cssi/SciSciGPT-SciSciNet huggingface dataset:
Knot concordance and higher-order Blanchfield duality

In 1997, T Cochran, K Orr, and P Teichner [Ann. of Math. (2) 157 (2003) 433-519] defined a filtration of the classical knot concordance group C, ⋯ ⊆ ℱ n ⊆ ⋯ ⊆ ℱ 1 ⊆ ℱ 0 . 5 ⊆ ℱ 0 ⊆ C . The filtration is important because of its strong connection to the classification of topological 4–manifolds. Here we introduce new techniques for studying C and use them to prove that, for each n∈ℕ0, the group ℱn∕ℱn.5 has infinite rank. We establish the same result for the corresponding filtration of the smooth concordance group. We also resolve a long-standing question as to whether certain natural families of knots, first considered by Casson–Gordon and Gilmer, contain slice knots.
Interesting evidence for a low-level oscillation superimposed on the local Hubble flow

Historically the velocity scatter seen on local Hubble plots has been attributed to the peculiar velocities of individual galaxies. Although most galaxies also have uncertainties in their distances, when galaxies with accurate distances are used recent studies have found that these supposed peculiar velocities may have preferred, or discrete, values. Here we report the interesting result that when these discrete components are identified and removed from the radial velocities of the SNeIa galaxies studied in the Hubble Key Project, there is evidence for a residual oscillation, or ripple, superimposed on the Hubble flow. This oscillation has a wavelength near 40 Mpc and, because its amplitude is small compared to that of the scatter in velocities, it becomes visible only after the discrete components are removed. This result is interesting because even if this ripple has been produced by a selection effect, the fact that it is only revealed after the discrete velocities are removed implies that the discrete velocities are real. Alternatively, if no selection effect can be identified to explain the ripple, then both the discrete velocities and the ripple together become very difficult to explain by chance and these results could then have interesting cosmological consequences.
Long-lived Light Mediator to Dark Matter and Primordial Small Scale Spectrum

We calculate the early universe evolution of perturbations in the dark matter energy density in the context of simple dark sector models containing a GeV scale light mediator. We consider the case that the mediator is long-lived, with lifetime up to a second, and before decaying it temporarily dominates the energy density of the universe. We show that for primordial perturbations that enter the horizon around this period, the interplay between linear growth during matter domination and collisional damping can generically lead to a sharp peak in the spectrum of dark matter density perturbation. As a result, the population of the smallest DM halos gets enhanced. Possible implications of this scenario are discussed.
Upper semi-continuity of the Hilbert–Kunz multiplicity

We prove that the Hilbert–Kunz multiplicity is upper semi-continuous in F-finite rings and algebras of essentially finite type over an excellent local ring.
Vector-valued Hirzebruch–Zagier series and class number sums

For any number $$m \equiv 0,1 \, (4)$$ , we correct the generating function of Hurwitz class number sums $$\sum _r H(4n - mr^2)$$ to a modular form (or quasimodular form if m is a square) of weight two for the Weil representation attached to a binary quadratic form of discriminant m and determine its behavior in the Petersson scalar product. This modular form arises through holomorphic projection of the zero-value of a nonholomorphic Jacobi Eisenstein series of index 1 / m. When m is prime, we recover the classical Hirzebruch–Zagier series whose coefficients are intersection numbers of curves on a Hilbert modular surface. Finally, we calculate certain sums over class numbers by comparing coefficients with an Eisenstein series.
Arithmetic Spectral Transitions for the Maryland Model

We give a precise description of spectra of the Maryland model (hλ,α,θu)n=un+1+un−1+λtanπ(θ+nα)un for all values of parameters. We introduce an arithmetically defined index δ(α,θ) and show that for α∉ℚ, σsc(hλ,α,θ)={e:γλ(e)<δ(α,θ)}¯ and σpp(hλ,α,θ)={e:γλ(e)≥δ(α,θ)}. Since σac(hλ,α,θ)=∅, this gives a complete description of the spectral decomposition for all values of parameters λ, α, and θ, making it the first case of a family where arithmetic spectral transition is described without any parameter exclusion. The set of eigenvalues can be explicitly identified for all parameters, using the quantization condition. We also establish, for the first time for this or any other model, a quantization condition for singular continuous spectrum (an arithmetically defined measure zero set that supports singular continuous measures) for all parameters.© 2017 Wiley Periodicals, Inc.
An optimal resource allocation with joint carrier aggregation in 4G-LTE

In this paper, we introduce a novel approach for optimal resource allocation from multiple carriers for users with elastic and inelastic traffic in fourth generation long term evolution (4G-LTE) system. In our model, we use logarithmic and sigmoidal-like utility functions to represent the user applications running on different user equipments (UE)s. We use utility proportional fairness policy, where the fairness among users is in utilization (i.e utility percentage) of the application running on the mobile station. Our objective is to allocate the resources to the users optimally from multiple carriers. In addition, every user subscribing for the mobile service is guaranteed to have a minimum quality-of-service (QoS) with a priority criterion. Our rate allocation algorithm selects the carrier or multiple carriers that provide the minimum price for the needed resources. We prove that the novel resource allocation optimization problem with joint carrier aggregation is convex and therefore the optimal solution is tractable. We present a distributed algorithm to allocate the resources optimally from multiple evolved NodeBs (eNodeB)s. Finally, we present simulation results for the performance of our rate allocation algorithm.
An Atomic-Array Optical Clock with Single-Atom Readout

