cssi/SciSciGPT-SciSciNet huggingface dataset:
Realizing Petabyte Scale Acoustic Modeling

Large scale machine learning (ML) systems such as the Alexa automatic speech recognition (ASR) system continue to improve with increasing amounts of manually transcribed training data. Instead of scaling manual transcription to impractical levels, we utilize semi-supervised learning (SSL) to learn acoustic models (AM) from the vast firehose of untranscribed audio data. Learning an AM from 1 Million hours of audio presents unique ML and system design challenges. We present the design and evaluation of a highly scalable and resource efficient SSL system for AM. Employing the student/teacher learning paradigm, we focus on the student learning subsystem: a scalable and robust data pipeline that generates features and targets from raw audio, and an efficient model pipeline, including the distributed trainer, that builds a student model. Our evaluations show that, even without extensive hyper-parameter tuning, we obtain relative accuracy improvements in the 10 to 20% range, with higher gains in noisier conditions. The end-to-end processing time of this SSL system was 12 days, and several components in this system can trivially scale linearly with more compute resources.
Scalar Casimir energies of tetrahedra and prisms

New results for scalar Casimir self-energies arising from interior modes are presented for the three integrable tetrahedral cavities. Since the eigenmodes are all known, the energies can be directly evaluated by mode summation, with a point-splitting regulator, which amounts to evaluation of the cylinder kernel. The correct Weyl divergences, depending on the volume, surface area and the edges, are obtained, which is strong evidence that the counting of modes is correct. Because there is no curvature, the finite part of the quantum energy may be unambiguously extracted. Cubic, rectangular parallelepipedal, triangular prismatic and spherical geometries are also revisited. Dirichlet and Neumann boundary conditions are considered for all geometries. Systematic behavior of the energy in terms of geometric invariants for these different cavities is explored. A smooth interpolation between short and long prisms is further demonstrated. When scaled by the ratio of the volume to the surface area, the energies for the tetrahedra and the prisms of maximal isoareal quotient lie very close to a universal curve. The physical significance of these results is discussed.
Fully self-referenced frequency comb consuming 5 Watts of electrical power

We present a hybrid fiber/waveguide design for a 100-MHz frequency comb that is fully self-referenced and temperature controlled with less than 5 W of electrical power. Self-referencing is achieved by supercontinuum generation in a silicon nitride waveguide, which requires much lower pulse energies (~200 pJ) than with highly nonlinear fiber. These low-energy pulses are achieved with an erbium fiber oscillator/amplifier pumped by two 250-mW passively-cooled pump diodes that consume less than 5 W of electrical power. The temperature tuning of the oscillator, necessary to stabilize the repetition rate in the presence of environmental temperature changes, is achieved by resistive heating of a section of gold-palladium-coated fiber within the laser cavity. By heating only the small thermal mass of the fiber, the repetition rate is tuned over 4.2 kHz (corresponding to an effective temperature change of 4.2 °C) with a fast time constant of 0.5 s, at a low power consumption of 0.077 W/°C, compared to 2.5 W/°C in the conventional 200-MHz comb design.
Polariton Condensation and Lasing

The similarities and differences between polariton condensation in microcavities and standard lasing in a semiconductor cavity structure are reviewed. The recent experiments on “photon condensation” are also reviewed.
Quasi-local energy in presence of gravitational radiation

We discuss our recent work [P.-N. Chen, M.-T. Wang and S.-T. Yau, Quasi-local mass in the gravitational perturbations of black holes, to appear.] in which gravitational radiation was studied by evaluating the Wang–Yau quasi-local mass of surfaces of fixed size at the infinity of both axial and polar perturbations of the Schwarzschild spacetime, a la Chandrasekhar. [S. Chandrasekhar, The Mathematical Theory of Black Holes, Oxford Classic Texts in the Physical Sciences (Oxford University Press, New York, 1998).]
Chance-Constrained Shrunken-Primal-Dual Subgradient (CC-SPDS) Approach for Decentralized Electric Vehicle Charging Control

In this paper, we develop a chance-constrained decentralized electric vehicle (EV) charging control framework to achieve "valley-filling" meanwhile meeting individual charging requirements and satisfying distribution network constraints. The control design is formulated as an optimization problem with a stochastic non-separable objective function and globally coupled chance constraints. We propose a novel chance-constrained shrunken-primal-dual subgradient (CC-SPDS) algorithm to support the chance-constrained decentralized control scheme and verify its efficacy and convergence with a representative distribution network model.
Median Statistics Estimate of the Galactic Rotational Velocity

