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2015-03-16
|
Impact of Current on Static and Kinetic Depinning Fields of Domain Wall in Ferromagnetic Nanostrip
|
The impact of current on static and kinetic depinning fields of a domain wall
in an one dimensional ferromagnetic nanostrip is investigated by solving the
Landau-Lifshitz-Gilbert equation with adiabatic and non-adiabatic spin-transfer
torques analytically and numerically. The results show that in the absence of
current, the static depinning field is greater than the kinetic depinning field
and both the depinning fields decrease by the increase of current applied in a
direction opposite to the direction of the applied field. Both the depinning
fields can also be tuned by the current to make them equal.
|
1503.04553v1
|
2015-04-17
|
Critical analysis and remedy of switching failures in straintronic logic using Bennett clocking in the presence of thermal fluctuations
|
Straintronic logic is a promising platform for beyond Moore's law computing.
Using Bennett clocking mechanism, information can propagate through an array of
strain-mediated multiferroic nanomagnets exploiting the dipolar coupling
between the magnets without having to physically interconnect them. Here we
perform a critical analysis of switching failures, i.e., error in information
propagation due to thermal fluctuations through a chain of such straintronic
devices. We solved stochastic Landau-Lifshitz-Gilbert equation considering
room-temperature thermal perturbations and show that magnetization switching
may fail due to inherent magnetization dynamics accompanied by thermally
broadened switching delay distribution. Avenues available to circumvent such
issue are proposed.
|
1504.04618v1
|
2015-06-18
|
Landauer limit of energy dissipation in a magnetostrictive particle
|
According to Landauer's principle, a minimum amount of energy proportional to
temperature must be dissipated during the erasure of a classical bit of
information compensating the entropy loss, thereby linking the information and
thermodynamics. Here we show that the Landauer limit of energy dissipation is
achievable in a shape-anisotropic single-domain magnetostrictive nanomagnet
having two mutually anti-parallel degenerate magnetization states that store a
bit of information. We model the magnetization dynamics using stochastic
Landau-Lifshitz-Gilbert equation in the presence of thermal fluctuations and
show that on average the Landauer bound is satisfied, i.e., it accords to the
generalized Landauer's principle for small systems with stochastic
fluctuations.
|
1506.07897v1
|
2015-06-29
|
Pseudo-Spin Based Dynamical Model for Polarisation Switching in Ferroelectrics
|
A microscopic view of the response of the electric dipoles to a dynamic
external field in a ferroelectric (FE) chain has been studied by two spin
dynamics methods. One is the prominent micromagnetic approach, and the other is
the micromagnetic approach with a variable size of the pseudo-spin. The energy
stored in the ferroelectric chain is described by the transverse Ising model
(TIM) with electric pseudo-spins. The simulations are based on a modified
Landau-Lifshitz-Gilbert (LLG) equation which is precession free. The results
obtained are shown and compared with the result supplemented by
Landau-Devonshire (L-D) theory in the Appendix.
|
1506.08500v2
|
2015-07-13
|
Explicit Construction of AG Codes from Generalized Hermitian Curves
|
We present multi-point algebraic geometric codes overstepping the
Gilbert-Varshamov bound. The construction is based on the generalized Hermitian
curve introduced by A. Bassa, P. Beelen, A. Garcia, and H. Stichtenoth. These
codes are described in detail by constrcting a generator matrix. It turns out
that these codes have nice properties similar to those of Hermitian codes. It
is shown that the duals are also such codes and an explicit formula is given.
|
1507.03418v1
|
2015-07-22
|
Reflexive insensitive modal logics
|
We analyze a class of modal logics rendered insensitive to reflexivity by way
of a modification to the semantic definition of the modal operator. We explore
the extent to which these logics can be characterized, and prove a general
completeness theorem on the basis of a translation between normal modal logics
and their reflexive-insensitive counterparts. Lastly, we provide a sufficient
semantic condition describing when a similarly general soundness result is also
available.
|
1507.06113v1
|
2015-08-24
|
Spin Dynamics Simulation of the Magneto-Electric Effect in a Composite Multiferroic Chain
|
A composite multiferroic chain with an interfacial linear magneto-electric
coupling is used to study the magnetic and electric responses to an external
magnetic or electric field. The simulation uses continuous spin dynamics
through the Landau-Lifshitz-Gilbert equations of the magnetic spin and the
electric pseudo-spin. The results demonstrate an accurate description of the
distribution of the magnetisation and polarisation are induced by applied
electric and magnetic field, respectively.
|
1508.05693v1
|
2015-10-16
|
Reaction diffusion dynamics and the Schryer-Walker solution for domain walls of the Landau-Lifshitz-Gilbert equation
|
We study the dynamics of the equation obtained by Schryer and Walker for the
motion of domain walls. The reduced equation is a reaction diffusion equation
for the angle between the applied field and the magnetization vector. If the
hard axis anisotropy $K_d$ is much larger than the easy axis anisotropy $K_u$,
there is a range of applied fields where the dynamics does not select the
Schryer-Walker solution. We give analytic expressions for the speed of the
domain wall in this regime and the conditions for its existence.
|
1510.04927v1
|
2015-11-06
|
Dynamic Response in a Finite Size Composite Multiferroic Thin Film
|
Composite multiferroics, heterostructures of ferromagnetic (FM) and
ferroelectric (FE) materials, are characterized by a remarkable magnetoelectric
effect at the interface. Previous work has supported the ferromagnetic
structure with magnetic spins and the ferroelectric with pseudospins which act
as electric dipoles in a microscopic model, coupled with a magnetoelectric
interaction [J. Appl. Phys. 118, 124109 (2015)]. In this work, by solving the
stochastic Landau-Lifshitz-Gilbert equation, the electric-field-induced
magnetization switching in a twisted boundary condition has been studied, and a
behavior of domain wall in the ferromagnetic structure is discussed.
|
1511.01982v2
|
2015-12-18
|
Existence of travelling-wave solutions representing domain wall motion in a thin ferromagnetic nanowire
|
We study the dynamics of a domain wall under the influence of applied
magnetic fields in a one-dimensional ferromagnetic nanowire, governed by the
Landau--Lifshitz--Gilbert equation. Existence of travelling-wave solutions
close to two known static solutions is proven using
implicit-function-theorem-type arguments.
|
1512.06016v2
|
2016-01-18
|
On Simultaneous Percolation with Two Disk Types
|
In this paper we consider the simultaneous percolation of two Gilbert disk
models. The two models are connected through excluding disks, which prevent
elements of the second model to be in the vicinity of the first model. Under
these assumptions we characterize the region of densities in which the two
models both have a unique infinite connected component. The motivation for this
work is the co-existence of two cognitive radio networks.
|
1601.04471v2
|
2016-01-22
|
Toward a New Microscopic Framework for Kondo Lattice Materials
|
Understanding the emergence and subsequent behavior of heavy electrons in
Kondo lattice materials is one of the grand challenges in condensed matter
physics. In this perspective we review the progress that has been made during
the past decade and suggest some directions for future research. Our focus will
be on developing a new microscopic framework that incorporates the basic
concepts that emerge from a phenomenological description of the key
experimental findings.
|
1601.06050v1
|
2016-02-01
|
The Eddy Current-LLG Equations-Part I: FEM-BEM Coupling
|
We analyse a numerical method for the coupled system of the eddy current
equations in $\mathbb{R}^3$ with the Landau-Lifshitz-Gilbert equation in a
bounded domain. The unbounded domain is discretised by means of
finite-element/boundary-element coupling. Even though the considered problem is
strongly nonlinear, the numerical approach is constructed such that only two
linear systems per time step have to be solved. In this first part of the
paper, we prove unconditional weak convergence (of a subsequence) of the
finite-element solutions towards a weak solution. A priori error estimates will
be presented in the second part.
|
1602.00744v1
|
2016-02-01
|
The Eddy Current--LLG Equations: FEM-BEM Coupling and A Priori Error Estimates
|
We analyze a numerical method for the coupled system of the eddy current
equations in $\mathbb{R}^3$ with the Landau-Lifshitz-Gilbert equation in a
bounded domain. The unbounded domain is discretized by means of
finite-element/boundary-element coupling. Even though the considered problem is
strongly nonlinear, the numerical approach is constructed such that only two
linear systems per time step have to be solved. We prove unconditional weak
convergence (of a subsequence) of the finite-element solutions towards a weak
solution. We establish a priori error estimates if a sufficiently smooth strong
solution exists. Numerical experiments underlining the theoretical results are
presented.
|
1602.00745v2
|
2016-02-24
|
Partial Category Actions on Sets and Topological Spaces
|
We introduce (continuous) partial category actions on sets (topological
spaces) and show that each such action admits a universal globalization.
