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2018-04-05
|
Stochastic ferrimagnetic Landau-Lifshitz-Bloch equation for finite magnetic structures
|
Precise modeling of the magnetization dynamics of nanoparticles with finite
size effects at fast varying temperatures is a computationally challenging
task. Based on the Landau-Lifshitz-Bloch (LLB) equation we derive a coarse
grained model for disordered ferrimagnets, which is both fast and accurate.
First, we incorporate stochastic fluctuations to the existing ferrimagnetic LLB
equation. Further, we derive a thermodynamic expression for the temperature
dependent susceptibilities, which is essential to model finite size effects.
Together with the zero field equilibrium magnetization the susceptibilities are
used in the stochastic ferrimagnetic LLB to simulate a $5\times10$ nm$^2$
ferrimagnetic GdFeCo particle with 70 % FeCo and 30 % Gd under various external
applied fields and heat pulses. The obtained trajectories agree well with those
of an atomistic model, which solves the stochastic Landau-Lifshitz-Gilbert
equation for each atom. Additionally, we derive an expression for the
intergrain exchange field which couple the ferromagnetic sublattices of a
ferrimagnet. A comparison of the magnetization dynamics obtained from this
simpler model with those of the ferrimagnetic LLB equation shows a perfect
agreement.
|
1804.01724v1
|
2018-04-06
|
Temperature dependence of bulk viscosity within lattice simulation of $SU(3)$--gluodynamics
|
In this paper the temperature dependence of the $SU(3)$--gluodynamics bulk
viscosity is studied within lattice simulations. To carry out this study we
measure the correlation function of the trace of the energy-momentum tensor for
a set of temperatures within the range $T/T_c \in (0.9, 1.5)$. To extract the
bulk viscosity from the correlation function we apply the Backus-Gilbert method
and the Tikhonov regularization method. We show that the ratio $\zeta/s$ is
small in the region $T/T_c \geqslant 1.1-1.2$ and in the vicinity of the
transition $T/T_c \leqslant 1.1-1.2$ it quickly rises. Our results are in
agreement with previous lattice studies and in a reasonable agreement with
other phenomenological approaches. Obtained values of the bulk viscosity are
significantly larger than perturbative results, what confirms that QGP is a
strongly correlated system.
|
1804.02382v2
|
2018-04-16
|
Anisotropy of exchange stiffness based on atomic-scale magnetic properties in rare-earth permanent magnet Nd$_2$Fe$_{14}$B
|
We examine the anisotropic properties of the exchange stiffness constant,
$\mathcal{A}$, for rare-earth permanent magnet, Nd$_2$Fe$_{14}$B, by connecting
analyses with two different scales of length, i.e., Monte Carlo (MC) method
with an atomistic spin model and Landau-Lifshitz-Gilbert (LLG) equation with a
continuous magnetic model. The atomistic MC simulations are performed on the
spin model of Nd$_2$Fe$_{14}$B constructed from ab-initio calculations, and the
LLG micromagnetics simulations are performed with the parameters obtained by
the MC simulations. We clarify that the amplitude and the thermal property of
$\mathcal{A}$ depend on the orientation in the crystal, which are attributed to
the layered structure of Nd atoms and weak exchange couplings between Nd and Fe
atoms. We also confirm that the anisotropy of $\mathcal{A}$ significantly
affects the threshold field for the magnetization reversal (coercivity) given
by the depinning process.
|
1804.05824v2
|
2018-03-29
|
Percolative Mechanism of Aging in Zirconia-Containing Ceramics for Medical Applications
|
Recently, several episodes of fracture of zirconia ceramic femoral heads of
total hip prostheses have alarmed the medical and scientific community
regarding aging problems in zirconia prostheses. Such fractures cause immediate
local tissue reactions, which require urgent medical intervention to prevent
further complications. As a result, it has been promoted that yttria-stabilized
zirconia (Y-TZP) hip prostheses be substituted by alumina and alumina/Y-TZP
ceramics. In the present investigation, we have found an upper limit of Y-TZP
concentration in alumina/Y-TZP composites (16 vol.%) to avoid future aging
problems. This limit coincides with the percolation threshold measured by
infrared (IR) reflectance in a series of alumina/Y-TZP composites.
|
1804.08696v1
|
2018-03-30
|
Reliability assessment in advanced nanocomposite materials for orthopaedic applications
|
Alumina-zirconia nano-composites were recently developed as alternative
bearing materials for orthopedics. Previous, preliminary reports show that such
alumina-zirconia nanocomposites exhibit high crack resistance and low wear
rate. In this paper, additional information is given in terms of wear, crack
resistance and ageing behaviour: femoral heads are inspected after 7 million
cycles of wear testing on a hip simulator, crack resistance is measured and
compared to other ceramics used today in orthopedics, slow crack growth is
reported under static and cyclic fatigue, and aging resistance is assessed. We
also report on the load to failure of femoral heads prototypes during
compression tests. This overall reliability assessment ensures a potential
future development for these kinds of new nanocomposites in the orthopedic
field.
|
1804.08702v1
|
2018-04-26
|
Shape of a skyrmion
|
We propose a method of determining the shape of a two-dimensional magnetic
skyrmion, which can be parameterized as the position dependence of the
orientation of the local magnetic moment, by using the expansion in terms of
the eigenfunctions of the Schr\"{o}dinger equation of a harmonic oscillator. A
variational calculation is done, up to the next-to-next-to-leading order. This
result is verified by a lattice simulation based on Landau-Lifshitz-Gilbert
equation. Our method is also applied to the dissipative matrix in the Thiele
equation as well as two interacting skyrmions in a bilayer system.
|
1804.10162v3
|
2018-04-30
|
Modular Compact Modeling of Magnetic Tunnel Junction Devices
|
This paper describes a robust, modular, and physics- based circuit framework
to model conventional and emerging Magnetic Tunnel Junction (MTJ) devices.
Magnetization dynamics are described by the stochastic Landau-Lifshitz-Gilbert
(sLLG) equation whose results are rigorously benchmarked with a Fokker-Planck
Equation (FPE) description of magnet dynamics. We then show how sLLG is coupled
to transport equations of MTJ-based devices in a unified circuit platform. Step
by step, we illustrate how the physics-based MTJ model can be extended to
include different spintronics phenomena, including spin-transfer-torque (STT),
voltage-control of magnetic anisotropy (VCMA) and spin-orbit torque (SOT)
phenomena by experimentally benchmarked examples. To demonstrate how our
approach can be used in the exploration of novel MTJ-based devices, we also
present a recently proposed MEMS resonator- driven spin-torque nano oscillator
(STNO) that can reduce the phase noise of STNOs. We briefly elaborate on the
use of our framework beyond conventional devices.
|
1805.00066v2
|
2018-05-22
|
Loss of Hall Conductivity Quantization in a Non-Hermitian Quantum Anomalous Hall Insulator
|
Recent work has extended topological band theory to open, non-Hermitian
Hamiltonians, yet little is understood about how non-Hermiticity alters the
topological quantization of associated observables. We address this problem by
studying the quantum anomalous Hall effect (QAHE) generated in the Dirac
surface states of a 3D time-reversal-invariant topological insulator (TI) that
is proximity-coupled to a metallic ferromagnet. By constructing a contact
self-energy for the ferromagnet, we show that in addition to generating a mass
gap in the surface spectrum, the ferromagnet can introduce a non-Hermitian
broadening term, which can obscure the mass gap in the spectral function. We
calculate the Hall conductivity for the effective non-Hermitian Hamiltonian
describing the heterostructure and show that it is no longer quantized despite
being classified as a Chern insulator based on non-Hermitian topological band
theory. Our results indicate that the QAHE will be challenging to
experimentally observe in ferromagnet-TI heterostructures due to the finite
lifetime of quasi-particles at the interface.
|
1805.08892v2
|
2018-05-31
|
Spin-orbit torque induced dipole skyrmion motion at room temperature
|
We demonstrate deterministic control of dipole-field-stabilized skyrmions by
means of spin-orbit torques arising from heavy transition-metal seed layers.
Experiments are performed on amorphous Fe/Gd multilayers that are patterned
into wires and exhibit stripe domains and dipole skyrmions at room temperature.
We show that while the domain walls and skyrmions are achiral on average due to
lack of Dzyaloshinskii-Moriya interactions, the N\'eel-like closure domain
walls at each surface are chiral and can couple to spin-orbit torques. The
current-induced domain evolutions are reported for different magnetic phases,
including disordered stripe domains, coexisting stripes and dipole skyrmions
and a closed packed dipole skyrmion lattice. The magnetic textures exhibit
motion under current excitations with a current density ~10^8 A/m2. By
comparing the motion resulting from magnetic spin textures in Fe/Gd films with
different heavy transition-metal interfaces, we confirm spin currents can be
used to manipulate achiral dipole skyrmions via spin-orbit torques.
|
1805.12517v1
|
2018-06-11
|
Geometric Lagrangian averaged Euler-Boussinesq and primitive equations
|
In this article we derive the equations for a rotating stratified fluid
governed by inviscid Euler-Boussinesq and primitive equations that account for
the effects of the perturbations upon the mean. Our method is based on the
concept of geometric generalized Lagrangian mean recently introduced by Gilbert
and Vanneste, combined with generalized Taylor and horizontal isotropy of
fluctuations as turbulent closure hypotheses. The models we obtain arise as
Euler-Poincar\'{e} equations and inherit from their parent systems conservation
laws for energy and potential vorticity. They are structurally and
geometrically similar to Euler-Boussinesq-$\alpha$ and primitive
equations-$\alpha$ models, however feature a different regularizing second
order operator.
|
1806.05053v2
|
2018-06-14
|
Topological quantization of the flow of magnetic skyrmions driven by a ratchet-like potential under thermal fluctuations
|
We consider a magnetic skyrmion adiabatically driven by a spin-polarized
electrical current periodic in both space and time and asymmetric in space, and
also subject to a random magnetic field representing the thermal fluctuations.
We show that when the random magnetic field is low enough, while the time
variation of the driving current is slow enough, the skyrmion flow is an
integer multiply of the ratio between the space and time periods, the integer
being a topological invariant called Chern number. This result is also
demonstrated by numerically solving the stochastic Landau-Lifshitz-Gilbert
(sLLG) and Langevin equations. Our work suggests a novel method of manipulating
skyrmions with topological stability.
|
1806.05354v1
|
2018-06-17
|
Skyrmion Formation Induced by Antiferromagnetic-enhanced Interfacial Dzyaloshinskii Moriya Interaction
|
Ne\'el skyrmions originate from interfacial Dzyaloshinskii Moriya interaction
(DMI). Recent studies have explored using ferromagnet to host Ne\'el skyrmions
for device applications. However, challenges remain to reduce the size of
skyrmion to near 10 nm. Amorphous rare-earth-transitional-metal ferrimagnets
are attractive alternative materials to obtain ultrasmall skyrmions at room
temperature. Their intrinsic perpendicular magnetic anisotropy and tunable
magnetization provides a favorable environment for skyrmion stability. In this
work, we employ atomistic stochastic Landau-Liftshitz-Gilbert (LLG) algorithm
to investigate skyrmions in GdFe within the interfacial DMI model. Despite the
rapid decay of DMI away from the interface, small skyrmions of near 10 nm are
found in thick ~ 5 nm amorphous GdFe film at 300K. We have also considered
three scenarios for the sign of DMI between Gd-Fe pair. It is revealed that
antiferromagnetic coupling in the ferrimagnet plays an important role in
enhancing the effect of interfacial DMI and to stabilize skyrmion. These
results show that ferrimagnets and antiferromagnets with intrinsic
antiferromagnetic couplings are appealing materials to host small skyrmions at
room temperature, which is crucial to improve density and energy efficiency in
skyrmion based devices.
|
1806.06334v1
|
2018-06-17
|
Property Testing for Differential Privacy
|
We consider the problem of property testing for differential privacy: with
black-box access to a purportedly private algorithm, can we verify its privacy
guarantees? In particular, we show that any privacy guarantee that can be
efficiently verified is also efficiently breakable in the sense that there
exist two databases between which we can efficiently distinguish. We give lower
bounds on the query complexity of verifying pure differential privacy,
approximate differential privacy, random pure differential privacy, and random
approximate differential privacy. We also give algorithmic upper bounds. The
lower bounds obtained in the work are infeasible for the scale of parameters
that are typically considered reasonable in the differential privacy
literature, even when we suppose that the verifier has access to an (untrusted)
description of the algorithm. A central message of this work is that verifying
privacy requires compromise by either the verifier or the algorithm owner.