We compile a complete collection of 18 recent (from 2000 to 2017) measurements of $\varTheta_{0}$ , the rotational velocity of the Milky Way at $R_{0}$ (the radial distance of the Sun from the Galactic center). These measurements use tracers that are believed to more accurately reflect the systematic rotation of the Milky Way. Unlike other recent compilations of $\varTheta_{0}$ , our collection includes only independent measurements. We find that these 18 measurements are distributed in a mildly non-Gaussian fashion and a median statistics estimate indicates $\varTheta_{0} = 220 \pm 10$ km s−1 (2 $\sigma$ error) as the most reliable summary, at $R_{0} = 8.0 \pm0.3$ kpc (2 $\sigma$ error).
Neutron star pulse profile observations as extreme gravity probes

The x-ray emission of hot spots on the surface of neutron stars is the prime target of the Neutron star Interior Composition Explorer (NICER). These x-ray pulse profiles not only encode information of the bulk properties of these stars, which teaches us about matter at supranuclear densities, but also about the spacetime curvature around them which teaches us about relativistic gravity. We explore the possibility of performing strong-gravity tests with NICER observations using a recently developed pulse profile model beyond general relativity. Our results suggest that NICER can in principle place constraints on deviations from general relativity due to an additional scalar degree of freedom which are independent and competitive relative to constraints with binary pulsar observations.
Vertex Operators, Grassmannians, and Hilbert Schemes

We approximate the infinite Grassmannian by finite-dimensional cutoffs, and define a family of fermionic vertex operators as the limit of geometric correspondences on the equivariant cohomology groups, with respect to a one-dimensional torus action. We prove that in the localization basis, these are the well-known fermionic vertex operators on the infinite wedge representation. Furthermore, the boson-fermion correspondence, locality, and intertwining properties with the Virasoro algebra are the limits of relations on the finite-dimensional cutoff spaces, which are true for geometric reasons. We then show that these operators are also, almost by definition, the vertex operators defined by Okounkov and the author in Carlsson and Okounkov (http://arXiv.org/abs/0801.2565v2 [math.AG], 2009), on the equivariant cohomology groups of the Hilbert scheme of points on \({\mathbb C^2}\) , with respect to a special torus action.
Entropy Maximization for Markov Decision Processes Under Temporal Logic Constraints

We study the problem of synthesizing a policy that maximizes the entropy of a Markov decision process (MDP) subject to a temporal logic constraint. Such a policy minimizes the predictability of the paths it generates, or dually, maximizes the exploration of different paths in an MDP while ensuring the satisfaction of a temporal logic specification. We first show that the maximum entropy of an MDP can be finite, infinite, or unbounded. We provide necessary and sufficient conditions under which the maximum entropy of an MDP is finite, infinite, or unbounded. We then present an algorithm which is based on a convex optimization problem to synthesize a policy that maximizes the entropy of an MDP. We also show that maximizing the entropy of an MDP is equivalent to maximizing the entropy of the paths that reach a certain set of states in the MDP. Finally, we extend the algorithm to an MDP subject to a temporal logic specification. In numerical examples, we demonstrate the proposed method on different motion planning scenarios and illustrate the relation between the restrictions imposed on the paths by a specification, the maximum entropy, and the predictability of paths.
Dynamics of a Massive Piston in an Ideal Gas: Oscillatory Motion and Approach to Equilibrium

We study numerically and theoretically (on a heuristic level) the time evolution of a gas confined to a cube of size L3 divided into two parts by a piston with mass ML∼L2 which can only move in the x-direction. Starting with a uniform “double-peaked” (non Maxwellian) distribution of the gas and a stationary piston, we find that (a) after an initial quiescent period the system becomes unstable and the piston performs a damped oscillatory motion, and (b) there is a thermalization of the system leading to a Maxwellian distribution of the gas velocities. The time of the onset of the instability appears to grow like L log L while the relaxation time to the Maxwellian grows like L7/2.
Parametric Estimation from Approximate Data: Non-Gaussian Diffusions

We study the problem of parameters estimation in indirect observability contexts, where \(X_t \in R^r\) is an unobservable stationary process parametrized by a vector of unknown parameters and all observable data are generated by an approximating process \(Y^{\varepsilon }_t\) which is close to \(X_t\) in \(L^4\) norm.We construct consistent parameter estimators which are smooth functions of the sub-sampled empirical mean and empirical lagged covariance matrices computed from the observable data. We derive explicit optimal sub-sampling schemes specifying the best paired choices of sub-sampling time-step and number of observations. We show that these choices ensure that our parameter estimators reach optimized asymptotic \(L^2\)-convergence rates, which are constant multiples of the \(L^4\) norm \(|| Y^{\varepsilon }_t - X_t ||\).
Generalized Heegner cycles at Eisenstein primes and the Katz p-adic L-function

