• #### Variational Dropout and the Local Reparameterization Trick

We explore an as yet unexploited opportunity for drastically improving the efficiency of stochastic gradient variational Bayes (SGVB) with global model parameters. Regular SGVB estimators rely on sampling of parameters once per minibatch of data, and have variance that is constant w.r.t. the minibatch size. The efficiency of such estimators can be drastically improved upon by translating uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such reparameterizations with local noise can be trivially parallelized and have variance that is inversely proportional to the minibatch size, generally leading to much faster convergence. We find an important connection with regularization by dropout: the original Gaussian dropout objective corresponds to SGVB with local noise, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose \emph{variational dropout}, a generalization of Gaussian dropout, but with a more flexibly parameterized posterior, often leading to better generalization. The method is demonstrated through several experiments.
RegularizationNeural networkBayesian approachMonte Carlo methodHyperparameterBayesianScale invarianceBinary starMarginal likelihoodClassification...
• #### Crossing Stocks and the Positive Grassmannian I: The Geometry behind Stock Marketver. 2

It seems to be very unlikely that all relevant information in the stock market could be fully encoded in a geometrical shape. Still,the present paper will reveal the geometry behind the stock market transactions. The prices of market index (DJIA) stock components are arranged in ascending order from the smallest one in the left to the highest in the right. In such arrangement, as stock prices changes due to daily market quotations, it could be noticed that the price of a certain stock get over /under the price of a neighbor stock. These stocks are crossing. Arranged this way, the diagram of successive stock crossings is nothing else than a permutation diagram. From this point on the financial and combinatorial concepts are netted together to build a bridge connecting the stock market to a beautiful geometrical object that will be called stock market polytope. The stock market polytope is associated with the remarkable structure of positive Grassmannian . This procedure makes all the relevant information about the stock market encoded in the geometrical shape of the stock market polytope more readable.
Stock MarketGrassmannianPolytopePermutationGeometryObjective...
• #### Decoding Stock Market Behavior with the Topological Quantum Computer

A surprising image of the stock market arises if the price time series of all Dow Jones Industrial Average stock components are represented in one chart at once. The chart evolves into a braid representation of the stock market by taking into account only the crossing of stocks and fixing a convention defining overcrossings and undercrossings. The braid of stocks prices has a remarkable connection with the topological quantum computer. Using pairs of quasi-particles, called non-abelian anyons, having their trajectories braided in time, topological quantum computer can effectively simulate the stock market behavior encoded in the braiding of stocks. In a typically topological quantum computation process the trajectories of non-abelian anyons are manipulated according to the braiding of stocks and the outcome reflects the probability of the future state of stock market. The probability depends only on the Jones polynomial of the knot formed by plat closing the quantum computation. The Jones polynomial of the knotted stock market acts, making a parallel with the common financial literature, in a topological quantum computation as a counterpart of a classical technical indicator in trading the stock market. The type of knot stock market formed is an indicator of its future tendencies.
Stock MarketTopological quantum computerNon-Abelian anyonJones polynomialTime SeriesQuantum computerTrajectoryProbabilitySimulationsQuasiparticle...
• #### On Discrete Physics (Digital Philosophy/Digital Cosmology) and the Cellular Automaton: A Perfect Mathematical Deterministic Structure for Reality - as A Huge Computational Simulationver. 5

In this paper we provide an analysis and overview of some notable definitions, works and thoughts concerning discrete physics (digital philosophy) that mainly suggest a finite and discrete characteristic for the physical world, as well as, of the cellular automaton, which could serve as the basis of a (or the only) perfect mathematical deterministic model for the physical reality. In particular and as a confirmation, in the reference [37] (expounded in Appendix 1) also has been proven that the laws (the field equations) of all the fundamental forces of nature, mathematically and uniquely, could be derived based on a new algebraic approach - where it is assumed that certain physical quantities are discrete.
Foundations of quantum field theoryCosmologyFundamental forceSimulationsAlgebraField...
• #### Review of NMR studies of nanoscale molecular magnets composed of geometrically frustrated antiferromagnetic triangles

We present a comprehensive review of nuclear magnetic resonance (NMR) studies performed on three nanoscale molecular magnets with different configurations of geometrically frustrated antiferromagnetic (AFM) triangles, new spin frustration systems with different novel structures: (1) the isolated single AFM triangle K$_6$[V$_{15}$As$_6$O$_{42}$(H$_2$O)]$\cdot$8H$_2$O (in short V15), (2) the spin ball [Mo$_{72}$Fe$_{30}$O$_{252}$(Mo$_2$O$_7$(H$_2$O))$_2$ (Mo$_2$O$_8$H$_2$(H$_2$O))(CH$_3$COO)$_{12}$(H$_2$O)$_{91}$]$\cdot$150H$_2$O (in short Fe30 spin ball), and (3) the twisted triangular spin tube [(CuCl$_2$tachH)$_3$Cl]Cl$_2$ (in short Cu3 spin tube).
MagnetNuclear magnetic resonanceAntiferromagnetMolecular magnetEigenfunctionFreezingFull width at half maximumChiralityRelaxationGeometrical frustration...
• #### Analog Systems for Gravity Dualsver. 2

We show that analog gravity systems exist for charged, planar black holes in asymptotic Anti-de Sitter space. These black holes have been employed to describe, via the gauge-gravity duality, strongly coupled condensed matter systems on the boundary of AdS-space. The analog gravity system is a different condensed matter system that, in a suitable limit, describes the same bulk physics as the theory on the AdS boundary. This combination of the gauge-gravity duality and analog gravity therefore suggests a duality between different condensed matter systems.
CondensationContinuity equationBlack holeDimensionsSpeed of soundEuler equationsWave equationEffective massDualityLine element...
• #### Double Field Theory: A Pedagogical Reviewver. 2