Either the verifier has to be satisfied with a weak privacy guarantee, or the
algorithm owner has to compromise on side information or access to the
algorithm.
|
1806.06427v2
|
2018-06-25
|
Coupled Wire Models of Interacting Dirac Nodal Superconductors
|
Topological nodal superconductors possess gapless low energy excitations that
are characterized by point or line nodal Fermi surfaces. In this work, using a
coupled wire construction, we study topological nodal superconductors that have
protected Dirac nodal points. In this construction, the low-energy electronic
degrees of freedom are confined in a three dimensional array of wires, which
emerge as pairing vortices of a microscopic superconducting system. The vortex
array harbors an antiferromagnetic time-reversal and a mirror glide symmetry
that protect the massless Dirac fermion in the single-body non-interacting
limit. Within this model, we demonstrate exact-solvable many-body interactions
that preserve the underlying symmetries and introduce a finite excitation
energy gap. These gapping interactions support fractionalization and
generically lead to non-trivial topological order. We also construct a special
case of $N=16$ Dirac fermions where corresponding the gapping interaction leads
to a trivial $E_8$ topological order that is closely related to the
cancellation of the large gravitational anomaly.
|
1806.09599v1
|
2018-07-02
|
A Broader View on Bias in Automated Decision-Making: Reflecting on Epistemology and Dynamics
|
Machine learning (ML) is increasingly deployed in real world contexts,
supplying actionable insights and forming the basis of automated
decision-making systems. While issues resulting from biases pre-existing in
training data have been at the center of the fairness debate, these systems are
also affected by technical and emergent biases, which often arise as
context-specific artifacts of implementation. This position paper interprets
technical bias as an epistemological problem and emergent bias as a dynamical
feedback phenomenon. In order to stimulate debate on how to change machine
learning practice to effectively address these issues, we explore this broader
view on bias, stress the need to reflect on epistemology, and point to
value-sensitive design methodologies to revisit the design and implementation
process of automated decision-making systems.
|
1807.00553v2
|
2018-07-06
|
Spin-torque-induced magnetization dynamics in ferrimagnets based on Landau-Lifshitz-Bloch Equation
|
A theoretical model based on the Landau-Lifshitz-Bloch equation is developed
to study the spin-torque effect in ferrimagnets. Experimental findings, such as
the temperature dependence, the peak in spin torque, and the angular-momentum
compensation, can be well captured. In contrast to the ferromagnet system, the
switching trajectory in ferrimagnets is found to be precession free. The two
sublattices are not always collinear, which produces large exchange field
affecting the magnetization dynamics. The study of material composition shows
the existence of an oscillation region at intermediate current density, induced
by the nondeterministic switching. Compared to the Landau-Lifshitz-Gilbert
model, our developed model based on the Landau-Lifshitz-Bloch equation enables
the systematic study of spin-torque effect and the evaluation of
ferrimagnet-based devices.
|
1807.02445v1
|
2018-07-10
|
Plumbing Constructions and the Domain of Outer Communication for 5-Dimensional Stationary Black Holes
|
The topology of the domain of outer communication for 5-dimensional
stationary bi-axisymmetric black holes is classified in terms of disc bundles
over the 2-sphere and plumbing constructions. In particular we find an
algorithmic bijective correspondence between the plumbing of disc bundles and
the rod structure formalism for such spacetimes. Furthermore, we describe a
canonical fill-in for the black hole region and cap for the asymptotic region.
The resulting compactified domain of outer communication is then shown to be
homeomorphic to $S^4$, a connected sum of $S^2\times S^2$'s, or a connected sum
of complex projective planes $\mathbb{CP}^2$. Combined with recent existence
results, it is shown that all such topological types are realized by vacuum
solutions. In addition, our methods treat all possible types of asymptotic
ends, including spacetimes which are asymptotically flat, asymptotically
Kaluza-Klein, or asymptotically locally Euclidean.
|
1807.03452v1
|
2018-07-13
|
Deep Learning in the Wild
|
Deep learning with neural networks is applied by an increasing number of
people outside of classic research environments, due to the vast success of the
methodology on a wide range of machine perception tasks. While this interest is
fueled by beautiful success stories, practical work in deep learning on novel
tasks without existing baselines remains challenging. This paper explores the
specific challenges arising in the realm of real world tasks, based on case
studies from research \& development in conjunction with industry, and extracts
lessons learned from them. It thus fills a gap between the publication of
latest algorithmic and methodical developments, and the usually omitted
nitty-gritty of how to make them work. Specifically, we give insight into deep
learning projects on face matching, print media monitoring, industrial quality
control, music scanning, strategy game playing, and automated machine learning,
thereby providing best practices for deep learning in practice.
|
1807.04950v1
|
2018-07-16
|
Digital frequency multiplexing with sub-Kelvin SQUIDs
|
Digital frequency multiplexing (dfMux) is a readout architecture for
transition edge sensor-based detector arrays and is used on telescopes
including SPT-3G, POLARBEAR-2, and LiteBIRD. Here, we present recent progress
and plans for development of a sub-Kelvin SQUID architecture for digital
frequency multiplexed bolometers. This scheme moves the SQUID from the 4 K
stage to the 250 mK stage, adjacent to the bolometers. Operating the SQUID on
the detector stage may offer lower noise and greater scalability. Electrical
performance will be improved as a result of decreased wiring length and reduced
parasitics, allowing for higher multiplexing factors and lower bolometer
R_normal . These performance improvements will enable ultra-large focal planes
for future instruments such as CMB-S4.
|
1807.05995v1
|
2018-07-20
|
Sphinx: a massively multiplexed fiber positioner for MSE
|
In this paper we present the Australian Astronomical Observatory's concept
design for Sphinx - a fiber positioned with 4332 spines on a 7.77mm pitch for
CFHT's Mauna Kea Spectroscopic Explorer (MSE) Telescope. Based on the Echidna
technology used with FMOS (on Subaru) and 4MOST (on VISTA), the next evolution
of the tilting spine design delivers improved performance and superior
allocation efficiency. Several prototypes have been constructed that
demonstrate the suitability of the new design for MSE. Results of prototype
testing are presented, along with an analysis of the impact of tilting spines
on the overall survey efficiency. The Sphinx fiber positioned utilizes a novel
metrology system for spine position feedback. The metrology design and the
careful considerations required to achieve reliable, high accuracy measurements
of all fibres in a realistic telescope environment are also presented.
|
1807.09181v1
|
2018-07-30
|
Graphs admitting only constant splines
|
We study {\em generalized graph splines,} introduced by Gilbert, Viel, and
the last author. For a large class of rings, we characterize the graphs that
only admit constant splines. To do this, we prove that if a graph has a
particular type of cutset (e.g., a bridge), then the space of splines naturally
decomposes as a certain direct sum of submodules. As an application, we use
these results to describe splines on a triangulation studied by Zhou and Lai,
but over a different ring than they used.
|
1807.11515v2
|
2018-08-05
|
Searching for patchy reionization from cosmic microwave background with hybrid quadratic estimators
|
We propose a hybrid quadratic estimator to measure cross correlations between
gravitational lensing of the cosmic microwave background (CMB) and differential
screening effects arising from fluctuations in the electron column density,
such as could arise from patchy reionization. The hybrid quadratic estimators
are validated by simulated data sets with both Planck and CMB-Stage 4 (CMB-S4)
instrumental properties and found to be able to recover the cross-power spectra
with almost no biases. We apply this technique to Planck 2015 temperature data
and obtain cross-power spectra between gravitational lensing and differential
screening effects. Planck data alone cannot detect the
patchy-reionization-induced cross-power spectrum but future experiment like
CMB-S4 will be able to robustly measure the expected signal and deliver new
insights on reionization.
|
1808.01592v1
|
2018-08-08
|
Revisiting Gilbert Strang's "A Chaotic Search for $i$"
|
In the paper "A Chaotic Search for $i$"~(\cite{strang1991chaotic}), Strang
completely explained the behaviour of Newton's method when using real initial
guesses on $f(x) = x^{2}+1$, which has only a pair of complex roots $\pm i$. He
explored an exact symbolic formula for the iteration, namely $x_{n}=\cot{
\left( 2^{n} \theta_{0} \right) }$, which is valid in exact arithmetic. In this
paper, we extend this to to $k^{th}$ order Householder methods, which include
Halley's method, and to the secant method. Two formulae, $x_{n}=\cot{ \left(
\theta_{n-1}+\theta_{n-2} \right) }$ with
$\theta_{n-1}=\mathrm{arccot}{\left(x_{n-1}\right)}$ and
$\theta_{n-2}=\mathrm{arccot}{\left(x_{n-2}\right)}$, and $x_{n}=\cot{ \left(
(k+1)^{n} \theta_{0} \right) }$ with $\theta_{0} = \mathrm{arccot}(x_{0})$, are
provided. The asymptotic behaviour and periodic character are illustrated by
experimental computation. We show that other methods (Schr\"{o}der iterations
of the first kind) are generally not so simple. We also explain an old method
that can be used to allow Maple's \textsl{Fractals[Newton]} package to
visualize general one-step iterations by disguising them as Newton iterations.
|
1808.03229v1
|
2018-08-11
|
Micromagnetic modeling of Terahertz oscillations in an antiferromagnetic material driven by spin-Hall effect
|
The realization of THz sources is a fundamental aspect for a wide range of
applications. Over different approaches, compact THz oscillators can be
realized taking advantage of dynamics in antiferromagnetic (AFMs) thin films
driven by spin-Hall effect. Here we perform a systematic study of these THz
oscillators within a full micromagnetic solver based on the numerical solution
of two coupled Landau-Lifshitz-Gilbert-Slonczewski equations, for the case of
ultra-thin films, i.e. when the N\'eel temperature of an AFM is substantially
reduced. We have found two different dynamical modes depending on the strength
of the Dzyaloshinskii-Moriya interaction (DMI). At low DMI, a large amplitude
precession is excited where both the magnetizations of the sublattices are in a
uniform state and rotate in the same direction. At large enough DMI, the ground
state of the AFM becomes non-uniform and the antiferromagnetic dynamics is
characterized by ultrafast domain wall motion.
|
1808.03773v1
|
2018-08-30
|
Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics
|
The tangent plane scheme is a time-marching scheme for the numerical solution
of the nonlinear parabolic Landau-Lifshitz-Gilbert equation (LLG), which
describes the time evolution of ferromagnetic configurations. Exploiting the
geometric structure of LLG, the tangent plane scheme requires only the solution
of one linear variational form per time-step, which is posed in the discrete
tangent space determined by the nodal values of the current magnetization. We
develop an effective solution strategy for the arising constrained linear
systems, which is based on appropriate Householder reflections. We derive
possible preconditioners, which are (essentially) independent of the time-step,
and prove that the preconditioned GMRES algorithm leads to linear convergence.
