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2023-12-24
Sphaleron rate as an inverse problem: a novel lattice approach
We compute the sphaleron rate on the lattice. We adopt a novel strategy based on the extraction of the spectral density via a modified version of the Backus-Gilbert method from finite-lattice-spacing and finite-smoothing-radius Euclidean topological charge density correlators. The physical sphaleron rate is computed by performing controlled continuum limit and zero-smoothing extrapolations both in pure gauge and, for the first time, in full QCD.
2312.15468v1
1999-12-17
Expectations For an Interferometric Sunyaev-Zel'dovich Effect Survey for Galaxy Clusters
Non-targeted surveys for galaxy clusters using the Sunyaev-Zel'dovich effect (SZE) will yield valuable information on both cosmology and evolution of the intra-cluster medium (ICM). The redshift distribution of detected clusters will constrain cosmology, while the properties of the discovered clusters will be important for studies of the ICM and galaxy formation. Estimating survey yields requires a detailed model for both cluster properties and the survey strategy. We address this by making mock observations of galaxy clusters in cosmological hydrodynamical simulations. The mock observatory consists of an interferometric array of ten 2.5 m diameter telescopes, operating at a central frequency of 30 GHz with a bandwidth of 8 GHz. We find that clusters with a mass above $2.5 \times 10^{14} h_{50}^{-1} M_\odot$ will be detected at any redshift, with the exact limit showing a very modest redshift dependence. Using a Press-Schechter prescription for evolving the number densities of clusters with redshift, we determine that such a survey should find hundreds of galaxy clusters per year, many at high redshifts and relatively low mass -- an important regime uniquely accessible to SZE surveys. Currently favored cosmological models predict roughly 25 clusters per square degree.
9912364v2
2000-02-17
K-Band Spectroscopy of an Obscured Massive Stellar Cluster in the Antennae Galaxies (NGC 4038/4039) with NIRSPEC
We present infrared spectroscopy of the Antennae Galaxies (NGC 4038/4039) with NIRSPEC at the W. M. Keck Observatory. We imaged the star clusters in the vicinity of the southern nucleus (NGC 4039) in 0.39" seeing in K-band using NIRSPEC's slit-viewing camera. The brightest star cluster revealed in the near-IR (M_K(0) = -17.9) is insignificant optically, but coincident with the highest surface brightness peak in the mid-IR (12-18 um) ISO image presented by Mirabel et al (1998). We obtained high signal-to-noise 2.03-2.45 um spectra of the nucleus and the obscured star cluster at R = 1900. The cluster is very young (age ~ 4 Myr), massive (M ~ 16E6 M_sun), and compact (density ~ 115 M_sun pc^(-3) within a 32 pc half-light radius), assuming a Salpeter IMF (0.1-100 M_sun). Its hot stars have a radiation field characterized by T_eff ~ 39,000 K, and they ionize a compact HII region with n_e ~ 10^4 cm^(-3). The stars are deeply embedded in gas and dust (A_V = 9-10 mag), and their strong FUV field powers a clumpy photodissociation region with densities n_H > 10^5 cm^(-3) on scales of ~ 200 pc, radiating L{H_2 1-0 S(1)}= 9600 L_sun.
0002357v1
2003-02-20
The Reionization History at High Redshifts II: Estimating the Optical Depth to Thomson Scattering from CMB Polarization
In light of the recent inference of a high optical depth to Thomson scattering, tau, from the WMAP data we investigate the effects of extended periods of partial ionization and ask if the value of tau inferred by assuming a single sharp transition is an unbiased estimate. We construct and consider several representative ionization models and evaluate their signatures in the CMB. If tau is estimated with a single sharp transition we show that there can be a significant bias in the derived value (and therefore a bias in sigma8 as well). For WMAP noise levels the bias in tau is smaller than the statistical uncertainty, but for Planck or a cosmic variance limited experiment the tau bias could be much larger than the statistical uncertainties. This bias can be reduced in the ionization models we consider by fitting a slightly more complicated ionization history, such as a two-step ionization process. Assuming this two-step process we find the Planck satellite can simultaneously determine the initial redshift of reionization to +-2 and tau to +-0.01 Uncertainty about the ionization history appears to provide a limit of about 0.005 on how well tau can be estimated from CMB polarization data, much better than expected from WMAP but significantly worse than expected from cosmic-variance limits.
0302404v2
2007-02-27
The Sunyaev-Zeldovich Background
The cosmic background due to the Sunyaev-Zeldovich (SZ) effect is expected to be the largest signal at mm and cm wavelengths at a resolution of a few arcminutes. We investigate some simple statistics of SZ maps and their scaling with the normalization of the matter power spectrum, sigma_8, as well as the effects of the unknown physics of the intracluster medium on these statistics. We show that the SZ background provides a significant background for SZ cluster searches, with the onset of confusion occurring around 10^{14} h^{-1} solar masses in a cosmology-dependent way, where confusion is defined as typical errors in recovered flux larger than 20%. The confusion limit, corresponds to the mass at which there are roughly ten clusters per square degree, with this number nearly independent of cosmology and cluster gas physics. Typical errors grow quickly as lower mass objects are included in the catalog. We also point out that there is nothing in particular about the rms of the filtered map that makes it especially well-suited for capturing aspects of the SZ effect, and other indicators of the one-point SZ probability distribution function are at least as well suited for the task. For example, the full width at half maximum of the one point probability distribution has a field-to-field scatter that is about 60% that of the rms. The simplest statistics of SZ maps are largely unaffected by cluster physics such aspreheating, although the impact of preheating is clear by eye in the maps.Studies aimed at learning about the physics of the intracluster medium will apparently require more specialized statistical indicators.
0702727v1
1998-01-23
An Analytical Construction of the SRB Measures for Baker-type Maps
For a class of dynamical systems, called the axiom-A systems, Sinai, Ruelle and Bowen showed the existence of an invariant measure (SRB measure) weakly attracting the temporal average of any initial distribution that is absolutely continuous with respect to the Lebesgue measure. Recently, the SRB measures were found to be related to the nonequilibrium stationary state distribution functions for thermostated or open systems. Inspite of the importance of these SRB measures, it is difficult to handle them analytically because they are often singular functions. In this article, for three kinds of Baker-type maps, the SRB measures are analytically constructed with the aid of a functional equation, which was proposed by de Rham in order to deal with a class of singular functions. We first briefly review the properties of singular functions including those of de Rham. Then, the Baker-type maps are described, one of which is non-conservative but time reversible, the second has a Cantor-like invariant set, and the third is a model of a simple chemical reaction $R \leftrightarrow I \leftrightarrow P$. For the second example, the cases with and without escape are considered. For the last example, we consider the reaction processes in a closed system and in an open system under a flux boundary condition. In all cases, we show that the evolution equation of the distribution functions partially integrated over the unstable direction is very similar to de Rham's functional equation and, employing this analogy, we explicitly construct the SRB measures.
9801031v2
1998-04-08
Entropy Production : From Open Volume Preserving to Dissipative Systems
We generalize Gaspard's method for computing the \epsilon-entropy production rate in Hamiltonian systems to dissipative systems with attractors considered earlier by T\'el, Vollmer, and Breymann. This approach leads to a natural definition of a coarse grained Gibbs entropy which is extensive, and which can be expressed in terms of the SRB measures and volumes of the coarse graining sets which cover the attractor. One can also study the entropy and entropy production as functions of the degree of resolution of the coarse graining process, and examine the limit as the coarse graining size approaches zero. We show that this definition of the Gibbs entropy leads to a positive rate of irreversible entropy production for reversible dissipative systems. We apply the method to the case of a two dimensional map, based upon a model considered by Vollmer, T\'el and Breymann, that is a deterministic version of a biased-random walk. We treat both volume preserving and dissipative versions of the basic map, and make a comparison between the two cases. We discuss the \epsilon-entropy production rate as a function of the size of the coarse graining cells for these biased-random walks and, for an open system with flux boundary conditions, show regions of exponential growth and decay of the rate of entropy production as the size of the cells decreases. This work describes in some detail the relation between the results of Gaspard, those of T\'el, Vollmer and Breymann, and those of Ruelle, on entropy production in various systems described by Anosov or Anosov-like maps.
9804009v2
1998-07-23
A priori bounds for co-dimension one isometric embeddings
We prove a priori bounds for the trace of the second fundamental form of a $C^4$ isometric embedding into $R^{n+1}$ of a metric $g$ of non-negative sectional curvature on $S^n$, in terms of the scalar curvature, and the diameter of $g$. These estimates give a bound on the extrinsic geometry in terms of intrinsic quantities. They generalize estimates originally obtained by Weyl for the case $n=2$ and positive curvature, and then by P. Guan and the first author for non-negative curvature and $n=2$. Using $C^{2,\alpha}$ interior estimates of Evans and Krylov for concave fully nonlinear elliptic partial differential equations, these bounds allow us to obtain the following convergence theorem: For any $\epsilon>0$, the set of metrics of non-negative sectional curvature and scalar curvature bounded below by $\epsilon$ which are isometrically embedable in Euclidean space $R^{n+1}$ is closed in the H\"older space $C^{4,\alpha}$, $0<\alpha<1$. These results are obtained in an effort to understand the following higher dimensional version of the Weyl embedding problem which we propose: \emph{Suppose that $g$ is a smooth metric of non-negative sectional curvature and positive scalar curvature on \S^n$ which is locally isometrically embeddable in $R^{n+1}$. Does $(S^n,g)$ then admit a smooth global isometric embedding into $R^{n+1}$?}
9807130v1
2002-07-02
Active and Passive Fields in Turbulent Transport: the Role of Statistically Preserved Structures
We have recently proposed that the statistics of active fields (which affect the velocity field itself) in well-developed turbulence are also dominated by the Statistically Preserved Structures of auxiliary passive fields which are advected by the same velocity field. The Statistically Preserved Structures are eigenmodes of eigenvalue 1 of an appropriate propagator of the decaying (unforced) passive field, or equivalently, the zero modes of a related operator. In this paper we investigate further this surprising finding via two examples, one akin to turbulent convection in which the temperature is the active scalar, and the other akin to magneto-hydrodynamics in which the magnetic field is the active vector. In the first example, all the even correlation functions of the active and passive fields exhibit identical scaling behavior. The second example appears at first sight to be a counter-example: the statistical objects of the active and passive fields have entirely different scaling exponents. We demonstrate nevertheless that the Statistically Preserved Structures of the passive vector dominate again the statistics of the active field, except that due to a dynamical conservation law the amplitude of the leading zero mode cancels exactly. The active vector is then dominated by the sub-leading zero mode of the passive vector. Our work thus suggests that the statistical properties of active fields in turbulence can be understood with the same generality as those of passive fields.
0207005v1
2001-06-07
Secrecy, Computational Loads and Rates in Practical Quantum Cryptography
A number of questions associated with practical implementations of quantum cryptography systems having to do with unconditional secrecy, computational loads and effective secrecy rates in the presence of perfect and imperfect sources are discussed. The different types of unconditional secrecy, and their relationship to general communications security, are discussed in the context of quantum cryptography. In order to actually carry out a quantum cryptography protocol it is necessary that sufficient computational resources be available to perform the various processing steps, such as sifting, error correction, privacy amplification and authentication. We display the full computer machine instruction requirements needed to support a practical quantum cryptography implementation. We carry out a numerical comparison of system performance characteristics for implementations that make use of either weak coherent sources of light or perfect single photon sources, for eavesdroppers making individual attacks on the quantum channel characterized by different levels of technological capability. We find that, while in some circumstances it is best to employ perfect single photon sources, in other situations it is preferable to utilize weak coherent sources. In either case the secrecy level of the final shared cipher is identical, with the relevant distinguishing figure-of-merit being the effective throughput rate.
0106043v2
2001-08-02
Privacy Amplification in Quantum Key Distribution: Pointwise Bound versus Average Bound
In order to be practically useful, quantum cryptography must not only provide a guarantee of secrecy, but it must provide this guarantee with a useful, sufficiently large throughput value. The standard result of generalized privacy amplification yields an upper bound only on the average value of the mutual information available to an eavesdropper. Unfortunately this result by itself is inadequate for cryptographic applications. A naive application of the standard result leads one to incorrectly conclude that an acceptable upper bound on the mutual information has been achieved. It is the pointwise value of the bound on the mutual information, associated with the use of some specific hash function, that corresponds to actual implementations. We provide a fully rigorous mathematical derivation that shows how to obtain a cryptographically acceptable upper bound on the actual, pointwise value of the mutual information. Unlike the bound on the average mutual information, the value of the upper bound on the pointwise mutual information and the number of bits by which the secret key is compressed are specified by two different parameters, and the actual realization of the bound in the pointwise case is necessarily associated with a specific failure probability. The constraints amongst these parameters, and the effect of their values on the system throughput, have not been previously analyzed. We show that the necessary shortening of the key dictated by the cryptographically correct, pointwise bound, can still produce viable throughput rates that will be useful in practice.
0108013v1
2008-03-27
Assessing surrogate endpoints in vaccine trials with case-cohort sampling and the Cox model
Assessing immune responses to study vaccines as surrogates of protection plays a central role in vaccine clinical trials. Motivated by three ongoing or pending HIV vaccine efficacy trials, we consider such surrogate endpoint assessment in a randomized placebo-controlled trial with case-cohort sampling of immune responses and a time to event endpoint. Based on the principal surrogate definition under the principal stratification framework proposed by Frangakis and Rubin [Biometrics 58 (2002) 21--29] and adapted by Gilbert and Hudgens (2006), we introduce estimands that measure the value of an immune response as a surrogate of protection in the context of the Cox proportional hazards model. The estimands are not identified because the immune response to vaccine is not measured in placebo recipients. We formulate the problem as a Cox model with missing covariates, and employ novel trial designs for predicting the missing immune responses and thereby identifying the estimands. The first design utilizes information from baseline predictors of the immune response, and bridges their relationship in the vaccine recipients to the placebo recipients. The second design provides a validation set for the unmeasured immune responses of uninfected placebo recipients by immunizing them with the study vaccine after trial closeout. A maximum estimated likelihood approach is proposed for estimation of the parameters. Simulated data examples are given to evaluate the proposed designs and study their properties.
0803.3919v1
2008-06-13
The Formation and Evolution of Massive Stellar Clusters in IC 4662
We present a multiwavelength study of the formation of massive stellar clusters, their emergence from cocoons of gas and dust, and their feedback on surrounding matter. Using data that span from radio to optical wavelengths, including Spitzer and Hubble ACS observations, we examine the population of young star clusters in the central starburst region of the irregular Wolf-Rayet galaxy IC 4662. We model the radio-to-IR spectral energy distributions of embedded clusters to determine the properties of their HII regions and dust cocoons (sizes, masses, densities, temperatures), and use near-IR and optical data with mid-IR spectroscopy to constrain the properties of the embedded clusters themselves (mass, age, extinction, excitation, abundance). The two massive star-formation regions in IC 4662 are excited by stellar populations with ages of ~ 4 million years and masses of ~ 3 x 10^5 M_sun (assuming a Kroupa IMF). They have high excitation and sub-solar abundances, and they may actually be comprised of several massive clusters rather than the single monolithic massive compact objects known as Super Star Clusters (SSCs). Mid-IR spectra reveal that these clusters have very high extinctions, A_V ~ 20-25 mag, and that the dust in IC 4662 is well-mixed with the emitting gas, not in a foreground screen.
