publicationDate stringlengths 1 2.79k | title stringlengths 1 36.5k ⌀ | abstract stringlengths 1 37.3k ⌀ | id stringlengths 9 47 |
|---|---|---|---|
2011-10-27 | George Augustus Linhart - as a "widely unknown" thermodynamicist | The name of George Augustus Linhart is in fact "widely unknown". In effect,
he was a Viennese-born USA-American physicist-chemist, partially associated
with the Gilbert Newton Lewis' school of thermodynamics at the University of
California in Berkeley. As a lone small boy, he had arrived (from Austria via
Hamburg) at New York in 1896, but was officially USA-naturalized only in 1912.
He was able to pick up English in the streets of New York and Philadelphia,
when occasionally working as a waiter and/or as a tailor - just to somehow
survive. But, nonetheless, he could successfully graduate a high school in
about one year - and then went to the universities for his further education.
After obtaining his BS from the University of Pennsylvania, he could manage
getting both MA and then PhD from the Yale University, Kent Chemical
Laboratory. George Augustus Linhart was afterwards definitely able to
successfully work out the true foundations of thermodynamics and could thus
outdistance many famous thermodynamicists of his time and even the later ones.
Linhart's view of the Second Law of Thermodynamics was and is extremely
fruitful. The interconnection of Linhart's ideas with those of Gilbert Newton
Lewis, as well as with the modern standpoints are discussed here in detail. | 1110.6352v1 |
2012-03-29 | Power Allocation over Two Identical Gilbert-Elliott Channels | We study the problem of power allocation over two identical Gilbert-Elliot
communication channels. Our goal is to maximize the expected discounted number
of bits transmitted over an infinite time horizon. This is achieved by choosing
among three possible strategies: (1) betting on channel 1 by allocating all the
power to this channel, which results in high data rate if channel 1 happens to
be in good state, and zero bits transmitted if channel 1 is in bad state (even
if channel 2 is in good state) (2) betting on channel 2 by allocating all the
power to the second channel, and (3) a balanced strategy whereby each channel
is allocated half the total power, with the effect that each channel can
transmit a low data rate if it is in good state. We assume that each channel's
state is only revealed upon transmission of data on that channel. We model this
problem as a partially observable Markov decision processes (MDP), and derive
key threshold properties of the optimal policy. Further, we show that by
formulating and solving a relevant linear program the thresholds can be
determined numerically when system parameters are known. | 1203.6630v2 |
2012-04-11 | A short note on spin pumping theory with Landau-Lifshitz-Gilbert equation under quantum fluctuation; necessity for quantization of localized spin | We would like to point out the blind spots of the approach combining the spin
pumping theory proposed by Tserkovnyak et al. with the Landau-Lifshitz-Gilbert
equation; this method has been widely used for interpreting vast experimental
results. The essence of the spin pumping effect is the quantum fluctuation.
Thus, localized spin degrees of freedom should be quantized, i.e. be treated as
magnons not as classical variables. Consequently, the precessing ferromagnet
can be regarded as a magnon battery. This point of view will be useful for
further progress of spintronics. | 1204.2339v1 |
2012-05-22 | Signature of Phase Transitions in the Disordered Quantum Spin Hall State From the Entanglement Spectrum | Of the available classes of insulators which have been shown to contain
topologically non-trivial properties one of the most important is class AII,
which contains systems that possess time-reversal symmetry $T$ with $T^2=-1.$
This class has been the subject of significant attention as it encompasses
non-trivial Z$_2$ topological insulators such as the quantum spin Hall (QSH)
state and the 3D strong topological insulator. One of the defining properties
of this system is the robustness of the state under the addition of disorder
that preserves $T.$ In this letter, we explore the phase diagram of the
disordered QSH state as a function of disorder strength and chemical potential
by examining the entanglement spectrum for disordered class AII symplectic
systems. As for the case of the $T$ breaking Chern insulator we show that there
is a correspondence between the level-spacing statistics of the Hamiltonian and
that of the level spacing statistics of the entanglement spectrum. We observe a
feature in the statistics of the entanglement spectrum that aids the
identification of delocalized states and consequently critical energies across
which phase transitions occur. | 1205.5071v1 |
2012-07-03 | The unusual smoothness of the extragalactic unresolved radio background | If the radio background is coming from cosmological sources, there should be
some amount of clustering due to the large scale structure in the universe.
Simple models for the expected clustering combined with the recent measurement
by ARCADE-2 of the mean extragalactic temperature lead to predicted clustering
levels that are substantially above upper limits from searches for anisotropy
on arcminute scales using ATCA and the VLA. The rms temperature variations in
the cosmic radio background appear to be more than a factor of 10 smaller (in
temperature) than the fluctuations in the cosmic infrared background. It is
therefore extremely unlikely that this background comes from galaxies, galaxy
clusters, or any sources that trace dark matter halos at z<5, unless typical
sources are smooth on arcminute scales, requiring typical sizes of several Mpc. | 1207.0856v1 |
2012-10-12 | Optimal Power Allocation Policy over Two Identical Gilbert-Elliott Channels | We study the fundamental problem of optimal power allocation over two
identical Gilbert-Elliott (Binary Markov) communication channels. Our goal is
to maximize the expected discounted number of bits transmitted over an infinite
time span by judiciously choosing one of the four actions for each time slot:
1) allocating power equally to both channels, 2) allocating all the power to
channel 1, 3) allocating all the power to channel 2, and 4) allocating no power
to any of the channels. As the channel state is unknown when power allocation
decision is made, we model this problem as a partially observable Markov
decision process(POMDP), and derive the optimal policy which gives the optimal
action to take under different possible channel states. Two different
structures of the optimal policy are derived analytically and verified by
linear programming simulation. We also illustrate how to construct the optimal
policy by the combination of threshold calculation and linear programming
simulation once system parameters are known. | 1210.3609v1 |
2013-03-16 | A convergent linear finite element scheme for the Maxwell-Landau-Lifshitz-Gilbert equation | We consider a lowest-order finite element discretization of the nonlinear
system of Maxwell's and Landau-Lifshitz-Gilbert equations (MLLG). Two
algorithms are proposed to numerically solve this problem, both of which only
require the solution of at most two linear systems per timestep. One of the
algorithms is fully decoupled in the sense that each timestep consists of the
sequential computation of the magnetization and afterwards the magnetic and
electric field. Under some mild assumptions on the effective field, we show
that both algorithms converge towards weak solutions of the MLLG system.
Numerical experiments for a micromagnetic benchmark problem demonstrate the
performance of the proposed algorithms. | 1303.4009v1 |
2013-03-17 | On the Landau-Lifshitz-Gilbert equation with magnetostriction | To describe and simulate dynamic micromagnetic phenomena, we consider a
coupled system of the nonlinear Landau-Lifshitz-Gilbert equation and the
conservation of momentum equation. This coupling allows to include
magnetostrictive effects into the simulations. Existence of weak solutions has
recently been shown in [Carbout et al. 2011]. In our contribution, we give an
alternate proof which additionally provides an effective numerical integrator.
The latter is based on lowest-order finite elements in space and a
linear-implicit Euler time-stepping. Despite the nonlinearity, only two linear
systems have to be solved per timestep, and the integrator fully decouples both
equations. Finally, we prove unconditional convergence---at least of a
subsequence---towards, and hence existence of, a weak solution of the coupled
system, as timestep size and spatial mesh-size tend to zero. Numerical
experiments conclude the work and shed new light on the existence of blow-up in
micromagnetic simulations. | 1303.4060v2 |
2013-03-27 | Optimal Power Allocation over Multiple Identical Gilbert-Elliott Channels | We study the fundamental problem of power allocation over multiple
Gilbert-Elliott communication channels. In a communication system with time
varying channel qualities, it is important to allocate the limited transmission
power to channels that will be in good state. However, it is very challenging
to do so because channel states are usually unknown when the power allocation
decision is made. In this paper, we derive an optimal power allocation policy
that can maximize the expected discounted number of bits transmitted over an
infinite time span by allocating the transmission power only to those channels
that are believed to be good in the coming time slot. We use the concept belief
to represent the probability that a channel will be good and derive an optimal
power allocation policy that establishes a mapping from the channel belief to
an allocation decision.
Specifically, we first model this problem as a partially observable Markov
decision processes (POMDP), and analytically investigate the structure of the
optimal policy. Then a simple threshold-based policy is derived for a
three-channel communication system. By formulating and solving a linear
programming formulation of this power allocation problem, we further verified
the derived structure of the optimal policy. | 1303.6771v1 |
2013-04-29 | Generalized Baumslag-Solitar groups: rank and finite index subgroups | A generalized Baumslag-Solitar (GBS) group is a finitely generated group
acting on a tree with infinite cyclic edge and vertex stabilizers. We show how
to determine effectively the rank (minimal cardinality of a generating set) of
a GBS group; as a consequence, one can compute the rank of the mapping torus of
a finite order outer automorphism of a free group $F_n$. We also show that the
rank of a finite index subgroup of a GBS group G cannot be smaller than the
rank of G. We determine which GBS groups are large (some finite index subgroup
maps onto $F_2$), and we solve the commensurability problem (deciding whether
two groups have isomorphic finite index subgroups) in a particular family of
GBS groups. | 1304.7582v2 |
2013-06-02 | On the Riemannian Penrose inequality with charge and the cosmic censorship conjecture | We note an area-charge inequality orignially due to Gibbons: if the outermost
horizon $S$ in an asymptotically flat electrovacuum initial data set is
connected then $|q|\leq r$, where $q$ is the total charge and $r=\sqrt{A/4\pi}$
is the area radius of $S$. A consequence of this inequality is that for
connected black holes the following lower bound on the area holds: $r\geq
m-\sqrt{m^2-q^2}$. In conjunction with the upper bound $r\leq m +
\sqrt{m^2-q^2}$ which is expected to hold always, this implies the natural
generalization of the Riemannian Penrose inequality: $m\geq 1/2(r+q^2/r)$. | 1306.0206v3 |
2013-08-19 | A finite element approximation for the stochastic Landau-Lifshitz-Gilbert equation | The stochastic Landau--Lifshitz--Gilbert (LLG) equation describes the
behaviour of the magnetization under the influence of the effective field
consisting of random fluctuations. We first reformulate the equation into an
equation the unknown of which is differentiable with respect to the time
variable. We then propose a convergent $\theta$-linear scheme for the numerical
solution of the reformulated equation. As a consequence, we show the existence
of weak martingale solutions to the stochastic LLG equation. A salient feature
of this scheme is that it does not involve a nonlinear system, and that no
condition on time and space steps is required when $\theta\in(\frac{1}{2},1]$.
