cssi/SciSciGPT-SciSciNet huggingface dataset:
Explicit bounds for the pseudospectra of various classes of matrices and operators

We study the $\epsilon$-pseudospectra $\sigma_\epsilon(A)$ of square matrices $A \in \mathbb{C}^{N \times N}$. We give a complete characterization of the $\epsilon$-pseudospectrum of any $2 \times 2$ matrix and describe the asymptotic behavior (as $\epsilon \to 0$) of $\sigma_\epsilon(A)$ for any square matrix $A$. We also present explicit upper and lower bounds for the $\epsilon$-pseudospectra of bidiagonal matrices, as well as for finite rank operators.
Anomalous currents on closed surfaces: extended proximity, partial quantization and qubits.

Motivated by the surfaces of topological insulators, the Dirac anomaly?s discontinuous dependence on the sign of the mass, m/|m|, is investigated on closed topologies when the mass terms are weak or only partially cover the surface. It is found that, unlike the massive Dirac theory on an infinite plane, there is a smoothly decreasing current when the mass region is not infinite; also, a massive finite region fails to exhibit a Hall current edge?exerting an extended proximity effect, which can, however, be uniformly small?and oppositely orientated Hall phases are fully quantized while accompanied by diffuse chiral modes. Examples are computed using Dirac energy eigenstates on a flat torus (genus one topology) and a closed cap cylinder (genus zero topology) for various mass-term geometries. Finally, from the resulting properties of the surface spectra, a potential application for a flux-charge qubit is presented.
Zero Temperature Limit for Directed Polymers and Inviscid Limit for Stationary Solutions of Stochastic Burgers Equation

We consider a space-continuous and time-discrete polymer model for positive temperature and the associated zero temperature model of last passage percolation type. In our previous work, we constructed and studied infinite-volume polymer measures and one-sided infinite minimizers for the associated variational principle, and used these objects for the study of global stationary solutions of the Burgers equation with positive or zero viscosity and random kick forcing, on the entire real line. In this paper, we prove that in the zero temperature limit, the infinite-volume polymer measures concentrate on the one-sided minimizers and that the associated global solutions of the viscous Burgers equation with random kick forcing converge to the global solutions of the inviscid equation.
A CLASS OF PHYSICALLY MOTIVATED CLOSURES FOR RADIATION HYDRODYNAMICS

Radiative transfer and radiation hydrodynamics use the relativistic Boltzmann equation to describe the kinetics of photons. It is difficult to solve the six-dimensional time-dependent transfer equation unless the problem is highly symmetric or in equilibrium. When the radiation field is smooth, it is natural to take angular moments of the transfer equation to reduce the degrees of freedom. However, low order moment equations contain terms that depend on higher order moments. To close the system of moment equations, approximations are made to truncate this hierarchy. Popular closures used in astrophysics include flux-limited diffusion and the M 1 closure, which are rather ad hoc and do not necessarily capture the correct physics. In this paper, we propose a new class of closures for radiative transfer and radiation hydrodynamics. We start from a different perspective and highlight the consistency of a fully relativistic formalism. We present a generic framework to approximate radiative transfer based on relativistic Grad's moment method. We then derive a 14-field method that minimizes unphysical photon self-interaction.
Near-infrared and X-Ray Quasi-periodic Oscillations in Numerical Models of Sgr A*

We report transient quasi-periodic oscillations (QPOs) on minute timescales in relativistic, radiative models of the galactic center source Sgr A*. The QPOs result from nonaxisymmetric m = 1 structure in the accretion flow excited by MHD turbulence. Near-infrared (NIR) and X-ray power spectra show significant peaks at frequencies comparable to the orbital frequency at the innermost stable circular orbit (ISCO) f{sub o} . The excess power is associated with inward propagating magnetic filaments inside the ISCO. The amplitudes of the QPOs are sensitive to the electron distribution function. We argue that transient QPOs appear at a range of frequencies in the neighborhood of f{sub o} and that the power spectra, averaged over long times, likely show a broad bump near f{sub o} rather than distinct, narrow QPO features.
A dynamical model of plasma turbulence in the solar wind

A dynamical approach, rather than the usual statistical approach, is taken to explore the physical mechanisms underlying the nonlinear transfer of energy, the damping of the turbulent fluctuations, and the development of coherent structures in kinetic plasma turbulence. It is argued that the linear and nonlinear dynamics of Alfven waves are responsible, at a very fundamental level, for some of the key qualitative features of plasma turbulence that distinguish it from hydrodynamic turbulence, including the anisotropic cascade of energy and the development of current sheets at small scales. The first dynamical model of kinetic turbulence in the weakly collisional solar wind plasma that combines self-consistently the physics of Alfven waves with the development of small-scale current sheets is presented and its physical implications are discussed. This model leads to a simplified perspective on the nature of turbulence in a weakly collisional plasma: the nonlinear interactions responsible for the turbulent cascade of energy and the formation of current sheets are essentially fluid in nature, while the collisionless damping of the turbulent fluctuations and the energy injection by kinetic instabilities are essentially kinetic in nature.
Towards the understanding of jet shapes and cross sections in heavy ion collisions using soft-collinear effective theory