Thereby, we obtain a simultaneous generalization of corresponding results for
groups, by Kellendonk and Lawson, and for monoids, by Megrelishvili and
Schroder. We apply this result to the special case of partial groupoid actions
where we obtain a sharpening of a result by Gilbert, concerning ordered
groupoids, in the sense that mediating functions between universal
globalizations always are injective.
|
1602.07541v4
|
2016-05-20
|
Interlayer interaction in multilayer CoPt/Co structures
|
We report a study of interlayer exchange interaction in multilayer CoPt/Co
structures consisting of periodic CoPt multilayer film with an "easy axis"
anisotropy and thick Co layer with an "easy plane" anisotropy separated by Pt
spacer with variable thickness. The magnetooptical Kerr effect (MOKE) and
ferromagnetic resonance (FMR) measurements show up the essentially
non-collinear state of magnetic moments of the layers and strong exchange
coupling between CoPt and Co subsystems. The estimation of effective anisotropy
and exchange coupling in a simple model based on the Landau-Lifshitz-Gilbert
equation describing magnetization dynamics was performed.
|
1605.06468v1
|
2016-06-02
|
On self-dual double negacirculant codes
|
Double negacirculant (DN) codes are the analogues in odd characteristic of
double circulant codes. Self-dual DN codes of odd dimension are shown to be
consta-dihedral. Exact counting formulae are derived for DN codes. The special
class of length a power of two is studied by means of Dickson polynomials, and
is shown to contain families of codes with relative distances satisfying a
modified Gilbert-Varshamov bound.
|
1606.00815v1
|
2016-07-12
|
Tailoring the topological details of the magnetic skyrmion by the spin configuration at the edges
|
The magnetic skyrmion structure can be formed in the chiral magnets (CMs)
with strong Dzyaloshinskii-Moriya interactions. In this work, we propose a way
of artificially tailoring the topological details of the skyrmion such as its
radial and whirling symmetric patterns by external magnetic fields besieging
the CM slab. As long as the boundary magnetic fields are strong enough to fix
the boundary ferromagnetism, the attained skyrmion profile is stable over time.
The dynamics of spins is considered by numerically solving the non-equilibrium
Landau-Lifshitz-Gilbert equation.
|
1607.03268v2
|
2016-09-07
|
Entanglement manipulation by a magnetic pulse in Gd3N@C80 endohedral metallofullerenes on a Cu(001) surface
|
In this paper we present result of theoretical calculation of entanglement
within a spin structure of Gd3N@C80 under the in uence of rectangular impulses.
Research is conducted using general spin Hamiltonian within SSNQ (spin system
of N-qubits). Calculation of entanglement with variable impulse is performed
using the time-dependent Landau-Lifshitz-Gilbert equation with spin-spin
correlation function. We show that long rectangular impulse (t=850ps) can be
used for maintaining of entanglement value. This allows us to offer a new
algorithm which can be used to reduce the challenge of decoherence to logical
scheme optimization.
|
1609.01959v1
|
2016-09-10
|
Optical tomography on graphs
|
We present an algorithm for solving inverse problems on graphs analogous to
those arising in diffuse optical tomography for continuous media. In
particular, we formulate and analyze a discrete version of the inverse Born
series, proving estimates characterizing the domain of convergence,
approximation errors, and stability of our approach. We also present a
modification which allows additional information on the structure of the
potential to be incorporated, facilitating recovery for a broader class of
problems.
|
1609.03041v1
|
2016-09-30
|
Interaction Between a Domain Wall and Spin Supercurrent in Easy-cone Magnets
|
A domain wall and spin supercurrent can coexist in magnets with easy-cone
anisotropy owing to simultaneous spontaneous breaking of Z$_2$ and U(1)
symmetries. Their interaction is theoretically investigated in quasi
one-dimensional ferromagnets within the Landau-Lifshitz-Gilbert phenomenology.
Specifically, we show that spin supercurrent can exert the torque on a domain
wall and thereby drive it. We also show, as a reciprocal phenomenon, a
field-induced motion of a domain wall can generate spin supercurrent.
|
1610.00034v1
|
2016-10-04
|
A Local Inverse Formula and a Factorization
|
When a matrix has a banded inverse there is a remarkable formula that quickly
computes that inverse, using only local information in the original matrix.
This local inverse formula holds more generally, for matrices with sparsity
patterns that are examples of chordal graphs or perfect eliminators. The
formula has a long history going back at least as far as the completion problem
for covariance matrices with missing data. Maximum entropy estimates,
log-determinants, rank conditions, the Nullity Theorem and wavelets are all
closely related, and the formula has found wide applications in machine
learning and graphical models. We describe that local inverse and explain how
it can be understood as a matrix factorization.
|
1610.01230v1
|
2016-10-10
|
Parametric frequency mixing in the magneto-elastically driven FMR-oscillator
|
We demonstrate the nonlinear frequency conversion of ferromagnetic resonance
(FMR) frequency by optically excited elastic waves in a thin metallic film on
dielectric substrates. Time-resolved probing of the magnetization directly
witnesses magneto-elastically driven second harmonic generation, sum- and
difference frequency mixing from two distinct frequencies, as well as
parametric downconversion of each individual drive frequency. Starting from the
Landau-Lifshitz-Gilbert equations, we derive an analytical equation of an
elastically driven nonlinear parametric oscillator and show that frequency
mixing is dominated by the parametric modulation of FMR frequency.
|
1610.02926v1
|
2016-11-05
|
Magnonic analog of relativistic Zitterbewegung in an antiferromagnetic spin chain
|
We theoretically investigate the spin wave (magnon) excitations in a
classical antiferromagnetic spin chain with easy-axis anisotropy. We obtain a
Dirac-like equation by linearizing the Landau- Lifshitz-Gilbert equation in
this antiferromagnetic system, in contrast to the ferromagnetic system in which
a Schr\"{o}dinger equation is derived. The Hamiltonian operator in the
Dirac-like equation is a pseudo-Hermitian. We compute and demonstrate the
relativistic Zitterbewegung (trembling motion) in the antiferromagnetic spin
chain by measuring the expectation values of the wave packet position.
|
1611.01512v2
|
2016-11-15
|
The norm of the Fourier transform on compact or discrete abelian groups
|
We calculate the norm of the Fourier operator from $L^p(X)$ to $L^q(\hat{X})$
when $X$ is an infinite locally compact abelian group that is, furthermore,
compact or discrete. This subsumes the sharp Hausdorff-Young inequality on such
groups. In particular, we identify the region in $(p,q)$-space where the norm
is infinite, generalizing a result of Fournier, and setting up a contrast with
the case of finite abelian groups, where the norm was determined by Gilbert and
Rzeszotnik. As an application, uncertainty principles on such groups expressed
in terms of R\'enyi entropies are discussed.
|
1611.04692v1
|
2016-12-01
|
Optimizing Quantiles in Preference-based Markov Decision Processes
|
In the Markov decision process model, policies are usually evaluated by
expected cumulative rewards. As this decision criterion is not always suitable,
we propose in this paper an algorithm for computing a policy optimal for the
quantile criterion. Both finite and infinite horizons are considered. Finally
we experimentally evaluate our approach on random MDPs and on a data center
control problem.
