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2020-08-10
|
Coherent spin qubit transport in silicon
|
A fault-tolerant quantum processor may be configured using stationary qubits
interacting only with their nearest neighbours, but at the cost of significant
overheads in physical qubits per logical qubit. Such overheads could be reduced
by coherently transporting qubits across the chip, allowing connectivity beyond
immediate neighbours. Here we demonstrate high-fidelity coherent transport of
an electron spin qubit between quantum dots in isotopically-enriched silicon.
We observe qubit precession in the inter-site tunnelling regime and assess the
impact of qubit transport using Ramsey interferometry and quantum state
tomography techniques. We report a polarization transfer fidelity of 99.97% and
an average coherent transfer fidelity of 99.4%. Our results provide key
elements for high-fidelity, on-chip quantum information distribution, as long
envisaged, reinforcing the scaling prospects of silicon-based spin qubits.
|
2008.04020v2
|
2020-08-20
|
Linear hash-functions and their applications to error detection and correction
|
We describe and explore so-called linear hash functions and show how they can
be used to build error detection and correction codes. The method can be
applied for different types of errors (for example, burst errors). When the
method is applied to a model where number of distorted letters is limited, the
obtained estimate of its performance is slightly better than the known
Varshamov-Gilbert bound. We also describe random code whose performance is
close to the same boundary, but its construction is much simpler. In some cases
the obtained methods are simpler and more flexible than the known ones. In
particular, the complexity of the obtained error detection code and the
well-known CRC code is close, but the proposed code, unlike CRC, can detect
with certainty errors whose number does not exceed a predetermined limit.
|
2008.08955v1
|
2020-08-27
|
Electrical conductivity of the quark-gluon plasma: perspective from lattice QCD
|
A discussion on the electrical conductivity of the quark-gluon plasma as
determined by lattice QCD is given. After a reminder of basic definitions and
expectations, various methods for spectral reconstruction are reviewed,
including the use of Ans\"atze and sum rules, the Maximum Entropy and
Backus-Gilbert methods, and Tikhonov regularisation. A comprehensive overview
of lattice QCD results obtained so far is given, including a comparison of the
different lattice formulations. A noticeable consistency for the conductivities
obtained is seen, in spite of the differences in the lattice setups and
spectral reconstruction methods. It is found that in the case of quenched QCD
little temperature dependence of $\sigma/T$ is seen in the temperature range
investigated, while for QCD with dynamical quarks a reduction of $\sigma/T$ in
the vicinity of the thermal crossover is observed, compared to its value in the
QGP. Several open questions are posed at the end.
|
2008.12326v1
|
2020-09-02
|
Heterobilayer moiré magnets: moiré skyrmions and the commensurate-incommensurate transition
|
We study untwisted heterobilayers of ferromagnetic and antiferromagnetic van
der Waals materials, with in particular a Dzyaloshinskii-Moriya interaction in
the ferromagnetic layer. A continuum low energy field theory is utilized to
study such systems. We develop a phase diagram as a function of the strength of
inter-layer exchange and Dzyaloshinskii-Moriya interactions, combining
perturbative and strong coupling analyses with numerical simulations using
Landau-Lifshitz-Gilbert equations. Various moir\'e-periodic commensurate phases
are found, and the commensurate-incommensurate transition is discussed. Among
the commensurate phases, we observe an interesting skyrmion lattice phase
wherein each moir\'e unit cell hosts one skyrmion.
|
2009.00860v3
|
2020-09-04
|
5-Dimensional Space-Periodic Solutions of the Static Vacuum Einstein Equations
|
An affirmative answer is given to a conjecture of Myers concerning the
existence of 5-dimensional regular static vacuum solutions that balance an
infinite number of black holes, which have Kasner asymptotics. A variety of
examples are constructed, having different combinations of ring $S^1\times S^2$
and sphere $S^3$ cross-sectional horizon topologies. Furthermore, we show the
existence of 5-dimensional vacuum solitons with Kasner asymptotics. These are
regular static space-periodic vacuum spacetimes devoid of black holes.
Consequently, we also obtain new examples of complete Riemannian manifolds of
nonnegative Ricci curvature in dimension 4, and zero Ricci curvature in
dimension 5, having arbitrarily large as well as infinite second Betti number.
|
2009.01999v2
|
2020-09-24
|
Quarantined! Examining the Effects of a Community-Wide Moderation Intervention on Reddit
|
Should social media platforms override a community's self-policing when it
repeatedly break rules? What actions can they consider? In light of this
debate, platforms have begun experimenting with softer alternatives to outright
bans. We examine one such intervention called quarantining, that impedes direct
access to and promotion of controversial communities. Specifically, we present
two case studies of what happened when Reddit quarantined the influential
communities r/TheRedPill (TRP) and r/The_Donald (TD). Using over 85M Reddit
posts, we apply causal inference methods to examine the quarantine's effects on
TRP and TD. We find that the quarantine made it more difficult to recruit new
members: new user influx to TRP and TD decreased by 79.5% and 58%,
respectively. Despite quarantining, existing users' misogyny and racism levels
remained unaffected. We conclude by reflecting on the effectiveness of this
design friction in limiting the influence of toxic communities and discuss
broader implications for content moderation.
|
2009.11483v3
|
2020-10-24
|
Hunting for Dark Matter Subhalos in Strong Gravitational Lensing with Neural Networks
|
Dark matter substructures are interesting since they can reveal the
properties of dark matter. Collisionless N-body simulations of cold dark matter
show more substructures compared with the population of dwarf galaxy satellites
observed in our local group. Therefore, understanding the population and
property of subhalos at cosmological scale would be an interesting test for
cold dark matter. In recent years, it has become possible to detect individual
dark matter subhalos near images of strongly lensed extended background
galaxies. In this work, we discuss the possibility of using deep neural
networks to detect dark matter subhalos, and showing some preliminary results
with simulated data. We found that neural networks not only show promising
results on detecting multiple dark matter subhalos, but also learn to reject
the subhalos on the lensing arc of a smooth lens where there is no subhalo.
|
2010.12960v2
|
2020-10-28
|
Skyrmions Near Defects
|
We study the impact of an exchange-reducing defect on a skyrmion for a thin
film of finite thickness. Attraction of the skyrmion to a defect is
demonstrated in a lattice model by computing the micromagnetic energy
accounting for the exchange, Dzyaloshinskii-Moriya interaction, magnetic
anisotropy, and dipole-dipole coupling. The spiraling dynamics of the skyrmion
towards the defect is illustrated by solving numerically the full
Landau-Lifshitz-Gilbert equations on a lattice and, independently, the Thiele
equation, with the two methods in agreement with each other. We find that the
skyrmion deforms when approaching the defect. Deformation is small in the
parameter space far from the phase boundary that determines stability of
skyrmions. It increases dramatically near the phase boundary, leading to the
transformation of the skyrmion by the defect into a snake-like magnetic domain.
|
2010.14683v2
|
2020-10-29
|
Micromagnetics of thin films in the presence of Dzyaloshinskii-Moriya interaction
|
In this paper, we study the thin-film limit of the micromagnetic energy
functional in the presence of bulk Dzyaloshinskii-Moriya interaction (DMI). Our
analysis includes both a stationary $\Gamma$-convergence result for the
micromagnetic energy, as well as the identification of the asymptotic behavior
of the associated Landau-Lifshitz-Gilbert equation. In particular, we prove
that, in the limiting model, part of the DMI term behaves like the projection
of the magnetic moment onto the normal to the film, contributing this way to an
increase in the shape anisotropy arising from the magnetostatic self-energy.
Finally, we discuss a convergent finite element approach for the approximation
of the time-dependent case and use it to numerically compare the original
three-dimensional model with the two-dimensional thin-film limit.
|
2010.15541v1
|
2020-11-11
|
Role of impurity clusters for the current-driven motion of magnetic Skyrmions
|
We study how impurities influence the current-induced dynamics of magnetic
Skyrmions moving in a racetrack geometry. For this, we solve numerically the
generalized Landau-Lifshitz-Gilbert equation extended by the current-induced
spin transfer torque. In particular, we investigate two classes of impurities,
non-conducting and magnetic impurities. The former are magnetically rigid
objects and yield to an inhomogeneous current density over the racetrack which
we determine separately by solving the fundamental electrostatic equations. In
contrast, magnetic impurities leave the applied current density homogeneous
throughout the stripe. Depending on parameters, we observe four different
scenarios of Skyrmion motions in the presence of disorder, the Skyrmion decay,
the pinning, the creation of additional Skyrmions, and ordinary Skyrmion
passage. We calculate and discuss phase diagrams in dependence of the impurity
concentration and radii of the impurities.
|
2011.06027v1
|
2020-11-12
|
Communication Efficient Coresets for Maximum Matching
|
In this paper we revisit the problem of constructing randomized composable
coresets for bipartite matching. In this problem the input graph is randomly
partitioned across $k$ players, each of which sends a single message to a
coordinator, who then must output a good approximation to the maximum matching
in the input graph. Assadi and Khanna gave the first such coreset, achieving a
$1/9$-approximation by having every player send a maximum matching, i.e. at
most $n/2$ words per player. The approximation factor was improved to $1/3$ by
Bernstein et al.
In this paper, we show that the matching skeleton construction of Goel,
Kapralov and Khanna, which is a carefully chosen (fractional) matching, is a
randomized composable coreset that achieves a $1/2-o(1)$ approximation using at
most $n-1$ words of communication per player. We also show an upper bound of
$2/3+o(1)$ on the approximation ratio achieved by this coreset.
|
2011.06481v1
|
2020-11-17
|
Thermally assisted magnetization reversal of a magnetic nanoparticle driven by a down-chirp microwave field pulse
|
It has been shown that a single-domain magnetic nanoparticle can be
effectively switched by a linear down-chirp microwave field pulse (DCMWP) in
zero temperature limit. However, finite temperature is ubiquitous in practice.
Here, we study the effect of finite temperature on the DCMWP-induced
magnetization reversal based on the stochastic Landau-Lifshitz-Gilbert
equation. It is found that any one of the three controlling parameters of a
DCMWP, i.e. the amplitude, chirp rate, or initial frequency, decreases with
increasing temperature while the other two are fixed. The maximal temperature
at which the reversal can happen increases with enlarging the system size.
These phenomena are related to the facts that the energy barrier induced by
anisotropy increases with the system volume, and the effective magnetization
decreases with temperature. We also provide a set of optimal parameters for
practical realization of our proposal. These findings may provide a way to
realize low-cost and fast magnetization reversal with a wide operating
temperature.
|
2011.08610v2
|
2020-11-17
|
Sum-frequency excitation of coherent magnons
|
Coherent excitation of magnons is conventionally achieved through Raman
scattering processes, in which the difference-frequency components of the
driving field are resonant with the magnon energy. Here, we describe mechanisms
by which the sum-frequency components of the driving field can be used to
coherently excite magnons through two-particle absorption processes. We use the
Landau-Lifshitz-Gilbert formalism to compare the spin-precession amplitudes
that different types of impulsive stimulated and ionic Raman scattering
processes and their sum-frequency counterparts induce in an antiferromagnetic
model system. We show that sum-frequency mechanisms enabled by linearly
polarized driving fields yield excitation efficiencies comparable or larger
than established Raman techniques, while elliptical polarizations produce only
weak and circularly polarizations no sum-frequency components at all. The
mechanisms presented here complete the map for dynamical spin control by the
means of Raman-type processes.
|
2011.08730v1
|
2020-11-26
|
3D Nanomagnetism in Low Density Interconnected Nanowire Networks
|
Free-standing, interconnected metallic nanowire networks with density as low
as 40 mg/cm^{3} have been achieved over cm-scale areas, using electrodeposition
into polycarbonate membranes that have been ion-tracked at multiple angles.