We calculate the jet shape and the jet cross section in heavy ion collisions using soft-collinear effective theory (SCET) and its extension with Glauber gluon interactions in the medium (SCETG). We use the previously developed framework to systematically resum the jet shape at next-to-leading logarithmic accuracy, and we consistently include the medium modification by incorporating the leading order medium-induced splitting functions. The calculation provides, for the first time, a quantitative understanding of the jet shape modification measurement in lead-lead collisions at $$ \sqrt{s_{\mathrm{NN}}} = 2.76 $$ TeV at the LHC. The inclusive jet suppression is also calculated within the same framework beyond the traditional concept of parton energy loss, and the dependence on the centrality, the jet radius and the jet kinematics is examined. In the end we present predictions for the anticipated jet shape and cross section measurements in lead-lead collisions at $$ \sqrt{s_{\mathrm{NN}}} \approx 5.1 $$ TeV at the LHC.
Small deformations of kinks and walls

Abstract A Rayleigh–Schrodinger type of perturbation scheme is employed to study weak self-interacting scalar potential perturbations occurring in scalar field models describing 1D domain kinks and 3D domain walls. The solutions for the unperturbed defects are modified by the perturbing potentials. An illustration is provided by adding a cubic potential to the familiar quartic kink potential and solving for the first order correction to the kink solution, using a “slab approximation”. A result is the appearance of an asymmetric scalar potential with different, nondegenerate, vacuum values and the subsequent formation of vacuum bubbles.
Nucleation of symmetric domains in the coupled leaflets of a bilayer

We study the kinetics governing the attainment of inter-leaflet domain symmetry in a phase-separating amphiphilic bilayer. "Indirect" inter-leaflet coupling via hydrophobic mismatch can induce an instability towards a metastable pattern of locally asymmetric domains upon quenching from high temperature. This necessitates a nucleation step to form the conventional symmetric domains, which are favoured by a "direct" inter-leaflet coupling. We model the energetics for a symmetric domain to nucleate from the metastable state, and find that an interplay between hydrophobic mismatch and thickness stretching/compression causes the effective hydrophobic mismatch, and thus line tension, to depend on domain size. This leads to strong departure from classical nucleation theory. We speculate on implications for cell membrane rafts or clusters, whose size may be of similar magnitude to estimated critical radii for domain symmetry.
THE KHOVANOV HOMOLOGY OF (p, -p, q) PRETZEL KNOTS

In this paper, we compute the Khovanov homology over ℚ for (p, -p, q) pretzel knots for 3 ≤ p ≤ 15, p odd, and arbitrarily large q. We provide a conjecture for the general form of the Khovanov homology of (p, -p, q) pretzel knots. These computations reveal that these knots have thin Khovanov homology (over ℚ or ℤ). Because Greene has shown that these knots are not quasi-alternating, this provides an infinite class of non-quasi-alternating knots with thin Khovanov homology.
A COMBINATORIAL DGA FOR LEGENDRIAN KNOTS FROM GENERATING FAMILIES

For a Legendrian knot L ⊂ ℝ3, with a chosen Morse complex sequence (MCS), we construct a differential graded algebra (DGA) whose differential counts "chord paths" in the front projection of L. The definition of the DGA is motivated by considering Morse-theoretic data from generating families. In particular, when the MCS arises from a generating family F, we give a geometric interpretation of our chord paths as certain broken gradient trajectories which we call "gradient staircases". Given two equivalent MCS's we prove the corresponding linearized complexes of the DGA are isomorphic. If the MCS has a standard form, then we show that our DGA agrees with the Chekanov–Eliashberg DGA after changing coordinates by an augmentation.
Critical groups for Hopf algebra modules

This paper considers an invariant of modules over a finite-dimensional Hopf algebra, called the critical group. This generalises the critical groups of complex finite group representations studied in [1, 11]. A formula is given for the cardinality of the critical group generally, and the critical group for the regular representation is described completely. A key role in the formulas is played by the greatest common divisor of the dimensions of the indecomposable projective representations.
Direct observation of charge mediated lattice distortions in complex oxide solid solutions

Using aberration corrected scanning transmission electron microscopy combined with advanced imaging methods, we directly observe atom column specific, picometer-scale displacements induced by local chemistry in a complex oxide solid solution. Displacements predicted from density functional theory were found to correlate with the observed experimental trends. Further analysis of bonding and charge distribution was used to clarify the mechanisms responsible for the detected structural behavior. By extending the experimental electron microscopy measurements to previously inaccessible length scales, we identified correlated atomic displacements linked to bond differences within the complex oxide structure.
Theory of Kerr and Faraday rotations and linear dichroism in Topological Weyl Semimetals