Numerical experiments underpin the theoretical findings.
|
1808.10281v1
|
2018-09-12
|
Iterative Delegations in Liquid Democracy with Restricted Preferences
|
In this paper, we study liquid democracy, a collective decision making
paradigm which lies between direct and representative democracy. One main
feature of liquid democracy is that voters can delegate their votes in a
transitive manner so that: A delegates to B and B delegates to C leads to A
delegates to C. Unfortunately, this process may not converge as there may not
even exist a stable state (also called equilibrium). In this paper, we
investigate the stability of the delegation process in liquid democracy when
voters have restricted types of preference on the agent representing them
(e.g., single-peaked preferences). We show that various natural structures of
preferences guarantee the existence of an equilibrium and we obtain both
tractability and hardness results for the problem of computing several
equilibria with some desirable properties.
|
1809.04362v2
|
2018-09-25
|
Phase change materials for nano-polaritonics: a case study of hBN/VO2 heterostructures
|
Polaritonic excitation and control in van der Waals (vdW) materials exhibit
superior merits than conventional materials and thus hold new promise for
exploring light matter interactions. In this work, we created vdW
heterostructures combining hexagonal boron nitride (hBN) and a representative
phase change material - vanadium dioxide (VO2). Using infrared
nano-spectroscopy and nano-imaging, we demonstrated the dynamic tunability of
hyperbolic phonon polaritons in hBN/VO2 heterostructures by temperature control
in a precise and reversible fashion. The dynamic tuning of the polaritons stems
from the change of local dielectric properties of the VO2 sublayer through
insulator to metal transition by the temperature control. The high
susceptibility of polaritons to electronic phase transitions opens
possibilities for applications of vdW materials in combination with correlated
phase change materials.
|
1809.09652v1
|
2018-10-08
|
Causal isotonic regression
|
In observational studies, potential confounders may distort the causal
relationship between an exposure and an outcome. However, under some
conditions, a causal dose-response curve can be recovered using the
G-computation formula. Most classical methods for estimating such curves when
the exposure is continuous rely on restrictive parametric assumptions, which
carry significant risk of model misspecification. Nonparametric estimation in
this context is challenging because in a nonparametric model these curves
cannot be estimated at regular rates. Many available nonparametric estimators
are sensitive to the selection of certain tuning parameters, and performing
valid inference with such estimators can be difficult. In this work, we propose
a nonparametric estimator of a causal dose-response curve known to be monotone.
We show that our proposed estimation procedure generalizes the classical
least-squares isotonic regression estimator of a monotone regression function.
Specifically, it does not involve tuning parameters, and is invariant to
strictly monotone transformations of the exposure variable. We describe
theoretical properties of our proposed estimator, including its irregular limit
distribution and the potential for doubly-robust inference. Furthermore, we
illustrate its performance via numerical studies, and use it to assess the
relationship between BMI and immune response in HIV vaccine trials.
|
1810.03269v2
|
2018-10-10
|
On the Approximation Properties of Random ReLU Features
|
We study the approximation properties of random ReLU features through their
reproducing kernel Hilbert space (RKHS). We first prove a universality theorem
for the RKHS induced by random features whose feature maps are of the form of
nodes in neural networks. The universality result implies that the random ReLU
features method is a universally consistent learning algorithm. We prove that
despite the universality of the RKHS induced by the random ReLU features,
composition of functions in it generates substantially more complicated
functions that are harder to approximate than those functions simply in the
RKHS. We also prove that such composite functions can be efficiently
approximated by multi-layer ReLU networks with bounded weights. This depth
separation result shows that the random ReLU features models suffer from the
same weakness as that of shallow models. We show in experiments that the
performance of random ReLU features is comparable to that of random Fourier
features and, in general, has a lower computational cost. We also demonstrate
that when the target function is the composite function as described in the
depth separation theorem, 3-layer neural networks indeed outperform both random
ReLU features and 2-layer neural networks.
|
1810.04374v3
|
2018-10-15
|
ABACUS: Unsupervised Multivariate Change Detection via Bayesian Source Separation
|
Change detection involves segmenting sequential data such that observations
in the same segment share some desired properties. Multivariate change
detection continues to be a challenging problem due to the variety of ways
change points can be correlated across channels and the potentially poor
signal-to-noise ratio on individual channels. In this paper, we are interested
in locating additive outliers (AO) and level shifts (LS) in the unsupervised
setting. We propose ABACUS, Automatic BAyesian Changepoints Under Sparsity, a
Bayesian source separation technique to recover latent signals while also
detecting changes in model parameters. Multi-level sparsity achieves both
dimension reduction and modeling of signal changes. We show ABACUS has
competitive or superior performance in simulation studies against
state-of-the-art change detection methods and established latent variable
models. We also illustrate ABACUS on two real application, modeling genomic
profiles and analyzing household electricity consumption.
|
1810.06167v1
|
2018-10-24
|
Photoinduced topological spin texture in a metallic ferromagnet
|
Photoinduced nonequilibrium spin structure is examined in the double-exchange
model, in which itinerant electrons couple with localized spins through the
ferromagnetic Hund coupling. In particular, we focus on the transient spin
structure from the initial ferromagnetic metallic state to the steady
antiferromagnetic ordered state reported in [Phys. Rev. Lett. 119, 207202
(2017)]. By solving the Schr\"odinger equation combined with the
Landau-Lifshitz-Gilbert equation, we find finite winding number and chirality,
which implies emergence of topological chiral spin textures. These observations
are reproduced by a calculation where spin dynamics after sudden quench of the
chemical potential are examined in larger clusters. A possible mechanism of the
topological spin texture in the transient dynamics is discussed.
|
1810.10244v1
|
2018-11-01
|
Time Quantified Monte Carlo Method for Long-range Interacting Systems
|
We propose a method for simulating the stochastic dynamics of classical spin
systems with long-range interactions. The method incorporates the stochastic
cutoff (SCO) method, which is originally specialized for simulating equilibrium
state, into time quantified Monte Carlo (TQMC) method. We analytically prove
that the present method gives the same real-time dynamics with the stochastic
Landau-Lifshitz-Gilbert (s-LLG) equation, i.e., both method derives the same
Fokker-Planck coefficients. We demonstrate magnetization reversal processes and
confirm that the result is in good agreement with the result obtained by s-LLG.
Using our method enables us to analyze complicated lattice systems consisting
of many spins in a unit cell. Technical improvement of TQMC is also proposed.
|
1811.00237v2
|
2018-11-01
|
Spatial Functional Linear Model and its Estimation Method
|
The classical functional linear regression model (FLM) and its extensions,
which are based on the assumption that all individuals are mutually
independent, have been well studied and are used by many researchers. This
independence assumption is sometimes violated in practice, especially when data
with a network structure are collected in scientific disciplines including
marketing, sociology and spatial economics. However, relatively few studies
have examined the applications of FLM to data with network structures. We
propose a novel spatial functional linear model (SFLM), that incorporates a
spatial autoregressive parameter and a spatial weight matrix into FLM to
accommodate spatial dependencies among individuals. The proposed model is
relatively flexible as it takes advantage of FLM in handling high-dimensional
covariates and spatial autoregressive (SAR) model in capturing network
dependencies. We develop an estimation method based on functional principal
component analysis (FPCA) and maximum likelihood estimation. Simulation studies
show that our method performs as well as the FPCA-based method used with FLM
when no network structure is present, and outperforms the latter when network
structure is present. A real weather data is also employed to demonstrate the
utility of the SFLM.
|
1811.00314v1
|
2018-11-12
|
New Theoretical Bounds and Constructions of Permutation Codes under Block Permutation Metric
|
Permutation codes under different metrics have been extensively studied due
to their potentials in various applications. Generalized Cayley metric is
introduced to correct generalized transposition errors, including previously
studied metrics such as Kendall's $\tau$-metric, Ulam metric and Cayley metric
as special cases. Since the generalized Cayley distance between two
permutations is not easily computable, Yang et al. introduced a related metric
of the same order, named the block permutation metric. Given positive integers
$n$ and $d$, let $\mathcal{C}_{B}(n,d)$ denote the maximum size of a
permutation code in $S_n$ with minimum block permutation distance $d$. In this
paper, we focus on the theoretical bounds of $\mathcal{C}_{B}(n,d)$ and the
constructions of permutation codes under block permutation metric. Using a
graph theoretic approach, we improve the Gilbert-Varshamov type bound by a
factor of $\Omega(\log{n})$, when $d$ is fixed and $n$ goes into infinity. We
also propose a new encoding scheme based on binary constant weight codes.
Moreover, an upper bound beating the sphere-packing type bound is given when
$d$ is relatively close to $n$.
|
1811.04600v1
|
2018-11-13
|
Classical Access Structures of Ramp Secret Sharing Based on Quantum Stabilizer Codes
|
In this paper we consider to use the quantum stabilizer codes as secret
sharing schemes for classical secrets. We give necessary and sufficient
conditions for qualified and forbidden sets in terms of quantum stabilizers.
Then we give a Gilbert-Varshamove-type sufficient condition for existence of
secret sharing schemes with given parameters, and by using that sufficient
condition, we show that roughly 19% of participants can be made forbidden
independently of the size of classical secret, in particular when an $n$-bit
classical secret is shared among $n$ participants having 1-qubit share each. We
also consider how much information is obtained by an intermediate set and
express that amount of information in terms of quantum stabilizers. All the
results are stated in terms of linear spaces over finite fields associated with
the quantum stabilizers.
|
1811.05217v7
|
2018-11-13
|
Enhanced domain wall velocity near a ferromagnetic instability
|
Assuming a Fermi liquid behavior for $s$-conduction electrons, we rewrite the
extended Landau-Lifshitz-Gilbert (LLG) equation renormalized by interactions
through the Landau parameters $F^{a}_{l}$ ($l=0,1,2 \cdots$) in an explicit
form to describe the dynamic of a domain wall (DW) due to spin transfer torque
phenomenon. The interaction between spins of the \textit{s}-conduction
electrons explains qualitatively the DW velocity experimental observations in
$\mathrm{Ni_{81}}\mathrm{Fe_{19}}$ (Permalloy) recalculated by us without
defects or impurity hypothesis. Close to Stoner ferromagnetic instability point
where $F^{a}_{0} \approx -0.99$, the DW velocity becomes high
($v^{*}_{DW}\approx 600$ $ms^{-1}$) and critical spin current density becomes
reduced ($j^{*}_{c}\approx1\times10^{12}$ $Am^{-2}$) when compared to that
calculated by nonadiabatic approach. At the critical point, the DW velocity
diverges while critical spin current density at the same point goes to zero.
Our theory also provides a prediction to looking for materials in which is
possible applies a smallest critical spin current density and observes higher
DW velocity.
|
1811.05380v4
|
2018-12-07
|
Coding over Sets for DNA Storage
|
In this paper we study error-correcting codes for the storage of data in
synthetic deoxyribonucleic acid (DNA). We investigate a storage model where a
data set is represented by an unordered set of $M$ sequences, each of length
$L$. Errors within that model are a loss of whole sequences and point errors
inside the sequences, such as insertions, deletions and substitutions. We
derive Gilbert-Varshamov lower bounds and sphere packing upper bounds on
achievable cardinalities of error-correcting codes within this storage model.
