cssi/SciSciGPT-SciSciNet huggingface dataset:
Alternative Gravity Rotation Curves for the LITTLE THINGS Survey

Galactic rotation curves have proven to be the testing ground for dark matter bounds in spiral galaxies of all morphologies. Dwarf galaxies serve as an increasingly interesting case of rotation curve dynamics due to their typically rising rotation curve as opposed to the flattening curve of large spirals. Dwarf galaxies usually vary in galactic structure and mostly terminate at small radial distances. This, coupled with the fact that Cold Dark Matter theories struggle with the universality of galactic rotation curves, allow for exclusive features of alternative gravitational models to be analyzed. Recently, The H i Nearby Galactic Survey (THINGS) has been extended to include a sample of 25 dwarf galaxies now known as the LITTLE THINGS Survey. Here, we show an application of alternative gravitational models to the LITTLE THINGS survey, specifically focusing on conformal gravity (CG) and Modified Newtonian Dynamics (MOND). In this work, we provide an analysis and discussion of the rotation curve predictions of each theory to the sample. Furthermore, we show how these two alternative gravitational models account for the recently observed universal trends in centripetal accelerations in spiral galaxies. This work highlights the similarities and differences of the predictions of the two theories in dwarf galaxies. The sample is not large or diverse enough to strongly favor a single theory, but we posit that both CG and MOND can provide an accurate description of the galactic dynamics in the LITTLE THINGS sample without the need for dark matter.
Renormalization flow, duality, and supersymmetry breaking in some N = 1 product-group theories

We discuss the renormalization group flow, duality, and supersymmetry breaking in N = 1 supersymmetric SU ( N ) × SU ( M ) gauge theories.
Deep-PowerX: a deep learning-based framework for low-power approximate logic synthesis

This paper aims at integrating three powerful techniques namely Deep Learning, Approximate Computing, and Low Power Design into a strategy to optimize logic at the synthesis level. We utilize advances in deep learning to guide an approximate logic synthesis engine to minimize the dynamic power consumption of a given digital CMOS circuit, subject to a predetermined error rate at the primary outputs. Our framework, Deep-PowerX1, focuses on replacing or removing gates on a technology-mapped network and uses a Deep Neural Network (DNN) to predict error rates at primary outputs of the circuit when a specific part of the netlist is approximated. The primary goal of Deep-PowerX is to reduce the dynamic power whereas area reduction serves as a secondary objective. Using the said DNN, Deep-PowerX is able to reduce the exponential time complexity of standard approximate logic synthesis to linear time. Experiments are done on numerous open source benchmark circuits. Results show significant reduction in power and area by up to 1.47× and 1.43× compared to exact solutions and by up to 22% and 27% compared to state-of-the-art approximate logic synthesis tools while having orders of magnitudes lower run-time.
Sample Efficient Reinforcement Learning via Low-Rank Matrix Estimation

We consider the question of learning $Q$-function in a sample efficient manner for reinforcement learning with continuous state and action spaces under a generative model. If $Q$-function is Lipschitz continuous, then the minimal sample complexity for estimating $\epsilon$-optimal $Q$-function is known to scale as ${\Omega}(\frac{1}{\epsilon^{d_1+d_2 +2}})$ per classical non-parametric learning theory, where $d_1$ and $d_2$ denote the dimensions of the state and action spaces respectively. The $Q$-function, when viewed as a kernel, induces a Hilbert-Schmidt operator and hence possesses square-summable spectrum. This motivates us to consider a parametric class of $Q$-functions parameterized by its "rank" $r$, which contains all Lipschitz $Q$-functions as $r \to \infty$. As our key contribution, we develop a simple, iterative learning algorithm that finds $\epsilon$-optimal $Q$-function with sample complexity of $\widetilde{O}(\frac{1}{\epsilon^{\max(d_1, d_2)+2}})$ when the optimal $Q$-function has low rank $r$ and the discounting factor $\gamma$ is below a certain threshold. Thus, this provides an exponential improvement in sample complexity. To enable our result, we develop a novel Matrix Estimation algorithm that faithfully estimates an unknown low-rank matrix in the $\ell_\infty$ sense even in the presence of arbitrary bounded noise, which might be of interest in its own right. Empirical results on several stochastic control tasks confirm the efficacy of our "low-rank" algorithms.
Quivers with loops and generalized crystals

In the context of varieties of representations of arbitrary quivers, possibly carrying loops, we define a generalization of Lusztig Lagrangian subvarieties. From the combinatorial study of their irreducible components arises a structure richer than the usual Kashiwara crystals. Along with the geometric study of Nakajima quiver varieties, in the same context, this yields a notion of generalized crystals, coming with a tensor product. As an application, we define the semicanonical basis of the Hopf algebra generalizing quantum groups, which was already equipped with a canonical basis. The irreducible components of the Nakajima varieties provide the family of highest weight crystals associated to dominant weights, as in the classical case.
Electromagnetic momentum in a dielectric and the energy-momentum tensor