We consider the electromagnetic response of a topological Weyl semimetal (TWS) with a pair of Weyl nodes in the bulk and corresponding Fermi arcs in the surface Brillouin zone. We compute the frequency-dependent complex conductivities σαβ(ω) and also take into account the modification of Maxwell equations by the topological θ-term to obtain the Kerr and Faraday rotations in a variety of geometries. For TWS films thinner than the wavelength, the Kerr and Faraday rotations, determined by the separation between Weyl nodes, are significantly larger than in topological insulators. In thicker films, the Kerr and Faraday angles can be enhanced by choice of film thickness and substrate refractive index. We show that, for radiation incident on a surface with Fermi arcs, there is no Kerr or Faraday rotation but the electric field develops a longitudinal component inside the TWS, and there is linear dichroism signal. Our results have implications for probing the TWS phase in various experimental systems.
Big Bang Nucleosynthesis and the Helium Isotope Ratio

The conventional approach to search for departures from the standard model of physics during Big Bang Nucleosynthesis involves a careful, and subtle measurement of the mass fraction of baryons consisting of helium. Recent measurements of this quantity tentatively support new physics beyond the standard model but, historically, this method has suffered from hidden systematic uncertainties. In this letter, I show that a combined measurement of the primordial deuterium abundance and the primordial helium isotope ratio has the potential to provide a complementary and reliable probe of new physics beyond the standard model. Using the recent determination of the primordial deuterium abundance and assuming that the measured pre-solar meteoritic abundance reflects the primordial value, a bound can be placed on the effective number of neutrino species, (BBN) (with 95% confidence). Although this value of supports the standard model, it is presently unclear if the pre-solar ratio reflects the primordial value. New astrophysical measurements of the helium isotope ratio in near-pristine environments, together with updated calculations and experimental values of several important nuclear reactions (some of which are already being attempted), will lead to much improved limits on possible departures from the standard model. To this end, I describe an analysis strategy to measure the 3He i flux emitted from nearby low metallicity H ii regions. The proposed technique can be attempted with the next generation of large telescopes, and will be easier to realize in metal-poor H ii regions with quiescent kinematics.
Bimodules in bordered Heegaard Floer homology

Bordered Heegaard Floer homology is a three-manifold invariant which associates to a surface F an algebra A.F/ and to a three-manifold Y with boundary identified with F a module over A.F/. In this paper, we establish naturality properties of this invariant. Changing the diffeomorphism between F and the boundary of Y tensors the bordered invariant with a suitable bimodule over A.F/. These bimodules give an action of a suitably based mapping class group on the category of modules over A.F/. The Hochschild homology of such a bimodule is identified with the knot Floer homology of the associated open book decomposition. In the course of establishing these results, we also calculate the homology of A.F/. We also prove a duality theorem relating the two versions of the 3‐manifold invariant. Finally, in the case of a genus-one surface, we calculate the mapping class group action explicitly. This completes the description of bordered Heegaard Floer homology for knot complements in terms of the knot Floer homology. 57R57; 53D40
FOLLOWING the COSMIC EVOLUTION of PRISTINE GAS. I. IMPLICATIONS for MILKY WAY HALO STARS

We make use of new subgrid model of turbulent mixing to accurately follow the cosmological evolution of the first stars, the mixing of their supernova ejecta, and the impact on the chemical composition of the Galactic Halo. Using the cosmological adaptive mesh refinement code RAMSES, we implement a model for the pollution of pristine gas as described in Pan et al. Tracking the metallicity of Pop III stars with metallicities below a critical value allows us to account for the fraction of Z < Zcrit stars formed even in regions in which the gas' average metallicity is well above Zcrit. We demonstrate that such partially-mixed regions account for 0.5 to 0.7 of all Pop III stars formed up to z = 5. Additionally, we track the creation and transport of "primordial metals" (PM) generated by Pop III supernovae (SNe). These neutron-capture deficient metals are taken up by second-generation stars and likely lead to unique abundance signatures characteristic of carbon-enhanced, metal-poor (CEMP-no) stars. As an illustrative example, we associate primordial metals with abundance ratios used by Keller et al. to explain the source of metals in the star SMSS J031300.36-670839.3, finding good agreement with the observed [Fe/H], [C/H], [O/H], and [Mg/Ca] ratios in CEMP-no Milky Way halo stars. Similar future simulations will aid in further constraining the properties of Pop III stars using CEMP observations, as well as improve predictions of the spatial distribution of Pop III stars, as will be explored by the next generation of ground- and space-based telescopes.
Iterative machine learning for precision trajectory tracking with series elastic actuators