|
1612.00094v1
|
2017-02-02
|
Magnon Condensation and Spin Superfluidity
|
We consider the phenomenon of Bose-Einstein condensation of quasi-equilibrium
magnons which leads to a spin superfluidity, the coherent quantum transfer of
magnetization in magnetic materials. These phenomena are beyond the classical
Landau-Lifshitz-Gilbert paradigm. The critical conditions for excited magnon
density for ferro- and antiferromagnets, bulk and thin films are estimated and
discussed. The BEC should occur in the antiferromagnetic hematite at much lower
excited magnon density compared to the ferromagnetic YIG.
|
1702.00846v2
|
2017-02-09
|
Transient spin dynamics in a single-molecule magnet
|
We explore the limitations and validity of semi-classically formulated spin
equations of motion. Using a single-molecule magnet as a test model, we employ
three qualitatively different approximation schemes. From a microscopic model,
we derive a generalized spin equation of motion in which the parameters have a
non-local time-dependence. This dynamical equation is simplified to the
Landau-Lifshitz-Gilbert equation with i) time-dependent, and ii)
time-independent parameters. We show that transient dynamics is essentially
non-existing in the latter approximation, while the former breaks down in the
regime of strong coupling between the spin and the itinerant electrons.
|
1702.02820v2
|
2017-03-05
|
On the VC-Dimension of Binary Codes
|
We investigate the asymptotic rates of length-$n$ binary codes with
VC-dimension at most $dn$ and minimum distance at least $\delta n$. Two upper
bounds are obtained, one as a simple corollary of a result by Haussler and the
other via a shortening approach combining Sauer-Shelah lemma and the linear
programming bound. Two lower bounds are given using Gilbert-Varshamov type
arguments over constant-weight and Markov-type sets.
|
1703.01586v2
|
2017-03-09
|
Long quasi-polycyclic $t-$CIS codes
|
We study complementary information set codes of length $tn$ and dimension $n$
of order $t$ called ($t-$CIS code for short). Quasi-cyclic and quasi-twisted
$t$-CIS codes are enumerated by using their concatenated structure. Asymptotic
existence results are derived for one-generator and have co-index $n$ by
Artin's conjecture for quasi cyclic and special case for quasi twisted. This
shows that there are infinite families of long QC and QT $t$-CIS codes with
relative distance satisfying a modified Varshamov-Gilbert bound for rate $1/t$
codes.
Similar results are defined for the new and more general class of
quasi-polycyclic codes introduced recently by Berger and Amrani.
|
1703.03109v1
|
2017-09-05
|
On the Lagrangian branched transport model and the equivalence with its Eulerian formulation
|
First we present two classical models of Branched Transport: the Lagrangian
model introduced by Bernot, Caselles, Morel, Maddalena, Solimini, and the
Eulerian model introduced by Xia. An emphasis is put on the Lagrangian model,
for which we give a complete proof of existence of minimizers in a
--hopefully-- simplified manner. We also treat in detail some
$\sigma$-finiteness and rectifiability issues to yield rigorously the energy
formula connecting the irrigation cost I$\alpha$ to the Gilbert Energy
E$\alpha$. Our main purpose is to use this energy formula and exploit a Smirnov
decomposition of vector flows, which was proved via the Dacorogna-Moser
approach by Santambrogio, to establish the equivalence between the Lagrangian
and Eulerian models.
|
1709.01414v1
|
2017-09-09
|
On Low-Risk Heavy Hitters and Sparse Recovery Schemes
|
We study the heavy hitters and related sparse recovery problems in the
low-failure probability regime. This regime is not well-understood, and has
only been studied for non-adaptive schemes. The main previous work is one on
sparse recovery by Gilbert et al.(ICALP'13). We recognize an error in their
analysis, improve their results, and contribute new non-adaptive and adaptive
sparse recovery algorithms, as well as provide upper and lower bounds for the
heavy hitters problem with low failure probability.
|
1709.02919v3
|
2017-10-30
|
Lattice calculation of hadronic tensor of the nucleon
|
We report an attempt to calculate the deep inelastic scattering structure
functions from the hadronic tensor calculated on the lattice. We used the
Backus-Gilbert reconstruction method to address the inverse Laplace
transformation for the analytic continuation from the Euclidean to the
Minkowski space.
|
1710.11145v1
|
2017-10-31
|
TF Boosted Trees: A scalable TensorFlow based framework for gradient boosting
|
TF Boosted Trees (TFBT) is a new open-sourced frame-work for the distributed
training of gradient boosted trees. It is based on TensorFlow, and its
distinguishing features include a novel architecture, automatic loss
differentiation, layer-by-layer boosting that results in smaller ensembles and
faster prediction, principled multi-class handling, and a number of
regularization techniques to prevent overfitting.
|
1710.11555v1
|
2017-11-08
|
Micromagnetic simulation study of a disordered model for one-dimensional granular perovskite manganite oxide nanostructures
|
Chemical techniques are an efficient method to synthesize one-dimensional
perovskite manganite oxide nanostructures with a granular morphology, that is,
formed by arrays of monodomain magnetic nanoparticles. Integrating the
stochastic Landau-Lifshitz-Gilbert equation, we simulate the dynamics of a
simple disordered model for such materials that only takes into account the
morphological characteristics of their nanograins. We show that it is possible
to describe reasonably well experimental hysteresis loops reported in the
literature for single La_0.67Ca_0.33MnO_3 nanotubes and powders of these
nanostructures, simulating small systems consisting of only 100 nanoparticles.
|
1711.03159v2
|
2017-11-21
|
Construction of asymptotically good locally repairable codes via automorphism groups of function fields
|
Locally repairable codes have been investigated extensively in recent years
due to practical application in distributed storage as well as theoretical
interest. However, not much work on asymptotical behavior of locally repairable
codes has been done until now. In particular, there is a little result on
constructive lower bound on asymptotical behavior of locally repairable codes.
In this paper, we extend the construction given in \cite{BTV17} via
automorphism groups of function field towers. The main advantage of our
construction is to allow more flexibility of locality. Furthermore, we show
that the Gilbert-Varshamov type bound on locally repairable codes can be
improved for all sufficiently large alphabet size $q$.
|
1711.07703v1
|
2017-11-21
|
Stability of axisymmetric chiral skyrmions
|
We examine topological solitons in a minimal variational model for a chiral
magnet, so-called chiral skyrmions. In the regime of large background fields,
we prove linear stability of axisymmetric chiral skyrmions under arbitrary
perturbations in the energy space, a long-standing open question in physics
literature. Moreover, we show strict local minimality of axisymmetric chiral
skyrmions and nearby existence of moving soliton solution for the
Landau-Lifshitz-Gilbert equation driven by a small spin transfer torque.
|
1711.07717v1
|
2017-12-13
|
Mutual synchronization of spin-torque oscillators consisting of perpendicularly magnetized free layers and in-plane magnetized pinned layers
|
A mutual synchronization of spin-torque oscillators coupled through current
injection is studied theoretically. Models of electrical coupling in parallel
and series circuits are proposed. Solving the Landau-Lifshitz-Gilbert equation,
excitation of in-phase or antiphase synchronization, depending on the ways the
oscillators are connected, is found. It is also found from both analytical and
numerical calculations that the current-frequency relations for both parallel
and series circuits are the same as that for a single spin-torque oscillator.
|
1712.04591v1
|
2018-01-25
|
Pharmacokinetics Simulations for Studying Correlates of Prevention Efficacy of Passive HIV-1 Antibody Prophylaxis in the Antibody Mediated Prevention (AMP) Study
|
A key objective in two phase 2b AMP clinical trials of VRC01 is to evaluate
whether drug concentration over time, as estimated by non-linear mixed effects
pharmacokinetics (PK) models, is associated with HIV infection rate. We
conducted a simulation study of marker sampling designs, and evaluated the
effect of study adherence and sub-cohort sample size on PK model estimates in
multiple-dose studies. With m=120, even under low adherence (about half of
study visits missing per participant), reasonably unbiased and consistent
estimates of most fixed and random effect terms were obtained. Coarsened marker
sampling schedules were also studied.
