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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 |
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 |
2019-08-05 | 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 |
2012-10-04 | All Spin Nano-magnetic State Elements | We propose an all spin state element to enable all spin state machines using
spin currents and nanomagnets. We demonstrate via numerical simulations the
operation of a state element a critical building block for synchronous,
sequential logic computation. The numerical models encompass
Landau-Lifshitz-Gilbert (LLG) nanomagnet dynamics with stochastic models and
vector spin-transport in metallic magnetic and non-magnetic channels. Combined
with all spin combinatorial logic, the state elements can enable synchronous
and asynchronous computing elements. | 1210.1613v1 |
2012-11-02 | Effect of Spin Torque on Magnetization Switching Speed Having Nonuniform Spin Distribution | We study the influence of the spin torque, which depends on the space and
time derivative of magnetization, on magnetization reversal time in a
ferromagnetic fine particle. The spin torque operates to dissipate the angular
momentum of the magnetization precession, and the torque increases in a spin
vortex structure. We calculate the magnetization reversal time under a DC
magnetic field using the Landau-Lifshitz-Gilbert equation containing a spin
torque term. We found that the spin torque changes the magnetization switching
speed significantly during the reversal process by maintaining a spin vortex in
an intermediate state. | 1211.0360v1 |
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 |
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 |
2018-10-17 | 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 |
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 |
2012-09-07 | Self-sustained current oscillations in spin-blockaded quantum dots | Self-sustained current oscillation observed in spin-blockaded double quantum
dots is explained as a consequence of periodic motion of dynamically polarized
nuclear spins (along a limit cycle) in the spin-blockaded regime under an
external magnetic field and a spin-transfer torque. It is shown, based on the
Landau-Lifshtz-Gilbert equation, that a sequence of semistable limit cycle,
Hopf and homoclinic bifurcations occurs as the external field is tuned. The
divergent period near the homoclinic bifurcation explains well why the period
in the experiment is so long and varies by many orders of magnitudes. | 1209.1548v1 |
2015-12-18 | Existence of travelling-wave solutions representing domain wall motion in a thin ferromagnetic nanowire | We study the dynamics of a domain wall under the influence of applied
magnetic fields in a one-dimensional ferromagnetic nanowire, governed by the
Landau--Lifshitz--Gilbert equation. Existence of travelling-wave solutions
close to two known static solutions is proven using
implicit-function-theorem-type arguments. | 1512.06016v2 |
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 |
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 |
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 |
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 |
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 |
2020-08-06 | 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 |
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 |
2014-01-08 | Tri-Dirac Surface Modes in Topological Superconductors | We propose a new type of topological surface modes having cubic dispersion in
three-dimensional topological superconductors. Lower order dispersions are
prohibited by the threefold rotational symmetry and time-reversal symmetry.
Cooper pairing in the bulk changes sign under improper rotations, akin
to$^{3}$He-B. The surface manifestations are a divergent surface density of
states at the Fermi level and isospins that rotate three times as they circle
the origin in momentum space. We propose that Heusler alloys with band
inversion are candidate materials to harbor the novel topological
superconductivity. | 1401.1823v1 |
2014-01-09 | Automated Code Generation for Lattice Quantum Chromodynamics and beyond | We present here our ongoing work on a Domain Specific Language which aims to
simplify Monte-Carlo simulations and measurements in the domain of Lattice
Quantum Chromodynamics. The tool-chain, called Qiral, is used to produce
high-performance OpenMP C code from LaTeX sources. We discuss conceptual issues
and details of implementation and optimization. The comparison of the
performance of the generated code to the well-established simulation software
is also made. | 1401.2039v1 |
2014-01-13 | Effect of Dzyaloshinskii Moriya interaction on magnetic vortex | The effect of the Dzyaloshinskii Moriya interaction on the vortex in magnetic
microdisk was investigated by micro magnetic simulation based on the Landau
Lifshitz Gilbert equation. Our results show that the DM interaction modifies
the size of the vortex core, and also induces an out of plane magnetization
component at the edge and inside the disk. The DM interaction can destabilizes
one vortex handedness, generate a bias field to the vortex core and couple the
vortex polarity and chirality. This DM-interaction-induced coupling can
therefore provide a new way to control vortex polarity and chirality. | 1401.3292v1 |
2014-01-31 | Self-Oscillation in Spin Torque Oscillator Stabilized by Field-like Torque | The self-oscillation of the magnetization in a spin torque oscillator (STO)
with a perpendicularly magnetized free layer and an in-plane magnetized pinned
layer in the absence of an applied magnetic field was studied by numerically
solving the Landau-Lifshitz-Gilbert equation. It was pointed out that
field-like torque was necessary to realize stable self-oscillation in this type
of STO at zero field. The numerical simulation at finite temperature showed
that the presence of the field-like torque led to a high power with a
relatively high oscillation frequency. | 1401.8088v2 |
2014-04-18 | Sparse Approximation, List Decoding, and Uncertainty Principles | We consider list versions of sparse approximation problems, where unlike the
