cssi/SciSciGPT-SciSciNet huggingface dataset:
The preon sector of the SLq(2) model and the binding problem

There are suggestive experimental indications that the leptons, neutrinos, and quarks might be composite and that their structure is described by the quantum group SLq(2). Since the hypothetical preons must be very heavy relative to the masses of the leptons, neutrinos, and quarks, there must be a very strong binding field to permit these composite particles to form. Unfortunately there are no experiments direct enough to establish the order of magnitude needed to make the SLq(2) Lagrangian dynamics quantitative. It is possible, however, to parametrize the preon masses and interactions that would be necessary to stabilize the three particle composite representing the leptons, neutrinos, and quarks. In this note we examine possible parametrizations of the masses and the interactions of these hypothetical structures. We also note an alternative view of SLq(2) preons.
Asymptotic freedom and confinement imply spontaneously broken chiral symmetry in quantum chromodynamics

We utilize Coleman's theorem and show that quantum chromodynamics based on asymptotic freedom and confinement must have chiral symmetry realized as a spontaneously broken symmetry.
Hierarchical memory management for mutable state

It is well known that modern functional programming languages are naturally amenable to parallel programming. Achieving efficient parallelism using functional languages, however, remains difficult. Perhaps the most important reason for this is their lack of support for efficient in-place updates, i.e., mutation, which is important for the implementation of both parallel algorithms and the run-time system services (e.g., schedulers and synchronization primitives) used to execute them. In this paper, we propose techniques for efficient mutation in parallel functional languages. To this end, we couple the memory manager with the thread scheduler to make reading and updating data allocated by nested threads efficient. We describe the key algorithms behind our technique, implement them in the MLton Standard ML compiler, and present an empirical evaluation. Our experiments show that the approach performs well, significantly improving efficiency over existing functional language implementations.
Framed graphs and the non-local ideal in the knot Floer cube of resolutions

This article addresses the two significant aspects of Ozsvath and Szabo’s knot Floer cube of resolutions that differentiate it from Khovanov and Rozansky’s HOMFLYPT chain complex: (1) the use of twisted coefficients and (2) the appearance of a mysterious non-local ideal. Our goal is to facilitate progress on Rasmussen’s conjecture that a spectral sequence relates the two knot homologies. We replace the language of twisted coefficients with the more quantum-topological language of framings on trivalent graphs. We define a homology theory for framed trivalent graphs with boundary that — for a particular non-blackboard framing — specializes to the homology of singular knots underlying the knot Floer cube of resolutions. For blackboard-framed graphs, our theory conjecturally recovers the graph homology underlying the HOMFLY-PT chain complex. We explain the appearance of the nonlocal ideal by expressing it as an ideal quotient of an ideal that appears in both the HOMFLY-PT and knot Floer cubes of resolutions. This result is a corollary of our main theorem, which is that closing a strand in a braid graph corresponds to taking an ideal quotient of its non-local ideal. The proof is a Grobner basis argument that connects the combinatorics of the non-local ideal to those of Buchberger’s algorithm.
Gravitational Radiation from First-Order Phase Transitions

It is believed that first-order phase transitions at or around the GUT scale will produce high-frequency gravitational radiation. This radiation is a consequence of the collisions and coalescence of multiple bubbles during the transition. We employ high-resolution lattice simulations to numerically evolve a system of bubbles using only scalar fields, track the anisotropic stress during the process and evolve the metric perturbations associated with gravitational radiation. Although the radiation produced during the bubble collisions has previously been estimated, we find that the coalescence phase enhances this radiation even in the absence of a coupled fluid or turbulence. We comment on how these simulations scale and propose that the same enhancement should be found at the Electroweak scale; this modification should make direct detection of a first-order electroweak phase transition easier.
No Paradox in Wave–Particle Duality

The assertion that an experiment by Afshar et al. demonstrates violation of Bohr’s Principle of Complementarity is based on the faulty assumption that which-way information in a double-slit interference experiment can be retroactively determined from a future measurement.
Cholla : A New Massively-Parallel Hydrodynamics Code For Astrophysical Simulation

We present Cholla (Computational Hydrodynamics On ParaLLel Architectures), a new three-dimensional hydrodynamics code that harnesses the power of graphics processing units (GPUs) to accelerate astrophysical simulations. Cholla models the Euler equations on a static mesh using state-of-the-art techniques, including the unsplit Corner Transport Upwind (CTU) algorithm, a variety of exact and approximate Riemann solvers, and multiple spatial reconstruction techniques including the piecewise parabolic method (PPM). Using GPUs, Cholla evolves the fluid properties of thousands of cells simultaneously and can update over ten million cells per GPU-second while using an exact Riemann solver and PPM reconstruction. Owing to the massively-parallel architecture of GPUs and the design of the Cholla code, astrophysical simulations with physically interesting grid resolutions (> 256^3) can easily be computed on a single device. We use the Message Passing Interface library to extend calculations onto multiple devices and demonstrate nearly ideal scaling beyond 64 GPUs. A suite of test problems highlights the physical accuracy of our modeling and provides a useful comparison to other codes. We then use Cholla to simulate the interaction of a shock wave with a gas cloud in the interstellar medium, showing that the evolution of the cloud is highly dependent on its density structure. We reconcile the computed mixing time of a turbulent cloud with a realistic density distribution destroyed by a strong shock with the existing analytic theory for spherical cloud destruction by describing the system in terms of its median gas density.
SoftNull: Many-Antenna Full-Duplex Wireless via Digital Beamforming