In this paper, we consider normalized newforms $f\in S_k(\Gamma_0(N),\varepsilon_f)$ whose non-constant term Fourier coefficients are congruent to those of an Eisenstein series modulo some prime ideal above a rational prime $p$. In this situation, we establish a congruence between the anticyclotomic $p$-adic $L$-function of Bertolini-Darmon-Prasanna and the Katz two-variable $p$-adic $L$-function. From this, we derive congruences between images under the $p$-adic Abel-Jacobi map of certain generalized Heegner cycles attached to $f$ and special values of the Katz $p$-adic $L$-function. In particular, our results apply to newforms associated with elliptic curves $E/\mathbb{Q}$ whose mod $p$ Galois representations $E[p]$ are reducible at a good prime $p$. As a consequence, we show the following: if $K$ is an imaginary quadratic field satisfying the Heegner hypothesis with respect to $E$ and in which $p$ splits, and if the bad primes of $E$ satisfy certain congruence conditions mod $p$ and $p$ does not divide certain Bernoulli numbers, then the Heegner point $P_{E}(K)$ is non-torsion, in particular implying that $\text{rank}_{\mathbb{Z}}E(K) = 1$. From this, we show that when $E$ is semistable with reducible mod $3$ Galois representation, then a positive proportion of real quadratic twists of $E$ have rank 1 and a positive proportion of imaginary quadratic twists of $E$ have rank 0.
Going Deeper With Contextual CNN for Hyperspectral Image Classification

In this paper, we describe a novel deep convolutional neural network (CNN) that is deeper and wider than other existing deep networks for hyperspectral image classification. Unlike current state-of-the-art approaches in CNN-based hyperspectral image classification, the proposed network, called contextual deep CNN, can optimally explore local contextual interactions by jointly exploiting local spatio-spectral relationships of neighboring individual pixel vectors. The joint exploitation of the spatio-spectral information is achieved by a multi-scale convolutional filter bank used as an initial component of the proposed CNN pipeline. The initial spatial and spectral feature maps obtained from the multi-scale filter bank are then combined together to form a joint spatio-spectral feature map. The joint feature map representing rich spectral and spatial properties of the hyperspectral image is then fed through a fully convolutional network that eventually predicts the corresponding label of each pixel vector. The proposed approach is tested on three benchmark data sets: the Indian Pines data set, the Salinas data set, and the University of Pavia data set. Performance comparison shows enhanced classification performance of the proposed approach over the current state-of-the-art on the three data sets.
Algebraic Methods for Quantum Codes on Lattices

This is a note from a series of lectures at Encuentro Colombiano de Computacion Cuantica, Universidad de los Andes, Bogota, Colombia, 2015. The purpose is to introduce additive quantum error correcting codes, with emphasis on the use of binary representation of Pauli matrices and modules over a translation group algebra. The topics include symplectic vector spaces, Cliord group, cleaning lemma, an error correcting criterion, entanglement spectrum, implications of the locality of stabilizer group generators, and the classication of translation-invariant one-dimensional additive codes and two-dimensional CSS codes with large code distances. In particular, we describe an algorithm to find a Cliord quantum circuit (CNOTs) to transform any two-dimensional translation-invariant CSS code on qudits of a prime dimension with code distance being the linear system size, into a tensor product of finitely many copies of the qudit toric code and a product state. Thus, the number of embedded toric codes is the complete invariant of these CSS codes under local Cliord circuits.
Conductivity of a strange metal: from holography to memory functions

We study the electrical response of a wide class of strange metal phases without quasiparticles at finite temperature and charge density, with explicitly broken translational symmetry, using holography. The low frequency electrical conductivity exhibits a Drude peak, so long as momentum relaxation is slow. The relaxation time and the direct current conductivity are exactly equal to what is computed, independently of holography, via the memory function framework.
Self-accelerating massive gravity: how zweibeins walk through determinant singularities

The theory of massive gravity possesses ambiguities when the spacetime metric evolves far from the non-dynamical fiducial metric used to define it. We explicitly construct a spherically symmetric example case where the metric evolves to a coordinate-independent determinant singularity which does not exist in the initial conditions. Both the metric and the vierbein formulation of the theory are ill-defined at this point. In unitary gauge, the chart of the spacetime ends at this point and does not cover the full spacetime whereas the spherically symmetric vierbeins, or zweibeins, of the fiducial metric become non-invertible and do not describe a valid metric. Nonetheless it is possible to continuously join a zweibein solution on the other side of the singularity which picks one of the degenerate solutions of the metric square root. This continuous solution is not the choice conventionally made in the previous literature. We also show that the Stuckelberg equations of motion on the self-accelerating branch prevent solutions from evolving to a more pathological situation in which the spacetime vierbeins lack a crucial symmetry with the fiducial vierbeins and real square roots fail to exist.
Velocity-resolved Hot Water Emission Detected toward HL Tau with the Submillimeter Array

