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2016-09-30
Interaction Between a Domain Wall and Spin Supercurrent in Easy-cone Magnets
A domain wall and spin supercurrent can coexist in magnets with easy-cone anisotropy owing to simultaneous spontaneous breaking of Z$_2$ and U(1) symmetries. Their interaction is theoretically investigated in quasi one-dimensional ferromagnets within the Landau-Lifshitz-Gilbert phenomenology. Specifically, we show that spin supercurrent can exert the torque on a domain wall and thereby drive it. We also show, as a reciprocal phenomenon, a field-induced motion of a domain wall can generate spin supercurrent.
1610.00034v1
2016-10-04
A Local Inverse Formula and a Factorization
When a matrix has a banded inverse there is a remarkable formula that quickly computes that inverse, using only local information in the original matrix. This local inverse formula holds more generally, for matrices with sparsity patterns that are examples of chordal graphs or perfect eliminators. The formula has a long history going back at least as far as the completion problem for covariance matrices with missing data. Maximum entropy estimates, log-determinants, rank conditions, the Nullity Theorem and wavelets are all closely related, and the formula has found wide applications in machine learning and graphical models. We describe that local inverse and explain how it can be understood as a matrix factorization.
1610.01230v1
2016-10-10
Parametric frequency mixing in the magneto-elastically driven FMR-oscillator
We demonstrate the nonlinear frequency conversion of ferromagnetic resonance (FMR) frequency by optically excited elastic waves in a thin metallic film on dielectric substrates. Time-resolved probing of the magnetization directly witnesses magneto-elastically driven second harmonic generation, sum- and difference frequency mixing from two distinct frequencies, as well as parametric downconversion of each individual drive frequency. Starting from the Landau-Lifshitz-Gilbert equations, we derive an analytical equation of an elastically driven nonlinear parametric oscillator and show that frequency mixing is dominated by the parametric modulation of FMR frequency.
1610.02926v1
2016-11-05
Magnonic analog of relativistic Zitterbewegung in an antiferromagnetic spin chain
We theoretically investigate the spin wave (magnon) excitations in a classical antiferromagnetic spin chain with easy-axis anisotropy. We obtain a Dirac-like equation by linearizing the Landau- Lifshitz-Gilbert equation in this antiferromagnetic system, in contrast to the ferromagnetic system in which a Schr\"{o}dinger equation is derived. The Hamiltonian operator in the Dirac-like equation is a pseudo-Hermitian. We compute and demonstrate the relativistic Zitterbewegung (trembling motion) in the antiferromagnetic spin chain by measuring the expectation values of the wave packet position.
1611.01512v2
2016-11-15
The norm of the Fourier transform on compact or discrete abelian groups
We calculate the norm of the Fourier operator from $L^p(X)$ to $L^q(\hat{X})$ when $X$ is an infinite locally compact abelian group that is, furthermore, compact or discrete. This subsumes the sharp Hausdorff-Young inequality on such groups. In particular, we identify the region in $(p,q)$-space where the norm is infinite, generalizing a result of Fournier, and setting up a contrast with the case of finite abelian groups, where the norm was determined by Gilbert and Rzeszotnik. As an application, uncertainty principles on such groups expressed in terms of R\'enyi entropies are discussed.
1611.04692v1
2016-12-01
Optimizing Quantiles in Preference-based Markov Decision Processes
In the Markov decision process model, policies are usually evaluated by expected cumulative rewards. As this decision criterion is not always suitable, we propose in this paper an algorithm for computing a policy optimal for the quantile criterion. Both finite and infinite horizons are considered. Finally we experimentally evaluate our approach on random MDPs and on a data center control problem.
1612.00094v1
2017-02-02
Magnon Condensation and Spin Superfluidity
We consider the phenomenon of Bose-Einstein condensation of quasi-equilibrium magnons which leads to a spin superfluidity, the coherent quantum transfer of magnetization in magnetic materials. These phenomena are beyond the classical Landau-Lifshitz-Gilbert paradigm. The critical conditions for excited magnon density for ferro- and antiferromagnets, bulk and thin films are estimated and discussed. The BEC should occur in the antiferromagnetic hematite at much lower excited magnon density compared to the ferromagnetic YIG.
1702.00846v2
2017-02-09
Transient spin dynamics in a single-molecule magnet
We explore the limitations and validity of semi-classically formulated spin equations of motion. Using a single-molecule magnet as a test model, we employ three qualitatively different approximation schemes. From a microscopic model, we derive a generalized spin equation of motion in which the parameters have a non-local time-dependence. This dynamical equation is simplified to the Landau-Lifshitz-Gilbert equation with i) time-dependent, and ii) time-independent parameters. We show that transient dynamics is essentially non-existing in the latter approximation, while the former breaks down in the regime of strong coupling between the spin and the itinerant electrons.
1702.02820v2
2017-03-05
On the VC-Dimension of Binary Codes
We investigate the asymptotic rates of length-$n$ binary codes with VC-dimension at most $dn$ and minimum distance at least $\delta n$. Two upper bounds are obtained, one as a simple corollary of a result by Haussler and the other via a shortening approach combining Sauer-Shelah lemma and the linear programming bound. Two lower bounds are given using Gilbert-Varshamov type arguments over constant-weight and Markov-type sets.
1703.01586v2
2017-03-09
Long quasi-polycyclic $t-$CIS codes
We study complementary information set codes of length $tn$ and dimension $n$ of order $t$ called ($t-$CIS code for short). Quasi-cyclic and quasi-twisted $t$-CIS codes are enumerated by using their concatenated structure. Asymptotic existence results are derived for one-generator and have co-index $n$ by Artin's conjecture for quasi cyclic and special case for quasi twisted. This shows that there are infinite families of long QC and QT $t$-CIS codes with relative distance satisfying a modified Varshamov-Gilbert bound for rate $1/t$ codes. Similar results are defined for the new and more general class of quasi-polycyclic codes introduced recently by Berger and Amrani.