The Abraham–Minkowski momentum controversy is the outwardly visible symptom of an inconsistency in the use of the energy–momentum tensor in the case of a plane quasimonochromatic field in a simple linear dielectric. We show that the Gordon form of the electromagnetic momentum is conserved in a thermodynamically closed system. We regard conservation of the components of the four-momentum in a thermodynamically closed system as a fundamental property of the energy–momentum tensor. Then the first row and column of the energy–momentum tensor is populated by the electromagnetic energy density and the Gordon momentum density. We derive new electromagnetic continuity equations for the electromagnetic energy and momentum that are based on the Gordon momentum density. These continuity equations can be represented in the energy–momentum tensor using a material four-divergence operator in which temporal differentiation is performed with respect to ct/n.
Zero-One Laws for Connectivity in Inhomogeneous Random Key Graphs

We introduce a new random key predistribution scheme for securing heterogeneous wireless sensor networks. Each of the $n$ sensors in the network is classified into $r$ classes according to some probability distribution $\boldsymbol {\mu }=\{\mu _{1},\ldots ,\mu _{r}\}$ . Before deployment, a class- $i$ sensor is assigned $K_{i}$ cryptographic keys that are selected uniformly at random from a common pool of $P$ keys. Once deployed, a pair of sensors can communicate securely if and only if they have a key in common. We model the communication topology of this network by a newly defined inhomogeneous random key graph. We establish scaling conditions on the parameters $P$ and $\{K_{1},\ldots , K_{r}\}$ so that this graph: 1) has no isolated nodes and 2) is connected, both with high probability. The results are given in the form of zero-one laws with the number of sensors $n$ growing unboundedly large; critical scalings are identified and shown to coincide for both graph properties. Our results are shown to complement and improve those given by Godehardt et al. and Zhao et al. for the same model, therein referred to as the general random intersection graph.
On thermalization of magnetic nano-arrays at fabrication

We propose a model to predict and control the statistical ensemble of magnetic degrees of freedom in artificial spin ice (ASI) during thermalized adiabatic growth?(Wang et al 2006 Nature 439 303; Morgan et al Nature Phys. 7 75). We predict that as-grown arrays are controlled by the temperature at fabrication and by their lattice constant, and that they can be described by an effective temperature. If the geometry is conducive to a phase transition, then the lowest-temperature phase is accessed in arrays of lattice constant smaller than a critical value, which depends on the temperature at deposition. Alternatively, for arrays of equal lattice constant, there is a temperature threshold at deposition and the lowest-temperature phase is accessed for fabrication temperatures larger rather than smaller than this temperature threshold. Finally, we show how to define and control the effective temperature of the as-grown array and how to measure critical exponents directly. We discuss the role of kinetics at the critical point, and applications to experiments, in particular to as-grown thermalized square ASI and to magnetic monopole crystallization in as-grown honeycomb ASI.
DRAKE EQUATION FOR THE MULTIVERSE: FROM THE STRING LANDSCAPE TO COMPLEX LIFE

It is argued that the selection criteria usually referred to as "anthropic conditions" for the existence of intelligent (typical) observers widely adopted in cosmology amount only to preconditions for primitive life. The existence of life does not imply in the existence of intelligent life. On the contrary, the transition from single-celled to complex, multicellular organisms is far from trivial, requiring stringent additional conditions on planetary platforms. An attempt is made to disentangle the necessary steps leading from a selection of universes out of a hypothetical multiverse to the existence of life and of complex life. It is suggested that what is currently called the "anthropic principle" should instead be named the "prebiotic principle."
Multi-element Abundance Measurements from Medium-resolution Spectra. I. The Sculptor Dwarf Spheroidal Galaxy

We present measurements of Fe, Mg, Si, Ca, and Ti abundances for 388 radial velocity member stars in the Sculptor dwarf spheroidal galaxy (dSph), a satellite of the Milky Way (MW). This is the largest sample of individual alpha element (Mg, Si, Ca, and Ti) abundance measurements in any single dSph. The measurements are made from Keck/Deep Imaging Multi-Object Spectrometer medium-resolution spectra (6400-9000 A, R approx 6500). Based on comparisons to published high-resolution (R approx> 20,000) spectroscopic measurements, our measurements have uncertainties of sigma[Fe/H] = 0.14 and sigma[alpha/Fe] = 0.13. The Sculptor [Fe/H] distribution has a mean ([Fe/H]) = -1.58 and is asymmetric with a long, metal-poor tail, indicative of a history of extended star formation. Sculptor has a larger fraction of stars with [Fe/H] < -2 than the MW halo. We have discovered one star with [Fe/H] = -3.80 +- 0.28, which is the most metal-poor star known anywhere except the MW halo, but high-resolution spectroscopy is needed to measure this star's detailed abundances. As has been previously reported based on high-resolution spectroscopy, [alpha/Fe] in Sculptor falls as [Fe/H] increases. The metal-rich stars ([Fe/H] approx -1.5) have lower [alpha/Fe] than Galactic halo field stars of comparable metallicity. This indicatesmore » that star formation proceeded more gradually in Sculptor than in the Galactic halo. We also observe radial abundance gradients of -0.030 +- 0.003 dex arcmin{sup -1} in [Fe/H] and +0.013 +- 0.003 dex arcmin{sup -1} in [alpha/Fe] out to 11 arcmin (275 pc). Together, these measurements cast Sculptor and possibly other surviving dSphs as representative of the dwarf galaxies from which the metal-poor tail of the Galactic halo formed.« less
Cascaded Stokes and anti-Stokes laser based on an optical resonator with a self-assembled organic monolayer