Numerical results are presented to show the applicability of the method. | 1308.3912v2 |
2014-01-14 | Constructions of Pure Asymmetric Quantum Alternant Codes Based on Subclasses of Alternant Codes | In this paper, we construct asymmetric quantum error-correcting codes(AQCs)
based on subclasses of Alternant codes. Firstly, We propose a new subclass of
Alternant codes which can attain the classical Gilbert-Varshamov bound to
construct AQCs. It is shown that when $d_x=2$, $Z$-parts of the AQCs can attain
the classical Gilbert-Varshamov bound. Then we construct AQCs based on a famous
subclass of Alternant codes called Goppa codes. As an illustrative example, we
get three $[[55,6,19/4]],[[55,10,19/3]],[[55,15,19/2]]$ AQCs from the well
known $[55,16,19]$ binary Goppa code. At last, we get asymptotically good
binary expansions of asymmetric quantum GRS codes, which are quantum
generalizations of Retter's classical results. All the AQCs constructed in this
paper are pure. | 1401.3215v2 |
2014-03-19 | Numerical integration of the stochastic Landau-Lifshitz-Gilbert equation in generic time-discretisation schemes | We introduce a numerical method to integrate the stochastic
Landau-Lifshitz-Gilbert equation in spherical coordinates for generic
discretization schemes. This method conserves the magnetization modulus and
ensures the approach to equilibrium under the expected conditions. We test the
algorithm on a benchmark problem: the dynamics of a uniformly magnetized
ellipsoid. We investigate the influence of various parameters, and in
particular, we analyze the efficiency of the numerical integration, in terms of
the number of steps needed to reach a chosen long time with a given accuracy. | 1403.4822v2 |
2014-05-05 | Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards | We perform numerical measurements of the moments of the position of a tracer
particle in a two-dimensional periodic billiard model (Lorentz gas) with
infinite corridors. This model is known to exhibit a weak form of
super-diffusion, in the sense that there is a logarithmic correction to the
linear growth in time of the mean-squared displacement. We show numerically
that this expected asymptotic behavior is easily overwhelmed by the subleading
linear growth throughout the time-range accessible to numerical simulations. We
compare our simulations to the known analytical results for the variance of the
anomalously-rescaled limiting normal distributions. | 1405.0975v2 |
2014-05-12 | Efficient Energy-minimization in Finite-Difference Micromagnetics: Speeding up Hysteresis Computations | We implement an efficient energy-minimization algorithm for finite-difference
micromagnetics that proofs especially useful for the computation of hysteresis
loops. Compared to results obtained by time integration of the
Landau-Lifshitz-Gilbert equation, a speedup of up to two orders of magnitude is
gained. The method is implemented in a finite-difference code running on CPUs
as well as GPUs. This setup enables us to compute accurate hysteresis loops of
large systems with a reasonable computational effort. As a benchmark we solve
the {\mu}Mag Standard Problem #1 with a high spatial resolution and compare the
results to the solution of the Landau-Lifshitz-Gilbert equation in terms of
accuracy and computing time. | 1405.2728v3 |
2014-07-26 | Magnetization reversal condition for a nanomagnet within a rotating magnetic field | The reversal condition of magnetization in a nanomagnet under the effect of
rotating magnetic field generated by a microwave is theoretically studied based
on the Landau-Lifshitz-Gilbert equation. In a rotating frame, the microwave
produces a dc magnetic field pointing in the reversed direction, which
energetically stabilizes the reversed state. We find that the microwave
simultaneously produces a torque preventing the reversal. It is pointed out
that this torque leads to a jump in the reversal field with respect to the
frequency. We derive the equations determining the reversal fields in both the
low- and high-frequency regions from the energy balance equation. The
validities of the formulas are confirmed by a comparison with the numerical
simulation of the Landau-Lifshitz-Gilbert equation. | 1407.7095v1 |
2014-09-17 | Aharonov-Bohm Oscillations in a Quasi-Ballistic 3D Topological Insulator Nanowire | In three-dimensional topological insulators (3D TI) nanowires, transport
occurs via gapless surface states where the spin is fixed perpendicular to the
momentum[1-6]. Carriers encircling the surface thus acquire a \pi Berry phase,
which is predicted to open up a gap in the lowest-energy 1D surface subband.
Inserting a magnetic flux ({\Phi}) of h/2e through the nanowire should cancel
the Berry phase and restore the gapless 1D mode[7-8]. However, this signature
has been missing in transport experiments reported to date[9-11]. Here, we
report measurements of mechanically-exfoliated 3D TI nanowires which exhibit
Aharonov-Bohm oscillations consistent with topological surface transport. The
use of low-doped, quasi-ballistic devices allows us to observe a minimum
conductance at {\Phi} = 0 and a maximum conductance reaching e^2/h at {\Phi} =
h/2e near the lowest subband (i.e. the Dirac point), as well as the carrier
density dependence of the transport. | 1409.5095v1 |
2014-10-13 | [$α$/Fe] Abundances of Four Outer M 31 Halo Stars | We present alpha element to iron abundance ratios, [$\alpha$/Fe], for four
stars in the outer stellar halo of the Andromeda Galaxy (M 31). The stars were
identified as high-likelihood field halo stars by Gilbert et al. (2012) and lie
at projected distances between 70 and 140 kpc from M 31's center. These are the
first alpha abundances measured for a halo star in a galaxy beyond the Milky
Way. The stars range in metallicity between [Fe/H]= -2.2 and [Fe/H]= -1.4. The
sample's average [$\alpha$/Fe] ratio is +0.20+/-0.20. The best-fit average
value is elevated above solar which is consistent with rapid chemical
enrichment from Type II supernovae. The mean [$\alpha$/Fe] ratio of our M31
outer halo sample agrees (within the uncertainties) with that of Milky Way
inner/outer halo stars that have a comparable range of [Fe/H]. | 1410.3475v1 |
2014-11-05 | Kalman Filtering over Gilbert-Elliott Channels: Stability Conditions and the Critical Curve | This paper investigates the stability of Kalman filtering over
Gilbert-Elliott channels where random packet drop follows a time-homogeneous
two-state Markov chain whose state transition is determined by a pair of
failure and recovery rates. First of all, we establish a relaxed condition
guaranteeing peak-covariance stability described by an inequality in terms of
the spectral radius of the system matrix and transition probabilities of the
Markov chain. We further show that that condition can be interpreted using a
linear matrix inequality feasibility problem. Next, we prove that the
peak-covariance stability implies mean-square stability, if the system matrix
has no defective eigenvalues on the unit circle. This connection between the
two stability notions holds for any random packet drop process. We prove that
there exists a critical curve in the failure-recovery rate plane, below which
the Kalman filter is mean-square stable and no longer mean-square stable above,
via a coupling method in stochastic processes. Finally, a lower bound for this
critical failure rate is obtained making use of the relationship we establish
between the two stability criteria, based on an approximate relaxation of the
system matrix. | 1411.1217v1 |
2015-03-02 | An Anisotropic Landau-Lifschitz-Gilbert model of dissipation in qubits | We derive a microscopic model for dissipative dynamics in a system of
mutually interacting qubits coupled to a thermal bath that generalises the
dissipative model of Landau-Lifschitz-Gilbert to the case of anisotropic bath
couplings. We show that the dissipation acts to bias the quantum trajectories
towards a reduced phase space. This model applies to a system of
superconducting flux qubits whose coupling to the environment is necessarily
anisotropic. We study the model in the context of the D-Wave computing device
and show that the form of environmental coupling in this case produces dynamics
that are closely related to several models proposed on phenomenological
grounds. | 1503.00651v2 |
2015-03-25 | Optimising the neutron environment of Radiation Portal Monitors: a computational optimisation study | Efficient and reliable detection of radiological or nuclear threats is a
crucial part of national and international efforts to prevent terrorist
activities. Radiation Portal Monitors (RPMs), which are deployed worldwide, are
intended to interdict smuggled fissile material by detecting emissions of
neutrons and gamma rays. However, considering the range and variety of threat
sources, vehicular and shielding scenarios, and that only a small signature is
present, it is important that the design of the RPMs allows these signatures to
be accurately differentiated from the environmental background. Using
Monte-Carlo neutron-transport simulations of a model helium-3 detector system
we have conducted a parameter study to identify the optimum combination of
detector shielding and collimation that maximises the sensitivity of RPMs.
These structures, which could be simply and cost-effectively added to existing
RPMs, can improve the detector response by more than a factor of two relative
to an unmodified, bare design. Furthermore, optimisation of the air gap
surrounding the helium tubes also improves detector efficiency. | 1503.07346v1 |
2015-06-29 | Energy spectra of primary knock-on atoms under neutron irradiation | Materials subjected to neutron irradiation will suffer from a build-up of
damage caused by the displacement cascades initiated by nuclear reactions.
Previously, the main "measure" of this damage accumulation has been through the
displacements per atom (dpa) index. There are known limitations associated with
the dpa quantity and its domain of application and therefore this paper
describes a more rigorous methodology to calculate the primary atomic recoil
events (often called the primary knock-on atoms or PKAs) that lead to cascade
damage events as a function of energy and recoiling species for any simulated
or measured neutron irradiation scenario. Via examples of fusion relevant
materials, it is shown that the PKA spectra can be complex, involving many
different recoiling species, potentially differing in both proton and neutron
number from the original target nuclei, including high energy recoils of light
emitted particles such as alpha-particles and protons. The variations in PKA
spectra as a function of time, neutron field, and material are explored.
Example PKA spectra are applied to radiation damage quantification using the
binary collision approximation and stochastic cluster dynamics, and the results
from these different approaches are discussed and compared. | 1506.08554v1 |
2015-08-25 | Direct Visualization of Memory Effects in Artificial Spin Ice | We experimentally demonstrate that arrays of interacting nanoscale
ferromagnetic islands, known as artificial spin ice, develop reproducible
microstates upon cycling an applied magnetic field. The onset of this memory
effect is determined by the strength of the applied field relative to the array
coercivity. Specifically, when the applied field strength is almost exactly
equal to the array coercivity, several training cycles are required before the
array achieves a nearly completely repeatable microstate, whereas when the
applied field strength is stronger or weaker than the array coercivity, a
repeatable microstate is achieved after the first minor loop. We show through
experiment and simulation that this memory exhibited by artificial spin ice is
due to a ratchet effect on interacting, magnetically-charged defects in the
island moment configuration and to the complexity of the network of strings of
reversed moments that forms during magnetization reversal. | 1508.06330v1 |
2015-10-21 | On the limiting Markov process of energy exchanges in a rarely interacting ball-piston gas | We analyse the process of energy exchanges generated by the elastic
collisions between a point-particle, confined to a two-dimensional cell with
convex boundaries, and a `piston', i.e. a line-segment, which moves back and
forth along a one-dimensional interval partially intersecting the cell. This
model can be considered as the elementary building block of a spatially
extended high-dimensional billiard modeling heat transport in a class of hybrid
materials exhibiting the kinetics of gases and spatial structure of solids.
Using heuristic arguments and numerical analysis, we argue that, in a regime of
rare interactions, the billiard process converges to a Markov jump process for
the energy exchanges and obtain the expression of its generator. | 1510.06408v2 |
2015-10-29 | Deligne--Langlands gamma factors in families | Let F be a p-adic field, W_F its absolute Weil group, and let k be an
algebraically closed field of prime characteristic l different from p. Attached
to any l-adic representation of W_F are local epsilon- and L-factors. There are
natural notions of families of l-adic representations of W_F, such as the
theory of Galois deformations or, more generally, families over arbitrary
Noetherian W(k)-algebras. However, the epsilon and L-factors do not interpolate
well in such families. In this paper it is shown that the gamma factor, which
is the product of the epsilon factor with a ratio of L-factors, interpolates
over such families. | 1510.08743v3 |
2015-11-01 | Verification of commercial motor performance for WEAVE at the William Herschel Telescope | WEAVE is a 1000-fiber multi-object spectroscopic facility for the 4.2~m
William Herschel Telescope. It will feature a double-headed pick-and-place
fiber positioning robot comprising commercially available robotic axes. This
paper presents results on the performance of these axes, obtained by testing a
prototype system in the laboratory. Positioning accuracy is found to be better
than the manufacturer's published values for the tested cases, indicating that
the requirement for a maximum positioning error of 8.0~microns is achievable.