1703.03109v1
2017-09-05
On the Lagrangian branched transport model and the equivalence with its Eulerian formulation
First we present two classical models of Branched Transport: the Lagrangian model introduced by Bernot, Caselles, Morel, Maddalena, Solimini, and the Eulerian model introduced by Xia. An emphasis is put on the Lagrangian model, for which we give a complete proof of existence of minimizers in a --hopefully-- simplified manner. We also treat in detail some $\sigma$-finiteness and rectifiability issues to yield rigorously the energy formula connecting the irrigation cost I$\alpha$ to the Gilbert Energy E$\alpha$. Our main purpose is to use this energy formula and exploit a Smirnov decomposition of vector flows, which was proved via the Dacorogna-Moser approach by Santambrogio, to establish the equivalence between the Lagrangian and Eulerian models.
1709.01414v1
2017-09-09
On Low-Risk Heavy Hitters and Sparse Recovery Schemes
We study the heavy hitters and related sparse recovery problems in the low-failure probability regime. This regime is not well-understood, and has only been studied for non-adaptive schemes. The main previous work is one on sparse recovery by Gilbert et al.(ICALP'13). We recognize an error in their analysis, improve their results, and contribute new non-adaptive and adaptive sparse recovery algorithms, as well as provide upper and lower bounds for the heavy hitters problem with low failure probability.
1709.02919v3
2017-10-30
Lattice calculation of hadronic tensor of the nucleon
We report an attempt to calculate the deep inelastic scattering structure functions from the hadronic tensor calculated on the lattice. We used the Backus-Gilbert reconstruction method to address the inverse Laplace transformation for the analytic continuation from the Euclidean to the Minkowski space.
1710.11145v1
2017-10-31
TF Boosted Trees: A scalable TensorFlow based framework for gradient boosting
TF Boosted Trees (TFBT) is a new open-sourced frame-work for the distributed training of gradient boosted trees. It is based on TensorFlow, and its distinguishing features include a novel architecture, automatic loss differentiation, layer-by-layer boosting that results in smaller ensembles and faster prediction, principled multi-class handling, and a number of regularization techniques to prevent overfitting.
1710.11555v1
2017-11-08
Micromagnetic simulation study of a disordered model for one-dimensional granular perovskite manganite oxide nanostructures
Chemical techniques are an efficient method to synthesize one-dimensional perovskite manganite oxide nanostructures with a granular morphology, that is, formed by arrays of monodomain magnetic nanoparticles. Integrating the stochastic Landau-Lifshitz-Gilbert equation, we simulate the dynamics of a simple disordered model for such materials that only takes into account the morphological characteristics of their nanograins. We show that it is possible to describe reasonably well experimental hysteresis loops reported in the literature for single La_0.67Ca_0.33MnO_3 nanotubes and powders of these nanostructures, simulating small systems consisting of only 100 nanoparticles.
1711.03159v2
2017-11-21
Construction of asymptotically good locally repairable codes via automorphism groups of function fields
Locally repairable codes have been investigated extensively in recent years due to practical application in distributed storage as well as theoretical interest. However, not much work on asymptotical behavior of locally repairable codes has been done until now. In particular, there is a little result on constructive lower bound on asymptotical behavior of locally repairable codes. In this paper, we extend the construction given in \cite{BTV17} via automorphism groups of function field towers. The main advantage of our construction is to allow more flexibility of locality. Furthermore, we show that the Gilbert-Varshamov type bound on locally repairable codes can be improved for all sufficiently large alphabet size $q$.
1711.07703v1
2017-11-21
Stability of axisymmetric chiral skyrmions
We examine topological solitons in a minimal variational model for a chiral magnet, so-called chiral skyrmions. In the regime of large background fields, we prove linear stability of axisymmetric chiral skyrmions under arbitrary perturbations in the energy space, a long-standing open question in physics literature. Moreover, we show strict local minimality of axisymmetric chiral skyrmions and nearby existence of moving soliton solution for the Landau-Lifshitz-Gilbert equation driven by a small spin transfer torque.
1711.07717v1
2017-12-13
Mutual synchronization of spin-torque oscillators consisting of perpendicularly magnetized free layers and in-plane magnetized pinned layers
A mutual synchronization of spin-torque oscillators coupled through current injection is studied theoretically. Models of electrical coupling in parallel and series circuits are proposed. Solving the Landau-Lifshitz-Gilbert equation, excitation of in-phase or antiphase synchronization, depending on the ways the oscillators are connected, is found. It is also found from both analytical and numerical calculations that the current-frequency relations for both parallel and series circuits are the same as that for a single spin-torque oscillator.
1712.04591v1
2018-01-25
Pharmacokinetics Simulations for Studying Correlates of Prevention Efficacy of Passive HIV-1 Antibody Prophylaxis in the Antibody Mediated Prevention (AMP) Study
A key objective in two phase 2b AMP clinical trials of VRC01 is to evaluate whether drug concentration over time, as estimated by non-linear mixed effects pharmacokinetics (PK) models, is associated with HIV infection rate. We conducted a simulation study of marker sampling designs, and evaluated the effect of study adherence and sub-cohort sample size on PK model estimates in multiple-dose studies. With m=120, even under low adherence (about half of study visits missing per participant), reasonably unbiased and consistent estimates of most fixed and random effect terms were obtained. Coarsened marker sampling schedules were also studied.
1801.08626v1
2018-03-30
Nanostructured Ceramic Oxides with a Slow Crack Growth Resistance Close to Covalent Materials
Oxide ceramics are sensitive to slow crack growth because adsorption of water can take place at the crack tip, leading to a strong decrease of the surface energy in humid (or air) conditions. This is a major drawback concerning demanding, long-term applications such as orthopaedic implants. Here we show that a specific nanostructuration of ceramic oxides can lead to a crack resistance never reached before, similar to that of covalent ceramics.