Double Field Theory (DFT) is a proposal to incorporate T-duality, a distinctive symmetry of string theory, as a symmetry of a field theory defined on a double configuration space. The aim of this review is to provide a pedagogical presentation of DFT and its applications. We first introduce some basic ideas on T-duality and supergravity in order to proceed to the construction of generalized diffeomorphisms and an invariant action on the double space. Steps towards the construction of a geometry on the double space are discussed. We then address generalized Scherk-Schwarz compactifications of DFT and their connection to gauged supergravity and flux compactifications. We also discuss U-duality extensions, and present a brief parcours on world-sheet approaches to DFT. Finally, we provide a summary of other developments and applications that are not discussed in detail in the review.
T-dualitySupergravityCompactificationTwo-formDualityCovarianceDiffeomorphismString theoryGauged supergravityLie derivative...
• #### A Hidden Signal in the Ulam sequence

The Ulam sequence is defined as $a_1 =1, a_2 = 2$ and $a_n$ being the smallest integer that can be written as the sum of two distinct earlier elements in a unique way. This gives $$1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26, 28, 36, 38, 47, \dots$$ Virtually nothing is known about the behavior of the sequence. Consecutive differences do not seem to be periodic and can be large, e.g. $a_{18858} - a_{18857} = 315.$ The purpose of this short note is to report the following empirical discovery: there seems to exist a real $\alpha \sim 2.571447499\dots$ such that $$\left\{\alpha a_n: n\in \mathbb{N}\right\} \qquad \mbox{is not uniformly distributed mod} ~2\pi.$$ The distribution function of $\alpha a_n~\mbox{mod}~2\pi$ seems to be supported on an interval of length $\sim 3$ and has a curious shape. Indeed, for the first $10^7$ elements of Ulam's sequence, we have $$\cos{\left( 2.5714474995~ a_n\right)} < 0 \qquad \mbox{for all}~a_n \notin \left\{2, 3, 47, 69\right\}.$$ We hope that this very rigid structure will eventually provide a way of understanding properties of the Ulam sequence and believe that the arising phenomenon might be of interest in itself.
DilationUniform distributionUlam numberRegularizationDimensionsStatisticalQuasiperiodicityErgodicityPeriodateFrequency...
• #### The optical torque: Electromagnetic spin and orbital angular momenta conservation laws and their significance

The physics involved in the fundamental conservation equations of the spin and orbital angular momenta leads to new laws and phenomena that I disclose. To this end, I analyse the scattering of an electromagnetic wavefield by the canonical system constituted by a small particle, which I assume dipolar in the wide sense. Specifically, under quite general conditions these laws lead to understanding how is the contribution and weight of each of those angular momenta to the electromagnetic torque exerted by the field on the object, which is shown to consist of an extinction and a scattering, or recoil, part. This leads to an interpretation of its effect different to that taken up till now by many theoretical and experimental works, and implies that a part of the recoil torque cancels the usually called intrinsic torque which was often considered responsible of the particle spinning. In addition, I obtain the contribution of the spatial structure of the wave to this torque, unknown to this date, showing its effect in the orbiting of the object, and demonstrating that it often leads to a negative torque on a single particle, i.e. opposite to the incident helicity, producing an orbital motion contrary to its spinning. Furthermore, I establish a decomposition of the electromagnetic torque into conservative and non-conservative components in which the helicity and its flow play a role analogous to the energy and its flux for electromagnetic forces. I illustrate these phenomena with examples of beams, also showing the difficulties of some paraxial formulations whose fields do not hold the transversality condition.
ElectromagnetismHelicityObjectSpin angular momentum of lightPlane waveExtinctionChiralityOrbital angular momentum of lightElectricity and magnetismPolarizability...
• #### Quantum spin Hall effect of lightver. 3

Maxwell's equations, formulated 150 years ago, ultimately describe properties of light, from classical electromagnetism to quantum and relativistic aspects. The latter ones result in remarkable geometric and topological phenomena related to the spin-1 massless nature of photons. By analyzing fundamental spin properties of Maxwell waves, we show that free-space light exhibits an intrinsic quantum spin Hall effect, i.e., surface modes with strong spin-momentum locking. These modes are evanescent waves that form, e.g., surface plasmon-polaritons at vacuum-metal interfaces. Our findings illuminate the unusual transverse spin in evanescent waves and explain recent experiments demonstrating the transverse spin-direction locking in the excitation of surface optical modes. This deepens our understanding of Maxwell's theory, reveals analogies with topological insulators for electrons, and offers applications for robust spin-directional optical interfaces.
Topological insulatorSpin Quantum Hall EffectSurface Plasmon PolaritonEvanescent waveChern numberSpin-orbit interactionSpinMaxwell's equationsTopologyMetals...
• #### From Competition to Complementarity: Comparative Influence Diffusion and Maximization

Influence maximization is a well-studied problem that asks for a small set of influential users from a social network, such that by targeting them as early adopters, the expected total adoption through influence cascades over the network is maximized. However, almost all prior work focuses on cascades of a single propagating entity or purely-competitive entities. In this work, we propose the Comparative Independent Cascade (Com-IC) model that covers the full spectrum of entity interactions from competition to complementarity. In Com-IC, users' adoption decisions depend not only on edge-level information propagation, but also on a node-level automaton whose behavior is governed by a set of model parameters, enabling our model to capture not only competition, but also complementarity, to any possible degree. We study two natural optimization problems, Self Influence Maximization and Complementary Influence Maximization, in a novel setting with complementary entities. Both problems are NP-hard, and we devise efficient and effective approximation algorithms via non-trivial techniques based on reverse-reachable sets and a novel "sandwich approximation". The applicability of both techniques extends beyond our model and problems. Our experiments show that the proposed algorithms consistently outperform intuitive baselines in four real-world social networks, often by a significant margin. In addition, we learn model parameters from real user action logs.
ComplementarityGraphSocial networkNP-hard problemMarketReachabilityGreedy algorithmDirected graphMonte Carlo methodRandom permutation...
• #### Cosmological Higgs-Axion Interplay for a Naturally Small Electroweak Scale