Currently, the most accurate and stable clocks use optical interrogation of either a single ion or an ensemble of neutral atoms confined in an optical lattice. Here, we demonstrate a new optical clock system based on an array of individually trapped neutral atoms with single-atom readout, merging many of the benefits of ion and lattice clocks as well as creating a bridge to recently developed techniques in quantum simulation and computing with neutral atoms. We evaluate single-site resolved frequency shifts and short-term stability via self-comparison. Atom-by-atom feedback control enables direct experimental estimation of laser noise contributions. Results agree well with an ab initio Monte Carlo simulation that incorporates finite temperature, projective read-out, laser noise, and feedback dynamics. Our approach, based on a tweezer array, also suppresses interaction shifts while retaining a short dead time, all in a comparatively simple experimental setup. These results establish the foundations for a third optical clock platform suited to advance stationary and transportable clock systems, while providing a novel starting point for entanglement-enhanced metrology and quantum clock networks as well as applications in quantum computing and communication with individual neutral atoms requiring optical clock state control.
Event Loops as First-Class Values: A Case Study in Pedagogic Language Design

The World model is an existing functional input-output mechanism for event-driven programming. It is used in numerous popular textbooks and curricular settings. The World model conflates two different tasks -- the definition of an event processor and its execution -- into one. This conflation imposes a significant (even unacceptable) burden on student users in several educational settings where we have tried to use it, e.g., for teaching physics. While it was tempting to pile on features to address these issues, we instead used the Scheme language design dictum of removing weaknesses that made them seem necessary. By separating the two tasks above, we arrived at a slightly different primitive, the reactor, as our basis. This only defines the event processor, and a variety of execution operators dictate how it runs. The new design enables programmatic control over event-driven programs. This simplifies reflecting on program behavior, and eliminates many unnecessary curricular dependencies imposed by the old design. This work has been implemented in the Pyret programming language. The separation of concerns has enabled new curricula, such as the Bootstrap:Physics curriculum, to take flight. Thousands of students use this new mechanism every year. We believe that reducing impedance mismatches improves their educational experience.
Vizic: A Jupyter-based interactive visualization tool for astronomical catalogs

Abstract The ever-growing datasets in observational astronomy have challenged scientists in many aspects, including an efficient and interactive data exploration and visualization. Many tools have been developed to confront this challenge. However, they usually focus on displaying the actual images or focus on visualizing patterns within catalogs in a predefined way. In this paper we introduce Vizic , a Python visualization library that builds the connection between images and catalogs through an interactive map of the sky region. Vizic visualizes catalog data over a custom background canvas using the shape, size and orientation of each object in the catalog. The displayed objects in the map are highly interactive and customizable comparing to those in the observation images. These objects can be filtered by or colored by their property values, such as redshift and magnitude. They also can be sub-selected using a lasso-like tool for further analysis using standard Python functions and everything is done from inside a Jupyter notebook. Furthermore, Vizic allows custom overlays to be appended dynamically on top of the sky map. We have initially implemented several overlays, namely, Voronoi, Delaunay, Minimum Spanning Tree and HEALPix grid layer, which are helpful for visualizing large-scale structure. All these overlays can be generated, added or removed interactively with just one line of code. The catalog data is stored in a non-relational database, and the interfaces have been developed in JavaScript and Python to work within Jupyter Notebook, which allows to create customizable widgets, user generated scripts to analyze and plot the data selected/displayed in the interactive map. This unique design makes Vizic a very powerful and flexible interactive analysis tool. Vizic can be adopted in variety of exercises, for example, data inspection, clustering analysis, galaxy alignment studies, outlier identification or just large scale visualizations.
Symplectic embeddings of ellipsoids in dimension greater than four

We study symplectic embeddings of ellipsoids into balls. In the main construction, we show that a given embedding of 2m‐dimensional ellipsoids can be suspended to embeddings of ellipsoids in any higher dimension. In dimension 6, if the ratio of the areas of any two axes is sufficiently large then the ellipsoid is flexible in the sense that it fully fills a ball. We also show that the same property holds in all dimensions for sufficiently thin ellipsoids E.1;:::;a/. A consequence of our study is that in arbitrary dimension a ball can be fully filled by any sufficiently large number of identical smaller balls, thus generalizing a result of Biran valid in dimension 4. 53D35, 57R17
Updating the Chandra HETGS efficiencies using in-orbit observations