Using the Submillimeter Array (SMA) on Mauna Kea, the –9 transition ( = 1863 K) at 321.2 GHz has been detected toward the embedded low-mass protostar HL Tau. The line centroid is blueshifted by 20 km s−1 with respect to the source velocity, and it has a FWHM of 25 km s−1. The emission is tentatively resolved and extends ~3''–4'' over the sky (~2 beams), or ~500 au at the distance of Taurus. The velocity offset, and to a lesser degree the spatial extent of the emission, show that the line originates in the protostellar jet or wind. This result suggests that at least some water emission observed with Herschel and Spitzer toward embedded sources, and perhaps also disk sources, contains a wind or jet component, which is crucial for interpreting these data. These pathfinder observations done with the SMA open a new window into studying the origin of water emission with e.g., ALMA, thus providing new insights into where water is in protostellar systems.
ESP4ML: platform-based design of systems-on-chip for embedded machine learning

We present esp4ml, an open-source system-level design flow to build and program SoC architectures for embedded applications that require the hardware acceleration of machine learning and signal processing algorithms. We realized esp4ml by combining two established open-source projects (esp and hls4ml) into a new, fully-automated design flow. For the SoC integration of accelerators generated by hls4ml, we designed a set of new parameterized interface circuits synthesizable with high-level synthesis. For accelerator configuration and management, we developed an embedded software runtime system on top of Linux. With this HW/SW layer, we addressed the challenge of dynamically shaping the data traffic on a network-on-chip to activate and support the reconfigurable pipelines of accelerators that are needed by the application workloads currently running on the SoC. We demonstrate our vertically-integrated contributions with the FPGA-based implementations of complete SoC instances booting Linux and executing computer-vision applications that process images taken from the Google Street View database
Probing entanglement in a many-body–localized system

An interacting quantum system that is subject to disorder may cease to thermalize owing to localization of its constituents, thereby marking the breakdown of thermodynamics. The key to understanding this phenomenon lies in the system’s entanglement, which is experimentally challenging to measure. We realize such a many-body–localized system in a disordered Bose-Hubbard chain and characterize its entanglement properties through particle fluctuations and correlations. We observe that the particles become localized, suppressing transport and preventing the thermalization of subsystems. Notably, we measure the development of nonlocal correlations, whose evolution is consistent with a logarithmic growth of entanglement entropy, the hallmark of many-body localization. Our work experimentally establishes many-body localization as a qualitatively distinct phenomenon from localization in noninteracting, disordered systems.
EFFECTS OF PROXIMA CENTAURI ON PLANET FORMATION IN ALPHA CENTAURI

Proxima Centauri is an M dwarf approximately 15,000 au from the Alpha Centauri binary, comoving and likely in a loosely bound orbit. Dynamic simulations show that this configuration can form from a more tightly bound triple system. As our nearest neighbors, these stars command great interest as potential planet hosts, and the dynamics of the stars govern the formation of any planets within the system. Here we present a scenario for the evolution of Alpha Centauri A and B and Proxima Centauri as a triple system. Based on N-body simulations, we determine that this pathway to formation is plausible, and we quantify the implications for planet formation in the Alpha Centauri binary. We expect that this formation scenario may have truncated the circumstellar disk slightly more than a system that formed in the current configuration, but that it most likely does not prevent terrestrial planet formation. We simulate planet formation in this system and find that, in most scenarios, two or more terrestrial planets can be expected around either Alpha Centauri A or B, orbiting in a region out to approximately 2 au, assuming that planetesimals and planetary embryos are able to form in the system first. Additionally, terrestrial planet formation and stability in Proxima Centauri's habitable zone are also plausible. However, an absence of planets around these stars may be indicative of highly disruptive stellar dynamics in the past.
Divergence Rates of Markov Order Estimators and Their Application to Statistical Estimation of Stationary Ergodic Processes

Stationary ergodic processes with finite alphabets are estimated by finite memory processes from a sample, an n-length realization of the process, where the memory depth of the estimator process is also estimated from the sample using penalized maximum likelihood (PML). Under some assumptions on the continuity rate and the assumption of non-nullness, a rate of convergence in ¯ d-distance is obtained, with explicit constants. The result requires an analysis of the divergence of PML Markov order estimators for not necessarily finite memory processes. This divergence problem is investigated in more generality for three information criteria: the Bayesian information criterion with generalized penalty term yielding the PML, and the normalized maximum likelihood and the Krichevsky–Trofimov code lengths. Lower and upper bounds on the estimated order are obtained. The notion of consistent Markov order estimation is generalized for infinite memory processes using the concept of oracle order estimates, and generalized consistency of the PML Markov order estimator is presented.
Pulsed Excitation Dynamics of an Optomechanical Crystal Resonator near Its Quantum Ground State of Motion

Using pulsed optical excitation and read-out along with single-phonon-counting techniques, we measure the transient backaction, heating, and damping dynamics of a nanoscale silicon optomechanical crystal cavity mounted in a dilution refrigerator at a base temperature of T_f ≈ 11 mK. In addition to observing a slow (approximately 740-ns) turn-on time for the optical-absorption-induced hot-phonon bath, we measure for the 5.6-GHz “breathing” acoustic mode of the cavity an initial phonon occupancy as low as ⟨n⟩ = 0.021±0.007 (mode temperature T_(min) ≈ 70 mK) and an intrinsic mechanical decay rate of γ_0 = 328±14 Hz (Q_m ≈ 1.7×10^7). These measurements demonstrate the feasibility of using short pulsed measurements for a variety of quantum optomechanical applications despite the presence of steady-state optical heating.
Network Protection Codes Against Link Failures Using Network Coding