Networks of interconnected magnetic nanowires further provide an exciting
platform to explore 3-dimensional nanomagnetism, where their structure,
topology and frustration may be used as additional degrees of freedom to tailor
the materials properties. New magnetization reversal mechanisms in cobalt
networks are captured by the first-order reversal curve method, which
demonstrate the evolution from strong demagnetizing dipolar interactions to
intersections-mediated domain wall pinning and propagation, and eventually to
shape-anisotropy dominated magnetization reversal. These findings open up new
possibilities for 3-dimensional integrated magnetic devices for memory, complex
computation, and neuromorphics.
|
2011.13468v2
|
2020-12-02
|
Quantum Annealed Criticality: A Scaling Description
|
Experimentally there exist many materials with first-order phase transitions
at finite temperature that display quantum criticality. Classically, a
strain-energy density coupling is known to drive first-order transitions in
compressible systems, and here we generalize this Larkin-Pikin mechanism to the
quantum case. We show that if the T=0 system lies above its upper critical
dimension, the line of first-order transitions ends in a "quantum annealed
critical point" where zero-point fluctuations restore the underlying
criticality of the order parameter. The generalized Larkin-Pikin phase diagram
is presented and experimental consequences are discussed.
|
2012.01601v1
|
2020-12-04
|
Rethinking movie genre classification with fine-grained semantic clustering
|
Movie genre classification is an active research area in machine learning.
However, due to the limited labels available, there can be large semantic
variations between movies within a single genre definition. We expand these
'coarse' genre labels by identifying 'fine-grained' semantic information within
the multi-modal content of movies. By leveraging pre-trained 'expert' networks,
we learn the influence of different combinations of modes for multi-label genre
classification. Using a contrastive loss, we continue to fine-tune this
'coarse' genre classification network to identify high-level intertextual
similarities between the movies across all genre labels. This leads to a more
'fine-grained' and detailed clustering, based on semantic similarities while
still retaining some genre information. Our approach is demonstrated on a newly
introduced multi-modal 37,866,450 frame, 8,800 movie trailer dataset,
MMX-Trailer-20, which includes pre-computed audio, location, motion, and image
embeddings.
|
2012.02639v3
|
2020-12-04
|
Nutation in antiferromagnetic resonance
|
The effect of inertial spin dynamics is compared between ferromagnetic,
antiferromagnetic and ferrimagnetic systems. The linear response to an
oscillating external magnetic field is calculated within the framework of the
inertial Landau--Lifshitz--Gilbert equation using analytical theory and
computer simulations. Precession and nutation resonance peaks are identified,
and it is demonstrated that the precession frequencies are reduced by the spin
inertia, while the lifetime of the excitations is enhanced. The interplay
between precession and nutation is found to be the most prominent in
antiferromagnets, where the timescale of the exchange-driven sublattice
dynamics is comparable to inertial relaxation times. Consequently,
antiferromagnetic resonance techniques should be better suited for the search
for intrinsical inertial spin dynamics on ultrafast timescales than
ferromagnetic resonance.
|
2012.02790v3
|
2020-12-14
|
Thermally induced spin torque and domain wall motion in superconductor/antiferromagnetic insulator bilayers
|
We theoretically investigate domain wall motion in an antiferromagnetic
insulator layer caused by thermally generated spin currents in an adjacent
spin-split superconductor layer. An uncompensated antiferromagnet interface
enables the two crucial ingredients underlying the mechanism - spin splitting
in the superconductor and absorption of spin currents by the antiferromagnet.
Treating the superconductor using the quasiclassical theory and the
antiferromagnet via Landau-Lifshitz-Gilbert description, we find domain wall
propagation along the thermal gradient with relatively large velocities $\sim
100$ m/s. Our proposal exploits the giant thermal response of spin-split
superconductors in achieving large spin torques towards driving domain wall and
other spin textures in antiferromagnets.
|
2012.07405v1
|
2020-11-04
|
A note on the intuitionistic logic of false belief
|
In this paper we analyse logic of false belief in intuitionistic setting.
This logic, studied in its classical version by Steinsvold, Fan, Gilbert and
Venturi, describes the following situation: a formula F is not satisfied in a
given world, but we still believe in it (or we think that it should be
accepted). Another interpretations are also possible: e.g. that we do not
accept F but it is imposed on us by a kind of council or advisory board. From
the mathematical point of view, the idea is expressed by an adequate form of
modal operator W which is interpreted in relational frames with neighborhoods.
We discuss monotonicity of forcing, soundness, completeness and several other
issues. We present also some simple systems in which confirmation of previously
accepted formula is modelled.
|
2012.08309v1
|
2021-01-05
|
Efficient domain wall motion in asymmetric magnetic tunnel junctions with vertical current flow
|
In this paper, we study the domain wall motion induced by vertical current
flow in asymmetric magnetic tunnel junctions. The domain wall motion in the
free layer is mainly dictated by the current-induced field-like torque acting
on it. We show that as we increase the MTJ asymmetry, by considering dissimilar
ferromagnetic contacts, a linear-in-voltage field-like torque behavior is
accompanied by an enhancement in the domain wall displacement efficiency and a
higher degree of bidirectional propagation. Our analysis is based on a
combination of a quantum transport model and magnetization dynamics as
described by the Landau-Lifshitz-Gilbert equation, along with comparison to the
intrinsic characteristics of a benchmark in-plane current injection domain wall
device.
|
2101.01581v1
|
2021-01-12
|
Modeling of Thermal Magnetic Fluctuations in Nanoparticle Enhanced Magnetic Resonance Detection
|
We present a systematic numerical modeling investigation of magnetization
dynamics and thermal magnetic moment fluctuations of single magnetic domain
nanoparticles in a configuration applicable to enhancing inductive magnetic
resonance detection signal to noise ratio (SNR). Previous proposals for
oriented anisotropic single magnetic domain nanoparticle amplification of
magnetic flux in MRI coil focused only on the coil pick-up voltage signal
enhancement. Here we extend the analysis to the numerical evaluation of the SNR
by modeling the inherent thermal magnetic noise introduced into the detection
coil by the insertion of such anisotropic nanoparticle-filled coil core. We
utilize the Landau-Lifshitz-Gilbert equation under the Stoner-Wohlfarth single
magnetic domain (macrospin) assumption to simulate the magnetization dynamics
in such nanoparticles due to AC drive field as well as thermal noise. These
simulations are used to evaluate the nanoparticle configurations and shape
effects on enhancing SNR. Finally, we explore the effect of narrow band
filtering of the broadband magnetic moment thermal fluctuation noise on the
SNR. Our results provide the impetus for relatively simple modifications to
existing MRI systems for achieving enhanced detection SNR in scanners with
modest polarizing magnetic fields.
|
2101.04649v1
|
2021-01-20
|
Spin-current mediated exchange coupling in MgO-based magnetic tunnel junctions
|
Heterostructures composed of ferromagnetic layers that are mutually
interacting through a nonmagnetic spacer are at the core of magnetic sensor and
memory devices. In the present study, layer-resolved ferromagnetic resonance
was used to investigate the coupling between the magnetic layers of a
Co/MgO/Permalloy magnetic tunnel junction. Two magnetic resonance peaks were
observed for both magnetic layers, as probed at the Co and Ni L3 x-ray
absorption edges, showing a strong interlayer interaction through the
insulating MgO barrier. A theoretical model based on the
Landau-Lifshitz-Gilbert-Slonczewski equation was developed, including exchange
coupling and spin pumping between the magnetic layers. Fits to the experimental
data were carried out, both with and without a spin pumping term, and the
goodness of the fit was compared using a likelihood ratio test. This rigorous
statistical approach provides an unambiguous proof of the existence of
interlayer coupling mediated by spin pumping.
|
2101.08157v1
|
2021-01-27
|
Numerical simulation of the viral entry into a cell driven by receptor diffusion
|
The present study focuses on the receptor driven endocytosis typical of viral
entry into a cell. A locally increased density of receptors at the time of
contact between the cell and the virus is necessary in this case. The virus is
considered as a substrate with fixed receptors on its surface, whereas the
receptors of the host cell are free to move over its membrane, allowing a local
change in their concentration. In the contact zone the membrane inflects and
forms an envelope around the virus. The created vesicle imports its cargo into
the cell. This paper assumes the diffusion equation accompanied by boundary
conditions requiring the conservation of binders to describe the process.
Moreover, it introduces a condition defining the energy balance at the front of
the adhesion zone. The latter yields the upper limit for the size of virus
which can be engulfed by the cell membrane. The described moving boundary
problem in terms of the binder density and the velocity of the adhesion front
is well posed and numerically solved by using the finite difference method. The
illustrative examples have been chosen to show the influence of the process
parameters on the initiation and the duration of the process.
|
2101.11515v1
|
2021-02-04
|
AI Development for the Public Interest: From Abstraction Traps to Sociotechnical Risks
|
Despite interest in communicating ethical problems and social contexts within
the undergraduate curriculum to advance Public Interest Technology (PIT) goals,
interventions at the graduate level remain largely unexplored. This may be due
to the conflicting ways through which distinct Artificial Intelligence (AI)
research tracks conceive of their interface with social contexts. In this paper
we track the historical emergence of sociotechnical inquiry in three distinct
subfields of AI research: AI Safety, Fair Machine Learning (Fair ML) and
Human-in-the-Loop (HIL) Autonomy. We show that for each subfield, perceptions
of PIT stem from the particular dangers faced by past integration of technical
systems within a normative social order. We further interrogate how these
histories dictate the response of each subfield to conceptual traps, as defined
in the Science and Technology Studies literature. Finally, through a
comparative analysis of these currently siloed fields, we present a roadmap for
a unified approach to sociotechnical graduate pedagogy in AI.
|
2102.04255v1
|
2021-02-15
|
An In-Depth Investigation of the Performance Characteristics of Hyperledger Fabric
|
Private permissioned blockchains are deployed in ever greater numbers to
facilitate cross-organizational processes in various industries, particularly
in supply chain management. One popular example of this trend is Hyperledger
Fabric. Compared to public permissionless blockchains, it promises improved
performance and provides certain features that address key requirements of
enterprises. However, also permissioned blockchains are still not as scalable
as centralized systems, and due to the scarcity of theoretical results and
empirical data, their real-world performance cannot be predicted with the
necessary precision. We intend to address this issue by conducting an in-depth
performance analysis of Hyperledger Fabric. The paper presents a detailed
compilation of various performance characteristics using an enhanced version of
the Distributed Ledger Performance Scan (DLPS). Researchers and practitioners
alike can use the various performance properties identified and discussed as
guidelines to better configure and implement their Hyperledger Fabric network.
Likewise, they are encouraged to use the DLPS framework to conduct their
measurements.
|
2102.07731v2
|
2021-02-18
|
On isodual double Toeplitz codes
|
Double Toeplitz (shortly DT) codes are introduced here as a generalization of
double circulant codes. We show that such a code is isodual, hence formally
self-dual. Self-dual DT codes are characterized as double circulant or double
negacirculant. Likewise, even DT binary codes are characterized as double
circulants. Numerical examples obtained by exhaustive search show that the
codes constructed have best-known minimum distance, up to one unit, amongst
formally self-dual codes, and sometimes improve on the known values. Over
$\F_4$ an explicit construction of DT codes, based on quadratic residues in a
prime field, performs equally well. We show that DT codes are asymptotically
good over $\F_q$. Specifically, we construct DT codes arbitrarily close to the
asymptotic varshamov-Gilbert bound for codes of rate one half.
|
2102.09233v1
|
2021-02-20
|
Design of Ciphers based on the Geometric Structure of the Möbius Plane
|
Till now geometric structures don't play a major role in cryptography.