0806.2302v1
2009-01-28
Searching for Main-Belt Comets Using the Canada-France-Hawaii Telescope Legacy Survey
The Canada-France-Hawaii Telescope Legacy Survey, specifically the Very Wide segment of data, is used to search for possible main-belt comets. In the first data set, 952 separate objects with asteroidal orbits within the main-belt are examined using a three-level technique. First, the full-width-half-maximum of each object is compared to stars of similar magnitude, to look for evidence of a coma. Second, the brightness profiles of each object are compared with three stars of the same magnitude, which are nearby on the image to ensure any extended profile is not due to imaging variations. Finally, the star profiles are subtracted from the asteroid profile and the residuals are compared with the background using an unpaired T-test. No objects in this survey show evidence of cometary activity. The second survey includes 11438 objects in the main-belt, which are examined visually. One object, an unknown comet, is found to show cometary activity. Its motion is consistent with being a main-belt asteroid, but the observed arc is too short for a definitive orbit calculation. No other body in this survey shows evidence of cometary activity. Upper limits of the number of weakly and strongly active main-belt comets are derived to be 630+/-77 and 87+/-28, respectively. These limits are consistent with those expected from asteroid collisions. In addition, data extracted from the Canada-France-Hawaii Telescope image archive of main-belt comet 176P/LINEAR is presented.
0901.4511v1
2009-10-02
Spectroscopic Observations of New Oort Cloud Comet 2006 VZ13 and Four Other Comets
Spectral data are presented for comets 2006 VZ13 (LINEAR), 2006 K4 (NEAT), 2006 OF2 (Broughton), 2P/Encke, and 93P/Lovas I, obtained with the Cerro-Tololo Inter-American Observatory 1.5-m telescope in August 2007. Comet 2006 VZ13 is a new Oort cloud comet and shows strong lines of CN (3880 angstroms), the Swan band sequence for C_2 (4740, 5160, and 5630 angstroms), C_3 (4056 angstroms), and other faint species. Lines are also identified in the spectra of the other comets. Flux measurements of the CN, C_2 (Delta v = +1,0), and C_3 lines are recorded for each comet and production rates and ratios are derived. When considering the comets as a group, there is a correlation of C_2 and C_3 production with CN, but there is no conclusive evidence that the production rate ratios depend on heliocentric distance. The continuum is also measured, and the dust production and dust-to-gas ratios are calculated. There is a general trend, for the group of comets, between the dust-to-gas ratio and heliocentric distance, but it does not depend on dynamical age or class. Comet 2006 VZ13 is determined to be in the carbon-depleted (or Tempel 1 type) class.
0910.0416v1
2009-12-01
Approximate Sparse Recovery: Optimizing Time and Measurements
An approximate sparse recovery system consists of parameters $k,N$, an $m$-by-$N$ measurement matrix, $\Phi$, and a decoding algorithm, $\mathcal{D}$. Given a vector, $x$, the system approximates $x$ by $\widehat x =\mathcal{D}(\Phi x)$, which must satisfy $\| \widehat x - x\|_2\le C \|x - x_k\|_2$, where $x_k$ denotes the optimal $k$-term approximation to $x$. For each vector $x$, the system must succeed with probability at least 3/4. Among the goals in designing such systems are minimizing the number $m$ of measurements and the runtime of the decoding algorithm, $\mathcal{D}$. In this paper, we give a system with $m=O(k \log(N/k))$ measurements--matching a lower bound, up to a constant factor--and decoding time $O(k\log^c N)$, matching a lower bound up to $\log(N)$ factors. We also consider the encode time (i.e., the time to multiply $\Phi$ by $x$), the time to update measurements (i.e., the time to multiply $\Phi$ by a 1-sparse $x$), and the robustness and stability of the algorithm (adding noise before and after the measurements). Our encode and update times are optimal up to $\log(N)$ factors.
0912.0229v1
2010-04-07
Concatenated quantum codes can attain the quantum Gilbert-Varshamov bound
A family of quantum codes of increasing block length with positive rate is asymptotically good if the ratio of its distance to its block length approaches a positive constant. The asymptotic quantum Gilbert-Varshamov (GV) bound states that there exist $q$-ary quantum codes of sufficiently long block length $N$ having fixed rate $R$ with distance at least $N H^{-1}_{q^2}((1-R)/2)$, where $H_{q^2}$ is the $q^2$-ary entropy function. For $q < 7$, only random quantum codes are known to asymptotically attain the quantum GV bound. However, random codes have little structure. In this paper, we generalize the classical result of Thommesen to the quantum case, thereby demonstrating the existence of concatenated quantum codes that can asymptotically attain the quantum GV bound. The outer codes are quantum generalized Reed-Solomon codes, and the inner codes are random independently chosen stabilizer codes, where the rates of the inner and outer codes lie in a specified feasible region.
1004.1127v6
2010-09-02
Stable and unstable regimes in higher-dimensional convex billiards with cylindrical shape
We introduce a class of convex, higher-dimensional billiard models which generalise stadium billiards. These models correspond to the free motion of a point-particle in a region bounded by cylinders cut by planes. They are motivated by models of particles interacting via a string-type mechanism, and confined by hard walls. The combination of these elements may give rise to a defocusing mechanism, similar to that in two dimensions, which allows large chaotic regions in phase space. The remaining part of phase space is associated with marginally stable behaviour. In fact periodic orbits in these systems generically come in continuous parametric families, sociated with a pair of parabolic eigen-directions: the periodic orbits are unstable in the presence of a defocusing mechanism, but marginally stable otherwise. By performing the stability analysis of families of periodic orbits at a nonlinear level, we establish the conditions under which families are nonlinearly stable or unstable. As a result, we identify regions in the parameter space of the models which admit non-linearly stable oscillations in the form of whispering gallery modes. Where no families of periodic orbits are stable, the billiards are completely chaotic, i.e.\ the Lyapunov exponents of the billiard map are non-zero.
1009.0337v1
2011-08-29
Magnetization Dynamics, Throughput and Energy Dissipation in a Universal Multiferroic Nanomagnetic Logic Gate with Fan-in and Fan-out
The switching dynamics of a multiferroic nanomagnetic NAND gate with fan-in/fan-out is simulated by solving the Landau-Lifshitz-Gilbert (LLG) equation while neglecting thermal fluctuation effects. The gate and logic wires are implemented with dipole-coupled 2-phase (magnetostrictive/piezoelectric) multiferroic elements that are clocked with electrostatic potentials of ~50 mV applied to the piezoelectric layer generating 10 MPa stress in the magnetostrictive layers for switching. We show that a pipeline bit throughput rate of ~ 0.5 GHz is achievable with proper magnet layout and sinusoidal four-phase clocking. The gate operation is completed in 2 ns with a latency of 4 ns. The total (internal + external) energy dissipated for a single gate operation at this throughput rate is found to be only ~ 1000 kT in the gate and ~3000 kT in the 12-magnet array comprising two input and two output wires for fan-in and fan-out. This makes it respectively 3 and 5 orders of magnitude more energy-efficient than complementary-metal-oxide-semiconductor-transistor (CMOS) based and spin-transfer-torque-driven nanomagnet based NAND gates. Finally, we show that the dissipation in the external clocking circuit can always be reduced asymptotically to zero using increasingly slow adiabatic clocking, such as by designing the RC time constant to be 3 orders of magnitude smaller than the clocking period. However, the internal dissipation in the device must remain and cannot be eliminated if we want to perform fault-tolerant classical computing. Keywords: Nanomagnetic logic, multiferroics, straintronics and spintronics, Landau-Lifshitz-Gilbert equation.
1108.5758v1
2011-09-15
Stato evolutivo delle stelle della Cintura di Orione ed implicazioni archeoastronomiche
In the present work it is evaluated the evolutionary state of the Orion Belt stars, an asterism very important for the ancient Egyptians, finding that, when the pyramids were built, the brightness of the three stars of the Belt was practically the same as today. This not trivial result has important implications in the framework of the so-called Orion Correlation Theory, a controversial theory proposed by Bauval and Gilbert (1994), according to which a perfect coincidence would exist between the disposition of the three stars of the Orion Belt and that of the main Giza pyramids, so that the latter would represent the monumental reproduction on the ground of that important asterism. ---- Nel presente lavoro viene determinato lo stato evolutivo delle stelle della Cintura di Orione, ricavando che, all'epoca della costruzione delle piramidi, la luminosita' delle tre stelle della Cintura era di fatto uguale a quella odierna. Tale non banale risultato riveste una importanza fondamentale nell'ambito della verifica della controversa Teoria della Correlazione di Orione proposta da Bauval e Gilbert nel 1994, secondo la quale esisterebbe una perfetta coincidenza tra la disposizione delle tre stelle della Cintura e quella delle tre piramidi nella piana di Giza.
1109.3284v2
2012-07-31
Surface Acoustic Wave-Driven Ferromagnetic Resonance in Nickel Thin Films: Theory and Experiment
We present an extensive experimental and theoretical study of surface acoustic wave-driven ferromagnetic resonance. In a first modeling approach based on the Landau-Lifshitz-Gilbert equation, we derive expressions for the magnetization dynamics upon magnetoelastic driving that are used to calculate the absorbed microwave power upon magnetic resonance as well as the spin current density generated by the precessing magnetization in the vicinity of a ferromagnet/normal metal interface. In a second modeling approach, we deal with the backaction of the magnetization dynamics on the elastic wave by solving the elastic wave equation and the Landau-Lifshitz-Gilbert equation selfconsistently, obtaining analytical solutions for the acoustic wave phase shift and attenuation. We compare both modeling approaches with the complex forward transmission of a LiNbO$_3$/Ni surface acoustic wave hybrid device recorded experimentally as a function of the external magnetic field orientation and magnitude, rotating the field within three different planes and employing three different surface acoustic wave frequencies. We find quantitative agreement of the experimentally observed power absorption and surface acoustic wave phase shift with our modeling predictions using one set of parameters for all field configurations and frequencies.
1208.0001v1
2012-09-27
Vortex Lattices in the Superconducting Phases of Doped Topological Insulators and Heterostructures
Majorana fermions are predicted to play a crucial role in condensed matter realizations of topological quantum computation. These heretofore undiscovered quasiparticles have been predicted to exist at the cores of vortex excitations in topological superconductors and in heterostructures of superconductors and materials with strong spin-orbit coupling. In this work we examine topological insulators with bulk s-wave superconductivity in the presence of a vortex-lattice generated by a perpendicular magnetic field. Using self-consistent Bogoliubov-de Gennes, calculations we confirm that beyond the semi-classical, weak-pairing limit that the Majorana vortex states appear as the chemical potential is tuned from either side of the band edge so long as the density of states is sufficient for superconductivity to form. Further, we demonstrate that the previously predicted vortex phase transition survives beyond the semi-classical limit. At chemical potential values smaller than the critical chemical potential, the vortex lattice modes hybridize within the top and bottom surfaces giving rise to a dispersive low-energy mid-gap band. As the chemical potential is increased, the Majorana states become more localized within a single surface but spread into the bulk toward the opposite surface. Eventually, when the chemical potential is sufficiently high in the bulk bands, the Majorana modes can tunnel between surfaces and eventually a critical point is reached at which modes on opposite surfaces can freely tunnel and annihilate leading to the topological phase transition previously studied in the work of Hosur et al.
1209.6373v1
2013-04-23
L2/L2-foreach sparse recovery with low risk
In this paper, we consider the "foreach" sparse recovery problem with failure probability $p$. The goal of which is to design a distribution over $m \times N$ matrices $\Phi$ and a decoding algorithm $\algo$ such that for every $\vx\in\R^N$, we have the following error guarantee with probability at least $1-p$ \[\|\vx-\algo(\Phi\vx)\|_2\le C\|\vx-\vx_k\|_2,\] where $C$ is a constant (ideally arbitrarily close to 1) and $\vx_k$ is the best $k$-sparse approximation of $\vx$. Much of the sparse recovery or compressive sensing literature has focused on the case of either $p = 0$ or $p = \Omega(1)$. We initiate the study of this problem for the entire range of failure probability. Our two main results are as follows: \begin{enumerate} \item We prove a lower bound on $m$, the number measurements, of $\Omega(k\log(n/k)+\log(1/p))$ for $2^{-\Theta(N)}\le p <1$. Cohen, Dahmen, and DeVore \cite{CDD2007:NearOptimall2l2} prove that this bound is tight. \item We prove nearly matching upper bounds for \textit{sub-linear} time decoding. Previous such results addressed only $p = \Omega(1)$. \end{enumerate} Our results and techniques lead to the following corollaries: (i) the first ever sub-linear time decoding $\lolo$ "forall" sparse recovery system that requires a $\log^{\gamma}{N}$ extra factor (for some $\gamma<1$) over the optimal $O(k\log(N/k))$ number of measurements, and (ii) extensions of Gilbert et al. \cite{GHRSW12:SimpleSignals} results for information-theoretically bounded adversaries.
1304.6232v1
2013-11-28
Starbugs: all-singing, all-dancing fibre positioning robots
Starbugs are miniature piezoelectric 'walking' robots with the ability to simultaneously position many optical fibres across a telescope's focal plane. Their simple design incorporates two piezoceramic tubes to form a pair of concentric 'legs' capable of taking individual steps of a few microns, yet with the capacity to move a payload several millimetres per second. The Australian Astronomical Observatory has developed this technology to enable fast and accurate field reconfigurations without the inherent limitations of more traditional positioning techniques, such as the 'pick and place' robotic arm. We report on our recent successes in demonstrating Starbug technology, driven principally by R&D efforts for the planned MANIFEST (many instrument fibre-system) facility for the Giant Magellan Telescope. Significant performance gains have resulted from improvements to the Starbug system, including i) the use of a vacuum to attach Starbugs to the underside of a transparent field plate, ii) optimisation of the control electronics, iii) a simplified mechanical design with high sensitivity piezo actuators, and iv) the construction of a dedicated laboratory 'test rig'. A method of reliably rotating Starbugs in steps of several arcminutes has also been devised, which integrates with the pre-existing x-y movement directions and offers greater flexibility while positioning. We present measured performance data from a prototype system of 10 Starbugs under full (closed-loop control), at field plate angles of 0-90 degrees.