When robots operate in unknown environments small errors in positions can lead to large variations in the contact forces, especially with typical high-impedance designs. This can potentially damage the surroundings and/or the robot. Series elastic actuators (SEAs) are a popular way to reduce the output impedance of a robotic arm to improve control authority over the force exerted on the environment. However this increased control over forces with lower impedance comes at the cost of lower positioning precision and bandwidth. This article examines the use of an iteratively-learned feedforward command to improve position tracking when using SEAs. Over each iteration, the output responses of the system to the quantized inputs are used to estimate a linearized local system models. These estimated models are obtained using a complex-valued Gaussian Process Regression (cGPR) technique and then, used to generate a new feedforward input command based on the previous iteration's error. This article illustrates this iterative machine learning (IML) technique for a two degree of freedom (2-DOF) robotic arm, and demonstrates successful convergence of the IML approach to reduce the tracking error.
Resilient linear classification: an approach to deal with attacks on training data

Data-driven techniques are used in cyber-physical systems (CPS) for controlling autonomous vehicles, handling demand responses for energy management, and modeling human physiology for medical devices. These data-driven techniques extract models from training data, where their performance is often analyzed with respect to random errors in the training data. However, if the training data is maliciously altered by attackers, the effect of these attacks on the learning algorithms underpinning data-driven CPS have yet to be considered. In this paper, we analyze the resilience of classification algorithms to training data attacks. Specifically, a generic metric is proposed that is tailored to measure resilience of classification algorithms with respect to worst-case tampering of the training data. Using the metric, we show that traditional linear classification algorithms are resilient under restricted conditions. To overcome these limitations, we propose a linear classification algorithm with a majority constraint and prove that it is strictly more resilient than the traditional algorithms. Evaluations on both synthetic data and a real-world retrospective arrhythmia medical case-study show that the traditional algorithms are vulnerable to tampered training data, whereas the proposed algorithm is more resilient (as measured by worst-case tampering).
Using Markov Models and Statistics to Learn, Extract, Fuse, and Detect Patterns in Raw Data

Many systems are partially stochastic in nature. We have derived data-driven approaches for extracting stochastic state machines (Markov models) directly from observed data. This chapter provides an overview of our approach with numerous practical applications. We have used this approach for inferring shipping patterns, exploiting computer system side-channel information, and detecting botnet activities. For contrast, we include a related data-driven statistical inferencing approach that detects and localizes radiation sources.
Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics

We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.
Toward ab initio density functional theory for nuclei

We survey approaches to non-relativistic density functional theory (DFT) for nuclei using progress toward ob initio DFT for Coulomb systems as a guide. Ab initio DFT starts with a microscopic Hamiltonian and is naturally formulated using orbital-based functionals, which generalize the conventional 'local density plus gradients' form. The orbitals satisfy single-particle equations with multiplicative (local) potentials. The DFT functionals can be developed starting from internucleon forces using wavefunction-based methods or by Legendre transform via effective actions. We describe known and unresolved issues for applying these formulations to the nuclear many-body problem and discuss how ab initio approaches can help improve empirical energy density functionals. (C) 2009 Elsevier B.V. All rights reserved.
Brownian dynamics of fully confined suspensions of rigid particles without Green's functions.

We introduce a Rigid-Body Fluctuating Immersed Boundary (RB-FIB) method to perform large-scale Brownian dynamics simulations of suspensions of rigid particles in fully confined domains, without any need to explicitly construct Green’s functions or mobility operators. In the RB-FIB approach, discretized fluctuating Stokes equations are solved with prescribed boundary conditions in conjunction with a rigid-body immersed boundary method to discretize arbitrarily shaped colloidal particles with no-slip or active-slip prescribed on their surface. We design a specialized Split–Euler–Maruyama temporal integrator that uses a combination of random finite differences to capture the stochastic drift appearing in the overdamped Langevin equation. The RB-FIB method presented in this work only solves mobility problems in each time step using a preconditioned iterative solver and has a computational complexity that scales linearly in the number of particles and fluid grid cells. We demonstrate that the RB-FIB method correctly reproduces the Gibbs-Boltzmann equilibrium distribution and use the method to examine the time correlation functions for two spheres tightly confined in a cuboid. We model a quasi–two-dimensional colloidal crystal confined in a narrow microchannel and hydrodynamically driven across a commensurate periodic substrate potential mimicking the effect of a corrugated wall. We observe partial and full depinning of the colloidal monolayer from the substrate potential above a certain wall speed, consistent with a transition from static to kinetic friction through propagating kink solitons. Unexpectedly, we find that particles nearest to the boundaries of the domain are the first to be displaced, followed by particles in the middle of the domain.
An Intrinsic Geometrical Approach for Statistical Process Control of Surface and Manifold Data

We present a new method for statistical process control (SPC) of a discrete part manufacturing system based on intrinsic geometrical properties of the parts, estimated from three-dimensional sensor...
CRAD: Clustering with Robust Autocuts and Depth