We further propose explicit code constructions than can correct errors in such
a storage system that can be encoded and decoded efficiently. Comparing the
sizes of these codes to the upper bounds, we show that many of the
constructions are close to optimal.
|
1812.02936v3
|
2018-12-14
|
Computational micromagnetics with Commics
|
We present our open-source Python module Commics for the study of the
magnetization dynamics in ferromagnetic materials via micromagnetic
simulations. It implements state-of-the-art unconditionally convergent finite
element methods for the numerical integration of the Landau-Lifshitz-Gilbert
equation. The implementation is based on the multiphysics finite element
software Netgen/NGSolve. The simulation scripts are written in Python, which
leads to very readable code and direct access to extensive post-processing.
Together with documentation and example scripts, the code is freely available
on GitLab.
|
1812.05931v1
|
2019-01-10
|
Multi-Parameter Regression Survival Modelling: An Alternative to Proportional Hazards
|
It is standard practice for covariates to enter a parametric model through a
single distributional parameter of interest, for example, the scale parameter
in many standard survival models. Indeed, the well-known proportional hazards
model is of this kind. In this paper we discuss a more general approach whereby
covariates enter the model through more than one distributional parameter
simultaneously (e.g., scale and shape parameters). We refer to this practice as
"multi-parameter regression" (MPR) modelling and explore its use in a survival
analysis context. We find that multi-parameter regression leads to more
flexible models which can offer greater insight into the underlying data
generating process. To illustrate the concept, we consider the two-parameter
Weibull model which leads to time-dependent hazard ratios, thus relaxing the
typical proportional hazards assumption and motivating a new test of
proportionality. A novel variable selection strategy is introduced for such
multi-parameter regression models. It accounts for the correlation arising
between the estimated regression coefficients in two or more linear predictors
-- a feature which has not been considered by other authors in similar
settings. The methods discussed have been implemented in the mpr package in R.
|
1901.03277v1
|
2019-02-01
|
A Penrose-Type Inequality with Angular Momentum and Charge for Axisymmetric Initial Data
|
A lower bound for the ADM mass is established in terms of angular momentum,
charge, and horizon area in the context of maximal, axisymmetric initial data
for the Einstein-Maxwell equations which satisfy the weak energy condition. If,
on the horizon, the given data agree to a certain extent with the associated
model Kerr-Newman data, then the inequality reduces to the conjectured Penrose
inequality with angular momentum and charge. In addition, a rigidity statement
is also proven whereby equality is achieved if and only if the data set arises
from the canonical slice of a Kerr-Newman spacetime.
|
1902.00501v3
|
2019-02-08
|
Field-tuned spin excitation spectrum of $kπ$-skyrmion
|
We study spin-wave excitation modes of $k\pi$ skyrmion in a magnetic nanodot
under an external magnetic field along $z$-direction using micromagnetic
simulations based on Landau-Lifshitz-Gilbert equation. We find that a
transition of $k\pi$ skyrmion to other skyrmion-like structures appears under
some critical external field, the corresponding spin-wave spectra are simulated
for each state in the process of applying magnetic field. For skyrmion, the
frequencies of excitation modes increases and then decreases with the low
frequency modes splitting at a critical magnetic field. In addition to the well
known two in-plane rotational modes and a out-of-plane breathing mode of
skyrmion, a higher number of excitation modes are found with increasing $k$
($k=2, 3$). The excitation modes vary as a function of magnetic field, and the
excitation frequencies for different modes exhibit a rapid or slight change
depending on the field induced change of magnetization profile. Our study
indicates the rich spin-wave excitations for $k\pi$ skyrmion and opens a
possibility in theoretical or experimental investigation of magnonics
application.
|
1902.02901v2
|
2019-02-08
|
Simulation of the Magnetization Dynamics of a Single Domain BiFeO$_3$ Thin Film
|
The switching dynamics of a single-domain BiFeO$_3$ thin films is
investigated through combining the dynamics of polarization and Neel vector.
The evolution of the ferroelectric polarization is described by the
Landau-Khalatnikov (LK) equation, and the Landau-Lifshitz-Gilbert (LLG)
equations for spins in two sublattices to model the time evolution of the
antiferromagnetic order (Neel vector) in a G-type antiferromagnet. This work
theoretically demonstrates that due to the rotation of the magnetic hard axis
following the polarization reversal, the Neel vector can be switched by 180
degrees, while the weak magnetization can remain unchanged. The simulation
results are consistent with the ab initio calculation, where the Neel vector
rotates during polarization rotation, and also match our calculation of the
dynamics of order parameter using Landau-Ginzburg theory. We also find that the
switching time of the Neel vector is determined by the speed polarization
switching and is predicted to be as short as 30 ps.
|
1902.03330v1
|
2019-02-13
|
Dynamics of ferromagnetic domain walls under extreme fields
|
We report the existence of a new regime for domain wall motion in uniaxial
and near-uniaxial ferromagnetic nanowires, characterised by applied magnetic
fields sufficiently strong that one of the domains becomes unstable. There
appears a new stable solution of the Landau-Lifshitz-Gilbert equation,
describing a nonplanar domain wall moving with constant velocity and precessing
with constant frequency. Even in the presence of thermal noise, the new
solution can propagate for distances on the order of 500 times the field-free
domain wall width before fluctuations in the unstable domain become
appreciable.
|
1902.04968v3
|
2019-02-28
|
Topological $d$-wave Superconductivity and Nodal Line-Arc Intersections in Weyl Semimetals
|
Superconducting Weyl semimetals present a novel and promising system to
harbor new forms of unconventional topological superconductivity. Within the
context of time-reversal symmetric Weyl semimetals with $d$-wave
superconductivity, we demonstrate that the number of Majorana cones equates to
the number of intersections between the $d$-wave nodal lines and the Fermi
arcs. We illustrate the importance of nodal line-arc intersections by
demonstrating the existence of locally stable surface Majorana cones that the
winding number does not predict. The discrepancy between Majorana cones and the
winding number necessitates an augmentation of the winding number formulation
to account for each intersection. In addition, we show that imposing additional
mirror symmetries globally protect the nodal line-arc intersections and the
corresponding Majorana cones.
|
1903.00024v2
|
2019-03-07
|
Stronger L2/L2 Compressed Sensing; Without Iterating
|
We consider the extensively studied problem of $\ell_2/\ell_2$ compressed
sensing. The main contribution of our work is an improvement over [Gilbert, Li,
Porat and Strauss, STOC 2010] with faster decoding time and significantly
smaller column sparsity, answering two open questions of the aforementioned
work.
Previous work on sublinear-time compressed sensing employed an iterative
procedure, recovering the heavy coordinates in phases. We completely depart
from that framework, and give the first sublinear-time $\ell_2/\ell_2$ scheme
which achieves the optimal number of measurements without iterating; this new
approach is the key step to our progress. Towards that, we satisfy the
$\ell_2/\ell_2$ guarantee by exploiting the heaviness of coordinates in a way
that was not exploited in previous work. Via our techniques we obtain improved
results for various sparse recovery tasks, and indicate possible further
applications to problems in the field, to which the aforementioned iterative
procedure creates significant obstructions.
|
1903.02742v1
|
2019-03-17
|
A Brief history of mangnetism
|
In this article an overview of the historical development of the key ideas in
the field of magnetism is presented. The presentation is semi-technical in
nature.Starting by noting down important contribution of Greeks, William
Gilbert, Coulomb, Poisson, Oersted, Ampere, Faraday, Maxwell, and Pierre Curie,
we review early 20th century investigations by Paul Langevin and Pierre Weiss.
The Langevin theory of paramagnetism and the Weiss theory of ferromagnetism
were partly successful and real understanding of magnetism came with the advent
of quantum mechanics. Van Vleck was the pioneer in applying quantum mechanics
to the problem of magnetism and we discuss his main contributions: (1) his
detailed quantum statistical mechanical study of magnetism of real gases; (2)
his pointing out the importance of the crystal fields or ligand fields in the
magnetic behavior of iron group salts (the ligand field theory); and (3) his
many contributions to the elucidation of exchange interactions in d electron
metals. Next, the pioneering contributions (but lesser known) of Dorfman are
discussed. Then, in chronological order, the key contributions of Pauli,
Heisenberg, and Landau are presented. Finally, we discuss a modern topic of
quantum spin liquids.
|
1903.07031v1
|
2019-03-19
|
Separability Properties of Nilpotent $\mathbb{Q}[x]$-Powered Groups
|
In this paper we study conjugacy and subgroup separability properties in the
class of nilpotent $\mathbb{Q}[x]$-powered groups. Many of the techniques used
to study these properties in the context of ordinary nilpotent groups carry
over naturally to this more general class. Among other results, we offer a
generalization of a theorem due to G. Baumslag. The generalized version states
that if $G$ is a finitely $\mathbb{Q}[x]$-generated
$\mathbb{Q}[x]$-torsion-free nilpotent $\mathbb{Q}[x]$-powered group and $H$ is
a $\mathbb{Q}[x]$-isolated subgroup of $G,$ then for any prime $\pi \in
\mathbb{Q}[x]$, $\bigcap_{i = 1}^{\infty} G^{{\pi}^{i}}H = H.$
|
1903.08220v1
|
2019-03-24
|
Synchronized, periodic, and chaotic dynamics in spin torque oscillator with two free layers
|
A phase diagram of the magnetization dynamics is studied by numerically
solving the Landau-Lifshitz-Gilbert (LLG) equation in a spin torque oscillator
consisting of asymmetric two free layers that are magnetized in in-plane
direction. We calculated the dynamics for a wide range of current density for
both low and high field cases, and found many dynamical phases such as
synchronization, auto-oscillation with different frequencies, and chaotic
dynamics. The observation of the synchronization indicates the presence of a
dynamical phase which has not been found experimentally by using the
conventional electrical detection method. The auto-oscillations with different
frequencies lead to an oscillation of magnetoresistance with a high frequency,
which can be measured experimentally. The chaotic and/or periodic behavior of
magnetoresistance in a high current region, on the other hand, leads to a
discontinuous change of the peak frequency in Fourier spectrum.
|
1903.09938v2
|
2019-04-07
|
Hybrid Approaches to Detect Comments Violating Macro Norms on Reddit
|
In this dataset paper, we present a three-stage process to collect Reddit
comments that are removed comments by moderators of several subreddits, for
violating subreddit rules and guidelines. Other than the fact that these
comments were flagged by moderators for violating community norms, we do not
have any other information regarding the nature of the violations. Through this
procedure, we collect over 2M comments removed by moderators of 100 different
Reddit communities, and publicly release the data. Working with this dataset of
removed comments, we identify 8 macro norms---norms that are widely enforced on
most parts of Reddit. We extract these macro norms by employing a hybrid
approach---classification, topic modeling, and open-coding---on comments
identified to be norm violations within at least 85 out of the 100 study
subreddits. Finally, we label over 40K Reddit comments removed by moderators
according to the specific type of macro norm being violated, and make this
dataset publicly available. By breaking down a collection of removed comments
into more granular types of macro norm violation, our dataset can be used to
train more nuanced machine learning classifiers for online moderation.
|
1904.03596v2
|
2019-04-11
|
Triangular array of iron-oxide nanoparticles: A simulation study of intra- and inter-particle magnetism
|
A study of spherical maghemite nanoparticles on a two dimensional triangular
array was carried out using a stochastic Landau-Lifshitz-Gilbert (sLLG)
approach. The simulation method was first validated with a triangular array of
simple dipoles, where results show the expected phase transition to a
ferromagnetic state at a finite temperature. The ground state exhibited a
continuous degeneracy that was lifted by an order-from-disorder mechanism at
infinitesimal temperatures with the appearance of a six-fold planar anisotropy.