|
1801.08626v1
|
2018-03-30
|
Nanostructured Ceramic Oxides with a Slow Crack Growth Resistance Close to Covalent Materials
|
Oxide ceramics are sensitive to slow crack growth because adsorption of water
can take place at the crack tip, leading to a strong decrease of the surface
energy in humid (or air) conditions. This is a major drawback concerning
demanding, long-term applications such as orthopaedic implants. Here we show
that a specific nanostructuration of ceramic oxides can lead to a crack
resistance never reached before, similar to that of covalent ceramics.
|
1804.01393v1
|
2018-05-30
|
Quantum Annealed Criticality
|
Experimentally there exist many materials with first-order phase transitions
at finite temperature that display quantum criticality. Classically a
strain-energy density coupling is known to drive first-order transitions in
compressible systems, and here we generalize this Larkin-Pikin mechanism to the
quantum case. We show that if the T=0 system lies above its upper critical
dimension, the line of first-order transitions can end in a quantum annealed
critical point where zero-point fluctuations restore the underlying criticality
of the order parameter.
|
1805.11771v1
|
2018-08-03
|
A thermally driven spin-transfer-torque system far from equilibrium: enhancement of the thermoelectric current via pumping current
|
We consider a small itinerant ferromagnet exposed to an external magnetic
field and strongly driven by a thermally induced spin current. For this model,
we derive the quasi-classical equations of motion for the magnetization where
the effects of a dynamical non-equilibrium distribution function are taken into
account self-consistently. We obtain the Landau-Lifshitz-Gilbert equation
supplemented by a spin-transfer torque term of Slonczewski form. We identify a
regime of persistent precessions in which we find an enhancement of the
thermoelectric current by the pumping current.
|
1808.01192v1
|
2018-09-12
|
But How Does It Work in Theory? Linear SVM with Random Features
|
We prove that, under low noise assumptions, the support vector machine with
$N\ll m$ random features (RFSVM) can achieve the learning rate faster than
$O(1/\sqrt{m})$ on a training set with $m$ samples when an optimized feature
map is used. Our work extends the previous fast rate analysis of random
features method from least square loss to 0-1 loss. We also show that the
reweighted feature selection method, which approximates the optimized feature
map, helps improve the performance of RFSVM in experiments on a synthetic data
set.
|
1809.04481v3
|
2018-09-22
|
Optimizing a Generalized Gini Index in Stable Marriage Problems: NP-Hardness, Approximation and a Polynomial Time Special Case
|
This paper deals with fairness in stable marriage problems. The idea studied
here is to achieve fairness thanks to a Generalized Gini Index (GGI), a
well-known criterion in inequality measurement, that includes both the
egalitarian and utilitarian criteria as special cases. We show that determining
a stable marriage optimizing a GGI criterion of agents' disutilities is an
NP-hard problem. We then provide a polynomial time 2-approximation algorithm in
the general case, as well as an exact algorithm which is polynomial time in the
case of a constant number of non-zero weights parametrizing the GGI criterion.
|
1809.08453v1
|
2018-10-17
|
Out-of-plane auto-oscillation in spin Hall oscillator with additional polarizer
|
The theoretical investigation on magnetization dynamics excited by the spin
Hall effect in metallic multilayers having two ferromagnets is discussed. The
relaxation of the transverse spin in one ferromagnet enables us to manipulate
the direction of the spin-transfer torque excited in another ferromagnet,
although the spin-polarization originally generated by the spin Hall effect is
geometrically fixed. Solving the Landau-Lifshitz-Gilbert-Slonczewski equation,
the possibility to excite an out-of-plane auto-oscillation of an in-plane
magnetized ferromagnet is presented. An application to magnetic recording using
microwave-assisted magnetization reversal is also discussed.
|
1810.07831v1
|
2018-11-23
|
Most Graphs are Knotted
|
We present four models for a random graph and show that, in each case, the
probability that a graph is intrinsically knotted goes to one as the number of
vertices increases. We also argue that, for $k \geq 18$, most graphs of order
$k$ are intrinsically knotted and, for $k \geq 2n+9$, most of order $k$ are not
$n$-apex. We observe that $p(n) = 1/n$ is the threshold for intrinsic knotting
and linking in Gilbert's model.
|
1811.09726v1
|
2018-12-13
|
Entanglement-assisted quantum error-correcting codes over arbitrary finite fields
|
We prove that the known formulae for computing the optimal number of
maximally entangled pairs required for entanglement-assisted quantum
error-correcting codes (EAQECCs) over the binary field hold for codes over
arbitrary finite fields as well. We also give a Gilbert-Varshamov bound for
EAQECCs and constructions of EAQECCs coming from punctured self-orthogonal
linear codes which are valid for any finite field.
|
1812.05312v4
|
2019-01-23
|
Coupled dynamics of magnetizations in spin-Hall oscillators via spin current injection
|
An array of spin torque oscillators (STOs) for practical applications such as
pattern recognition was recently proposed, where several STOs are connected by
a common nonmagnet. In this structure, in addition to the electric and/or
magnetic interactions proposed in previous works, the STOs are spontaneously
coupled to each other through the nonmagnetic connector, due to the injection
of spin current. Solving the Landau-Lifshitz-Gilbert equation numerically for
such system consisting of three STOs driven by the spin Hall effect, it is
found that both in-phase and antiphase synchronization of the STOs can be
achieved by adjusting the current density and appropriate distance between the
oscillators.
|
1901.07669v1
|
2019-01-28
|
A Multi-parameter regression model for interval censored survival data
|
We develop flexible multi-parameter regression survival models for interval
censored survival data arising in longitudinal prospective studies and
longitudinal randomised controlled clinical trials. A multi-parameter Weibull
regression survival model, which is wholly parametric, and has non-proportional
hazards, is the main focus of the paper. We describe the basic model, develop
the interval-censored likelihood and extend the model to include gamma frailty
and a dispersion model. We evaluate the models by means of a simulation study
and a detailed re-analysis of data from the Signal Tandmobiel$^{\circledR}$
study. The results demonstrate that the multi-parameter regression model with
frailty is computationally efficient and provides an excellent fit to the data.
|
1901.09634v1
|
2019-02-15
|
Stochastic homogenization of the Landau-Lifshitz-Gilbert equation
|
Following the ideas of V. V. Zhikov and A. L. Pyatnitski, and more precisely
the stochastic two-scale convergence, this paper establishes a homogenization
theorem in a stochastic setting for two nonlinear equations : the equation of
harmonic maps into the sphere and the Landau-Lifschitz equation. These
equations have strong nonlinear features, in particular, in general their
solutions are not unique.
|
1902.05743v1
|
2019-03-06
|
Cluster multipole dynamics in non-collinear antiferromagnets
|
A systematic framework to investigate spin dynamics in non-collinear
antiferromagnet is proposed. Taking Mn$_3$Sn as a representative example, we
derive an effective low energy model based on the multipole expansion of the
magnetic structure, and investigate the uniform precession and the domain wall
dynamics. We show that the solution for the effective model accurately
reproduces the numerical calculation of the Landau-Lifshitz-Gilbert equations.