existing results in sparse approximation that consider situations with unique
solutions, we are interested in multiple solutions. We introduce these problems
and present the first combinatorial results on the output list size. These
generalize and enhance some of the existing results on threshold phenomenon and
uncertainty principles in sparse approximations. Our definitions and results
are inspired by similar results in list decoding. We also present lower bound
examples that bolster our results and show they are of the appropriate size. | 1404.5190v2 |
2014-04-25 | Linewidth of Power Spectrum Originated from Thermal Noise in Spin Torque Oscillator | A theoretical formula of the linewidth caused by the thermal activation in a
spin torque oscillator with a perpendicularly magnetized free layer and an
in-plane magnetized pinned layer was developed by solving the stochastic
Landau-Lifshitz-Gilbert equation in the energy-phase representation. It is
shown that the linewidth can be suppressed down to 0.1 MHz by applying a large
current (10 mA for typical material parameters). A quality factor larger than
10^{4} is predicted in the large current limit, which is two orders of
magnitude larger than the recently observed experimental value. | 1404.6558v1 |
2015-02-14 | Energy dissipation in single-domain ferromagnetic nanoparticles: Dynamical approach | We study, both analytically and numerically, the phenomenon of energy
dissipation in single-domain ferromagnetic nanoparticles driven by an
alternating magnetic field. Our interest is focused on the power loss resulting
from the Landau-Lifshitz-Gilbert equation, which describes the precessional
motion of the nanoparticle magnetic moment. We determine the power loss as a
function of the field amplitude and frequency and analyze its dependence on
different regimes of forced precession induced by circularly and linearly
polarized magnetic fields. The conditions to maximize the nanoparticle heating
are also analyzed. | 1502.04222v1 |
2015-02-23 | The Positive Mass Theorem for Multiple Rotating Charged Black Holes | In this paper a lower bound for the ADM mass is given in terms of the angular
momenta and charges of black holes present in axisymmetric initial data sets
for the Einstein-Maxwell equations. This generalizes the mass-angular
momentum-charge inequality obtained by Chrusciel and Costa to the case of
multiple black holes. We also weaken the hypotheses used in the proof of this
result for single black holes, and establish the associated rigidity statement. | 1502.06290v2 |
2015-02-24 | An Upper Bound on the Minimum Distance of LDPC Codes over GF(q) | In [1] a syndrome counting based upper bound on the minimum distance of
regular binary LDPC codes is given. In this paper we extend the bound to the
case of irregular and generalized LDPC codes over GF(q). The comparison to the
lower bound for LDPC codes over GF(q) and to the upper bound for non-binary
codes is done. The new bound is shown to lie under the Gilbert-Varshamov bound
at high rates. | 1502.06874v1 |
2016-06-02 | On self-dual double negacirculant codes | Double negacirculant (DN) codes are the analogues in odd characteristic of
double circulant codes. Self-dual DN codes of odd dimension are shown to be
consta-dihedral. Exact counting formulae are derived for DN codes. The special
class of length a power of two is studied by means of Dickson polynomials, and
is shown to contain families of codes with relative distances satisfying a
modified Gilbert-Varshamov bound. | 1606.00815v1 |
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 |
2017-12-13 | 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 |
2018-05-30 | 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 |
2018-11-23 | 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 |
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 |
2019-07-28 | 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 |
2019-12-09 | 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 |
2020-05-11 | 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 |
2020-10-13 | 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 |
2021-07-07 | 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 |
2023-03-15 | Algebraic Geometry codes in the sum-rank metric | We introduce the first geometric construction of codes in the sum-rank
metric, which we called linearized Algebraic Geometry codes, using quotients of
the ring of Ore polynomials with coefficients in the function field of an
algebraic curve. We study the parameters of these codes and give lower bounds
for their dimension and minimum distance. Our codes exhibit quite good
parameters, respecting a similar bound to Goppa's bound for Algebraic Geometry
codes in the Hamming metric. Furthermore, our construction yields codes
asymptotically better than the sum-rank version of the Gilbert-Varshamov bound. | 2303.08903v2 |
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 |
2023-07-21 | Thermomechanics of ferri-antiferromagnetic phase transition in finitely-strained rocks towards paleomagnetism | The thermodynamic model of visco-elastic deformable magnetic materials at
finite strains is formulated in a fully Eulerian way in rates with the aim to
describe thermoremanent paleomagnetism in crustal rocks. The Landau theory
applied to a ferro-to-para-magnetic phase transition, the gradient theory for
magnetization (leading to exchange energy) with general mechanically dependent
coefficient, hysteresis in magnetization evolution by Gilbert equation
involving objective corotational time derivative of magnetization, and
demagnetizing field are considered in the model. The Jeffreys viscoelastic
rheology is used with temperature-dependent creep to model solidification or
melting transition. The model complies with energy conservation and the
Clausius-Duhem entropy inequality. | 2307.11826v2 |
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 |
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 |
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 |
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 |
2014-11-20 | 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 |
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