1311.7371v1
2014-02-05
Magnetization dynamics: path-integral formalism for the stochastic Landau-Lifshitz-Gilbert equation
We construct a path-integral representation of the generating functional for the dissipative dynamics of a classical magnetic moment as described by the stochastic generalization of the Landau-Lifshitz-Gilbert equation proposed by Brown, with the possible addition of spin-torque terms. In the process of constructing this functional in the Cartesian coordinate system, we critically revisit this stochastic equation. We present it in a form that accommodates for any discretization scheme thanks to the inclusion of a drift term. The generalized equation ensures the conservation of the magnetization modulus and the approach to the Gibbs-Boltzmann equilibrium in the absence of non-potential and time-dependent forces. The drift term vanishes only if the mid-point Stratonovich prescription is used. We next reset the problem in the more natural spherical coordinate system. We show that the noise transforms non-trivially to spherical coordinates acquiring a non-vanishing mean value in this coordinate system, a fact that has been often overlooked in the literature. We next construct the generating functional formalism in this system of coordinates for any discretization prescription. The functional formalism in Cartesian or spherical coordinates should serve as a starting point to study different aspects of the out-of-equilibrium dynamics of magnets. Extensions to colored noise, micro-magnetism and disordered problems are straightforward.
1402.1200v2
2014-10-17
The fixed irreducible bridge ensemble for self-avoiding walks
We define a new ensemble for self-avoiding walks in the upper half-plane, the fixed irredicible bridge ensemble, by considering self-avoiding walks in the upper half-plane up to their $n$-th bridge height, $Y_n$, and scaling the walk by $1/Y_n$ to obtain a curve in the unit strip, and then taking $n\to\infty$. We then conjecture a relationship between this ensemble to $\SLE$ in the unit strip from $0$ to a fixed point along the upper boundary of the strip, integrated over the conjectured exit density of self-avoiding walk spanning a strip in the scaling limit. We conjecture that there exists a positive constant $\sigma$ such that $n^{-\sigma}Y_n$ converges in distribution to that of a stable random variable as $n\to\infty$. Then the conjectured relationship between the fixed irreducible bridge scaling limit and $\SLE$ can be described as follows: If one takes a SAW considered up to $Y_n$ and scales by $1/Y_n$ and then weights the walk by $Y_n$ to an appropriate power, then in the limit $n\to\infty$, one should obtain a curve from the scaling limit of the self-avoiding walk spanning the unit strip. In addition to a heuristic derivation, we provide numerical evidence to support the conjecture and give estimates for the boundary scaling exponent.
1410.4796v1
2014-11-20
Type II Seesaw Higgsology and LEP/LHC constraints
In the {\sl type II seesaw} model, if spontaneous violation of the lepton number conservation prevails over that of explicit violation, a rich Higgs sector phenomenology is expected to arise with light scalar states having mixed charged-fermiophobic/neutrinophilic properties. We study the constraints on these light CP-even ($h^0$) and CP-odd ($A^0$) states from LEP exclusion limits, combined with the so far established limits and properties of the $125-126$~GeV ${\cal H}$ boson discovered at the LHC. We show that, apart from a fine-tuned region of the parameter space, masses in the $\sim 44$ to $80$ GeV range escape from the LEP limits if the vacuum expectation value of the Higgs triplet is $\lesssim {\cal O}(10^{-3})$GeV, that is comfortably in the region for 'natural' generation of Majorana neutrino masses within this model. In the lower part of the scalar mass spectrum the decay channels ${\cal H} \to h^0 h^0, A^0 A^0$ lead predominantly to heavy flavor plus missing energy or to totally invisible Higgs decays, mimicking dark matter signatures without a dark matter candidate. Exclusion limits at the percent level of these (semi-)invisible decay channels would be needed, together with stringent bounds on the (doubly-)charged states, to constrain significantly this scenario. We also revisit complementary constraints from ${\cal H} \to \gamma \gamma$ and ${\cal H} \to Z \gamma$ channels on the (doubly)charged scalar sector of the model, pinpointing non-sensitivity regions, and carry out a likeliness study for the theoretically allowed couplings in the scalar potential.
1411.5645v1
2015-01-11
Epidemic Threshold of an SIS Model in Dynamic Switching Networks
In this paper, we analyze dynamic switching networks, wherein the networks switch arbitrarily among a set of topologies. For this class of dynamic networks, we derive an epidemic threshold, considering the SIS epidemic model. First, an epidemic probabilistic model is developed assuming independence between states of nodes. We identify the conditions under which the epidemic dies out by linearizing the underlying dynamical system and analyzing its asymptotic stability around the origin. The concept of joint spectral radius is then used to derive the epidemic threshold, which is later validated using several networks (Watts-Strogatz, Barabasi-Albert, MIT reality mining graphs, Regular, and Gilbert). A simplified version of the epidemic threshold is proposed for undirected networks. Moreover, in the case of static networks, the derived epidemic threshold is shown to match conventional analytical results. Then, analytical results for the epidemic threshold of dynamic networksare proved to be applicable to periodic networks. For dynamic regular networks, we demonstrate that the epidemic threshold is identical to the epidemic threshold for static regular networks. An upper bound for the epidemic spread probability in dynamic Gilbert networks is also derived and verified using simulation.
1501.02472v2
2015-04-29
Entropy measures as geometrical tools in the study of cosmology
Classical chaos is often characterized as exponential divergence of nearby trajectories. In many interesting cases these trajectories can be identified with geodesic curves. We define here the entropy by $S = \ln \chi (x)$ with $\chi(x)$ being the distance between two nearby geodesics. We derive an equation for the entropy which by transformation to a Ricatti-type equation becomes similar to the Jacobi equation. We further show that the geodesic equation for a null geodesic in a double warped space time leads to the same entropy equation. By applying a Robertson-Walker metric for a flat three-dimensional Euclidian space expanding as a function of time, we again reach the entropy equation stressing the connection between the chosen entropy measure and time. We finally turn to the Raychaudhuri equation for expansion, which also is a Ricatti equation similar to the transformed entropy equation. Those Ricatti-type equations have solutions of the same form as the Jacobi equation. The Raychaudhuri equation can be transformed to a harmonic oscillator equation, and it has been shown that the geodesic deviation equation of Jacobi is essentially equivalent to that of a harmonic oscillator. The Raychaudhuri equations are strong geometrical tools in the study of General Relativity and Cosmology. We suggest a refined entropy measure applicable in Cosmology and defined by the average deviation of the geodesics in a congruence.
1504.07855v2
2015-06-24
Ebb: A DSL for Physical Simulation on CPUs and GPUs
Designing programming environments for physical simulation is challenging because simulations rely on diverse algorithms and geometric domains. These challenges are compounded when we try to run efficiently on heterogeneous parallel architectures. We present Ebb, a domain-specific language (DSL) for simulation, that runs efficiently on both CPUs and GPUs. Unlike previous DSLs, Ebb uses a three-layer architecture to separate (1) simulation code, (2) definition of data structures for geometric domains, and (3) runtimes supporting parallel architectures. Different geometric domains are implemented as libraries that use a common, unified, relational data model. By structuring the simulation framework in this way, programmers implementing simulations can focus on the physics and algorithms for each simulation without worrying about their implementation on parallel computers. Because the geometric domain libraries are all implemented using a common runtime based on relations, new geometric domains can be added as needed, without specifying the details of memory management, mapping to different parallel architectures, or having to expand the runtime's interface. We evaluate Ebb by comparing it to several widely used simulations, demonstrating comparable performance to hand-written GPU code where available, and surpassing existing CPU performance optimizations by up to 9$\times$ when no GPU code exists.
1506.07577v3
2016-04-27
Scoping of material response under DEMO neutron irradiation: comparison with fission and influence of nuclear library selection
Predictions of material activation inventories will be a key input to virtually all aspects of the operation, safety and environmental assessment of future fusion nuclear plants. Additionally, the neutron-induced transmutation (change) of material composition (inventory) with time, and the creation and evolution of configurational damage from atomic displacements, require precise quantification because they can lead to significant changes in material properties, and thus influence reactor-component lifetime. A comprehensive scoping study has been performed to quantify the activation, transmutation (depletion and build-up) and immediate damage response under neutron irradiation for all naturally occurring elements from hydrogen to bismuth. The resulting database provides a global picture of the response of a material, covering the majority of nuclear technological space, but focussing specifically on typical conditions expected for a demonstration fusion power plant (DEMO). Results from fusion are compared against typical fission conditions for selected fusion relevant materials, demonstrating that the latter cannot be relied upon to give accurate scalable experimental predictions of material response in a future fusion reactor. Results from different nuclear data libraries are also compared, highlighting the variations and deficiencies.
1604.08496v1
2016-05-23
Beyond the Interface Limit: Structural and Magnetic Depth Profiles of Voltage-Controlled Magneto-Ionic Heterostructures
Electric-field control of magnetism provides a promising route towards ultralow power information storage and sensor technologies. The effects of magneto-ionic motion have so far been prominently featured in the direct modification of interface chemical and physical characteristics. Here we demonstrate magnetoelectric coupling moderated by voltage-driven oxygen migration beyond the interface limit in relatively thick AlOx/GdOx/Co (15 nm) films. Oxygen migration and its ramifications on the Co magnetization are quantitatively mapped with polarized neutron reflectometry under thermal and electro-thermal conditionings. The depth-resolved profiles uniquely identify interfacial and bulk behaviors and a semi-reversible suppression and recovery of the magnetization. Magnetometry measurements show that the conditioning changes the microstructure so as to disrupt long-range ferromagnetic ordering, resulting in an additional magnetically soft phase. X-ray spectroscopy confirms electric field induced changes in the Co oxidation state but not in the Gd, suggesting that the GdOx transmits oxygen but does not source or sink it. These results together provide crucial insight into controlling magnetic heterostructures via magneto-ionic motion, not only at the interface, but also throughout the bulk of the films.
1605.07209v1
2016-06-02
RankSign: an efficient signature algorithm based on the rank metric
In this paper we propose a new approach to code-based signatures that makes use in particular of rank metric codes. When the classical approach consists in finding the unique preimage of a syndrome through a decoding algorithm, we propose to introduce the notion of mixed decoding of erasures and errors for building signature schemes. In that case the difficult problem becomes, as is the case in lattice-based cryptography, finding a preimage of weight above the Gilbert-Varshamov bound (case where many solutions occur) rather than finding a unique preimage of weight below the Gilbert-Varshamov bound. The paper describes RankSign: a new signature algorithm for the rank metric based on a new mixed algorithm for decoding erasures and errors for the recently introduced Low Rank Parity Check (LRPC) codes. We explain how it is possible (depending on choices of parameters) to obtain a full decoding algorithm which is able to find a preimage of reasonable rank weight for any random syndrome with a very strong probability. We study the semantic security of our signature algorithm and show how it is possible to reduce the unforgeability to direct attacks on the public matrix, so that no information leaks through signatures. Finally, we give several examples of parameters for our scheme, some of which with public key of size $11,520$ bits and signature of size $1728$ bits. Moreover the scheme can be very fast for small base fields.
1606.00629v2
2016-09-09
Image and Video Mining through Online Learning
Within the field of image and video recognition, the traditional approach is a dataset split into fixed training and test partitions. However, the labelling of the training set is time-consuming, especially as datasets grow in size and complexity. Furthermore, this approach is not applicable to the home user, who wants to intuitively group their media without tirelessly labelling the content. Our interactive approach is able to iteratively cluster classes of images and video. Our approach is based around the concept of an image signature which, unlike a standard bag of words model, can express co-occurrence statistics as well as symbol frequency. We efficiently compute metric distances between signatures despite their inherent high dimensionality and provide discriminative feature selection, to allow common and distinctive elements to be identified from a small set of user labelled examples. These elements are then accentuated in the image signature to increase similarity between examples and pull correct classes together. By repeating this process in an online learning framework, the accuracy of similarity increases dramatically despite labelling only a few training examples. To demonstrate that the approach is agnostic to media type and features used, we evaluate on three image datasets (15 scene, Caltech101 and FG-NET), a mixed text and image dataset (ImageTag), a dataset used in active learning (Iris) and on three action recognition datasets (UCF11, KTH and Hollywood2). On the UCF11 video dataset, the accuracy is 86.7% despite using only 90 labelled examples from a dataset of over 1200 videos, instead of the standard 1122 training videos. The approach is both scalable and efficient, with a single iteration over the full UCF11 dataset of around 1200 videos taking approximately 1 minute on a standard desktop machine.
1609.02770v2
2016-11-17
Stashing the stops in multijet events at the LHC
While the presence of a light stop is increasingly disfavored by the experimental limits set on R-parity conserving scenarios, the naturalness of supersymmetry could still be safely concealed in the more challenging final states predicted by the existence of non-null R-parity violating couplings. Although R-parity violating signatures are extensively looked for at the Large Hadron Collider, these searches always assume 100\% branching ratios for the direct decays of supersymmetric particles into Standard Model ones. In this paper we scrutinize the implications of relaxing this assumption by focusing on one motivated scenario where the lightest stop is heavier than a chargino and a neutralino. Considering a class of R-parity baryon number violating couplings, we show on general grounds that while the direct decay of the stop into Standard Model particles is dominant for large values of these couplings, smaller values give rise, instead, to the dominance of a plethora of longer decay chains and richer final states that have not yet been analyzed at the LHC, thus weakening the impact of the present experimental stop mass limits. We characterize the case for R-parity baryon number violating couplings in the $10^{-7} - 10^{-1}$ range, in two different benchmark points scenarios within the model-independent setting of the low-energy phenomenological Minimal Supersymmetric Standard Model. We identify the different relevant experimental signatures, estimate the corresponding proton--proton cross sections at $\sqrt{s}=14$ TeV and discuss signal versus background issues.
1611.05850v2
2017-02-18
Inf-sup stable finite-element methods for the Landau--Lifshitz--Gilbert and harmonic map heat flow equation
In this paper we propose and analyze a finite element method for both the harmonic map heat and Landau--Lifshitz--Gilbert equation, the time variable remaining continuous. Our starting point is to set out a unified saddle point approach for both problems in order to impose the unit sphere constraint at the nodes since the only polynomial function satisfying the unit sphere constraint everywhere are constants. A proper inf-sup condition is proved for the Lagrange multiplier leading to the well-posedness of the unified formulation. \emph{A priori} energy estimates are shown for the proposed method. When time integrations are combined with the saddle point finite element approximation some extra elaborations are required in order to ensure both \emph{a priori} energy estimates for the director or magnetization vector depending on the model and an inf-sup condition for the Lagrange multiplier. This is due to the fact that the unit length at the nodes is not satisfied in general when a time integration is performed. We will carry out a linear Euler time-stepping method and a non-linear Crank--Nicolson method. The latter is solved by using the former as a non-linear solver.