Gilbert, MacWilliams and Sloane introduced in 1974 an authentication scheme in
the projective plane and showed its perfectness in the sense of the definition
of Shannon. In this paper we will show that this authentication scheme also
fulfills the requirement of completeness according to Kam and Davida and we
will extend the application of geometric structures in cryptography by
introducing an encryption scheme in the M\"obius plane. We will further examine
its properties, showing that it also fulfills the requirement of completeness
and Shannon's requirement of perfectness in first approximation. The results of
this paper can be used to define similar encryption schemes in the circle
geometries of Laguerre and Minkowski.
|
2102.10321v2
|
2021-03-02
|
Struwe-like solutions for an evolutionary model of magnetoviscoelastic fluids
|
In this work we investigate the existence and uniqueness of Struwe-like
solutions for a system of partial differential equations modeling the dynamics
of magnetoviscoelastic fluids. The considered system couples a Navier-Stokes
type equation with a dissipative equation for the deformation tensor and a
Landau-Lifshitz-Gilbert type equation for the magnetization field. The main
purpose is to establish a well-posedness theory in a two-dimensional periodic
domain under standard assumption of critical regularity for the (possibly
large) initial data. We prove that the considered weak solutions are everywhere
smooth, except for a discrete set of time values. The proof of the uniqueness
is based on suitable energy estimates for the solutions within a functional
framework which is less regular than the one of the Struwe energy level. These
estimates rely on several techniques of harmonic analysis and paradifferential
calculus.
|
2103.01647v1
|
2021-03-07
|
Design of Ciphers based on the Geometric Structure of the Laguerre and Minkowski Planes
|
Till now geometric structures don't play a major role in cryptography.
Gilbert, MacWilliams and Sloane introduced an authentication scheme in the
projective plane and showed its perfectness in the sense of Shannon. In
arXiv:2102.10321 we introduced an encryption scheme in the M\"obius plane and
showed that it fulfills Shannon's requirement of perfectness in first
approximation and also the requirement of completeness according to Kam and
Davida. In this paper we will apply a similar approach to define encryption
schemes in the geometries of the Laguerre plande and the Minkowski plane. We
will show that the encryption scheme in the Laguerre geometry meets Shannon's
requirement of perfectness sharp and that the encryption scheme in the
Minkowski geometry meets this requirement in first approximation. The Laguerre
cipher also fulfills the requirement of completeness according to Kam and
Davida.
|
2103.04428v1
|
2021-03-09
|
An atomic perspective on the serpentine-chlorite solid-state transformation
|
Serpentine minerals are important components of metamorphic rocks and
promising geo-materials for nanotechnology. Lizardite, the most abundant
serpentine mineral, can be transformed into chlorite during metamorphism. This
intriguing phase transformation should affect the deformation behavior during
aseismic creep and slow slip at the base of the subduction zone, but has not
been understood structurally and chemically at the atomic scale. Here we
visualized cations and oxygen atoms using the state-of-the-art low-dose
scanning transmission electron microscopy and found that restructuring mainly
involves the synergistic migration of tetrahedral cations and oxygen anions,
coupled with the migration of octahedral trivalent cations into the
brucite-like interlayer. Further, we show that different serpentine polytypes
result in distinct regular interstratifications of serpentine and chlorite. Our
results clarify the long-standing puzzle of how solid-state layer silicate
transformations occur and lead to long-period ordered structures.
|
2103.05210v1
|
2021-03-13
|
On Bounds for Ring-Based Coding Theory
|
Coding Theory where the alphabet is identified with the elements of a ring or
a module has become an important research topic over the last 30 years. Such
codes over rings had important applications and many interesting mathematical
problems are related to this line of research.
It has been well established, that with the generalization of the algebraic
structure to rings there is a need to also generalize the underlying metric
beyond the usual Hamming weight used in traditional coding theory over finite
fields.
This paper introduces a new weight, called the overweight, which can be seen
as a generalization of the Lee weight on the integers modulo $4$. For this new
weight we provide a number of well-known bounds, like a Plotkin bound, a
sphere-packing bound, and a Gilbert-Varshamov bound. A further highlight is the
proof of a Johnson bound for the homogeneous weight on a general finite
Frobenius ring.
|
2103.07749v2
|
2021-03-17
|
ALADIN: All Layer Adaptive Instance Normalization for Fine-grained Style Similarity
|
We present ALADIN (All Layer AdaIN); a novel architecture for searching
images based on the similarity of their artistic style. Representation learning
is critical to visual search, where distance in the learned search embedding
reflects image similarity. Learning an embedding that discriminates
fine-grained variations in style is hard, due to the difficulty of defining and
labelling style. ALADIN takes a weakly supervised approach to learning a
representation for fine-grained style similarity of digital artworks,
leveraging BAM-FG, a novel large-scale dataset of user generated content
groupings gathered from the web. ALADIN sets a new state of the art accuracy
for style-based visual search over both coarse labelled style data (BAM) and
BAM-FG; a new 2.62 million image dataset of 310,000 fine-grained style
groupings also contributed by this work.
|
2103.09776v1
|
2021-03-23
|
A Massively Parallel Time-Domain Coupled Electrodynamics-Micromagnetics Solver
|
We present a new, high-performance coupled electrodynamics-micromagnetics
solver for full physical modeling of signals in microelectronic circuitry. The
overall strategy couples a finite-difference time-domain (FDTD) approach for
Maxwell's equations to a magnetization model described by the
Landau-Lifshitz-Gilbert (LLG) equation. The algorithm is implemented in the
Exascale Computing Project software framework, AMReX, which provides effective
scalability on manycore and GPU-based supercomputing architectures.
Furthermore, the code leverages ongoing developments of the Exascale
Application Code, WarpX, primarily developed for plasma wakefield accelerator
modeling. Our novel temporal coupling scheme provides second-order accuracy in
space and time by combining the integration steps for the magnetic field and
magnetization into an iterative sub-step that includes a trapezoidal
discretization for the magnetization. The performance of the algorithm is
demonstrated by the excellent scaling results on NERSC multicore and GPU
systems, with a significant (59x) speedup on the GPU using a node-by-node
comparison. We demonstrate the utility of our code by performing simulations of
an electromagnetic waveguide and a magnetically tunable filter.
|
2103.12819v1
|
2021-04-06
|
Geometry and Symmetry in Skyrmion Dynamics
|
The uniform motion of chiral magnetic skyrmions induced by a spin-transfer
torque displays an intricate dependence on the skyrmions' topological charge
and shape. We reveal surprising patterns in this dependence through simulations
of the Landau-Lifshitz-Gilbert equation with Zhang-Li torque and explain them
through a geometric analysis of Thiele's equation. In particular, we show that
the velocity distribution of topologically non-trivial skyrmions depends on
their symmetry: it is a single circle for skyrmions of high symmetry and a
family of circles for low-symmetry configurations. We also show that the
velocity of the topologically trivial skyrmions, previously believed to be the
fastest objects, can be surpassed, for instance, by antiskyrmions. The
generality of our approach suggests the validity of our results for exchange
frustrated magnets, bubble materials, and others.
|
2104.02342v1
|
2021-04-06
|
Diffusion of a magnetic skyrmion in 2-dimensional space
|
Two-dimensional magnetic skyrmions are particle-like magnetic domains in
magnetic thin films. The kinetic property of the magnetic skyrmions at finite
temperature is well described by the Thiele equation, including a stochastic
field and a finite mass. In this paper, the validity of the constant-mass
approximation is examined by comparing the Fourier spectrum of Brownian motions
described by the Thiele equation and the Landau-Lifshitz-Gilbert equation.
Then, the 4-dimensional Fokker-Planck equation is derived from the Thiele
equation with a mass-term. Consequently, an expression of the diffusion flow
and diffusion constant in a tensor form is derived, extending Chandrasekhar's
method for Thiele dynamics.
|
2104.02345v2
|
2021-04-08
|
Computation and Bribery of Voting Power in Delegative Simple Games
|
Following Zhang and Grossi~(AAAI 2021), we study in more depth a variant of
weighted voting games in which agents' weights are induced by a transitive
support structure. This class of simple games is notably well suited to study
the relative importance of agents in the liquid democracy framework. We first
propose a pseudo-polynomial time algorithm to compute the Banzhaf and
Shapley-Shubik indices for this class of game. Then, we study a bribery
problem, in which one tries to maximize/minimize the voting power/weight of a
given agent by changing the support structure under a budget constraint. We
show that these problems are computationally hard and provide several
parameterized complexity results.
|
2104.03692v2
|
2021-05-10
|
Role of higher-order effects in spin-misalignment small-angle neutron scattering of high-pressure torsion nickel
|
Magnetic-field-dependent unpolarized small-angle neutron scattering (SANS)
experiments demonstrate that high-pressure torsion (HPT) straining induces spin
misalignments in pure Ni, which persist in magnetic fields up to 4 T. The
spin-misalignment scattering patterns are elongated perpendicular to the
applied magnetic field due to an unusual predominant longitudinal
$sin^2(\theta)$-type angular anisotropy. Such a contribution cannot be
explained by the conventional second order (in spin misalignment amplitude)
micromagnetic SANS theory in the approach-to-saturation regime, nor can its
magnitude relative to the other features of the cross sections by the third
order micromagnetic SANS theory. This indicates that the high-density of
crystal defects induced via HPT straining in Ni makes such higher-order effects
in the micromagnetic SANS cross sections observable.
|
2105.04167v1
|
2021-04-26
|
Axes for Sociotechnical Inquiry in AI Research
|
The development of artificial intelligence (AI) technologies has far exceeded
the investigation of their relationship with society. Sociotechnical inquiry is
needed to mitigate the harms of new technologies whose potential impacts remain
poorly understood. To date, subfields of AI research develop primarily
individual views on their relationship with sociotechnics, while tools for
external investigation, comparison, and cross-pollination are lacking. In this
paper, we propose four directions for inquiry into new and evolving areas of
technological development: value--what progress and direction does a field
promote, optimization--how the defined system within a problem formulation
relates to broader dynamics, consensus--how agreement is achieved and who is
included in building it, and failure--what methods are pursued when the problem
specification is found wanting. The paper provides a lexicon for sociotechnical
inquiry and illustrates it through the example of consumer drone technology.
|
2105.06551v1
|
2021-05-21
|
$\mathbb{F}_q$-zeros of sparse trivariate polynomials and toric 3-fold codes
|
For a given lattice polytope $P$ in $\mathbb{R}^3$, consider the space
$\mathcal{L}_P$ of trivariate polynomials over a finite field $\mathbb{F}_q$,
whose Newton polytopes are contained in $P$. We give an upper bound for the
maximum number of $\mathbb{F}_q$-zeros of polynomials in $\mathcal{L}_P$ in
terms of the Minkowski length of $P$ and $q$, the size of the field.