Due to their high circulating intensities, ultra-high quality factor dielectric whispering gallery mode resonators have enabled the development of low threshold Raman microlasers. Subsequently, other Raman-related phenomena, such as cascaded stimulated Raman scattering (CSRS) and stimulated anti-Stokes Raman scattering (SARS), were observed. While low threshold frequency conversion and generation have clear applications, CSRS and SARS have been limited by the low Raman gain. In this work, the surface of a silica resonator is modified with an organic monolayer, increasing the Raman gain. Up to four orders of CSRS are observed with sub-milliwatt (mW) input power, and the SARS efficiency is improved by three orders of magnitude compared to previous studies with hybrid resonators.
Automorphy and irreducibility of some l-adic representations

In this paper we prove that a pure, regular, totally odd, polarizable weakly compatible system of are irreducible.
Geometric Kinematic Control of a Spherical Rolling Robot

We give a geometric account of kinematic control of a spherical rolling robot controlled by two internal wheels just like the toy robot Sphero. Particularly, we introduce the notion of shape space and fibers to the system by exploiting its symmetry and the principal bundle structure of its configuration space; the shape space encodes the rotational angles of the wheels, whereas each fiber encodes the translational and rotational configurations of the robot for a particular shape. We show that the system is fiber controllable—meaning any translational and rotational configuration modulo shapes is reachable—as well as find exact expressions of the geometric phase or holonomy under some particular controls. We also solve an optimal control problem of the spherical robot, show that it is completely integrable, and find an explicit solution of the problem.
Degradation and healing in a generalized neo-Hookean solid due to infusion of a fluid

The mechanical response and load bearing capacity of high performance polymer composites changes due to degradation or healing associated with diffusion of a fluid, temperature, oxidation or the extent of the deformation. Hence, there is a need to study the response of bodies under such degradation/healing mechanisms. In this paper, we study the effect of degradation and healing due to the diffusion of a fluid on the response of a solid which prior to the diffusion can be described by the generalized neo-Hookean model. We show that a generalized neo-Hookean solid—which behaves like an elastic body (i.e., it does not produce entropy) within a purely mechanical context—creeps and stress relaxes due to degradation/healing when infused with a fluid and behaves like a body whose material properties are time dependent. We specifically investigate the torsion of a degrading/healing generalized neo-Hookean circular cylindrical annulus infused with a fluid. The equations of equilibrium for a generalized neo-Hookean solid are solved together with the convection–diffusion equation for the fluid concentration. Different boundary conditions for the fluid concentration are also considered. We also solve the problem for the case when the diffusivity of the fluid depends on the deformation of the generalized neo-Hookean solid.
Uniqueness of conformal Ricci flow using energy methods

We analyze an energy functional associated to Conformal Ricci Flow along closed manifolds with constant negative scalar curvature. Given initial conditions we use this functional to demonstrate the uniqueness of both the metric and the pressure function along Conformal Ricci Flow.
Vanishing largest Lyapunov exponent and Tsallis entropy

We present a geometric argument that explains why some systems having vanishing largest Lyapunov exponent have underlying dynamic aspects which can be effectively described by the Tsallis entropy. We rely on a comparison of the generalised additivity of the Tsallis entropy versus the ordinary additivity of the BGS entropy. We translate this comparison, in metric terms, by using an effective hyperbolic metric on the configuration/phase space for the Tsallis entropy versus the Euclidean one in the case of the BGS entropy. Solving the Jacobi equation for such hyperbolic metrics effectively sets the largest Lyapunov exponent computed, with respect to the corresponding Euclidean metric, to zero. This conclusion is in agreement with all currently known results on systems that have a simple asymptotic behaviour, and are described by the Tsallis entropy.
A method for large-scale implantation of 3D microdevice ensembles into brain and soft tissue.