The nanoparticle array consisted of 7.5 nm diameter maghemite spheres with
bulk-like superexchange interactions between Fe-ions in the core, and weaker
exchange between surface Fe-ions and a radial anisotropy. The triangular
nanoparticle array ordered at the same reduced temperature as the simple dipole
array, but exhibited different behaviour at low temperatures due to the surface
anisotropy. We find that the vacancies on the octahedral sites in the
nanoparticles combine with the surface anisotropy to produce an effective
random temperature-dependent anisotropy for each particle. This leads to a
reduction in the net magnetization of the nanoparticle array at zero
temperature compared to the simple dipole array.
|
1904.05515v1
|
2019-04-15
|
Mathematical analysis of weak and strong solutions to an evolutionary model for magnetoviscoelasticity
|
The paper is concerned with the analysis of an evolutionary model for
magnetoviscoelastic materials in two dimensions. The model consists of a
Navier-Stokes system featuring a dependence of the stress tensor on elastic and
magnetic terms, a regularized system for the evolution of the deformation
gradient and the Landau-Lifshitz-Gilbert system for the dynamics of the
magnetization.
First, we show that our model possesses global in time weak solutions, thus
extending work by Bene\v{s}ov\'a et al. 2018. Compared to that work, we include
the stray field energy and relax the assumptions on the elastic energy density.
Second, we prove the local in time existence of strong solutions. Both
existence results are based on the Galerkin method. Finally, we show a
weak-strong uniqueness property.
|
1904.07179v1
|
2019-04-25
|
Message Randomization and Strong Security in Quantum Stabilizer-Based Secret Sharing for Classical Secrets
|
We improve the flexibility in designing access structures of quantum
stabilizer-based secret sharing schemes for classical secrets, by introducing
message randomization in their encoding procedures. We generalize the
Gilbert-Varshamov bound for deterministic encoding to randomized encoding of
classical secrets. We also provide an explicit example of a ramp secret sharing
scheme with which multiple symbols in its classical secret are revealed to an
intermediate set, and justify the necessity of incorporating strong security
criterion of conventional secret sharing. Finally, we propose an explicit
construction of strongly secure ramp secret sharing scheme by quantum
stabilizers, which can support twice as large classical secrets as the
McEliece-Sarwate strongly secure ramp secret sharing scheme of the same share
size and the access structure.
|
1904.11114v3
|
2019-05-02
|
Benchmark Instances and Branch-and-Cut Algorithm for the Hashiwokakero Puzzle
|
Hashiwokakero, or simply Hashi, is a Japanese single-player puzzle played on
a rectangular grid with no standard size. Some cells of the grid contain a
circle, called island, with a number inside it ranging from one to eight. The
remaining positions of the grid are empty. The player must connect all of the
islands by drawing a series of horizontal or vertical bridges between them,
respecting a series of rules: the number of bridges incident to an island
equals the number indicated in the circle, at most two bridges are incident to
any side of an island, bridges cannot cross each other or pass through islands,
and each island must eventually be reachable from any other island. In this
paper, we present some complexity results and relationships between Hashi and
well-known graph theory problems. We give a formulation of the problem by means
of an integer linear mathematical programming model, and apply a branch-and-cut
algorithm to solve the model in which connectivity constraints are dynamically
generated. We also develop a puzzle generator. Our experiments on 1440 Hashi
puzzles show that the algorithm can consistently solve hard puzzles with up to
400 islands.
|
1905.00973v1
|
2019-05-06
|
An excess of non-Gaussian fluctuations in the cosmic infrared background consistent with gravitational lensing
|
The cosmic infrared background (CIB) is gravitationally lensed. A
quadratic-estimator technique that is inherited from lensing analyses of the
cosmic microwave background (CMB) can be applied to detect the CIB lensing
effects. However, the CIB fluctuations are intrinsically strongly non-Gaussian,
making CIB lensing reconstruction highly biased. We perform numerical
simulations to estimate the intrinsic non-Gaussianity and establish a
cross-correlation approach to precisely extract the CIB lensing signal from raw
data. We apply this technique to CIB data from the Planck satellite and
cross-correlate the resulting lensing estimate with the CIB data, galaxy number
counts and the CMB lensing potential. We detect an excess that is consistent
with a lensing contribution at $>4\sigma$.
|
1905.02084v1
|
2019-05-14
|
Multi-reference quantum chemistry protocol for simulating autoionization spectra: Test of ionization continuum models for the neon atom
|
In this contribution we present a protocol to evaluate partial and total
Auger decay rates combining the restricted active space self-consistent field
electronic structure method for the bound part of the spectrum and numerically
obtained continuum orbitals in the single-channel scattering theory framework.
On top of that, the two-step picture is employed to evaluate the partial rates.
The performance of the method is exemplified for the prototypical Auger decay
of the neon $1s^{-1}3p$ resonance. Different approximations to obtain the
continuum orbitals, the partial rate matrix elements, and the electronic
structure of the bound part are tested against theoretical and experimental
reference data. It is demonstrated that the partial and total rates are most
sensitive to the accuracy of the continuum orbitals. For instance, it is
necessary to account for the direct Coulomb potential of the ion for the
determination of the continuum wave functions. The Auger energies can be
reproduced quite well already with a rather small active space. Finally,
perspectives of the application of the proposed protocol to molecular systems
are discussed.
|
1905.05785v2
|
2019-06-16
|
A concise guide to existing and emerging vehicle routing problem variants
|
Vehicle routing problems have been the focus of extensive research over the
past sixty years, driven by their economic importance and their theoretical
interest. The diversity of applications has motivated the study of a myriad of
problem variants with different attributes. In this article, we provide a
concise overview of existing and emerging problem variants. Models are
typically refined along three lines: considering more relevant objectives and
performance metrics, integrating vehicle routing evaluations with other
tactical decisions, and capturing fine-grained yet essential aspects of modern
supply chains. We organize the main problem attributes within this structured
framework. We discuss recent research directions and pinpoint current
shortcomings, recent successes, and emerging challenges.
|
1906.06750v2
|
2019-07-01
|
Formation process of skyrmion lattice domain boundaries: The role of grain boundaries
|
We report on the formation process of skyrmion lattice (SkL) domain
boundaries in FeGe using Lorentz transmission electron microscopy and
small-angle electron diffraction. We observed that grain boundaries and edges
play an important role in the formation of SkL domain boundaries; The SkL
domain boundary is stabilized at the intersection of two grains. A
micromagnetic simulation using the Landau-Lifshitz-Gilbert equation revealed
that the SkL domains separated by a boundary represent the lowest energy
configuration. Conversely, in a wide area, SkL domain boundaries were not
formed and SkL domains with different orientations rotated to form a single SkL
domain.
|
1907.00774v1
|
2019-07-02
|
Quantum Data-Syndrome Codes
|
Performing active quantum error correction to protect fragile quantum states
highly depends on the correctness of error information--error syndromes. To
obtain reliable error syndromes using imperfect physical circuits, we propose
the idea of quantum data-syndrome (DS) codes that are capable of correcting
both data qubits and syndrome bits errors. We study fundamental properties of
quantum DS codes, including split weight enumerators, generalized MacWilliams
identities, and linear programming bounds. In particular, we derive Singleton
and Hamming-type upper bounds on degenerate quantum DS codes. Then we study
random DS codes and show that random DS codes with a relatively small
additional syndrome measurements achieve the Gilbert-Varshamov bound of
stabilizer codes. Constructions of quantum DS codes are also discussed. A
family of quantum DS codes is based on classical linear block codes, called
syndrome measurement codes, so that syndrome bits are encoded in additional
redundant stabilizer measurements. Another family of quantum DS codes is
CSS-type quantum DS codes based on classical cyclic codes, and this includes
the Steane code and the quantum Golay code.
|
1907.01393v1
|
2019-07-02
|
Prediction of topological Hall effect in a driven magnetic domain wall
|
We investigate the possible emergence of topological Hall effect (THE) in a
driven magnetic DW. Numerical simulation based on the
Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation shows that the emergent
magnetic flux appears when the DW is in a non-equilibrium state. The magnitude
of magnetic flux is modulated by Dzyaloshinskii-Moriya interaction (DMI) or
in-plane longitudinal magnetic field, providing an experimental test of the
predicted THE. These results indicate that the THE can be observed even in a
topologically trivial magnetic DW, and therefore open up new possibility to
electrically detect the dynamical spin structure.
|
1907.01648v2
|
2019-07-04
|
Resonant Acoustic Wave Assisted Spin-Transfer-Torque Switching of Nanomagnets
|
We report the possibility of achieving an order of magnitude reduction in the
energy dissipation needed to write bits in perpendicular magnetic tunnel
junctions (p-MTJs) by simulating the magnetization dynamics under a combination
of resonant surface acoustic waves (r-SAW) and spin-transfer-torque (STT). The
magnetization dynamics were simulated using the Landau-Lifshitz-Gilbert
equation under macrospin assumption with the inclusion of thermal noise. The
resonant magnetization dynamics in the magnetostrictive nanomagnet build over
few 10s of cycles of SAW application that drives the magnetization to precess
in a cone with a deflection of ~45 degrees from the perpendicular direction.
This reduces the STT current density required to switch the magnetization
direction without increasing the STT application time or degrading the
switching probability in the presence of room temperature thermal noise. This
could lead to a pathway to achieve energy efficient switching of spin transfer
torque random access memory (STTRAM) whose lateral dimensions can be scaled
aggressively despite using materials with low magnetostriction by employing
resonant excitation.
|
1907.02255v1
|
2019-07-04
|
Second-order semi-implicit projection methods for micromagnetics simulations
|
Micromagnetics simulations require accurate approximation of the
magnetization dynamics described by the Landau-Lifshitz-Gilbert equation, which
is nonlinear, nonlocal, and has a non-convex constraint, posing interesting
challenges in developing numerical methods. In this paper, we propose two
second-order semi-implicit projection methods based on the second-order
backward differentiation formula and the second-order interpolation formula
using the information at previous two temporal steps. Unconditional unique
solvability of both methods is proved, with their second-order accuracy
verified through numerical examples in both 1D and 3D. The efficiency of both
methods is compared to that of another two popular methods. In addition, we
test the robustness of both methods for the first benchmark problem with a
ferromagnetic thin film material from National Institute of Standards and
Technology.
|
1907.02358v1
|
2019-07-11
|
Astro2020 Activity, Project of State of the Profession Consideration (APC) White Paper: All-Sky Near Infrared Space Astrometry. State of the Profession Considerations: Development of Scanning NIR Detectors for Astronomy
|
Gaia is a revolutionary space mission developed by ESA and is delivering 5
parameter astrometry, photometry and radial velocities over the whole sky with
astrometric accuracies down to a few tens of micro-arcseconds. A weakness of
Gaia is that it only operates at optical wavelengths. However, much of the
Galactic centre and the spiral arm regions, important for certain studies, are
obscured by interstellar extinction and this makes it difficult for Gaia to
deeply probe. This problem can be overcome by switching to the Near Infra-Red
(NIR) but this is not possible with silicon CCDs. Additionally, to scan the
entire sky and make global absolute parallax measurements the spacecraft must
have a constant rotation and this requires the detectors operate in Time
Delayed Integration (TDI) mode or similar.
|
1907.05191v1
|
2019-07-21
|
Performance of a low-parasitic frequency-domain multiplexing readout
|
Frequency-domain multiplexing is a readout technique for transition edge
sensor bolometer arrays used on modern CMB experiments, including the SPT-3G
receiver. Here, we present design details and performance measurements for a
low-parasitic frequency-domain multiplexing readout. Reducing the parasitic
impedance of the connections between cryogenic components provides a path to
improving both the crosstalk and noise performance of the readout. Reduced
crosstalk will in turn allow higher multiplexing factors. We have demonstrated
a factor of two improvement in parasitic resistance compared to SPT-3G
hardware. Reduced parasitics also permits operation of lower-resistance
bolometers, which enables better optimization of R$_{\rm{bolo}}$ for improved
readout noise performance. The prototype system exhibits noise performance
comparable to SPT-3G readout hardware when operating SPT-3G detectors.