Our results indicate that Mn$_3$Sn has preferable properties for applications
to a racetrack memory and a spin torque oscillator, and thus, is a promising
candidate for new devices by using the multipole degrees of freedom.
|
1903.02259v1
|
2019-03-22
|
Learning magnetization dynamics
|
Deep neural networks are used to model the magnetization dynamics in magnetic
thin film elements. The magnetic states of a thin film element can be
represented in a low dimensional space. With convolutional autoencoders a
compression ratio of 1024:1 was achieved. Time integration can be performed in
the latent space with a second network which was trained by solutions of the
Landau-Lifshitz-Gilbert equation. Thus the magnetic response to an external
field can be computed quickly.
|
1903.09499v1
|
2019-04-01
|
Synchrony breakdown and noise-induced oscillation death in ensembles of serially connected spin-torque oscillators
|
We consider collective dynamics in the ensemble of serially connected
spin-torque oscillators governed by the Landau-Lifshitz-Gilbert-Slonczewski
magnetization equation. Proximity to homoclinicity hampers synchronization of
spin-torque oscillators: when the synchronous ensemble experiences the
homoclinic bifurcation, the Floquet multiplier, responsible for the temporal
evolution of small deviations from the ensemble mean, diverges. Depending on
the configuration of the contour, sufficiently strong common noise, exemplified
by stochastic oscillations of the current through the circuit, may suppress
precession of the magnetic field for all oscillators. We derive the explicit
expression for the threshold amplitude of noise, enabling this suppression.
|
1904.00897v1
|
2019-04-21
|
Global classical solutions to an evolutionary model for magnetoelasticity
|
In this paper, we first prove the local-in-time existence of the evolutionary
model for magnetoelasticity with finite initial energy by employing the
nonlinear iterative approach given in \cite{Jiang-Luo-2019-SIAM} to deal with
the geometric constraint $M \in \mathbb{S}^{d-1}$ in the
Landau-Lifshitz-Gilbert (LLG) equation. Inspired by
\cite{Lin-Liu-Zhang-CPAM2005, Lin-Zhang-2008-CPAM}, we reformulate the
evolutionary model for magnetoelasticity with vanishing external magnetic field
$H_{ext}$, so that a further dissipative term will be sought from the elastic
stress. We thereby justify the global well-posedness to the evolutionary model
for magnetoelasticity with zero external magnetic field under small size of
initial data.
|
1904.09531v1
|
2019-06-21
|
Thermal Collapse of a Skyrmion
|
Thermal collapse of an isolated skyrmion on a two-dimensional spin lattice
has been investigated. The method is based upon solution of the system of
stochastic Landau-Lifshitz-Gilbert equations for up $10^4$ spins. Recently
developed pulse-noise algorithm has been used for the stochastic component of
the equations. The collapse rate follows the Arrhenius law. Analytical formulas
derived within a continuous spin-field model support numerically-obtained
values of the energy barrier and the pre-exponential factor, and their
dependence on the magnetic field. Our findings agree with experiments, as well
as with recent numerical results obtained by other methods.
|
1906.09132v3
|
2019-06-23
|
Random subgroups, automorphisms, splittings
|
We show that, if $H$ is a random subgroup of a finitely generated free group
$F_k$, only inner automorphisms of $F_k$ may leave $H$ invariant. A similar
result holds for random subgroups of toral relatively hyperbolic groups, more
generally of groups which are hyperbolic relative to slender subgroups. These
results follow from non-existence of splittings over slender groups which are
relative to a random group element. Random subgroups are defined using random
walks or balls in a Cayley tree of $F_k$.
|
1906.09654v1
|
2019-07-28
|
Polarization of the Cosmic Infrared Background Fluctuations
|
The cosmic infrared background (CIB) is slightly polarized. Polarization
directions of individual galaxies could be aligned with tidal fields around
galaxies, resulting in nonzero CIB polarization. We use a linear intrinsic
alignment model to theoretically predict angular correlations of the CIB
polarization fluctuations and find that electriclike and curl-like ($B$-mode)
polarization modes are equally generated with power four orders of magnitude
less than its intensity. The CIB $B$-mode signal is negligible and not a
concerning foreground for the inflationary $B$-mode searches at nominal
frequencies for cosmic microwave background measurements, but could be detected
at submillimetre wavelengths by future space missions.
|
1907.12085v1
|
2019-08-05
|
Constructive asymptotic bounds of locally repairable codes via function fields
|
Locally repairable codes have been investigated extensively in recent years
due to practical applications in distributed and cloud storage systems.
However, there are few asymptotical constructions of locally repairable codes
in the literature. In this paper, we provide an explicit asymptotic
construction of locally repairable codes over arbitrary finite fields from
local expansions of functions at a rational place. This construction gives a
Tsfasman-Vladut-Zink type bound for locally repairable codes. Its main
advantage is that there are no constraints on both locality and alphabet size.
Furthermore, we show that the Gilbert-Varshamov type bound on locally
repairable codes over non-prime finite fields can be exceeded for sufficiently
large alphabet size.
|
1908.01471v1
|
2019-10-25
|
Application-Layer Coding with Intermittent Feedback under Delay and Duty-Cycle Constraints
|
We propose two application-layer coding schemes for delay-constrained
point-to-point packet communications with restrictions on the transmitter's
maximum duty-cycle. The schemes operate over GF(2) and utilize intermittently
available receiver feedback for erasure correction. Applications that will
benefit from the proposed schemes include wireless sensor networks in which
energy-constrained sensors must deliver readings to a gateway within a
deadline. Simulation results for independent Bernoulli erasure channels,
Gilbert-Elliott channels, and Long Range (LoRa) communications demonstrate
orders-of-magnitude reductions in the delivery failure rate as compared to
feedback-assisted repetition redundancy and a blind coding scheme that does not
utilize feedback.
|
1910.11700v2
|
2019-10-28
|
Dissipative solutions to a system for the flow of magnetoviscoelastic materials
|
We address the question of global in time existence of solutions to a
magnetoviscoelastic system with general initial data. We show that the notion
of dissipative solutions allows to prove such an existence in two and three
dimensions. This extends an earlier result for the viscoelastic subsystem to
the setting which includes the magnetization vector and its evolution in terms
of a Landau-Lifshitz-Gilbert equation.
|
1910.12751v2
|
2019-12-09
|
Multi-reference protocol for (auto)ionization spectra: application to molecules
|
We present the application of the spherically averaged continuum model to the
evaluation of molecular photoelectron and resonant Auger electron spectra. In
this model, the continuum wave function is obtained in a numerically efficient
way by solving the radial Schr\"odinger equation with a spherically averaged
molecular potential. Different approximations to the Auger transition matrix
element and, in particular, the one-center approximation are thoroughly tested
against experimental data for the CH$_4$, O$_2$, NO$_2$, and pyrimidine
molecules. In general, this approach appears to estimate the shape of the
photoelectron and autoionization spectra as well as the total Auger decay rates
with reasonable accuracy, allowing for the interpretation of experimental
results.
|
1912.04139v1
|
2020-01-25
|
Phase estimation of spin-torque oscillator by nonlinear spin-torque diode effect
|
A theoretical analysis is developed on spin-torque diode effect in nonlinear
region. An analytical solution of the diode voltage generated from spin-torque
oscillator by the rectification of an alternating current is derived. The diode
voltage is revealed to depend nonlinearly on the phase difference between the
oscillator and the alternating current. The validity of the analytical
prediction is confirmed by numerical simulation of the Landau-Lifshitz-Gilbert
equation. The results indicate that the spin-torque diode effect is useful to
evaluate the phase of a spin-torque oscillator in forced synchronization state.
|
2001.09247v1
|
2020-04-06
|
Frequency enhancement and power tunability in tilted polarizer spin-torque nano oscillator
|
In the absence of an applied magnetic field, a spin-torque nano
oscillator(STNO) with a tilted polarizer is studied using numerical simulation
of the associated Landau-Lifshitz-Gilbert-Slonczewski equation. We find
considerable enhancement of frequency by tilting the polarizer out-of-plane
appropriately. Also, we observe improved tunability of frequency of
oscillations from 15 GHz to 75 GHz and increment in the power spectral density
by current and tilt angle. In addition, our findings and insights pave a simple
way for nanoscale level microwave generators to be implemented.