In this paper, we present and study a digital-controlled method, called SoftNull, to enable full-duplex in many-antenna systems. Unlike most designs that rely on analog cancelers to suppress self-interference, SoftNull relies on digital transmit beamforming to reduce self-interference. SoftNull does not attempt to perfectly null self-interference, but instead seeks to reduce self-interference sufficiently to prevent swamping the receiver’s dynamic range. Residual self-interference is then cancelled digitally by the receiver. We evaluate the performance of SoftNull using measurements from a 72-element antenna array in both indoor and outdoor environments. We find that SoftNull can significantly outperform half-duplex for small cells operating in the many-antenna regime, where the number of antennas is many more than the number of users served simultaneously.
Linear Power Spectra in Cold+Hot Dark Matter Models: Analytical Approximations and Applications

This paper presents simple analytic approximations to the linear power spectra, linear growth rates, and rms mass fluctuations for both components in a family of cold + hot dark matter (CDM+HDM) models that are of current cosmological interest. The formulas are valid for a wide range of wave numbers, neutrino fractions, redshifts, and Hubble constants: k 10 h Mpc−1, 0.05 Ωv 0.3, 0 ≤ z ≤ 15, and 0.5 ≤ h ≤ 0.8. A new, redshift-dependent shape parameter, Γv = a1/2 Ωv h2, is introduced to simplify the multidimensional parameter space and to characterize the effect of massive neutrinos on the power spectrum. The physical origin of Γv lies in the neutrino free-streaming process, and the analytic approximations can be simplified to depend only on this variable and Ωv. Linear calculations with these power spectra as input are performed to compare the predictions of Ωv 0.3 models with observational constraints from the reconstructed linear power spectrum and cluster abundance. The usual assumption of an exact scale-invariant primordial power spectrum is relaxed to allow a spectral index of 0.8 n ≤ 1. It is found that a slight tilt of n = 0.9 (no tensor mode) or n = 0.95 (with tensor mode) in Ωv ~ 0.1–0.2 CDM + HDM models gives a power spectrum similar to that of an open CDM model with a shape parameter Γ = 0.25, providing good agreement with the power spectrum reconstructed by Peacock & Dodds and the observed cluster abundance at low redshifts. Late galaxy formation at high redshifts, however, will be a more severe problem in tilted models.
On the Approximation of the Black Hole Shadow with a Simple Polar Curve

A black hole embedded within a bright, optically thin emitting region imprints a nearly circular "shadow" on its image, corresponding to the observer's line-of-sight into the black hole. The shadow boundary depends on the black hole's mass and spin, providing an observable signature of both properties via high resolution images. However, standard expressions for the shadow boundary are most naturally parametrized by Boyer-Lindquist radii rather than by image coordinates. We explore simple, approximate parameterizations for the shadow boundary using ellipses and a family of curves known as limacons. We demonstrate that these curves provide excellent and efficient approximations for all black hole spins and inclinations. In particular, we show that the two parameters of the limacon naturally account for the three primary shadow deformations resulting from mass and spin: size, displacement, and asymmetry. These curves are convenient for parametric model fitting directly to interferometric data, they reveal the degeneracies expected when estimating black hole properties from images with practical measurement limitations, and they provide a natural framework for parametric tests of the Kerr metric using black hole images.
Addendum and correction to: “Homology cylinders: an enlargement of the mapping class group”

In a previous paper [Homology cylinders: an enlargement of the mapping class group, Algebr. Geom. Topol. 1 (2001) 243–270], a group ℋg of homology cylinders over the oriented surface of genus g is defined. A filtration of ℋg is defined, using the Goussarov-Habiro notion of finite-type. It is erroneously claimed that this filtration essentially coincides with the relative weight filtration. The present note corrects this error and studies the actual relation between the two filtrations.
BPS equations and non-trivial compactifications