Wireless networks of implantable electronic sensors and actuators at the microscale (sub-mm) level are being explored for monitoring and modulation of physiological activity for medical diagnostics and therapeutic purposes. Beyond the requirement of integrating multiple electronic or chemical functions within small device volumes, a key challenge is the development of high-throughput methods for the implantation of large numbers of microdevices into soft tissues with minimal damage. To that end, we have developed a method for high-throughput implantation of ~100–200 µm size devices, which are here simulated by proxy microparticle ensembles. While generally applicable to subdermal tissue, our main focus and experimental testbed is the implantation of microparticles into the brain. The method deploys a scalable delivery tool composed of a 2-dimensional array of polyethylene glycol-tipped microneedles that confine the microparticle payloads. Upon dissolution of the bioresorbable polyethylene glycol, the supporting array structure is retrieved, and the microparticles remain embedded in the tissue, distributed spatially and geometrically according to the design of the microfabricated delivery tool. We first evaluated the method in an agarose testbed in terms of spatial precision and throughput for up to 1000 passive spherical and planar microparticles acting as proxy devices. We then performed the same evaluations by implanting particles into the rat cortex under acute conditions and assessed the tissue injury produced by our method of implantation under chronic conditions. A low-injury, high-throughput technique to embed neural interfaces into brain tissue brings the idea of a ‘smart body’ closer to home. While some research groups focus on miniaturizing sensors and bio-actuators to implantable sizes, Brown University’s Stefan Sigurdsson and a team of US researchers have developed a technique to embed these devices into cortical tissue. In their method, microparticles (used in lieu of functional implants) are suspended in super-thin needles of polyethylene glycol, which are driven into the brain at high speed to minimize tissue damage. The polyethylene glycol is absorbed into the brain and the injection apparatus is removed, leaving the implants behind. The method can be scaled for rapid implantation of high numbers of devices and could see use in the development of human-computer integrations.
Control of optical properties of hybrid materials with chirped femtosecond laser pulses under strong coupling conditions

The interaction of chirped femtosecond laser pulses with hybrid materials—materials comprised of plasmon sustaining structures and resonant molecules—is scrutinized using a self-consistent model of coupled Maxwell-Bloch equations. The optical properties of such systems are examined with the example of periodic sinusoidal gratings. It is shown that under strong coupling conditions one can control light transmission using chirped pulses in a spatiotemporal manner. The temporal origin of control relies on chirps non-symmetric in time while the space control is achieved via spatial localization of electromagnetic energy due to plasmon resonances.
RECONSIDERING THE EFFECTS OF LOCAL STAR FORMATION ON TYPE Ia SUPERNOVA COSMOLOGY

Recent studies found a correlation with $\sim$3 sigma significance between the local star formation measured by GALEX in Type Ia supernova (SN Ia) host galaxies and the distances or dispersions derived from these SNe. We search for these effects by using data from recent cosmological analyses to greatly increase the SN Ia sample; we include 179 GALEX-imaged SN Ia hosts with distances from the JLA and Pan-STARRS SN Ia cosmology samples and 157 GALEX-imaged SN Ia hosts with distances from the Riess et al. (2011) H$_0$ measurement. We find little evidence that SNe Ia in locally star-forming environments are fainter after light curve correction than SNe Ia in locally passive environments. We find a difference of only 0.000$\pm$0.018 (stat+sys) mag for SNe fit with SALT2 and 0.029$\pm$0.027 (stat+sys) mag for SNe fit with MLCS2k2 (R$_V$ = 2.5), which suggests that proposed changes to recent measurements of H$_0$ and w are not significant and numerically smaller than the parameter measurement uncertainties. We find the greatly reduced significance of these distance modulus differences compared to Rigault et al. (2013) and Rigault et al. (2015) result from two improvements with fairly equal effects, our larger sample size and the use of JLA and Riess et al. (2011) sample selection criteria. Without these improvements, we recover the results of Rigault et al. (2015). We find that both populations have more similar dispersion in distance than found by Rigault et al. (2013), Rigault et al. (2015), and Kelly et al. (2015), with slightly smaller dispersion for locally passive SNe Ia fit with MLCS, the opposite of the effect seen by Rigault et al. (2015) and Kelly et al. (2015). We caution that measuring local SNe Ia environments in the future may require a higher-resolution instrument than GALEX and that SN sample selection has a significant effect on local star formation biases.
The critical exponent for generalized doubly nonnegative matrices

It is known that the critical exponent (CE) for conventional, continuous powers of n-by-n doubly nonnegative (DN) matrices is . Here, we consider the larger class of diagonalizable, entrywise nonnegative n-by-n matrices with nonnegative eigenvalues (generalized doubly nonnegative (GDN)). We show that, again, a CE exists and is able to bind with a low-coefficient quadratic. However, the CE is larger than in the DN case; in particular, 2 for . There seems to be a connection with the index of primitivity, and a number of other observations are made and questions raised. It is shown that there is no CE for continuous Hadamard powers of GDN matrices, despite it also being for DN matrices.
Infrared Emission from Kilonovae: The Case of the Nearby Short Hard Burst GRB 160821B

We present constraints on Ks-band emission from one of the nearest short hard gamma-ray bursts, GRB 160821B, at z = 0.16, at three epochs. We detect a red relativistic afterglow from the jetted emission in the first epoch but do not detect any excess kilonova emission in the second two epochs. We compare upper limits obtained with Keck I/MOSFIRE to multi-dimensional radiative transfer models of kilonovae, that employ composition-dependent nuclear heating and LTE opacities of heavy elements. We discuss eight models that combine toroidal dynamical ejecta and two types of wind and one model with dynamical ejecta only. We also discuss simple, empirical scaling laws of predicted emission as a function of ejecta mass and ejecta velocity. Our limits for GRB 160821B constrain the ejecta mass to be lower than 0.03 M⊙ for velocities greater than 0.1 c. At the distance sensitivity range of advanced LIGO, similar ground-based observations would be sufficiently sensitive to the full range of predicted model emission including models with only dynamical ejecta. The color evolution of these models shows that I–K color spans 7–16 mag, which suggests that even relatively shallow infrared searches for kilonovae could be as constraining as optical searches.
Probing the Structure of Accreting Compact Sources through X-Ray Time Lags and Spectra