The efficiencies of the gratings in the High Energy Transmission Grating Spectrometer (HETGS) were updated using in-light observations of bright continuum sources. The procedure first involved verifying that fluxes obtained from the +1 and -1 orders match, which checks that the contaminant model and the CCD quantum efficiencies agree. Then the fluxes derived using the high energy gratings (HEGs) were compared to those derived from the medium energy gratings (MEGs). The flux ratio was fit to a low order polynomial, which was allocated to the MEGs above 1 keV or the HEGs below 1 keV. The resultant efficiencies were tested by examining fits to blazar spectra.
Modified Regge calculus as an explanation of dark energy

Using the Regge calculus, we construct a Regge differential equation for the time evolution of the scale factor a(t) in the Einstein–de Sitter cosmology model (EdS). We propose two modifications to the Regge calculus approach: (1) we allow the graphical links on spatial hypersurfaces to be large, as in direct particle interaction when the interacting particles reside in different galaxies, and (2) we assume that luminosity distance DL is related to graphical proper distance Dp by the equation , where the inner product can differ from its usual trivial form. The modified Regge calculus model (MORC), EdS and ΛCDM are compared using the data from the Union2 Compilation, i.e. distance moduli and redshifts for type Ia supernovae. We find that a best fit line through versus log z gives a correlation of 0.9955 and a sum of squares error (SSE) of 1.95. By comparison, the best fit ΛCDM gives SSE = 1.79 using Ho = 69.2 km s−1 Mpc, ΩM = 0.29 and ΩΛ = 0.71. The best fit EdS gives SSE = 2.68 using Ho = 60.9 km s−1 Mpc. The best-fit MORC gives SSE = 1.77 and Ho = 73.9 km s−1 Mpc using R = A−1 = 8.38 Gcy and m = 1.71 × 1052 kg, where R is the current graphical proper distance between nodes, A−1 is the scaling factor from our non-trivial inner product, and m is the nodal mass. Thus, the MORC improves the EdS as well as ΛCDM in accounting for distance moduli and redshifts for type Ia supernovae without having to invoke accelerated expansion, i.e. there is no dark energy and the universe is always decelerating.
Half Heusler compounds: promising materials for mid-to-high temperature thermoelectric conversion

Half-Heusler compounds (space group Fm3m) has garnered increasing attention in recent years in the thermoelectric community. Three decades ago, refractory RNiSn half-Heusler compounds (R represents refractory metals such as Hf, Zr, Ti) were found to be narrow-gap semiconductors with large Seebeck coefficients in 100s of micro-volt per Kelvin. Today, half-Heusler (HH) compounds have emerged as promising thermoelectric materials in the intermediate temperature range (400-800oC). HH materials are endowed with good thermal stability and scalability. Thermoelectric n-p modules based on HH materials demonstrate conversion efficiency near 10% and power density output near 9 W/cm2. The objective of this article is to present a historical account of the research and development of thermoelectric half-Heusler compounds. Particularly, there have been notable achievements since 2012 thanks to the emergence of new approaches. As a result, ZT has risen from ~1 to 1.5. The various advances made since the early 1990s to the present are recounted by categorizing half-Heusler materials into three generations (Gen): Gen-1 Gen-2, and Gen-3 HH materials.
A Learning-Based Framework for Two-Dimensional Vehicle Maneuver Prediction over V2V Networks

Situational awareness in vehicular networks could be substantially improved utilizing reliable trajectory prediction methods. More precise situational awareness, in turn, results in notably better performance of critical safety applications, such as Forward Collision Warning (FCW), as well as comfort applications like Cooperative Adaptive Cruise Control (CACC). Therefore, vehicle trajectory prediction problem needs to be deeply investigated in order to come up with an end to end framework with enough precision required by the safety applications’ controllers. This problem has been tackled in the literature using different methods. However, machine learning, which is a promising and emerging field with remarkable potential for time series prediction, has not been explored enough for this purpose. In this paper, a two-layer neural network-based system is developed which predicts the future values of vehicle parameters, such as velocity, acceleration, and yaw rate, in the first layer and then predicts the twodimensional, i.e. longitudinal and lateral, trajectory points based on the first layer’s outputs. The performance of the proposed framework has been evaluated in realistic cut-in scenarios from Safety Pilot Model Deployment (SPMD) dataset and the results show a noticeable improvement in the prediction accuracy in comparison with the kinematics model which is the dominant employed model by the automotive industry. Both ideal and nonideal communication circumstances have been investigated for our system evaluation. For non-ideal case, an estimation step is included in the framework before the parameter prediction block to handle the drawbacks of packet drops or sensor failures and reconstruct the time series of vehicle parameters at a desirable frequency.
The Effects on Supernova Shock Breakout and Swift Light Curves Due to the Mass of the Hydrogen-rich Envelope

Mass loss remains one of the primary uncertainties in stellar evolution. In the most massive stars, mass loss dictates the circumstellar medium and can significantly alter the fate of the star. Mass loss is caused by a variety of wind mechanisms and also through binary interactions. Supernovae (SNe) are excellent probes of this mass loss, both the circumstellar material and the reduced mass of the hydrogen-rich envelope. In this paper, we focus on the effects of reducing the hydrogen-envelope mass on the SN light curve, studying both the shock breakout and peak light-curve emission for a wide variety of mass-loss scenarios. Even though the trends of this mass loss will be masked somewhat by variations caused by different progenitors, explosion energies, and circumstellar media, these trends have significant effects on the SN light curves that should be seen in SN surveys. We conclude with a comparison of our results to a few key observations.
Non-Gaussian component analysis using entropy methods