We develop a new density-based clustering algorithm named CRAD which is based on a new neighbor searching function with a robust data depth as the dissimilarity measure. Our experiments prove that the new CRAD is highly competitive at detecting clusters with varying densities, compared with the existing algorithms such as DBSCAN, OPTICS and DBCA. Furthermore, a new effective parameter selection procedure is developed to select the optimal underlying parameter in the real-world clustering, when the ground truth is unknown. Lastly, we suggest a new clustering framework that extends CRAD from spatial data clustering to time series clustering without a-priori knowledge of the true number of clusters. The performance of CRAD is evaluated through extensive experimental studies.
Development and evaluation of a tutorial to improve students’ understanding of a lock-in amplifier

Development and evaluation of a research-based tutorial to help students develop an understanding of the lock-in amplifier.
Inapproximability of the Partition Function for the Antiferromagnetic Ising and Hard-Core Models

Recent inapproximability results of Sly (2010), together with an approximation algorithm presented by Weitz (2006), establish a beautiful picture of the computational complexity of approximating the partition function of the hard-core model. Let λ c ( ) denote the critical activity for the hard-model on the infinite Δ-regular tree. Weitz presented an FPTAS for the partition function when λ 0 such that (unless RP = NP) there is no FPRAS for approximating the partition function on graphs of maximum degree Δ for activities λ satisfying λ c ( ) < λ < λ c ( ) + eΔ. We prove that a similar phenomenon holds for the antiferromagnetic Ising model. Sinclair, Srivastava and Thurley (2014) extended Weitz's approach to the antiferromagnetic Ising model, yielding an FPTAS for the partition function for all graphs of constant maximum degree Δ when the parameters of the model lie in the uniqueness region of the infinite Δ-regular tree. We prove the complementary result for the antiferromagnetic Ising model without external field, namely, that unless RP = NP, for all Δ ⩾ 3, there is no FPRAS for approximating the partition function on graphs of maximum degree Δ when the inverse temperature lies in the non-uniqueness region of the infinite tree . Our proof works by relating certain second moment calculations for random Δ-regular bipartite graphs to the tree recursions used to establish the critical points on the infinite tree.
Terrestrial planet formation in extra-solar planetary systems

Terrestrial planets form in a series of dynamical steps from the solid component of circumstellar disks. First, km-sized planetesimals form likely via a combination of sticky collisions, turbulent concentration of solids, and gravitational collapse from micron-sized dust grains in the thin disk midplane. Second, planetesimals coalesce to form Moon- to Mars-sized protoplanets, also called “planetary embryos”. Finally, full-sized terrestrial planets accrete from protoplanets and planetesimals. This final stage of accretion lasts about 10-100 Myr and is strongly affected by gravitational perturbations from any gas giant planets, which are constrained to form more quickly, during the 1-10 Myr lifetime of the gaseous component of the disk. It is during this final stage that the bulk compositions and volatile (e.g., water) contents of terrestrial planets are set, depending on their feeding zones and the amount of radial mixing that occurs. The main factors that influence terrestrial planet formation are the mass and surface density profile of the disk, and the perturbations from giant planets and binary companions if they exist. Simple accretion models predicts that low-mass stars should form small, dry planets in their habitable zones. The migration of a giant planet through a disk of rocky bodies does not completely impede terrestrial planet growth. Rather, “hot Jupiter” systems are likely to also contain exterior, very water-rich Earth-like planets, and also “hot Earths”, very close-in rocky planets. Roughly one third of the known systems of extra-solar (giant) planets could allow a terrestrial planet to form in the habitable zone.
The algebraic duality resolution at p = 2

The goal of this paper is to develop some of the machinery necessary for doing $K(2)$-local computations in the stable homotopy category using duality resolutions at the prime $p=2$. The Morava stabilizer group $\mathbb{S}_2$ admits a norm whose kernel we denote by $\mathbb{S}_2^1$. The algebraic duality resolution is a finite resolution of the trivial $\mathbb{Z}_2[[\mathbb{S}_2^1]]$-module $\mathbb{Z}_2$ by modules induced from representations of finite subgroups of $\mathbb{S}_2^1$. Its construction is due to Goerss, Henn, Mahowald and Rezk. It is an analogue of their finite resolution of the trivial $\mathbb{Z}_3[[\mathbb{G}_2^1]]$-module $\mathbb{Z}_3$ at the prime $p=3$. The construction was never published and it is the main result in this paper. In the process, we give a detailed description of the structure of Morava stabilizer group $\mathbb{S}_2$ at the prime $2$. We also describe the maps in the algebraic duality resolution with the precision necessary for explicit computations.
Unsupervised manifold alignment for single-cell multi-omics data