We exhibit, by compiling all data sets we can acquire, that the Fourier-frequency-dependent, hard X-ray lags, first observed in the analysis of aperiodic variability of the light curves of the black hole candidate Cyg X-1, appear to be a property shared by several other accreting black hole candidate sources and also by the different spectral states of this source. We then present both analytic and numerical models of these time lags resulting by the process of Comptonization in a variety of hot electron configurations. We argue that, under the assumption that the observed spectra are due to Comptonization, the dependence of the lags on the Fourier period provides a means for mapping the spatial density profile of the hot electron plasma, while the period at which the lags eventually level off provides an estimate of the size of the scattering cloud. We further examine the influence of the location and spatial extent of the soft photon source on the form of the resulting lags for a variety of configurations; we conclude that the study of the X-ray hard lags can provide clues about these parameters of the Comptonization process, too. Fits of the existing data with our models indicate that the size of the Comptonizing clouds are quite large in extent (~1 lt-s) with inferred radial density profiles that are in many instances inconsistent with those of the standard dynamical models, whereas the extent of the source of soft photons appears to be much smaller than those of the hot electrons by roughly 2 orders of magnitude and its location consistent with the center of the hot electron corona.
Flat structures on surface bundles

We show that there exist flat surface bundles with closed leaves having nontrivial normal bundles. This leads us to compute the abelianisation of surface diffeomorphism groups with marked points. We also extend a formula of Tsuboi that expresses the Euler class of a flat circle bundle in terms of the Calabi invariant of certain Hamiltonian diffeomorphisms to surfaces of higher genus and derive a similar formula for the first MMM‐class of surface bundles with punctured fibre. 37E30, 57R30, 57R50; 57R17 In this paper we study properties of the horizontal foliations of certain kinds of flat bundles. The paper divides into two main parts, the first of which is concerned with closed leaves of flat surface bundles and the second of which deals with fillings of flat circle bundles.
Future Prospects for Ground-based Gravitational-wave Detectors: The Galactic Double Neutron Star Merger Rate Revisited

We present the Galactic merger rate for double neutron star (DNS) binaries using the observed sample of eight DNS systems merging within a Hubble time. This sample includes the recently discovered, highly relativistic DNS systems J1757$-$1854 and J1946+2052, and is approximately three times the sample size used in previous estimates of the Galactic merger rate by Kim et al. Using this sample, we calculate the vertical scale height for DNS systems in the Galaxy to be $z_0 = 0.4 \pm 0.1$ kpc. We calculate a Galactic DNS merger rate of $\mathcal{R}_{\rm MW} = 42^{+30}_{-14}$ Myr$^{-1}$ at the 90% confidence level. The corresponding DNS merger detection rate for Advanced LIGO is $\mathcal{R}_{\rm LIGO} = 0.18^{+0.13}_{-0.06} \times \left( D_{\rm r}/100 \ \rm Mpc \right)^3 \rm yr^{-1}$, where $D_{\rm r}$ is the range distance. Using this merger detection rate and the predicted range distance of 120$-$170 Mpc for the third observing run of LIGO (Laser Interferometer Gravitational-wave Observatory, Abbott et al.), we predict, accounting for 90% confidence intervals, that LIGO$-$Virgo will detect anywhere between zero and two DNS mergers. We explore the effects of the underlying pulsar population properties on the merger rate and compare our merger detection rate with those estimated using different formation and evolutionary scenario of DNS systems. As we demonstrate, reconciling the rates is sensitive to assumptions about the DNS population, including its radio pulsar luminosity function. Future constraints from further gravitational wave DNS detections and pulsar surveys anticipated in the near future should permit tighter constraints on these assumptions.
Approximation Algorithms for Optimization of Combinatorial Dynamical Systems

We consider an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide computationally tractable solution methods even when the dimension of the system and the number of the binary variables are large. The proposed method employs a linear approximation of the objective function such that the approximate problem is defined over the feasible space of the binary decision variables, which is a discrete set. To define such a linear approximation, we propose two different variation methods: one uses continuous relaxation of the discrete space and the other uses convex combinations of the vector field and running payoff. The approximate problem is a 0-1 linear program, which can be solved by existing polynomial-time exact or approximation algorithms, and does not require the solution of the dynamical system. Furthermore, we characterize a sufficient condition ensuring the approximate solution has a provable suboptimality bound. We show that this condition can be interpreted as the concavity of the objective function or that of a reformulated objective function.
Effects of Collisions with Rocky Planets on the Properties of Hot Jupiters