We consider the problem of finding exact, eleven-dimensional, BPS supergravity solutions in which the compactification involves a non-trivial Calabi-Yau manifold, $$ \mathcal{Y} $$ , as opposed to simply a T 6. Since there are no explicitly-known metrics on non-trivial, compact Calabi-Yau manifolds, we use a non-compact “local model” and take the compactification manifold to be $$ \mathcal{Y}={\mathrm{\mathcal{M}}}_{\mathrm{GH}}\times {T}^2 $$ , where ℳGH is a hyper-Kahler, Gibbons-Hawking ALE space. We focus on backgrounds with three electric charges in five dimensions and find exact families of solutions to the BPS equations that have the same four supersymmetries as the three-charge black hole. Our exact solution to the BPS system requires that the Calabi-Yau manifold be fibered over the space-time using compensators on $$ \mathcal{Y} $$ . The role of the compensators is to ensure smoothness of the eleven-dimensional metric when the moduli of $$ \mathcal{Y} $$ depend on the space-time. The Maxwell field Ansatz also implicitly involves the compensators through the frames of the fibration. We examine the equations of motion and discuss the brane distributions on generic internal manifolds that do not have enough symmetry to allow smearing.
Attractors for strongly damped wave equations with nonlinear hyperbolic dynamic boundary conditions

We establish the well-posedness of a strongly damped semilinear wave equation equipped with nonlinear hyperbolic dynamic boundary conditions. Results are carried out with the presence of a parameter distinguishing whether the underlying operator is analytic, , or only of Gevrey class, . We establish the existence of a global attractor for each and we show that the family of global attractors is upper-semicontinuous as Furthermore, for each , we show the existence of a weak exponential attractor. A weak exponential attractor is a finite dimensional compact set in the weak topology of the phase space. This result ensures the corresponding global attractor also possesses finite fractal dimension in the weak topology; moreover, the dimension is independent of the perturbation parameter α. In both settings, attractors are found under minimal assumptions on the nonlinear terms.
The Gauge-String Duality and Heavy Ion Collisions

I review at a non-technical level the use of the gauge-string duality to study aspects of heavy ion collisions, with special emphasis on the trailing string calculation of heavy quark energy loss. I include some brief speculations on how variants of the trailing string construction could provide a toy model of black hole formation and evaporation. This essay is an invited contribution to “Forty Years of String Theory” and is aimed at philosophers and historians of science as well as physicists.
Resonant delocalization on the Bethe strip

Recently, Aizenman and Warzel discovered a mechanism for the appearance of absolutely continuous spectrum for random Schrodinger operators on the Bethe lattice through rare resonances (resonant delocalization). We extend their analysis to operators with matrix-valued random potentials drawn from ensembles such as the Gaussian Orthogonal Ensemble. These operators can be viewed as random operators on the Bethe strip, a graph (lattice) with loops.
Reactionaries and Einstein’s Fame: “German Scientists for the Preservation of Pure Science,” Relativity, and the Bad Nauheim Meeting

Two important and unpleasant events occurred in Albert Einstein’s life in 1920: That August an antirelativity rally was held in the large auditorium of the Berlin Philharmonic, and a few weeks later Einstein was drawn into a tense and highly publicized debate with Philipp Lenard on the merits of relativity at a meeting in Bad Nauheim, Germany. I review these events and discuss how they affected Einstein in light of new documentary evidence that has become available through the publication of Volume 10 of the Collected Papers of Albert Einstein.
Rigidity of graph products of abelian groups

We show that if G is a group and G has a graph-product decomposition with finitely generated abelian vertex groups, then G has two canonical decompositions as a graph product of groups: a unique decomposition in which each vertex group is a directly indecomposable cyclic group, and a unique decomposition in which each vertex group is a finitely generated abelian group and the graph satisfies the To property. Our results build on results by Droms, Laurence and Radcliffe.
Holographic entanglement entropy for general higher derivative gravity

We propose a general formula for calculating the entanglement entropy in theories dual to higher derivative gravity where the Lagrangian is a contraction of Riemann tensors. Our formula consists of Wald’s formula for the black hole entropy, as well as corrections involving the extrinsic curvature. We derive these corrections by noting that they arise from naively higher order contributions to the action which are enhanced due to would-be logarithmic divergences. Our formula reproduces the Jacobson-Myers entropy in the context of Lovelock gravity, and agrees with existing results for general four-derivative gravity. We emphasize that the formula should be evaluated on a particular bulk surface whose location can in principle be determined by solving the equations of motion with conical boundary conditions. This may be difficult in practice, and an alternative method is desirable. A natural prescription is simply minimizing our formula, analogous to the Ryu-Takayanagi prescription for Einstein gravity. We show that this is correct in several examples including Lovelock and general four-derivative gravity.
A Sample Path Measure of Causal Influence

We present a sample path dependent measure of causal influence between two time series. The proposed measure is a random variable whose expected sum is the directed information. A realization of the proposed measure may be used to identify the specific patterns in the data that yield a greater flow of information from one process to another, even in stationary processes. We demonstrate how sequential prediction theory may be leveraged to obtain accurate estimates of the causal measure at each point in time and introduce a notion of regret for assessing the performance of estimators of the measure. We prove a finite sample bound on this regret that is determined by the regret of the sequential predictors used in obtaining the estimate. We estimate the causal measure for a simulated collection of binary Markov processes using a Bayesian updating approach. Finally, given that the measure is a function of time, we demonstrate how estimators of the causal measure may be extended to effectively capture causality in time-varying scenarios.
Coherence switching of a degenerate VECSEL for multimodality imaging