Consequently, this produces lower bounds for the minimum distance of toric
codes defined by evaluating elements of $\mathcal{L}_P$ at the points of the
algebraic torus $(\mathbb{F}_q^*)^3$. Our approach is based on understanding
factorizations of polynomials in $\mathcal{L}_P$ with the largest possible
number of non-unit factors. The related combinatorial result that we obtain is
a description of Minkowski sums of lattice polytopes contained in $P$ with the
largest possible number of non-trivial summands.
|
2105.10071v2
|
2021-05-24
|
Spatio-temporal dynamics of voltage-induced resistance transition in the double-exchange model
|
We present multi-scale dynamical simulations of voltage-induced
insulator-to-metal transition in the double exchange model, a canonical example
of itinerant magnet and correlated electron systems. By combining
nonequilibrium Green's function method with large-scale Landau-Lifshitz-Gilbert
dynamics, we show that the transition from an antiferromagnetic insulator to
the low-resistance state is initiated by the nucleation of a thin ferromagnetic
conducting layer at the anode. The metal-insulator interface separating the two
phases is then driven toward the opposite electrode by the voltage stress,
giving rise to a growing metallic region. We further show that the initial
transformation kinetics is well described by the Kolmogorov-Avrami-Ishibashi
model with an effective spatial-dimension that depends on the applied voltage.
Implications of our findings for the resistive switching in colossal
magnetoresistant materials are also discussed.
|
2105.11076v2
|
2021-05-26
|
High-speed programmable photonic circuits in a cryogenically compatible, visible-NIR 200 mm CMOS architecture
|
Recent advances in photonic integrated circuits (PICs) have enabled a new
generation of "programmable many-mode interferometers" (PMMIs) realized by
cascaded Mach Zehnder Interferometers (MZIs) capable of universal
linear-optical transformations on N input-output optical modes. PMMIs serve
critical functions in photonic quantum information processing, quantum-enhanced
sensor networks, machine learning and other applications. However, PMMI
implementations reported to date rely on thermo-optic phase shifters, which
limit applications due to slow response times and high power consumption. Here,
we introduce a large-scale PMMI platform, based on a 200 mm CMOS process, that
uses aluminum nitride (AlN) piezo-optomechanical actuators coupled to silicon
nitride (SiN) waveguides, enabling low-loss propagation with phase modulation
at greater than 100 MHz in the visible to near-infrared wavelengths. Moreover,
the vanishingly low holding-power consumption of the piezo-actuators enables
these PICs to operate at cryogenic temperatures, paving the way for a fully
integrated device architecture for a range of quantum applications.
|
2105.12531v1
|
2021-05-27
|
On the Complexity of Load Balancing in Dynamic Networks
|
In the load balancing problem, each node in a network is assigned a load, and
the goal is to equally distribute the loads among the nodes, by preforming
local load exchanges. While load balancing was extensively studied in static
networks, only recently a load balancing algorithm for dynamic networks with a
bounded convergence time was presented. In this paper, we further study the
time complexity of load balancing in the context of dynamic networks.
First, we show that randomness is not necessary, and present a deterministic
algorithm which slightly improves the running time of the previous algorithm,
at the price of not being matching-based. Then, we consider integral loads,
i.e., loads that cannot be split indefinitely, and prove that no matching-based
algorithm can have a bounded convergence time for this case.
To circumvent both this impossibility result, and a known one for the
non-integral case, we apply the method of smoothed analysis, where random
perturbations are made over the worst-case choices of network topologies. We
show both impossibility results do not hold under this kind of analysis,
suggesting that load-balancing in real world systems might be faster than the
lower bounds suggest.
|
2105.13194v1
|
2021-06-09
|
A Compact Model for Scalable MTJ Simulation
|
This paper presents a physics-based modeling framework for the analysis and
transient simulation of circuits containing Spin-Transfer Torque (STT) Magnetic
Tunnel Junction (MTJ) devices. The framework provides the tools to analyze the
stochastic behavior of MTJs and to generate Verilog-A compact models for their
simulation in large VLSI designs, addressing the need for an industry-ready
model accounting for real-world reliability and scalability requirements.
Device dynamics are described by the Landau-Lifshitz-Gilbert-Slonczewsky
(s-LLGS ) stochastic magnetization considering Voltage-Controlled Magnetic
Anisotropy (VCMA) and the non-negligible statistical effects caused by thermal
noise. Model behavior is validated against the OOMMF magnetic simulator and its
performance is characterized on a 1-Mb 28 nm Magnetoresistive-RAM (MRAM) memory
product.
|
2106.04976v1
|
2021-06-14
|
Can Explainable AI Explain Unfairness? A Framework for Evaluating Explainable AI
|
Many ML models are opaque to humans, producing decisions too complex for
humans to easily understand. In response, explainable artificial intelligence
(XAI) tools that analyze the inner workings of a model have been created.
Despite these tools' strength in translating model behavior, critiques have
raised concerns about the impact of XAI tools as a tool for `fairwashing` by
misleading users into trusting biased or incorrect models. In this paper, we
created a framework for evaluating explainable AI tools with respect to their
capabilities for detecting and addressing issues of bias and fairness as well
as their capacity to communicate these results to their users clearly. We found
that despite their capabilities in simplifying and explaining model behavior,
many prominent XAI tools lack features that could be critical in detecting
bias. Developers can use our framework to suggest modifications needed in their
toolkits to reduce issues likes fairwashing.
|
2106.07483v1
|
2021-06-17
|
Density of Free Modules over Finite Chain Rings
|
In this paper we focus on modules over a finite chain ring $\mathcal{R}$ of
size $q^s$. We compute the density of free modules of $\mathcal{R}^n$, where we
separately treat the asymptotics in $n,q$ and $s$. In particular, we focus on
two cases: one where we fix the length of the module and one where we fix the
rank of the module. In both cases, the density results can be bounded by the
Andrews-Gordon identities. We also study the asymptotic behaviour of modules
generated by random matrices over $\mathcal{R}$. Since linear codes over
$\mathcal{R}$ are submodules of $\mathcal{R}^n$ we get direct implications for
coding theory. For example, we show that random codes achieve the
Gilbert-Varshamov bound with high probability.
|
2106.09403v2
|
2021-06-28
|
Combinatorial BLAS 2.0: Scaling combinatorial algorithms on distributed-memory systems
|
Combinatorial algorithms such as those that arise in graph analysis, modeling
of discrete systems, bioinformatics, and chemistry, are often hard to
parallelize. The Combinatorial BLAS library implements key computational
primitives for rapid development of combinatorial algorithms in
distributed-memory systems. During the decade since its first introduction, the
Combinatorial BLAS library has evolved and expanded significantly.
This paper details many of the key technical features of Combinatorial BLAS
version 2.0, such as communication avoidance, hierarchical parallelism via
in-node multithreading, accelerator support via GPU kernels, generalized
semiring support, implementations of key data structures and functions, and
scalable distributed I/O operations for human-readable files. Our paper also
presents several rules of thumb for choosing the right data structures and
functions in Combinatorial BLAS 2.0, under various common application
scenarios.
|
2106.14402v1
|
2021-07-01
|
From Epidemic to Pandemic Modelling
|
We present a methodology for systematically extending epidemic models to
multilevel and multiscale spatio-temporal pandemic ones. Our approach builds on
the use of coloured stochastic and continuous Petri nets facilitating the sound
component-based extension of basic SIR models to include population
stratification and also spatio-geographic information and travel connections,
represented as graphs, resulting in robust stratified pandemic metapopulation
models. This method is inherently easy to use, producing scalable and reusable
models with a high degree of clarity and accessibility which can be read either
in a deterministic or stochastic paradigm. Our method is supported by a
publicly available platform PetriNuts; it enables the visual construction and
editing of models; deterministic, stochastic and hybrid simulation as well as
structural and behavioural analysis. All the models are available as
supplementary material, ensuring reproducibility.
|
2107.00835v1
|
2021-07-12
|
Primitive Rateless Codes
|
In this paper, we propose primitive rateless (PR) codes. A PR code is
characterized by the message length and a primitive polynomial over
$\mathbf{GF}(2)$, which can generate a potentially limitless number of coded
symbols. We show that codewords of a PR code truncated at any arbitrary length
can be represented as subsequences of a maximum-length sequence ($m$-sequence).
We characterize the Hamming weight distribution of PR codes and their duals and
show that for a properly chosen primitive polynomial, the Hamming weight
distribution of the PR code can be well approximated by the truncated binomial
distribution. We further find a lower bound on the minimum Hamming weight of PR
codes and show that there always exists a PR code that can meet this bound for
any desired codeword length. We provide a list of primitive polynomials for
message lengths up to $40$ and show that the respective PR codes closely meet
the Gilbert-Varshamov bound at various rates. Simulation results show that PR
codes can achieve similar block error rates as their BCH counterparts at
various signal-to-noise ratios (SNRs) and code rates. PR codes are
rate-compatible and can generate as many coded symbols as required; thus,
demonstrating a truly rateless performance.
|
2107.05774v1
|
2021-07-16
|
Linear Programming Bounds for Almost-Balanced Binary Codes
|
We revisit the linear programming bounds for the size vs. distance trade-off
for binary codes, focusing on the bounds for the almost-balanced case, when all
pairwise distances are between $d$ and $n-d$, where $d$ is the code distance
and $n$ is the block length. We give an optimal solution to Delsarte's LP for
the almost-balanced case with large distance $d \geq (n - \sqrt{n})/2 + 1$,
which shows that the optimal value of the LP coincides with the Grey-Rankin
bound for self-complementary codes.
We also show that a limitation of the asymptotic LP bound shown by
Samorodnitsky, namely that it is at least the average of the first MRRW upper
bound and Gilbert-Varshamov bound, continues to hold for the almost-balanced
case.
|
2107.07672v1
|
2021-07-17
|
Magnetization switching in the inertial regime
|
We have numerically solved the Landau-Lifshitz-Gilbert (LLG) equation in its
standard and inertial forms to study the magnetization switching dynamics in a
$3d$ thin film ferromagnet. The dynamics is triggered by ultrashort magnetic
field pulses of varying width and amplitude in the picosecond and Tesla range.
We have compared the solutions of the two equations in terms of switching
characteristic, speed and energy analysis. Both equations return qualitatively
similar switching dynamics, characterized by regions of slower precessional
behavior and faster ballistic motion. In case of inertial dynamics, ballistic
switching is found in a 25 % wider region in the parameter space given by the
magnetic field amplitude and width. The energy analysis of the dynamics is
qualitatively different for the standard and inertial LLG equations. In the
latter case, an extra energy channel, interpreted as the kinetic energy of the
system, is available. Such extra channel is responsible for a resonant energy
absorption at THz frequencies, consistent with the occurence of spin nutation.
|
2107.08234v1
|
2021-10-06
|
Controlled-Phase Gate by Dynamic Coupling of Photons to a Two-Level Emitter
|
We propose an architecture for achieving high-fidelity deterministic quantum
logic gates on dual-rail encoded photonic qubits by letting photons interact
with a two-level emitter (TLE) inside an optical cavity. The photon wave
packets that define the qubit are preserved after the interaction due to a
quantum control process that actively loads and unloads the photons from the
cavity and dynamically alters their effective coupling to the TLE. The controls
rely on nonlinear wave mixing between cavity modes enhanced by strong
externally modulated electromagnetic fields or on AC Stark shifts of the TLE
transition energy. We numerically investigate the effect of imperfections in
terms of loss and dephasing of the TLE as well as control field miscalibration.
Our results suggest that III-V quantum dots in GaAs membranes is a promising
platform for photonic quantum information processing.
|
2110.02960v2
|
2021-10-12
|
Magnetization dynamics in the density matrix formalism
|
Magnetization dynamics described by the Landau-Lifshitz-Gilbert-Slonczewski
(LLGS) equation can be formulated to have the form of the well-known
two-level-system (TLS) equations. Recently, we showed that a DC spin-transfer
torque (STT) term in the LLGS equation can be mapped to a modulation of the
carrier relaxation rates in the analogous TLS equations. Here, we extend the
analogy to the TLS dynamics by including the AC magnetic field, AC
demagnetization field, and AC STT excitation that we show constitute the
interaction term in the analogous TLS picture. Interestingly, we find that the
carrier injection rate in the TLS equations that is responsible for transitions
between the excited and ground states of the system naturally translates to an
intense short magnetic pulse that reverses the magnetization state.