1804.01393v1
2018-05-30
Quantum Annealed Criticality
Experimentally there exist many materials with first-order phase transitions at finite temperature that display quantum criticality. Classically a strain-energy density coupling is known to drive first-order transitions in compressible systems, and here we generalize this Larkin-Pikin mechanism to the quantum case. We show that if the T=0 system lies above its upper critical dimension, the line of first-order transitions can end in a quantum annealed critical point where zero-point fluctuations restore the underlying criticality of the order parameter.
1805.11771v1
2018-08-03
A thermally driven spin-transfer-torque system far from equilibrium: enhancement of the thermoelectric current via pumping current
We consider a small itinerant ferromagnet exposed to an external magnetic field and strongly driven by a thermally induced spin current. For this model, we derive the quasi-classical equations of motion for the magnetization where the effects of a dynamical non-equilibrium distribution function are taken into account self-consistently. We obtain the Landau-Lifshitz-Gilbert equation supplemented by a spin-transfer torque term of Slonczewski form. We identify a regime of persistent precessions in which we find an enhancement of the thermoelectric current by the pumping current.
1808.01192v1
2018-09-12
But How Does It Work in Theory? Linear SVM with Random Features
We prove that, under low noise assumptions, the support vector machine with $N\ll m$ random features (RFSVM) can achieve the learning rate faster than $O(1/\sqrt{m})$ on a training set with $m$ samples when an optimized feature map is used. Our work extends the previous fast rate analysis of random features method from least square loss to 0-1 loss. We also show that the reweighted feature selection method, which approximates the optimized feature map, helps improve the performance of RFSVM in experiments on a synthetic data set.
1809.04481v3
2018-09-22
Optimizing a Generalized Gini Index in Stable Marriage Problems: NP-Hardness, Approximation and a Polynomial Time Special Case
This paper deals with fairness in stable marriage problems. The idea studied here is to achieve fairness thanks to a Generalized Gini Index (GGI), a well-known criterion in inequality measurement, that includes both the egalitarian and utilitarian criteria as special cases. We show that determining a stable marriage optimizing a GGI criterion of agents' disutilities is an NP-hard problem. We then provide a polynomial time 2-approximation algorithm in the general case, as well as an exact algorithm which is polynomial time in the case of a constant number of non-zero weights parametrizing the GGI criterion.
1809.08453v1
2018-10-17
Out-of-plane auto-oscillation in spin Hall oscillator with additional polarizer
The theoretical investigation on magnetization dynamics excited by the spin Hall effect in metallic multilayers having two ferromagnets is discussed. The relaxation of the transverse spin in one ferromagnet enables us to manipulate the direction of the spin-transfer torque excited in another ferromagnet, although the spin-polarization originally generated by the spin Hall effect is geometrically fixed. Solving the Landau-Lifshitz-Gilbert-Slonczewski equation, the possibility to excite an out-of-plane auto-oscillation of an in-plane magnetized ferromagnet is presented. An application to magnetic recording using microwave-assisted magnetization reversal is also discussed.
1810.07831v1
2018-11-23
Most Graphs are Knotted
We present four models for a random graph and show that, in each case, the probability that a graph is intrinsically knotted goes to one as the number of vertices increases. We also argue that, for $k \geq 18$, most graphs of order $k$ are intrinsically knotted and, for $k \geq 2n+9$, most of order $k$ are not $n$-apex. We observe that $p(n) = 1/n$ is the threshold for intrinsic knotting and linking in Gilbert's model.
1811.09726v1
2018-12-13
Entanglement-assisted quantum error-correcting codes over arbitrary finite fields
We prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over the binary field hold for codes over arbitrary finite fields as well. We also give a Gilbert-Varshamov bound for EAQECCs and constructions of EAQECCs coming from punctured self-orthogonal linear codes which are valid for any finite field.
1812.05312v4
2019-01-23
Coupled dynamics of magnetizations in spin-Hall oscillators via spin current injection
An array of spin torque oscillators (STOs) for practical applications such as pattern recognition was recently proposed, where several STOs are connected by a common nonmagnet. In this structure, in addition to the electric and/or magnetic interactions proposed in previous works, the STOs are spontaneously coupled to each other through the nonmagnetic connector, due to the injection of spin current. Solving the Landau-Lifshitz-Gilbert equation numerically for such system consisting of three STOs driven by the spin Hall effect, it is found that both in-phase and antiphase synchronization of the STOs can be achieved by adjusting the current density and appropriate distance between the oscillators.
1901.07669v1
2019-01-28
A Multi-parameter regression model for interval censored survival data
We develop flexible multi-parameter regression survival models for interval censored survival data arising in longitudinal prospective studies and longitudinal randomised controlled clinical trials. A multi-parameter Weibull regression survival model, which is wholly parametric, and has non-proportional hazards, is the main focus of the paper. We describe the basic model, develop the interval-censored likelihood and extend the model to include gamma frailty and a dispersion model. We evaluate the models by means of a simulation study and a detailed re-analysis of data from the Signal Tandmobiel$^{\circledR}$ study. The results demonstrate that the multi-parameter regression model with frailty is computationally efficient and provides an excellent fit to the data.
1901.09634v1
2019-02-15
Stochastic homogenization of the Landau-Lifshitz-Gilbert equation
Following the ideas of V. V. Zhikov and A. L. Pyatnitski, and more precisely the stochastic two-scale convergence, this paper establishes a homogenization theorem in a stochastic setting for two nonlinear equations : the equation of harmonic maps into the sphere and the Landau-Lifschitz equation. These equations have strong nonlinear features, in particular, in general their solutions are not unique.
1902.05743v1
2019-03-06
Cluster multipole dynamics in non-collinear antiferromagnets
A systematic framework to investigate spin dynamics in non-collinear antiferromagnet is proposed. Taking Mn$_3$Sn as a representative example, we derive an effective low energy model based on the multipole expansion of the magnetic structure, and investigate the uniform precession and the domain wall dynamics. We show that the solution for the effective model accurately reproduces the numerical calculation of the Landau-Lifshitz-Gilbert equations. Our results indicate that Mn$_3$Sn has preferable properties for applications to a racetrack memory and a spin torque oscillator, and thus, is a promising candidate for new devices by using the multipole degrees of freedom.