ABSTRACT.Observed hot Jupiters exhibit a wide range of physical properties. For a given mass, many planets have inflated radii, while others are surprisingly compact and may harbor large central cores. Motivated by the observational sample, this article considers possible effects from collisions of smaller rocky planets with gas giant planets. In this scenario, the Jovian planets migrate first and enter into ∼4∼4 day orbits, whereas rocky planets (mass mp = 0.1–20 M⊕mass mp=0.1–20 M⊕) migrate later and then encounter the gaseous giants. Previous work indicates that the collision rates are high for such systems. This paper calculates the trajectories of incoming rocky planets as they orbit within the gaseous planets and are subjected to gravitational, frictional, and tidal forces. These collisions always increase the metallicity of the Jovian planets. If the incoming rocky bodies survive tidal destruction and reach the central regions, they provide a means of producing large planetary cores. Both the adde...
Splittings of non-finitely generated groups

In geometric group theory one uses group actions on spaces to gain information about groups. One natural space to use is the Cayley graph of a group. The Cayley graph arguments that one encounters tend to require local finiteness, and hence finite generation of the group. In this paper, I take the theory of intersection numbers of splittings of finitely generated groups (as developed by Scott, Swarup, Niblo and Sageev), and rework it to remove finite generation assumptions. I show that when working with splittings, instead of using the Cayley graph, one can use Bass–Serre trees.
Brief, embedded, spontaneous metacognitive talk indicates thinking like a physicist

Citation: Sayre, E. C., & Irving, P. W. (2015). Brief, embedded, spontaneous metacognitive talk indicates thinking like a physicist. Physical Review Special Topics-Physics Education Research, 11(2), 17. doi:10.1103/PhysRevSTPER.11.020121
Plausible Compositions of the Seven TRAPPIST-1 Planets Using Long-term Dynamical Simulations

TRAPPIST-1 is a nearby ultra-cool dwarf that is host to a remarkable planetary system consisting of seven transiting planets. The orbital properties and radii of the planets have been well constrained, and recently, the masses of the inner six planets have been measured with additional ground- and space-based photometric observations. Large uncertainties in these mass measurements have prevented a robust analysis of the planetary compositions. Here, we perform many thousands of N-body dynamical simulations with planet properties perturbed from the observed values and identify those that are stable for millions of years. This allows us to identify self-consistent orbital solutions that can be used in future studies. From our range of dynamical masses, we find that most of the planets are consistent with an Earth-like composition, where TRAPPIST-1f is likely to have a volatile-rich envelope.
The average number of divisors of the Euler function

The upper bound and the lower bound of the average number of divisors of Euler Phi function and Carmichael Lambda function were obtained by Luca and Pomerance (see Publ Math Debr 70(1–2):125–148, 2007). We improve the lower bound and provide a heuristic argument which suggests that the upper bound given by Luca and Pomerance (Publ Math Debr 70(1–2):125–148, 2007) is indeed close to the truth.
Searching for new physics with ultrahigh energy cosmic rays

Ultrahigh energy cosmic rays that produce giant extensive showers of charged particles and photons when they interact in the Earth's atmosphere provide a unique tool to search for new physics. Of particular interest is the possibility of detecting a very small violation of Lorentz invariance such as may be related to the structure of space-time near the Planck scale of approximately 10 (exp -35) m. We discuss here the possible signature of Lorentz invariance violation on the spectrum of ultrahigh energy cosmic rays as compared with present observations of giant air showers. We also discuss the possibilities of using more sensitive detection techniques to improve searches for Lorentz invariance violation in the future. Using the latest data from the Pierre Auger Observatory, we derive a best fit to the LIV parameter of 3 .0 + 1.5 - 3:0 x 10 (exp -23) ,corresponding to an upper limit of 4.5 x 10-23 at a proton Lorentz factor of approximately 2 x 10(exp 11) . This result has fundamental implications for quantum gravity models.
A Mixed Discontinuous Galerkin Method Without Interior Penalty for Time-Dependent Fourth Order Problems

A novel discontinuous Galerkin (DG) method is developed to solve time-dependent bi-harmonic type equations involving fourth derivatives in one and multiple space dimensions. We present the spatial DG discretization based on a mixed formulation and central interface numerical fluxes so that the resulting semi-discrete schemes are $$L^2$$ stable even without interior penalty. For time discretization, we use Crank–Nicolson so that the resulting scheme is unconditionally stable and second order in time. We present the optimal $$L^2$$ error estimate of $$O(h^{k+1})$$ for polynomials of degree k for semi-discrete DG schemes, and the $$L^2$$ error of $$O(h^{k+1} +(\Delta t)^2)$$ for fully discrete DG schemes. Extensions to more general fourth order partial differential equations and cases with non-homogeneous boundary conditions are provided. Numerical results are presented to verify the stability and accuracy of the schemes. Finally, an application to the one-dimensional Swift–Hohenberg equation endowed with a decay free energy is presented.
An efficient k-means-type algorithm for clustering datasets with incomplete records