Speckle formation is a limiting factor when using coherent sources for imaging and sensing, but can provide useful information about the motion of an object. Illumination sources with tunable spatial coherence are therefore desirable as they can offer both speckled and speckle-free images. Efficient methods of coherence switching have been achieved with a solid-state degenerate laser, and here we demonstrate a degenerate laser system that can be switched between a large number of mutually incoherent spatial modes and few-mode operation. This technology enables multimodality imaging, where low spatial coherence illumination is used for traditional high-speed videomicroscopy and high spatial coherence illumination is used to extract dynamic information of flow processes. Our implementation is based on a vertical external-cavity surface-emitting laser (VECSEL) architecture. This architecture uses a semiconductor gain module that is electrically pumped, mechanically compact, and supports continuous-wave emission. As an initial example, we perform dynamic multimodality biomedical imaging in Xenopus embryo (tadpole) hearts, an important animal model of human heart disease.
Small instanton transitions in heterotic M-theory

We discuss non-perturbative phase transitions, within the context of heterotic M-theory, which occur when all, or part, of the wrapped five-branes in the five-dimensional bulk space come into direct contact with a boundary brane. These transitions involve the transformation of the five-brane into a ``small instanton'' on the Calabi-Yau space at the boundary brane, followed by the ``smoothing out'' of the small instanton into a holomorphic vector bundle. Small instanton phase transitions change the number of families, the gauge group or both on the boundary brane, depending upon whether a base component, fiber component or both components of the five-brane class are involved in the transition. We compute the conditions under which a small instanton phase transition can occur and present a number of explicit, phenomenologically relevant examples.
THE CHEMICAL COMPOSITION OF RED GIANT BRANCH STARS IN THE GALACTIC GLOBULAR CLUSTERS NGC 6342 AND NGC 6366

We present radial velocities and chemical abundances for red giant branch stars in the Galactic bulge globular clusters NGC 6342 and NGC 6366. The velocities and abundances are based on measurements of high resolution (R > 20,000) spectra obtained with the MMT-Hectochelle and WIYN-Hydra spectrographs. We find that NGC 6342 has a heliocentric radial velocity of +112.5 km/s (sigma = 8.6 km/s), NGC 6366 has a heliocentric radial velocity of -122.3 km/s (sigma = 1.5 km/s), and that both clusters have nearly identical metallicities ([Fe/H] ~ -0.55). NGC 6366 shows evidence of a moderately extended O-Na anti-correlation, but more data are needed for NGC 6342 to determine if this cluster also exhibits the typical O-Na relation likely found in all other Galactic globular clusters. The two clusters are distinguished from similar metallicity field stars as having larger [Na/Fe] spreads and enhanced [La/Fe] ratios, but we find that NGC 6342 and NGC 6366 display alpha and Fe-peak element abundance patterns that are typical of other metal-rich ([Fe/H] > -1) inner Galaxy clusters. However, the median [La/Fe] abundance may vary from cluster-to-cluster.
Radio Emission from Supernovae

I consider radio emission from the remarkable supernova (SN) 1998bw. Decay of 56Ni and 56Co produces a gamma-ray flux, whose Compton-scattered electrons naturally explain the observed mildly relativistic expansion of the radio source and its double-peaked history. Such models require a surrounding plasma, perhaps produced by the supernova progenitor, whose interaction with the nonrelativistic debris may account for the observed X-ray source. The radio spectrum appears to be self-absorbed. This interpretation determines the brightness temperature, and hence the energy, of the radiating electrons, which implies a surprisingly large magnetic field. Attempts to avoid this conclusion by interpreting the spectrum as the result of inverse bremsstrahlung absorption do not lead to significantly lower fields. The large inferred field may have several explanations, such as radiation from a central pulsar, electromagnetic plasma instabilities, or a turbulent hydrodynamic dynamo, but a frozen-in field from the supernova progenitor is not an adequate explanation. The electron-ion and particle-field equipartition problems are discussed. Compton electrons also explain the inferred expansion speed of the spots of SN 1987A.
Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolution

Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often require proper regularization (e.g., trimming, regularized cost, projection) in order to guarantee fast convergence. For vanilla procedures such as gradient descent, however, prior theory either recommends highly conservative learning rates to avoid overshooting, or completely lacks performance guarantees. This paper uncovers a striking phenomenon in nonconvex optimization: even in the absence of explicit regularization, gradient descent enforces proper regularization implicitly under various statistical models. In fact, gradient descent follows a trajectory staying within a basin that enjoys nice geometry, consisting of points incoherent with the sampling mechanism. This “implicit regularization” feature allows gradient descent to proceed in a far more aggressive fashion without overshooting, which in turn results in substantial computational savings. Focusing on three fundamental statistical estimation problems, i.e., phase retrieval, low-rank matrix completion, and blind deconvolution, we establish that gradient descent achieves near-optimal statistical and computational guarantees without explicit regularization. In particular, by marrying statistical modeling with generic optimization theory, we develop a general recipe for analyzing the trajectories of iterative algorithms via a leave-one-out perturbation argument. As a by-product, for noisy matrix completion, we demonstrate that gradient descent achieves near-optimal error control—measured entrywise and by the spectral norm—which might be of independent interest.
Three-dimensional Spontaneous Magnetic Reconnection

Magnetic reconnection is best known from observations of the Sun where it causes solar flares. Observations estimate the reconnection rate a small, but non-negligible fraction of the Alfv\'en speed, so-called fast reconnection. Until recently, the prevailing pictures of reconnection were referring to either resistivity or plasma microscopic effects, which was contradictory to the observed rates. The alternative picture was either reconnection due to the stochasticity of magnetic field lines in turbulence or the tearing instability of the thin current sheet. In this paper I simulated long-term three-dimensional nonlinear evolution of a thin, planar current sheet subject to fast oblique tearing instability using direct numerical simulations of resistive-viscous MHD. The late-time evolution resembles generic turbulence with -5/3 power spectrum and scale-dependent anisotropy, so I conclude that the tearing-driven reconnection becomes turbulent reconnection. The turbulence is local in scale, so microscopic diffusivity should not affect large-scale quantities. This is confirmed by convergence of the reconnection rate towards $\sim 0.015 v_A$ with increasing Lundquist number. In this spontaneous reconnection with mean field and without driving the dissipation rate per unit area also converge to $\sim 0.006 \rho v_A^3$, the dimensionless constants $0.015$ and $0.006$ are governed only by self-driven nonlinear dynamics of the sheared magnetic field. Remarkably, this also means that thin current sheet has a universal fluid resistance depending only on its length to width ratio and to $v_A/c$.
Investigating the Essential of Meaningful Automated Formative Feedback for Programming Assignments

This study investigated the essential of meaningful automated feedback for programming assignments. Three different types of feedback were tested, including (a) What’s wrong- what test cases were testing and which failed, (b) Gap comparisons between expected and actual outputs, and (c) Hint hints on how to fix problems if test cases failed. 46 students taking a CS2 participated in this study. They were divided into three groups, and the feedback configurations for each group were different: (1) Group One -What’s wrong, (2) Group Two -What’s wrong + Gap, (3) Group Three -What’s wrong+ Gap + Hint. This study found that simply knowing what failed did not help students sufficiently, and might stimulate system gaming behavior. Hints were not found to be impactful on student performance or their usage of automated feedback. Based on the findings, this study provides practical guidance on the design of automated feedback.
Perturbative Dynamics of Fractional Strings on Multiply Wound D-Strings

Fractional strings in the spectrum of states of open strings attached to a multiply wound D-brane is explained. We first describe the fractional string states in the low energy effective theory where the topology of multiple winding is encoded in the gauge holonomy. The holonomy induces twisted boundary conditions responsible for the fractional moding of these states. We also describe fractional strings in world sheet formulation and compute simple scattering amplitudes for Hawking emission/absorption. Generalization to fractional DN-strings in a one-brane five-brane bound state is described. When a one-brane and a five-brane wraps Q1 and Q5 times respectively around a circle, the momentum of DN-strings is quantized in units of 2π/LQ1Q5. These fractional states appear naturally in the perturbative spectrum of the theory.
Template Guided Text Generation for Task-Oriented Dialogue

Virtual assistants such as Google Assistant, Amazon Alexa, and Apple Siri enable users to interact with a large number of services and APIs on the web using natural language. In this work, we investigate two methods for Natural Language Generation (NLG) using a single domain-independent model across a large number of APIs. First, we propose a schema-guided approach which conditions the generation on a schema describing the API in natural language. Our second method investigates the use of a small number of templates, growing linearly in number of slots, to convey the semantics of the API. To generate utterances for an arbitrary slot combination, a few simple templates are first concatenated to give a semantically correct, but possibly incoherent and ungrammatical utterance. A pre-trained language model is subsequently employed to rewrite it into coherent, natural sounding text. Through automatic metrics and human evaluation, we show that our method improves over strong baselines, is robust to out-of-domain inputs and shows improved sample efficiency.
Some root invariants at the prime 2

This paper consists of two parts. The first part consists of the lecture notes of a series of talks on the root invariant given by the author at a workshop held at the Nagoya Institute of Technology. The second part is a detailed computation, using the methods of Part I, of some low dimensional root invariants at the prime 2. More detailed descriptions of the contents of these parts are given at the beginning of each part.
The Ohm–Rush content function