Recently, a new mechanism to generate a naturally small electroweak scale has been proposed. It exploits the coupling of the Higgs to an axion-like field and a long era in the early universe where the axion unchains a dynamical screening of the Higgs mass. We present a new realization of this idea with the new feature that it leaves no signs of new physics up to a rather large scale, 10^9 GeV, except for two very light and weakly coupled axion-like states. One of the scalars can be a viable Dark Matter candidate. Such a cosmological Higgs-axion interplay could be tested with a number of experimental strategies.
CosmologyElectroweak scaleHiggs boson massThermalisationSlow rollDark matter candidateHiggs fieldHierarchy problemBig bang nucleosynthesisScale of new physics...
• #### Cosmological Relaxation of the Electroweak Scalever. 2

A new class of solutions to the electroweak hierarchy problem is presented that does not require either weak scale dynamics or anthropics. Dynamical evolution during the early universe drives the Higgs mass to a value much smaller than the cutoff. The simplest model has the particle content of the standard model plus a QCD axion and an inflation sector. The highest cutoff achieved in any technically natural model is 10^8 GeV.
Vacuum expectation valueQCD axionHierarchy problemTechnical NaturalnessHiggs boson massAxionElectroweak scaleStandard ModelSlow rollEternal inflation...
• #### The contributions of matter inside and outside of haloes to the matter power spectrumver. 2

Halo-based models have been successful in predicting the clustering of matter. However, the validity of the postulate that the clustering is fully determined by matter inside haloes remains largely untested, and it is not clear a priori whether non-virialised matter might contribute significantly to the non-linear clustering signal. Here, we investigate the contribution of haloes to the matter power spectrum as a function of both scale and halo mass by combining a set of cosmological N-body simulations to calculate the contributions of different spherical overdensity regions, Friends-of-Friends (FoF) groups and matter outside haloes to the power spectrum. We find that matter inside spherical overdensity regions of size R200,mean cannot account for all power for 1<k<100 h/Mpc, regardless of the minimum halo mass. At most, it accounts for 95% of the power (k>20 h/Mpc). For 2<k<10 h/Mpc, haloes with mass M200,mean<10^11 Msun/h contribute negligibly to the power spectrum, and our results appear to be converged with decreasing halo mass. When haloes are taken to be regions of size R200,crit, the amount of power unaccounted for is larger on all scales. Accounting also for matter inside FoF groups but outside R200,mean increases the contribution of halo matter on most scales probed here by 5-15%. Matter inside FoF groups with M200,mean>10^9 Msun/h accounts for essentially all power for 3<k<100 h/Mpc. We therefore expect halo models that ignore the contribution of matter outside R200,mean to overestimate the contribution of haloes of any mass to the power on small scales (k>1 h/Mpc).
Virial massFriends of friends algorithmMatter power spectrumHalo modelSpherical OverdensityVirial radiusN-body simulationHalo mass functionDark matterDensity contrast...
• #### Imprint of topological degeneracy in quasi-one-dimensional fractional quantum Hall statesver. 2

We consider an annular superconductor-insulator-superconductor Josephson-junction, with the insulator being a double layer of electron and holes at Abelian fractional quantum Hall states of identical fillings. When the two superconductors gap out the edge modes, the system has a topological ground state degeneracy in the thermodynamic limit akin to the fractional quantum Hall degeneracy on a torus. In the quasi-one-dimensional limit, where the width of the insulator becomes small, the ground state energies are split. We discuss several implications of the topological degeneracy that survive the crossover to the quasi-one-dimensional limit. In particular, the Josephson effect shows a $2\pi d$-periodicity, where $d$ is the ground state degeneracy in the 2 dimensional limit. We find that at special values of the relative phase between the two superconductors there are protected crossing points in which the degeneracy is not completely lifted. These features occur also if the insulator is a time-reversal-invariant fractional topological insulator. We describe the latter using a construction based on coupled wires. Furthermore, when the superconductors are replaced by systems with an appropriate magnetic order that gap the edges via a spin-flipping backscattering, the Josephson effect is replaced by a spin Josephson effect.
SuperconductorTorusFractional topological insulatorFractional quantum Hall stateTopological degeneracyHamiltonianJosephson effectSpin-orbit interactionInsulatorsQuantum Hall Effect...
• #### Nonequilibrium Quantum Fields: From Cold Atoms to Cosmology

Lecture notes of the Les Houches Summer School on 'Strongly interacting quantum systems out of equilibrium'.
Nonequilibrium Quantum Field TheoryCosmologyStrong interactionsAtom...
• #### Probing the Majorana neutrinos and their CP violation in decays of charged scalar mesons $\pi, K, D, D_s, B, B_c$ver. 3

Some of the outstanding questions of particle physics today concern the neutrino sector, in particular whether there are more neutrinos than those already known and whether they are Dirac or Majorana particles.There are different ways to explore these issues. In this article we describe neutrino-mediated decays of charged pseudoscalar mesons such as $\pi^{\pm}$, $K^{\pm}$ and $B^{\pm}$, in scenarios where extra neutrinos are heavy and can be on their mass shell. We discuss semileptonic and leptonic decays of such kinds. We investigate possible ways of using these decays in order to distinguish between the Dirac and Majorana character of neutrinos. Further, we argue that there are significant possibilities of detecting CP violation in such decays when there are at least two almost degenerate Majorana neutrinos involved. This latter type of scenario fits well into the known neutrino minimal standard model ($\nu$MSM) which could simultaneously explain the Dark Matter and Baryon Asymmetry of the Universe.
Branching ratioNeutrinoSterile neutrinoCP violationDecay widthMajorana neutrinoSemileptonic decayStandard ModelCharged pionsInterference...
• #### Package-X: A Mathematica package for the analytic calculation of one-loop integrals

Package-X, a Mathematica package for the analytic computation of one-loop integrals dimensionally regulated near 4 spacetime dimensions is described. Package-X computes arbitrarily high rank tensor integrals with up to three propagators, and gives compact expressions of UV divergent, IR divergent, and finite parts for any kinematic configuration involving real-valued external invariants and internal masses. Output expressions can be readily evaluated numerically and manipulated symbolically with built-in Mathematica functions. Emphasis is on evaluation speed, on readability of results, and especially on user-friendliness. Also included is a routine to compute traces of products of Dirac matrices, and a collection of projectors to facilitate the computation of fermion form factors at one-loop. The package is intended to be used both as a research tool and as an educational tool.
Loop integralGamma matricesFeynman parameterCovarianceOne-loop integralsWolfram Mathematica packageEuler beta functionSelf-energyDirect integralRanking...
• #### The broadening of Lyman-alpha forest absorption linesver. 2