Field reconfiguration times well within the planned 60 minute observation
window are shown to be likely when individual axis movements are combined in an
efficient way. | 1511.00202v1 |
2015-11-02 | Learning from history: Adaptive calibration of 'tilting spine' fiber positioners | This paper discusses a new approach for determining the calibration
parameters of independently-actuated optical fibers in multi-object
astronomical fiber positioning systems. This work comes from the development of
a new type of piezoelectric motor intended to enhance the 'tilting spine' fiber
positioning technology originally created by the Australian Astronomical
Observatory. Testing has shown that the motor's performance can vary depending
on the fiber's location within its accessible field, meaning that an individual
fiber is difficult calibrate with a one-time routine. Better performance has
resulted from constantly updating calibration parameters based on the observed
movements of the fiber during normal closed-loop positioning. Over time,
location-specific historical data is amassed that can be used to better predict
the results of a future fiber movement. This is similar to a technique
previously proposed by the Australian Astronomical Observatory, but with the
addition of location-specific learning. Results from a prototype system are
presented, showing a significant reduction in overall positioning error when
using this new approach. | 1511.00737v1 |
2016-06-23 | Echidna Mark II: one giant leap for 'tilting spine' fibre positioning technology | The Australian Astronomical Observatory's 'tilting spine' fibre positioning
technology has been redeveloped to provide superior performance in a smaller
package. The new design offers demonstrated closed-loop positioning errors of
2.8 {\mu}m RMS in only five moves (~10 s excluding metrology overheads) and an
improved capacity for open-loop tracking during observations. Tilt-induced
throughput losses have been halved by lengthening spines while maintaining
excellent accuracy. New low-voltage multilayer piezo actuator technology has
reduced a spine's peak drive amplitude from ~150 V to <10 V, simplifying the
control electronics design, reducing the system's overall size, and improving
modularity. Every spine is now a truly independent unit with a dedicated drive
circuit and no restrictions on the timing or direction of fibre motion. | 1606.07305v1 |
2016-08-15 | Inverse subsemigroups of finite index in finitely generated inverse semigroups | The index of a subgroup of a group counts the number of cosets of that
subgroup. A subgroup of finite index often shares structural properties with
the group, and the existence of a subgroup of finite index with some particular
property can therefore imply useful structural information for the overgroup. A
developed theory of cosets in inverse semigroups exists, originally due to
Schein: it is defined only for closed inverse subsemigroups, and the structural
correspondences between an inverse semigroup and a closed inverse subsemigroup
of finite index are weaker than in the group case. Nevertheless, many aspects
of this theory are of interest, and some of them are addressed in this paper.
We study the basic theory of cosets in inverse semigroups, including an index
formula for chains of subgroups and an analogue of M. Hall's Theorem on
counting subgroups of finite index in finitely generated groups. We then look
in detail at the connection between the following properties of a closed
inverse submonoid of an inverse monoid: having finite index; being a
recognisable subset; being a rational subset; being finitely generated (as a
closed inverse submonoid). A remarkable result of Margolis and Meakin shows
that these properties are equivalent for closed inverse submonoids of free
inverse monoids. | 1608.04254v1 |
2016-10-03 | Magnetic microscopy and simulation of strain-mediated control of magnetization in Ni/PMN-PT nanostructures | Strain-mediated thin film multiferroics comprising
piezoelectric/ferromagnetic heterostructures enable the electrical manipulation
of magnetization with much greater efficiency than other methods; however, the
investigation of nanostructures fabricated from these materials is limited.
Here we characterize ferromagnetic Ni nanostructures grown on a ferroelectric
PMN-PT substrate using scanning electron microscopy with polarization analysis
(SEMPA) and micromagnetic simulations. The magnetization of the Ni
nanostructures can be controlled with a combination of sample geometry and
applied electric field, which strains the ferroelectric substrate and changes
the magnetization via magnetoelastic coupling. We evaluate two types of
simulations of ferromagnetic nanostructures on strained ferroelectric
substrates: conventional micromagnetic simulations including a simple uniaxial
strain, and coupled micromagnetic-elastodynamic simulations. Both simulations
qualitatively capture the response of the magnetization changes produced by the
applied strain, with the coupled solution providing more accurate
representation. | 1610.00746v1 |
2016-10-17 | Formalising Real Numbers in Homotopy Type Theory | Cauchy reals can be defined as a quotient of Cauchy sequences of rationals.
The limit of a Cauchy sequence of Cauchy reals is defined through lifting it to
a sequence of Cauchy sequences of rationals. This lifting requires the axiom of
countable choice or excluded middle, neither of which is available in homotopy
type theory. To address this, the Univalent Foundations Program uses a higher
inductive-inductive type to define the Cauchy reals as the free Cauchy complete
metric space generated by the rationals. We generalize this construction to
define the free Cauchy complete metric space generated by an arbitrary metric
space. This forms a monad in the category of metric spaces with Lipschitz
functions. When applied to the rationals it defines the Cauchy reals. Finally,
we can use Altenkirch and Danielson (2016)'s partiality monad to define a
semi-decision procedure comparing a real number and a rational number.
The entire construction has been formalized in the Coq proof assistant. It is
available at https://github.com/SkySkimmer/HoTTClasses/tree/CPP2017 . | 1610.05072v2 |
2016-11-04 | The flow and evolution of ice-sucrose crystal mushes | We study the rheology of suspensions of ice crystals at moderate to high
volume fractions in a sucrose solution in which they are partially soluble; a
model system for a wide class of crystal mushes or slurries. Under step changes
in shear rate, the viscosity changes to a new `relaxed' value over several
minutes, in a manner well fitted by a single exponential. The behavior of the
relaxed viscosity is power-law shear thinning with shear rate, with an exponent
of $-1.76 \pm 0.25$, so that shear stress falls with increasing shear rate. On
longer timescales, the crystals ripen (leading to a falling viscosity) so that
the mean radius increases with time to the power $0.14 \pm 0.07$. We speculate
that this unusually small exponent is due to the interaction of classical
ripening dynamics with abrasion or breakup under flow. We compare the
rheological behavior to mechanistic models based on flow-induced aggregation
and breakup of crystal clusters, finding that the exponents can be predicted
from liquid phase sintering and breakup by brittle fracture. | 1611.01365v1 |
2016-11-08 | Convergence of an implicit-explicit midpoint scheme for computational micromagnetics | Based on lowest-order finite elements in space, we consider the numerical
integration of the Landau-Lifschitz-Gilbert equation (LLG). The dynamics of LLG
is driven by the so-called effective field which usually consists of the
exchange field, the external field, and lower-order contributions such as the
stray field. The latter requires the solution of an additional partial
differential equation in full space. Following Bartels and Prohl (2006)
(Convergence of an implicit finite element method for the
Landau-Lifschitz-Gilbert equation. SIAM J. Numer. Anal. 44), we employ the
implicit midpoint rule to treat the exchange field. However, in order to treat
the lower-order terms effectively, we combine the midpoint rule with an
explicit Adams-Bashforth scheme. The resulting integrator is formally of
second-order in time, and we prove unconditional convergence towards a weak
solution of LLG. Numerical experiments underpin the theoretical findings. | 1611.02465v2 |
2016-11-17 | Dynamical contribution to the heat conductivity in stochastic energy exchanges of locally confined gases | We present a systematic computation of the heat conductivity of the Markov
jump process modeling the energy exchanges in an array of locally confined hard
spheres at the conduction threshold. Based on a variational formula [Sasada M.
2016, {\it Thermal conductivity for stochastic energy exchange models},
arXiv:1611.08866], explicit upper bounds on the conductivity are derived, which
exhibit a rapid power-law convergence towards an asymptotic value. We thereby
conclude that the ratio of the heat conductivity to the energy exchange
frequency deviates from its static contribution by a small negative correction,
its dynamic contribution, evaluated to be $-0.000\,373$ in dimensionless units.
This prediction is corroborated by kinetic Monte Carlo simulations which were
substantially improved compared to earlier results. | 1611.05809v3 |
2016-11-27 | Thermal conductivity for stochastic energy exchange models | We consider a class of stochastic models for energy transport and study
relations between the thermal conductivity and some static observables, such as
the static conductivity, which is defined as the contribution of static
correlations in Green-Kubo formula. The class of models is a generalization of
two specific models derived by Gaspard and Gilbert as mesoscopic dynamics of
energies for two-dimensional and three-dimensional locally confined hard-discs.
They claim some equalities hold between the thermal conductivity and several
static observables and also conjecture that these equations are universal in
the sense that they hold for mesoscopic dynamics of energies for confined
particles interacting through hard-core collisions. In this paper, we give
sufficient and necessary conditions for these equalities to hold in the class
we introduce. In particular, we prove that the equality between the thermal
conductivity and other static observables holds if and only if the model obeys
the gradient condition. Since the gradient condition does not hold for models
derived by Gaspard and Gilbert, our result implies a part of their claim is
incorrect. | 1611.08866v1 |
2016-12-07 | Spatial heterogeneity of W transmutation in a fusion device | Accurately quantifying the transmutation rate of tungsten (W) under neutron
irradiation is a necessary requirement in the assessment of its performance as
an armour material in a fusion power plant. The usual approach of calculating
average responses, assuming large, homogenised material volumes, is
insufficient to capture the full complexity of the transmutation picture in the
context of a realistic fusion power plant design, particularly for rhenium (Re)
production from W. Combined neutron transport and inventory simulations for
representative {\it spatially heterogeneous} models of a fusion power plant
show that the production rate of Re is strongly influenced by the local spatial
environment. Localised variation in neutron moderation (slowing down) due to
structural steel and coolant, particularly water, can dramatically increase Re
production because of the huge cross sections of giant resolved resonances in
the neutron-capture reaction of \(^{186}\)W at low neutron energies.
Calculations using cross section data corrected for temperature (Doppler)
effects suggest that temperature may have a relatively lesser influence on
transmutation rates. | 1612.03892v1 |
2017-01-20 | Structure of optimal strategies for remote estimation over Gilbert-Elliott channel with feedback | We investigate remote estimation over a Gilbert-Elliot channel with feedback.