Furthermore, we also show that the two helicities of circularly polarized
magnetic pulses correspond to the two carrier injection rates in the analogous
TLS picture. In the context of the highly debated all-optical helicity
dependent switching experiment, it offers a new explanation of the
magnetization reversal from first principles.
|
2110.06138v3
|
2021-10-12
|
Period Ratio Sculpting Near Second-Order Mean-Motion Resonances
|
Second-order mean-motion resonances lead to an interesting phenomenon in the
sculpting of the period ratio distribution due to their shape and width in
period-ratio/eccentricity space. As the osculating periods librate in
resonance, the time-averaged period ratio approaches the exact
commensurability. The width of second-order resonances increases with
increasing eccentricity, and thus more eccentric systems have a stronger peak
at commensurability when averaged over sufficient time. The libration period is
short enough that this time-averaging behavior is expected to appear on the
timescale of the Kepler mission. Using N-body integrations of simulated planet
pairs near the 5:3 and 3:1 mean-motion resonances, we investigate the
eccentricity distribution consistent with the planet pairs observed by Kepler.
This analysis, an approach independent from previous studies, shows no
statistically significant peak at the 3:1 resonance and a small peak at the 5:3
resonance, placing an upper limit on the Rayleigh scale parameter, $\sigma$, of
the eccentricity of the observed Kepler planets at $\sigma=0.245$ (3:1) and
$\sigma=0.095$ (5:3) at 95% confidence, consistent with previous results from
other methods.
|
2110.06317v1
|
2021-10-15
|
Macroscopic elastic stress and strain produced by irradiation
|
Using the notion of eigenstrain produced by the defects formed in a material
exposed to high energy neutron irradiation, we develop a method for computing
macroscopic elastic stress and strain arising in components of a fusion power
plant during operation. In a microstructurally isotropic material, the primary
cause of macroscopic elastic stress and strain fields is the spatial variation
of neutron exposure. We show that under traction-free boundary conditions, the
volume-average elastic stress always vanishes, signifying the formation of a
spatially heterogeneous stress state, combining compressive and tensile elastic
deformations at different locations in the same component, and resulting solely
from the spatial variation of radiation exposure. Several case studies
pertinent to the design of a fusion power plant are analysed analytically and
numerically, showing that a spatially varying distribution of defects produces
significant elastic stresses in ion-irradiated thin films, pressurised
cylindrical tubes and breeding blanket modules.
|
2110.07955v1
|
2021-10-21
|
Physics-Based Models for Magneto-Electric Spin-Orbit Logic Circuits
|
Spintronic devices are a promising beyond-CMOS device option thanks to their
energy efficiency and compatibility with CMOS. To accurately capture their
multi-physics dynamics, a rigorous treatment of both spin and charge and their
inter-conversion is required. Here we present physics-based device models based
on 4x4 matrices for the spin-orbit coupling part of the magneto-electric
spin-orbit (MESO) device. Also, a more rigorous physics model of ferroelectric
and magnetoelectric switching of ferromagnets, based on Landau-Lifshitz-Gilbert
(LLG) and Landau-Khalatnikov (LK) equations, is presented. With the combined
model implemented in a SPICE circuit simulator environment, simulation results
were obtained which show feasibility of MESO implementation and functional
operation of buffers, oscillators, and majority gates.
|
2110.10890v1
|
2021-10-29
|
Thermal melting of discrete time crystals: a dynamical phase transition induced by thermal fluctuations
|
The stability of a discrete time crystal against thermal fluctuations has
been studied numerically by solving a stochastic Landau-Lifshitz-Gilbert
equation of a periodically-driven classical system composed of interacting
spins, each of which couples to a thermal bath. It is shown that in the
thermodynamic limit, even though the long-range temporary crystalline order is
stable at low temperature, it is melting above a critical temperature, at which
the system experiences a non-equilibrium phase transition. The critical
behaviors of the continuous phase transition have been systematically
investigated, and it is shown that despite the genuine non-equilibrium feature
of such a periodically driven system, its critical properties fall into the 3D
Ising universality class with a dynamical exponent ($z=2$) identical to that in
the critical dynamics of kinetic Ising model without driving.
|
2110.15506v3
|
2021-10-29
|
Magnetism and Magnetotransport in the Kagome Antiferromagnet $\text{Mn}_3\text{Ge}$
|
We perform classical Monte Carlo and stochastic Landau-Lifshitz-Gilbert
simulations to study temperature dependent magnetism of Kagome antiferromagnet
(AFM) Weyl metal $\text{Mn}_3\text{Ge}$ and find that a long range chiral order
sets in at a transition temperature well below the N{\'e}el temperature
($T_N$). Based on the crystalline symmetries, imposed by the chiral magnetic
order, we argue for the presence of multiple iso-energetic Weyl nodes (nodes
that are at same energy and with congruent Fermi surface around them) near
chemical potential. Using the semi-classical Boltzmann equations, we show that
the combined contribution to the net longitudinal magnetoconductance (LMC) and
the planar Hall conductance (PHC) from tilted Weyl nodes can lead to
signatures, qualitatively distinct from that of a single pair of Weyl nodes. In
particular, we show that magnetic orders with different chiralities can give
rise to different periods in LMC and PHC as a function of the in-plane magnetic
field direction. This is ultimately related to differences in the
symmetry-imposed constraints on the Weyl nodes.
|
2110.15864v2
|
2021-11-10
|
Experimental Search for Neutron to Mirror Neutron Oscillations as an Explanation of the Neutron Lifetime Anomaly
|
An unexplained $>4\,\sigma$ discrepancy persists between "beam" and "bottle"
measurements of the neutron lifetime. A new model proposed that conversions of
neutrons $n$ into mirror neutrons $n'$, part of a dark mirror sector, can
increase the apparent neutron lifetime by $1\%$ via a small mass splitting
$\Delta{m}$ between $n$ and $n'$ inside the 4.6 T magnetic field of the
National Institute of Standards and Technology Beam Lifetime experiment. A
search for neutron conversions in a 6.6 T magnetic field was performed at the
Spallation Neutron Source which excludes this explanation for the neutron
lifetime discrepancy.
|
2111.05543v2
|
2021-11-12
|
Whirling interlayer fields as a source of stable topological order in moiré CrI3
|
The moir\'e engineering of two-dimensional magnets opens unprecedented
opportunities to design novel magnetic states with promises for spintronic
device applications. The possibility of stabilizing skyrmions in these
materials without chiral spin-orbit couplings or dipolar interactions is yet to
be explored. Here, we investigate the formation and control of ground state
topological spin textures (TSTs) in moir\'e CrI3 using stochastic
Landau-Lifshitz-Gilbert simulations. We unveil the emergence of interlayer
vortex and antivortex Heisenberg exchange fields, stabilizing spontaneous and
field-assisted ground state TSTs with various topologies. The developed study
accounts for the full bilayer spin dynamics, thermal fluctuations, and
intrinsic spin-orbit couplings. By examining the effect of the Kitaev
interaction and the next nearest-neighbor Dzyaloshinskii-Moriya interaction, we
propose the latter as the unique spin-orbit coupling mechanism compatible with
experiments on monolayer and twisted CrI3. Our findings contribute to the
current knowledge about moir\'e skyrmionics and uncover the nature of
spin-orbit coupling in CrI3.
|
2111.06936v2
|
2021-11-21
|
Explicit complex-valued solutions of the 2D eikonal equation
|
We present a method to obtain explicit solutions of the complex eikonal
equation in the plane. This equation arises in the approximation of Helmholtz
equation by the WKBJ or EWT methods. We obtain the complex-valued solutions
(called eikonals) as parameterizations in a complex variable. We consider both
the cases of constant and non-constant index of refraction. In both cases, the
relevant parameterizations depend on some holomorphic function. In the case of
non-constant index of refraction, the parametrization also depends on some
extra exponential complex-valued function and on a quasi-conformal
homeomorphism. This is due to the use of the theory of pseudo-analytic
functions and the related similarity principle. The parameterizations give
information about the formation of caustics and the light and shadow regions
for the relevant eikonals.
|
2111.10852v1
|
2021-12-08
|
A comparison of spectral reconstruction methods applied to non-zero temperature NRQCD meson correlation functions
|
We present results from the fastsum collaboration's programme to determine
the spectrum of the bottomonium system as a function of temperature. Three
different methods of extracting spectral information are discussed: a Maximum
Likelihood approach using a Gaussian spectral function for the ground state,
the Backus Gilbert method, and the Kernel Ridge Regression machine learning
procedure. We employ the fastsum anisotropic lattices with 2+1 dynamical quark
flavours, with temperatures ranging from 47 to 375 MeV.
|
2112.04201v1
|
2021-12-23
|
Nutation spin waves in ferromagnets
|
Magnetization dynamics and spin waves in ferromagnets are investigated using
the inertial Landau-Lifshitz-Gilbert equation. Taking inertial magnetization
dynamics into account, dispersion relations describing the propagation of
nutation spin waves in an arbitrary direction relative to the applied magnetic
field are derived via Maxwell's equations. It is found that the inertia of
magnetization causes the hybridization of electromagnetic waves and nutation
spin waves in ferromagnets, hybrid nutation spin waves emerge, and the redshift
of frequencies of precession spin waves is initiated, which transforms to
precession-nutation spin waves. These effects depend sharply on the direction
of wave propagation relative to the applied magnetic field. Moreover, the waves
propagating parallel to the applied field are circularly polarized, while the
waves propagating perpendicular to that field are elliptically polarized. The
characteristics of these spin nutation waves are also analyzed.
|
2112.12503v3
|
2021-12-30
|
Spin Torque Oscillations Triggered by In-plane Field
|
We study the dynamics of a spin torque nano oscillator that consists of
parallelly magnetized free and pinned layers by numerically solving the
associated Landau-Lifshitz-Gilbert-Slonczewski equation in the presence of a
field-like torque. We observe that an in-plane magnetic field which is applied
for a short interval of time ($<$1ns) triggers the magnetization to exhibit
self-oscillations from low energy initial magnetization state. Also, we confirm
that the frequency of oscillations can be tuned over the range $\sim$25 GHz to
$\sim$72 GHz by current, even in the absence of field-like torque. We find the
frequency enhancement up to 10 GHz by the presence of field-like torque. We
determine the Q-factor for different frequencies and show that it increases
with frequency. Our analysis with thermal noise confirms that the system is
stable against thermal noise and the dynamics is not altered appreciably by it.
|
2112.15004v1
|
2022-01-11
|
Ultrahigh quality infrared polaritonic resonators based on bottom-up-synthesized van der Waals nanoribbons
|
van der Waals nanomaterials supporting phonon polariton quasiparticles
possess unprecedented light confinement capabilities, making them ideal systems
for molecular sensing, thermal emission, and subwavelength imaging
applications, but they require defect-free crystallinity and nanostructured
form factors to fully showcase these capabilities. We introduce
bottom-up-synthesized {\alpha}-MoO3 structures as nanoscale phonon polaritonic
systems that feature tailorable morphologies and crystal qualities consistent
with bulk single crystals. {\alpha}-MoO3 nanoribbons serve as low-loss
hyperbolic Fabry-P\'erot nanoresonators, and we experimentally map hyperbolic
resonances over four Reststrahlen bands spanning the far- and mid-infrared
spectral range, including resonance modes beyond the tenth order. The measured
quality factors are the highest from phonon polaritonic van der Waals
structures to date. We anticipate that bottom-up-synthesized polaritonic van
der Waals nanostructures will serve as an enabling high-performance and
low-loss platform for infrared optical and optoelectronic applications.
|
2201.03748v1
|
2022-01-12
|
The angular dependence of magnetization dynamics induced by a GHz range strain pulse
|
The dynamics of magnetization is important in spintronics, where the coupling
between phonon and magnon attracts much attention. In this work, we study the
angular dependence of the coupling between longitudinal-wave phonon and magnon.