Protecting against link failures in communication networks is essential to increase robustness, accessibility, and reliability of data transmission. Recently, network coding has been proposed as a solution to provide agile and cost efficient network protection against link failures, which does not require data rerouting, or packet retransmission. To achieve this, separate paths have to be provisioned to carry encoded packets, hence requiring either the addition of extra links, or reserving some of the resources for this purpose. In this paper, we propose network protection codes against a single link failure using network coding, where a separate path using reserved links is not needed. In this case portions of the link capacities are used to carry the encoded packets. The scheme is extended to protect against multiple link failures and can be implemented at an overlay layer. Although this leads to reducing the network capacity, the network capacity reduction is asymptotically small in most cases of practical interest. We demonstrate that such network protection codes are equivalent to error correcting codes for erasure channels. Finally, we study the encoding and decoding operations of such codes over the binary field.
A new equilibrium torus solution and GRMHD initial conditions

Context. General relativistic magnetohydrodynamic (GRMHD) simulations are providing influential models for black hole spin measurements, gamma ray bursts, and supermassive black hole feedback. Many of these simulations use the same initial condition: a rotating torus of fluid in hydrostatic equilibrium. A persistent concern is that simulation results sometimes depend on arbitrary features of the initial torus. For example, the Bernoulli parameter (which is related to outflows), appears to be controlled by the Bernoulli parameter of the initial torus.Aims. In this paper, we give a new equilibrium torus solution and describe two applications for the future. First, it can be used as a more physical initial condition for GRMHD simulations than earlier torus solutions. Second, it can be used in conjunction with earlier torus solutions to isolate the simulation results that depend on initial conditions.Methods. We assume axisymmetry, an ideal gas equation of state, constant entropy, and ignore self-gravity. We fix an angular momentum distribution and solve the relativistic Euler equations in the Kerr metric.Results. The Bernoulli parameter, rotation rate, and geometrical thickness of the torus can be adjusted independently. Our torus tends to be more bound and have a larger radial extent than earlier torus solutions.Conclusions. While this paper was in preparation, several GRMHD simulations appeared based on our equilibrium torus. We believe it will continue to provide a more realistic starting point for future simulations.
Abelian Duality at Higher Genus

In three dimensions, a free, periodic scalar field is related by duality to an abelian gauge field. Here I explore aspects of this duality when both theories are quantized on a Riemann surface of genus g. At higher genus, duality involves an identification of winding with momentum on the Jacobian variety of the Riemann surface. I also consider duality for monopole and loop operators on the surface and exhibit the operator algebra, a refinement of the Wilson-’t Hooft algebra.
SNE-RoadSeg: Incorporating Surface Normal Information into Semantic Segmentation for Accurate Freespace Detection

Freespace detection is an essential component of visual perception for self-driving cars. The recent efforts made in data-fusion convolutional neural networks (CNNs) have significantly improved semantic driving scene segmentation. Freespace can be hypothesized as a ground plane, on which the points have similar surface normals. Hence, in this paper, we first introduce a novel module, named surface normal estimator (SNE), which can infer surface normal information from dense depth/disparity images with high accuracy and efficiency. Furthermore, we propose a data-fusion CNN architecture, referred to as RoadSeg, which can extract and fuse features from both RGB images and the inferred surface normal information for accurate freespace detection. For research purposes, we publish a large-scale synthetic freespace detection dataset, named Ready-to-Drive (R2D) road dataset, collected under different illumination and weather conditions. The experimental results demonstrate that our proposed SNE module can benefit all the state-of-the-art CNNs for freespace detection, and our SNE-RoadSeg achieves the best overall performance among different datasets.
Flory exponents from a self-consistent renormalization group

The wandering exponent ν for an isotropic polymer is predicted remarkably well by a simple argument due to Flory. By considering oriented polymers living in a one-parameter family of background tangent fields, we are able to relate the wandering exponent to the exponent in the background field through an ϵ-expansion. We then choose the background field to have the same correlations as the individual polymer, thus self-consistently solving for ν. We find ν= 3/(d + 2) for d < 4 and ν= 1/2 for d ≥4, which is exactly the Flory result.
Epidemics on networks: Reducing disease transmission using health emergency declarations and peer communication.