Integrating single-cell measurements that capture different properties of the genome is vital to extending our understanding of genome biology. This task is challenging due to the lack of a shared axis across datasets obtained from different types of single-cell experiments. For most such datasets, we lack corresponding information among the cells (samples) and the measurements (features). In this scenario, unsupervised algorithms that are capable of aligning single-cell experiments are critical to learning an in silico co-assay that can help draw correspondences among the cells. Maximum mean discrepancy-based manifold alignment (MMD-MA) is such an unsupervised algorithm. Without requiring correspondence information, it can align single-cell datasets from different modalities in a common shared latent space, showing promising results on simulations and a small-scale single-cell experiment with 61 cells. However, it is essential to explore the applicability of this method to larger single-cell experiments with thousands of cells so that it can be of practical interest to the community. In this paper, we apply MMD-MA to two recent datasets that measure transcriptome and chromatin accessibility in ~2000 single cells. To scale the runtime of MMD-MA to a more substantial number of cells, we extend the original implementation to run on GPUs. We also introduce a method to automatically select one of the user-defined parameters, thus reducing the hyperparameter search space. We demonstrate that the proposed extensions allow MMD-MA to accurately align state-of-the-art single-cell experiments.
Branches of Triangulated Origami Near the Unfolded State

Origami structures can potentially lead to the development of self-assembling devices, and understanding the many ways that such a structure can end up in an undesired configuration is essential to that goal. New theoretical work analyzes an origami structure composed of triangles and characterizes the various ways it can unfold.
New Gauge Field from Extension of Space Time Parallel Transport of Vector Spaces to the Underlying Number Systems

One way of describing gauge theories in physics is to assign a vector space $\bar{V}_{x}$ to each space time point x. For each x the field ψ takes values ψ(x) in $\bar{V}_{x}$ . The freedom to choose a basis in each $\bar{V}_{x}$ introduces gauge group operators and their Lie algebra representations to define parallel transformations between vector spaces. This paper is an exploration of the extension of these ideas to include the underlying scalar complex number fields. Here a Hilbert space, $\bar{H}_{x}$ , as an example of $\bar{V}_{x}$ , and a complex number field, $\bar{C}_{x}$ , are associated with each space time point. The freedom to choose a basis in $\bar{H}_{x}$ is expanded to include the freedom to choose complex number fields. This expansion is based on the discovery that there exist representations of complex (and other) number systems that differ by arbitrary scale factors. Compensating changes must be made in the basic field operations so that the relevant axioms are satisfied. This results in the presence of a new real valued gauge field A(x). Inclusion of A(x) into covariant derivatives in Lagrangians results in the description of A(x) as a gauge boson for which mass is optional. The great accuracy of QED suggests that the coupling constant of A(x) to matter fields is very small compared to the fine structure constant. Other physical properties of A(x) are not known at present.
Sparse bounds for the discrete cubic Hilbert transform

Consider the discrete cubic Hilbert transform defined on finitely supported functions f on ℤ by H 3 f ( n ) = ∑ m ≠ 0 f ( n − m 3 ) m . We prove that there exists r<2 and universal constant C such that for all finitely supported f,g on ℤ there exists an (r,r)-sparse form Λr,r for which | 〈 H 3 f , g 〉 | ≤ C Λ r , r ( f , g ) . This is the first result of this type concerning discrete harmonic analytic operators. It immediately implies some weighted inequalities, which are also new in this setting.
Decentralized algorithms for 3D symmetric formations in robotic networks - a contraction theory approach

This paper presents distributed algorithms for formation control of multiple robots in three dimensions. In particular, we leverage the mathematical properties of cyclic pursuit along with results from contraction and partial contraction theory to design distributed control algorithms ensuring global convergence to symmetric formations. As a base case we consider regular polygons as desired formations and then provide extensions to Johnson solid formations. Finally, we analyze the robustness of the control algorithms under bounded additive disturbances and provide performance bounds with respect to the formation error.
Mirror symmetry for honeycombs

We prove a homological mirror symmetry equivalence between an $A$-brane category for the pair of pants, computed as a wrapped microlocal sheaf category, and a $B$-brane category for a mirror LG model, understood as a category of matrix factorizations. The equivalence improves upon prior results in two ways: it intertwines evident affine Weyl group symmetries on both sides, and it exhibits the relation of wrapped microlocal sheaves along different types of Lagrangian skeleta for the same hypersurface. The equivalence proceeds through the construction of a combinatorial realization of the $A$-model via arboreal singularities. The constructions here represent the start of a program to generalize to higher dimensions many of the structures which have appeared in topological approaches to Fukaya categories of surfaces.
DETERMINING INCLINATIONS OF ACTIVE GALACTIC NUCLEI VIA THEIR NARROW-LINE REGION KINEMATICS. I. OBSERVATIONAL RESULTS*