|
1907.09035v1
|
2019-08-09
|
MakeSense: An IoT Testbed for Social Research of Indoor Activities
|
There has been increasing interest in deploying IoT devices to study human
behaviour in locations such as homes and offices. Such devices can be deployed
in a laboratory or `in the wild' in natural environments. The latter allows one
to collect behavioural data that is not contaminated by the artificiality of a
laboratory experiment. Using IoT devices in ordinary environments also brings
the benefits of reduced cost, as compared with lab experiments, and less
disturbance to the participants' daily routines which in turn helps with
recruiting them into the research. However, in this case, it is essential to
have an IoT infrastructure that can be easily and swiftly installed and from
which real-time data can be securely and straightforwardly collected. In this
paper, we present MakeSense, an IoT testbed that enables real-world
experimentation for large scale social research on indoor activities through
real-time monitoring and/or situation-aware applications. The testbed features
quick setup, flexibility in deployment, the integration of a range of IoT
devices, resilience, and scalability. We also present two case studies to
demonstrate the use of the testbed, one in homes and one in offices.
|
1908.03380v1
|
2019-08-13
|
On Steane-Enlargement of Quantum Codes from Cartesian Product Point Sets
|
In this work, we study quantum error-correcting codes obtained by using
Steane-enlargement. We apply this technique to certain codes defined from
Cartesian products previously considered by Galindo et al. in [4]. We give
bounds on the dimension increase obtained via enlargement, and additionally
give an algorithm to compute the true increase. A number of examples of codes
are provided, and their parameters are compared to relevant codes in the
literature, which shows that the parameters of the enlarged codes are
advantageous. Furthermore, comparison with the Gilbert-Varshamov bound for
stabilizer quantum codes shows that several of the enlarged codes match or
exceed the parameters promised by the bound.
|
1908.04560v1
|
2019-08-17
|
Band-pass Magnetic Tunnel Junction based Magnetoresistive Random Access Memory
|
We propose spin transfer torque--magnetoresistive random access memory
(STT-MRAM) based on magneto-resistance and spin transfer torque physics of
band-pass spin filtering. Utilizing the electronic analogs of optical phenomena
such as anti-reflection coating and resonance for spintronic devices, we
present the design of an STT-MRAM device with improved features when compared
with a traditional trilayer device. The device consists of a superlattice
heterostructure terminated with the anti-reflective regions sandwiched between
the fixed and free ferromagnetic layers. Employing the Green's function spin
transport formalism coupled self-consistently with the stochastic
Landau-Lifshitz-Gilbert-Slonczewski equation, we present the design of an
STT-MRAM based on the band-pass filtering having an ultra-high TMR (3.5*10e4)
and large spin current. We demonstrate that the STT-MRAM design having
band-pass spin filtering are nearly 1100% more energy efficient than
traditional trilayer magnetic tunnel junction (MTJ) based STT-MRAM. We also
present detailed probabilistic switching and energy analysis for a trilayer MTJ
and band-pass filtering based STT-MRAM. Our predictions serve as a template to
consider the heterostructures for next-generation spintronic device
applications.
|
1908.06279v1
|
2019-09-09
|
Narrow autoresonant magnetization structures in finite length ferromagnetic nanoparticles
|
The autoresonant approach to excitation and control of large amplitude
uniformly precessing magnetization structures in finite length easy axis
ferromagnetic nanoparticles is suggested and analyzed within the
Landau-Lifshitz-Gilbert model. These structures are excited by using a
spatially uniform, oscillating, chirped frequency magnetic field, while the
localization is imposed via boundary conditions. The excitation requires the
amplitude of the driving oscillations to exceed a threshold. The dissipation
effect on the threshold is also discussed. The autoresonant driving effectively
compensates the effect of dissipation, but lowers the maximum amplitude of the
excited structures. Fully nonlinear localized autoresonant solutions are
illustrated in simulations and described via an analog of a quasi-particle in
an effective potential. The precession frequency of these solutions is
continuously locked to that of the drive, while the spatial magnetization
profile approaches the soliton limit when the length of the nanoparticle and
the amplitude of the excited solution increase.
|
1909.03671v1
|
2019-09-09
|
Reliability and Error Burst Length Analysis of Wireless Multi-Connectivity
|
Multi-connectivity offers diversity in terms of multiple interfaces through
which the data can be sent, thereby improving simultaneously the overall
reliability and latency. This makes interface diversity a natural candidate for
supporting Ultra-Reliable Low Latency Communications (URLLC). This work
investigates how the packet error statistics from different interfaces impacts
the overall reliability-latency characteristics. We use the simple
Gilbert-Elliott model for burst errors and estimate its parameters based on
experimental measurement traces from LTE and {Wi-Fi} packet transmissions
collected over several days. The results show that using interface diversity
configurations that include at least one {Wi-Fi} interface leads to, somewhat
surprisingly, since Wi-Fi is generally less reliable than LTE, superior results
in terms of packet success and error burst duration. Another interesting
finding is that {Wi-Fi}-based interface diversity configurations outperform
even ultra-reliable single links.
|
1909.03875v1
|
2019-09-13
|
Hidden spin-orbital order in the Kitaev hyperhoneycomb $β$-Li$_2$IrO$_3$
|
We report the existence of a phase transition at high temperature in the 3D
Kitaev candidate material, $\beta$-Li$_2$IrO$_3$. We show that the transition
is bulk, intrinsic and orders a tiny magnetic moment with a spatially
anisotropic saturation moment. We show that even though this transition is
global, it does not freeze the local Ir moments, which order at much lower
temperatures into an incommensurate state. Rather, the ordered moment has an
orbital origin that is coupled to spin correlations, likely of a Kitaev origin.
The separate ordering of spin-correlated orbital moments and of local Ir
moments reveals a novel way in which magnetic frustration in Kitaev systems can
lead to coexisting magnetic states.
|
1909.06355v1
|
2019-10-08
|
Gravitational Lensing of the Cosmic Neutrino Background
|
We study gravitational lensing of the cosmic neutrino background. This signal
is undetectable for the foreseeable future, but there is a rich trove of
information available. At least some of the neutrinos from the early universe
will be non-relativistic today, with a closer surface of last scattering
(compared to the cosmic microwave background) and with larger angles of
deflection. Lensing of massive neutrinos is strongly chromatic: both the
amplitude of lensing and the cosmic time at which the potential is traversed
depend on neutrino momentum, in principle giving access to our entire causal
volume, not restricted to the light cone. As a concrete example, we focus on
the case where the cosmic neutrino background would be strongly lensed when
passing through halos of galaxy clusters and galaxies. We calculate the
Einstein radius for cosmic neutrinos and investigate the impact of neutrino
mass.
|
1910.03550v3
|
2019-10-17
|
A multi-scale approach for magnetisation dynamics: Unraveling exotic magnetic states of matter
|
Crystallographic lattice defects strongly influence dynamical properties of
magnetic materials at both microscopic and macroscopic length scales. A
multi-scale approach to magnetisation dynamics, which is presented in this
paper, accurately captures such effects. The method is illustrated using
examples of systems with localized, non-trivial topological properties, e.g. in
the form of skyrmions and chiral domain walls that interact with lattice
dislocations. Technical aspects of the methodology involve multi-scale
magnetisation dynamics that connects atomistic and continuum descriptions. The
technique is capable of solving the Landau-Lifshitz-Gilbert equations
efficiently in two regions of a magnetic material --- the mesoscopic and the
atomistic regions, which are coupled in a seamless way. It is demonstrated that
this methodology allows simulating realistically-sized magnetic skyrmions
interacting with material defects and novel physical effects, uncovered using
this theoretical methodology, are described.
|
1910.07807v1
|
2019-10-21
|
Generation of exchange magnons in thin ferromagnetic films by ultrashort acoustic pulses
|
We investigate generation of exchange magnons by ultrashort, picosecond
acoustic pulses propagating through ferromagnetic thin films. Using the
Landau-Lifshitz-Gilbert equations we derive the dispersion relation for
exchange magnons for an external magnetic field tilted with respect to the film
normal. Decomposing the solution in a series of standing spin wave modes, we
derive a system of ordinary differential equations and driven harmonic
oscillator equations describing the dynamics of individual magnon mode. The
external magnetoelastic driving force is given by the time-dependent spatial
Fourier components of acoustic strain pulses inside the layer. Dependencies of
the magnon excitation efficiencies on the duration of the acoustic pulses and
the external magnetic field highlight the role of acoustic bandwidth and
phonon-magnon phase matching. Our simulations for ferromagnetic nickel evidence
the possibility of ultrafast magneto-acoustic excitation of exchange magnons
within the bandwidth of acoustic pulses in thin samples under conditions
readily obtained in femtosecond pump-probe experiments.
|
1910.09481v1
|
2019-11-05
|
Numerical methods for antiferromagnetics
|
Compared with ferromagnetic counterparts, antiferromagnetic materials are
considered as the future of spintronic applications since these materials are
robust against the magnetic perturbation, produce no stray field, and display
ultrafast dynamics. There are (at least) two sets of magnetic moments in
antiferromagnets (with magnetization of the same magnitude but antiparallel
directions) and ferrimagnets (with magnetization of the different magnitude).
The coupled dynamics for the bipartite collinear antiferromagnets is modeled by
a coupled system of Landau-Lifshitz-Gilbert equations with an additional term
originated from the antiferromagnetic exchange, which leads to femtosecond
magnetization dynamics. In this paper, we develop three Gauss-Seidel projection
methods for micromagnetics simulation in antiferromagnets and ferrimagnets.
They are first-order accurate in time and second-order in space, and only solve
linear systems of equations with constant coefficients at each step.
Femtosecond dynamics, N\'{e}el wall structure, and phase transition in presence
of an external magnetic field for antiferromagnets are provided with the
femtosecond stepsize.
|
1911.01717v1
|
2019-11-08
|
A filamentary cascade model of the inertial range
|
This paper develops a simple model of the inertial range of turbulent flow,
based on a cascade of vortical filaments. A binary branching structure is
proposed, involving the splitting of filaments at each step into pairs of
daughter filaments with differing properties, in effect two distinct
simultaneous cascades. Neither of these cascades has the Richardson-Kolmogorov
exponent of 1/3. This bimodal structure is also different from bifractal models
as vorticity volume is conserved. If cascades are assumed to be initiated
continuously and throughout space we obtain a model of the inertial range of
stationary turbulence. We impose the constraint associated with Kolmogorov's
four-fifths law and then adjust the splitting to achieve good agreement with
the observed structure exponents $\zeta_p$. The presence of two elements to the
cascade is responsible for the nonlinear dependence of $\zeta_p$ upon $p$.
A single cascade provides a model for the initial-value problem of the
Navier--Stokes equations in the limit of vanishing viscosity. To simulate this
limit we let the cascade continue indefinitely, energy removal occurring in the
limit. We are thus able to compute the decay of energy in the model.
|
1911.03537v2
|
2019-11-14
|
Beyond Pairwise Comparisons in Social Choice: A Setwise Kemeny Aggregation Problem
|
In this paper, we advocate the use of setwise contests for aggregating a set
of input rankings into an output ranking. We propose a generalization of the
Kemeny rule where one minimizes the number of k-wise disagreements instead of
pairwise disagreements (one counts 1 disagreement each time the top choice in a
subset of alternatives of cardinality at most k differs between an input
ranking and the output ranking). After an algorithmic study of this k-wise
Kemeny aggregation problem, we introduce a k-wise counterpart of the majority
graph. This graph reveals useful to divide the aggregation problem into several
sub-problems, which enables to speed up the exact computation of a consensus
ranking. By introducing a k-wise counterpart of the Spearman distance, we also
provide a 2-approximation algorithm for the k-wise Kemeny aggregation problem.