We provide an analytical description of the line broadening of HI absorbers in the Lyman-alpha forest resulting from Doppler broadening and Jeans smoothing. We demonstrate that our relation captures the dependence of the line-width on column density for narrow lines in z~3 mock spectra remarkably well. Broad lines at a given column density arise when the underlying density structure is more complex, and such clustering is not captured by our model. Our understanding of the line broadening opens the way to a new method to characterise the thermal state of the intergalactic medium and to determine the sizes of the absorbing structures.
Temperature-density relationIntergalactic mediumPeculiar velocityJeans lengthReionizationDensity contrastAbsorption lineLyman-alpha forestRadiative coolingAbsorptivity...

• #### Infinity - A simple, but not too simple introduction

This text tries to give an elementary introduction to the mathematical properties of infinite sets. The aim is to keep the approach as simple as possible. Advanced knowledge of mathematics is not necessary for a proper understanding, and there is (almost) no use of formulas. At the same time, it is tried to keep the reasoning rigorous and transparent. Major arguments are explained in great detail, while it is explicitly stated if something is not further explained. However, also a fully guided trail can become difficult at times. Persistence is necessary to follow. No reader should be discouraged when he or she cannot understand everything on first readings - infinity is not a piece of cake. The reasoning presented here is mainly due to the famous German mathematician Georg Cantor (1845 - 1918). Despite the resistance from the mathematical community at that time, he opened the door to infinity almost on his own, dramatically changing the foundations of mathematics. The following notions and topics are treated: potential und actual infinity, cardinality and countability, Hilbert's hotel, Cantor's diagonal arguments and the highly astonishing answer to the question of the validity of Cantor's continuum hypothesis.
Foundations of mathematicsPotentialResist
• #### Attention-Based Models for Speech Recognition

Recurrent sequence generators conditioned on input data through an attention mechanism have recently shown very good performance on a range of tasks in- cluding machine translation, handwriting synthesis and image caption gen- eration. We extend the attention-mechanism with features needed for speech recognition. We show that while an adaptation of the model used for machine translation in reaches a competitive 18.7% phoneme error rate (PER) on the TIMIT phoneme recognition task, it can only be applied to utterances which are roughly as long as the ones it was trained on. We offer a qualitative explanation of this failure and propose a novel and generic method of adding location-awareness to the attention mechanism to alleviate this issue. The new method yields a model that is robust to long inputs and achieves 18% PER in single utterances and 20% in 10-times longer (repeated) utterances. Finally, we propose a change to the at- tention mechanism that prevents it from concentrating too much on single frames, which further reduces PER to 17.6% level.
HybridizationRecurrent neural networkFeature vectorArchitectureTraining setLong short term memoryClassificationRegularizationGaussian mixture modelObject...
• #### Axial anomaly: the modern statusver. 2

The modern status of the problem of axial anomaly in QED and QCD is reviewed. Two methods of the derivation of the axial anomaly are presented: 1) by splitting of coordinates in the expression for the axial current and 2) by calculation of triangle diagrams, where the anomaly arises from the surface terms in momentum space. It is demonstrated, that the equivalent formulation of the anomaly can be given, as a sum rule for the structure function in dispersion representation of three point function of AVV interaction. It is argued, that such integral representation of the anomaly has some advantages in the case of description of the anomaly by contribution of hadronic states in QCD. The validity of the t'Hooft consistency condition is discussed. Few examples of the physical application of the axial anomaly are given.
Axial anomalyTriangle diagramsDimensionsFlavourGauge invarianceRadiative correctionMomentum spaceCondensationDualityDecay rate...
• #### Single-electron coherence: finite temperature versus pure dephasing

We analyze a coherent injection of single electrons on top of the Fermi sea in two situations, at finite-temperature and in presence of pure dephasing. Both finite-temperature and pure dephasing change the property of the injected quantum states from pure to mixed. However, we show that the temperature-induced mixedness does not alter the coherence properties of these single-electronic states. In particular two such mixed states exhibit perfect antibunching while colliding at an electronic wave splitter. This is in striking difference with the dephasing-induced mixedness which suppresses antibunching. On the contrary, a single-particle shot noise is suppressed at finite temperatures but is not affected by pure dephasing. This work therefore extends the investigation of the coherence properties of single-electronic states to the case of mixed states and clarifies the difference between different types of mixedness.
DephasingTwo-point correlation functionMixed statesInterferenceFermi seaCross-correlation functionThermalisationScattering amplitudeWave guideRelaxation...
• #### Einstein's Third Postulate

Einstein's own demonstration of time dilation taken from his book with L. Infeld (1938) is analyzed. His ingenious circumnavigation of an apparent discrepancy between clock synchronisation and Lorentz transformation is discussed.
Lorentz transformationTime dilationElectrodynamicsWave equationHomogenizationDilationSpecial relativityGeneral relativityPrinciple of relativityGalilean transformation...
• #### Why Mathematics Works So Well

A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the physical universe? We review the well-known fact that the symmetries of the laws of physics are their defining properties. We show that there are similar symmetries of mathematical facts and that these symmetries are the defining properties of mathematics. By examining the symmetries of physics and mathematics, we show that the effectiveness is actually quite reasonable. In essence, we show that the regularities of physics are a subset of the regularities of mathematics.
RegularizationSymmetryUniverse
• #### Introduction to Machine Learning: Class Notes 67577

Introduction to Machine learning covering Statistical Inference (Bayes, EM, ML/MaxEnt duality), algebraic and spectral methods (PCA, LDA, CCA, Clustering), and PAC learning (the Formal model, VC dimension, Double Sampling theorem).
VC dimensionConcept classStatisticsTraining setLinear discriminant analysisMass to light ratioCovariance matrixShatteringGaussian distributionExpectation maximization...
• #### On the Trail of the Higgs Boson