1702.05588v2
2017-06-15
Generalized Voltage-based State-Space Modelling of Modular Multilevel Converters with Constant Equilibrium in Steady-State
This paper demonstrates that the sum and difference of the upper and lower arm voltages are suitable variables for deriving a generalized state-space model of an MMC which settles at a constant equilibrium in steady-state operation, while including the internal voltage and current dynamics. The presented modelling approach allows for separating the multiple frequency components appearing within the MMC as a first step of the model derivation, to avoid variables containing multiple frequency components in steady-state. On this basis, it is shown that Park transformations at three different frequencies ($+\omega$, $-2\omega$ and $+3\omega$) can be applied for deriving a model formulation where all state-variables will settle at constant values in steady-state, corresponding to an equilibrium point of the model. The resulting model is accurately capturing the internal current and voltage dynamics of a three-phase MMC, independently from how the control system is implemented. The main advantage of this model formulation is that it can be linearised, allowing for eigenvalue-based analysis of the MMC dynamics. Furthermore, the model can be utilized for control system design by multi-variable methods requiring any stable equilibrium to be defined by a fixed operating point. Time-domain simulations in comparison to an established average model of the MMC, as well as results from a detailed simulation model of an MMC with 400 sub-modules per arm, are presented as verification of the validity and accuracy of the developed model.
1706.04959v1
2017-11-07
Global Properties of M31's Stellar Halo from the SPLASH Survey: III. Measuring the Stellar Velocity Dispersion Profile
We present the velocity dispersion of red giant branch (RGB) stars in M31's halo, derived by modeling the line of sight velocity distribution of over 5000 stars in 50 fields spread throughout M31's stellar halo. The dataset was obtained as part of the SPLASH (Spectroscopic and Photometric Landscape of Andromeda's Stellar Halo) Survey, and covers projected radii of 9 to 175 kpc from M31's center. All major structural components along the line of sight in both the Milky Way (MW) and M31 are incorporated in a Gaussian Mixture Model, including all previously identified M31 tidal debris features in the observed fields. The probability an individual star is a constituent of M31 or the MW, based on a set of empirical photometric and spectroscopic diagnostics, is included as a prior probability in the mixture model. The velocity dispersion of stars in M31's halo is found to decrease only mildly with projected radius, from 108 km/s in the innermost radial bin (8.2 to 14.1 kpc) to $\sim 80$ to 90 km/s at projected radii of $\sim 40$ to 130 kpc, and can be parameterized with a power-law of slope $-0.12\pm 0.05$. The quoted uncertainty on the power-law slope reflects only the precision of the method, although other sources of uncertainty we consider contribute negligibly to the overall error budget.
1711.02700v1
2017-12-19
Efficient implementations of the Multivariate Decomposition Method for approximating infinite-variate integrals
In this paper we focus on efficient implementations of the Multivariate Decomposition Method (MDM) for approximating integrals of $\infty$-variate functions. Such $\infty$-variate integrals occur for example as expectations in uncertainty quantification. Starting with the anchored decomposition $f = \sum_{\mathfrak{u}\subset\mathbb{N}} f_\mathfrak{u}$, where the sum is over all finite subsets of $\mathbb{N}$ and each $f_\mathfrak{u}$ depends only on the variables $x_j$ with $j\in\mathfrak{u}$, our MDM algorithm approximates the integral of $f$ by first truncating the sum to some `active set' and then approximating the integral of the remaining functions $f_\mathfrak{u}$ term-by-term using Smolyak or (randomized) quasi-Monte Carlo (QMC) quadratures. The anchored decomposition allows us to compute $f_\mathfrak{u}$ explicitly by function evaluations of $f$. Given the specification of the active set and theoretically derived parameters of the quadrature rules, we exploit structures in both the formula for computing $f_\mathfrak{u}$ and the quadrature rules to develop computationally efficient strategies to implement the MDM in various scenarios. In particular, we avoid repeated function evaluations at the same point. We provide numerical results for a test function to demonstrate the effectiveness of the algorithm.
1712.06782v3
2018-05-24
Impact of thermal fluctuations on transport in antiferromagnetic semimetals
Recent demonstrations on manipulating antiferromagnetic (AF) order have triggered a growing interest in antiferromagnetic metal (AFM), and potential high-density spintronic applications demand further improvements in the anisotropic magnetoresistance (AMR). The antiferromagnetic semimetals (AFS) are newly discovered materials that possess massless Dirac fermions that are protected by the crystalline symmetries. In this material, a reorientation of the AF order may break the underlying symmetries and induce a finite energy gap. As such, the possible phase transition from the semimetallic to insulating phase gives us a choice for a wide range of resistance ensuring a large AMR. To further understand the robustness of the phase transition, we study thermal fluctuations of the AF order in AFS at a finite temperature. For macroscopic samples, we find that the thermal fluctuations effectively decrease the magnitude of the AF order by renormalizing the effective Hamiltonian. Our finding suggests that the insulating phase exhibits a gap narrowing at elevated temperatures, which leads to a substantial decrease in AMR. We also examine spatially correlated thermal fluctuations for microscopic samples by solving the microscopic Landau-Lifshitz-Gilbert equation finding a qualitative difference of the gap narrowing in the insulating phase. For both cases, the semimetallic phase shows a minimal change in its transmission spectrum illustrating the robustness of the symmetry protected states in AFS. Our finding may serve as a guideline for estimating and maximizing AMR of the AFS samples at elevated temperatures.
1805.09826v1
2018-05-29
An exact solution for choosing the largest measurement from a sample drawn from an uniform distribution
In "Recognizing the Maximum of a Sequence", Gilbert and Mosteller analyze a full information game where n measurements from an uniform distribution are drawn and a player (knowing n) must decide at each draw whether or not to choose that draw. The goal is to maximize the probability of choosing the draw that corresponds to the maximum of the sample. In their calculations of the optimal strategy, the optimal probability and the asymptotic probability, they assume that after a draw x the probability that the next i numbers are all smaller than x is $x^i$; but this fails to recognize that continuing the game (not choosing a draw because it is lower than a cutoff and waiting for the next draw) conditions the distribution of the following i numbers such that their expected maximum is higher then i/(i+1). The problem is now redefined with each draw leading to a win, a false positive loss, a false negative loss and a continuation. An exact formula for these probabilities is deduced, both for the general case of n-1 different indifference numbers (assuming 0 as the last cutoff) and the particular case of the same indifference number for all cutoffs but the last. An approximation is found that preserves the main characteristics of the optimal solution (slow decay of win probability, quick decay of false positives and linear decay of false negatives). This new solution and the original Gilbert and Mosteller formula are compared against simulations, and their asymptotic behavior is studied.
1805.11556v1
2018-06-28
From clusters to queries: exploiting uncertainty in the modularity landscape of complex networks
Uncovering latent community structure in complex networks is a field that has received an enormous amount of attention. Unfortunately, whilst potentially very powerful, unsupervised methods for uncovering labels based on topology alone has been shown to suffer from several difficulties. For example, the search space for many module extraction approaches, such as the modularity maximisation algorithm, appears to be extremely glassy, with many high valued solutions that lack any real similarity to one another. However, in this paper we argue that this is not a flaw with the modularity maximisation algorithm but, rather, information that can be used to aid the context specific classification of functional relationships between vertices. Formally, we present an approach for generating a high value modularity consensus space for a network, based on the ensemble space of locally optimal modular partitions. We then use this approach to uncover latent relationships, given small query sets. The methods developed in this paper are applied to biological and social datasets with ground-truth label data, using a small number of examples used as seed sets to uncover relationships. When tested on both real and synthetic datasets our method is shown to achieve high levels of classification accuracy in a context specific manner, with results comparable to random walk with restart methods.
1806.10904v1
2018-07-05
Veloce Rosso: Australia's new precision radial velocity spectrograph
Veloce is an ultra-stable fibre-fed R4 echelle spectrograph for the 3.9 m Anglo-Australian Telescope. The first channel to be commissioned, Veloce 'Rosso', utilises multiple low-cost design innovations to obtain Doppler velocities for Sun-like and M-dwarf stars at <1 m/s precision. The spectrograph has an asymmetric white-pupil format with a 100-mm beam diameter, delivering R>75,000 spectra over a 580-950 nm range for the Rosso channel. Simultaneous calibration is provided by a single-mode pulsed laser frequency comb in tandem with a traditional arc lamp. A bundle of 19 object fibres provides a 2.4" field of view for full sampling of stellar targets from the AAT site. Veloce is housed in dual environmental enclosures that maintain positive air pressure at a stability of +/-0.3 mbar, with a thermal stability of +/-0.01 K on the optical bench. We present a technical overview and early performance data from Australia's next major spectroscopic machine.
1807.01938v1
2018-07-19
Generalized Metric Repair on Graphs
Many modern data analysis algorithms either assume that or are considerably more efficient if the distances between the data points satisfy a metric. These algorithms include metric learning, clustering, and dimensionality reduction. Because real data sets are noisy, the similarity measures often fail to satisfy a metric. For this reason, Gilbert and Jain [11] and Fan, et al. [8] introduce the closely related problems of $\textit{sparse metric repair}$ and $\textit{metric violation distance}$. The goal of each problem is to repair as few distances as possible to ensure that the distances between the data points satisfy a metric. We generalize these problems so as to no longer require all the distances between the data points. That is, we consider a weighted graph $G$ with corrupted weights w and our goal is to find the smallest number of modifications to the weights so that the resulting weighted graph distances satisfy a metric. This problem is a natural generalization of the sparse metric repair problem and is more flexible as it takes into account different relationships amongst the input data points. As in previous work, we distinguish amongst the types of repairs permitted (decrease, increase, and general repairs). We focus on the increase and general versions and establish hardness results and show the inherent combinatorial structure of the problem. We then show that if we restrict to the case when $G$ is a chordal graph, then the problem is fixed parameter tractable. We also present several classes of approximation algorithms. These include and improve upon previous metric repair algorithms for the special case when $G = K_n$
1807.07619v1
2018-10-17
Precipitating Ordered Skyrmion Lattices from Helical Spaghetti
Magnetic skyrmions have been the focus of intense research due to their potential applications in ultra-high density data and logic technologies, as well as for the unique physics arising from their antisymmetric exchange term and topological protections. In this work we prepare a chiral jammed state in chemically disordered (Fe, Co)Si consisting of a combination of randomly-oriented magnetic helices, labyrinth domains, rotationally disordered skyrmion lattices and/or isolated skyrmions. Using small angle neutron scattering, (SANS) we demonstrate a symmetry-breaking magnetic field sequence which disentangles the jammed state, resulting in an ordered, oriented skyrmion lattice. The same field sequence was performed on a sample of powdered Cu2OSeO3 and again yields an ordered, oriented skyrmion lattice, despite relatively non-interacting nature of the grains. Micromagnetic simulations confirm the promotion of a preferred skyrmion lattice orientation after field treatment, independent of the initial configuration, suggesting this effect may be universally applicable. Energetics extracted from the simulations suggest that approaching a magnetic hard axis causes the moments to diverge away from the magnetic field, increasing the Dzyaloshinskii-Moriya energy, followed subsequently by a lattice re-orientation. The ability to facilitate an emergent ordered magnetic lattice with long-range orientation in a variety of materials despite overwhelming internal disorder enables the study of skyrmions even in imperfect powdered or polycrystalline systems and greatly improves the ability to rapidly screen candidate skyrmion materials.
1810.07631v1
2018-11-09
Post-randomization Biomarker Effect Modification in an HIV Vaccine Clinical Trial
While the HVTN 505 trial showed no overall efficacy of the tested vaccine to prevent HIV infection over placebo, previous studies, biological theories, and the finding that immune response markers strongly correlated with infection in vaccine recipients generated the hypothesis that a qualitative interaction occurred. This hypothesis can be assessed with statistical methods for studying treatment effect modification by an intermediate response variable (i.e., principal stratification effect modification (PSEM) methods). However, available PSEM methods make untestable structural risk assumptions, such that assumption-lean versions of PSEM methods are needed in order to surpass the high bar of evidence to demonstrate a qualitative interaction. Fortunately, the survivor average causal effect (SACE) literature is replete with assumption-lean methods that can be readily adapted to the PSEM application for the special case of a binary intermediate response variable. We map this adaptation, opening up a host of new PSEM methods for a binary intermediate variable measured via two-phase sampling, for a dichotomous or failure time final outcome and including or excluding the SACE monotonicity assumption. The new methods support that the vaccine partially protected vaccine recipients with a high polyfunctional CD8+ T cell response, an important new insight for the HIV vaccine field.
1811.03930v1
2019-03-22
Natural reward as the fundamental macroevolutionary force
Darwin's theory of evolution by natural selection does not predict long-term progress or advancement, nor does it provide a useful way to define or understand these concepts. Nevertheless, the history of life is marked by major trends that appear progressive, and seemingly more advanced forms of life have appeared. To reconcile theory and fact, evolutionists have proposed novel theories that extend natural selection to levels and time frames not justified by the original structure of Darwin's theory. To extend evolutionary theory without violating the most basic tenets of Darwinism, I here identify a separate struggle and an alternative evolutionary force. Owing to the abundant free energy in our universe, there is a struggle for supremacy that naturally rewards those that are first to invent novelties that allow exploitation of untapped resources. This natural reward comes in form of a temporary monopoly, which is granted to those who win a competitive race to innovate. By analogy to human economies, natural selection plays the role of nature's inventor, gradually fashioning inventions to the situation at hand, while natural reward plays the role of nature's entrepreneur, choosing which inventions to first disseminate to large markets. Natural reward leads to progress through a process of invention-conquest macroevolution, in which the dual forces of natural selection and natural reward create and disseminate major innovations. Over vast time frames, natural reward drives the advancement of life by a process of extinction-replacement megaevolution that releases constraints on progress and increases the innovativeness of life.
1903.09567v1
2019-07-15
Entanglement-assisted Quantum Codes from Algebraic Geometry Codes
Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a way for quantum error correcting codes to achieve higher rates than the one obtained via the traditional stabilizer formalism. Such codes are called entanglement-assisted quantum (QUENTA) codes. In this paper, we use algebraic geometry codes to construct several families of QUENTA codes via the Euclidean and the Hermitian construction. Two of the families created have maximal entanglement and have quantum Singleton defect equal to zero or one. Comparing the other families with the codes with the respective quantum Gilbert-Varshamov bound, we show that our codes have a rate that surpasses that bound. At the end, asymptotically good towers of linear complementary dual codes are used to obtain asymptotically good families of maximal entanglement QUENTA codes. Furthermore, a simple comparison with the quantum Gilbert-Varshamov bound demonstrates that using our construction it is possible to create an asymptotically family of QUENTA codes that exceeds this bound.