We assume that the channel state is observed by the receiver and fed back to
the transmitter with one unit delay. In addition, the transmitter gets ACK/NACK
feedback for successful/unsuccessful transmission. Using ideas from team
theory, we establish the structure of optimal transmission and estimation
strategies and identify a dynamic program to determine optimal strategies with
that structure. We then consider first-order autoregressive sources where the
noise process has unimodal and symmetric distribution. Using ideas from
majorization theory, we show that the optimal transmission strategy has a
threshold structure and the optimal estimation strategy is Kalman-like. | 1701.05943v1 |
2017-02-04 | Fabrication of Atomically Precise Nanopores in Hexagonal Boron Nitride | We demonstrate the fabrication of individual nanopores in hexagonal boron
nitride (hBN) with atomically precise control of the pore size. Previous
methods of pore production in other 2D materials create pores of irregular
geometry with imprecise diameters. By taking advantage of the preferential
growth of boron vacancies in hBN under electron beam irradiation, we are able
to observe the pore growth via transmission electron microscopy, and terminate
the process when the pore has reached its desired size. Careful control of beam
conditions allows us to nucleate and grow individual triangular and hexagonal
pores with diameters ranging from subnanometer to 6nm over a large area of
suspended hBN using a conventional TEM. These nanopores could find application
in molecular sensing, DNA sequencing, water desalination, and molecular
separation. Furthermore, the chemical edge-groups along the hBN pores can be
made entirely nitrogen terminated or faceted with boron-terminated edges,
opening avenues for tailored functionalization and extending the applications
of these hBN nanopores. | 1702.01220v1 |
2017-02-10 | A finite element approximation for the stochastic Maxwell--Landau--Lifshitz--Gilbert system | The stochastic Landau--Lifshitz--Gilbert (LLG) equation coupled with the
Maxwell equations (the so called stochastic MLLG system) describes the creation
of domain walls and vortices (fundamental objects for the novel nanostructured
magnetic memories). We first reformulate the stochastic LLG equation into an
equation with time-differentiable solutions. We then propose a convergent
$\theta$-linear scheme to approximate the solutions of the reformulated system.
As a consequence, we prove convergence of the approximate solutions, with no or
minor conditions on time and space steps (depending on the value of $\theta$).
Hence, we prove the existence of weak martingale solutions of the stochastic
MLLG system. Numerical results are presented to show applicability of the
method. | 1702.03027v1 |
2017-03-07 | The extrapolated explicit midpoint scheme for variable order and step size controlled integration of the Landau-Lifschitz-Gilbert equation | A practical and efficient scheme for the higher order integration of the
Landau-Lifschitz-Gilbert (LLG) equation is presented. The method is based on
extrapolation of the two-step explicit midpoint rule and incorporates adaptive
time step and order selection. We make use of a piecewise time-linear stray
field approximation to reduce the necessary work per time step. The
approximation to the interpolated operator is embedded into the extrapolation
process to keep in step with the hierarchic order structure of the scheme. We
verify the approach by means of numerical experiments on a standardized NIST
problem and compare with a higher order embedded Runge-Kutta formula. The
efficiency of the presented approach increases when the stray field computation
takes a larger portion of the costs for the effective field evaluation. | 1703.02479v1 |
2017-09-06 | Adaptively time stepping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: implementation and validation in MuMax3 | Thermal fluctuations play an increasingly important role in micromagnetic
research relevant for various biomedical and other technological applications.
Until now, it was deemed necessary to use a time stepping algorithm with a
fixed time step in order to perform micromagnetic simulations at nonzero
temperatures. However, Berkov and Gorn have shown that the drift term which
generally appears when solving stochastic differential equations can only
influence the length of the magnetization. This quantity is however fixed in
the case of the stochastic Landau-Lifshitz-Gilbert equation. In this paper, we
exploit this fact to straightforwardly extend existing high order solvers with
an adaptive time stepping algorithm. We implemented the presented methods in
the freely available GPU-accelerated micromagnetic software package MuMax3 and
used it to extensively validate the presented methods. Next to the advantage of
having control over the error tolerance, we report a twenty fold speedup
without a loss of accuracy, when using the presented methods as compared to the
hereto best practice of using Heun's solver with a small fixed time step. | 1709.01682v1 |
2017-09-18 | Growth-Induced In-Plane Uniaxial Anisotropy in V$_{2}$O$_{3}$/Ni Films | We report on a strain-induced and temperature dependent uniaxial anisotropy
in V$_{2}$O$_{3}$/Ni hybrid thin films, manifested through the interfacial
strain and sample microstructure, and its consequences on the angular dependent
magnetization reversal. X-ray diffraction and reciprocal space maps identify
the in-plane crystalline axes of the V$_{2}$O$_{3}$; atomic force and scanning
electron microscopy reveal oriented rips in the film microstructure.
Quasi-static magnetometry and dynamic ferromagnetic resonance measurements
identify a uniaxial magnetic easy axis along the rips. Comparison with films
grown on sapphire without rips shows a combined contribution from strain and
microstructure in the V$_{2}$O$_{3}$/Ni films. Magnetization reversal
characteristics captured by angular-dependent first order reversal curve
measurements indicate a strong domain wall pinning along the direction
orthogonal to the rips, inducing an angular-dependent change in the reversal
mechanism. The resultant anisotropy is tunable with temperature and is most
pronounced at room temperature, which is beneficial for potential device
applications. | 1709.06100v1 |
2018-05-07 | Generalized Random Gilbert-Varshamov Codes | We introduce a random coding technique for transmission over discrete
memoryless channels, reminiscent of the basic construction attaining the
Gilbert-Varshamov bound for codes in Hamming spaces. The code construction is
based on drawing codewords recursively from a fixed type class, in such a way
that a newly generated codeword must be at a certain minimum distance from all
previously chosen codewords, according to some generic distance function. We
derive an achievable error exponent for this construction, and prove its
tightness with respect to the ensemble average. We show that the exponent
recovers the Csisz\'{a}r and K{\"o}rner exponent as a special case, which is
known to be at least as high as both the random-coding and expurgated
exponents, and we establish the optimality of certain choices of the distance
function. In addition, for additive distances and decoding metrics, we present
an equivalent dual expression, along with a generalization to infinite
alphabets via cost-constrained random coding. | 1805.02515v2 |
2018-07-04 | Deep Autoencoder for Combined Human Pose Estimation and body Model Upscaling | We present a method for simultaneously estimating 3D human pose and body
shape from a sparse set of wide-baseline camera views. We train a symmetric
convolutional autoencoder with a dual loss that enforces learning of a latent
representation that encodes skeletal joint positions, and at the same time
learns a deep representation of volumetric body shape. We harness the latter to
up-scale input volumetric data by a factor of $4 \times$, whilst recovering a
3D estimate of joint positions with equal or greater accuracy than the state of
the art. Inference runs in real-time (25 fps) and has the potential for passive
human behaviour monitoring where there is a requirement for high fidelity
estimation of human body shape and pose. | 1807.01511v1 |
2018-10-08 | Hiding the weights -- CBC black box algorithms with a guaranteed error bound | The component-by-component (CBC) algorithm is a method for constructing good
generating vectors for lattice rules for the efficient computation of
high-dimensional integrals in the "weighted" function space setting introduced
by Sloan and Wo\'zniakowski. The "weights" that define such spaces are needed
as inputs into the CBC algorithm, and so a natural question is, for a given
problem how does one choose the weights? This paper introduces two new CBC
algorithms which, given bounds on the mixed first derivatives of the integrand,
produce a randomly shifted lattice rule with a guaranteed bound on the
root-mean-square error. This alleviates the need for the user to specify the
weights. We deal with "product weights" and "product and order dependent (POD)
weights". Numerical tables compare the two algorithms under various assumed
bounds on the mixed first derivatives, and provide rigorous upper bounds on the
root-mean-square integration error. | 1810.03394v1 |
2018-10-11 | Alternative Stacking Sequences in Hexagonal Boron Nitride | The relative orientation of successive sheets, i.e. the stacking sequence, in
layered two-dimensional materials is central to the electronic, thermal, and
mechanical properties of the material. Often different stacking sequences have
comparable cohesive energy, leading to alternative stable crystal structures.
Here we theoretically and experimentally explore different stacking sequences
in the van der Waals bonded material hexagonal boron nitride (h-BN). We examine
the total energy, electronic bandgap, and dielectric response tensor for five
distinct high symmetry stacking sequences for both bulk and bilayer forms of
h-BN. Two sequences, the generally assumed AA' sequence and the relatively
unknown (for h-BN) AB (Bernal) sequence, are predicted to have comparably low
energy. We present a scalable modified chemical vapor deposition method that
produces large flakes of virtually pure AB stacked h-BN; this new material
complements the generally available AA' stacked h-BN. | 1810.04814v1 |
2018-10-17 | Unified theory of magnetization dynamics with relativistic and nonrelativistic spin torques | Spin torques play a crucial role in operative properties of modern spintronic
devices. To study current-driven magnetization dynamics, spin-torque terms
providing the action of spin-polarized currents have previously often been
added in a phenomenological way to the Landau-Lifshitz-Gilbert equation
describing the local spin dynamics, yet without derivation from fundamental
principles. Here, starting from the Dirac-Kohn-Sham theory and incorporating
nonlocal spin transport we rigorously derive the various spin-torque terms that
appear in current-driven magnetization dynamics. In particular we obtain an
extended magnetization dynamics equation that precisely contains the
nonrelativistic adiabatic and relativistic nonadiabatic spin-transfer torques
(STTs) of the Berger and Zhang-Li forms as well as relativistic spin-orbit
torques (SOTs). We derive in addition a previously unnoticed relativistic
spin-torque term and moreover show that the various obtained spin-torque terms
do not appear in the same mathematical form in both the Landau-Lifshitz and
Landau-Lifshitz-Gilbert equations of spin dynamics. | 1810.07438v1 |
2018-10-23 | Resource-Constrained Simultaneous Detection and Labeling of Objects in High-Resolution Satellite Images | We describe a strategy for detection and classification of man-made objects
in large high-resolution satellite photos under computational resource
constraints. We detect and classify candidate objects by using five pipelines
of convolutional neural network processing (CNN), run in parallel. Each
pipeline has its own unique strategy for fine tunning parameters, proposal
region filtering, and dealing with image scales. The conflicting region
proposals are merged based on region confidence and not just based on overlap
areas, which improves the quality of the final bounding-box regions selected.