Active galactic nuclei (AGNs) are axisymmetric systems to first order; their observed properties are likely strong functions of inclination with respect to our line of sight (LOS). However, except for a few special cases, the specific inclinations of individual AGNs are unknown. We have developed a promising technique for determining the inclinations of nearby AGNs by mapping the kinematics of their narrow-line regions (NLRs), which are often easily resolved with Hubble Space Telescope [O III] imaging and long-slit spectra from the Space Telescope Imaging Spectrograph. Our studies indicate that NLR kinematics dominated by radial outflow can be fit with simple biconical outflow models that can be used to determine the inclination of the bicone axis, and hence the obscuring torus, with respect to our LOS. We present NLR analysis of 53 Seyfert galaxies and the resulting inclinations from models of 17 individual AGNs with clear signatures of biconical outflows. Our model results agree with the unified model in that Seyfert 1 AGNs have NLRs inclined further toward our LOS than Seyfert 2 AGNs. Knowing the inclinations of these AGN NLRs, and thus their accretion disk and/or torus axes, will allow us to determine how their observed properties vary as a function of polar angle. We find no correlation between the inclinations of the AGN NLRs and the disks of their host galaxies, indicating that the orientation of the gas in the torus is independent of that of the host disk.
Obstructions to Lagrangian cobordisms between Legendrians via generating families

The technique of generating families produces obstructions to the existence of embedded Lagrangian cobordisms between Legendrian submanifolds in the symplectizations of 1‐jet bundles. In fact, generating families may be used to construct a TQFT-like theory that, in addition to giving the aforementioned obstructions, yields structural information about invariants of Legendrian submanifolds. For example, the obstructions devised in this paper show that there is no generating family compatible Lagrangian cobordism between the Chekanov‐Eliashberg Legendrian m.52/ knots. Further, the generating family cohomology groups of a Legendrian submanifold restrict the topology of a Lagrangian filling. Structurally, the generating family cohomology of a Legendrian submanifold satisfies a type of Alexander duality that, when the Legendrian is null-cobordant, can be seen as Poincare duality of the associated Lagrangian filling. This duality implies the Arnold Conjecture for Legendrian submanifolds with linear-at-infinity generating families. These results are obtained by developing a generating family version of wrapped Floer cohomology and establishing long exact sequences that arise from viewing the spaces underlying these cohomology groups as mapping cones. 53D12, 57R17; 57Q60
Evidence for Binarity and Possible Disk Obscuration in Kepler Observations of the Pulsating RV Tau Variable DF Cygni

The Kepler light curve of DF Cyg is unparalleled in precision and cadence for any RV Tau star to date spanning a baseline of $\sim$4 years and clearly displaying the signature pulsating behavior of alternating deep and shallow minima as well as the long-term trend indicative of an RVb-type variable. We measured DF Cyg's formal period (the time interval between two successive deep minima) to be $~49.84 \pm 0.02~$days. The trend in the arrival times emulates that of the long-term period. There appears to be precisely 16 deep+shallow minima cycles in one long-term cycle, suggesting a long-term cycle period of $\approx$ $795 \pm 5~$days. We argue that binarity may naturally explain the long-term periodicity in DF Cyg. The spectral energy distribution of DF Cyg features an infrared excess indicative of a disk possibly linked to a binary companion. From a recent Gaia parallax measurement for DF Cyg, we calculated that it has a distance of $990 \pm 372$pc and a physical radius of $R_\star = 10.3 \pm 3.8$ R$_\odot$. From kinematics and geometric arguments, we argue that the most likely interpretation for the decrease in flux from the long-period maximum to the long-period minimum, as well as the reduction of short-term pulsation amplitude, is caused by an occulting body such as a disk surrounding DF Cyg and its binary companion.
Hexatonic Systems and Dual Groups in Mathematical Music Theory

Motivated by the music-theoretical work of Richard Cohn and David Clampitt on late-nineteenth century harmony, we mathematically prove that the PL-group of a hexatonic cycle is dual (in the sense of Lewin) to its T/I-stabilizer. Our point of departure is Cohn's notions of maximal smoothness and hexatonic cycle, and the symmetry group of the 12-gon; we do not make use of the duality between the T/I-group and PLR-group. We also discuss how some ideas in the present paper could be used in the proof of T/I-PLR duality by Crans--Fiore--Satyendra.
LESS is More: Rethinking Probabilistic Models of Human Behavior

Robots need models of human behavior for both inferring human goals and preferences, and predicting what people will do. A common model is the Boltzmann noisily-rational decision model, which assumes people approximately optimize a reward function and choose trajectories in proportion to their exponentiated reward. While this model has been successful in a variety of robotics domains, its roots lie in econometrics, and in modeling decisions among different discrete options, each with its own utility or reward. In contrast, human trajectories lie in a continuous space, with continuous-valued features that influence the reward function. We propose that it is time to rethink the Boltzmann model, and design it from the ground up to operate over such trajectory spaces. We introduce a model that explicitly accounts for distances between trajectories, rather than only their rewards. Rather than each trajectory affecting the decision independently, similar trajectories now affect the decision together. We start by showing that our model better explains human behavior in a user study. We then analyze the implications this has for robot inference, first in toy environments where we have ground truth and find more accurate inference, and finally for a 7DOF robot arm learning from user demonstrations. ACM Reference Format: Andreea Bobu, Dexter R.R. Scobee, Jaime F. Fisac, S. Shankar Sastry, and Anca D. Dragan. 2020. LESS is More: Rethinking Probabilistic Models of Human Behavior. In Proceedings of the 2020 ACM/IEEE International Conference on Human-Robot Interaction (HRI ’20), March 23–26, 2020, Cambridge, United Kingdom. ACM, New York, NY, USA, 9 pages. https://doi.org/10.1145/ 3319502.3374811
The Multiplication Game