We conclude with numerical tests.
|
1911.06226v2
|
2019-11-15
|
A geometric look at momentum flux and stress in fluid mechanics
|
We develop a geometric formulation of fluid dynamics, valid on arbitrary
Riemannian manifolds, that regards the momentum-flux and stress tensors as
1-form valued 2-forms, and their divergence as a covariant exterior derivative.
We review the necessary tools of differential geometry and obtain the
corresponding coordinate-free form of the equations of motion for a variety of
inviscid fluid models -- compressible and incompressible Euler equations,
Lagrangian-averaged Euler-$\alpha$ equations, magnetohydrodynamics and
shallow-water models -- using a variational derivation which automatically
yields a symmetric momentum flux. We also consider dissipative effects and
discuss the geometric form of the Navier--Stokes equations for viscous fluids
and of the Oldroyd-B model for visco-elastic fluids.
|
1911.06613v2
|
2019-11-18
|
Theoretical condition for switching the magnetization in a perpendicularly magnetized ferromagnet via the spin Hall effect
|
A theoretical formula is derived for the threshold current to switch a
perpendicular magnetization in a ferromagnet by the spin Hall effect. The
numerical simulation of the Landau-Lifshitz-Gilbert equation indicates that
magnetization switching is achieved when the steady-state solution of the
magnetization in the presence of the current is outside an energetically
unstable region. Based on the numerical result, an analytical theory deriving
the threshold current is developed by focusing on the first-order perturbation
to the unstable state. The analytical formula clarifies that the magnitude of
the magnetic field applied to the current direction should be larger than 15\%
of the perpendicular magnetic anisotropy field, and the current is less than
the derived threshold value.
|
1911.07961v1
|
2019-12-11
|
Constructions of quasi-twisted quantum codes
|
In this work, our main objective is to construct quantum codes from
quasi-twisted (QT) codes. At first, a necessary and sufficient condition for
Hermitian self-orthogonality of QT codes is introduced by virtue of the Chinese
Remainder Theorem (CRT). Then we utilize these self-orthogonal QT codes to
provide quantum codes via the famous Hermitian Construction. Moreover, we
present a new construction method of q-ary quantum codes, which can be viewed
as an effective generalization of the Hermitian Construction. General QT codes
that are not self-orthogonal are also employed to construct quantum codes. As
the computational results, some binary, ternary and quaternary quantum codes
are constructed and their parameters are determined, which all exceed the
Quantum Gilbert-Varshamov (GV) Bound. In the binary case, a small number of
quantum codes are derived with strictly improved parameters compared with the
current records. In the ternary and quaternary cases, our codes fill some gaps
or have better performances than the current results.
|
1912.05142v2
|
2019-12-12
|
The strange metal Hall effect connects quantum criticality and superconductivity in an iron-based superconductor
|
Many unconventional superconductors exhibit a common set of anomalous charge
transport properties that characterize them as `strange metals', which provides
hope that there is single theory that describes them. However,
model-independent connections between the strange metal and superconductivity
have remained elusive. In this letter, we show that the Hall effect of the
unconventional superconductor BaFe$_2$(As$_{1-x}$P$_x$)$_2$ contains an
anomalous contribution arising from the correlations within the strange metal.
This term has a distinctive dependence on magnetic field, which allows us to
track its behavior across the doping-temperature phase diagram, even under the
superconducting dome. These measurements demonstrate that the strange metal
Hall component emanates from a quantum critical point and, in the zero
temperature limit, decays in proportion to the superconducting critical
temperature. This creates a clear and novel connection between quantum
criticality and superconductivity, and suggests that similar connections exist
in other strange metal superconductors.
|
1912.06130v1
|
2019-12-17
|
SINR percolation for Cox point processes with random powers
|
Signal-to-interference plus noise ratio (SINR) percolation is an
infinite-range dependent variant of continuum percolation modeling connections
in a telecommunication network. Unlike in earlier works, in the present paper
the transmitted signal powers of the devices of the network are assumed random,
i.i.d. and possibly unbounded. Additionally, we assume that the devices form a
stationary Cox point process, i.e., a Poisson point process with stationary
random intensity measure, in two or higher dimensions. We present the following
main results. First, under suitable moment conditions on the signal powers and
the intensity measure, there is percolation in the SINR graph given that the
device density is high and interferences are sufficiently reduced, but not
vanishing. Second, if the interference cancellation factor $\gamma$ and the
SINR threshold $\tau$ satisfy $\gamma \geq 1/(2\tau)$, then there is no
percolation for any intensity parameter. Third, in the case of a Poisson point
process with constant powers, for any intensity parameter that is supercritical
for the underlying Gilbert graph, the SINR graph also percolates with some
small but positive interference cancellation factor.
|
1912.07895v2
|
2019-12-18
|
Magnetic hysteresis behavior of granular manganite La$_{0.67}$Ca$_{0.33}$MnO$_3$ nanotubes
|
A silicon micromechanical torsional oscillator is used to measure the
hysteresis loops of two manganite La_0.67Ca_0.33MnO_3 nanotubes at different
temperatures, applying an external field along its main axes. These structures
are composed of nanograins with a ferromagnetic core surrounded by a dead
layer. Micromagnetic calculations based on the stochastic
Landau-Lifshitz-Gilbert equation, are performed to validate a simple model that
allows for quantitatively describing the ferromagnetic behavior of the system.
Further simulations are used to analyze the experimental data more in depth and
to calculate the coercive field, the saturation and remanent magnetizations,
and the effective magnetic volume for single nanotubes, over a wide temperature
range.
|
1912.08844v2
|
2019-12-30
|
Distribution of the minimal distance of random linear codes
|
In this paper, we study the distribution of the minimal distance (in the
Hamming metric) of a random linear code of dimension $k$ in $\mathbb{F}_q^n$.
We provide quantitative estimates showing that the distribution function of the
minimal distance is close ({\it{}superpolynomially} in $n$)to the cumulative
distribution function of the minimum of $(q^k-1)/(q-1)$ independent binomial
random variables with parameters $\frac{1}{q}$ and $n$. The latter, in turn,
converges to a Gumbel distribution at integer points when $\frac{k}{n}$
converges to a fixed number in $(0,1)$. Our result confirms in a strong sense
that apart from identification of the weights of proportional codewords, the
probabilistic dependencies introduced by the linear structure of the random
code, produce a negligible effect on the minimal code weight. As a corollary of
the main result, we obtain an improvement of the Gilbert--Varshamov bound for
$2<q<49$.
|
1912.12833v2
|
2020-01-12
|
Magnetic Skyrmions in FePt Square-Based Nanoparticles Around Room-Temperature
|
Magnetic skyrmions formed at temperatures around room temperature in
square-based parallelepiped magnetic FePt nanoparticles with perpendicular
magnetocrystalline anisotropy (MCA) were studied during the magnetization
reversal using micromagnetic simulations. Finite Differences (FD) method were
used for the solution of the Landau-Lifshitz-Gilbert equation. Magnetic
configurations exhibiting N\'eel skyrmionic formations were detected. The
magnetic skyrmions can be created in different systems generated by the
variation of external field, side length and width of the squared-based
parallelepiped magnetic nanoparticles. Micromagnetic configurations revealed a
variety of states which include skyrmionic textures with one distinct skyrmion
formed and being stable for a range of external fields around room-temperature.
The size of the formed N\'eel skyrmion is calculated as a function of the
external field, temperature, MCA and nanoparticle's geometrical characteristic
lengths which can be adjusted to produce N\'eel type skyrmions on demand having
diameters down to 12 nm. The micromagnetic simulations revealed that stable
skyrmions at the temperature range 270 - 330 K can be created for FePt magnetic
nanoparticle systems lacking of chiral interactions such as
Dzyaloshinskii-Moriya.
|
2001.03902v3
|
2020-01-20
|
Investigation of Patient-sharing Networks Using a Bayesian Network Model Selection Approach for Congruence Class Models
|
A Bayesian approach to conduct network model selection is presented for a
general class of network models referred to as the congruence class models
(CCMs). CCMs form a broad class that includes as special cases several common
network models, such as the Erd\H{o}s-R\'{e}nyi-Gilbert model, stochastic block
model and many exponential random graph models. Due to the range of models able
to be specified as a CCM, investigators are better able to select a model
consistent with generative mechanisms associated with the observed network
compared to current approaches. In addition, the approach allows for
incorporation of prior information. We utilize the proposed Bayesian network
model selection approach for CCMs to investigate several mechanisms that may be
responsible for the structure of patient-sharing networks, which are associated
with the cost and quality of medical care. We found evidence in support of
heterogeneity in sociality but not selective mixing by provider type nor
degree.
|
2001.06974v1
|
2020-02-11
|
Fidimag -- a finite difference atomistic and micromagnetic simulation package
|
Fidimag is an open-source scientific code for the study of magnetic materials
at the nano- or micro-scale using either atomistic or finite difference
micromagnetic simulations, which are based on solving the
Landau-Lifshitz-Gilbert equation. In addition, it implements simple procedures
for calculating energy barriers in the magnetisation through variants of the
nudged elastic band method. This computer software has been developed with the
aim of creating a simple code structure that can be readily installed, tested,
and extended. An agile development approach was adopted, with a strong emphasis
on automated builds and tests, and reproducibility of results. The main code
and interface to specify simulations are written in Python, which allows simple
and readable simulation and analysis configuration scripts. Computationally
costly calculations are written in C and exposed to the Python interface as
Cython extensions. Docker containers are shipped for a convenient setup
experience. The code is freely available on GitHub and includes documentation
and examples in the form of Jupyter notebooks.
|
2002.04318v1
|
2020-01-13
|
Malware propagation in urban D2D networks
|
We introduce and analyze models for the propagation of malware in pure D2D
networks given via stationary Cox-Gilbert graphs. Here, the devices form a
Poisson point process with random intensity measure $\lambda\Lambda$, where
$\Lambda$ is stationary and given, for example, by the edge-length measure of a
realization of a Poisson-Voronoi tessellation that represents an urban street
system. We assume that, at initial time, a typical device at the center of the
network carries a malware and starts to infect neighboring devices after random
waiting times. Here we focus on Markovian models, where the waiting times are
exponential random variables, and non-Markovian models, where the waiting times
feature strictly positive minimal and finite maximal waiting times. We present
numerical results for the speed of propagation depending on the system
parameters. In a second step, we introduce and analyze a counter measure for
the malware propagation given by special devices called white knights, which
have the ability, once attacked, to eliminate the malware from infected devices
and turn them into white knights. Based on simulations, we isolate parameter
regimes in which the malware survives or is eliminated, both in the Markovian
and non-Markovian setting.
|
2002.06248v1
|
2020-02-17
|
How fast can you update your MST? (Dynamic algorithms for cluster computing)
|
Imagine a large graph that is being processed by a cluster of computers,
e.g., described by the $k$-machine model or the Massively Parallel Computation
Model. The graph, however, is not static; instead it is receiving a constant
stream of updates. How fast can the cluster process the stream of updates? The
fundamental question we want to ask in this paper is whether we can update the
graph fast enough to keep up with the stream. We focus specifically on the
problem of maintaining a minimum spanning tree (MST), and we give an algorithm
for the $k$-machine model that can process $O(k)$ graph updates per $O(1)$
rounds with high probability. (And these results carry over to the Massively
Parallel Computation (MPC) model.) We also show a lower bound, i.e., it is
impossible to process $k^{1+\epsilon}$ updates in $O(1)$ rounds. Thus we
provide a nearly tight answer to the question of how fast a cluster can respond
to a stream of graph modifications while maintaining an MST.