1903.02259v1
2019-03-22
Learning magnetization dynamics
Deep neural networks are used to model the magnetization dynamics in magnetic thin film elements. The magnetic states of a thin film element can be represented in a low dimensional space. With convolutional autoencoders a compression ratio of 1024:1 was achieved. Time integration can be performed in the latent space with a second network which was trained by solutions of the Landau-Lifshitz-Gilbert equation. Thus the magnetic response to an external field can be computed quickly.
1903.09499v1
2019-04-01
Synchrony breakdown and noise-induced oscillation death in ensembles of serially connected spin-torque oscillators
We consider collective dynamics in the ensemble of serially connected spin-torque oscillators governed by the Landau-Lifshitz-Gilbert-Slonczewski magnetization equation. Proximity to homoclinicity hampers synchronization of spin-torque oscillators: when the synchronous ensemble experiences the homoclinic bifurcation, the Floquet multiplier, responsible for the temporal evolution of small deviations from the ensemble mean, diverges. Depending on the configuration of the contour, sufficiently strong common noise, exemplified by stochastic oscillations of the current through the circuit, may suppress precession of the magnetic field for all oscillators. We derive the explicit expression for the threshold amplitude of noise, enabling this suppression.
1904.00897v1
2019-04-21
Global classical solutions to an evolutionary model for magnetoelasticity
In this paper, we first prove the local-in-time existence of the evolutionary model for magnetoelasticity with finite initial energy by employing the nonlinear iterative approach given in \cite{Jiang-Luo-2019-SIAM} to deal with the geometric constraint $M \in \mathbb{S}^{d-1}$ in the Landau-Lifshitz-Gilbert (LLG) equation. Inspired by \cite{Lin-Liu-Zhang-CPAM2005, Lin-Zhang-2008-CPAM}, we reformulate the evolutionary model for magnetoelasticity with vanishing external magnetic field $H_{ext}$, so that a further dissipative term will be sought from the elastic stress. We thereby justify the global well-posedness to the evolutionary model for magnetoelasticity with zero external magnetic field under small size of initial data.
1904.09531v1
2019-06-21
Thermal Collapse of a Skyrmion
Thermal collapse of an isolated skyrmion on a two-dimensional spin lattice has been investigated. The method is based upon solution of the system of stochastic Landau-Lifshitz-Gilbert equations for up $10^4$ spins. Recently developed pulse-noise algorithm has been used for the stochastic component of the equations. The collapse rate follows the Arrhenius law. Analytical formulas derived within a continuous spin-field model support numerically-obtained values of the energy barrier and the pre-exponential factor, and their dependence on the magnetic field. Our findings agree with experiments, as well as with recent numerical results obtained by other methods.
1906.09132v3
2019-06-23
Random subgroups, automorphisms, splittings
We show that, if $H$ is a random subgroup of a finitely generated free group $F_k$, only inner automorphisms of $F_k$ may leave $H$ invariant. A similar result holds for random subgroups of toral relatively hyperbolic groups, more generally of groups which are hyperbolic relative to slender subgroups. These results follow from non-existence of splittings over slender groups which are relative to a random group element. Random subgroups are defined using random walks or balls in a Cayley tree of $F_k$.
1906.09654v1
2019-07-28
Polarization of the Cosmic Infrared Background Fluctuations
The cosmic infrared background (CIB) is slightly polarized. Polarization directions of individual galaxies could be aligned with tidal fields around galaxies, resulting in nonzero CIB polarization. We use a linear intrinsic alignment model to theoretically predict angular correlations of the CIB polarization fluctuations and find that electriclike and curl-like ($B$-mode) polarization modes are equally generated with power four orders of magnitude less than its intensity. The CIB $B$-mode signal is negligible and not a concerning foreground for the inflationary $B$-mode searches at nominal frequencies for cosmic microwave background measurements, but could be detected at submillimetre wavelengths by future space missions.
1907.12085v1
2019-08-05
Constructive asymptotic bounds of locally repairable codes via function fields
Locally repairable codes have been investigated extensively in recent years due to practical applications in distributed and cloud storage systems. However, there are few asymptotical constructions of locally repairable codes in the literature. In this paper, we provide an explicit asymptotic construction of locally repairable codes over arbitrary finite fields from local expansions of functions at a rational place. This construction gives a Tsfasman-Vladut-Zink type bound for locally repairable codes. Its main advantage is that there are no constraints on both locality and alphabet size. Furthermore, we show that the Gilbert-Varshamov type bound on locally repairable codes over non-prime finite fields can be exceeded for sufficiently large alphabet size.
1908.01471v1
2019-10-25
Application-Layer Coding with Intermittent Feedback under Delay and Duty-Cycle Constraints
We propose two application-layer coding schemes for delay-constrained point-to-point packet communications with restrictions on the transmitter's maximum duty-cycle. The schemes operate over GF(2) and utilize intermittently available receiver feedback for erasure correction. Applications that will benefit from the proposed schemes include wireless sensor networks in which energy-constrained sensors must deliver readings to a gateway within a deadline. Simulation results for independent Bernoulli erasure channels, Gilbert-Elliott channels, and Long Range (LoRa) communications demonstrate orders-of-magnitude reductions in the delivery failure rate as compared to feedback-assisted repetition redundancy and a blind coding scheme that does not utilize feedback.
1910.11700v2
2019-10-28
Dissipative solutions to a system for the flow of magnetoviscoelastic materials
We address the question of global in time existence of solutions to a magnetoviscoelastic system with general initial data. We show that the notion of dissipative solutions allows to prove such an existence in two and three dimensions. This extends an earlier result for the viscoelastic subsystem to the setting which includes the magnetization vector and its evolution in terms of a Landau-Lifshitz-Gilbert equation.