AbstractThe Multiplication Game is a two-person game in which each player chooses a positive integer without knowledge of the other player's number. The two numbers are then multiplied together and the first digit of the product determines the winner. Rather than analyzing this game directly, we consider a closely related game in which the players choose positive real numbers between 1 and 10, multiply them together, and move the decimal point, if necessary, so that the result is between 1 and 10. The mixed strategies are probability distributions on this interval, and it is shown that for both players it is optimal to choose their numbers from the Benford distribution. Furthermore, this strategy is optimal for any winning set, and the probability of winning is the Benford measure of the player's winning set. Using these results we prove that the original game in which the players choose integers has a well-defined value and that strategies exist that are arbitrarily close to optimal. Finally, we consider...
Noise and Signal for Spectra of Intermittent Noiselike Emission

We show that intermittency of noiselike emission, after propagation through a scattering medium, affects the distribution of noise in the observed correlation function. Intermittency also affects correlation of noise among channels of the spectrum, but leaves the average spectrum, average correlation function, and distribution of noise among channels of the spectrum unchanged. Pulsars are examples of such sources: intermittent and affected by interstellar propagation. We assume that the source emits Gaussian white noise, modulated by a time envelope. Propagation convolves the resulting time series with an impulse-response function that represents effects of dispersion, scattering, and absorption. We assume that this propagation kernel is shorter than the time for an observer to accumulate a single spectrum. We show that rapidly varying intermittent emission tends to concentrate noise near the central lag of the correlation function. We derive mathematical expressions for this effect, in terms of the time envelope and the propagation kernel. We present examples, discuss effects of background noise, and compare our results with observations.
Modeling microlensing events with MulensModel

Abstract We introduce MulensModel , a software package for gravitational microlensing modeling. The package provides a framework for calculating microlensing model magnification curves and goodness-of-fit statistics for microlensing events with single and binary lenses as well as a variety of higher-order effects: extended sources with limb-darkening, annual microlensing parallax, satellite microlensing parallax, and binary lens orbital motion. The software could also be used for analysis of the planned microlensing survey by the NASA flag-ship WFIRST satellite. MulensModel is available at https://github.com/rpoleski/MulensModel/ .
K3 surfaces and equations for Hilbert modular surfaces

We outline a method to compute rational models for the Hilbert modular surfaces Y−(D), which are coarse moduli spaces for principally polarized abelian surfaces with real multiplication by the ring of integers in ℚ(D), via moduli spaces of elliptic K3 surfaces with a Shioda–Inose structure. In particular, we compute equations for all thirty fundamental discriminants D with 1<D<100, and analyze rational points and curves on these Hilbert modular surfaces, producing examples of genus-2 curves over ℚ whose Jacobians have real multiplication over ℚ.
Witness algebra and anyon braiding

Topological quantum computation employs two-dimensional quasiparticles called anyons. The generally accepted mathematical basis for the theory of anyons is the framework of modular tensor categories. That framework involves a substantial amount of category theory and is, as a result, considered rather difficult to understand. Is the complexity of the present framework necessary? The computations of associativity and braiding matrices can be based on a much simpler framework, which looks less like category theory and more like familiar algebra. We introduce that framework here.
Inherently unstable internal gravity waves due to resonant harmonic generation

Here we show that there exist internal gravity waves that are inherently unstable, that is, they cannot exist in nature for a long time. The instability mechanism is a one-way (irreversible) harmonic-generation resonance that permanently transfers the energy of an internal wave to its higher harmonics. We show that, in fact, there are a countably infinite number of such unstable waves. For the harmonic-generation resonance to take place, the nonlinear terms in the free surface boundary condition play a pivotal role, and the instability does not occur in a linearly stratified fluid if a simplified boundary condition, such as a rigid lid or a linearized boundary condition, is employed. Harmonic-generation resonance presented here provides a mechanism for the transfer of internal wave energy to the higher-frequency part of the spectrum hence affecting, potentially significantly, the evolution of the internal waves spectrum.
Length spectra of sub-Riemannian metrics on compact Lie groups

Length spectra for Riemannian metrics are well studied, while sub-Riemannian length spectra have been largely unexplored. Here we give the length spectrum for a canonical sub-Riemannian structure attached to any compact Lie group by restricting its Killing form to the sum of the root spaces. Surprisingly, the shortest loops are the same in both the Riemannian and sub-Riemannian cases. We provide specific calculations for SU(2) and SU(3).