We demonstrate this strategy using the recent xView challenge, which is a
complex benchmark with more than 1,100 high-resolution images, spanning 800,000
aerial objects around the world covering a total area of 1,400 square
kilometers at 0.3 meter ground sample distance. To tackle the
resource-constrained problem posed by the xView challenge, where inferences are
restricted to be on CPU with 8GB memory limit, we used lightweight CNN's
trained with the single shot detector algorithm. Our approach was competitive
on sequestered sets; it was ranked third. | 1810.10110v1 |
2018-11-01 | Ludometrics: Luck, and How to Measure It | Game theory is the study of tractable games which may be used to model more
complex systems. Board games, video games and sports, however, are intractable
by design, so "ludological" theories about these games as complex phenomena
should be grounded in empiricism. A first "ludometric" concern is the empirical
measurement of the amount of luck in various games. We argue against a narrow
view of luck which includes only factors outside any player's control, and
advocate for a holistic definition of luck as complementary to the variation in
effective skill within a population of players. We introduce two metrics for
luck in a game for a given population - one information theoretical, and one
Bayesian, and discuss the estimation of these metrics using sparse,
high-dimensional regression techniques. Finally, we apply these techniques to
compare the amount of luck between various professional sports, between Chess
and Go, and between two hobby board games: Race for the Galaxy and Seasons. | 1811.00673v1 |
2019-01-28 | Topology and Observables of the Non-Hermitian Chern Insulator | Topology plays a central role in nearly all disciplines of physics, yet its
applications have so far been restricted to closed, lossless systems in
thermodynamic equilibrium. Given that many physical systems are open and may
include gain and loss mechanisms, there is an eminent need to reexamine
topology within the context of non-Hermitian theories that describe open, lossy
systems. The recent generalization of the Chern number to non-Hermitian
Hamiltonians initiated this reexamination; however, there is so far no
established connection between a non-Hermitian topological invariant and the
quantization of an observable. In this work, we show that no such relationship
exists between the Chern number of non-Hermitian bands and the quantization of
the Hall conductivity. Using field theoretical techniques, we calculate the
longitudinal and Hall conductivities of a non-Hermitian Hamiltonian with a
finite Chern number to explicitly demonstrate the physics of a non-quantized
Hall conductivity despite an invariable Chern number. These results demonstrate
that the Chern number does not provide a physically meaningful classification
of non-Hermitian Hamiltonians. | 1901.09961v2 |
2019-03-25 | Deep Shape from Polarization | This paper makes a first attempt to bring the Shape from Polarization (SfP)
problem to the realm of deep learning. The previous state-of-the-art methods
for SfP have been purely physics-based. We see value in these principled
models, and blend these physical models as priors into a neural network
architecture. This proposed approach achieves results that exceed the previous
state-of-the-art on a challenging dataset we introduce. This dataset consists
of polarization images taken over a range of object textures, paints, and
lighting conditions. We report that our proposed method achieves the lowest
test error on each tested condition in our dataset, showing the value of
blending data-driven and physics-driven approaches. | 1903.10210v2 |
2019-04-30 | The algebra of rewriting for presentations of inverse monoids | We describe a formalism, using groupoids, for the study of rewriting for
presentations of inverse monoids, that is based on the Squier complex
construction for monoid presentations. We introduce the class of pseudoregular
groupoids, an example of which now arises as the fundamental groupoid of our
version of the Squier complex. A further key ingredient is the factorisation of
the presentation map from a free inverse monoid as the composition of an
idempotent pure map and an idempotent separating map. The relation module of a
presentation is then defined as the abelianised kernel of this idempotent
separating map. We then use the properties of idempotent separating maps to
derive a free presentation of the relation module. The construction of its
kernel - the module of identities - uses further facts about pseudoregular
groupoids. | 1904.13135v1 |
2019-07-18 | The homology of groups, profinite completions, and echoes of Gilbert Baumslag | We present novel constructions concerning the homology of finitely generated
groups. Each construction draws on ideas of Gilbert Baumslag. There is a
finitely presented acyclic group $U$ such that $U$ has no proper subgroups of
finite index and every finitely presented group can be embedded in $U$. There
is no algorithm that can determine whether or not a finitely presentable
subgroup of a residually finite, biautomatic group is perfect. For every
recursively presented abelian group $A$ there exists a pair of groups
$i:P_A\hookrightarrow G_A$ such that $i$ induces an isomorphism of profinite
completions, where $G_A$ is a torsion-free biautomatic group that is residually
finite and superperfect, while $P_A$ is a finitely generated group with
$H_2(P_A,\mathbb{Z})\cong A$. | 1907.08072v2 |
2019-08-08 | Semantic Estimation of 3D Body Shape and Pose using Minimal Cameras | We aim to simultaneously estimate the 3D articulated pose and high fidelity
volumetric occupancy of human performance, from multiple viewpoint video (MVV)
with as few as two views. We use a multi-channel symmetric 3D convolutional
encoder-decoder with a dual loss to enforce the learning of a latent embedding
that enables inference of skeletal joint positions and a volumetric
reconstruction of the performance. The inference is regularised via a prior
learned over a dataset of view-ablated multi-view video footage of a wide range
of subjects and actions, and show this to generalise well across unseen
subjects and actions. We demonstrate improved reconstruction accuracy and lower
pose estimation error relative to prior work on two MVV performance capture
datasets: Human 3.6M and TotalCapture. | 1908.03030v2 |
2019-09-06 | The universal unramified module for GL(n) and the Ihara conjecture | Let $F$ be a finite extension of $\mathbb{Q}_p$. Let $W(k)$ denote the Witt
vectors of an algebraically closed field $k$ of characteristic $\ell$ different
from $p$ and $2$, and let $\mathcal{Z}$ be the spherical Hecke algebra for
$GL_n(F)$ over $W(k)$. Given a Hecke character $\lambda:\mathcal{Z}\to R$,
where $R$ is an arbitrary $W(k)$-algebra, we introduce the universal unramified
module $\mathcal{M}_{\lambda,R}$. We show $\mathcal{M}_{\lambda,R}$ embeds in
its Whittaker space and is flat over $R$, resolving a conjecture of Lazarus. It
follows that $\mathcal{M}_{\lambda,k}$ has the same semisimplification as any
unramified principle series with Hecke character $\lambda$.
In the setting of mod-$\ell$ automorphic forms, Clozel, Harris, and Taylor
formulate a conjectural analogue of Ihara's lemma. It predicts that every
irreducible submodule of a certain cyclic module $V$ of mod-$\ell$ automorphic
forms is generic. Our result on the Whittaker model of
$\mathcal{M}_{\lambda,k}$ reduces the Ihara conjecture to the statement that
$V$ is generic. | 1909.02709v3 |
2019-10-10 | Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics | We consider the time-dependent Landau-Lifshitz-Gilbert equation. We prove
that each weak solution coincides with the (unique) strong solution, as long as
the latter exists in time. Unlike available results in the literature, our
analysis also includes the physically relevant lower-order terms like Zeeman
contribution, anisotropy, stray field, and the Dzyaloshinskii-Moriya
interaction (which accounts for the emergence of magnetic Skyrmions). Moreover,
our proof gives a template on how to approach weak-strong uniqueness for even
more complicated problems, where LLG is (nonlinearly) coupled to other
(nonlinear) PDE systems. | 1910.04630v2 |
2019-11-20 | Hard Choices in Artificial Intelligence: Addressing Normative Uncertainty through Sociotechnical Commitments | As AI systems become prevalent in high stakes domains such as surveillance
and healthcare, researchers now examine how to design and implement them in a
safe manner. However, the potential harms caused by systems to stakeholders in
complex social contexts and how to address these remains unclear. In this
paper, we explain the inherent normative uncertainty in debates about the
safety of AI systems. We then address this as a problem of vagueness by
examining its place in the design, training, and deployment stages of AI system
development. We adopt Ruth Chang's theory of intuitive comparability to
illustrate the dilemmas that manifest at each stage. We then discuss how
stakeholders can navigate these dilemmas by incorporating distinct forms of
dissent into the development pipeline, drawing on Elizabeth Anderson's work on
the epistemic powers of democratic institutions. We outline a framework of
sociotechnical commitments to formal, substantive and discursive challenges
that address normative uncertainty across stakeholders, and propose the
cultivation of related virtues by those responsible for development. | 1911.09005v1 |
2019-11-22 | Asymmetric entanglement-assisted quantum error-correcting codes and BCH codes | The concept of asymmetric entanglement-assisted quantum error-correcting code
(asymmetric EAQECC) is introduced in this article. Codes of this type take
advantage of the asymmetry in quantum errors since phase-shift errors are more
probable than qudit-flip errors. Moreover, they use pre-shared entanglement
between encoder and decoder to simplify the theory of quantum error correction
and increase the communication capacity. Thus, asymmetric EAQECCs can be
constructed from any pair of classical linear codes over an arbitrary field.
Their parameters are described and a Gilbert-Varshamov bound is presented.
Explicit parameters of asymmetric EAQECCs from BCH codes are computed and
examples exceeding the introduced Gilbert-Varshamov bound are shown. | 1911.10031v2 |
2019-12-16 | Nanosecond-timescale development of Faraday rotation in an ultracold gas | When a gas of ultracold atoms is suddenly illuminated by light that is nearly
resonant with an atomic transition, the atoms cannot respond instantaneously.
This non-instantaneous response means the gas is initially more transparent to
the applied light than in steady-state. The timescale associated with the
development of light absorption is set by the atomic excited state lifetime.
Similarly, the index of refraction in the gas also requires time to reach a
steady-state value, but the development of the associated phase response is
expected to be slower than absorption effects. Faraday rotation is one
manifestation of differing indices of refraction for orthogonal circular light
polarization components. We have performed experiments measuring the
time-dependent development of polarization rotation in an ultracold gas
subjected to a magnetic field. Our measurements match theoretical predictions
based on solving optical Bloch equations. We are able to identify how
parameters such as steady-state optical thickness and applied magnetic field
strength influence the development of Faraday rotation. | 1912.07553v1 |
2020-03-24 | An information theoretic framework for classifying exoplanetary system architectures | We propose several descriptive measures to characterize the arrangements of
planetary masses, periods, and mutual inclinations within exoplanetary systems.