1910.12751v2
2019-12-09
Multi-reference protocol for (auto)ionization spectra: application to molecules
We present the application of the spherically averaged continuum model to the evaluation of molecular photoelectron and resonant Auger electron spectra. In this model, the continuum wave function is obtained in a numerically efficient way by solving the radial Schr\"odinger equation with a spherically averaged molecular potential. Different approximations to the Auger transition matrix element and, in particular, the one-center approximation are thoroughly tested against experimental data for the CH$_4$, O$_2$, NO$_2$, and pyrimidine molecules. In general, this approach appears to estimate the shape of the photoelectron and autoionization spectra as well as the total Auger decay rates with reasonable accuracy, allowing for the interpretation of experimental results.
1912.04139v1
2020-01-25
Phase estimation of spin-torque oscillator by nonlinear spin-torque diode effect
A theoretical analysis is developed on spin-torque diode effect in nonlinear region. An analytical solution of the diode voltage generated from spin-torque oscillator by the rectification of an alternating current is derived. The diode voltage is revealed to depend nonlinearly on the phase difference between the oscillator and the alternating current. The validity of the analytical prediction is confirmed by numerical simulation of the Landau-Lifshitz-Gilbert equation. The results indicate that the spin-torque diode effect is useful to evaluate the phase of a spin-torque oscillator in forced synchronization state.
2001.09247v1
2020-04-06
Frequency enhancement and power tunability in tilted polarizer spin-torque nano oscillator
In the absence of an applied magnetic field, a spin-torque nano oscillator(STNO) with a tilted polarizer is studied using numerical simulation of the associated Landau-Lifshitz-Gilbert-Slonczewski equation. We find considerable enhancement of frequency by tilting the polarizer out-of-plane appropriately. Also, we observe improved tunability of frequency of oscillations from 15 GHz to 75 GHz and increment in the power spectral density by current and tilt angle. In addition, our findings and insights pave a simple way for nanoscale level microwave generators to be implemented.
2004.02659v1
2020-05-11
Perspective on Metallic Antiferromagnets
Antiferromagnet materials have recently gained renewed interest due to their possible use in spintronics technologies, where spin transport is the foundation of their functionalities. In that respect metallic antiferromagnets are of particular interest, since they enable complex interplays between electronic charge transport, spin, optical, and magnetization dynamics. Here we review phenomena where the metallic conductivity provides unique perspectives for the practical use and fundamental properties of antiferromagnetic materials.
2005.05247v1
2020-07-09
Enumerating alternating matrix spaces over finite fields with explicit coordinates
We initiate the study of enumerating linear subspaces of alternating matrices over finite fields with explicit coordinates. We postulate that this study can be viewed as a linear algebraic analogue of the classical topic of enumerating labelled graphs. To support this viewpoint, we present q-analogues of Gilbert's formula for enumerating connected graphs (Can. J. Math., 1956), and Read's formula for enumerating c-colored graphs (Can. J. Math., 1960). We also develop an analogue of Riddell's formula relating the exponential generating function of graphs with that of connected graphs (Riddell's PhD thesis, 1951), building on Eulerian generating functions developed by Srinivasan (Discrete Math., 2006).
2007.05108v1
2020-08-06
On Passivity, Feedback Passivity, And Feedback Passivity Over Erasure Network: A Piecewise Affine Approximation Approach
In this paper, we deal with the problem of passivity and feedback passification of smooth discrete-time nonlinear systems by considering their piecewise affine approximations. Sufficient conditions are derived for passivity and feedback passivity. These results are then extended to systems that operate over Gilbert-Elliott type communication channels. As a special case, results for feedback passivity of piecewise affine systems over a lossy channel are also derived.
2008.02748v1
2020-08-20
Hyperbolic groups of Fibonacci type and T(5) cyclically presented groups
Building on previous results concerning hyperbolicity of groups of Fibonacci type, we give an almost complete classification of the (non-elementary) hyperbolic groups within this class. We are unable to determine the hyperbolicity status of precisely two groups, namely the Gilbert-Howie groups H(9,4), H(9,7). We show that if H(9,4) is torsion-free then it is not hyperbolic. We consider the class of T(5) cyclically presented groups and classify the (non-elementary) hyperbolic groups and show that the Tits alternative holds.
2008.08986v2
2020-10-13
Mechanistic Modelling of Chromatin Folding to Understand Function
Experimental approaches have been applied to address questions in understanding three-dimensional chromatin organisation and function. As datasets increase in size and complexity, it becomes a challenge to reach a mechanistic interpretation of experimental results. Polymer simulations and mechanistic modelling have been applied to explain experimental observations, and the links to different aspects of genome function. Here, we provide a guide for biologists, explaining different simulation approaches and the contexts in which they have been used.
2010.06413v1
2020-12-05
Dual Regularized Optimal Transport
In this paper, we present a new formulation of unbalanced optimal transport called Dual Regularized Optimal Transport (DROT). We argue that regularizing the dual formulation of optimal transport results in a version of unbalanced optimal transport that leads to sparse solutions and that gives us control over mass creation and destruction. We build intuition behind such control and present theoretical properties of the solutions to DROT. We demonstrate that due to recent advances in optimization techniques, we can feasibly solve such a formulation at large scales and present extensive experimental evidence for this formulation and its solution.
2012.03126v1
2020-12-20
Achieving positive rates with predetermined dictionaries
In the first part of the paper we consider binary input channels that are not necessarily stationary and show how positive rates can be achieved using codes constrained to be within predetermined dictionaries. We use a Gilbert-Varshamov-like argument to obtain the desired rate achieving codes. Next we study the corresponding problem for channels with arbitrary alphabets and use conflict-set decoding to show that if the dictionaries are contained within nice sets, then positive rates are achievable.