The content of a polynomial over a ring R is a well-understood notion. Ohm and Rush generalized this concept of a content map to an arbitrary ring extension of R, although it can behave quite badly. We examine five properties an algebra may have with respect to this function — content algebra, weak content algebra, semicontent algebra (our own definition), Gaussian algebra, and Ohm–Rush algebra. We show that the Gaussian, weak content, and semicontent algebra properties are all transitive. However, transitivity is unknown for the content algebra property. We then compare the Ohm–Rush notion with the more usual notion of content in the power series context. We show that many of the given properties coincide for the power series extension map over a valuation ring of finite dimension, and that they are equivalent to the value group being order-isomorphic to the integers or the reals. Along the way, we give a new characterization of Prufer domains.
Symmetry breaking of gauge theories via internal space dynamics

In this paper, I explain how gauge symmetry can be broken in a geometric way, a la Kaluza-Klein. In higher dimensional gravitational theories, one usually considers the extra dimensions to be ``frozen'' in time. However, the internal manifold is actually a dynamic entity. For example, its metric can change even if one expects its topological properties to be invariant. It is conceivable then, that at an earlier epoch the internal manifold made a geometric transition from say a maximally symmetric metric space to a less symmetric one. We know in a Kaluza-Klein reduction scheme, the massless gauge bosons are associated with the Killing vectors of the internal manifold. After the transition of the internal manifold, the gauge bosons associated with the broken Killing isometries will pick up a mass thereby breaking the gauge invariance partially. In this paper, I explore this idea, work out the mass of broken gauge bosons for some simple examples, and also point out how a mechanism similar to that of Higgs may be at work.
From Bypass Transition to Flow Control and Data-Driven Turbulence Modeling: An Input–Output Viewpoint

Transient growth and resolvent analyses are routinely used to assess nonasymptotic properties of fluid flows. In particular, resolvent analysis can be interpreted as a special case of viewing flow ...
The IR/UV connection in the non-commutative gauge theories

Quantum field theory on non-commutative spaces does not enjoy the usual ultraviolet-infrared decoupling that forms the basis for conventional renormalization. The high momentum contributions to loop integrations can lead to unfamiliar long distance behavior which can potentially undermine naive expectations for the IR behavior of the theory. These ``anomalies" involve non-analytic behavior in the noncommutativity parameter θ making the limit θ→0 singular. In this paper we will analyze such effects in the one loop approximation to gauge theories on non-commutative space. We will see that contrary to expectations poles in θ do occur and lead to large discrepancies between the expected and actual infrared behavior. We find that poles in θ are absent in supersymmetric theories. The ``anomalies" are generally still present, but only at the logarithmic level. A notable exception is non-commutative super Yang-Mills theory with 16 real supercharges in which anomalous effects seem to be absent altogether.
Periodic and Chaotic Orbits of Plane-Confined Micro-rotors in Creeping Flows

We explore theoretically the complex dynamics and emergent behaviors of spinning spheres immersed in viscous fluid. The particles are coupled to each other via the fluid in which they are suspended: Each particle disturbs the surrounding fluid with a rotlet field and that fluid flow affects the motion of the other particles. We notice the emergence of intricate periodic or chaotic trajectories that depend on the rotors initial position and separation. The point-rotor motions confined to a plane bear similarities to the classic 2D point-vortex dynamics. Our analyses highlight the complexity of the interaction between just a few rotors and suggest richer behavior in denser populations. We discuss how the model gives insight into more complex systems and suggest possible extensions for future theoretical studies.
Analytic number theory for 0-cycles

There is a well-known analogy between integers and polynomials over 𝔽q, and a vast literature on analytic number theory for polynomials. From a geometric point of view, polynomials are equivalent to effective 0-cycles on the affine line. This leads one to ask: Can the analogy between integers and polynomials be extended to 0-cycles on more general varieties? In this paper we study prime factorisation of effective 0-cycles on an arbitrary connected variety V over 𝔽q, emphasizing the analogy between integers and 0-cycles. For example, inspired by the works of Granville and Rhoades, we prove that the prime factors of 0-cycles are typically Poisson distributed.
Approximate optimal cooperative decentralized control for consensus in a topological network of agents with uncertain nonlinear dynamics

Efforts in this paper seek to combine graph theory with adaptive dynamic programming (ADP) as a reinforcement learning (RL) framework to determine forward-in-time, real-time, approximate optimal controllers for distributed multi-agent systems with uncertain nonlinear dynamics. A decentralized continuous time-varying control strategy is proposed, using only local communication feedback from two-hop neighbors on a communication topology that has a spanning tree. An actor-critic-identifier architecture is proposed that employs a nonlinear state derivative estimator to estimate the unknown dynamics online and uses the estimate thus obtained for value function approximation.
Strongly interacting Higgs sector in the minimal Standard Model