I review theoretical issues associated with the Higgs boson and the mystery of spontaneous breaking of the electroweak gauge symmetry. This essay is intended as an introduction to the special issue of Annalen der Physik, "Particle Physics after the Higgs".
Higgs bosonGauge symmetryParticle physics
• #### Contribution of right-handed neutrinos and standard fermions to W and Z massesver. 2

We present expressions of the Pagels--Stokar type for the masses of the W and Z bosons in terms of the quark and lepton self-energies. By introducing a genuine new term in the gauge boson--fermion--anti-fermion vertex we manage to accomplish three main achievements: First, we show that the similar results existing in literature lead, in general, to a non-symmetric gauge boson mass matrix and we fix this flaw. Second, we consider the case of any number of fermion generations with general mixing. Third, we include in our analysis also an arbitrary number of right-handed neutrinos, together with the left-handed and right-handed neutrino Majorana masses (self-energies). On top of that, we give also a correction to the original Pagels--Stokar formula for the pion decay constant in QCD.
Self-energySterile neutrinoElectroweak symmetryPion decay constantGauge symmetryMajorana massElectroweak symmetry breakingStandard ModelPolarization tensorGauge coupling constant...
• #### A W' boson near 2 TeV: predictions for Run 2 of the LHCver. 2

We present a renormalizable theory that includes a $W'$ boson of mass in the 1.8-2 TeV range, which may explain the excess events reported by the ATLAS Collaboration in a $WZ$ final state, and by the CMS Collaboration in $e^+\!e^- jj$, $Wh^0$ and $jj$ final states. The $W'$ boson couples to right-handed quarks and leptons, including Dirac neutrinos with TeV-scale masses. This theory predicts a $Z'$ boson of mass in the 3.4-4.5 TeV range. The cross section times branching fractions for the narrow $Z'$ dijet and dilepton peaks at the 13 TeV LHC are 10 fb and 1 fb, respectively, for $M_{Z'}= 3.4$ TeV, and an order of magnitude smaller for $M_{Z'}= 4.5$ TeV.
CMS experimentATLAS Experiment at CERNStandard ModelW' bosonBranching ratioTeV scaleDirac neutrinoLeft-right symmetric modelGravitonGauge symmetry...
• #### Neural Machine Translation by Jointly Learning to Align and Translatever. 6

Neural machine translation is a recently proposed approach to machine translation. Unlike the traditional statistical machine translation, the neural machine translation aims at building a single neural network that can be jointly tuned to maximize the translation performance. The models proposed recently for neural machine translation often belong to a family of encoder-decoders and consists of an encoder that encodes a source sentence into a fixed-length vector from which a decoder generates a translation. In this paper, we conjecture that the use of a fixed-length vector is a bottleneck in improving the performance of this basic encoder-decoder architecture, and propose to extend this by allowing a model to automatically (soft-)search for parts of a source sentence that are relevant to predicting a target word, without having to form these parts as a hard segment explicitly. With this new approach, we achieve a translation performance comparable to the existing state-of-the-art phrase-based system on the task of English-to-French translation. Furthermore, qualitative analysis reveals that the (soft-)alignments found by the model agree well with our intuition.
ArchitectureStatisticsRecurrent neural networkFeedforward neural networkNeural networkMultigraphConjunctionGoogle+Long short term memoryStrong focusing...
• #### Generation of the magnetic helicity in a neutron star driven by the electroweak electron-nucleon interactionver. 2

We study the instability of magnetic fields in a neutron star core driven by the parity violating part of the electron-nucleon interaction in the Standard Model. Assuming a seed field of the order $10^{12}\thinspace\text{G}$, that is a common value for pulsars, one obtains its amplification due to such a novel mechanism by about five orders of magnitude, up to $10^{17}\thinspace\text{G}$, at time scales $\sim (10^3 - 10^5)\thinspace\text{yr}$. This effect is suggested to be a possible explanation of the origin of the strongest magnetic fields observed in magnetars. The growth of a seed magnetic field energy density is stipulated by the corresponding growth of the magnetic helicity density due to the presence of the anomalous electric current in the Maxwell equation. Such an anomaly is the sum of the two competitive effects: (i) the chiral magnetic effect driven by the difference of chemical potentials for the right and left handed massless electrons and (ii) constant chiral electroweak electron-nucleon interaction term, which has the polarization origin and depends on the constant neutron density in a neutron star core. The remarkable issue for the decisive role of the magnetic helicity evolution in the suggested mechanism is the arbitrariness of an initial magnetic helicity including the case of non-helical fields from the beginning. The tendency of the magnetic helicity density to the maximal helicity case at large evolution times provides the growth of a seed magnetic field to the strongest magnetic fields in astrophysics.
Neutron starMagnetic helicityCoolingMagnetic energyHelicityStandard ModelChirality imbalanceMagnetarAbundanceKinetic equation...
• #### The role of self-interacting right-handed neutrinos in galactic structure

We show that warm dark matter keV fermions (`inos') can be responsible for both core and halo galactic structure, in agreement with current astrophysical/cosmological constraints. We identify the inos with sterile right-handed neutrinos. The possible mass range of up to a few tens of keV, obtained independently from the galactic structure and dark matter astroparticle physics, points towards an important role of the right-handed neutrinos in the cosmic structure.
Sterile neutrinoDark matterGalactic structureStandard ModelCore radiusWarm dark matterRotation CurveBlack holeMilky WayCircular velocity...
• #### Show, Attend and Tell: Neural Image Caption Generation with Visual Attentionver. 2