|
2002.06762v1
|
2020-02-22
|
Bose-Einstein Condensation of Nonequilibrium Magnons in Confined Systems
|
We study the formation of a room temperature magnon Bose-Einstein condensate
(BEC) in nanoscopic systems and demonstrate that its lifetime is influenced by
the spatial confinement. We predict how dipolar interactions and nonlinear
magnon scattering assist in the generation of a metastable magnon BEC in
energy-quantized nanoscopic devices. We verify our prediction by a full
numerical simulation of the Landau-Lifshitz-Gilbert equation and demonstrate
the generation of magnon BEC in confined insulating magnets of yttrium iron
garnet. We directly map out the nonlinear magnon scattering processes behind
this phase transition to show how fast quantized thermalization channels allow
the BEC formation in confined structures. Based on our results, we discuss a
new mechanism to manipulate the BEC lifetime in nanoscaled systems. Our study
greatly extends the freedom to study the dynamics of magnon BEC in realistic
systems and to design integrated circuits for BEC-based applications at room
temperature.
|
2002.09777v2
|
2020-02-25
|
Bias-field-free spin Hall nano-oscillators with an out-of-plane precession mode
|
Spin Hall nano-oscillators (SHNOs) are promising candidates for new microwave
oscillators with high durability due to a small driving current. However,
conventional SHNOs with an in-plane precession (IPP) mode require a bias field
for stable oscillations which is not favored in certain applications such as
neuromorphic computing. Here, we propose and theoretically analyze a
bias-field-free SHNO with an in-plane hard axis and an out-of-plane precession
(OPP) mode by solving the Landau-Lifshitz-Gilbert (LLG) equation analytically
and numerically. We derive formulas for driving currents and precession
frequency, and show that they are in good agreement with numerical simulation
results. We show that our proposed SHNOs can be driven by much smaller bias
current than conventional spin torque nano-oscillators.
|
2002.10753v1
|
2020-03-06
|
Spin-accumulation induced magnetic texture in a metal-insulator bilayer
|
We consider the influence of a spin accumulation in a normal metal on the
magnetic statics and dynamics in an adjacent magnetic insulator. In particular,
we focus on arbitary angles between the spin accumulation and the easy-axis of
the magnetic insulator. Based on Landau-Lifshitz-Gilbert phenomenology
supplemented with magnetoelectronic circuit theory, we find that the magnetic
texture twists into a stable configuration that turns out to be described by a
virtual, or image, domain wall configuration, i.e., a domain wall outside the
ferromagnet. We show that even when the spin accumulation is perpendicular to
the anisotropy axis, the magnetic texture develops a component parallel to the
spin accumulation for sufficiently large spin bias. The emergence of this
parallel component gives rise to threshold behavior in the spin Hall
magnetoresistance and nonlocal magnon transport. This threshold can be used to
design novel spintronic and magnonic devices that can be operated without
external magnetic fields.
|
2003.03226v1
|
2020-04-05
|
Domain wall diode based on functionally graded Dzyaloshinskii-Moriya interaction
|
We present a general approach for studying the dynamics of domain walls in
biaxial ferromagnetic stripes with functionally graded Dzyaloshinskii-Moriya
interaction (DMI). By engineering the spatial profile of the DMI parameter we
propose the concept of a diode, which implements filtering of domain walls of
certain topological charge and helicity. We base our study on phenomenological
Landau-Lifshitz-Gilbert equations with additional Zhang-Li spin-transfer terms
using a collective variable approach. In the effective equations of motion the
gradients of DMI play the role of a driving force which competes with current
driving. All analytical predictions are confirmed by numerical simulations.
|
2004.02175v1
|
2020-05-03
|
Philosophy-Guided Mathematical Formalism for Complex Systems Modelling
|
We recently presented the so-called allagmatic method, which includes a
system metamodel providing a framework for describing, modelling, simulating,
and interpreting complex systems. Its development and programming was guided by
philosophy, especially by Gilbert Simondon's philosophy of individuation,
Alfred North Whitehead's philosophy of organism, and concepts from cybernetics.
Here, a mathematical formalism is presented to better describe and define the
system metamodel of the allagmatic method, thereby further generalising it and
extending its reach to a more formal treatment and allowing more theoretical
studies. By using the formalism, an example for such a further study is
provided with mathematical definitions and proofs for model creation and
equivalence of cellular automata and artificial neural networks.
|
2005.01192v5
|
2020-05-07
|
A closer look at the non-Hopfianness of $BS(2,3)$
|
The Baumslag-Solitar group $BS(2,3)$, is a so-called non-Hopfian group,
meaning that it has an epimorphism $\phi$ onto itself, that is not injective.
In particular this is equivalent to saying that $BS(2,3)$ has a non-trivial
quotient that is isomorphic to itself. As a consequence the Cayley graph of
$BS(2,3)$ has a quotient that is isomorphic to itself up to change of
generators. We describe this quotient on the graph-level and take a closer look
at the most common epimorphism $\phi$. We show its kernel is a free group of
infinite rank with an explicit set of generators. Finally we show how $\phi$
appears as a morphism on fundamental groups induced by some continuous map.
This point of view was communicated to the author by Gilbert Levitt.
|
2005.03396v2
|
2020-05-08
|
Project and Forget: Solving Large-Scale Metric Constrained Problems
|
Given a set of dissimilarity measurements amongst data points, determining
what metric representation is most "consistent" with the input measurements or
the metric that best captures the relevant geometric features of the data is a
key step in many machine learning algorithms. Existing methods are restricted
to specific kinds of metrics or small problem sizes because of the large number
of metric constraints in such problems. In this paper, we provide an active set
algorithm, Project and Forget, that uses Bregman projections, to solve metric
constrained problems with many (possibly exponentially) inequality constraints.
We provide a theoretical analysis of \textsc{Project and Forget} and prove that
our algorithm converges to the global optimal solution and that the $L_2$
distance of the current iterate to the optimal solution decays asymptotically
at an exponential rate. We demonstrate that using our method we can solve large
problem instances of three types of metric constrained problems: general weight
correlation clustering, metric nearness, and metric learning; in each case,
out-performing the state of the art methods with respect to CPU times and
problem sizes.
|
2005.03853v2
|
2020-05-27
|
The Kirillov model in families
|
Let $F$ be a non-archimedean local field, let $k$ be an algebraically closed
field of characteristic $\ell$ different from the residual characteristic of
$F$, and let $A$ be a commutative Noetherian $W(k)$-algebra, where $W(k)$
denotes the Witt vectors. Using the Rankin-Selberg functional equations and
extending recent results of the second author, we show that if $V$ is an
$A[\text{GL}_n(F)]$-module of Whittaker type, then the mirabolic restriction
map on its Whittaker space is injective. This gives a new quick proof of the
existence of Kirillov models for representations of Whittaker type, including
complex representations, which generalizes to the $\ell$-modular and families
setting, in contrast with the previous proofs. In the special case where
$A=k=\overline{\mathbb{F}_{\ell}}$ and $V$ is irreducible generic, our result
in particular answers a question of Vign\'eras from 1989.
|
2005.13484v3
|
2020-05-29
|
An Explicit Formula for the Zero-Error Feedback Capacity of a Class of Finite-State Additive Noise Channels
|
It is known that for a discrete channel with correlated additive noise, the
ordinary capacity with or without feedback both equal $ \log q-\mathcal{H} (Z)
$, where $ \mathcal{H}(Z) $ is the entropy rate of the noise process $ Z $ and
$ q $ is the alphabet size. In this paper, a class of finite-state additive
noise channels is introduced. It is shown that the zero-error feedback capacity
of such channels is either zero or $C_{0f} =\log q -h (Z) $, where $ h (Z) $ is
the {\em topological entropy} of the noise process. A topological condition is
given when the zero-error capacity is zero, with or without feedback. Moreover,
the zero-error capacity without feedback is lower-bounded by $ \log q-2 h (Z)
$. We explicitly compute the zero-error feedback capacity for several examples,
including channels with isolated errors and a Gilbert-Elliot channel.
|
2006.00892v1
|
2020-06-01
|
BBN constraints on dark radiation isocurvature
|
The existence of dark radiation that is completely decoupled from the
standard model in the early Universe leaves open the possibility of an
associated dark radiation isocurvature mode. We show that the presence of dark
radiation isocurvature leads to spatial variation in the primordial abundances
of helium and deuterium due to spatial variation in $N_{\rm eff}$ during Big
Bang nucleosynthesis. We use the result to constrain the existence of such an
isocurvature mode on scales down to $\sim 1$ Mpc scales. By measuring the
excess variance in the primordial helium to hydrogen and deuterium to hydrogen
ratio in different galaxies, we constrain the variance in average isocurvature
in a galaxy to be less than $0.13/\Delta \bar{N}_{\rm eff}$ at 95\% confidence.
Here $\Delta \bar{N}_{\rm eff}$ is the spatially averaged increase in $N_{\rm
eff}$ due to the additional dark radiation component.
|
2006.01165v2
|
2020-06-12
|
Enhanced Stability of Antiferromagnetic Skyrmion during Its Motion by Anisotropic Dzyaloshinskii Moriya Interaction
|
Searching for new methods to enhance the stability of antiferromagnetic (AFM)
skyrmion during its motion is an important issue for AFM spintronic devices.
Herein, the spin polarized current-induced dynamics of a distorted AFM skyrmion
is numerically studied, based on the Landau Lifshitz Gilbert simulations of the
model with an anisotropic Dzyaloshinskii Moriya (DM) interaction. It is
demonstrated that the DM interaction anisotropy induces the skyrmion
deformation, which suppresses the distortion during the motion and enhances the
stability of the skyrmion. Moreover, the effect of the DM interaction
anisotropy on the skyrmion velocity is investigated in detail, and the
simulated results are further explained by Thiele theory. This work unveils a
promising strategy to enhance the stability and the maximum velocity of AFM
skyrmion, benefiting future spintronic applications.
|
2006.06938v1
|
2020-07-02
|
Spectral Methods for Ranking with Scarce Data
|
Given a number of pairwise preferences of items, a common task is to rank all
the items. Examples include pairwise movie ratings, New Yorker cartoon caption
contests, and many other consumer preferences tasks. What these settings have
in common is two-fold: a scarcity of data (it may be costly to get comparisons
for all the pairs of items) and additional feature information about the items
(e.g., movie genre, director, and cast). In this paper we modify a popular and
well studied method, RankCentrality for rank aggregation to account for few
comparisons and that incorporates additional feature information. This method
returns meaningful rankings even under scarce comparisons. Using diffusion
based methods, we incorporate feature information that outperforms
state-of-the-art methods in practice. We also provide improved sample
complexity for RankCentrality in a variety of sampling schemes.
|
2007.01346v1
|
2020-07-23
|
High Precision Real Time Collision Detection
|
Collision detection and collision avoidance are essential components in these
systems for safe human-robot interactions. Robotics systems that can work
"out-of-the-box" without excessive amount of installation and calibration from
the experts is highly ideal. For this, we propose a generic, high precision,
collision detect system that only requires the unified robot description format
(URDF) and is capable of running in real time. We extended the
Gilbert-Johnson-Keerthi (GJK) algorithm by utilizing a geometrical approach to
determine the distance between each rigid body in the environment and check for
collisions. The proposed system's performance is shown by checking the
self-collision of the KUKA LBR iiwa 7 R800 and the Mecademic Meca500. The
performance is compared to the Flexible Collision Library (FCL).
|
2007.12045v2
|
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