Abstract The triviality Higgs mass bound is studied with a higher derivative regulating in the spontaneously broken phase of the four dimensional O(4) symmetric scalar fiel-theory with quartic self-interaction. The phase diagram of the O(4) model is determined in a Monte Carlo simulation which interpolates between the hypercubic lattice regulator and the higher derivative regulator in continuum space-time. The same method can be used to calculate the Higgs mass bound in continuum space-time. In a large- N analysis, when compared with a hypercubic lattice, we find a relative increase in the triviality bound of the higher derivative regulator suggesting a strongly interacting Higgs sector in the TeV region with negligible dependence on regulator parameters. When the higher derivative regulator mass is brought close to the Higgs mass the model requires a more elaborate analysis of complex ghost states in scattering amplitudes.
A theory of jet shapes and cross sections: from hadrons to nuclei

For jets, with great power comes great opportunity. The unprecedented center of mass energies available at the LHC open new windows on the QGP: we demonstrate that jet shape and jet cross section measurements become feasible as a new, differential and accurate test of the underlying QCD theory. We present a first step in understanding these shapes and cross sections in heavy ion reactions. Our approach allows for detailed simulations of the experimental acceptance/cuts that help isolate jets in such high-multiplicity environment. It is demonstrated for the first time that the pattern of stimulated gluon emission can be correlated with a variable quenching of the jet rates and provide an approximately model-independent approach to determining the characteristics of the medium-induced bremsstrahlung spectrum. Surprisingly, in realistic simulations of parton propagation through the QGP we find a minimal increase in the mean jet radius even for large jet attenuation. Jet broadening is manifest in the tails of the energy distribution away from the jet axis and its quantification requires high statistics measurements that will be possible at the LHC.
Decay of Correlations and Uniqueness of the Infinite-Volume Gibbs Measure of the Canonical Ensemble of 1d-Lattice Systems

We consider a one-dimensional lattice system of unbounded, real-valued spins with arbitrary strong, quadratic, finite-range interaction. We show the equivalence of correlations of the grand canonical (gce) and the canonical ensemble (ce). As a corollary we obtain that the correlations of the ce decay exponentially plus a volume correction term. Then, we use the decay of correlation to verify a conjecture that the infinite-volume Gibbs measure of the ce is unique on a one-dimensional lattice. For the equivalence of correlations, we modify a method that was recently used by the authors to show the equivalence of the ce and the gce on the level of thermodynamic functions. In this article we also show that the equivalence of the ce and the gce holds on the level of observables. One should be able to extend the methods and results to graphs with bounded degree as long as the gce has a sufficient strong decay of correlations.
Visual Text Correction

This paper introduces a new problem, called Visual Text Correction (VTC), i.e., finding and replacing an inaccurate word in the textual description of a video. We propose a deep network that can simultaneously detect an inaccuracy in a sentence, and fix it by replacing the inaccurate word(s). Our method leverages the semantic interdependence of videos and words, as well as the short-term and long-term relations of the words in a sentence. Our proposed formulation can solve the VTC problem employing an End-to-End network in two steps: (1) Inaccuracy detection, and (2) correct word prediction. In detection step, each word of a sentence is reconstructed such that the reconstruction for the inaccurate word is maximized. We exploit both Short Term and Long Term Dependencies employing respectively Convolutional N-Grams and LSTMs to reconstruct the word vectors. For the correction step, the basic idea is to simply substitute the word with the maximum reconstruction error for a better one. The second step is essentially a classification problem where the classes are the words in the dictionary as replacement options. Furthermore, to train and evaluate our model, we propose an approach to automatically construct a large dataset for the VTC problem. Our experiments and performance analysis demonstrates that the proposed method provides very good results and also highlights the general challenges in solving the VTC problem. To the best of our knowledge, this work is the first of its kind for the Visual Text Correction task.
The quantum Boltzmann equation in semiconductor physics

The quantum Boltzmann equation, or Fokker-Planck equation, has been used to successfully explain a number of experiments in semiconductor optics in the past two decades. This paper reviews some of the developments of this work, including models of excitons in bulk materials, electron-hole plasmas, and polariton gases. Copyright line will be provided by the publisher odinger equation for many-particle systems. The equation for the time evolution of the distribution function of a quantum many-body system is variously called a quantum Boltzmann equation (after the collision term in the classical Boltzmann equation, discussed in Ref. (1), Section 5.9), a master equation (when the states are discrete), or a Fokker- Planck equation. While the formalism of time-dependent quantum mechanics of many-particle systems was well de- veloped in the mid-twentieth century, two developments occurred in the 1980's that allowed much more quantitative application to experiments on nonequilibrium systems. The first was the arrival of cheap, fast computers that allowed numerical solution of the quantum Boltzmann equation using iterative meth- ods. The second was the development of ultrafast optics methods which allowed direct observation of the distribution function of carriers in semiconductors (and in some metals) out of equilibrium. A related development, in the 1990's, was the accomplishment of trapped cold atom gases, which also allowed direct measurement of the distribution function of a gas. The results of quantum Boltzmann equations could thus be directly compared to experimental measurements of particle distribution functions instead of only average properties. In the limit of low particle density, the quantum Boltzmann equation has the form of simply adding all the rates determined by Fermi's golden rule for all possible scattering processes. For evolution due to single-particle transitions, this is given by @ni @t = X
Topological rigidity and actions on contractible manifolds with discrete singular set