Inspired by recent work in machine translation and object detection, we introduce an attention based model that automatically learns to describe the content of images. We describe how we can train this model in a deterministic manner using standard backpropagation techniques and stochastically by maximizing a variational lower bound. We also show through visualization how the model is able to automatically learn to fix its gaze on salient objects while generating the corresponding words in the output sequence. We validate the use of attention with state-of-the-art performance on three benchmark datasets: Flickr8k, Flickr30k and MS COCO.
Neural networkBackpropagationFeature vectorArchitectureRegularizationConvolutional neural networkImage ProcessingRankingRecurrent neural networkLearning rule...
• #### A New Derivation of the Time-Dependent Schr\"odinger Equation from Wave and Matrix Mechanics

An alternative method is proposed for deriving the time dependent Schroedinger equation from the pictures of wave and matrix mechanics. The derivation is of a mixed classical quantum character, since time is treated as a classical variable, thus avoiding any controversy over its meaning in quantum mechanics. The derivation method proposed in this paper requires no ad hoc assumption and avoids going through a second-order differential equation that can be reduced to the well known time-dependent Schroedinger equation only postulating a complex wavefunction with an exponential time dependence, as did by Schroedinger in its original paper of 1926.
Quantum mechanicsWavefunctionSchrodinger equationPictureDifferential equations...
• #### A Statistical Modelling and Analysis of PHEVs' Power Demand in Smart Grids

Electric vehicles (EVs) and particularly plug-in hybrid electric vehicles (PHEVs) are foreseen to become popular in the near future. Not only are they much more environmentally friendly than conventional internal combustion engine (ICE) vehicles, their fuel can also be catered from diverse energy sources and resources. However, they add significant load on the power grid as they become widespread. The characteristics of this extra load follow the patterns of people's driving behaviours. In particular, random parameters such as arrival time and driven distance of the vehicles determine their expected demand profile from the power grid. In this paper, we first present a model for uncoordinated charging power demand of PHEVs based on a stochastic process and accordingly we characterize the EV's expected daily power demand profile. Next, we adopt different distributions for the EV's charging time following some available empirical research data in the literature. Simulation results show that the EV's expected daily power demand profiles obtained under the uniform, Gaussian with positive support and Rician distributions for charging time are identical when the first and second order statistics of these distributions are the same. This gives us useful insights into the long-term planning for upgrading power systems' infrastructure to accommodate PHEVs. In addition, the results from this modelling can be incorporated into designing demand response (DR) algorithms and evaluating the available DR techniques more accurately.
Plug-in hybridInternal combustion engineElectric vehicleOrder statisticMarketGreenhouse gasesConcurrenceRamificationIntensityCharge...
• #### The Artists who Forged Themselves: Detecting Creativity in Art

Creativity and the understanding of cognitive processes involved in the creative process are relevant to all of human activities. Comprehension of creativity in the arts is of special interest due to the involvement of many scientific and non scientific disciplines. Using digital representation of paintings, we show that creative process in painting art may be objectively recognized within the mathematical framework of self organization, a process characteristic of nonlinear dynamic systems and occurring in natural and social sciences. Unlike the artist identification process or the recognition of forgery, which presupposes the knowledge of the original work, our method requires no prior knowledge on the originality of the work of art. The original paintings are recognized as realizations of the creative process which, in general, is shown to correspond to self-organization of texture features which determine the aesthetic complexity of the painting. The method consists of the wavelet based statistical digital image processing and the measure of statistical complexity which represents the minimal (average) information necessary for optimal prediction. The statistical complexity is based on the properly defined causal states with optimal predictive properties. Two different time concepts related to the works of art are introduced: the internal time and the artistic time. The internal time of the artwork is determined by the span of causal dependencies between wavelet coefficients while the artistic time refers to the internal time during which complexity increases where complexity refers to compositional, aesthetic and structural arrangement of texture features. The method is illustrated by recognizing the original paintings from the copies made by the artists themselves, including the works of the famous surrealist painter Ren\'{e} Magritte.
WaveletSelf-organizationCausalityOrientationInternal timeImage ProcessingWavelet transformEntropyObjectCognitive process...
• #### On the Brukner-Zeilinger approach to information in quantum measurements

We address the problem of proper quantifying an informational content in quantum theory. Brukner and Zeilinger proposed the concept of an operationally invariant measure based on measurement statistics. Their measure of information is calculated with probabilities generated in a complete set of mutually complementary observations. This approach has later been criticized for several reasons. It is related to the problem of existence of a complete set of mutually unbiased bases. In general, this open problem seems to be very hard. Another serious question concerns an inevitable role of "no-click" events in real experiments. We aim to show that some critical points can essentially be overcome by means of natural extension or reformulation of the Brukner-Zeilinger approach. In particular, this approach is shown to be connected with symmetric informationally complete measurements. The "total information" of Brukner and Zeilinger can naturally be treated in the context of mutually unbiased measurements as well as general symmetric informationally complete measurements. We also study the Brukner-Zeilinger measure of information in the case of detection inefficiencies. It is shown to be decreasing under the action of bistochastic maps. This observation may be connected with the role of unitality as the condition for the physicality of reverse processes. Relations between the non-unitality operator and the Brukner-Zeilinger total information are discussed.
POVMQuantum measurementEntropyDimensionsComplete mixingMutually unbiased basesUnitary transformationQuantum theoryUniform distributionDensity matrix...
• #### Magnetic helicity density and its flux in weakly inhomogeneous turbulencever. 2

A gauge invariant and hence physically meaningful definition of magnetic helicity density for random fields is proposed, using the Gauss linking formula, as the density of correlated field line linkages. This definition is applied to the random small scale field in weakly inhomogeneous turbulence, whose correlation length is small compared with the scale on which the turbulence varies. For inhomogeneous systems, with or without boundaries, our technique then allows one to study the local magnetic helicity density evolution in a gauge independent fashion, which was not possible earlier. This evolution equation is governed by local sources (owing to the mean field) and by the divergence of a magnetic helicity flux density. The role of magnetic helicity fluxes in alleviating catastrophic quenching of mean field dynamos is discussed.
Magnetic helicityTurbulenceGauge invarianceHelicityEvolution equationQuenchingSunHomogenizationSolar windCurrent density...
• #### The Brightest Ly$\alpha$ Emitter: Pop III or Black Hole?