2012.10897v1
2020-12-25
Colossal stability of antiferromagnetically exchange coupled nanomagnets
Bistable nanomagnets store a binary bit of information. Exchange coupled nanomagnets can increase the thermal stability at low dimensions. Here we show that the antiferromagnetically (AFM) coupled nanomagnets can be highly stable at low dimensions than that of the ferromagnetically (FM) coupled nanomagnets. By solving stochastic Landau-Lifshitz-Gilbert equation of magnetization dynamics at room temperature, we analyze the stability of the exchange coupled nanomagnets in the presence of correlated, uncorrelated, and anti-correlated noise. The results show that the correlated noise can make the stability of the AFM coupled nanomagnets very high. Such finding will lead to very high-density non-volatile storage and logic devices in our future information processing systems.
2012.13590v1
2021-03-08
Cutoff for the Asymmetric Riffle Shuffle
In the Gilbert-Shannon-Reeds shuffle, a deck of $N$ cards is cut into two approximately equal parts which are then riffled uniformly at random. Bayer and Diaconis famously showed that this Markov chain undergoes cutoff in total variation after $\frac{3\log(N)}{2 \log(2)}$ shuffles. We establish cutoff for the more general asymmetric riffle shuffles in which one cuts the deck into differently sized parts before riffling. The value of the cutoff point confirms a conjecture of Lalley from 2000. Some appealing consequences are that asymmetry always slows mixing and that total variation mixing is strictly faster than separation and $L^{\infty}$ mixing.
2103.05068v3
2021-03-24
Information Freshness Analysis of Slotted ALOHA in Gilbert-Elliot Channels
This letter analyzes a class of information freshness metrics for large IoT systems in which terminals employ slotted ALOHA to access a common channel. Considering a Gilbert- Elliot channel model, information freshness is evaluated through a penalty function that follows a power law of the time elapsed since the last received update, in contrast with the linear growth of age of information. By means of a signal flow graph analysis of Markov processes, we provide exact closed form expressions for the average penalty and for the peak penalty violation probability.
2103.13346v2
2021-04-30
Micromagnetic modeling of magnon coherent states in a nonuniform magnetic field
The study of the dynamics of magnetically ordered states in strong excitation through micromagnetic modeling has become relevant due to the observation of magnon Bose condensation. In particular, the question has arisen about the possibility of describing the coherent quantum state by the quasi-classical Landau-Lifshitz-Gilbert equations. We performed micromagnetic simulations of magnetization precession with a high angle of deviation in an out-of-plane nonuniform dc field. Our results confirm the formation of coherent magnon state under conditions of high excitation. This coherent state extends over long distances and described by a spatially inhomogeneous amplitude and a homogeneous precession phase.
2104.14804v1
2021-07-07
Superconducting Magnets
Superconductivity allows to construct and operate magnets at field values beyond 2 Tesla, the practical limitation of normal-conducting magnets exploiting ferro-magnetism. The field of superconducting magnets is dominated by the field generated in the coil. The stored energy and the electromagnetic forces generated by the coil are the main challenges to be overcome in the design of these magnets. For further reading you may consult the following books: [1], [2], [3], [4] or the proceedings of two specialized CAS courses: [5] and [6].
2107.03177v1
2021-08-14
An Experimental-Design Perspective on Population Genetic Variation
We consider the hypothesis that Evolution promotes population-wide genome patterns that, under randomization, ensures the External Validity of adaptations across population members. An adaptation is Externally Valid (EV) if its effect holds under a wide range of population genetic variations. A prediction following the hypothesis is that pairwise base substitutions in segregating regions must be 'random' as in Erdos-Renyi-Gilbert random graphs, but with edge probabilities derived from Experimental-Design concepts. We demonstrate these probabilities, and consequent mutation rates, in the full-genomes of 2504 humans, 1135 flowering plants, 1170 flies, 453 domestic sheep and 1223 brown rats.
2108.06580v1
2021-12-14
Extending the team with a project-specific bot
While every other software team is adopting off-the-shelf bots to automate everyday tasks, the Coq team has made a different choice by developing and maintaining a project-specific bot from the ground up. In this article, we describe the reasons for this choice, what kind of automation this has allowed us to implement, how the many features of this custom bot have evolved based on internal feedback, and the technology and architecture choices that have made it possible.
2112.07365v1
2021-12-29
Multi-Adversarial Safety Analysis for Autonomous Vehicles
This work in progress considers reachability-based safety analysis in the domain of autonomous driving in multi-agent systems. We formulate the safety problem for a car following scenario as a differential game and study how different modelling strategies yield very different behaviors regardless of the validity of the strategies in other scenarios. Given the nature of real-life driving scenarios, we propose a modeling strategy in our formulation that accounts for subtle interactions between agents, and compare its Hamiltonian results to other baselines. Our formulation encourages reduction of conservativeness in Hamilton-Jacobi safety analysis to provide better safety guarantees during navigation.
2112.14344v1
2022-01-26
Analyzing Ta-Shma's Code via the Expander Mixing Lemma
Random walks in expander graphs and their various derandomizations (e.g., replacement/zigzag product) are invaluable tools from pseudorandomness. Recently, Ta-Shma used s-wide replacement walks in his breakthrough construction of a binary linear code almost matching the Gilbert-Varshamov bound (STOC 2017). Ta-Shma's original analysis was entirely linear algebraic, and subsequent developments have inherited this viewpoint. In this work, we rederive Ta-Shma's analysis from a combinatorial point of view using repeated application of the expander mixing lemma. We hope that this alternate perspective will yield a better understanding of Ta-Shma's construction. As an additional application of our techniques, we give an alternate proof of the expander hitting set lemma.
2201.11166v1
2022-02-15
Further Collapses in TFNP
We show $\textsf{EOPL}=\textsf{PLS}\cap\textsf{PPAD}$. Here the class $\textsf{EOPL}$ consists of all total search problems that reduce to the End-of-Potential-Line problem, which was introduced in the works by Hubacek and Yogev (SICOMP 2020) and Fearnley et al. (JCSS 2020). In particular, our result yields a new simpler proof of the breakthrough collapse $\textsf{CLS}=\textsf{PLS}\cap\textsf{PPAD}$ by Fearnley et al. (STOC 2021). We also prove a companion result $\textsf{SOPL}=\textsf{PLS}\cap\textsf{PPADS}$, where $\textsf{SOPL}$ is the class associated with the Sink-of-Potential-Line problem.