The problem of equivariant rigidity is the $\Gamma$-homeomorphism classification of $\Gamma$-actions on manifolds with compact quotient and with contractible fixed sets for all finite subgroups of $\Gamma$. In other words, this is the classification of cocompact $E_{fin}\Gamma$-manifolds. We use surgery theory, algebraic $K$-theory, and the Farrell--Jones Conjecture to give this classification for a family of groups which satisfy the property that the normalizers of nontrivial finite subgroups are themselves finite. More generally, we study cocompact proper actions of these groups on contractible manifolds and prove that the $E_{fin}$-condition is always satisfied.
Tristable and multiple bistable activity in complex random binary networks of two-state units

We study complex networks of stochastic two-state units. Our aim is to model discrete stochastic excitable dynamics with a rest and an excited state. Both states are assumed to possess different waiting time distributions. The rest state is treated as an activation process with an exponentially distributed life time, whereas the latter in the excited state shall have a constant mean which may originate from any distribution. The activation rate of any single unit is determined by its neighbors according to a random complex network structure. In order to treat this problem in an analytical way, we use a heterogeneous mean-field approximation yielding a set of equations generally valid for uncorrelated random networks. Based on this derivation we focus on random binary networks where the network is solely comprised of nodes with either of two degrees. The ratio between the two degrees is shown to be a crucial parameter. Dependent on the composition of the network the steady states show the usual transition from disorder to homogeneously ordered bistability as well as new scenarios that include inhomogeneous ordered and disordered bistability as well as tristability. The various steady states differ in their spiking activity expressed by a state dependent spiking rate. Numerical simulations agree with analytic results of the heterogeneous mean-field approximation.
Hot Molecular Gas in the Circumnuclear Disk

We present an analysis of archival ISO observations of pure-rotational lines of H2 in three pointings in the central 3 parsecs of the Galaxy: toward the Southwest region and Northeast region of the Galactic center Circumnuclear Disk, and toward the supermassive black hole Sgr A*. We detect pure rotational lines from 0-0 S(0) to S(13), as well as a number of rovibrationally excited transitions. From the pure rotational lines, we are able to describe the molecular gas with three discrete temperature components: a `hot' component between 500-600 K, a `hotter' component at 1250-1350 K, and a `hottest' component at > 2600 K. Toward Sgr A*, likely due to a combination of poorer baselines and weaker emission, we only detect a single hot component, at 1100 K. The observed excitation is consistent with heating via C-shocks. We also fit a continuous temperature distribution to the the S(1) through S(7) lines by assuming a power-law distribution of temperatures. We measure power law indices of n = 3.22 for the Northeast region and n = 2.83 for the Southwest region, with a smaller index indicating a higher fraction of warm gas. These indices are lower than those measured for other galaxies or other Galactic center clouds, which are measured to have n= 4-6. If we extrapolate this temperature distribution down to a cutoff temperature of 50 K, then the total molecular gas mass that we would measure for the Southwest (Northeast) region is 32 (140) % of the total molecular gas mass inferred from the dust emission, and 26 (125) % of the total molecular gas mass inferred from the CO emission for these regions. Ultimately, we find that the disagreement in the amount of mass recovered for these two regions means that this method cannot yet be verified to yield a reliable and independent estimate of the mass in the local region of the Circumnuclear Disk.
Computing inclusions of Schur modules

We describe a software package for constructing minimal free resolutions of graded GLn(Q)-equivariant modules M over Q(x1;:::; xn) such that, for all i, the i-th syzygy module of M is generated in a single degree. We do so by describing some algorithms for manipulating polynomial representations of GLn(Q) following ideas of Olver and Eisenbud-Floystad-Weyman. INTRODUCTION. This article describes the Macaulay 2 package PieriMaps, which defines maps of representations of the general linear group GLn(Q) of the form Sm(Q n )! S(d)(Q n ) Sl(Q n ),
Enhanced photon-phonon coupling via dimerization in one-dimensional optomechanical crystals

We show that dimerization of an optomechanical crystal lattice, which leads to folding of the band diagram, can couple flexural mechanical modes to optical fields within the unit cell via radiation pressure. When compared to currently realized crystals, a substantial improvement in the coupling between photons and phonons is found. For experimental verification, we implement a dimerized lattice in a silicon optomechanical nanobeam cavity and measure a vacuum coupling rate of g0/2π= 1.7 MHz between an optical resonance at λc = 1545 nm and a mechanical resonance at 1.14 GHz.