), the rotation curves in specifically normalized units, look all alike and lead to the lower-mass version of the universal rotation curve of spiral galaxies found in Persic et al. 1996. We mass model $V(R/R_{opt})/V_{opt}$, the double normalized universal rotation curve of dwarf disk galaxies: the results show that these systems are totally dominated by dark matter whose density shows a core size between 2 and 3 stellar disk scale lengths. Similar to galaxies of different Hubble types and luminosities, the core radius $r_0$ and the central density $\rho_0$ of the dark matter halo of these objects are related by $\rho_0 r_0 \sim 100 M_\odot pc^{-2}$. The structural properties of the dark and luminous matter emerge very well correlated. In addition, to describe these relations, we need to introduce a new parameter, measuring the compactness of light distribution of a (dwarf) disk galaxy. These structural properties also indicate that there is no evidence of abrupt decline at the faint end of the baryonic to halo mass relation. Finally, we find that the distributions of the stellar disk and its dark matter halo are closely related.
Rotation CurveLuminosityDisk galaxyStellar diskDark matterDark matter haloVirial massMilky WayStructural propertiesCircular velocity...
• The radial dependence of dark matter distribution in M33ver. 2

The stellar and gaseous mass distributions, as well as the extended rotation curve in the nearby galaxy M33 are used to derive the radial distribution of dark matter density in the halo and to test cosmological models of galaxy formation and evolution. Two methods are examined to constrain dark mass density profiles. The first deals directly with fitting the rotation curve data in the range of galacto-centric distances $0.24\,\text{kpc}\leq r\leq 22.72\,\text{kpc}$. As found in a previous paper by Corbelli E. et. al. (2014), and using the results of recent collisionless $\Lambda$CDM numerical simulations, we confirm that the Navarro-Frenkel-White (hereafter NFW) dark matter profile provides a marginally better fit to the rotation curve data than the cored Burkert profile, also called the Universal Rotation Curve (hereafter URC) profile. The second method relies on the local equation of centrifugal equilibrium and on the rotation curve slope. In the aforementioned range of distances, we fit the observed velocity profile using a function which has a rational dependence on the radius. Following Salucci P. et. al. (2010), we then derive an expression for the slope of the rotation curve and for the radial dependence of the local dark matter distribution. In the radial range $9.53\,\text{kpc}\leq r \leq 22.72\,\text{kpc}$, where the uncertainties induced by the luminous matter (stars and gas) start to become negligible, we tested the NFW and the URC dark matter profiles. With this second method we confirm that both profiles are compatible with the data even though in this case the cored Burkert mass density profile provides a more reasonable value for the barionic-to-dark matter ratio.
Rotation CurveDark matterTriangulum GalaxyDark Matter Density ProfileDark matter haloGaseous disksStellar diskMilky WayStellar massStar...
• Notes on a reduction property for GLP-algebras

We consider some natural generalizations to the class of all GLP-algebras of the so-called reduction property for reflection algebras in arithmetic. An analogue of this property is established for the free GLP-algebras and for some topological GLP-algebras (GLP-spaces).
ArithmeticBoolean algebraConjunctionKripke semanticsAlgebraTopologyScatteringForceLanguageCommunication...
• Maxwell's equations as a special case of deformation of a solid lattice in Euler's coordinates

It is shown that the set of equations known as Maxwell's equations perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices, containing topological defects as dislocations and disclinations, in the case of constant and homogenous expansion. The analogy between these two physical systems is complete, as it is not restricted to one of the two Maxwell's equation couples in the vacuum, but generalized to the two equation couples as well as to the diverse phenomena of dielectric polarization and magnetization of matter, just as to the electrical charges and the electrical currents. The eulerian approach of the solid lattice developed here includes Maxwell's equations as a special case, since it stems from a tensor theory, which is reduced to a vector one by contraction on the tensor indices. Considering the tensor aspect of the eulerian solid lattice deformation theory, the analogy can be extended to other physical phenomena than electromagnetism, a point which is shortly discussed at the end of the paper.
DislocationMagnetizationElectromagnetismTopological defectMaxwell's equationsTensorVacuumChargeVectorPolarization...