2202.07761v2
2022-03-19
A proposed test of quantum mechanics with three connected atomic clock transitions
We consider possible extensions to quantum mechanics proposed by Steven Weinberg, and re-analyze his prediction of a new test based upon three atomic clocks in the same atom. We propose realistic experimental systems where this hypothesis can be tested. Two systems already set limits on deviations from quantum mechanics, while with another system, one would be able to search for new physics at the limit of sensitivity of the best atomic clocks.
2203.10269v3
2022-06-14
Generalized graph splines and the Universal Difference Property
We study the generalized graph splines introduced by Gilbert, Tymoczko, and Viel and focus on an attribute known as the Universal Difference Property (UDP). We prove that paths, trees, and cycles satisfy UDP. We explore UDP on graphs pasted at a single vertex and use Pr\"ufer domains to illustrate that not every edge labeled graph satisfies UDP. We show that UDP must hold for any edge labeled graph over a ring $R$ if and only if $R$ is a Pr\"ufer domain. Lastly, we prove that UDP is preserved by isomorphisms of edge labeled graphs.
2206.06981v2
2022-08-04
Total stability and Auslander-Reiten theory for Dynkin quivers
This paper concerns stability functions for Dynkin quivers, in the generality introduced by Rudakov. We show that relatively few inequalities need to be satisfied for a stability function to be totally stable (i.e. to make every indecomposable stable). Namely, a stability function $\mu$ is totally stable if and only if $\mu(\tau V) < \mu(V)$ for every almost split sequences $0 \to \tau V \to E \to V \to 0$ where $E$ is indecomposable. These can be visualized as those sequences around the "border" of the Auslander-Reiten quiver.
2208.02445v1
2022-09-09
Magnetization dynamics and reversal of two-dimensional magnets
Micromagnetics simulation based on the classical Landau-Lifshitz-Gilbert (LLG) equation has long been a powerful method for modeling magnetization dynamics and reversal of three-dimensional (3D) magnets. For two-dimensional (2D) magnets, the magnetization reversal always accompanies the collapse of the magnetization even at low temperatures due to intrinsic strong spin fluctuation. We propose a micromagnetic theory that explicitly takes into account the rapid demagnetization and remagnetization dynamics of 2D magnets during magnetization reversal. We apply the theory to a single-domain magnet to illustrate fundamental differences in magnetization trajectories and reversal times for 2D and 3D magnets.
2209.04483v1
2022-11-06
Two-Qutrit entanglement: 56-years old algorithm challenges machine learning
Classifying states as entangled or separable is a highly challenging task, while it is also one of the foundations of quantum information processing theory. This task is higly nontrivial even for relatively simple cases, such as two-qutrit Bell-diagonal states, i.e., mixture of nine mutually orthogonal maximally entangled states. In this article we apply the Gilbert algorithm to revise previously obtained results for this class. In particular we use ``cartography of entanglement'' to argue that most states left in [Hiesmayr, B. C. {\em Scientific Reports} {\bf 11}, 19739 (2021)] as unknown to be entangled or separable are most likely indeed separable, or very weakly entangled. The presented technique can find endless applications in more general cases.
2211.03213v1
2022-12-07
Quantitative CLTs on the Poisson space via Skorohod estimates and $p$-Poincaré inequalities
We establish new explicit bounds on the Gaussian approximation of Poisson functionals based on novel estimates of moments of Skorohod integrals. Combining these with the Malliavin-Stein method, we derive bounds in the Wasserstein and Kolmogorov distances whose application requires minimal moment assumptions on add-one cost operators $\unicode{x2014}$ thereby extending the results from (Last, Peccati and Schulte, 2016). Our applications include a CLT for the Online Nearest Neighbour graph, whose validity was conjectured in (Wade, 2009; Penrose and Wade, 2009). We also apply our techniques to derive quantitative CLTs for edge functionals of the Gilbert graph, of the $k$-Nearest Neighbour graph and of the Radial Spanning Tree, both in cases where qualitative CLTs are known and unknown.
2212.03782v1
2022-12-19
Bounds on Mixed Codes with Finite Alphabets
Mixed codes, which are error-correcting codes in the Cartesian product of different-sized spaces, model degrading storage systems well. While such codes have previously been studied for their algebraic properties (e.g., existence of perfect codes) or in the case of unbounded alphabet sizes, we focus on the case of finite alphabets, and generalize the Gilbert-Varshamov, sphere-packing, Elias-Bassalygo, and first linear programming bounds to that setting. In the latter case, our proof is also the first for the non-symmetric mono-alphabetic $q$-ary case using Navon and Samorodnitsky's Fourier-analytic approach.
2212.09314v1
2023-02-17
Codes Correcting Burst and Arbitrary Erasures for Reliable and Low-Latency Communication
Motivated by modern network communication applications which require low latency, we study codes that correct erasures with low decoding delay. We provide a simple explicit construction that yields convolutional codes that can correct both burst and arbitrary erasures under a maximum decoding delay constraint $T$. Our proposed code has efficient encoding/decoding algorithms and requires a field size that is linear in $T$. We study the performance of our code over the Gilbert-Elliot channel; our simulation results show significant performance gains over low-delay codes existing in the literature.
2302.08644v1
2023-03-10
On the coherence of one-relator groups and their group algebras
We prove that one-relator groups are coherent, solving a well-known problem of Gilbert Baumslag. Our proof strategy is readily applicable to many classes of groups of cohomological dimension two. We show that fundamental groups of two-complexes with non-positive immersions are homologically coherent, we show that groups with staggered presentations and many Coxeter groups are coherent and we show that group algebras over fields of characteristic zero of groups with reducible presentations without proper powers are coherent.