Non-Gaussian component analysis (NGCA) is a problem in multidimensional data analysis which, since its formulation in 2006, has attracted considerable attention in statistics and machine learning. In this problem, we have a random variable X in n-dimensional Euclidean space. There is an unknown subspace Γ of the n-dimensional Euclidean space such that the orthogonal projection of X onto Γ is standard multidimensional Gaussian and the orthogonal projection of X onto Γ⊥, the orthogonal complement of Γ, is non-Gaussian, in the sense that all its one-dimensional marginals are different from the Gaussian in a certain metric defined in terms of moments. The NGCA problem is to approximate the non-Gaussian subspace Γ⊥ given samples of X. Vectors in Γ⊥ correspond to ‘interesting’ directions, whereas vectors in Γ correspond to the directions where data is very noisy. The most interesting applications of the NGCA model is for the case when the magnitude of the noise is comparable to that of the true signal, a setting in which traditional noise reduction techniques such as PCA don’t apply directly. NGCA is also related to dimension reduction and to other data analysis problems such as ICA. NGCA-like problems have been studied in statistics for a long time using techniques such as projection pursuit. We give an algorithm that takes polynomial time in the dimension n and has an inverse polynomial dependence on the error parameter measuring the angle distance between the non-Gaussian subspace and the subspace output by the algorithm. Our algorithm is based on relative entropy as the contrast function and fits under the projection pursuit framework. The techniques we develop for analyzing our algorithm maybe of use for other related problems.
Searches for extra spatial dimensions with the CMS detector at the LHC

The success of the first three years of operations of the CERN Large Hadron Collider (LHC) at center-of-mass energies of 7 TeV and 8 TeV radically changed the landscape of searches for new physics beyond the Standard Model (BSM) and our very way of thinking about its possible origin and its hiding place. Among the paradigms of new physics that have been probed quite extensively at the LHC, are various models that predict the existence of extra spatial dimensions. In this review, the current status of searches for extra dimensions with the Compact Muon Solenoid (CMS) detector is presented, along with prospects for future searches at the full energy of the LHC, expected to be reached in the next few years.
Input design for system identification via convex relaxation

We consider the problem of designing an excitation input for a system idenfication experiment. The optimization problem considered is to maximize a reduced Fisher information matrix in any of the classical D-, E-, or A-optimal senses. In contrast to the majority of published work on this topic, we consider the problem in the time domain and subject to constraints on the amplitude of the input signal. This optimization problem is nonconvex. The main result of the paper is a convex relaxation that gives an upper bound accurate to within 2/π of the true maximum. A randomized algorithm is presented for finding a feasible solution which, in a certain sense is expected to be at least 2/π as informative as the globally optimal input signal. In the case of a single constraint on input power, the proposed approach recovers the true global optimum exactly. Extensions to situations with both power and amplitude constraints on both inputs and outputs are given. A simple simulation example illustrates the technique.
Solar Core Homology, Solar Neutrinos, and Helioseismology

Precise numerical standard solar models (SSMs) now agree with one another and with helioseismological observations in the convective and outer radiative zones. Nevertheless, these models obscure how luminosity, neutrino production, and g-mode core helioseismology depend on such inputs as opacity and nuclear cross sections. Although the Sun is not homologous, its inner core by itself is chemically evolved and almost homologous, because of its compactness, radiative energy transport, and hydrogen-burning—dominated luminosity production. We apply luminosity-fixed homology transformations to the core to estimate theoretical uncertainties in the SSM and to obtain a broad class of non-SSMs, parameterized by central temperature and density and purely radiative energy transport in the core.
Fuel-Efficient Powered Descent Guidance on Large Planetary Bodies via Theory of Functional Connections

In this paper we present a new approach to solve the fuel-efficient powered descent guidance problem on large planetary bodies with no atmosphere (e.g., Moon or Mars) using the recently developed Theory of Functional Connections. The problem is formulated using the indirect method which casts the optimal guidance problem as a system of nonlinear two-point boundary value problems. Using the Theory of Functional Connections, the problem’s linear constraints are analytically embedded into a functional, which maintains a free-function that is expanded using orthogonal polynomials with unknown coefficients. The constraints are always analytically satisfied regardless of the values of the unknown coefficients (e.g., the coefficients of the free-function) which converts the two-point boundary value problem into an unconstrained optimization problem. This process reduces the whole solution space into the admissible solution subspace satisfying the constraints and, therefore, simpler, more accurate, and faster numerical techniques can be used to solve it. In this paper a nonlinear least-squares method is used. In addition to the derivation of this technique, the method is validated in two scenarios and the results are compared to those obtained by the general purpose optimal control software, GPOPS-II. In general, the proposed technique produces solutions of $\mathcal {O}(10^{-10})$ accuracy. Additionally, for the proposed test cases, it is reported that each individual TFC-based inner-loop iteration converges within 6 iterations, each iteration exhibiting a computational time between 72 and 81 milliseconds, with a total execution time of 2.1 to 2.6 seconds using MATLAB. Consequently, the proposed methodology is potentially suitable for real-time computation of optimal trajectories.
A recipe for free-energy functionals of polarizable molecular fluids