|
2004.02659v1
|
2020-05-11
|
Perspective on Metallic Antiferromagnets
|
Antiferromagnet materials have recently gained renewed interest due to their
possible use in spintronics technologies, where spin transport is the
foundation of their functionalities. In that respect metallic antiferromagnets
are of particular interest, since they enable complex interplays between
electronic charge transport, spin, optical, and magnetization dynamics. Here we
review phenomena where the metallic conductivity provides unique perspectives
for the practical use and fundamental properties of antiferromagnetic
materials.
|
2005.05247v1
|
2020-07-09
|
Enumerating alternating matrix spaces over finite fields with explicit coordinates
|
We initiate the study of enumerating linear subspaces of alternating matrices
over finite fields with explicit coordinates. We postulate that this study can
be viewed as a linear algebraic analogue of the classical topic of enumerating
labelled graphs. To support this viewpoint, we present q-analogues of Gilbert's
formula for enumerating connected graphs (Can. J. Math., 1956), and Read's
formula for enumerating c-colored graphs (Can. J. Math., 1960). We also develop
an analogue of Riddell's formula relating the exponential generating function
of graphs with that of connected graphs (Riddell's PhD thesis, 1951), building
on Eulerian generating functions developed by Srinivasan (Discrete Math.,
2006).
|
2007.05108v1
|
2020-08-06
|
On Passivity, Feedback Passivity, And Feedback Passivity Over Erasure Network: A Piecewise Affine Approximation Approach
|
In this paper, we deal with the problem of passivity and feedback
passification of smooth discrete-time nonlinear systems by considering their
piecewise affine approximations. Sufficient conditions are derived for
passivity and feedback passivity. These results are then extended to systems
that operate over Gilbert-Elliott type communication channels. As a special
case, results for feedback passivity of piecewise affine systems over a lossy
channel are also derived.
|
2008.02748v1
|
2020-08-20
|
Hyperbolic groups of Fibonacci type and T(5) cyclically presented groups
|
Building on previous results concerning hyperbolicity of groups of Fibonacci
type, we give an almost complete classification of the (non-elementary)
hyperbolic groups within this class. We are unable to determine the
hyperbolicity status of precisely two groups, namely the Gilbert-Howie groups
H(9,4), H(9,7). We show that if H(9,4) is torsion-free then it is not
hyperbolic. We consider the class of T(5) cyclically presented groups and
classify the (non-elementary) hyperbolic groups and show that the Tits
alternative holds.
|
2008.08986v2
|
2020-10-13
|
Mechanistic Modelling of Chromatin Folding to Understand Function
|
Experimental approaches have been applied to address questions in
understanding three-dimensional chromatin organisation and function. As
datasets increase in size and complexity, it becomes a challenge to reach a
mechanistic interpretation of experimental results. Polymer simulations and
mechanistic modelling have been applied to explain experimental observations,
and the links to different aspects of genome function. Here, we provide a guide
for biologists, explaining different simulation approaches and the contexts in
which they have been used.
|
2010.06413v1
|
2020-12-05
|
Dual Regularized Optimal Transport
|
In this paper, we present a new formulation of unbalanced optimal transport
called Dual Regularized Optimal Transport (DROT). We argue that regularizing
the dual formulation of optimal transport results in a version of unbalanced
optimal transport that leads to sparse solutions and that gives us control over
mass creation and destruction. We build intuition behind such control and
present theoretical properties of the solutions to DROT. We demonstrate that
due to recent advances in optimization techniques, we can feasibly solve such a
formulation at large scales and present extensive experimental evidence for
this formulation and its solution.
|
2012.03126v1
|
2020-12-20
|
Achieving positive rates with predetermined dictionaries
|
In the first part of the paper we consider binary input channels that are not
necessarily stationary and show how positive rates can be achieved using codes
constrained to be within predetermined dictionaries. We use a
Gilbert-Varshamov-like argument to obtain the desired rate achieving codes.
Next we study the corresponding problem for channels with arbitrary alphabets
and use conflict-set decoding to show that if the dictionaries are contained
within nice sets, then positive rates are achievable.
|
2012.10897v1
|
2020-12-25
|
Colossal stability of antiferromagnetically exchange coupled nanomagnets
|
Bistable nanomagnets store a binary bit of information. Exchange coupled
nanomagnets can increase the thermal stability at low dimensions. Here we show
that the antiferromagnetically (AFM) coupled nanomagnets can be highly stable
at low dimensions than that of the ferromagnetically (FM) coupled nanomagnets.
By solving stochastic Landau-Lifshitz-Gilbert equation of magnetization
dynamics at room temperature, we analyze the stability of the exchange coupled
nanomagnets in the presence of correlated, uncorrelated, and anti-correlated
noise. The results show that the correlated noise can make the stability of the
AFM coupled nanomagnets very high. Such finding will lead to very high-density
non-volatile storage and logic devices in our future information processing
systems.
|
2012.13590v1
|
2021-03-08
|
Cutoff for the Asymmetric Riffle Shuffle
|
In the Gilbert-Shannon-Reeds shuffle, a deck of $N$ cards is cut into two
approximately equal parts which are then riffled uniformly at random. Bayer and
Diaconis famously showed that this Markov chain undergoes cutoff in total
variation after $\frac{3\log(N)}{2 \log(2)}$ shuffles. We establish cutoff for
the more general asymmetric riffle shuffles in which one cuts the deck into
differently sized parts before riffling. The value of the cutoff point confirms
a conjecture of Lalley from 2000. Some appealing consequences are that
asymmetry always slows mixing and that total variation mixing is strictly
faster than separation and $L^{\infty}$ mixing.
|
2103.05068v3
|
2021-03-24
|
Information Freshness Analysis of Slotted ALOHA in Gilbert-Elliot Channels
|
This letter analyzes a class of information freshness metrics for large IoT
systems in which terminals employ slotted ALOHA to access a common channel.
Considering a Gilbert- Elliot channel model, information freshness is evaluated
through a penalty function that follows a power law of the time elapsed since
the last received update, in contrast with the linear growth of age of
information. By means of a signal flow graph analysis of Markov processes, we
provide exact closed form expressions for the average penalty and for the peak
penalty violation probability.
|
2103.13346v2
|
2021-04-30
|
Micromagnetic modeling of magnon coherent states in a nonuniform magnetic field
|
The study of the dynamics of magnetically ordered states in strong excitation
through micromagnetic modeling has become relevant due to the observation of
magnon Bose condensation. In particular, the question has arisen about the
possibility of describing the coherent quantum state by the quasi-classical
Landau-Lifshitz-Gilbert equations. We performed micromagnetic simulations of
magnetization precession with a high angle of deviation in an out-of-plane
nonuniform dc field. Our results confirm the formation of coherent magnon state
under conditions of high excitation. This coherent state extends over long
distances and described by a spatially inhomogeneous amplitude and a
homogeneous precession phase.
|
2104.14804v1
|
2021-07-07
|
Superconducting Magnets
|
Superconductivity allows to construct and operate magnets at field values
beyond 2 Tesla, the practical limitation of normal-conducting magnets
exploiting ferro-magnetism. The field of superconducting magnets is dominated
by the field generated in the coil. The stored energy and the electromagnetic
forces generated by the coil are the main challenges to be overcome in the
design of these magnets. For further reading you may consult the following
books: [1], [2], [3], [4] or the proceedings of two specialized CAS courses:
[5] and [6].
|
2107.03177v1
|
2021-08-14
|
An Experimental-Design Perspective on Population Genetic Variation
|
We consider the hypothesis that Evolution promotes population-wide genome
patterns that, under randomization, ensures the External Validity of
adaptations across population members. An adaptation is Externally Valid (EV)
if its effect holds under a wide range of population genetic variations. A
prediction following the hypothesis is that pairwise base substitutions in
segregating regions must be 'random' as in Erdos-Renyi-Gilbert random graphs,
but with edge probabilities derived from Experimental-Design concepts. We
demonstrate these probabilities, and consequent mutation rates, in the
full-genomes of 2504 humans, 1135 flowering plants, 1170 flies, 453 domestic
sheep and 1223 brown rats.