Abstract Understanding individual decisions in a world where communications and information move instantly via cell phones and the internet, contributes to the development and implementation of policies aimed at stopping or ameliorating the spread of diseases. In this manuscript, the role of official social network perturbations generated by public health officials to slow down or stop a disease outbreak are studied over distinct classes of static social networks. The dynamics are stochastic in nature with individuals (nodes) being assigned fixed levels of education or wealth. Nodes may change their epidemiological status from susceptible, to infected and to recovered. Most importantly, it is assumed that when the prevalence reaches a pre-determined threshold level, P * , information, called awareness in our framework, starts to spread, a process triggered by public health authorities. Information is assumed to spread over the same static network and whether or not one becomes a temporary informer, is a function of his/her level of education or wealth and epidemiological status. Stochastic simulations show that threshold selection P * and the value of the average basic reproduction number impact the final epidemic size differentially. For the Erdős-Renyi and Small-world networks, an optimal choice for P * that minimize the final epidemic size can be identified under some conditions while for Scale-free networks this is not case.
Self-supervised learning of physics-guided reconstruction neural networks without fully sampled reference data.

Purpose To develop a strategy for training a physics-guided MRI reconstruction neural network without a database of fully sampled data sets. Methods Self-supervised learning via data undersampling (SSDU) for physics-guided deep learning reconstruction partitions available measurements into two disjoint sets, one of which is used in the data consistency (DC) units in the unrolled network and the other is used to define the loss for training. The proposed training without fully sampled data is compared with fully supervised training with ground-truth data, as well as conventional compressed-sensing and parallel imaging methods using the publicly available fastMRI knee database. The same physics-guided neural network is used for both proposed SSDU and supervised training. The SSDU training is also applied to prospectively two-fold accelerated high-resolution brain data sets at different acceleration rates, and compared with parallel imaging. Results Results on five different knee sequences at an acceleration rate of 4 shows that the proposed self-supervised approach performs closely with supervised learning, while significantly outperforming conventional compressed-sensing and parallel imaging, as characterized by quantitative metrics and a clinical reader study. The results on prospectively subsampled brain data sets, in which supervised learning cannot be used due to lack of ground-truth reference, show that the proposed self-supervised approach successfully performs reconstruction at high acceleration rates (4, 6, and 8). Image readings indicate improved visual reconstruction quality with the proposed approach compared with parallel imaging at acquisition acceleration. Conclusion The proposed SSDU approach allows training of physics-guided deep learning MRI reconstruction without fully sampled data, while achieving comparable results with supervised deep learning MRI trained on fully sampled data.
A Modified Riccati Transformation for Decentralized Computation of the Viability Kernel Under LTI Dynamics

Computing the viability kernel is key in providing guarantees of safety and proving existence of safety-preserving controllers for constrained dynamical systems. Current numerical techniques that approximate this construct suffer from a complexity that is exponential in the dimension of the state. We study conditions under which a linear time-invariant (LTI) system can be suitably decomposed into lower dimensional subsystems so as to admit a conservative computation of the viability kernel in a decentralized fashion in subspaces. We then present an isomorphism that imposes these desired conditions, most suitably on two-time-scale systems. Decentralized computations are performed in the transformed coordinates, yielding a conservative approximation of the viability kernel in the original state space. Significant reduction of complexity can be achieved, allowing the previously inapplicable tools to be employed for treatment of higher dimensional systems. We show the results on two examples including a 6-D system.
Bistability of buoyancy-driven exchange flows in vertical tubes

Buoyancy-driven exchange flows are common to a variety of natural and engineering systems, ranging from persistently active volcanoes to counterflows in oceanic straits. Laboratory experiments of exchange flows have been used as surrogates to elucidate the basic features of such flows. The resulting data have been analysed and interpreted mostly through core–annular flow solutions, the most common flow configuration at finite viscosity contrasts. These models have been successful in fitting experimental data, but less effective at explaining the variability observed in natural systems. In this paper, we demonstrate that some of the variability observed in laboratory experiments and natural systems is a consequence of the inherent bistability of core–annular flow. Using a core–annular solution to the classical problem of buoyancy-driven exchange flows in vertical tubes, we identify two mathematically valid solutions at steady state: a solution with fast flow in a thin core and a solution with relatively slow flow in a thick core. The theoretical existence of two solutions, however, does not necessarily imply that the system is bistable in the sense that flow switching may occur. Through direct numerical simulations, we confirm the hypothesis that core–annular flow in vertical tubes is inherently bistable. Our simulations suggest that the bistability of core–annular flow is linked to the boundary conditions of the domain, which implies that is not possible to predict the realized flow field from the material parameters of the fluids and the tube geometry alone. Our finding that buoyancy-driven exchange flows are inherently bistable systems is consistent with previous experimental data, but is in contrast to the underlying hypothesis of previous analytical models that the solution is unique and can be identified by maximizing the flux or extremizing the dissipation in the system. Our results have important implications for data interpretation by analytical models and may also have interesting ramifications for understanding volcanic degassing.
Framed M-branes, corners, and topological invariants