Classical density-functional theory is the most direct approach to equilibrium structures and free energies of inhomogeneous liquids, but requires the construction of an approximate free-energy functional for each liquid of interest. We present a general recipe for constructing functionals for small-molecular liquids based only on bulk experimental properties and ab initio calculations of a single solvent molecule. This recipe combines the exact free energy of the non-interacting system with fundamental measure theory for the repulsive contribution and a weighted density functional for the short-ranged attractive interactions. We add to these ingredients a weighted polarization functional for the long-range correlations in both the rotational and molecular-polarizability contributions to the dielectric response. We also perform molecular dynamics calculations for the free energy of cavity formation and the high-field dielectric response, and show that our free-energy functional adequately describes these properties (which are key for accurate solvation calculations) for all three solvents in our study: water, chloroform, and carbon tetrachloride.
The short toric polynomial

We introduce the short toric polynomial associated to a graded Eulerian poset. This polynomial contains the same information as the two toric polynomials introduced by Stanley, but allows different algebraic manipulations. The intertwined recurrence defining Stanley's toric polynomials may be replaced by a single recurrence, in which the degree of the discarded terms is independent of the rank. A short toric variant of the formula by Bayer and Ehrenborg, expressing the toric $h$-vector in terms of the $cd$-index, may be stated in a rank-independent form, and it may be shown using weighted lattice path enumeration and the reflection principle. We use our techniques to derive a formula expressing the toric $h$-vector of a dual simplicial Eulerian poset in terms of its $f$-vector. This formula implies Gessel's formula for the toric $h$-vector of a cube, and may be used to prove that the nonnegativity of the toric $h$-vector of a simple polytope is a consequence of the Generalized Lower Bound Theorem holding for simplicial polytopes.
Patterns of galaxy spin directions in SDSS and Pan-STARRS show parity violation and multipoles

The distribution of spin directions of $\sim 6.4\cdot 10^{4}$ SDSS spiral galaxies with spectra was examined, and compared to the distribution of $\sim 3.3\cdot 10^{4}$ Pan-STARRS galaxies. The analysis shows a statistically significant asymmetry between the number of SDSS galaxies with opposite spin directions, and the magnitude and direction of the asymmetry changes with the direction of observation and with the redshift. The redshift dependence shows that the distribution of the spin direction of SDSS galaxies becomes more asymmetric as the redshift gets higher. Fitting the distribution of the galaxy spin directions to a quadrupole alignment provides fitness with statistical significance $>5\sigma $ , which grows to $>8\sigma $ when just galaxies with $z>0.15$ are used. Similar analysis with Pan-STARRS galaxies provides dipole and quadrupole alignments nearly identical to the analysis of SDSS galaxies, showing that the source of the asymmetry is not necessarily a certain unknown flaw in a specific telescope system. While these observations are clearly provocative, there is no known error that could exhibit itself in such form. The data analysis process is fully automatic, and uses deterministic and symmetric algorithms with defined rules. It does not involve either manual analysis that can lead to human perceptual bias, or machine learning that can capture human biases or other subtle differences that are difficult to identify due to the complex nature of machine learning processes. Also, an error in the galaxy annotation process is expected to show consistent bias in all parts of the sky, rather than change with the direction of observation to form a clear and definable pattern.
Information of Structures in Galaxy Distribution

We introduce an information-theoretic measure, the Renyi information, to describe the galaxy distribution in space. We discuss properties of the information measure and demonstrate its relationship with the probability distribution function and multifractal descriptions. Using the First Look Survey galaxy samples observed by the Infrared Array Camera on board the Spitzer Space Telescope, we present measurements of the Renyi information, as well as the counts-in-cells distribution and multifractal properties of galaxies in mid-infrared wavelengths. Guided by a multiplicative cascade simulation based on a binomial model, we verify our measurements and discuss the spatial selection effects on measuring information of the spatial structures. We derive structure scan functions at scales where selection effects are small for the Spitzer samples. We discuss the results and the potential of applying the Renyi information to the measurement of other spatial structures.
Marginal Breaking of Conformal SUSY QCD

We provide an example of a 4D theory that exhibits the Contino-Pomarol-Rattazzi mechanism, where breaking conformal symmetry by an almost marginal operator leads to a light pseudo-Goldstone boson, the dilaton, and a parametrically suppressed contribution to vacuum energy. We consider SUSY QCD at the edge of the conformal window and break conformal symmetry by weakly gauging a subgroup of the flavor symmetry. Using Seiberg duality we show that for a range of parameters the singlet meson in the dual theory reaches the unitarity bound, however, this theory does not have a stable vacuum. We stabilize the vacuum with soft breaking terms, compute the mass of the dilaton, and determine the range of parameters where the leading contribution to the dilaton mass is from the almost marginal coupling.
Autonomous quantum state transfer by dissipation engineering