The $k$-means algorithm is arguably the most popular nonparametric clustering method but cannot generally be applied to datasets with incomplete records. The usual practice then is to either impute missing values under an assumed missing-completely-at-random mechanism or to ignore the incomplete records, and apply the algorithm on the resulting dataset. We develop an efficient version of the $k$-means algorithm that allows for clustering in the presence of incomplete records. Our extension is called $k_m$-means and reduces to the $k$-means algorithm when all records are complete. We also provide initialization strategies for our algorithm and methods to estimate the number of groups in the dataset. Illustrations and simulations demonstrate the efficacy of our approach in a variety of settings and patterns of missing data. Our methods are also applied to the analysis of activation images obtained from a functional Magnetic Resonance Imaging experiment.
Movie moves for singular link cobordisms in 4-dimensional space

Two singular links are cobordant if one can be obtained from the other by singular link isotopy together with a combination of births or deaths of simple unknotted curves, and saddle point transformations. A movie description of a singular link cobordism in 4-space is a sequence of singular link diagrams obtained from a projection of the cobordism into 3-space by taking 2-dimensional cross-sections perpendicular to a fixed direction. We present a set of movie moves that are sufficient to connect any two movies of isotopic singular link cobordisms.
LOTIS search for early-time optical afterglows: GRB 971227

We report on the very early time search for an optical afterglow from GRB 971227 with the Livermore Optical Transient Imaging System (LOTIS). LOTIS began imaging the "original" BATSE error box of GRB 971227 ~14 s after the onset of gamma-ray emission. Continuous monitoring of the position throughout the evening yielded a total of 499 images (10 s integration). Analysis of these images revealed no steady optical afterglow brighter than R = 12.3 ± 0.2 in any single image. Co-addition of the LOTIS images also failed to uncover transient optical emission. In particular, assuming a constant early-time flux, no optical afterglow brighter than R = 14.2 ± 0.2 was present within the first 1200 s, and no optical afterglow brighter than R = 15.0 ± 0.2 was present in the first 6.0 hr. Follow-up observations by other groups revealed a likely X-ray afterglow and a possible optical afterglow. Although subsequent deeper observations could not confirm a fading source, we show that these transients are not inconsistent with our present knowledge of the characteristics of gamma-ray burst afterglows. We also demonstrate that with the upgraded thermoelectrically cooled CCDs, LOTIS is capable of either detecting very early time optical afterglow or placing stringent constraints on the relationship between the gamma-ray emission and the longer wavelength afterglow in relativistic blast-wave models.
Algebraic families of groups and commuting involutions

Let G be a complex affine algebraic group, and let σ1 and σ2 be commuting anti-holomorphic involutions of G. We construct an algebraic family of algebraic groups over the complex projective line an...
Angoricity and compactivity describe the jamming transition in soft particulate matter

The application of concepts from equilibrium statistical mechanics to out-of-equilibrium systems has a long history of describing diverse systems ranging from glasses to granular materials. For dissipative jammed systems —particulate grains or droplets— a key concept is to replace the energy ensemble describing conservative systems by the volume-stress ensemble. Here, we test the applicability of the volume-stress ensemble to describe the jamming transition by comparing the jammed configurations obtained by dynamics with those averaged over the ensemble as a probe of ergodicity. Agreement between both methods suggests the idea of "thermalization" at a given angoricity and compactivity. We elucidate the thermodynamic order of the jamming transition by showing the absence of critical fluctuations in static observables like pressure and volume. The approach allows to calculate observables such as the entropy, volume, pressure, coordination number and distribution of forces to characterize the scaling laws near the jamming transition from a statistical mechanics viewpoint.
Computing on masked data: a high performance method for improving big data veracity

The growing gap between data and users calls for innovative tools that address the challenges faced by big data volume, velocity and variety. Along with these standard three V's of big data, an emerging fourth “V” is veracity, which addresses the confidentiality, integrity, and availability of the data. Traditional cryptographic techniques that ensure the veracity of data can have overheads that are too large to apply to big data. This work introduces a new technique called Computing on Masked Data (CMD), which improves data veracity by allowing computations to be performed directly on masked data and ensuring that only authorized recipients can unmask the data. Using the sparse linear algebra of associative arrays, CMD can be performed with significantly less overhead than other approaches while still supporting a wide range of linear algebraic operations on the masked data. Databases with strong support of sparse operations, such as SciDB or Apache Accumulo, are ideally suited to this technique. Examples are shown for the application of CMD to a complex DNA matching algorithm and to database operations over social media data.
The degree of the Alexander polynomial is an upper bound for the topological slice genus

We use the famous knot-theoretic consequence of Freedman’s disc theorem — knots with trivial Alexander polynomial bound a locally flat disc in the 4–ball — to prove the following generalization: the degree of the Alexander polynomial of a knot is an upper bound for twice its topological slice genus. We provide examples of knots where this determines the topological slice genus.
Detection of Late-time Optical Emission from SN 1941C in NGC 4136