|
2108.06580v1
|
2021-12-14
|
Extending the team with a project-specific bot
|
While every other software team is adopting off-the-shelf bots to automate
everyday tasks, the Coq team has made a different choice by developing and
maintaining a project-specific bot from the ground up. In this article, we
describe the reasons for this choice, what kind of automation this has allowed
us to implement, how the many features of this custom bot have evolved based on
internal feedback, and the technology and architecture choices that have made
it possible.
|
2112.07365v1
|
2021-12-29
|
Multi-Adversarial Safety Analysis for Autonomous Vehicles
|
This work in progress considers reachability-based safety analysis in the
domain of autonomous driving in multi-agent systems. We formulate the safety
problem for a car following scenario as a differential game and study how
different modelling strategies yield very different behaviors regardless of the
validity of the strategies in other scenarios. Given the nature of real-life
driving scenarios, we propose a modeling strategy in our formulation that
accounts for subtle interactions between agents, and compare its Hamiltonian
results to other baselines. Our formulation encourages reduction of
conservativeness in Hamilton-Jacobi safety analysis to provide better safety
guarantees during navigation.
|
2112.14344v1
|
2022-01-26
|
Analyzing Ta-Shma's Code via the Expander Mixing Lemma
|
Random walks in expander graphs and their various derandomizations (e.g.,
replacement/zigzag product) are invaluable tools from pseudorandomness.
Recently, Ta-Shma used s-wide replacement walks in his breakthrough
construction of a binary linear code almost matching the Gilbert-Varshamov
bound (STOC 2017). Ta-Shma's original analysis was entirely linear algebraic,
and subsequent developments have inherited this viewpoint. In this work, we
rederive Ta-Shma's analysis from a combinatorial point of view using repeated
application of the expander mixing lemma. We hope that this alternate
perspective will yield a better understanding of Ta-Shma's construction. As an
additional application of our techniques, we give an alternate proof of the
expander hitting set lemma.
|
2201.11166v1
|
2022-02-15
|
Further Collapses in TFNP
|
We show $\textsf{EOPL}=\textsf{PLS}\cap\textsf{PPAD}$. Here the class
$\textsf{EOPL}$ consists of all total search problems that reduce to the
End-of-Potential-Line problem, which was introduced in the works by Hubacek and
Yogev (SICOMP 2020) and Fearnley et al. (JCSS 2020). In particular, our result
yields a new simpler proof of the breakthrough collapse
$\textsf{CLS}=\textsf{PLS}\cap\textsf{PPAD}$ by Fearnley et al. (STOC 2021). We
also prove a companion result $\textsf{SOPL}=\textsf{PLS}\cap\textsf{PPADS}$,
where $\textsf{SOPL}$ is the class associated with the Sink-of-Potential-Line
problem.
|
2202.07761v2
|
2022-03-19
|
A proposed test of quantum mechanics with three connected atomic clock transitions
|
We consider possible extensions to quantum mechanics proposed by Steven
Weinberg, and re-analyze his prediction of a new test based upon three atomic
clocks in the same atom. We propose realistic experimental systems where this
hypothesis can be tested. Two systems already set limits on deviations from
quantum mechanics, while with another system, one would be able to search for
new physics at the limit of sensitivity of the best atomic clocks.
|
2203.10269v3
|
2022-06-14
|
Generalized graph splines and the Universal Difference Property
|
We study the generalized graph splines introduced by Gilbert, Tymoczko, and
Viel and focus on an attribute known as the Universal Difference Property
(UDP). We prove that paths, trees, and cycles satisfy UDP. We explore UDP on
graphs pasted at a single vertex and use Pr\"ufer domains to illustrate that
not every edge labeled graph satisfies UDP. We show that UDP must hold for any
edge labeled graph over a ring $R$ if and only if $R$ is a Pr\"ufer domain.
Lastly, we prove that UDP is preserved by isomorphisms of edge labeled graphs.
|
2206.06981v2
|
2022-08-04
|
Total stability and Auslander-Reiten theory for Dynkin quivers
|
This paper concerns stability functions for Dynkin quivers, in the generality
introduced by Rudakov. We show that relatively few inequalities need to be
satisfied for a stability function to be totally stable (i.e. to make every
indecomposable stable). Namely, a stability function $\mu$ is totally stable if
and only if $\mu(\tau V) < \mu(V)$ for every almost split sequences $0 \to \tau
V \to E \to V \to 0$ where $E$ is indecomposable. These can be visualized as
those sequences around the "border" of the Auslander-Reiten quiver.
|
2208.02445v1
|
2022-09-09
|
Magnetization dynamics and reversal of two-dimensional magnets
|
Micromagnetics simulation based on the classical Landau-Lifshitz-Gilbert
(LLG) equation has long been a powerful method for modeling magnetization
dynamics and reversal of three-dimensional (3D) magnets. For two-dimensional
(2D) magnets, the magnetization reversal always accompanies the collapse of the
magnetization even at low temperatures due to intrinsic strong spin
fluctuation. We propose a micromagnetic theory that explicitly takes into
account the rapid demagnetization and remagnetization dynamics of 2D magnets
during magnetization reversal. We apply the theory to a single-domain magnet to
illustrate fundamental differences in magnetization trajectories and reversal
times for 2D and 3D magnets.
|
2209.04483v1
|
2022-11-06
|
Two-Qutrit entanglement: 56-years old algorithm challenges machine learning
|
Classifying states as entangled or separable is a highly challenging task,
while it is also one of the foundations of quantum information processing
theory. This task is higly nontrivial even for relatively simple cases, such as
two-qutrit Bell-diagonal states, i.e., mixture of nine mutually orthogonal
maximally entangled states. In this article we apply the Gilbert algorithm to
revise previously obtained results for this class. In particular we use
``cartography of entanglement'' to argue that most states left in [Hiesmayr, B.
C. {\em Scientific Reports} {\bf 11}, 19739 (2021)] as unknown to be entangled
or separable are most likely indeed separable, or very weakly entangled. The
presented technique can find endless applications in more general cases.
|
2211.03213v1
|
2022-12-07
|
Quantitative CLTs on the Poisson space via Skorohod estimates and $p$-Poincaré inequalities
|
We establish new explicit bounds on the Gaussian approximation of Poisson
functionals based on novel estimates of moments of Skorohod integrals.
Combining these with the Malliavin-Stein method, we derive bounds in the
Wasserstein and Kolmogorov distances whose application requires minimal moment
assumptions on add-one cost operators $\unicode{x2014}$ thereby extending the
results from (Last, Peccati and Schulte, 2016). Our applications include a CLT
for the Online Nearest Neighbour graph, whose validity was conjectured in
(Wade, 2009; Penrose and Wade, 2009). We also apply our techniques to derive
quantitative CLTs for edge functionals of the Gilbert graph, of the $k$-Nearest
Neighbour graph and of the Radial Spanning Tree, both in cases where
qualitative CLTs are known and unknown.
|
2212.03782v1
|
2022-12-19
|
Bounds on Mixed Codes with Finite Alphabets
|
Mixed codes, which are error-correcting codes in the Cartesian product of
different-sized spaces, model degrading storage systems well. While such codes
have previously been studied for their algebraic properties (e.g., existence of
perfect codes) or in the case of unbounded alphabet sizes, we focus on the case
of finite alphabets, and generalize the Gilbert-Varshamov, sphere-packing,
Elias-Bassalygo, and first linear programming bounds to that setting. In the
latter case, our proof is also the first for the non-symmetric mono-alphabetic
$q$-ary case using Navon and Samorodnitsky's Fourier-analytic approach.