This work shows that a quantum state can be transferred between stationary qubits without time dependent control, by tailoring dissipation in an open quantum system. The minimum system dimension for transferring one qubit of information proves to be 3 x 2 (between one physical qutrit and one physical qubit), plus one auxiliary reservoir.
ALMA Thermal Observations of Europa

We present four daytime thermal images of Europa taken with the Atacama Large Millimeter Array. Together, these images comprise the first spatially resolved thermal data set with complete coverage of Europa's surface. The resulting brightness temperatures correspond to a frequency of 233 GHz (1.3 mm) and a typical linear resolution of roughly 200 km. At this resolution, the images capture spatially localized thermal variations on the scale of geologic and compositional units. We use a global thermal model of Europa to simulate the ALMA observations in order to investigate the thermal structure visible in the data. Comparisons between the data and model images suggest that the large-scale daytime thermal structure on Europa largely results from bolometric albedo variations across the surface. Using bolometric albedos extrapolated from Voyager measurements, a homogenous model reproduces these patterns well, but localized discrepancies exist. These discrepancies can be largely explained by spatial inhomogeneity of the surface thermal properties. Thus, we use the four ALMA images to create maps of the surface thermal inertia and emissivity at our ALMA wavelength. From these maps, we identify a region of either particularly high thermal inertia or low emissivity near 90° west and 23° north, which appears anomalously cold in two of our images.
Interpreting Short Gamma-Ray Burst Progenitor Kicks and Time Delays using the Host Galaxy-Dark Matter Halo Connection

Nearly 20% of short gamma-ray bursts (sGRBs) have no observed host galaxies. Combining this finding with constraints on galaxies' dark matter halo potential wells gives strong limits on the natal kick velocity distribution for sGRB progenitors. For the best-fitting velocity distribution, one in five sGRB progenitors receives a natal kick above 150 km s–1, consistent with merging neutron star models but not with merging white dwarf binary models. This progenitor model constraint is robust to a wide variety of systematic uncertainties, including the sGRB progenitor time-delay model, the Swift redshift sensitivity, and the shape of the natal kick velocity distribution. We also use constraints on the galaxy-halo connection to determine the host halo and host galaxy demographics for sGRBs, which match extremely well with available data. Most sGRBs are expected to occur in halos near 1012 M ☉ and in galaxies near 5 × 1010 M ☉ (L *); unobserved faint and high-redshift host galaxies contribute a small minority of the observed hostless sGRB fraction. We find that sGRB redshift distributions and host galaxy stellar masses weakly constrain the progenitor time-delay model; the active versus passive fraction of sGRB host galaxies may offer a stronger constraint. Finally, we discuss how searches for gravitational wave optical counterparts in the local universe can reduce follow-up times using these findings.
Low rank estimation of smooth kernels on graphs

Let $(V,A)$ be a weighted graph with a finite vertex set $V$, with a symmetric matrix of nonnegative weights $A$ and with Laplacian $\Delta$. Let $S_{\ast}: V\times V\mapsto{\mathbb{R}}$ be a symmetric kernel defined on the vertex set $V$. Consider $n$ i.i.d. observations $(X_{j},X_{j}',Y_{j})$, $j=1,\ldots,n$, where $X_{j}$, $X_{j}'$ are independent random vertices sampled from the uniform distribution in $V$ and $Y_{j}\in{\mathbb{R}}$ is a real valued response variable such that ${\mathbb{E}}(Y_{j}|X_{j},X_{j}')=S_{\ast}(X_{j},X_{j}')$, $j=1,\ldots,n$. The goal is to estimate the kernel $S_{\ast}$ based on the data $(X_{1},X_{1}',Y_{1}),\ldots,(X_{n},X_{n}',Y_{n})$ and under the assumption that $S_{\ast}$ is low rank and, at the same time, smooth on the graph (the smoothness being characterized by discrete Sobolev norms defined in terms of the graph Laplacian). We obtain several results for such problems including minimax lower bounds on the $L_{2}$-error and upper bounds for penalized least squares estimators both with nonconvex and with convex penalties.
Simple rules for a more inclusive economy

This paper explores some of the reasons why capitalism experiences periodic crises of legitimacy and asks whether Richard Epstein’s “simple rules” heuristic can help. The current legitimacy problem is exacerbated by the fact that we are also in a low growth situation. This means that some policy instruments that could have been used to increase legitimacy may no longer be available. The “simple rules” heuristic can help as a guide to reforms that would simultaneously address the legitimacy problem, while avoiding making the growth problem worse.
Evolution of Stellar Collision Products in Globular Clusters. I. Head-on Collisions