These measures are based in complexity theory and capture the global,
system-level trends of each architecture. Our approach considers all planets in
a system simultaneously, facilitating both intra-system and inter-system
analysis. We find that based on these measures, Kepler's high-multiplicity
($N\geq3$) systems can be explained if most systems belong to a single
intrinsic population, with a subset of high-multiplicity systems ($\sim20\%$)
hosting additional, undetected planets intermediate in period between the known
planets. We confirm prior findings that planets within a system tend to be
roughly the same size and approximately coplanar. We find that forward modeling
has not yet reproduced the high degree of spacing similarity (in log-period)
actually seen in the Kepler data. Although our classification scheme was
developed using compact Kepler multis as a test sample, our methods can be
immediately applied to any other population of exoplanetary systems. We apply
this classification scheme to (1) quantify the similarity between systems, (2)
resolve observational biases from physical trends, and (3) identify which
systems to search for additional planets and where to look for these planets. | 2003.11098v1 |
2020-05-14 | On the Performance Analysis of Streaming Codes over the Gilbert-Elliott Channel | The Gilbert-Elliot (GE) channel is a commonly-accepted model for packet
erasures in networks. Streaming codes are a class of packet-level erasure codes
designed to provide reliable communication over the GE channel. The design of a
streaming code may be viewed as a two-step process. In the first, a more
tractable, delay-constrained sliding window (DCSW) channel model is considered
as a proxy to the GE channel. The streaming code is then designed to reliably
recover from all erasures introduced by the DCSW channel model. Simulation is
typically used to evaluate the performance of the streaming code over the
original GE channel, as analytic performance evaluation is challenging. In the
present paper, we take an important first step towards analytical performance
evaluation. Recognizing that most, efficient constructions of a streaming code
are based on the diagonal embedding or horizontal embedding of scalar block
codes within a packet stream, this paper provides upper and lower bounds on the
block-erasure probability of the underlying scalar block code when operated
over the GE channel. | 2005.06921v2 |
2020-08-25 | Differentiating a Tensor Language | How does one compile derivatives of tensor programs, such that the resulting
code is purely functional (hence easier to optimize and parallelize) and
provably efficient relative to the original program? We show that naively
differentiating tensor code---as done in popular systems like Tensorflow and
PyTorch---can cause asymptotic slowdowns in pathological cases, violating the
Cheap Gradients Principle. However, all existing automatic differentiation
methods that guarantee this principle (for variable size data) do so by relying
on += mutation through aliases/pointers---which complicates downstream
optimization. We provide the first purely functional, provably efficient,
adjoint/reverse-mode derivatives of array/tensor code by explicitly accounting
for sparsity. We do this by focusing on the indicator function from Iverson's
APL. We also introduce a new "Tensor SSA" normal form and a new derivation of
reverse-mode automatic differentiation based on the universal property of
inner-products. | 2008.11256v1 |
2020-09-14 | Moduli of Langlands Parameters | Let $F$ be a nonarchimedean local field of residue characteristic $p$, let
$\hat{G}$ be a split reductive group over $\mathbb{Z}[1/p]$ with an action of
$W_F$, and let $^LG$ denote the semidirect product $\hat{G}\rtimes W_F$. We
construct a moduli space of Langlands parameters $W_F \to {^LG}$, and show that
it is locally of finite type and flat over $\mathbb{Z}[1/p]$, and that it is a
reduced local complete intersection. We give parameterizations of the connected
components and the irreducible components of the geometric fibers of this
space, and parameterizations of the connected components of the total space
over $\overline{\mathbb{Z}}[1/p]$ (under mild hypotheses) and over
$\overline{\mathbb{Z}}_{\ell}$ for $\ell\neq p$. In each case, we show
precisely how each connected component identifies with the "principal"
connected component attached to a smaller split reductive group scheme. Finally
we study the GIT quotient of this space by $\hat{G}$ and give a complete
description of its fibers up to homeomorphism, and a complete description of
its ring of functions after inverting an explicit finite set of primes
depending only on $^LG$. | 2009.06708v3 |
2020-09-30 | Spin-diffusion model for micromagnetics in the limit of long times | In this paper, we consider spin-diffusion Landau-Lifshitz-Gilbert equations
(SDLLG), which consist of the time-dependent Landau-Lifshitz-Gilbert (LLG)
equation coupled with a time-dependent diffusion equation for the electron spin
accumulation. The model takes into account the diffusion process of the spin
accumulation in the magnetization dynamics of ferromagnetic multilayers. We
prove that in the limit of long times, the system reduces to simpler equations
in which the LLG equation is coupled to a nonlinear and nonlocal steady-state
equation, referred to as SLLG. As a by-product, the existence of global weak
solutions to the SLLG equation is obtained. Moreover, we prove weak-strong
uniqueness of solutions of SLLG, i.e., all weak solutions coincide with the
(unique) strong solution as long as the latter exists in time. The results
provide a solid mathematical ground to the qualitative behavior originally
predicted by Zhang, Levy, and Fert in [Physical Review Letters 88 (2002)] in
ferromagnetic multilayers. | 2009.14534v1 |
2020-12-20 | Reconstructing phase-resolved hysteresis loops from first-order reversal curves | The first order reversal curve (FORC) method is a magnetometry based
technique used to capture nanoscale magnetic phase separation and interactions
with macroscopic measurements using minor hysteresis loop analysis. This makes
the FORC technique a powerful tool in the analysis of complex systems which
cannot be effectively probed using localized techniques. However, recovering
quantitative details about the identified phases which can be compared to
traditionally measured metrics remains an enigmatic challenge. We demonstrate a
technique to reconstruct phase-resolved magnetic hysteresis loops by
selectively integrating the measured FORC distribution. From these minor loops,
the traditional metrics - including the coercivity and saturation field, and
the remanent and saturation magnetization - can be determined. In order to
perform this analysis, special consideration must be paid to the accurate
quantitative management of the so-called reversible features. This technique is
demonstrated on three representative materials systems, high anisotropy FeCuPt
thin-films, Fe nanodots, and SmCo/Fe exchange spring magnet films, and shows
excellent agreement with the direct measured major loop, as well as the phase
separated loops. | 2012.11041v1 |
2021-01-13 | Self-organization in the one-dimensional Landau-Lifshitz-Gilbert-Slonczewski equation with non-uniform anisotropy fields | In magnetic films driven by spin-polarized currents, the
perpendicular-to-plane anisotropy is equivalent to breaking the time
translation symmetry, i.e., to a parametric pumping. In this work, we
numerically study those current-driven magnets via the
Landau-Lifshitz-Gilbert-Slonczewski equation in one spatial dimension. We
consider a space-dependent anisotropy field in the parametric-like regime. The
anisotropy profile is antisymmetric to the middle point of the system. We find
several dissipative states and dynamical behavior and focus on localized
patterns that undergo oscillatory and phase instabilities. Using numerical
simulations, we characterize the localized states' bifurcations and present the
corresponding diagram of phases. | 2101.05263v1 |
2021-01-20 | Global Optimization of the Mean First Passage Time for Narrow Capture Problems in Elliptic Domains | Narrow escape and narrow capture problems which describe the average times
required to stop the motion of a randomly travelling particle within a domain
have applications in various areas of science. While for general domains, it is
known how the escape time decreases with the increase of the trap sizes, for
some specific 2D and 3D domains, higher-order asymptotic formulas have been
established, providing the dependence of the escape time on the sizes and
locations of the traps. Such results allow the use of global optimization to
seek trap arrangements that minimize average escape times. In a recent paper
\cite{iyaniwura2021optimization}, an explicit size- and trap location-dependent
expansion of the average mean first passage time (MFPT) in a 2D elliptic domain
was derived. The goal of this work is to systematically seek global minima of
MFPT for $1\leq N\leq 50$ traps in elliptic domains using global optimization
techniques, and compare the corresponding putative optimal trap arrangements
for different values of the domain eccentricity. Further, an asymptotic formula
the for the average MFPT in elliptic domains with $N$ circular traps of
arbitrary sizes is derived, and sample optimal configurations involving
non-equal traps are computed. | 2101.08368v2 |
2021-02-03 | Bounds and Genericity of Sum-Rank-Metric Codes | We derive simplified sphere-packing and Gilbert--Varshamov bounds for codes
in the sum-rank metric, which can be computed more efficiently than previous
ones. They give rise to asymptotic bounds that cover the asymptotic setting
that has not yet been considered in the literature: families of sum-rank-metric
codes whose block size grows in the code length. We also provide two genericity
results: we show that random linear codes achieve almost the sum-rank-metric
Gilbert--Varshamov bound with high probability. Furthermore, we derive bounds
on the probability that a random linear code attains the sum-rank-metric
Singleton bound, showing that for large enough extension fields, almost all
linear codes achieve it. | 2102.02244v3 |
2021-03-01 | A pathwise stochastic Landau-Lifshitz-Gilbert equation with application to large deviations | Using a rough path formulation, we investigate existence, uniqueness and
regularity for the stochastic Landau-Lifshitz-Gilbert equation with
Stratonovich noise on the one dimensional torus. As a main result we show the
continuity of the so-called It\^o-Lyons map in the energy spaces
$L^\infty(0,T;H^k)\cap L^2(0,T;H^{k+1})$ for any $k\ge1$. The proof proceeds in
two steps. First, based on an energy estimate in the aforementioned space
together with a compactness argument we prove existence of a unique solution,
implying the continuous dependence in a weaker norm. This is then strengthened
in the second step where the continuity in the optimal norm is established
through an application of the rough Gronwall lemma. Our approach is direct and
does not rely on any transformation formula, which permits to treat
multidimensional noise. As an easy consequence we then deduce a Wong-Zakai type
result, a large deviation principle for the solution and a support theorem. | 2103.00926v1 |
2021-03-17 | Numerical analysis of the Landau-Lifshitz-Gilbert equation with inertial effects | We consider the numerical approximation of the inertial
Landau-Lifshitz-Gilbert equation (iLLG), which describes the dynamics of the
magnetization in ferromagnetic materials at subpicosecond time scales. We
propose and analyze two fully discrete numerical schemes: The first method is
based on a reformulation of the problem as a linear constrained variational
formulation for the linear velocity. The second method exploits a reformulation
of the problem as a first order system in time for the magnetization and the
angular momentum. Both schemes are implicit, based on first-order finite
elements, and generate approximations satisfying the unit-length constraint of
iLLG at the vertices of the underlying mesh. For both methods, we prove
convergence of the approximations towards a weak solution of the problem.
Numerical experiments validate the theoretical results and show the
applicability of the methods for the simulation of ultrafast magnetic
processes. | 2103.09888v2 |
2021-07-12 | Human-like Relational Models for Activity Recognition in Video | Video activity recognition by deep neural networks is impressive for many
classes. However, it falls short of human performance, especially for
challenging to discriminate activities. Humans differentiate these complex
activities by recognising critical spatio-temporal relations among explicitly
recognised objects and parts, for example, an object entering the aperture of a
container. Deep neural networks can struggle to learn such critical
relationships effectively. Therefore we propose a more human-like approach to
activity recognition, which interprets a video in sequential temporal phases
and extracts specific relationships among objects and hands in those phases.
Random forest classifiers are learnt from these extracted relationships. We
apply the method to a challenging subset of the something-something dataset and
achieve a more robust performance against neural network baselines on
challenging activities. | 2107.05319v2 |
2021-08-17 | Small-misorientation toughness in biominerals evolved convergently | The hardest materials in living organisms are biologically grown crystalline
minerals, or biominerals, which are also incredibly fracture-tough. Biomineral
mesostructure includes size, shape, spatial arrangement, and crystal
orientation of crystallites, observable at the mesoscale (10 nanometer - 10
micron). Here we show that diverse biominerals, including nacre and prisms from
mollusk shells, coral skeletons, and tunicate spicules have different
mesostructures, but they converged to similar, small (<30 degrees)
misorientations of adjacent crystals at the mesoscale. We show that such small
misorientations are an effective toughening mechanism. Combining
Polarization-dependent Imaging Contrast (PIC) mapping of mesostructures and
Molecular Dynamics (MD) simulations of misoriented bicrystals, we reveal here
that small misorientations toughen bicrystals, thus explaining why they evolved
independently but convergently: preventing fracture is a clear evolutionary
advantage for diverse organisms. | 2108.07877v1 |
2021-08-19 | Evidence for a liquid precursor to biomineral formation | The crystals in animal biominerals such as sea urchin spines, mollusk shells,
and coral skeletons, form by attachment of amorphous particles that
subsequently crystallize. Do these solid amorphous precursor particles have
liquid precursors? Polymer-induced liquid precursors (PILP), or prenucleation
clusters coalescing into a liquid precursor to calcium carbonate
crystallization have been observed extensively in synthetic systems. Molecular
dynamics simulations also predict liquid-liquid phase separation. However,
evidence for liquid precursors in natural biominerals remains elusive. Here we
present Scanning or PhotoEmission Electron Microscopy (SEM, PEEM) evidence
consistent with a dense liquid-like precursor in regenerating sea urchin
spines. The observed precursor originates in tissue and ultimately transforms
into a single crystal of calcite (CaCO3) with complex stereom morphology. | 2108.08429v1 |
2021-08-22 | Factors Enhancing E-Government Service Gaps in a Developing Country Context | Globally, the discourse of e-government has gathered momentum in public
service delivery. No country has been left untouched in the implementation of
e-government. Several government departments and agencies are now using
information and communication technology (ICTs) to deliver government services
and information to citizens, other government departments, and businesses.
However, most of the government departments have not provided all of their
services electronically or at least the most important ones. Thus, this creates
a phenomenon of e-government service gaps. The objective of this study was to
investigate the contextual factors enhancing e-government service gaps in a
developing country. To achieve this aim, the TOE framework was employed
together with a qualitative case study to guide data collection and analysis.