1907.06357v2
2019-09-06
Parameter identification for the Landau-Lifshitz-Gilbert equation in Magnetic Particle Imaging
Magnetic particle imaging (MPI) is a tracer-based technique for medical imaging where the tracer consists of ironoxide nanoparticles. The key idea is to measure the particle response to a temporally changing external magnetic field to compute the spatial concentration of the tracer inside the object. A decent mathematical model demands for a data-driven computation of the system function which does not only describe the measurement geometry but also encodes the interaction of the particles with the external magnetic field. The physical model of this interaction is given by the Landau-Lifshitz-Gilbert (LLG) equation. The determination of the system function can be seen as an inverse problem of its own which can be interpreted as a calibration problem for MPI. In this contribution the calibration problem is formulated as an inverse parameter identification problem for the LLG equation. We give a detailed analysis of the direct as well as the inverse problem in an all-at-once as well as in a reduced setting. The analytical results yield a deeper understanding of inverse problems connected to the LLG equation and provide a starting point for the development of robust numerical solution methods in MPI.
1909.02912v1
2019-11-06
Automated Left Ventricle Dimension Measurement in 2D Cardiac Ultrasound via an Anatomically Meaningful CNN Approach
Two-dimensional echocardiography (2DE) measurements of left ventricle (LV) dimensions are highly significant markers of several cardiovascular diseases. These measurements are often used in clinical care despite suffering from large variability between observers. This variability is due to the challenging nature of accurately finding the correct temporal and spatial location of measurement endpoints in ultrasound images. These images often contain fuzzy boundaries and varying reflection patterns between frames. In this work, we present a convolutional neural network (CNN) based approach to automate 2DE LV measurements. Treating the problem as a landmark detection problem, we propose a modified U-Net CNN architecture to generate heatmaps of likely coordinate locations. To improve the network performance we use anatomically meaningful heatmaps as labels and train with a multi-component loss function. Our network achieves 13.4%, 6%, and 10.8% mean percent error on intraventricular septum (IVS), LV internal dimension (LVID), and LV posterior wall (LVPW) measurements respectively. The design outperforms other networks and matches or approaches intra-analyser expert error.
1911.02448v1
2019-11-12
Linear-mode avalanche photodiode arrays for low-noise near-infrared imaging in space
Astronomical observations often require the detection of faint signals in the presence of noise, and the near-infrared regime is no exception. In particular, where the application has short exposure time constraints, we are frequently and unavoidably limited by the read noise of a system. A recent and revolutionary development in detector technology is that of linear-mode avalanche photodiode (LmAPD) arrays. By the introduction of a signal multiplication region within the device, effective read noise can be reduced to <0.2 e-, enabling the detection of very small signals at frame rates of up to 1 kHz. This is already impacting ground-based astronomy in high-speed applications such as wavefront sensing and fringe tracking, but has not yet been exploited for scientific space missions. We present the current status of a collaboration with Leonardo MW - creators of the 'SAPHIRA' LmAPD array - as we work towards the first in-orbit demonstration of a SAPHIRA device in 'Emu', a hosted payload on the International Space Station. The Emu mission will fully benefit from the 'noiseless' gains offered by LmAPD technology as it produces a time delay integration photometric sky survey at 1.4 microns, using compact readout electronics developed at the Australian National University. This is just one example of a use case that could not be achieved with conventional infrared sensors.
1911.04684v1
2020-03-17
Maximizing Influence-based Group Shapley Centrality
One key problem in network analysis is the so-called influence maximization problem, which consists in finding a set $S$ of at most $k$ seed users, in a social network, maximizing the spread of information from $S$. This paper studies a related but slightly different problem: We want to find a set $S$ of at most $k$ seed users that maximizes the spread of information, when $S$ is added to an already pre-existing - but unknown - set of seed users $T$. We consider such scenario to be very realistic. Assume a central entity wants to spread a piece of news, while having a budget to influence $k$ users. This central authority may know that some users are already aware of the information and are going to spread it anyhow. The identity of these users being however completely unknown. We model this optimization problem using the Group Shapley value, a well-founded concept from cooperative game theory. While the standard influence maximization problem is easy to approximate within a factor $1-1/e-\epsilon$ for any $\epsilon>0$, assuming common computational complexity conjectures, we obtain strong hardness of approximation results for the problem at hand in this paper. Maybe most prominently, we show that it cannot be approximated within $1/n^{o(1)}$ under the Gap Exponential Time Hypothesis. Hence, it is unlikely to achieve anything better than a polynomial factor approximation. Nevertheless, we show that a greedy algorithm can achieve a factor of $\frac{1-1/e}{k}-\epsilon$ for any $\epsilon>0$, showing that not all is lost in settings where $k$ is bounded.
2003.07966v1
2020-04-24
Single-electron operation of a silicon-CMOS 2x2 quantum dot array with integrated charge sensing
The advanced nanoscale integration available in silicon complementary metal-oxide-semiconductor (CMOS) technology provides a key motivation for its use in spin-based quantum computing applications. Initial demonstrations of quantum dot formation and spin blockade in CMOS foundry-compatible devices are encouraging, but results are yet to match the control of individual electrons demonstrated in university-fabricated multi-gate designs. We show here that the charge state of quantum dots formed in a CMOS nanowire device can be sensed by using floating gates to electrostatically couple it to a remote single electron transistor (SET) formed in an adjacent nanowire. By biasing the nanowire and gates of the remote SET with respect to the nanowire hosting the quantum dots, we controllably form ancillary quantum dots under the floating gates, thus enabling the demonstration of independent control over charge transitions in a quadruple (2x2) quantum dot array. This device overcomes the limitations associated with measurements based on tunnelling transport through the dots and permits the sensing of all charge transitions, down to the last electron in each dot. We use effective mass theory to investigate the necessary optimization of the device parameters in order to achieve the tunnel rates required for spin-based quantum computation.
2004.11558v1
2020-08-22
Measurement of magnetic fields using the voltage generated by a vibrating wire
A vibrating wire may be used as an instrument with a variety of applications, one of which is the measurement of magnetic fields. Often, the magnetic fields are determined by measuring the amplitude of the wire vibration under the action of a Lorentz force. Though generally adequate, this approach may be inconvenient in certain circumstances. One of these occurs when it is necessary to measure the amplitude of high-frequency vibration, as the amplitude is expected to decrease linearly with frequency, and thus becomes harder to measure. Another example may be found in situations where the sensor must operate over a wide range of vibration frequencies. In this case the sensor will be unresponsive to specific frequencies of wire vibration, which are determined by the placement of the sensor. This means that for the instrument to be robust, the sensor must be precisely mobile, or multiple sensors must be used. Here a technique which may be used to supplement the displacement sensor is described. This technique makes use of the voltage generated by the motion of the wire in the magnetic field under measurement. It is predicted that the technique may be more suitable for measurements requiring high frequency vibration, and is sensitive to all frequencies of vibration. Measurements of a magnetic field obtained using this technique are compared to those found using only a displacement sensor, and the benefits and drawbacks of the technique are discussed.
2008.09898v1
2020-11-25
Domain wall motion in axially symmetric spintronic nanowires
This article is concerned with the dynamics of magnetic domain walls (DWs) in nanowires as solutions to the classical Landau-Lifschitz-Gilbert equation augmented by a typically non-variational Slonczewski term for spin-torque effects. Taking applied field and spin-polarization as the primary parameters, we study dynamic stability as well as selection mechanisms analytically and numerically in an axially symmetric setting. Concerning the stability of the DWs' asymptotic states, we distinguish the bistable (both stable) and the monostable (one unstable, one stable) parameter regime. In the bistable regime, we extend known stability results of an explicit family of precessing solutions and identify a relation of applied field and spin-polarization for standing DWs. We verify that this family is convectively unstable into the monostable regime, thus forming so-called pushed fronts, before turning absolutely unstable. In the monostable regime, we present explicit formulas for the so-called absolute spectrum of more general matrix operators. This allows us to relate translation and rotation symmetries to the position of the singularities of the pointwise Green's function. Thereby, we determine the linear selection mechanism for the asymptotic velocity and frequency of DWs and corroborate these by long-time numerical simulations. All these results include the axially symmetric Landau-Lifschitz-Gilbert equation.
2012.01343v1
2020-12-08
Sparse Correspondence Analysis for Contingency Tables
Since the introduction of the lasso in regression, various sparse methods have been developed in an unsupervised context like sparse principal component analysis (s-PCA), sparse canonical correlation analysis (s-CCA) and sparse singular value decomposition (s-SVD). These sparse methods combine feature selection and dimension reduction. One advantage of s-PCA is to simplify the interpretation of the (pseudo) principal components since each one is expressed as a linear combination of a small number of variables. The disadvantages lie on the one hand in the difficulty of choosing the number of non-zero coefficients in the absence of a well established criterion and on the other hand in the loss of orthogonality for the components and/or the loadings. In this paper we propose sparse variants of correspondence analysis (CA)for large contingency tables like documents-terms matrices used in text mining, together with pPMD, a deation technique derived from projected deflation in s-PCA. We use the fact that CA is a double weighted PCA (for rows and columns) or a weighted SVD, as well as a canonical correlation analysis of indicator variables. Applying s-CCA or s-SVD allows to sparsify both rows and columns weights. The user may tune the level of sparsity of rows and columns and optimize it according to some criterium, and even decide that no sparsity is needed for rows (or columns) by relaxing one sparsity constraint. The latter is equivalent to apply s-PCA to matrices of row (or column) profiles.
2012.04271v1
2020-12-27
Vacuum Stability Conditions for Higgs Potentials with $SU(2)_L$ Triplets
Tree-level dynamical stability of scalar field potentials in renormalizable theories can in principle be expressed in terms of positivity conditions on quartic polynomial structures. However, these conditions cannot always be cast in a fully analytical resolved form, involving only the couplings and being valid for all field directions. In this paper we consider such forms in three physically motivated models involving $SU(2)$ triplet scalar fields: the Type-II seesaw model, the Georgi-Machacek model, and a generalized two-triplet model. A detailed analysis of the latter model allows to establish the full set of necessary and sufficient boundedness from below conditions. These can serve as a guide, together with unitarity and vacuum structure constraints, for consistent phenomenological (tree-level) studies. They also provide a seed for improved loop-level conditions, and encompass in particular the leading ones for the more specific Georgi-Machacek case. Incidentally, we present complete proofs of various properties and also derive general positivity conditions on quartic polynomials that are equivalent but much simpler than the ones used in the literature.
2012.13947v2
2021-03-25
Phases of Small Worlds: A Mean Field Formulation
A network is said to have the properties of a small world if a suitably defined average distance between any two nodes is proportional to the logarithm of the number of nodes, $N$. In this paper, we present a novel derivation of the small-world property for Gilbert-Erd\"os-Renyi random networks. We employ a mean field approximation that permits the analytic derivation of the distribution of shortest paths that exhibits logarithmic scaling away from the phase transition, inferable via a suitably interpreted order parameter. We begin by framing the problem in generality with a formal generating functional for undirected weighted random graphs with arbitrary disorder, recovering the result that the free energy associated with an ensemble of Gilbert graphs corresponds to a system of non-interacting fermions identified with the edge states. We then present a mean field solution for this model and extend it to more general realizations of network randomness. For a two family class of stochastic block models that we refer to as dimorphic networks, which allow for links within the different families to be drawn from two independent discrete probability distributions, we find the mean field approximation maps onto a spin chain combinatorial problem and again yields useful approximate analytic expressions for mean path lengths. Dimorophic networks exhibit a richer phase structure, where distinct small world regimes separate in analogy to the spinodal decomposition of a fluid. We find that is it possible to induce small world behavior in sub-networks that by themselves would not be in the small-world regime.
2103.14001v2
2021-05-04
Evaluating Metrics for Standardized Benchmarking of Remote Presence Systems
To reduce the need for business-related air travel and its associated energy consumption and carbon footprint, the U.S. Department of Energy's ARPA-E is supporting a research project called SCOTTIE - Systematic Communication Objectives and Telecommunications Technology Investigations and Evaluations. SCOTTIE tests virtual and augmented reality platforms in a functional comparison with face-to-face (FtF) interactions to derive travel replacement thresholds for common industrial training scenarios. The primary goal of Study 1 is to match the communication effectiveness and learning outcomes obtained from a FtF control using virtual reality (VR) training scenarios in which a local expert with physical equipment trains a remote apprentice without physical equipment immediately present. This application scenario is commonplace in industrial settings where access to expensive equipment and materials is limited and a number of apprentices must travel to a central location in order to undergo training. Supplying an empirically validated virtual training alternative constitutes a readily adoptable use-case for businesses looking to reduce time and monetary expenditures associated with travel. The technology used for three different virtual presence technologies was strategically selected for feasibility, relatively low cost, business relevance, and potential for impact through transition. The authors suggest that the results of this study might generalize to the challenge of virtual conferences.
2105.01772v1
2021-07-12
Partially Concatenated Calderbank-Shor-Steane Codes Achieving the Quantum Gilbert-Varshamov Bound Asymptotically
In this paper, we utilize a concatenation scheme to construct new families of quantum error correction codes achieving the quantum Gilbert-Varshamov (GV) bound asymptotically. We concatenate alternant codes with any linear code achieving the classical GV bound to construct Calderbank-Shor-Steane (CSS) codes. We show that the concatenated code can achieve the quantum GV bound asymptotically and can approach the Hashing bound for asymmetric Pauli channels. By combing Steane's enlargement construction of CSS codes, we derive a family of enlarged stabilizer codes achieving the quantum GV bound for enlarged CSS codes asymptotically. As applications, we derive two families of fast encodable and decodable CSS codes with parameters $\mathscr{Q}_1=[[N,\Omega(\sqrt{N}),\Omega( \sqrt{N})]],$ and $\mathscr{Q}_2=[[N,\Omega(N/\log N),\Omega(N/\log N)/\Omega(\log N)]].$ We show that $\mathscr{Q}_1$ can be encoded very efficiently by circuits of size $O(N)$ and depth $O(\sqrt{N})$. For an input error syndrome, $\mathscr{Q}_1$ can correct any adversarial error of weight up to half the minimum distance bound in $O(N)$ time. $\mathscr{Q}_1$ can also be decoded in parallel in $O(\sqrt{N})$ time by using $O(\sqrt{N})$ classical processors. For an input error syndrome, we proved that $\mathscr{Q}_2$ can correct a linear number of ${X}$-errors with high probability and an almost linear number of ${Z}$-errors in $O(N )$ time. Moreover, $\mathscr{Q}_2$ can be decoded in parallel in $O(\log(N))$ time by using $O(N)$ classical processors.