We explore the evolution of collisionally merged stars in the blue straggler region of the H-R diagram. The starting models for our stellar evolution calculations are the results of the smoothed particle hydrodynamics (SPH) simulations of parabolic collisions between main-sequence stars performed by Lombardi, Rasio, & Shapiro. Since SPH and stellar evolution codes employ different and often contradictory approximations, it is necessary to treat the evolution of these products carefully. The mixture and disparity of the relevant timescales (hydrodynamic, thermal relaxation, and nuclear burning) and of the important physical assumptions between the codes makes the combined analysis of the problem challenging, especially during the initial thermal relaxation of the star. In particular, the treatment of convection is important and semiconvection must be modeled in some detail. The products of seven head-on collisions are evolved through their initial thermal relaxation and then through the main-sequence phase to the base of the giant branch. Their evolutionary tracks are presented. In contrast to what was assumed in previous work, these collision products do not develop substantial convective regions during their thermal relaxation and therefore are not mixed significantly after the collision.
Conserved momenta of a ferromagnetic soliton

Abstract Linear and angular momenta of a soliton in a ferromagnet are commonly derived through the application of Noether’s theorem. We show that these quantities exhibit unphysical behavior: they depend on the choice of a gauge potential in the spin Lagrangian and can be made arbitrary. To resolve this problem, we exploit a similarity between the dynamics of a ferromagnetic soliton and that of a charged particle in a magnetic field. For the latter, canonical momentum is also gauge-dependent and thus unphysical; the physical momentum is the generator of magnetic translations, a symmetry combining physical translations with gauge transformations. We use this analogy to unambiguously define conserved momenta for ferromagnetic solitons. General considerations are illustrated on simple models of a domain wall in a ferromagnetic chain and of a vortex in a thin film.
Topology of quadrature domains

We address the problem of topology of quadrature domains, namely we give upper bounds on the connectivity of the domain in terms of the number of nodes and their multiplicities in the quadrature identity.
Path algebras, wave-particle duality, and quantization of phase space

Semigroup algebras admit certain ‘coherent’ deformations which, in the special case of a path algebra, may associate a periodic function to an evolving path; for a particle moving freely on a straight line after an initial impulse, the wave length is that hypothesized by de Broglie’s wave-particle duality. This theory leads to a model of “physical” phase space of which mathematical phase space, the cotangent bundle of configuration space, is a projection. This space is singular, quantized at the Planck level, its structure implies the existence of spin, and the spread of a packet can be described as a random walk. The wavelength associated to a particle moving in this space need not be constant and its phase can change discontinuously.
Learning to See Forces: Surgical Force Prediction with RGB-Point Cloud Temporal Convolutional Networks

Robotic surgery has been proven to offer clear advantages during surgical procedures, however, one of the major limitations is obtaining haptic feedback. Since it is often challenging to devise a hardware solution with accurate force feedback, we propose the use of “visual cues” to infer forces from tissue deformation. Endoscopic video is a passive sensor that is freely available, in the sense that any minimally-invasive procedure already utilizes it. To this end, we employ deep learning to infer forces from video as an attractive low-cost and accurate alternative to typically complex and expensive hardware solutions. First, we demonstrate our approach in a phantom setting using the da Vinci Surgical System affixed with an OptoForce sensor. Second, we then validate our method on an ex vivo liver organ. Our method results in a mean absolute error of 0.814 N in the ex vivo study, suggesting that it may be a promising alternative to hardware based surgical force feedback in endoscopic procedures.
Life at high Deborah number

In many biological systems, microorganisms swim through complex polymeric fluids, and usually deform the medium at a rate faster than the inverse fluid relaxation time. We address the basic properties of such life at high Deborah number analytically by considering the small-amplitude swimming of a body in an arbitrary complex fluid. Using asymptotic analysis and differential geometry, we show that for a given swimming gait, the time-averaged leading-order swimming kinematics of the body can be expressed as an integral equation on the solution to a series of simpler Newtonian problems. We then use our results to demonstrate that Purcell's scallop theorem, which states that time-reversible body motion cannot be used for locomotion in a Newtonian fluid, breaks down in polymeric fluid environments.
Dimensionless units in the SI

The International System of Units (SI) is supposed to be coherent. That is, when a combination of units is replaced by an equivalent unit, there is no additional numerical factor. Here we consider dimensionless units as defined in the SI, e.g. angular units like radians or steradians and counting units like radioactive decays or molecules. We show that an incoherence may arise when different units of this type are replaced by a single dimensionless unit, the unit 'one', and suggest how to properly include such units into the SI in order to remove the incoherence. In particular, we argue that the radian is the appropriate coherent unit for angles and that hertz is not a coherent unit in the SI. We also discuss how including angular and counting units affects the fundamental constants.
Size and Strength of Self-excited Dynamos in Jupiter-like Extrasolar Planets