We investigated the magnetization dynamics using the time-resolved
magneto-optical Kerr effect, which allows measuring spin-wave resonances and
the magnetic echo signal. The frequency, mode number, and amplitude of the
spin-wave resonance change with the out-of-plane angle of the external magnetic
field. The amplitude of the magnetic echo signal caused by the strain pulse
also changes with the angle. We calculate these angular dependences based on
the Landau-Lifshitz-Gilbert equation and find that the angles of the external
field and magnetic moment are important factors for the phonon-magnon coupling
when phonon propagates in the thickness direction under the out-of-plane
magnetic field.
|
2201.04396v1
|
2022-01-17
|
A Theory of Second-Order Wireless Network Optimization and Its Application on AoI
|
This paper introduces a new theoretical framework for optimizing second-order
behaviors of wireless networks. Unlike existing techniques for network utility
maximization, which only considers first-order statistics, this framework
models every random process by its mean and temporal variance. The inclusion of
temporal variance makes this framework well-suited for modeling stateful fading
wireless channels and emerging network performance metrics such as
age-of-information (AoI). Using this framework, we sharply characterize the
second-order capacity region of wireless access networks. We also propose a
simple scheduling policy and prove that it can achieve every interior point in
the second-order capacity region. To demonstrate the utility of this framework,
we apply it for an important open problem: the optimization of AoI over
Gilbert-Elliott channels. We show that this framework provides a very accurate
characterization of AoI. Moreover, it leads to a tractable scheduling policy
that outperforms other existing work.
|
2201.06486v1
|
2022-01-18
|
Self-Modifying Code in Open-Ended Evolutionary Systems
|
Having a model and being able to implement open-ended evolutionary systems is
important for advancing our understanding of open-endedness. Complex systems
science and newest generation high-level programming languages provide
intriguing possibilities to do so. First, some recent advances in modelling and
implementing open-ended evolutionary systems are reviewed. Then, the so-called
allagmatic method is introduced that describes, models, implements, and allows
interpretation of complex systems. After highlighting some current modelling
and implementation challenges, model building blocks of open-ended evolutionary
systems are identified, a system metamodel of open-ended evolution is
formalised in the allagmatic method, an implementation self-modifying code
prototype with a high-level programming language is provided, and guidance from
the allagmatic method to create code blocks is described. The proposed
prototype allows modifying code at runtime in a controlled way within a system
metamodel. Since the allagmatic method has been built based on metaphysical
concepts borrowed from Gilbert Simondon and Alfred N. Whitehead, the proposed
prototype provides a promising starting point to interpret novelty generated at
runtime with the help of a metaphysical framework.
|
2201.06858v2
|
2022-01-28
|
Piezo-optomechanical cantilever modulators for VLSI visible photonics
|
Visible-wavelength very large-scale integration (VLSI) photonic circuits have
potential to play important roles in quantum information and sensing
technologies. The realization of scalable, high-speed, and low-loss photonic
mesh circuits depends on reliable and well-engineered visible photonic
components. Here we report a low-voltage optical phase shifter based on
piezo-actuated mechanical cantilevers, fabricated on a CMOS compatible, 200 mm
wafer-based visible photonics platform. We show linear phase and amplitude
modulation with 6 V$_{\pi}$-cm in differential operation, -1.5 dB to -2 dB
insertion loss, and up to 40 dB contrast in the 700 nm - 780 nm range. By
adjusting selected cantilever parameters, we demonstrate a low-displacement and
a high-displacement device, both exhibiting a nearly flat frequency response
from DC to a peak mechanical resonance at 23 MHz and 6.8 MHz respectively,
which through resonant enhancement of Q~40, further decreases the operating
voltage down to 0.15 V$_{\pi}$-cm.
|
2201.12447v1
|
2022-01-30
|
Spintronics-compatible approach to solving maximum satisfiability problems with probabilistic computing, invertible logic and parallel tempering
|
The search of hardware-compatible strategies for solving NP-hard
combinatorial optimization problems (COPs) is an important challenge of today s
computing research because of their wide range of applications in real world
optimization problems. Here, we introduce an unconventional scalable approach
to face maximum satisfiability problems (Max-SAT) which combines probabilistic
computing with p-bits, parallel tempering, and the concept of invertible logic
gates. We theoretically show the spintronic implementation of this approach
based on a coupled set of Landau-Lifshitz-Gilbert equations, showing a
potential path for energy efficient and very fast (p-bits exhibiting ns time
scale switching) architecture for the solution of COPs. The algorithm is
benchmarked with hard Max-SAT instances from the 2016 Max-SAT competition
(e.g., HG-4SAT-V150-C1350-1.cnf which can be described with 2851 p-bits),
including weighted Max-SAT and Max-Cut problems.
|
2201.12858v1
|
2022-02-01
|
Numerical Model Of Harmonic Hall Voltage Detection For Spintronic Devices
|
We present a numerical macrospin model for harmonic voltage detection in
multilayer spintronic devices. The core of the computational backend is based
on the Landau-Lifshitz-Gilbert-Slonczewski equation, which combines high
performance with satisfactory, for large-scale applications, agreement with the
experimental results. We compare the simulations with the experimental findings
in Ta/CoFeB bilayer system for angular- and magnetic field-dependent resistance
measurements, electrically detected magnetisation dynamics, and harmonic Hall
voltage detection. Using simulated scans of the selected system parameters such
as the polar angle $\theta$, magnetisation saturation
($\mu_\textrm{0}M_\textrm{s}$) or uniaxial magnetic anisotropy ($K_\textrm{u}$)
we show the resultant changes in the harmonic Hall voltage, demonstrating the
dominating influence of the $\mu_\textrm{0}M_\textrm{s}$ on the first and
second harmonics. In the spin-diode ferromagnetic resonance (SD-FMR) technique
resonance method the ($\mu_\textrm{0}M_\textrm{s}$, $K_\textrm{u}$) parameter
space may be optimised numerically to obtain a set of viable curves that fit
the experimental data.
|
2202.00364v1
|
2022-02-03
|
Magnetic domain wall dynamics under external electric field in bilayer CrI$_3$
|
Motivated by manipulating the magnetic order of bilayer CrI$_3$, we carry out
microscopic calculations to find the magnetic order and various magnetic
domains of the system in the presence of an electric field. Making use of
density functional simulations, a spin model Hamiltonian is introduced
consisting of isotropic exchange couplings, Dzyaloshinskii-Moriya (DM)
interaction, and on-site magnetic anisotropy. The spin dynamics of two
well-known states of bilayer CrI$_3$, low temperature (LT) and high temperature
(HT) phases, are obtained by solving the Landau-Lifshitz-Gilbert equation. We
show that the magnetic texture is stacking-dependent in bilayer CrI$_3$ and
stable magnetic domains can appear in the HT stack which are tunable by
external electric and magnetic fields. Therefore, we suggest that the HT phase
represents a promising candidate for data storage in the modern generation of
spintronic devices working on magnetic domain engineering.
|
2202.01394v2
|
2022-02-07
|
Spin-transfer-assisted parametric pumping of magnons in yttrium iron garnet
|
The combination of parametric pumping and spin-transfer torque is a powerful
approach that enables high-level control over magnetic excitations in thin-film
ferromagnets. The excitation parameters, such as pumping power and external
field strength, affect the instabilities of individual magnon modes. We
theoretically explore how the simultaneous effects of parametric pumping and
spin transfer torque influence these magnetic instabilities in a thin-film
ferromagnet. Within the Landau-Lifshitz-Gilbert framework, we perform
micromagnetic simulations of magnon excitations in yttrium iron garnet by
pumping, spin transfer torque, and a combination of the two. We find that
consistent with experimental results, the magnitude and direction of the
spin-transfer torque tune the parametric instability thresholds.
|
2202.03247v2
|
2022-02-13
|
Critical-layer instability of shallow water magnetohydrodynamic shear flows
|
In this paper, the instability of shallow water shear flow with a sheared
parallel magnetic field is studied. Waves propagating in such magnetic shear
flows encounter critical levels where the phase velocity relative to the basic
flow $c-U(y)$ matches the Alfv\'en wave velocities $\pm B(y)/\sqrt{\mu\rho}$,
based on the local magnetic field $B(y)$, the magnetic permeability $\mu$ and
the mass density of the fluid $\rho$. It is shown that when the two critical
levels are close to each other, the critical layer can generate an instability.
The instability problem is solved, combining asymptotic solutions at large
wavenumbers and numerical solutions, and the mechanism of instability explained
using the conservation of momentum. For the shallow water MHD system, the paper
gives the general form of the local differential equation governing such
coalescing critical layers for any generic field and flow profiles, and
determines precisely how the magnetic field modifies the purely hydrodynamic
stability criterion based on the potential vorticity gradient in the critical
layer. The curvature of the magnetic field profile, or equivalently the
electric current gradient, $J' = - B''/\mu$ in the critical layer is found to
play a complementary role in the instability.
|
2202.06272v1
|
2022-02-21
|
On Grid Codes
|
Versions of the Hamming and Gilbert-Varshamov bounds for codes in
$\prod_{i=1}^{n}[0,m_{i}-1]$ with respect to the Manhattan distance are
presented. Given an abelian group $G$ isomorphic to $C_{m_{1}}\times \cdots
\times C_{m_{n}}$, the Hamming, Manhattan, and Lee distances are defined in
$G$; a formula for the minimum Hamming distance of codes that are cyclic
subgroups of $G$ is provided, and some lower bounds for the minimum Manhattan
distance of these codes are determined in terms of their minimum Hamming and
Lee distances. Examples illustrating the main results and an application of
these are provided.
|
2202.10005v4
|
2022-02-23
|
Convergence of Oja's online principal component flow
|
Online principal component analysis (PCA) has been an efficient tool in
practice to reduce dimension. However, convergence properties of the
corresponding ODE are still unknown, including global convergence, stable
manifolds, and convergence rate. In this paper, we focus on the stochastic
gradient ascent (SGA) method proposed by Oja. By regarding the corresponding
ODE as a Landau-Lifshitz-Gilbert (LLG) equation on the Stiefel manifold, we
proved global convergence of the ODE. Moreover, we developed a new technique to
determine stable manifolds. This technique analyzes the rank of the initial
datum. Using this technique, we derived the explicit expression of the stable
manifolds. As a consequence, exponential convergence to stable equilibrium
points was also proved. The success of this new technique should be attributed
to the semi-decoupling property of the SGA method: iteration of previous
components does not depend on that of later ones. As far as we know, our result
is the first complete one on the convergence of an online PCA flow, providing
global convergence, explicit characterization of stable manifolds, and closed
formula of exponential convergence depending on the spectrum gap.
|
2202.11308v1
|
2022-02-28
|
Curb Your Self-Modifying Code
|
Self-modifying code has many intriguing applications in a broad range of
fields including software security, artificial general intelligence, and
open-ended evolution. Having control over self-modifying code, however, is
still an open challenge since it is a balancing act between providing as much
freedom as possible so as not to limit possible solutions, while at the same
time imposing restriction to avoid security issues and invalid code or
solutions. In the present study, I provide a prototype implementation of how
one might curb self-modifying code by introducing control mechanisms for code
modifications within specific regions and for specific transitions between code
and data. I show that this is possible to achieve with the so-called allagmatic
method - a framework to formalise, model, implement, and interpret complex
systems inspired by Gilbert Simondon's philosophy of individuation and Alfred
North Whitehead's philosophy of organism. Thereby, the allagmatic method serves
as guidance for self-modification based on concepts defined in a metaphysical
framework. I conclude that the allagmatic method seems to be a suitable
framework for control mechanisms in self-modifying code and that there are
intriguing analogies between the presented control mechanisms and gene
regulation.