2303.05976v3
2023-05-11
Linear Codes with Prescribed Hull Dimension and Minimum Distance
The hull of a linear code (i.e., a finite field vector space)~\({\mathcal C}\) is defined to be the vector space formed by the intersection of~\({\mathcal C}\) with its dual~\({\mathcal C}^{\perp}.\) Constructing vector spaces with a specified hull dimension has important applications and it is therefore of interest to study minimum distance properties of such spaces. In this paper, we use the probabilistic method to obtain spaces with a given hull dimension and minimum distance and also derive Gilbert-Varshamov type sufficient conditions for their existence.
2305.07140v1
2023-05-18
Bounds on Size of Homopolymer Free Codes
For any given alphabet of size $q$, a Homopolymer Free code (HF code) refers to an $(n, M, d)_q$ code of length $n$, size $M$ and minimum Hamming distance $d$, where all the codewords are homopolymer free sequences. For any given alphabet, this work provides upper and lower bounds on the maximum size of any HF code using Sphere Packing bound and Gilbert-Varshamov bound. Further, upper and lower bounds on the maximum size of HF codes for various HF code families are calculated. Also, as a specific case, upper and lower bounds are obtained on the maximum size of homopolymer free DNA codes.
2305.10741v1
2023-06-08
A Macroscopic Theory of Saturated Ferromagnetic Conductors
A phenomenological theory of rigid and saturated ferromagnetic conductors is constructed from a four-continuum model consisting of a rigid lattice continuum, a bound charge continuum for polarization, a circulating current continuum for magnetization, and a free charge continuum for electrical conduction. The basic laws of physics are applied to the four continua. Thermal couplings and the related dissipative effects are also included. The theory includes the Landau-Lifshitz-Gilbert equation as one of a system of simultaneous equations.
2306.11525v1
2023-07-02
Unveiling Stable One-dimensional Magnetic Solitons in Magnetic Bilayers
We propose a novel model which efficiently describes the magnetization dynamics in a magnetic bilayer system. By applying a particular gauge transformation to the Landau-Lifshitz-Gilbert (LLG) equation, we successfully convert the model into an exactly integrable framework. Thus the obtained analytical solutions allows us to predict a 1D magnetic soliton pair existed by tunning the thickness of the spacing layer between the two ferrimagnetic layers. The decoupling-unlocking-locking transition of soliton motion is determined at various interaction intensitiy. Our results have implications for the manipulation of magnetic solitons and the design of magnetic soliton-based logic devices.
2307.00471v1
2023-09-22
Characterizing Smooth Safety Filters via the Implicit Function Theorem
Optimization-based safety filters, such as control barrier function (CBF) based quadratic programs (QPs), have demonstrated success in controlling autonomous systems to achieve complex goals. These CBF-QPs can be shown to be continuous, but are generally not smooth, let alone continuously differentiable. In this paper, we present a general characterization of smooth safety filters -- smooth controllers that guarantee safety in a minimally invasive fashion -- based on the Implicit Function Theorem. This characterization leads to families of smooth universal formulas for safety-critical controllers that quantify the conservatism of the resulting safety filter, the utility of which is demonstrated through illustrative examples.
2309.12614v1
2023-09-23
Sphaleron rate from lattice QCD
We compute the sphaleron rate on the lattice from the inversion of the Euclidean time correlators of the topological charge density, performing also controlled continuum and zero-smoothing extrapolations. The correlator inversion is performed by means of a recently-proposed modification of the Backus-Gilbert method.
2309.13327v1
2023-09-23
CA-PCA: Manifold Dimension Estimation, Adapted for Curvature
The success of algorithms in the analysis of high-dimensional data is often attributed to the manifold hypothesis, which supposes that this data lie on or near a manifold of much lower dimension. It is often useful to determine or estimate the dimension of this manifold before performing dimension reduction, for instance. Existing methods for dimension estimation are calibrated using a flat unit ball. In this paper, we develop CA-PCA, a version of local PCA based instead on a calibration of a quadratic embedding, acknowledging the curvature of the underlying manifold. Numerous careful experiments show that this adaptation improves the estimator in a wide range of settings.
2309.13478v1
2023-11-13
Dedukti: a Logical Framework based on the $λ$$Π$-Calculus Modulo Theory
Dedukti is a Logical Framework based on the $\lambda$$\Pi$-Calculus Modulo Theory. We show that many theories can be expressed in Dedukti: constructive and classical predicate logic, Simple type theory, programming languages, Pure type systems, the Calculus of inductive constructions with universes, etc. and that permits to used it to check large libraries of proofs developed in other proof systems: Zenon, iProver, FoCaLiZe, HOL Light, and Matita.
2311.07185v1
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
2005-05-20
On the expansion of the power of any polynomial 1+x+x^2+x^3+x^4+etc
In this paper, Euler gives the general trionomial coefficient as a sum of the binomial coefficients, the general quadrinomial coefficient as a sum of the binomial and trinomial coefficients, the general quintonomial coefficient as a sum of the binomial and quadrinomial coefficients, and gives a general determination of the coefficients of the expansion of any polynomial (1+x+x^2+...+x^m)^n as a sum of the coefficients of lower degree polynomial coefficients.
0505425v1
2023-12-05
Central limit theorem for the average closure coefficient
Many real-world networks exhibit the phenomenon of edge clustering, which is typically measured by the average clustering coefficient. Recently, an alternative measure, the average closure coefficient, is proposed to quantify local clustering. It is shown that the average closure coefficient possesses a number of useful properties and can capture complementary information missed by the classical average clustering coefficient. In this paper, we study the asymptotic distribution of the average closure coefficient of a heterogeneous Erd\"{o}s-R\'{e}nyi random graph. We prove that the standardized average closure coefficient converges in distribution to the standard normal distribution. In the Erd\"{o}s-R\'{e}nyi random graph, the variance of the average closure coefficient exhibits the same phase transition phenomenon as the average clustering coefficient.
2312.03142v1
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