The magnetization of solar and extrasolar gas giants is critically dependent on the electronic and mass transport coefficients of their convective fluid interiors. We analyze recent laboratory experimental results on metallic hydrogen to derive a new conductivity profile for the Jovian-like planets. We combine this revised conductivity with a polytropic-based thermodynamic equation of state to study the dynamo action in 100 extrasolar giant planets varying from synchronous hot Jupiters to fast rotators, with masses ranging from 0.3 M J to 15 M J. We find dynamo cores larger than previous estimates, but consistent with the results from Juno, suggesting that the field generation in the more massive planets might be shallow-seated. Our results reveal that most extrasolar giants are expected to possess dipole surface magnetic fields in the range of 0.1–10 Gauss. Assuming radio emission processes similar to our solar giants, the stronger emitters are expected to have maximal cyclotron frequencies between 20 and 40 MHz and for those within few 10 pc, few have flux densities greater than 1 mJy. Our work places new bounds on the observational detectability of extrasolar magnetic fields.
Exotic Ground States of Directional Pair Potentials via Collective-Density Variables

Collective-density variables have proved to be a useful tool in the prediction and manipulation of how spatial patterns form in the classical many-body problem. Previous work has employed properties of collective-density variables along with a robust numerical optimization technique to find the classical ground states of many-particle systems subject to radial pair potentials in one, two and three dimensions. That work led to the identification of ordered and disordered classical ground states. In this paper, we extend these collective-coordinate studies by investigating the ground states of directional pair potentials in two dimensions. Our study focuses on directional potentials whose Fourier representations are non-zero on compact sets that are symmetric with respect to the origin and zero everywhere else. We choose to focus on one representative set that has exotic ground-state properties: two circles whose centers are separated by some fixed distance. We obtain ground states for this “two-circle” potential that display large void regions in the disordered regime. As more degrees of freedom are constrained the ground states exhibit a collapse of dimensionality characterized by the emergence of filamentary structures and linear chains. This collapse of dimensionality has not been observed before in related studies.
Cycles in Random Meander Systems

A meander system is a union of two arc systems that represent non-crossing pairings of the set $$[2n] = \{1, \ldots , 2n\}$$ in the upper and lower half-plane. In this paper, we consider random meander systems. We show that for a class of random meander systems,—for simply-generated meander systems,—the number of cycles in a system of size n grows linearly with n and that the length of the largest cycle in a uniformly random meander system grows at least as $$c \log n$$ with $$c > 0$$ . We also present numerical evidence suggesting that in a simply-generated meander system of size n, (i) the number of cycles of length $$k \ll n$$ is $$\sim n k^{-\beta }$$ , where $$\beta \approx 2$$ , and (ii) the length of the largest cycle is $$\sim n^\alpha $$ , where $$\alpha $$ is close to 4/5. We compare these results with the growth rates in other families of meander systems, which we call rainbow meanders and comb-like meanders, and which show significantly different behavior.
Quantum nature of cosmological bounces

Several examples are known where quantum gravity effects resolve the classical big bang singularity by a bounce. The most detailed analysis has probably occurred for loop quantum cosmology of isotropic models sourced by a free, massless scalar. Once a bounce has been realized under fairly general conditions, the central questions are how strongly quantum it behaves, what influence quantum effects can have on its appearance, and what quantum space-time beyond the bounce may look like. This, then, has to be taken into account for effective equations which describe the evolution properly and can be used for further phenomenological investigations. Here, we provide the first analysis with interacting matter with new effective equations valid for weak self-interactions or small masses. They differ from the free scalar equations by crucial terms and have an important influence on the bounce and the space-time around it. Especially the role of squeezed states, which have often been overlooked in this context, is highlighted. The presence of a bounce is proven for uncorrelated states, but as squeezing is a dynamical property and may change in time, further work is required for a general conclusion.
Experimental data from a quantum computer verifies the generalized Pauli exclusion principle

“What are the consequences… that Fermi particles cannot get into the same state…” R. P. Feynman wrote of the Pauli exclusion principle, “In fact, almost all the peculiarities of the material world hinge on this wonderful fact.” In 1972 Borland and Dennis showed that there exist powerful constraints beyond the Pauli exclusion principle on the orbital occupations of Fermi particles, providing important restrictions on quantum correlation and entanglement. Here we use computations on quantum computers to experimentally verify the existence of these additional constraints. Quantum many-fermion states are randomly prepared on the quantum computer and tested for constraint violations. Measurements show no violation and confirm the generalized Pauli exclusion principle with an error of one part in one quintillion. The Pauli exclusion principle can be formulated in a generalized form where additional constraints are imposed to the orbital degrees of freedom of electrons. In this work these constraints are experimentally verified on a five qubit quantum computer with an error of one part in one quintillion.
Case studies of habitable Trojan planets in the system of HD 23079

We investigate the possibility of habitable Trojan planets in the HD 23079 star–planet system. This system consists of a solar-type star and a Jupiter-type planet, which orbits the star near the outer edge of the stellar habitable zone in an orbit of low eccentricity. We find that in agreement with previous studies Earth-mass habitable Trojan planets are possible in this system, although the success of staying within the zone of habitability is significantly affected by the orbital parameters of the giant planet and by the initial condition of the theoretical Earth-mass planet. In one of our simulations, the Earth-mass planet is captured by the giant planet and thus becomes a habitable moon.