2107.05174v2
2021-07-12
Assessment of Immune Correlates of Protection via Controlled Vaccine Efficacy and Controlled Risk
Immune correlates of protection (CoPs) are immunologic biomarkers accepted as a surrogate for an infectious disease clinical endpoint and thus can be used for traditional or provisional vaccine approval. To study CoPs in randomized, placebo-controlled trials, correlates of risk (CoRs) are first assessed in vaccine recipients. This analysis does not assess causation, as a CoR may fail to be a CoP. We propose a causal CoP analysis that estimates the controlled vaccine efficacy curve across biomarker levels $s$, $CVE(s)$, equal to one minus the ratio of the controlled-risk curve $r_C(s)$ at $s$ and placebo risk, where $r_C(s)$ is causal risk if all participants are assigned vaccine and the biomarker is set to $s$. The criterion for a useful CoP is wide variability of $CVE(s)$ in $s$. Moreover, estimation of $r_C(s)$ is of interest in itself, especially in studies without a placebo arm. For estimation of $r_C(s)$, measured confounders can be adjusted for by any regression method that accommodates missing biomarkers, to which we add sensitivity analysis to quantify robustness of CoP evidence to unmeasured confounding. Application to two harmonized phase 3 trials supports that 50% neutralizing antibody titer has value as a controlled vaccine efficacy CoP for virologically confirmed dengue (VCD): in CYD14 the point estimate (95% confidence interval) for $CVE(s)$ accounting for measured confounders and building in conservative margin for unmeasured confounding increases from 29.6% (95% CI 3.5 to 45.9) at titer 1:36 to 78.5% (95% CI 67.9 to 86.8) at titer 1:1200; these estimates are 17.4% (95% CI -14.4 to 36.5) and 84.5% (95% CI 79.6 to 89.1) for CYD15.
2107.05734v1
2021-07-23
Efficient nonparametric estimation of the covariate-adjusted threshold-response function, a support-restricted stochastic intervention
Identifying a biomarker or treatment-dose threshold that marks a specified level of risk is an important problem, especially in clinical trials. This risk, viewed as a function of thresholds and possibly adjusted for covariates, we call the threshold-response function. Extending the work of Donovan, Hudgens and Gilbert (2019), we propose a nonparametric efficient estimator for the covariate-adjusted threshold-response function, which utilizes machine learning and Targeted Minimum-Loss Estimation (TMLE). We additionally propose a more general estimator, based on sequential regression, that also applies when there is outcome missingness. We show that the threshold-response for a given threshold may be viewed as the expected outcome under a stochastic intervention where all participants are given a treatment dose above the threshold. We prove the estimator is efficient and characterize its asymptotic distribution. A method to construct simultaneous 95% confidence bands for the threshold-response function and its inverse is given. Furthermore, we discuss how to adjust our estimator when the treatment or biomarker is missing-at-random, as is the case in clinical trials with biased sampling designs, using inverse-probability-weighting. The methods are assessed in a diverse set of simulation settings with rare outcomes and cumulative case-control sampling. The methods are employed to estimate neutralizing antibody thresholds for virologically confirmed dengue risk in the CYD14 and CYD15 dengue vaccine trials.
2107.11459v2
2021-10-15
The radio SZ effect as a probe of the cosmological radio background
If there is a substantial cosmological radio background, there should be a radio Sunyaev-Zeldovich (SZ) effect that goes along with it. The radio background Comptonization leads to a slight photon excess at all wavelengths, while Comptonization of the CMB at low frequencies leads to a decrement. For levels of the radio background consistent with observations, these effects cancel each other around $\nu\simeq 735~$MHz, with an excess at lower frequencies and a decrement at higher frequencies. Assuming a purely cosmological origin of the observed ARCADE radio excess, at $\nu \lesssim 20\,{\rm GHz}$ the signal scales as $\Delta T / T_{\rm CMB}\simeq 2\,y\left[ (\nu/735\,{\rm MHz})^{-2.59}-1\right]$ with frequency and the Compton-$y$ parameter of the cluster. For a typical cluster, the total radio SZ signal is at the level of $\Delta T\simeq 1\,{\rm mK}$ around the null, with a steep scaling towards radio frequencies. This is above current raw sensitivity limits for many radio facilities at these wavelengths, providing a unique way to confirm the cosmological origin of the ARCADE excess and probe its properties (e.g., redshift dependence and isotropy). We also give an expression to compute the radio-analogue of the kinematic SZ effect, highlighting that this might provide a new tool to probe large-scale velocity fields and the cosmic evolution of the radio background.
2110.08373v1
2021-10-20
No Transits of Proxima Centauri Planets in High-Cadence TESS Data
Proxima Centauri is our nearest stellar neighbor and one of the most well-studied stars in the sky. In 2016, a planetary companion was detected through radial velocity measurements. Proxima Centauri b has a minimum mass of 1.3 Earth masses and orbits with a period of 11.2 days at 0.05 AU from its stellar host, and resides within the star's Habitable Zone. While recent work has shown that Proxima Centauri b likely does not transit, given the value of potential atmospheric observations via transmission spectroscopy of the closest possible Habitable Zone planet, we reevaluate the possibility that Proxima Centauri b is a transiting exoplanet using data from the Transiting Exoplanet Survey Satellite (TESS). We use three sectors (Sectors 11, 12, and 38 at 2-minute cadence) of observations from TESS to search for planets. Proxima Centauri is an extremely active M5.5 star, emitting frequent white-light flares; we employ a novel method that includes modeling the stellar activity in our planet search algorithm. We do not detect any planet signals. We injected synthetic transiting planets into the TESS and use this analysis to show that Proxima Centauri b cannot be a transiting exoplanet with a radius larger than 0.4 R$_\oplus$. Moreover, we show that it is unlikely that any Habitable Zone planets larger than Mars transit Proxima Centauri.
2110.10702v2
2021-12-20
Analysis of preintegration followed by quasi-Monte Carlo integration for distribution functions and densities
In this paper, we analyse a method for approximating the distribution function and density of a random variable that depends in a non-trivial way on a possibly high number of independent random variables, each with support on the whole real line. Starting with the integral formulations of the distribution and density, the method involves smoothing the original integrand by preintegration with respect to one suitably chosen variable, and then applying a suitable quasi-Monte Carlo (QMC) method to compute the integral of the resulting smoother function. Interpolation is then used to reconstruct the distribution or density on an interval. The preintegration technique is a special case of conditional sampling, a method that has previously been applied to a wide range of problems in statistics and computational finance. In particular, the pointwise approximation studied in this work is a specific case of the conditional density estimator previously considered in L'Ecuyer et al., arXiv:1906.04607. Our theory provides a rigorous regularity analysis of the preintegrated function, which is then used to show that the errors of the pointwise and interpolated estimators can both achieve nearly first-order convergence. Numerical results support the theory.
2112.10308v5
2021-12-21
Exponential decay of intersection volume with applications on list-decodability and Gilbert-Varshamov type bound
We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking, this happens when the metric space is (i) expanding and (ii) well-spread, and (iii) a certain random variable on the boundary of a ball has a small tail. As applications, we show that the volume of intersection of balls in Hamming, Johnson spaces and symmetric groups decay exponentially as their centers drift apart. To verify condition (iii), we prove some large deviation inequalities `on a slice' for functions with Lipschitz conditions. We then use these estimates on intersection volumes to $\bullet$ obtain a sharp lower bound on list-decodability of random $q$-ary codes, confirming a conjecture of Li and Wootters; and $\bullet$ improve the classical bound of Levenshtein from 1971 on constant weight codes by a factor linear in dimension, resolving a problem raised by Jiang and Vardy. Our probabilistic point of view also offers a unified framework to obtain improvements on other Gilbert--Varshamov type bounds, giving conceptually simple and calculation-free proofs for $q$-ary codes, permutation codes, and spherical codes. Another consequence is a counting result on the number of codes, showing ampleness of large codes.
2112.11274v2
2021-12-22
Preintegration is not smoothing when monotonicity fails
Preintegration is a technique for high-dimensional integration over $d$-dimensional Euclidean space, which is designed to reduce an integral whose integrand contains kinks or jumps to a $(d-1)$-dimensional integral of a smooth function. The resulting smoothness allows efficient evaluation of the $(d-1)$-dimensional integral by a Quasi-Monte Carlo or Sparse Grid method. The technique is similar to conditional sampling in statistical contexts, but the intention is different: in conditional sampling the aim is to reduce the variance, rather than to achieve smoothness. Preintegration involves an initial integration with respect to one well chosen real-valued variable. Griebel, Kuo, Sloan [Math. Comp. 82 (2013), 383--400] and Griewank, Kuo, Le\"ovey, Sloan [J. Comput. Appl. Maths. 344 (2018), 259--274] showed that the resulting $(d-1)$-dimensional integrand is indeed smooth under appropriate conditions, including a key assumption -- the integrand of the smooth function underlying the kink or jump is strictly monotone with respect to the chosen special variable when all other variables are held fixed. The question addressed in this paper is whether this monotonicity property with respect to one well chosen variable is necessary. We show here that the answer is essentially yes, in the sense that without this property the resulting $(d-1)$-dimensional integrand is generally not smooth, having square-root or other singularities.
2112.11621v1
2021-12-30
A causal inference framework for spatial confounding
Recently, addressing spatial confounding has become a major topic in spatial statistics. However, the literature has provided conflicting definitions, and many proposed definitions do not address the issue of confounding as it is understood in causal inference. We define spatial confounding as the existence of an unmeasured causal confounder with a spatial structure. We present a causal inference framework for nonparametric identification of the causal effect of a continuous exposure on an outcome in the presence of spatial confounding. We propose double machine learning (DML), a procedure in which flexible models are used to regress both the exposure and outcome variables on confounders to arrive at a causal estimator with favorable robustness properties and convergence rates, and we prove that this approach is consistent and asymptotically normal under spatial dependence. As far as we are aware, this is the first approach to spatial confounding that does not rely on restrictive parametric assumptions (such as linearity, effect homogeneity, or Gaussianity) for both identification and estimation. We demonstrate the advantages of the DML approach analytically and in simulations. We apply our methods and reasoning to a study of the effect of fine particulate matter exposure during pregnancy on birthweight in California.
2112.14946v7
2022-01-20
Accurate modeling of grazing transits using umbrella sampling
Grazing transits present a special problem for statistical studies of exoplanets. Even though grazing planetary orbits are rare (due to geometric selection effects), for many low to moderate signal-to-noise cases, a significant fraction of the posterior distribution is nonetheless consistent with a grazing geometry. A failure to accurately model grazing transits can therefore lead to biased inferences even for cases where the planet is not actually on a grazing trajectory. With recent advances in stellar characterization, the limiting factor for many scientific applications is now the quality of available transit fits themselves, and so the time is ripe to revisit the transit fitting problem. In this paper, we model exoplanet transits using a novel application of umbrella sampling and a geometry-dependent parameter basis that minimizes covariances between transit parameters. Our technique splits the transit fitting problem into independent Monte Carlo sampling runs for the grazing, non-grazing, and transition regions of the parameter space, which we then recombine into a single joint posterior probability distribution using a robust weighting scheme. Our method can be trivially parallelized and so requires no increase in the wall clock time needed for computations. Most importantly, our method produces accurate estimates of exoplanet properties for both grazing and non-grazing orbits, yielding more robust results than standard methods for many common star-planet configurations.
2201.08350v1
2022-04-22
Reward Reports for Reinforcement Learning
Building systems that are good for society in the face of complex societal effects requires a dynamic approach. Recent approaches to machine learning (ML) documentation have demonstrated the promise of discursive frameworks for deliberation about these complexities. However, these developments have been grounded in a static ML paradigm, leaving the role of feedback and post-deployment performance unexamined. Meanwhile, recent work in reinforcement learning has shown that the effects of feedback and optimization objectives on system behavior can be wide-ranging and unpredictable. In this paper we sketch a framework for documenting deployed and iteratively updated learning systems, which we call Reward Reports. Taking inspiration from various contributions to the technical literature on reinforcement learning, we outline Reward Reports as living documents that track updates to design choices and assumptions behind what a particular automated system is optimizing for. They are intended to track dynamic phenomena arising from system deployment, rather than merely static properties of models or data. After presenting the elements of a Reward Report, we discuss a concrete example: Meta's BlenderBot 3 chatbot. Several others for game-playing (DeepMind's MuZero), content recommendation (MovieLens), and traffic control (Project Flow) are included in the appendix.
2204.10817v3
2022-05-29
Generalized Stochastic Matching
In this paper, we generalize the recently studied Stochastic Matching problem to more accurately model a significant medical process, kidney exchange, and several other applications. Up until now the Stochastic Matching problem that has been studied was as follows: given a graph G = (V, E), each edge is included in the realized sub-graph of G mutually independently with probability p_e, and the goal is to find a degree-bounded sub-graph Q of G that has an expected maximum matching that approximates the expected maximum matching of the realized sub-graph. This model does not account for possibilities of vertex dropouts, which can be found in several applications, e.g. in kidney exchange when donors or patients opt out of the exchange process as well as in online freelancing and online dating when online profiles are found to be faked. Thus, we will study a more generalized model of Stochastic Matching in which vertices and edges are both realized independently with some probabilities p_v, p_e, respectively, which more accurately fits important applications than the previously studied model. We will discuss the first algorithms and analysis for this generalization of the Stochastic Matching model and prove that they achieve good approximation ratios. In particular, we show that the approximation factor of a natural algorithm for this problem is at least $0.6568$ in unweighted graphs, and $1/2 + \epsilon$ in weighted graphs for some constant $\epsilon > 0$. We further improve our result for unweighted graphs to $2/3$ using edge degree constrained subgraphs (EDCS).
2205.14717v1
2022-07-25
Spin-transfer and spin-orbit torques in the Landau-Lifshitz-Gilbert equation
Dynamic simulations of spin-transfer and spin-orbit torques are increasingly important for a wide range of spintronic devices including magnetic random access memory, spin-torque nano-oscillators and electrical switching of antiferromagnets. Here we present a computationally efficient method for the implementation of spin-transfer and spin-orbit torques within the Landau-Lifshitz-Gilbert equation used in micromagnetic and atomistic simulations. We consolidate and simplify the varying terminology of different kinds of torques into a physical action and physical origin that clearly shows the common action of spin torques while separating their different physical origins. Our formalism introduces the spin torque as an effective magnetic field, greatly simplifying the numerical implementation and aiding the interpretation of results. The strength of the effective spin torque field unifies the action of the spin torque and subsumes the details of experimental effects such as interface resistance and spin Hall angle into a simple transferable number between numerical simulations. We present a series of numerical tests demonstrating the mechanics of generalised spin torques in a range of spintronic devices. This revised approach to modelling spin-torque effects in numerical simulations enables faster simulations and a more direct way of interpreting the results, and thus it is also suitable to be used in direct comparisons with experimental measurements or in a modelling tool that takes experimental values as input.