We uncover and highlight relations between the M-branes in M-theory and various topological invariants: the Hopf invariant over Q, Z and Z2, the Kervaire invariant, the f-invariant, and the ν-invariant. This requires either a framing or a corner structure. The canonical framing provides a minimum for the classical action and the change of framing encodes the structure of the action and possible anomalies. We characterize the flux quantization condition on the C-field and the topological action of the M5-brane via the Hopf invariant, and the dual of the C-field as (a refinement of) an element of Hopf invariant two. In the signature formulation, the contribution to the M-brane effective action is given by the Maslov index of the corner. The Kervaire invariant implies that the effective action of the M5-brane is quadratic. Our study leads to viewing the self-dual string, which is the boundary of the M2-brane on the M5-brane worldvolume, as a string theory in the sense of cobordism of manifolds with corners. We show that the dynamics of the C-field and its dual are encoded in a unified way in the 4-sphere, which suggests the corresponding spectrum as the generalized cohomology theory describing the fields. The effective action of the corner is captured by the f-invariant, which is an invariant at chromatic level two. Finally, considering M-theory on manifolds with G2 holonomy, we show that the canonical G2 structure minimizes the topological part of the M5-brane action. This is done via the ν-invariant and a variant that we introduce related to the one-loop polynomial.We uncover and highlight relations between the M-branes in M-theory and various topological invariants: the Hopf invariant over Q, Z and Z2, the Kervaire invariant, the f-invariant, and the ν-invariant. This requires either a framing or a corner structure. The canonical framing provides a minimum for the classical action and the change of framing encodes the structure of the action and possible anomalies. We characterize the flux quantization condition on the C-field and the topological action of the M5-brane via the Hopf invariant, and the dual of the C-field as (a refinement of) an element of Hopf invariant two. In the signature formulation, the contribution to the M-brane effective action is given by the Maslov index of the corner. The Kervaire invariant implies that the effective action of the M5-brane is quadratic. Our study leads to viewing the self-dual string, which is the boundary of the M2-brane on the M5-brane worldvolume, as a string theory in the sense of cobordism of manifolds with corners. ...
Factorization problems in complex reflection groups

We enumerate factorizations of a Coxeter element in a well-generated complex reflection group into arbitrary factors, keeping track of the fixed space dimension of each factor. In the infinite families of generalized permutations, our approach is fully combinatorial. It gives results analogous to those of Jackson in the symmetric group and can be refined to encode a notion of cycle type. As one application of our results, we give a previously overlooked characterization of the poset of W-noncrossing partitions.
Turbulence and Star Formation in a Sample of Spiral Galaxies

We investigate turbulent gas motions in spiral galaxies and their importance to star formation in far outer disks, where the column density is typically far below the critical value for spontaneous gravitational collapse. Following the methods of Burkhart et al. on the Small Magellanic Cloud, we use the third and fourth statistical moments, as indicators of structures caused by turbulence, to examine the neutral hydrogen (H i) column density of a sample of spiral galaxies selected from The H i Nearby Galaxy Survey. We apply the statistical moments in three different methods—the galaxy as a whole, divided into a function of radii and then into grids. We create individual grid maps of kurtosis for each galaxy. To investigate the relation between these moments and star formation, we compare these maps with their far-ultraviolet images taken by the Galaxy Evolution Explorer satellite.We find that the moments are largely uniform across the galaxies, in which the variation does not appear to trace any star-forming regions. This may, however, be due to the spatial resolution of our analysis, which could potentially limit the scale of turbulent motions that we are sensitive to greater than ~700 pc. From comparison between the moments themselves, we find that the gas motions in our sampled galaxies are largely supersonic. This analysis also shows that the Burkhart et al. methods may be applied not just to dwarf galaxies but also to normal spiral galaxies.
Wall-bounded flow over a realistically rough superhydrophobic surface

Direct numerical simulation (DNS) is performed for two wall-bounded flow configurations: laminar Couette flow at is shown to depend on a competing effect between slip velocity and turbulent losses due to the Reynolds shear stress contribution. Presence of trapped air in the cavities significantly alters near-wall flow physics where we examine near-wall structures and propose a physical mechanism for their behaviour. The fully wetted roughness increases the peak value of turbulent intensities, whereas the presence of the interface suppresses them. The pressure fluctuations have competing contributions between turbulent pressure fluctuations and stagnation due to asperities, the near-wall structure is altered and breaks down with increasing slip. Overall, there exists a competing effect between the interface and the asperities, the interface suppresses turbulence whereas the asperities enhance them. The present work demonstrates DNS over a realistic multiphase SHS for the first time, to the best of our knowledge.
Linear unstable whistler eigenmodes excited by a finite electron beam