The data was collected through semi-structured interviews from government
employees who are involved in the implementation of e-government services in
Zimbabwe as well as from citizens and businesses. Eleven (11) factors were
identified and grouped under the TOE framework. This research contributes
significantly to the implementation and utilisation of e-government services in
Zimbabwe. The study also contributes to providing a strong theoretical
understanding of the factors that enhance e-government service gaps explored in
the research model. | 2108.09803v1 |
2021-09-23 | Cyclically presented groups as Labelled Oriented Graph groups | We use results concerning the Smith forms of circulant matrices to identify
when cyclically presented groups have free abelianisation and so can be
Labelled Oriented Graph (LOG) groups. We generalize a theorem of Odoni and
Cremona to show that for a fixed defining word, whose corresponding representer
polynomial has an irreducible factor that is not cyclotomic and not equal to
$\pm t$, there are at most finitely many $n$ for which the corresponding
$n$-generator cyclically presented group has free abelianisation. We classify
when Campbell and Robertson's generalized Fibonacci groups $H(r,n,s)$ are LOG
groups and when the Sieradski groups are LOG groups. We prove that amongst
Johnson and Mawdesley's groups of Fibonacci type, the only ones that can be LOG
groups are Gilbert-Howie groups $H(n,m)$. We conjecture that if a Gilbert-Howie
group is a LOG group, then it is a Sieradski group, and prove this in certain
cases (in particular, for fixed $m$, the conjecture can only be false for
finitely many $n$). We obtain necessary conditions for a cyclically presented
group to be a connected LOG group in terms of the representer polynomial and
apply them to the Prishchepov groups. | 2109.11463v1 |
2021-12-03 | Spectral reconstruction in NRQCD via the Backus-Gilbert method | We present progress results from the FASTSUM collaboration's programme to
determine the spectrum of the bottomonium system as a function of temperature
using a variety of approaches. In this contribution, the Backus Gilbert method
is used to reconstruct spectral functions from NRQCD meson correlator data from
FASTSUM's anisotropic ensembles at nonzero temperature. We focus in particular
on the resolving power of the method, providing a demonstration of how the
underlying resolution functions can be probed by exploiting the Laplacian
nature of the NRQCD kernel. We conclude with estimates of the bottomonium
ground state mass and widths at nonzero temperature. | 2112.02075v2 |
2021-12-23 | Energy minimizing maps with prescribed singularities and Gilbert-Steiner optimal networks | We investigate the relation between energy minimizing maps valued into
spheres having topological singularities at given points and optimal networks
connecting them (e.g. Steiner trees, Gilbert-Steiner irrigation networks). We
show the equivalence of the corresponding variational problems, interpreting in
particular the branched optimal transport problem as a homological Plateau
problem for rectifiable currents with values in a suitable normed group. This
generalizes the pioneering work by Brezis, Coron and Lieb [10]. | 2112.12511v4 |
2022-02-02 | Asymptotic stability of precessing domain walls for the Landau-Lifshitz-Gilbert equation in a nanowire with Dzyaloshinskii-Moriya interaction | We consider a ferromagnetic nanowire and we focus on an asymptotic regime
where the Dzyaloshinskii-Moriya interaction is taken into account. First we
prove a dimension reduction result via $\Gamma$-convergence that determines a
limit functional $E$ defined for maps $m:\mathbb{R}\to \mathbb{S}^2$ in the
direction $e_1$ of the nanowire. The energy functional $E$ is invariant under
translations in $e_1$ and rotations about the axis $e_1$. We fully classify the
critical points of finite energy $E$ when a transition between $-e_1$ and $e_1$
is imposed; these transition layers are called (static) domain walls. The
evolution of a domain wall by the Landau-Lifshitz-Gilbert equation associated
to $E$ under the effect of an applied magnetic field $h(t)e_1$ depending on the
time variable $t$ gives rise to the so-called precessing domain wall. Our main
result proves the asymptotic stability of precessing domain walls for small $h$
in $L^\infty([0, +\infty))$ and small $H^1(\mathbb{R})$ perturbations of the
static domain wall, up to a gauge which is intrinsic to invariances of the
functional $E$. | 2202.01005v1 |
2022-02-14 | The Higgs Boson Mass as Fundamental Parameter of the Minimal Supersymmetric Standard Model | In the Minimal Supersymmetric Standard Model (MSSM) the mass of the lightest
neutral Higgs boson is determined by the supersymmetric parameters. In the
$m_h$MSSM the precisely measured Higgs boson replaces the trilinear coupling
$A_t$ as input parameter. Expressions are derived to extract $A_t$ in a
semi-analytical form as a function of the light Higgs boson (pole) mass. An
algorithm is developed and implemented at two--loop precision, generalizable to
higher orders, to perform this inversion consistently. The result of the
algorithm, implemented in the SuSpect spectrum calculator, is illustrated on a
parameter set compatible with LHC measurements. | 2202.06919v2 |
2022-02-15 | Coding and Bounds for Partially Defective Memory Cells | This paper considers coding for so-called partially stuck (defect) memory
cells. Such memory cells can only store partial information as some of their
levels cannot be used fully due to, e.g., wearout. First, we present new
constructions that are able to mask $u$ partially stuck cells while correcting
at the same time $t$ random errors. The process of "masking" determines a word
whose entries coincide with writable levels at the (partially) stuck cells. For
$u>1$ and alphabet size $q>2$, our new constructions improve upon the required
redundancy of known constructions for $t=0$, and require less redundancy for
masking partially stuck cells than former works required for masking fully
stuck cells (which cannot store any information). Second, we show that treating
some of the partially stuck cells as erroneous cells can decrease the required
redundancy for some parameters. Lastly, we derive Singleton-like,
sphere-packing-like, and Gilbert--Varshamov-like bounds. Numerical comparisons
state that our constructions match the Gilbert--Varshamov-like bounds for
several code parameters, e.g., BCH codes that contain all-one word by our first
construction. | 2202.07541v1 |
2022-03-24 | Multi-platform Process Flow Models and Algorithms for Extraction and Documentation of Digital Forensic Evidence from Mobile Devices | The increasing need for the examination of evidence from mobile and portable
gadgets increases the essential need to establish dependable measures for the
investigation of these gadgets. Many differences exist while detailing the
requirement for the examination of each gadget, to help detectives and
examiners in guaranteeing that of any kind piece of evidence extracted/
collected from any mobile devices is well documented and the outcomes can be
repeatable, a reliable and well-documented investigation process must be
implemented if the results of the examination are to be repeatable and
defensible in courts of law. In this paper we developed a generic process flow
model for the extraction of digital evidence in mobile devices running on
android, Windows, iOs and Blackberry operating system. The research adopted
survey approach and extensive literature review a s means to collect data. The
models developed were validate through expert opinion. Results of this work can
guide solution developers in ensuring standardization of evidence extraction
tools for mobile devices. | 2203.13258v1 |
2022-06-07 | Implicit biases in transit models using stellar pseudo-density | The transit technique is responsible for the majority of exoplanet
discoveries to date. Characterizing these planets involves careful modeling of
their transit profiles. A common technique involves expressing the transit
duration using a density-like parameter, $\tilde{\rho}$, often called the
"circular density." Most notably, the Kepler project -- the largest analysis of
transit lightcurves to date -- adopted a linear prior on $\tilde{\rho}$. Here,
we show that such a prior biases measurements of impact parameter, $b$, due to
the non-linear relationship between $\tilde{\rho}$ and transit duration. This
bias slightly favors low values ($b \lesssim 0.3$) and strongly disfavors high
values ($b \gtrsim 0.7$) unless transit signal-to-noise ratio is sufficient to
provide an independent constraint on $b$, a criterion that is not satisfied for
the majority of Kepler planets. Planet-to-star radius ratio, $r$, is also
biased due to $r{-}b$ covariance. Consequently, the median Kepler DR25 target
suffers a $1.6\%$ systematic underestimate of $r$. We present a techniques for
correcting these biases and for avoiding them in the first place. | 2206.03432v1 |
2022-09-12 | GenLoco: Generalized Locomotion Controllers for Quadrupedal Robots | Recent years have seen a surge in commercially-available and affordable
quadrupedal robots, with many of these platforms being actively used in
research and industry. As the availability of legged robots grows, so does the
need for controllers that enable these robots to perform useful skills.
However, most learning-based frameworks for controller development focus on
training robot-specific controllers, a process that needs to be repeated for
every new robot. In this work, we introduce a framework for training
generalized locomotion (GenLoco) controllers for quadrupedal robots. Our
framework synthesizes general-purpose locomotion controllers that can be
deployed on a large variety of quadrupedal robots with similar morphologies. We
present a simple but effective morphology randomization method that
procedurally generates a diverse set of simulated robots for training. We show
that by training a controller on this large set of simulated robots, our models
acquire more general control strategies that can be directly transferred to
novel simulated and real-world robots with diverse morphologies, which were not
observed during training. | 2209.05309v1 |
2022-10-11 | Element-Specific First Order Reversal Curves Measured by Magnetic Transmission X-ray Microscopy | The first order reversal curve (FORC) method is a macroscopic measurement
technique which can be used to extract quantitative, microscopic properties of
hysteretic systems. Using magnetic transmission X-ray microscopy (MTXM), local
element-specific FORC measurements are performed on a 20 nm thick film of CoTb.
The FORCs measured with microscopy reveal a step-by-step domain evolution under
the magnetic field cycling protocol, and provide a direct visualization of the
mechanistic interpretation of FORC diagrams. They are compared with
magnetometry FORCs and show good quantitative agreement. Furthermore, the high
spatial resolution and element-specific sensitivity of MTXM provide new
capabilities to measure FORCs on small regions or specific phases within
multicomponent systems, including buried layers in heterostructures. The
ability to perform FORCs on very small features is demonstrated with the
MTXM-FORC measurement of a rectangular microstructure with vortex-like Landau
structures. This work demonstrates the confluence of two uniquely powerful
techniques to achieve quantitative insight into nanoscale magnetic behavior. | 2210.05739v1 |
2022-11-08 | Landau-Lifshitz-Gilbert equations: Controllability by Low Modes Forcing for deterministic version and Support Theorems for Stochastic version | In this article, we study the controllability issues of the
Landau-Lifshitz-Gilbert Equations (LLGEs), accompanied with non-zero exchange
energy only, in an interval in one spatial dimension with Neumann boundary
conditions. The paper is of twofold. In the first part of the paper, we study
the controllability issues of the LLGEs. The control force acting here is
degenerate i.e., it acts through a few numbers of low mode frequencies. We
exploit the Fourier series expansion of the solution. We borrow methods of
differential geometric control theory (Lie bracket generating property) to
establish the global controllability of the finite-dimensional Galerkin
approximations of LLGEs. We show $L^2$ approximate controllability of the full
system. In the second part, we consider the LLGEs with lower-dimensional
degenerate random forcing (finite-dimensional Brownian motions) and study
support theorems. | 2211.04204v1 |
2022-11-18 | Knowledge Graph Refinement based on Triplet BERT-Networks | Knowledge graph embedding techniques are widely used for knowledge graph
refinement tasks such as graph completion and triple classification. These
techniques aim at embedding the entities and relations of a Knowledge Graph
(KG) in a low dimensional continuous feature space. This paper adopts a
transformer-based triplet network creating an embedding space that clusters the
information about an entity or relation in the KG. It creates textual sequences
from facts and fine-tunes a triplet network of pre-trained transformer-based
language models. It adheres to an evaluation paradigm that relies on an
efficient spatial semantic search technique. We show that this evaluation
protocol is more adapted to a few-shot setting for the relation prediction
task. Our proposed GilBERT method is evaluated on triplet classification and
relation prediction tasks on multiple well-known benchmark knowledge graphs
such as FB13, WN11, and FB15K. We show that GilBERT achieves better or
comparable results to the state-of-the-art performance on these two refinement
tasks. | 2211.10460v1 |
2022-11-22 | Generalized Random Gilbert-Varshamov Codes: Typical Error Exponent and Concentration Properties | We find the exact typical error exponent of constant composition generalized
random Gilbert-Varshamov (RGV) codes over DMCs channels with generalized
likelihood decoding. We show that the typical error exponent of the RGV
ensemble is equal to the expurgated error exponent, provided that the RGV
codebook parameters are chosen appropriately. We also prove that the random
coding exponent converges in probability to the typical error exponent, and the
corresponding non-asymptotic concentration rates are derived. Our results show
that the decay rate of the lower tail is exponential while that of the upper
tail is double exponential above the expurgated error exponent. The explicit
dependence of the decay rates on the RGV distance functions is characterized. | 2211.12238v1 |
2023-01-05 | Improved Gilbert-Varshamov bounds for hopping cyclic codes and optical orthogonal codes | Hopping cyclic codes (HCCs) are (non-linear) cyclic codes with the additional
property that the $n$ cyclic shifts of every given codeword are all distinct,
where $n$ is the code length. Constant weight binary hopping cyclic codes are
also known as optical orthogonal codes (OOCs). HCCs and OOCs have various
practical applications and have been studied extensively over the years.