|
2202.13830v2
|
2022-03-03
|
A general adaptive framework for multivariate point null testing
|
As a common step in refining their scientific inquiry, investigators are
often interested in performing some screening of a collection of given
statistical hypotheses. For example, they may wish to determine whether any one
of several patient characteristics are associated with a health outcome of
interest. Existing generic methods for testing a multivariate hypothesis --
such as multiplicity corrections applied to individual hypothesis tests -- can
easily be applied across a variety of problems but can suffer from low power in
some settings. Tailor-made procedures can attain higher power by building
around problem-specific information but typically cannot be easily adapted to
novel settings. In this work, we propose a general framework for testing a
multivariate point null hypothesis in which the test statistic is adaptively
selected to provide increased power. We present theoretical large-sample
guarantees for our test under both fixed and local alternatives. In simulation
studies, we show that tests created using our framework can perform as well as
tailor-made methods when the latter are available, and we illustrate how our
procedure can be used to create tests in two settings in which tailor-made
methods are not currently available.
|
2203.01897v1
|
2022-03-09
|
KPE: Keypoint Pose Encoding for Transformer-based Image Generation
|
Transformers have recently been shown to generate high quality images from
text input. However, the existing method of pose conditioning using skeleton
image tokens is computationally inefficient and generate low quality images.
Therefore we propose a new method; Keypoint Pose Encoding (KPE); KPE is 10
times more memory efficient and over 73% faster at generating high quality
images from text input conditioned on the pose. The pose constraint improves
the image quality and reduces errors on body extremities such as arms and legs.
The additional benefits include invariance to changes in the target image
domain and image resolution, making it easily scalable to higher resolution
images. We demonstrate the versatility of KPE by generating photorealistic
multiperson images derived from the DeepFashion dataset. We also introduce a
evaluation method People Count Error (PCE) that is effective in detecting error
in generated human images.
|
2203.04907v2
|
2022-03-09
|
Finiteness for Hecke algebras of $p$-adic groups
|
Let $G$ be a reductive group over a non-archimedean local field $F$ of
residue characteristic $p$. We prove that the Hecke algebras of $G(F)$ with
coefficients in a ${\mathbb Z}_{\ell}$-algebra $R$ for $\ell$ not equal to $p$
are finitely generated modules over their centers, and that these centers are
finitely generated $R$-algebras. Following Bernstein's original strategy, we
then deduce that "second adjointness" holds for smooth representations of
$G(F)$ with coefficients in any ring $R$ in which $p$ is invertible. These
results had been conjectured for a long time. The crucial new tool that unlocks
the problem is the Fargues-Scholze morphism between a certain "excursion
algebra" defined on the Langlands parameters side and the Bernstein center of
$G(F)$. Using this bridge, our main results are representation theoretic
counterparts of the finiteness of certain morphisms between coarse moduli
spaces of local Langlands parameters that we also prove here, which may be of
independent interest
|
2203.04929v2
|
2022-03-10
|
StyleBabel: Artistic Style Tagging and Captioning
|
We present StyleBabel, a unique open access dataset of natural language
captions and free-form tags describing the artistic style of over 135K digital
artworks, collected via a novel participatory method from experts studying at
specialist art and design schools. StyleBabel was collected via an iterative
method, inspired by `Grounded Theory': a qualitative approach that enables
annotation while co-evolving a shared language for fine-grained artistic style
attribute description. We demonstrate several downstream tasks for StyleBabel,
adapting the recent ALADIN architecture for fine-grained style similarity, to
train cross-modal embeddings for: 1) free-form tag generation; 2) natural
language description of artistic style; 3) fine-grained text search of style.
To do so, we extend ALADIN with recent advances in Visual Transformer (ViT) and
cross-modal representation learning, achieving a state of the art accuracy in
fine-grained style retrieval.
|
2203.05321v2
|
2022-03-12
|
The mass-lumped midpoint scheme for computational micromagnetics: Newton linearization and application to magnetic skyrmion dynamics
|
We discuss a mass-lumped midpoint scheme for the numerical approximation of
the Landau-Lifshitz-Gilbert equation, which models the dynamics of the
magnetization in ferromagnetic materials. In addition to the classical
micromagnetic field contributions, our setting covers the non-standard
Dzyaloshinskii-Moriya interaction, which is the essential ingredient for the
enucleation and stabilization of magnetic skyrmions. Our analysis also includes
the inexact solution of the arising nonlinear systems, for which we discuss
both a constraint preserving fixed-point solver from the literature and a novel
approach based on the Newton method. We numerically compare the two
linearization techniques and show that the Newton solver leads to a
considerably lower number of nonlinear iterations. Moreover, in a numerical
study on magnetic skyrmions, we demonstrate that, for magnetization dynamics
that are very sensitive to energy perturbations, the midpoint scheme, due to
its conservation properties, is superior to the dissipative tangent plane
schemes from the literature.
|
2203.06445v1
|
2022-03-16
|
The Geometry and Topology of Stationary Multi-Axisymmetric Vacuum Black Holes in Higher Dimensions
|
Extending recent work in 5 dimensions, we prove the existence and uniqueness
of solutions to the reduced Einstein equations for vacuum black holes in
$(n+3)$-dimensional spacetimes admitting the isometry group $\mathbb{R}\times
U(1)^{n}$, with Kaluza-Klein asymptotics for $n\geq3$. This is equivalent to
establishing existence and uniqueness for singular harmonic maps $\varphi:
\mathbb{R}^3\setminus\Gamma\rightarrow SL(n+1,\mathbb{R})/SO(n+1)$ with
prescribed blow-up along $\Gamma$, a subset of the $z$-axis in $\mathbb{R}^3$.
We also analyze the topology of the domain of outer communication for these
spacetimes, by developing an appropriate generalization of the plumbing
construction used in the lower dimensional case. Furthermore, we provide a
counterexample to a conjecture of Hollands-Ishibashi concerning the topological
classification of the domain of outer communication. A refined version of the
conjecture is then presented and established in spacetime dimensions less than
8.
|
2203.08325v1
|
2022-03-18
|
Smectite phase separation is driven by emergent interfacial dynamics
|
Smectite clay minerals have an outsize impact on the response of clay-rich
media to common stimuli, such as water imbibition and ion exchange, motivating
extensive effort to understand microscopic behaviors resulting from these
processes such as swelling and exfoliation. Nonetheless, there is no general
consensus about the microscopic forces that govern smectite properties, which
are model systems for understanding colloidal and interfacial phenomena more
generally. We find that the complex free energy surface arising from the
interplay of at least four intermolecular forces and their nonlinear couplings
that control local particle-particle interactions leads to dynamic, unstable
equilibria between distinct phases. Mechanical disequilibrium arising from
osmotic gradients between curved or interacting interfaces drive the dynamic
exchange of layers and ions between dense and dilute phases via avalanche
transitions that are sustained by thermal fluctuations. We suggest that the
surprising interfacial dynamics displayed by smectite minerals, arising from
the vastly different mobilities of water, ions and mineral, makes them
fundamentally distinct from non-clay minerals because their structures are
easily perturbed away from simultaneous chemical and mechanical equilibrium.
|
2203.10129v1
|
2022-03-27
|
Low power In Memory Computation with Reciprocal Ferromagnet/Topological Insulator Heterostructures
|
The surface state of a 3D topological insulator (3DTI) is a spin-momentum
locked conductive state, whose large spin hall angle can be used for the
energy-efficient spin orbit torque based switching of an overlying ferromagnet
(FM). Conversely, the gated switching of the magnetization of a separate FM in
or out of the TI surface plane, can turn on and off the TI surface current. The
gate tunability of the TI Dirac cone gap helps reduce its sub-threshold swing.
By exploiting this reciprocal behaviour, we can use two FM/3DTI
heterostructures to design a 1-Transistor 1-magnetic tunnel junction random
access memory unit (1T1MTJ RAM) for an ultra low power Processing-in-Memory
(PiM) architecture. Our calculation involves combining the Fokker-Planck
equation with the Non-equilibrium Green Function (NEGF) based flow of
conduction electrons and Landau-Lifshitz-Gilbert (LLG) based dynamics of
magnetization. Our combined approach allows us to connect device performance
metrics with underlying material parameters, which can guide proposed
experimental and fabrication efforts.
|
2203.14389v3
|
2022-03-17
|
Symmetry effects on the static and dynamic properties of coupled magnetic oscillators
|
The effect of symmetry on the resonance spectra of antiferromagnetically
coupled oscillators has attracted new interest with the discovery of
symmetry-breaking induced anti-crossings. Here, we experimentally characterise
the resonance spectrum of a synthetic antiferromagnet Pt/CoFeB/Ru/CoFeB/Pt,
where we are able to independently tune the effective magnetisation of the two
coupled magnets. To model our results we apply the mathematical methods of
group theory to the solutions of the Landau Lifshitz Gilbert equation. This
general approach, usually applied to quantum mechanical systems, allows us to
identify the main features of the resonance spectrum in terms of symmetry
breaking and to make a direct comparison with crystal antiferromagnets.
|
2204.01490v1
|
2022-04-17
|
Gravitational Solitons and Complete Ricci Flat Riemannian Manifolds of Infinite Topological Type
|
We present several new space-periodic solutions of the static vacuum Einstein
equations in higher dimensions, both with and without black holes, having
Kasner asymptotics. These latter solutions are referred to as gravitational
solitons. Further partially compactified solutions are also obtained by taking
appropriate quotients, and the topologies are computed explicitly in terms of
connected sums of products of spheres. In addition, it is shown that there is a
correspondence, via Wick rotation, between the spacelike slices of the solitons
and black hole solutions in one dimension less. As a corollary, the solitons
give rise to complete Ricci flat Riemannian manifolds of infinite topological
type and generic holonomy, in dimensions 4 and higher.
|
2204.08048v2
|
2022-04-26
|
Cosmology from the kinetic polarized Sunyaev Zel'dovich effect
|
The cosmic microwave background (CMB) photons that scatter off free electrons
in the large-scale structure induce a linear polarization pattern proportional
to the remote CMB temperature quadrupole observed in the electrons' rest frame.