Electron beam-generated whistler waves are widely found in the Earth's space plasma environment and are intricately involved in a number of phenomena. Here, we study the linear growth of whistler eigenmodes excited by a finite gyrating electron beam, to facilitate the interpretation of relevant experiments on beam-generated whistler waves in the Large Plasma Device at UCLA. A linear instability analysis for an infinite gyrating beam is first performed. It is shown that the whistler waves are excited through a combination of cyclotron resonance, Landau resonance, and anomalous cyclotron resonance, consistent with our experimental results. By matching the whistler eigenmodes inside and outside the beam at the boundary, a linear growth rate is obtained for each wave mode and the corresponding mode structure is constructed. These eigenmodes peak near the beam boundary, leak out of the beam region, and decay to zero far away from the beam.Electron beam-generated whistler waves are widely found in the Earth's space plasma environment and are intricately involved in a number of phenomena. Here, we study the linear growth of whistler eigenmodes excited by a finite gyrating electron beam, to facilitate the interpretation of relevant experiments on beam-generated whistler waves in the Large Plasma Device at UCLA. A linear instability analysis for an infinite gyrating beam is first performed. It is shown that the whistler waves are excited through a combination of cyclotron resonance, Landau resonance, and anomalous cyclotron resonance, consistent with our experimental results. By matching the whistler eigenmodes inside and outside the beam at the boundary, a linear growth rate is obtained for each wave mode and the corresponding mode structure is constructed. These eigenmodes peak near the beam boundary, leak out of the beam region, and decay to zero far away from the beam.
On Bias in Social Reviews of University Courses

University course ranking forums are a popular means of disseminating information about satisfaction with the quality of course content and instruction, especially with undergraduate students. A variety of policy decisions by university administrators, instructional designers and teaching staff affect how students perceive the efficacy of pedagogies employed in a given course, in class and online. While there is a large body of research on qualitative driving factors behind the use of academic rating sites, there is little investigation of the (potential) implicit student bias on said forums towards desirable course outcomes at the institution level. To that end, we examine the connection between course outcomes (student-reported GPA) and the overall ranking of the primary course instructor, as well as rating disparity by nature of course outcomes, for several hundred courses taught at Virginia Tech based on data collected from a popular academic rating forum. We also replicate our analysis for several public universities across the US. Our experiments indicate that there is a discernible albeit complex bias towards course outcomes in the professor ratings registered by students.
Classification of tight contact structures on surgeries on the figure-eight knot

Two of the basic questions in contact topology are which manifolds admit tight contact structures, and on those that do, whether we can classify such structures. We present the first such classification on an infinite family of (mostly) hyperbolic 3–manifolds: surgeries on the figure-eight knot. We also determine which of the tight contact structures are symplectically fillable and which are universally tight.
Self-challenging Improves Cross-Domain Generalization.

Convolutional Neural Networks (CNN) conduct image classification by activating dominant features that correlated with labels. When the training and testing data are under similar distributions, their dominant features are similar, leading to decent test performance. The performance is nonetheless unmet when tested with different distributions, leading to the challenges in cross-domain image classification. We introduce a simple training heuristic, Representation Self-Challenging (RSC), that significantly improves the generalization of CNN to the out-of-domain data. RSC iteratively challenges (discards) the dominant features activated on the training data, and forces the network to activate remaining features that correlate with labels. This process appears to activate feature representations applicable to out-of-domain data without prior knowledge of the new domain and without learning extra network parameters. We present the theoretical properties and conditions of RSC for improving cross-domain generalization. The experiments endorse the simple, effective, and architecture-agnostic nature of our RSC method.
Light stage super-resolution: continuous high-frequency relighting

The light stage has been widely used in computer graphics for the past two decades, primarily to enable the relighting of human faces. By capturing the appearance of the human subject under different light sources, one obtains the light transport matrix of that subject, which enables image-based relighting in novel environments. However, due to the finite number of lights in the stage, the light transport matrix only represents a sparse sampling on the entire sphere. As a consequence, relighting the subject with a point light or a directional source that does not coincide exactly with one of the lights in the stage requires interpolation and resampling the images corresponding to nearby lights, and this leads to ghosting shadows, aliased specularities, and other artifacts. To ameliorate these artifacts and produce better results under arbitrary high-frequency lighting, this paper proposes a learning-based solution for the "super-resolution" of scans of human faces taken from a light stage. Given an arbitrary "query" light direction, our method aggregates the captured images corresponding to neighboring lights in the stage, and uses a neural network to synthesize a rendering of the face that appears to be illuminated by a "virtual" light source at the query location. This neural network must circumvent the inherent aliasing and regularity of the light stage data that was used for training, which we accomplish through the use of regularized traditional interpolation methods within our network. Our learned model is able to produce renderings for arbitrary light directions that exhibit realistic shadows and specular highlights, and is able to generalize across a wide variety of subjects. Our super-resolution approach enables more accurate renderings of human subjects under detailed environment maps, or the construction of simpler light stages that contain fewer light sources while still yielding comparable quality renderings as light stages with more densely sampled lights.