The main concern of this paper is to present improved Gilbert-Varshamov type
lower bounds for these codes, when the minimum distance is bounded below by a
linear factor of the code length. For HCCs, we improve the previously best
known lower bound of Niu, Xing, and Yuan by a linear factor of the code length.
For OOCs, we improve the previously best known lower bound of Chung, Salehi,
and Wei, and Yang and Fuja by a quadratic factor of the code length. As
by-products, we also provide improved lower bounds for frequency hopping
sequences sets and error-correcting weakly mutually uncorrelated codes. Our
proofs are based on tools from probability theory and graph theory, in
particular the McDiarmid's inequality on the concentration of Lipschitz
functions and the independence number of locally sparse graphs. | 2301.02042v1 |
2023-01-11 | Thou Shalt not Pick all Items if Thou are First: of Strategyproof and Fair Picking Sequences | When allocating indivisible items to agents, it is known that the only
strategyproof mechanisms that satisfy a set of rather mild conditions are
constrained serial dictatorships: given a fixed order over agents, at each step
the designated agent chooses a given number of items (depending on her position
in the sequence). With these rules, also known as non-interleaving picking
sequences, agents who come earlier in the sequence have a larger choice of
items. However, this advantage can be compensated by a higher number of items
received by those who come later. How to balance priority in the sequence and
number of items received is a nontrivial question. We use a previous model,
parameterized by a mapping from ranks to scores, a social welfare functional,
and a distribution over preference profiles. For several meaningful choices of
parameters, we show that the optimal sequence can be computed in polynomial
time. Last, we give a simple procedure for eliciting scoring vectors and we
study the impact of the assignment from agents to positions on the ex-post
social welfare. | 2301.06086v1 |
2023-01-17 | Comparison of Optical and Electrical Links for Highly-Interconnected Systems | As data rates for multi-gigabit serial interfaces within multi-node compute
systems approach and exceed 10 Gigabits per second (Gbps), board-to-board and
chip-to-chip optical signaling solutions become more attractive, particularly
for longer (e.g. 50-100 cm) links. The transition to optical signaling will
potentially allow new high performance compute (HPC) system architectures that
benefit from characteristics unique to optical links.
To examine these characteristics, we built and tested several optical
demonstration vehicles; one based on dense wavelength division multiplexing
(DWDM), and others based on multiple point-to-point links carried across
multimode fibers. All test vehicles were constructed to evaluate applicability
to a multi-node compute system. Test results, combined with data from recent
research efforts are summarized and compared to equivalent electrical links and
the advantages and design characteristics unique to optical signaling are
identified. | 2301.10169v1 |
2023-01-17 | PWB Manufacturing Variability Effects on High Speed SerDes Links: Statistical Insights from Thousands of 4-Port SParameter Measurements | Variability analysis is important in successfully deploying multi-gigabit
backplane printed wiring boards (PWBs) with growing numbers of high-speed
SerDes links. We discuss the need for large sample sizes to obtain accurate
variability estimates of SI metrics (eye height, phase skew, etc).
Using a dataset of 11,961 S-parameters, we demonstrate statistical techniques
to extract accurate estimates of PWB SI performance variations. We cite
numerical examples illustrating how these variations may contribute to
underestimated or overestimated design criteria, causing unnecessary design
expense. Tabular summaries of performance variation and key findings of broad
interest to the general SI community are highlighted. | 2301.10176v1 |
2023-01-17 | A Zero Sum Signaling Method for High Speed, Dense Parallel Bus Communications | Complex digital systems such as high performance computers (HPCs) make
extensive use of high-speed electrical interconnects, in routing signals among
processing elements, or between processing elements and memory. Despite
increases in serializer/deserializer (SerDes) and memory interface speeds,
there is demand for higher bandwidth busses in constrained physical spaces
which still mitigate simultaneous switching noise (SSN). The concept of zero
sum signaling utilizes coding across a data bus to allow the use of
single-ended buffers while still mitigating SSN, thereby reducing the number of
physical channels (e.g. circuit board traces) by nearly a factor of two when
compared with traditional differential signaling. Through simulation and
analysis of practical (non-ideal) data bus and power delivery network
architectures, we demonstrate the feasibility of zero sum signaling and compare
performance with that of traditional (single-ended and differential) methods. | 2302.05427v1 |
2023-03-20 | Dynamic Documentation for AI Systems | AI documentation is a rapidly-growing channel for coordinating the design of
AI technologies with policies for transparency and accessibility. Calls to
standardize and enact documentation of algorithmic harms and impacts are now
commonplace. However, documentation standards for AI remain inchoate, and fail
to match the capabilities and social effects of increasingly impactful
architectures such as Large Language Models (LLMs). In this paper, we show the
limits of present documentation protocols, and argue for dynamic documentation
as a new paradigm for understanding and evaluating AI systems. We first review
canonical approaches to system documentation outside the context of AI,
focusing on the complex history of Environmental Impact Statements (EISs). We
next compare critical elements of the EIS framework to present challenges with
algorithmic documentation, which have inherited the limitations of EISs without
incorporating their strengths. These challenges are specifically illustrated
through the growing popularity of Model Cards and two case studies of
algorithmic impact assessment in China and Canada. Finally, we evaluate more
recent proposals, including Reward Reports, as potential components of fully
dynamic AI documentation protocols. | 2303.10854v1 |
2023-01-17 | 56 Gbps PCB Design Strategies for Clean, Low-Skew Channels | Although next generation (>28 Gbps) SerDes standards have been contemplated
for several years, it has not been clear whether PCB structures supporting 56
Gbps NRZ will be feasible and practical. In this paper, we assess a number of
specific PCB design strategies (related to pin-field breakouts, via stubs, and
fiber weave skew) both through simulation and through measurement of a wide
range of structures on a PCB test vehicle. We demonstrate that conventional
approaches in many cases will not be sufficient, but that modest
(manufacturable) design changes can enable low-skew 56 Gbps NRZ channels having
acceptable insertion and return loss. | 2304.01909v1 |
2023-01-17 | Inverting the SerDes Link Design Flow Process | The traditional SerDes link simulation process begins with the extraction of
printed circuit board (PCB) physical stripline and via models, followed by
channel modeling and link simulation. We invert this simulation flow by first
creating link performance curves across an array of hypothetical channels
defined with specially-developed, high level, equation-based models; limited
physical extraction is later undertaken to relate PCB channel implementation to
these performance curves. These curves allow us to determine the system-level
SerDes channel requirements and to become better informed in choosing PCB
technologies for lower cost and easier manufacturability. The inverted modeling
process is very efficient, allowing for the rapid identification and avoidance
of problematic channel topologies and the study of other potentially useful
channel designs. | 2304.01911v1 |
2023-01-17 | Plated-Through-Hole Via Design Specifications for 112G Serial Links | An earlier study of a high layer-count test board using plated-through-hole
(PTH) vias and a limited quantity of laser vias was shown to be capable of
supporting 112 Gb/s PAM-4 links (or equivalent signaling having 28 GHz
(Nyquist) bandwidth). This original board design was then rebuilt using a
different fabricator, and the test results revealed a significant decrease in
the bandwidth of the vias. These results led to the development of a set of
design specifications that PCB vendors can easily validate, which will ensure
that the use of high layer-count boards with PTH technology are viable for
emerging 112 Gb/s PAM-4 links. | 2304.01913v1 |
2023-04-18 | Sample-and-Hold Safety with Control Barrier Functions | A common assumption on the deployment of safeguarding controllers on the
digital platform is that high sampling frequency translates to a small
violation of safety. This paper investigates and formalizes this assumption
through the lens of Input-to-State Safety. From this perspective, and
leveraging control barrier functions (CBFs), we propose an alternative solution
for maintaining safety of sample-and-hold controlled systems without any
violation to the original safe set. Our approach centers around modulating the
sampled control input in order to guarantee a more robust safety condition. We
analyze both the time-triggered and the event-triggered sample-and-hold
implementations, including the characterization of sampling frequency
requirements and trigger conditions. We demonstrate the effectiveness of our
approach in the context of adaptive cruise control through simulations. | 2304.08685v2 |
2023-01-17 | Efficient Circuit-Level Implementation of Knuth-Based Balanced and Nearly-Balanced Codes | Coding schemes are often used in high-speed processor-processor or
processor-memory busses in digital systems. In particular, we have introduced
(in a 2012 DesignCon paper) a zero sum (ZS) signaling method which uses
balanced or nearly-balanced coding to reduce simultaneous switching noise (SSN)
in a single-ended bus to a level comparable to that of differential signaling.
While several balanced coding schemes are known, few papers exist that describe
the necessary digital hardware implementations of (known) balanced coding
schemes, and no algorithms had previously been developed for nearly-balanced
coding. In this work, we extend a known balanced coding scheme to accommodate
nearly-balanced coding and demonstrate a range of coding and decoding circuits
through synthesis in 65 nm CMOS. These hardware implementations have minimal
impact on the energy efficiency and area when compared to current
serializer/deserializers (SerDes) at clock rates which would support SerDes
integration. | 2304.13497v1 |
2023-01-17 | Capacitor Optimization in Power Distribution Networks Using Numerical Computation Techniques | This paper presents a power distribution network (PDN) decoupling capacitor
optimization application with three primary goals: reduction of solution times
for large networks, development of flexible network scoring routines, and a
concentration strictly on achieving the best network performance. Example
optimizations are performed using broadband models of a printed circuit board
(PCB), a chip-package, on-die networks, and candidate capacitors. A novel
worst-case time-domain optimization technique is presented as an alternative to
the traditional frequency-domain approach. The trade-offs and criteria for
scoring the computed network are presented. The output is a recommended set of
capacitors which can then be applied to the product design. | 2305.01540v1 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.