The associated blackbody polarization anisotropies are known as the polarized
Sunyaev Zel'dovich (pSZ) effect. Relativistic corrections to the remote
quadrupole field give rise to a non-blackbody polarization anisotropy
proportional to the square of the transverse peculiar velocity field; this is
the kinetic polarized Sunyaev Zel'dovich (kpSZ) effect. In this paper, we
forecast the ability of future CMB and galaxy surveys to detect the kpSZ
effect, finding that a statistically significant detection is within the reach
of planned experiments. We further introduce a quadratic estimator for the
square of the peculiar velocity field based on a galaxy survey and CMB
polarization. Finally, we outline how the kpSZ effect is a probe of cosmic
birefringence and primordial non-Gaussianity, forecasting the reach of future
experiments.
|
2204.12503v2
|
2022-04-27
|
Advantages of maintaining a multi-task project-specific bot: an experience report
|
Bots are becoming a popular method for automating basic everyday tasks in
many software projects. This is true in particular because of the availability
of many off-the-shelf task-specific bots that teams can quickly adopt (which
are sometimes completed with additional task-specific custom bots). Based on
our experience in the Coq project, where we have developed and maintained a
multi-task project-specific bot, we argue that this alternative approach to
project automation should receive more attention because it strikes a good
balance between productivity and adaptibility. In this article, we describe the
kind of automation that our bot implements, what advantages we have gained by
maintaining a project-specific bot, and the technology and architecture choices
that have made it possible. We draw conclusions that should generalize to other
medium-sized software teams willing to invest in project automation without
disrupting their workflows.
|
2204.12758v1
|
2022-04-29
|
Self-consistent solution of magnetic and friction energy losses of a magnetic nanoparticle
|
We present a simple simulation model for analysing magnetic and frictional
losses of magnetic nano-particles in viscous fluids subject to alternating
magnetic fields. Assuming a particle size below the single-domain limit, we use
a macrospin approach and solve the Landau-Lifshitz-Gilbert equation coupled to
the mechanical torque equation. Despite its simplicity the presented model
exhibits surprisingly rich physics and enables a detailed analysis of the
different loss processes depending on field parameters and initial arrangement
of the particle and the field. Depending on those parameters regions of
different steady states emerge: a region with dominating N\'eel relaxation and
high magnetic losses and another region region with high frictional losses at
low fields or low frequencies. The energy increases continuously even across
regime boundaries up to frequencies above the Brownian relaxation limit. At
those higher frequencies the steady state can also depend on the initial
orientation of the particle in the external field. The general behavior and
special cases and their specific absorption rates are compared and discussed.
|
2204.14106v3
|
2022-05-04
|
Separations in Proof Complexity and TFNP
|
It is well-known that Resolution proofs can be efficiently simulated by
Sherali-Adams (SA) proofs. We show, however, that any such simulation needs to
exploit huge coefficients: Resolution cannot be efficiently simulated by SA
when the coefficients are written in unary. We also show that Reversible
Resolution (a variant of MaxSAT Resolution) cannot be efficiently simulated by
Nullstellensatz (NS).
These results have consequences for total NP search problems. First, we
characterise the classes PPADS, PPAD, SOPL by unary-SA, unary-NS, and
Reversible Resolution, respectively. Second, we show that, relative to an
oracle, PLS $\not\subseteq$ PPP, SOPL $\not\subseteq$ PPA, and EOPL
$\not\subseteq$ UEOPL. In particular, together with prior work, this gives a
complete picture of the black-box relationships between all classical TFNP
classes introduced in the 1990s.
|
2205.02168v2
|
2022-05-10
|
Programming Data Structures for Large-Scale Desktop Simulations of Complex Systems
|
The investigation of complex systems requires running large-scale simulations
over many temporal iterations. It is therefore important to provide efficient
implementations. The present study borrows philosophical concepts from Gilbert
Simondon to identify data structures and algorithms that have the biggest
impact on running time and memory usage. These are the entity $e$-tuple
$\mathcal{E}$ and the intertwined update function $\phi$. Focusing on
implementing data structures in C#, $\mathcal{E}$ is implemented as a list of
objects according to current software engineering practice and as an array of
pointers according to theoretical considerations. Cellular automaton
simulations with $10^9$ entities over one iteration reveal that the object-list
with dynamic typing and multi-state readiness has a drastic effect on running
time and memory usage, especially dynamic typing as it has a big impact on the
evolution time. Pointer-arrays are possible to implement in C# and are more
running time and memory efficient as compared to the object-list
implementation, however, they are cumbersome to implement. In conclusion,
avoiding dynamic typing in object-list based implementations or using
pointer-arrays gives evolution times that are acceptable in practice, even on
desktop computers.
|
2205.04837v2
|
2022-05-10
|
Sensible AI: Re-imagining Interpretability and Explainability using Sensemaking Theory
|
Understanding how ML models work is a prerequisite for responsibly designing,
deploying, and using ML-based systems. With interpretability approaches, ML can
now offer explanations for its outputs to aid human understanding. Though these
approaches rely on guidelines for how humans explain things to each other, they
ultimately solve for improving the artifact -- an explanation. In this paper,
we propose an alternate framework for interpretability grounded in Weick's
sensemaking theory, which focuses on who the explanation is intended for.
Recent work has advocated for the importance of understanding stakeholders'
needs -- we build on this by providing concrete properties (e.g., identity,
social context, environmental cues, etc.) that shape human understanding. We
use an application of sensemaking in organizations as a template for discussing
design guidelines for Sensible AI, AI that factors in the nuances of human
cognition when trying to explain itself.
|
2205.05057v1
|
2022-05-14
|
SaiNet: Stereo aware inpainting behind objects with generative networks
|
In this work, we present an end-to-end network for stereo-consistent image
inpainting with the objective of inpainting large missing regions behind
objects. The proposed model consists of an edge-guided UNet-like network using
Partial Convolutions. We enforce multi-view stereo consistency by introducing a
disparity loss. More importantly, we develop a training scheme where the model
is learned from realistic stereo masks representing object occlusions, instead
of the more common random masks. The technique is trained in a supervised way.
Our evaluation shows competitive results compared to previous state-of-the-art
techniques.
|
2205.07014v1
|
2022-05-15
|
Sociotechnical Specification for the Broader Impacts of Autonomous Vehicles
|
Autonomous Vehicles (AVs) will have a transformative impact on society.
Beyond the local safety and efficiency of individual vehicles, these effects
will also change how people interact with the entire transportation system.
This will generate a diverse range of large and foreseeable effects on social
outcomes, as well as how those outcomes are distributed. However, the ability
to control both the individual behavior of AVs and the overall flow of traffic
also provides new affordances that permit AVs to control these effects. This
comprises a problem of sociotechnical specification: the need to distinguish
which essential features of the transportation system are in or out of scope
for AV development. We present this problem space in terms of technical,
sociotechnical, and social problems, and illustrate examples of each for the
transport system components of social mobility, public infrastructure, and
environmental impacts. The resulting research methodology sketches a path for
developers to incorporate and evaluate more transportation system features
within AV system components over time.
|
2205.07395v1
|
2022-05-19
|
Collision Detection Accelerated: An Optimization Perspective
|
Collision detection between two convex shapes is an essential feature of any
physics engine or robot motion planner. It has often been tackled as a
computational geometry problem, with the Gilbert, Johnson and Keerthi (GJK)
algorithm being the most common approach today. In this work we leverage the
fact that collision detection is fundamentally a convex optimization problem.
In particular, we establish that the GJK algorithm is a specific sub-case of
the well-established Frank-Wolfe (FW) algorithm in convex optimization. We
introduce a new collision detection algorithm by adapting recent works linking
Nesterov acceleration and Frank-Wolfe methods. We benchmark the proposed
accelerated collision detection method on two datasets composed of strictly
convex and non-strictly convex shapes. Our results show that our approach
significantly reduces the number of iterations to solve collision detection
problems compared to the state-of-the-art GJK algorithm, leading to up to two
times faster computation times.
|
2205.09663v2
|
2022-05-31
|
Solutions of the matrix equation $p(X)=A$, with polynomial function $p(λ)$ over field extensions of $\mathbb{Q}$
|
Let $\mathbb{H}$ be a field with
$\mathbb{Q}\subset\mathbb{H}\subset\mathbb{C}$, and let $p(\lambda)$ be a
polynomial in $\mathbb{H}[\lambda]$, and let $A\in\mathbb{H}^{n\times n}$ be
nonderogatory. In this paper we consider the problem of finding a solution
$X\in\mathbb{H}^{n\times n}$ to $p(X)=A$. A necessary condition for this to be
possible is already known from a paper by M.P. Drazin. Under an additional
condition we provide an explicit construction of such solutions. The
similarities and differences with the derogatory case will be discussed as
well.
One of the tools needed in the paper is a new canonical form, which may be of
independent interest. It combines elements of the rational canonical form with
elements of the Jordan canonical form.
|
2205.15682v1
|
2022-06-02
|
A Fast Randomized Algorithm for Computing an Approximate Null Space
|
Randomized algorithms in numerical linear algebra can be fast, scalable and
robust. This paper examines the effect of sketching on the right singular
vectors corresponding to the smallest singular values of a tall-skinny matrix.
We analyze a fast algorithm by Gilbert, Park and Wakin for finding the trailing
right singular vectors using randomization by examining the quality of the
solution using multiplicative perturbation theory. For an $m\times n$ ($m\geq
n$) matrix, the algorithm runs with complexity $O(mn\log n +n^3)$ which is
faster than the standard $O(mn^2)$ methods. In applications, numerical
experiments show great speedups including a $30\times$ speedup for the AAA
algorithm and $10\times$ speedup for the total least squares problem.
|
2206.00975v3
|
2022-06-10
|
Differentiable Rendering of Neural SDFs through Reparameterization
|
We present a method to automatically compute correct gradients with respect
to geometric scene parameters in neural SDF renderers. Recent physically-based
differentiable rendering techniques for meshes have used edge-sampling to
handle discontinuities, particularly at object silhouettes, but SDFs do not
have a simple parametric form amenable to sampling. Instead, our approach
builds on area-sampling techniques and develops a continuous warping function
for SDFs to account for these discontinuities. Our method leverages the
distance to surface encoded in an SDF and uses quadrature on sphere tracer
points to compute this warping function. We further show that this can be done
by subsampling the points to make the method tractable for neural SDFs. Our
differentiable renderer can be used to optimize neural shapes from multi-view
images and produces comparable 3D reconstructions to recent SDF-based inverse
rendering methods, without the need for 2D segmentation masks to guide the
geometry optimization and no volumetric approximations to the geometry.
|
2206.05344v1
|
2022-06-15
|
Cautious Learning of Multiattribute Preferences
|
This paper is dedicated to a cautious learning methodology for predicting
preferences between alternatives characterized by binary attributes (formally,
each alternative is seen as a subset of attributes). By "cautious", we mean
that the model learned to represent the multi-attribute preferences is general
enough to be compatible with any strict weak order on the alternatives, and
that we allow ourselves not to predict some preferences if the data collected
are not compatible with a reliable prediction. A predicted preference will be
considered reliable if all the simplest models (following Occam's razor
principle) explaining the training data agree on it. Predictions are based on
an ordinal dominance relation between alternatives [Fishburn and LaValle,
1996]. The dominance relation relies on an uncertainty set encompassing the
possible values of the parameters of the multi-attribute utility function.
Numerical tests are provided to evaluate the richness and the reliability of
the predictions made.
|
2206.07341v1
|
2022-06-23
|
Probabilistic load forecasting for the low voltage network: forecast fusion and daily peaks
|
Short-term forecasts of energy consumption are invaluable for the operation
of energy systems, including low voltage electricity networks. However, network
loads are challenging to predict when highly desegregated to small numbers of
customers, which may be dominated by individual behaviours rather than the
smooth profiles associated with aggregate consumption. Furthermore,
distribution networks are challenged almost entirely by peak loads, and tasks
such as scheduling storage and/or demand flexibility maybe be driven by
predicted peak demand, a feature that is often poorly characterised by
general-purpose forecasting methods. Here we propose an approach to predict the
timing and level of daily peak demand, and a data fusion procedure for
combining conventional and peak forecasts to produce a general-purpose
probabilistic forecast with improved performance during peaks. The proposed
approach is demonstrated using real smart meter data and a hypothetical low
voltage network hierarchy comprising feeders, secondary and primary
substations. Fusing state-of-the-art probabilistic load forecasts with peak
forecasts is found to improve performance overall, particularly at smart-meter
and feeder levels and during peak hours, where improvement in terms of CRPS
exceeds 10%.
|
2206.11745v2
|
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