|
2212.09314v1
|
2023-02-17
|
Codes Correcting Burst and Arbitrary Erasures for Reliable and Low-Latency Communication
|
Motivated by modern network communication applications which require low
latency, we study codes that correct erasures with low decoding delay. We
provide a simple explicit construction that yields convolutional codes that can
correct both burst and arbitrary erasures under a maximum decoding delay
constraint $T$. Our proposed code has efficient encoding/decoding algorithms
and requires a field size that is linear in $T$. We study the performance of
our code over the Gilbert-Elliot channel; our simulation results show
significant performance gains over low-delay codes existing in the literature.
|
2302.08644v1
|
2023-03-10
|
On the coherence of one-relator groups and their group algebras
|
We prove that one-relator groups are coherent, solving a well-known problem
of Gilbert Baumslag. Our proof strategy is readily applicable to many classes
of groups of cohomological dimension two. We show that fundamental groups of
two-complexes with non-positive immersions are homologically coherent, we show
that groups with staggered presentations and many Coxeter groups are coherent
and we show that group algebras over fields of characteristic zero of groups
with reducible presentations without proper powers are coherent.
|
2303.05976v3
|
2023-03-15
|
Algebraic Geometry codes in the sum-rank metric
|
We introduce the first geometric construction of codes in the sum-rank
metric, which we called linearized Algebraic Geometry codes, using quotients of
the ring of Ore polynomials with coefficients in the function field of an
algebraic curve. We study the parameters of these codes and give lower bounds
for their dimension and minimum distance. Our codes exhibit quite good
parameters, respecting a similar bound to Goppa's bound for Algebraic Geometry
codes in the Hamming metric. Furthermore, our construction yields codes
asymptotically better than the sum-rank version of the Gilbert-Varshamov bound.
|
2303.08903v2
|
2023-05-11
|
Linear Codes with Prescribed Hull Dimension and Minimum Distance
|
The hull of a linear code (i.e., a finite field vector space)~\({\mathcal
C}\) is defined to be the vector space formed by the intersection
of~\({\mathcal C}\) with its dual~\({\mathcal C}^{\perp}.\) Constructing vector
spaces with a specified hull dimension has important applications and it is
therefore of interest to study minimum distance properties of such spaces. In
this paper, we use the probabilistic method to obtain spaces with a given hull
dimension and minimum distance and also derive Gilbert-Varshamov type
sufficient conditions for their existence.
|
2305.07140v1
|
2023-05-18
|
Bounds on Size of Homopolymer Free Codes
|
For any given alphabet of size $q$, a Homopolymer Free code (HF code) refers
to an $(n, M, d)_q$ code of length $n$, size $M$ and minimum Hamming distance
$d$, where all the codewords are homopolymer free sequences. For any given
alphabet, this work provides upper and lower bounds on the maximum size of any
HF code using Sphere Packing bound and Gilbert-Varshamov bound. Further, upper
and lower bounds on the maximum size of HF codes for various HF code families
are calculated. Also, as a specific case, upper and lower bounds are obtained
on the maximum size of homopolymer free DNA codes.
|
2305.10741v1
|
2023-05-31
|
Codes from Goppa codes
|
On a Goppa code whose structure polynomial has coefficients in the symbol
field, the Frobenius acts. Its fixed codewords form a subcode. Deleting the
naturally occurred redundance, we obtain a new code. It is proved that these
new codes approach the Gilbert-Varshamov bound. It is also proved that these
codes can be decoded within $O(n^2(\logn)^a)$ operations in the symbol field,
which is usually much small than the location field, where $n$ is the codeword
length, and $a$ a constant determined by the polynomial factorization
algorithm.
|
2305.19565v5
|
2023-06-08
|
A Macroscopic Theory of Saturated Ferromagnetic Conductors
|
A phenomenological theory of rigid and saturated ferromagnetic conductors is
constructed from a four-continuum model consisting of a rigid lattice
continuum, a bound charge continuum for polarization, a circulating current
continuum for magnetization, and a free charge continuum for electrical
conduction. The basic laws of physics are applied to the four continua. Thermal
couplings and the related dissipative effects are also included. The theory
includes the Landau-Lifshitz-Gilbert equation as one of a system of
simultaneous equations.
|
2306.11525v1
|
2023-07-02
|
Unveiling Stable One-dimensional Magnetic Solitons in Magnetic Bilayers
|
We propose a novel model which efficiently describes the magnetization
dynamics in a magnetic bilayer system. By applying a particular gauge
transformation to the Landau-Lifshitz-Gilbert (LLG) equation, we successfully
convert the model into an exactly integrable framework. Thus the obtained
analytical solutions allows us to predict a 1D magnetic soliton pair existed by
tunning the thickness of the spacing layer between the two ferrimagnetic
layers. The decoupling-unlocking-locking transition of soliton motion is
determined at various interaction intensitiy. Our results have implications for
the manipulation of magnetic solitons and the design of magnetic soliton-based
logic devices.
|
2307.00471v1
|
2023-07-21
|
Thermomechanics of ferri-antiferromagnetic phase transition in finitely-strained rocks towards paleomagnetism
|
The thermodynamic model of visco-elastic deformable magnetic materials at
finite strains is formulated in a fully Eulerian way in rates with the aim to
describe thermoremanent paleomagnetism in crustal rocks. The Landau theory
applied to a ferro-to-para-magnetic phase transition, the gradient theory for
magnetization (leading to exchange energy) with general mechanically dependent
coefficient, hysteresis in magnetization evolution by Gilbert equation
involving objective corotational time derivative of magnetization, and
demagnetizing field are considered in the model. The Jeffreys viscoelastic
rheology is used with temperature-dependent creep to model solidification or
melting transition. The model complies with energy conservation and the
Clausius-Duhem entropy inequality.
|
2307.11826v2
|
2023-09-22
|
Characterizing Smooth Safety Filters via the Implicit Function Theorem
|
Optimization-based safety filters, such as control barrier function (CBF)
based quadratic programs (QPs), have demonstrated success in controlling
autonomous systems to achieve complex goals. These CBF-QPs can be shown to be
continuous, but are generally not smooth, let alone continuously
differentiable. In this paper, we present a general characterization of smooth
safety filters -- smooth controllers that guarantee safety in a minimally
invasive fashion -- based on the Implicit Function Theorem. This
characterization leads to families of smooth universal formulas for
safety-critical controllers that quantify the conservatism of the resulting
safety filter, the utility of which is demonstrated through illustrative
examples.
|
2309.12614v1
|
2023-09-23
|
Sphaleron rate from lattice QCD
|
We compute the sphaleron rate on the lattice from the inversion of the
Euclidean time correlators of the topological charge density, performing also
controlled continuum and zero-smoothing extrapolations. The correlator
inversion is performed by means of a recently-proposed modification of the
Backus-Gilbert method.
|
2309.13327v1
|
2023-09-23
|
CA-PCA: Manifold Dimension Estimation, Adapted for Curvature
|
The success of algorithms in the analysis of high-dimensional data is often
attributed to the manifold hypothesis, which supposes that this data lie on or
near a manifold of much lower dimension. It is often useful to determine or
estimate the dimension of this manifold before performing dimension reduction,
for instance. Existing methods for dimension estimation are calibrated using a
flat unit ball. In this paper, we develop CA-PCA, a version of local PCA based
instead on a calibration of a quadratic embedding, acknowledging the curvature
of the underlying manifold. Numerous careful experiments show that this
adaptation improves the estimator in a wide range of settings.
|
2309.13478v1
|
2023-11-13
|
Dedukti: a Logical Framework based on the $λ$$Π$-Calculus Modulo Theory
|
Dedukti is a Logical Framework based on the $\lambda$$\Pi$-Calculus Modulo
Theory. We show that many theories can be expressed in Dedukti: constructive
and classical predicate logic, Simple type theory, programming languages, Pure
type systems, the Calculus of inductive constructions with universes, etc. and
that permits to used it to check large libraries of proofs developed in other
proof systems: Zenon, iProver, FoCaLiZe, HOL Light, and Matita.
|
2311.07185v1
|
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