2207.12071v2
2022-08-03
On ergodic invariant measures for the stochastic Landau-Lifschitz-Gilbert equation in 1D
We establish existence of an ergodic invariant measure on $H^1(D,\mathbb{R}^3)\cap L^2(D,\mathbb{S}^2)$ for the stochastic Landau-Lifschitz-Gilbert equation on a bounded one dimensional interval $D$. The conclusion is achieved by employing the classical Krylov-Bogoliubov theorem. In contrast to other equations, verifying the hypothesis of the Krylov-Bogoliubov theorem is not a standard procedure. We employ rough paths theory to show that the semigroup associated to the equation has the Feller property in $H^1(D,\mathbb{R}^3)\cap L^2(D,\mathbb{S}^2)$. It does not seem possible to achieve the same conclusion by the classical Stratonovich calculus. On the other hand, we employ the classical Stratonovich calculus to prove the tightness hypothesis. The Krein-Milman theorem implies existence of an ergodic invariant measure. In case of spatially constant noise, we show that there exists a unique Gibbs invariant measure and we establish the qualitative behaviour of the unique stationary solution. In absence of the anisotropic energy and for a spatially constant noise, we are able to provide a path-wise long time behaviour result: in particular, every solution synchronises with a spherical Brownian motion and it is recurrent for large times
2208.02136v2
2023-01-25
The Benchmark M Dwarf Eclipsing Binary CM Draconis With TESS: Spots, Flares and Ultra-Precise Parameters
A gold standard for the study of M dwarfs is the eclipsing binary CM Draconis. It is rare because it is bright ($J_{\rm mag}=8.5$) and contains twin fully convective stars on an almost perfectly edge-on orbit. Both masses and radii were previously measured to better than $1\%$ precision, amongst the best known. We use 15 sectors of data from the Transiting Exoplanet Survey Satellite (TESS) to show that CM Draconis is the gift that keeps on giving. Our paper has three main components. First, we present updated parameters, with radii and masses constrained to previously unheard of precisions of $\approx 0.06\%$ and $\approx 0.12\%$, respectively. Second, we discover strong and variable spot modulation, suggestive of spot clustering and an activity cycle on the order of $\approx 4$ years. Third, we discover 163 flares. We find a relationship between the spot modulation and flare rate, with flares more likely to occur when the stars appear brighter. This may be due to a positive correlation between flares and the occurrence of bright spots (plages). The flare rate is surprisingly not reduced during eclipse, but one flare may show evidence of being occulted. We suggest the flares may be preferentially polar, which has positive implications for the habitability of planets orbiting M dwarfs.
2301.10858v2
2023-02-23
Beyond Bias and Compliance: Towards Individual Agency and Plurality of Ethics in AI
AI ethics is an emerging field with multiple, competing narratives about how to best solve the problem of building human values into machines. Two major approaches are focused on bias and compliance, respectively. But neither of these ideas fully encompasses ethics: using moral principles to decide how to act in a particular situation. Our method posits that the way data is labeled plays an essential role in the way AI behaves, and therefore in the ethics of machines themselves. The argument combines a fundamental insight from ethics (i.e. that ethics is about values) with our practical experience building and scaling machine learning systems. We want to build AI that is actually ethical by first addressing foundational concerns: how to build good systems, how to define what is good in relation to system architecture, and who should provide that definition. Building ethical AI creates a foundation of trust between a company and the users of that platform. But this trust is unjustified unless users experience the direct value of ethical AI. Until users have real control over how algorithms behave, something is missing in current AI solutions. This causes massive distrust in AI, and apathy towards AI ethics solutions. The scope of this paper is to propose an alternative path that allows for the plurality of values and the freedom of individual expression. Both are essential for realizing true moral character.
2302.12149v1
2023-04-03
Three-Dimensional Structure of Hybrid Magnetic Skyrmions Determined by Neutron Scattering
Magnetic skyrmions are topologically protected chiral spin textures which present opportunities for next-generation magnetic data storage and logic information technologies. The topology of these structures originates in the geometric configuration of the magnetic spins - more generally described as the structure. While the skyrmion structure is most often depicted using a 2D projection of the three-dimensional structure, recent works have emphasized the role of all three dimensions in determining the topology and their response to external stimuli. In this work, grazing-incidence small-angle neutron scattering and polarized neutron reflectometry are used to determine the three-dimensional structure of hybrid skyrmions. The structure of the hybrid skyrmions, which includes a combination of N\'eel-like and Bloch-like components along their length, is expected to significantly contribute to their notable stability, which includes ambient conditions. To interpret the neutron scattering data, micromagnetic simulations of the hybrid skyrmions were performed, and the corresponding diffraction patterns were determined using a Born approximation transformation. The converged magnetic profile reveals the magnetic structure along with the skyrmion depth profile, including the thickness of the Bloch and N\'eel segments and the diameter of the core.
2304.01369v2
2023-05-18
Towards Intersectional Moderation: An Alternative Model of Moderation Built on Care and Power
Shortcomings of current models of moderation have driven policy makers, scholars, and technologists to speculate about alternative models of content moderation. While alternative models provide hope for the future of online spaces, they can fail without proper scaffolding. Community moderators are routinely confronted with similar issues and have therefore found creative ways to navigate these challenges. Learning more about the decisions these moderators make, the challenges they face, and where they are successful can provide valuable insight into how to ensure alternative moderation models are successful. In this study, I perform a collaborative ethnography with moderators of r/AskHistorians, a community that uses an alternative moderation model, highlighting the importance of accounting for power in moderation. Drawing from Black feminist theory, I call this "intersectional moderation." I focus on three controversies emblematic of r/AskHistorians' alternative model of moderation: a disagreement over a moderation decision; a collaboration to fight racism on Reddit; and a period of intense turmoil and its impact on policy. Through this evidence I show how volunteer moderators navigated multiple layers of power through care work. To ensure the successful implementation of intersectional moderation, I argue that designers should support decision-making processes and policy makers should account for the impact of the sociotechnical systems in which moderators work.
2305.11250v1
2023-06-08
Environmental Considerations in the age of Space Exploration: the Conservation and Protection of Non-Earth Environments
This document is an abbreviated version of the law review, led by Alexander Q. Gilbert, entitled: "Major Federal Actions Significantly Affecting the Quality of the Space Environment: Applying NEPA to Federal and Federally Authorized Outer Space Activities." Here, we discuss the future of the space environment, and how it is increasingly becoming a human environment with regard to continued robotic and human presence in orbit, planned and proposed robotic and human presence on bodies such as the Moon and Mars, planned space mining projects, the increase use of low-Earth orbit for communications satellites, and other human uses of space. As such, we must evaluate and protect these environments just as we do on Earth. In order to prioritize mitigating threat of contamination, avoiding conflict, and promoting sustainability in space, all to ensure that actors maintain equal and safe access to space, we propose applying the National Environmental Policy Act, or NEPA, to space missions. We put forward three examples of environmental best practices for those involved in space missions to consider: adopting precautionary and communicative structure to before, during, and after missions taking place off-world, environmental impact statements, and transparency in tools that may impact the environment (including radioisotope power sources, plans in case of vehicle loss or loss of trajectory, and others). For additional discussion related to potential space applications of NEPA, NEPA's statutory text, and NEPA's relation to space law and judicial precedent for space, we recommend reading the full law review.
2306.05594v1
2023-07-13
Accurate and efficient photo-eccentric transit modeling
A planet's orbital eccentricity is fundamental to understanding the present dynamical state of a system and is a relic of its formation history. There is high scientific value in measuring eccentricities of Kepler and TESS planets given the sheer size of these samples and the diversity of their planetary systems. However, Kepler and TESS lightcurves typically only permit robust determinations of planet-to-star radius ratio $r$, orbital period $P$, and transit mid-point $t_0$. Three other orbital properties, including impact parameter $b$, eccentricity $e$, and argument of periastron $\omega$, are more challenging to measure because they are all encoded in the lightcurve through subtle effects on a single observable -- the transit duration $T_{14}$. In Gilbert, MacDougall, & Petigura (2022), we showed that a five-parameter transit description $\{P, t_0, r, b, T_{14}\}$ naturally yields unbiased measurements of $r$ and $b$. Here, we build upon our previous work and introduce an accurate and efficient prescription to measure $e$ and $\omega$. We validate this approach through a suite of injection-and-recovery experiments. Our method agrees with previous approaches that use a seven-parameter transit description $\{P, t_0, r, b, \rho_\star, e, \omega\}$ which explicitly fits the eccentricity vector and mean stellar density. The five-parameter method is simpler than the seven-parameter method and is "future-proof" in that posterior samples can be quickly reweighted (via importance sampling) to accommodate updated priors and updated stellar properties. This method thus circumvents the need for an expensive reanalysis of the raw photometry, offering a streamlined path toward large-scale population analyses of eccentricity from transit surveys.
2307.07070v1
2023-09-01
A decoupled, convergent and fully linear algorithm for the Landau--Lifshitz--Gilbert equation with magnetoelastic effects
We consider the coupled system of the Landau--Lifshitz--Gilbert equation and the conservation of linear momentum law to describe magnetic processes in ferromagnetic materials including magnetoelastic effects in the small-strain regime. For this nonlinear system of time-dependent partial differential equations, we present a decoupled integrator based on first-order finite elements in space and an implicit one-step method in time. We prove unconditional convergence of the sequence of discrete approximations towards a weak solution of the system as the mesh size and the time-step size go to zero. Compared to previous numerical works on this problem, for our method, we prove a discrete energy law that mimics that of the continuous problem and, passing to the limit, yields an energy inequality satisfied by weak solutions. Moreover, our method does not employ a nodal projection to impose the unit length constraint on the discrete magnetisation, so that the stability of the method does not require weakly acute meshes. Furthermore, our integrator and its analysis hold for a more general setting, including body forces and traction, as well as a more general representation of the magnetostrain. Numerical experiments underpin the theory and showcase the applicability of the scheme for the simulation of the dynamical processes involving magnetoelastic materials at submicrometer length scales.
2309.00605v2
2023-11-09
Skyrmion-Excited Spin Wave Fractal Network
Magnetic skyrmions exhibit unique, technologically relevant pseudo-particle behaviors which arise from their topological protection, including well-defined, three-dimensional dynamic modes that occur at microwave frequencies. During dynamic excitation, spin waves are ejected into the interstitial regions between skyrmions, creating the magnetic equivalent of a turbulent sea. However, since the spin waves in these systems have a well-defined length scale, and the skyrmions are on an ordered lattice, ordered structures from spin wave interference can precipitate from the chaos. This work uses small angle neutron scattering (SANS) to capture the dynamics in hybrid skyrmions and investigate the spin wave structure. Performing simultaneous ferromagnetic resonance and SANS, the diffraction pattern shows a large increase in low-angle scattering intensity which is present only in the resonance condition. This scattering pattern is best fit using a mass fractal model, which suggests the spin waves form a long-range fractal network. The fractal structure is constructed of fundamental units with a size that encodes the spin wave emissions and are constrained by the skyrmion lattice. These results offer critical insights into the nanoscale dynamics of skyrmions, identify a new dynamic spin wave fractal structure, and demonstrates SANS as a unique tool to probe high-speed dynamics.
2311.05469v1
2023-12-08
Analysis of the magnetization control problem for the 2D evolutionary Landau-Lifshitz-Gilbert equation
The magnetization control problem for the Landau-Lifshitz-Gilbert (LLG) equation $m_t= m \times (\Delta m +u)- m \times (m \times (\Delta m +u)),\ (x,t) \in \Omega\times (0,T] $ with zero Neumann boundary data on a two-dimensional bounded domain $\Omega$ is studied when the control energy $u$ is applied on the effective field. First, we show the existence of a weak solution, and the magnetization vector field $m$ satisfies an energy inequality. If a weak solution $m$ obeys the condition that $\nabla m\in L^4(0,T;L^4(\Omega)),$ then we show that it is a regular solution. The classical cost functional is modified by incorporating $L^4(0,T;L^4(\Omega))$-norm of $\nabla m$ so that a rigorous study of the optimal control problem is established. Then, we justified the existence of an optimal control and derived first-order necessary optimality conditions using an adjoint problem approach. We have established the continuous dependency and Fr\'echet differentiability of the control-to-state and control-to-costate operators and shown the Lipschitz continuity of their Fr\'echet derivatives. Using these postulates, we derived a local second-order sufficient optimality condition when a control belongs to a critical cone. Finally, we also obtain another remarkable global optimality condition posed only in terms of the adjoint state associated with the control problem.
2312.05165v1
2024-01-05
Solutions to the Landau-Lifshitz-Gilbert equation in the frequency space: Discretization schemes for the dynamic-matrix approach
The dynamic matrix method addresses the Landau-Lifshitz-Gilbert (LLG) equation in the frequency domain by transforming it into an eigenproblem. Subsequent numerical solutions are derived from the eigenvalues and eigenvectors of the dynamic matrix. In this work we explore discretization methods needed to obtain a matrix representation of the dynamic operator, a fundamental counterpart of the dynamic matrix. Our approach opens a new set of linear algebra tools for the dynamic matrix method and expose the approximations and limitations intrinsic to it. Moreover, our discretization algorithms can be applied to various discretization schemes, extending beyond micromagnetism problems. We present some application examples, including a technique to obtain the dynamic matrix directly from the magnetic free energy function of an ensemble of macrospins, and an algorithmic method to calculate numerical micromagnetic kernels, including plane wave kernels. We also show how to exploit symmetries and reduce the numerical size of micromagnetic dynamic-matrix problems by a change of basis. This procedure significantly reduces the size of the dynamic matrix by several orders of magnitude while maintaining high numerical precision. Additionally, we calculate analytical approximations for the dispersion relations in magnonic crystals. This work contributes to the understanding of the current magnetization dynamics methods, and could help the development and formulations of novel analytical and numerical methods for solving the LLG equation within the frequency domain.
2401.02933v2
1995-10-27
Radiation Damping and Quantum Excitation for Longitudinal Charged Particle Dynamics in the Thermal Wave Model
On the basis of the recently proposed {\it Thermal Wave Model (TWM) for particle beams}, we give a description of the longitudinal charge particle dynamics in circular accelerating machines by taking into account both radiation damping and quantum excitation (stochastic effect), in presence of a RF potential well. The longitudinal dynamics is governed by a 1-D Schr\"{o}dinger-like equation for a complex wave function whose squared modulus gives the longitudinal bunch density profile. In this framework, the appropriate {\it r.m.s. emittance} scaling law, due to the damping effect, is naturally recovered, and the asymptotic equilibrium condition for the bunch length, due to the competition between quantum excitation (QE) and radiation damping (RD), is found. This result opens the possibility to apply the TWM, already tested for protons, to electrons, for which QE and RD are very important.