We report the detection of broad, high-velocity oxygen emission lines from the site of SN 1941C nearly eight decades after outburst, making it the oldest optically detected core-collapse supernova/youngest core-collapse supernova remnant with a well determined age. In contrast to the strongly blueshifted emission line profiles observed for all other late-time CCSNe thought to be due to dust extinction of rear hemisphere ejecta, SN 1941C's spectrum exhibits stronger redshifted than blueshifted emissions of [O I] 6300, 6364 A, [O II] 7319, 7330 A, and [O III] 4959, 5007 A. The oxygen emissions exhibit rest frame expansion velocities of -2200 to +4400 km/s. No other significant broad line emissions were detected including Halpha emission. We discuss possible causes for this unusual spectrum and compare SN 1941C's optical and X-ray luminosities to other evolved CCSNe.
A CODING OF BUNDLE GRAPHS AND THEIR EMBEDDINGS INTO BANACH SPACES

The purpose of this article is to generalize some known characterizations of Banach space properties in terms of graph preclusion. In particular, it is shown that superreflexivity can be characterized by the non-equi-bi-Lipschitz embeddability of any family of bundle graphs generated by a non-trivial finitely branching bundle graph. It is likewise shown that asymptotic uniform convexifiability can be characterized within the class of reflexive Banach spaces with an unconditional asymptotic structure by the non-equi-bi-Lipschitz embeddability of any family of bundle graphs generated by a non-trivial .
On the Vertical Structure of Radiation-dominated Accretion Disks

The vertical structure of black hole accretion disks in which radiation dominates the total pressure is investigated using a three-dimensional radiation-MHD calculation. The domain is a small patch of disk centered 100 Schwarzschild radii from a black hole of 108 M☉, and the stratified shearing-box approximation is used. Magnetorotational instability converts gravitational energy to turbulent magnetic and kinetic energy. The gas is heated by magnetic dissipation and by radiation damping of the turbulence, and cooled by diffusion and advection of radiation through the vertical boundaries. The resulting structure differs in several fundamental ways from the standard Shakura-Sunyaev picture. The disk consists of three layers. At the midplane, the density is large, and the magnetic pressure and total accretion stress are less than the gas pressure. In lower density surface layers that are optically thick, the magnetic pressure and stress are greater than the gas pressure but less than the radiation pressure. Horizontal density variations in the surface layers exceed an order of magnitude. Magnetic fields in the regions of greatest stress are buoyant, and dissipate as they rise, so the heating rate declines more slowly with height than the stress. Much of the dissipation occurs at low column depth, and the interior is cooler and less radiation-dominated than in the Shakura-Sunyaev model with the same surface mass density and flux. The mean structure is convectively stable.
Cosmological perturbation theory in 1+1 dimensions

Author(s): McQuinn, M; White, M | Abstract: Many recent studies have highlighted certain failures of the standard Eulerian-space cosmological perturbation theory (SPT). Its problems include (1) not capturing large-scale bulk flows [leading to an ( 1) error in the 1-loop SPT prediction for the baryon acoustic peak in the correlation function], (2) assuming that the Universe behaves as a pressureless, inviscid fluid, and (3) treating fluctuations on scales that are non-perturbative as if they were. Recent studies have highlighted the successes of perturbation theory in Lagrangian space or theories that solve equations for the effective dynamics of smoothed fields. Both approaches mitigate some or all of the aforementioned issues with SPT. We discuss these physical developments by specializing to the simplified 1D case of gravitationally interacting sheets, which allows us to substantially reduces the analytic overhead and still (as we show) maintain many of the same behaviors as in 3D. In 1D, linear-order Lagrangian perturbation theory ("the Zeldovich approximation") is exact up to shell crossing, and we prove that nth-order Eulerian perturbation theory converges to the Zeldovich approximation as narrow . In no 1D cosmology that we consider (including a CDM-like case and power-law models) do these theories describe accurately the matter power spectrum on any mildly nonlinear scale. We find that theories based on effective equations are much more successful at describing the dynamics. Finally, we discuss many topics that have recently appeared in the perturbation theory literature such as beat coupling, the shift and smearing of the baryon acoustic oscillation feature, and the advantages of Fourier versus configuration space. Our simplified 1D case serves as an intuitive review of these perturbation theory results.
Unlocking Sensitivity for Visibility-based Estimators of the 21 cm Reionization Power Spectrum

Radio interferometers designed to measure the cosmological 21 cm power spectrum require high sensitivity. Several modern low-frequency interferometers feature drift-scan antennas placed on a regular grid to maximize the number of instantaneously coherent (redundant) measurements. However, even for such maximum-redundancy arrays, significant sensitivity comes through partial coherence between baselines. Current visibility-based power-spectrum pipelines, though shown to ease control of systematics, lack the ability to make use of this partial redundancy. We introduce a method to leverage partial redundancy in such power-spectrum pipelines for drift-scan arrays. Our method cross-multiplies baseline pairs at a time lag and quantifies the sensitivity contributions of each pair of baselines. Using the configurations and beams of the 128-element Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER-128) and staged deployments of the Hydrogen Epoch of Reionization Array, we illustrate how our method applies to different arrays and predict the sensitivity improvements associated with pairing partially coherent baselines. As the number of antennas increases, we find partial redundancy to be of increasing importance in unlocking the full sensitivity of upcoming arrays.