CR7 is the brightest $z=6.6 \, {\rm Ly}\alpha$ emitter (LAE) known to date, and spectroscopic follow-up by Sobral et al. (2015) suggests that CR7 might host Population (Pop) III stars. We examine this interpretation using cosmological hydrodynamical simulations. Several simulated galaxies show the same "Pop III wave" pattern observed in CR7. However, to reproduce the extreme CR7 ${\rm Ly}\alpha$/HeII1640 line luminosities ($L_{\rm \alpha/He II}$) a top-heavy IMF and a massive ($>10^{7}{\rm M}_{\odot}$) PopIII burst with age $<2$ Myr are required. Assuming that the observed properties of ${\rm Ly}\alpha$ and HeII emission are typical for Pop III, we predict that in the COSMOS/UDS/SA22 fields, 14 out of the 30 LAEs at $z=6.6$ with $L_{\alpha} >10^{43.3}{\rm erg}\,{\rm s}^{-1}$ should also host Pop III stars producing an observable $L_{\rm He II}>10^{42.7}{\rm erg}\,{\rm s}^{-1}$. As an alternate explanation, we explore the possibility that CR7 is instead powered by accretion onto a Direct Collapse Black Hole (DCBH). Our model predicts $L_{\alpha}$, $L_{\rm He II}$, and X-ray luminosities that are in agreement with the observations. In any case, the observed properties of CR7 indicate that this galaxy is most likely powered by sources formed from pristine gas. We propose that further X-ray observations can distinguish between the two above scenarios.
Population IIIStarPopulation IILuminosityBlack holeInitial mass functionStellar massAccretionStar formationStellar populations...
• #### Compact Radio Sources within 30" of Sgr A*: Proper Motions, Stellar Winds and the Accretion Rate onto Sgr A*

Recent broad-band 34 and 44 GHz radio continuum observations of the Galactic center have revealed 41 massive stars identified with near-IR counterparts, as well as 44 proplyd candidates within 30" of Sgr A*. Radio observations obtained in 2011 and 2014 have been used to derive proper motions of eight young stars near Sgr A*. The accuracy of proper motion estimates based on near-IR observations by Lu et al. and Paumard et al. have been investigated by using their proper motions to predict the 2014 epoch positions of near-IR stars and comparing the predicted positions with those of radio counterparts in the 2014 radio observations. Predicted positions from Lu et al. show an rms scatter of 6 mas relative to the radio positions, while those from Paumard et al. show rms residuals of 20 mas, which is mainly due to uncertainties in the IR-based proper motions. Under the assumption of homogeneous ionized winds, we also determine the mass-loss rates of 11 radio stars, finding rates that are on average $\sim$2 times smaller than those determined from model atmosphere calculations and near-IR data. Clumpiness of ionized winds would reduce the mass loss rate of WR and O stars by additional factors of 3 and 10, respectively. One important implication of this is a reduction in the expected mass accretion rate onto Sgr A* from stellar winds by nearly an order of magnitude to a value of few$\times10^{-7}$ \msol\ yr$^{-1}$. Finally, we present the positions of 318 compact 34.5 GHz radio sources within 30\arcs\ of Sgr A*. At least 45 of these have stellar counterparts in the near-IR $K_s$ (2.18 $\mu$m) and $L'$ (3.8$\mu$m) bands.
• #### Near-Infrared Polarimetric Adaptive Optics Observations of NGC 1068: A torus created by a hydromagnetic outflow windver. 2

We present J' and K' imaging linear polarimetric adaptive optics observations of NGC 1068 using MMT-Pol on the 6.5-m MMT. These observations allow us to study the torus from a magnetohydrodynamical (MHD) framework. In a 0.5" (30 pc) aperture at K', we find that polarisation arising from the passage of radiation from the inner edge of the torus through magnetically aligned dust grains in the clumps is the dominant polarisation mechanism, with an intrinsic polarisation of 7.0%$\pm$2.2%. This result yields a torus magnetic field strength in the range of 4$-$82 mG through paramagnetic alignment, and 139$^{+11}_{-20}$ mG through the Chandrasekhar-Fermi method. The measured position angle (P.A.) of polarisation at K$'$ is found to be similar to the P.A. of the obscuring dusty component at few parsec scales using infrared interferometric techniques. We show that the constant component of the magnetic field is responsible for the alignment of the dust grains, and aligned with the torus axis onto the plane of the sky. Adopting this magnetic field configuration and the physical conditions of the clumps in the MHD outflow wind model, we estimate a mass outflow rate $\le$0.17 M$_{\odot}$ yr$^{-1}$ at 0.4 pc from the central engine for those clumps showing near-infrared dichroism. The models used were able to create the torus in a timescale of $\geq$10$^{5}$ yr with a rotational velocity of $\leq$1228 km s$^{-1}$ at 0.4 pc. We conclude that the evolution, morphology and kinematics of the torus in NGC 1068 can be explained within a MHD framework.
TorusMessier 77Magnetic field strengthNear-infraredActive Galactic NucleiDust grainMagnetohydrodynamicsMagnetizationAbsorptivityThermalisation...
• #### CASSIS: The Cornell Atlas of Spitzer/Infrared Spectrograph Sources. II. High-resolution observations

The Infrared Spectrograph (IRS) on board the Spitzer Space Telescope observed about 15,000 objects during the cryogenic mission lifetime. Observations provided low-resolution (R~60-127) spectra over ~5-38um and high-resolution (R~600) spectra over ~10-37um. The Cornell Atlas of Spitzer/IRS Sources (CASSIS) was created to provide publishable quality spectra to the community. Low-resolution spectra have been available in CASSIS since 2011, and we present here the addition of the high-resolution spectra. The high-resolution observations represent approximately one third of all staring observations performed with the IRS instrument. While low-resolution observations are adapted to faint objects and/or broad spectral features (e.g., dust continuum, molecular bands), high-resolution observations allow more accurate measurements of narrow features (e.g., ionic emission lines) as well as a better sampling of the spectral profile of various features. Given the narrow aperture of the two high-resolution modules, cosmic ray hits and spurious features usually plague the spectra. Our pipeline is designed to minimize these effects through various improvements. A super sampled point-spread function was created in order to enable the optimal extraction in addition to the full aperture extraction. The pipeline selects the best extraction method based on the spatial extent of the object. For unresolved sources, the optimal extraction provides a significant improvement in signal-to-noise ratio over a full aperture extraction. We have developed several techniques for optimal extraction, including a differential method that eliminates low-level rogue pixels (even when no dedicated background observation was performed). The updated CASSIS repository now includes all the spectra ever taken by the IRS, with the exception of mapping observations.
Point spread functionAlgorithmCalibrationUnresolved sourcesATLAS detectorObjectPoint sourceRegularizationDiffuse sourceSignal to noise ratio...
• #### Resonators coupled to voltage-biased Josephson junctions: From linear response to strongly driven nonlinear oscillations