9510004v1
1994-02-04
Constraints on Models of Galaxy Formation from the Evolution of Damped Ly$α$ Absorption Systems
There is accumulating observational evidence suggesting that damped Ly$\alpha$ absorption systems systems are the progenitors of present-day spiral galaxies. We use the observed properties of these systems to place constraints on the history of star formation in galactic disks, and on cosmological theories of structure formation in the universe. We show that the observed increase in $\Omega_{HI}$ contributed by damped Ly$\alpha$ systems at high redshift implies that star formation must have been considerably less efficient in the past. We also show that the data can constrain cosmological models in which structure forms at late epochs. A mixed dark matter (MDM) model with $\Omega_{\nu}=0.3$ is unable to reproduce the mass densities of cold gas seen at high redshift, even in the absence of any star formation. We show that at redshifts greater than 3, this model predicts that the total baryonic mass contained in dark matter halos with circular velocities $V_c > 35$ km s$^{-1}$ is less than the observed mass of HI in damped systems. At these redshifts, the photo-ionizing background would prevent gas from dissipating and collapsing to form high column density systems in halos smaller than 35 km s$^{-1}$. MDM models are thus ruled out by the observations.
9402015v1
1999-02-11
The HI Column Density Distribution Function at z=0: the Connection to Damped Ly alpha Statistics
We present a measurement of the HI column density distribution function, f(N), at the present epoch for column densities log N > 20 cm^-2. These high column densities compare to those measured in damped Ly alpha lines seen in absorption against background quasars. Although observationally rare, it appears that the bulk of the neutral gas in the Universe is associated with these damped Ly alpha systems. In order to obtain a good anchor point at z=0 we determine f(N) in the local Universe by using 21cm synthesis observations of a complete sample of spiral galaxies. We show that f(N) for damped Ly alpha systems has changed significantly from high z to the present and that change is greatest for the highest column densities. The measurements indicate that low surface brightness galaxies make a minor contribution to the cross section for HI, especially for log N > 21^-2.
9902171v1
2000-10-27
Planetary Torques as the Viscosity of Protoplanetary Disks
We revisit the idea that density-wave wakes of planets drive accretion in protostellar disks. The effects of many small planets can be represented as a viscosity if the wakes damp locally, but the viscosity is proportional to the damping length. Damping occurs mainly by shocks even for earth-mass planets. The excitation of the wake follows from standard linear theory including the torque cutoff. We use this as input to an approximate but quantitative nonlinear theory based on Burger's equation for the subsequent propagation and shock. Shock damping is indeed local but weakly so. If all metals in a minimum-mass solar nebula are invested in planets of a few earth masses each, dimensionless viscosities [alpha] of order dex(-4) to dex(-3) result. We compare this with observational constraints. Such small planets would have escaped detection in radial-velocity surveys and could be ubiquitous. If so, then the similarity of the observed lifetime of T Tauri disks to the theoretical timescale for assembling a rocky planet may be fate rather than coincidence.
0010576v1
2000-12-27
Constraining Dark Matter candidates from structure formation
We show that collisional damping of adiabatic primordial fluctuations yields constraints on the possible range of mass and interaction rates of Dark Matter particles. Our analysis relies on a general classification of Dark Matter candidates, that we establish independently of any specific particle theory or model. From a relation between the collisional damping scale and the Dark Matter interaction rate, we find that Dark Matter candidates must have cross-sections at decoupling smaller than $ 10^{-33} \frac{m_{dm}}{1 MeV} cm^2$ with photons and $10^{-37} \frac{m_{dm}}{1 MeV} cm^2$ with neutrinos, to explain the observed primordial structures of $10^9$ Solar mass. These damping constraints are particularly relevant for Warm Dark Matter candidates. They also leave open less known regions of parameter space corresponding to particles having rather high interaction rates with other species than neutrinos and photons.
0012504v2
2001-07-26
The Contribution of HI-Rich Galaxies to the Damped Absorber Population at z=0
We present a study of HI-rich galaxies in the local universe selected from blind emission-line surveys. These galaxies represent the emission-line counterparts of local damped Lyman-alpha systems. We find that the HI cross-section of galaxies is drawn from a large range of galaxy masses below M_star, 66% of the area comes from galaxies in the range 8.5 < Log M_star < 9.7. Both because of the low mass galaxy contribution, and because of the range of galaxy types and luminosities at any given HI mass, the galaxies contributing to the HI cross-section are not exclusively L_star spirals, as is often expected. The optical and near infrared counterparts of these galaxies cover a range of types (from spirals to irregulars), luminosities (from L_star to <0.01 L_star), and surface brightnesses. The range of optical and near infrared properties as well as the kinematics for this population are consistent with the properties for the low-z damped Lyman-alpha absorbers. We also show that the number of HI-rich galaxies in the local universe does not preclude evolution of the low-z damped absorber population, but it is consistent with no evolution.
0107495v1
2003-11-17
Cosmic Ray Scattering by Compressible Magnetohydrodynamic Turbulence
Recent advances in understanding of magnetohydrodynamic (MHD) turbulence call for substantial revisions in the picture of cosmic ray transport. In this paper we use recently obtained scaling laws for MHD modes to calculate the scattering frequency for cosmic rays in the ISM. We consider gyroresonance with MHD modes (Alfvenic, slow and fast) and transit-time damping (TTD) by fast modes. We provide calculations of cosmic ray scattering for various phases of interstellar medium with realistic interstellar turbulence driving that is consistent with the velocity dispersions observed in diffuse gas. We account for the turbulence cutoff arising from both collisional and collisionless damping. We obtain analytical expressions for diffusion coefficients that enter Fokker-Planck equation describing cosmic ray evolution. We calculate the scattering rate and parallel spatial diffusion coefficients of cosmic rays for both Alfvenic and fast modes. We conclude that fast modes provides the dominant contribution to cosmic ray scattering for the typical interstellar conditions in spite of the fact that fast modes are subjected to damping. We show that the efficiency of the scattering depends on the plasma beta since it determines the damping of the fast modes. We also show that the streaming instability is modified in the presence of turbulence.
0311369v1
2003-11-17
Wave damping by MHD turbulence and its effect upon cosmic ray propagation in the ISM
Cosmic rays scatter off magnetic irregularities (Alfven waves) with which they are resonant, that is waves of wavelength comparable to their gyroradii. These waves may be generated either by the cosmic rays themselves, if they stream faster than the Alfven speed, or by sources of MHD turbulence. Waves excited by streaming cosmic rays are ideally shaped for scattering, whereas the scattering efficiency of MHD turbulence is severely diminished by its anisotropy. We show that MHD turbulence has an indirect effect on cosmic ray propagation by acting as a damping mechanism for cosmic ray generated waves. The hot (``coronal'') phase of the interstellar medium is the best candidate location for cosmic ray confinement by scattering from self-generated waves. We relate the streaming velocity of cosmic rays to the rate of turbulent dissipation in this medium, for the case in which turbulent damping is the dominant damping mechanism. We conclude that cosmic rays with up to 10^2 GeV could not stream much faster than the Alfven speed, but that 10^6 GeV cosmic rays would stream unimpeded by self-generated waves unless the coronal gas were remarkably turbulence-free.
0311400v1
2004-10-25
Constraints on Dark Matter interactions from structure formation: Damping lengths
(Shortened) Weakly Interacting Massive Particles are often said to be the best Dark Matter candidates. Studies have shown however that rather large Dark Matter-photon or Dark Matter-baryon interactions could be allowed by cosmology. Here we address the question of the role of the Dark Matter interactions in more detail to determine at which extent Dark Matter has to be necessarily weakly interacting. To this purpose, we compute the collisional damping (and free-streaming) lengths of generic interacting Dark Matter candidates and compare them to the scale of the smallest primordial structures known to exist in the Universe. We obtain necessary conditions that any candidate must satisfy. We point out the existence of new Dark Matter scenarios and exhibit new damping regimes. For example, an interacting candidate may bear a similar damping than that of collisionless Warm Dark Matter particles. The main difference is due to the Dark Matter coupling to interacting (or even freely-propagating) species. Our approach yields a general classification of Dark Matter candidates which extends the definitions of the usual Cold, Warm and Hot Dark Matter scenarios when interactions, weak or strong, are considered.
0410591v1
2005-10-10
Collisional dissipation of Alfvén waves in a partially ionised solar chromosphere
Certain regions of the solar atmosphere are at sufficiently low temperatures to be only partially ionised. The lower chromosphere contains neutral atoms, the existence of which greatly increases the efficiency of the damping of waves due to collisional friction momentum transfer. More specifically the Cowling conductivity can be up to 12 orders of magnitude smaller than the Spitzer value, so that the main damping mechanism in this region is due to the collisions between neutrals and positive ions. Using values for the gas density and temperature as functions of height taken from the VAL C model of the quiet Sun, an estimate is made for the dependance of the Cowling conductivity on height and strength of magnetic field. Using both analytic and numerical approaches the passage of Alfven waves over a wide spectrum through this partially ionised region is investigated. Estimates of the efficiency of this region in the damping of Alfven waves are made and compared for both approaches. We find that Alfven waves with frequencies above 0.6Hz are completely damped and frequencies below 0.01 Hz unaffected.
0510265v1
2006-04-10
The Nearby Damped Lyman-alpha Absorber SBS 1543+593: A Large HI Envelope in a Gas-Rich Galaxy Group
We present a Very Large Array (VLA) HI 21cm map and optical observations of the region around one of the nearest damped Lyman-alpha absorbers beyond the local group, SBS 1543+593. Two previously uncataloged galaxies have been discovered and a redshift has been determined for a third. All three of these galaxies are at the redshift of SBS 1543+593 and are ~185 kpc from the damped Lyman-alpha absorber. We discuss the HI and optical properties of SBS 1543+593 and its newly identified neighbors. Both SBS 1543+593 and Dwarf 1 have baryonic components that are dominated by neutral gas -- unusual for damped Lyman-alpha absorbers for which only ~5% of the HI cross-section originates in such strongly gas-dominated systems. What remains unknown is whether low mass gas-rich groups are common surrounding gas-rich galaxies in the local universe and whether the low star-formation rate in these systems is indicative of a young system or a stable, slowly evolving system. We discuss these evolutionary scenarios and future prospects for answering these questions.
0604220v1
2006-08-02
SINS of Viscosity Damped Turbulence
The problems with explaining the Small Ionized and Neutral Structures (SINS) appealing to turbulence stem from inefficiency of the Kolmogorov cascade in creating large fluctuations at sufficiently small scales. However, other types of cascades are possible. When magnetic turbulence in a fluid with viscosity that is much larger than resistivity gets to a viscous damping scale, the turbulence does not vanish. Instead, it gets into a different new regime. Viscosity-damped turbulence produces fluctuations on the small scales. Magnetic fields sheared by turbulent motions by eddies not damped by turbulence create small scale filaments that are confined by the external plasma pressure. This creates small scale density fluctuations. In addition, extended current sheets create even stronger density gradients that accompany field reversals in the plane perpendicular to mean magnetic field. Those can be responsible for the SINS formation. This scenario is applicable to partially ionized gas. More studies of reconnection in the viscosity dominated regime are necessary to understand better the extend to which the magnetic reversals can compress the gas.
0608046v3
1998-01-13
Comparative Study of the Adiabatic Evolution of a Nonlinear Damped Oscillator and an Hamiltonian Generalized Nonlinear Oscillator
In this paper we study to what extent the canonical equivalence and the identity of the geometric phases of dissipative and conservative linear oscillators, established in a preceeding paper, can be generalized to nonlinear ones. Considering first the 1-D quartic generalized oscillator we determine, by means of a perturbative time dependent technic of reduction to normal forms, the canonical transformations which lead to the adiabatic invariant of the system and to the first order non linear correction to its Hannay angle. Then, applying the same transformations to the 1-D quartic damped oscillator we show that this oscillator is canonically equivalent to the linear generalized harmonic oscillator for finite values of the damping parameter (which implies no correction to the linear Hannay angle) whereas, in an appropriate weak damping limit, it becomes equivalent to the quartic generalized oscillator (which implies a non linear correction to this angle) .
9801017v1
1995-03-20
Quasiparticle damping in two-dimensional superconductors with unconventional pairing.
We calculate the damping of excitations due to four-fermionic interaction in the case of two-dimensional superconductor with nodes in the spectrum. At zero temperature and low frequencies it reveals gapless $\omega^3$ behavior at the nodal points. With the frequency increasing the crossover to the normal-state regimes appears. At high frequencies the damping strongly depends on details of a normal-state spectrum parametrization. Two important particular cases such as the models of almost free and tight-binding electrons are studied explicitly and the characteristic scales are expressed through the model-free parameters of the spectrum at the nodal points. The possibility of crossover in temperature dependence of damping in the superconducting phase is discussed.
9503112v1
1996-01-09
Relaxation of Collective Excitations in LJ-13 Cluster
We have performed classical molecular dynamics simulation of $Ar_{13}$ cluster to study the behavior of collective excitations. In the solid ``phase'' of the cluster, the collective oscillation of the monopole mode can be well fitted to a damped harmonic oscillator. The parameters of the equivalent damped harmonic oscillator-- the damping coefficient, spring constant, time period of oscillation and the mass of the oscillator -- all show a sharp change in behavior at a kinetic temperature of about $7.0^oK$. This marks yet another characteristic temperature of the system, a temperature $T_s$ below which collective excitations are very stable, and at higher temperatures the single particle excitations cause the damping of the collective oscillations. We argue that so long as the cluster remains confined within the global potential energy minimum the collective excitations do not decay; and once the cluster comes out of this well, the local potential energy minima pockets act as single particle excitation channels in destroying the collective motion. The effect is manifest in almost all the physical observables of the cluster.
9601026v2
1997-10-14
Damping of Hydrodynamic Modes in a Trapped Bose Gas above the Bose-Einstein Transition Temperature
We calculate the damping of low-lying collective modes of a trapped Bose gas in the hydrodynamic regime, and show that this comes solely from the shear viscosity, since the contributions from bulk viscosity and thermal conduction vanish. The hydrodynamic expression for the damping diverges due to the failure of hydrodynamics in the outer parts of the cloud, and we take this into account by a physically motivated cutoff procedure. Our analysis of available experimental data indicates that higher densities than have yet been achieved are necessary for investigating hydrodynamic modes above the Bose-Einstein transition temperature.
9710130v2
1997-12-24
Thermal dephasing and the echo effect in a confined Bose-Einstein condensate
It is shown that thermal fluctuations of the normal component induce dephasing -- reversible damping of the low energy collective modes of a confined Bose-Einstein condensate. The dephasing rate is calculated for the isotropic oscillator trap, where Landau damping is expected to be suppressed. This rate is characterized by a steep temperature dependence, and it is weakly amplitude dependent. In the limit of large numbers of bosons forming the condensate, the rate approaches zero. However, for the numbers employed by the JILA group, the calculated value of the rate is close to the experimental one. We suggest that a reversible nature of the damping caused by the thermal dephasing in the isotropic trap can be tested by the echo effect. A reversible nature of Landau damping is also discussed, and a possibility of observing the echo effect in an anisotropic trap is considered as well. The parameters of the echo are calculated in the weak echo limit for the isotropic trap. Results of the numerical simulations of the echo are also presented.
9712287v1