Motivated by recent experiments, where a voltage biased Josephson junction is placed in series with a resonator, the classical dynamics of the circuit is studied in various domains of parameter space. This problem can be mapped onto the dissipative motion of a single degree of freedom in a nonlinear time-dependent potential, where in contrast to conventional settings the nonlinearity appears in the driving while the static potential is purely harmonic. For long times the system approaches steady states which are analyzed in the underdamped regime over the full range of driving parameters including the fundamental resonance as well as higher and sub-harmonics. Observables such as the dc-Josephson current and the radiated microwave power give direct information about the underlying dynamics covering phenomena as bifurcations, irregular motion, up- and down conversion. Due to their tunability, present and future set-ups provide versatile platforms to explore the changeover from linear response to strongly nonlinear behavior in driven dissipative systems under well defined conditions.
Steady stateBifurcationPhase spaceThermalisationDissipationJosephson junctionsBessel functionDegree of freedomEffective potentialHarmonic oscillator...
• #### Topological nature of FeSe$_{0.5}$Te$_{0.5}$ superconductor

We demonstrate, using first-principles calculations, that the electronic structure of FeSe$_{1-x}$Te$_{x}$ ($x$=0.5) is topologically non-trivial, characterized by an odd $\mathbb Z_2$ invariant and Dirac cone type surface states, in sharp contrast to the end member FeSe ($x$=0). This topological state is induced by the enhanced three-dimensionality and spin-orbit coupling due to Te substitution (compared to FeSe), characterized by a band inversion at the $Z$ point of the Brillouin zone, which is confirmed by our ARPES measurements. The results suggest that the surface of FeSe$_{0.5}$Te$_{0.5}$ may support a non-trivial superconducting channel in proximity to the bulk.
HybridizationAngle resolved photoemission spectroscopySuperconductivitySuperconductorDensity functional theoryFermi surfaceIntensityDynamical Mean-Field TheoryBrillouin zoneEvaporation...
• #### The Sloan Digital Sky Survey Reverberation Mapping Project: Post-Starburst Signatures in Quasar Host Galaxies at z < 1

Quasar host galaxies are key for understanding the relation between galaxies and the supermassive black holes (SMBHs) at their cores. We present a study of 191 unobscured quasars and their host galaxies at z < 1, using high signal-to-noise ratio (SNR) spectra produced by the Sloan Digital Sky Survey Reverberation Mapping project. Clear detection of stellar absorption lines allows a reliable decomposition of the observed spectra into nuclear and host components, using spectral models of quasar and stellar radiations as well as emission lines from the interstellar medium. We estimate age, mass (M*), and velocity dispersion (sigma*) of the host stars, the star formation rate (SFR), quasar luminosity, and SMBH mass (Mbh), for each object. The quasars are preferentially hosted by massive galaxies with M* ~ 10^{11} Msun characterized by stellar ages around a billion years, which coincides with the transition phase of normal galaxies from the blue cloud to the red sequence. The host galaxies have relatively low SFRs and fall below the main sequence of star-forming galaxies at similar redshifts. These facts suggest that the hosts have experienced an episode of major star formation sometime in the past billion years which was subsequently quenched. The derived Mbh - sigma* and Mbh - M* relations agree with our past measurements and are consistent with no evolution from the local Universe. The present analysis demonstrates that reliable measurements of stellar properties of quasar host galaxies are possible with high-SNR fiber spectra, which will be acquired in large numbers with future powerful instruments such as the Subaru Prime Focus Spectrograph.
QuasarHost galaxyStar formation rateSupermassive black holeActive Galactic NucleiSloan Digital Sky SurveySignal to noise ratioObjectStellar massStar formation...
• #### E\"otv\"os Experiments with Supermassive Black Holes

By examining the locations of central black holes in two elliptical galaxies, M32 and M87, we derive constraints on the violation of the strong equivalence principle for purely gravitational objects, i.e. black holes, of less than eight percent, $|\eta_N|<0.08$ from M32. The constraints from M87 are substantially weaker but could improve dramatically with better astrometry.
Black holeSupermassive black holeElliptical galaxySouth ecliptic poleObjectStar systemsEquivalence principleAstrometryWide Field Camera 3Virgo Cluster...
• #### Terahertz time-domain spectroscopy of transient metallic and superconducting statesver. 2

Time-resolved terahertz time-domain spectroscopy (THz-TDS) is an ideal tool for probing photoinduced nonequilibrium metallic and superconducting states. Here, we focus on the interpretation of the two-dimensional response function $\Sigma(\omega;t)$ that it measures, examining whether it provides an accurate snapshot of the instantaneous optical conductivity, $\sigma(\omega;t)$. For the Drude model with a time-dependent carrier density, we show that $\Sigma(\omega;t)$ is not simply related to $\sigma(\omega;t)$. The difference in the two response functions is most pronounced when the momentum relaxation rate of photocarriers is long, as would be the case in a system that becomes superconducting following pulsed photoexcitation. From the analysis of our model, we identify signatures of photoinduced superconductivity that could be seen by time-resolved THz-TDS.
SuperconductivityTerahertz time-domain spectroscopyRelaxationDrude modelSuperfluidRelaxation timeSuperconductorRecombinationPhotoconductivityMetastate...