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2023-10-28 | Einstein-de Haas torque as a discrete spectroscopic probe allows nanomechanical measurement of a magnetic resonance | The Einstein-de Haas (EdH) effect is a fundamental, mechanical consequence of
any temporal change of magnetism in an object. EdH torque results from
conserving the object's total angular momentum: the angular momenta of all the
specimen's magnetic moments, together with its mechanical angular momentum.
Although the EdH effect is usually small and difficult to observe, it increases
in magnitude with detection frequency. We explore the frequency-dependence of
EdH torque for a thin film permalloy microstructure by employing a ladder of
flexural beam modes (with five distinct resonance frequencies spanning from 3
to 208 MHz) within a nanocavity optomechanical torque sensor via magnetic
hysteresis curves measured at mechanical resonances. At low DC fields the
gyrotropic resonance of a magnetic vortex spin texture overlaps the 208 MHz
mechanical mode. The massive EdH mechanical torques arising from this
co-resonance yield a fingerprint of vortex core pinning and depinning in the
sample. The experimental results are discussed in relation to mechanical
torques predicted from both macrospin (at high DC magnetic field) and
finite-difference solutions to the Landau-Lifshitz-Gilbert (LLG) equation. A
global fit of the LLG solutions to the frequency-dependent data reveals a
statistically significant discrepancy between the experimentally observed and
simulated torque phase behaviours at spin texture transitions that can be
reduced through the addition of a time constant to the conversion between
magnetic cross-product torque and mechanical torque, constrained by experiment
to be in the range of 0.5 - 4 ns. | 2310.18546v2 |
2023-10-31 | Ensemble models outperform single model uncertainties and predictions for operator-learning of hypersonic flows | High-fidelity computational simulations and physical experiments of
hypersonic flows are resource intensive. Training scientific machine learning
(SciML) models on limited high-fidelity data offers one approach to rapidly
predict behaviors for situations that have not been seen before. However,
high-fidelity data is itself in limited quantity to validate all outputs of the
SciML model in unexplored input space. As such, an uncertainty-aware SciML
model is desired. The SciML model's output uncertainties could then be used to
assess the reliability and confidence of the model's predictions. In this
study, we extend a DeepONet using three different uncertainty quantification
mechanisms: mean-variance estimation, evidential uncertainty, and ensembling.
The uncertainty aware DeepONet models are trained and evaluated on the
hypersonic flow around a blunt cone object with data generated via
computational fluid dynamics over a wide range of Mach numbers and altitudes.
We find that ensembling outperforms the other two uncertainty models in terms
of minimizing error and calibrating uncertainty in both interpolative and
extrapolative regimes. | 2311.00060v2 |
2023-11-11 | Double-Free-Layer Stochastic Magnetic Tunnel Junctions with Synthetic Antiferromagnets | Stochastic magnetic tunnel junctions (sMTJ) using low-barrier nanomagnets
have shown promise as fast, energy-efficient, and scalable building blocks for
probabilistic computing. Despite recent experimental and theoretical progress,
sMTJs exhibiting the ideal characteristics necessary for probabilistic bits
(p-bit) are still lacking. Ideally, the sMTJs should have (a) voltage bias
independence preventing read disturbance (b) uniform randomness in the
magnetization angle between the free layers, and (c) fast fluctuations without
requiring external magnetic fields while being robust to magnetic field
perturbations. Here, we propose a new design satisfying all of these
requirements, using double-free-layer sMTJs with synthetic antiferromagnets
(SAF). We evaluate the proposed sMTJ design with experimentally benchmarked
spin-circuit models accounting for transport physics, coupled with the
stochastic Landau-Lifshitz-Gilbert equation for magnetization dynamics. We find
that the use of low-barrier SAF layers reduces dipolar coupling, achieving
uncorrelated fluctuations at zero-magnetic field surviving up to diameters
exceeding ($D\approx 100$ nm) if the nanomagnets can be made thin enough
($\approx 1$-$2$ nm). The double-free-layer structure retains bias-independence
and the circular nature of the nanomagnets provides near-uniform randomness
with fast fluctuations. Combining our full sMTJ model with advanced transistor
models, we estimate the energy to generate a random bit as $\approx$ 3.6 fJ,
with fluctuation rates of $\approx$ 3.3 GHz per p-bit. Our results will guide
the experimental development of superior stochastic magnetic tunnel junctions
for large-scale and energy-efficient probabilistic computation for problems
relevant to machine learning and artificial intelligence. | 2311.06642v2 |
2023-11-14 | Toxicity Detection is NOT all you Need: Measuring the Gaps to Supporting Volunteer Content Moderators | Extensive efforts in automated approaches for content moderation have been
focused on developing models to identify toxic, offensive, and hateful content
with the aim of lightening the load for moderators. Yet, it remains uncertain
whether improvements on those tasks have truly addressed moderators' needs in
accomplishing their work. In this paper, we surface gaps between past research
efforts that have aimed to provide automation for aspects of content moderation
and the needs of volunteer content moderators, regarding identifying violations
of various moderation rules. To do so, we conduct a model review on Hugging
Face to reveal the availability of models to cover various moderation rules and
guidelines from three exemplar forums. We further put state-of-the-art LLMs to
the test, evaluating how well these models perform in flagging violations of
platform rules from one particular forum. Finally, we conduct a user survey
study with volunteer moderators to gain insight into their perspectives on
useful moderation models. Overall, we observe a non-trivial gap, as missing
developed models and LLMs exhibit moderate to low performance on a significant
portion of the rules. Moderators' reports provide guides for future work on
developing moderation assistant models. | 2311.07879v2 |
2023-11-14 | All Byzantine Agreement Problems are Expensive | Byzantine agreement, arguably the most fundamental problem in distributed
computing, operates among n processes, out of which t < n can exhibit arbitrary
failures. The problem states that all correct (non-faulty) processes must
eventually decide (termination) the same value (agreement) from a set of
admissible values defined by the proposals of the processes (validity).
Depending on the exact version of the validity property, Byzantine agreement
comes in different forms, from Byzantine broadcast to strong and weak
consensus, to modern variants of the problem introduced in today's blockchain
systems. Regardless of the specific flavor of the agreement problem, its
communication cost is a fundamental metric whose improvement has been the focus
of decades of research. The Dolev-Reischuk bound, one of the most celebrated
results in distributed computing, proved 40 years ago that, at least for
Byzantine broadcast, no deterministic solution can do better than Omega(t^2)
exchanged messages in the worst case. Since then, it remained unknown whether
the quadratic lower bound extends to seemingly weaker variants of Byzantine
agreement. This paper answers the question in the affirmative, closing this
long-standing open problem. Namely, we prove that any non-trivial agreement
problem requires Omega(t^2) messages to be exchanged in the worst case. To
prove the general lower bound, we determine the weakest Byzantine agreement
problem and show, via a novel indistinguishability argument, that it incurs
Omega(t^2) exchanged messages. | 2311.08060v2 |
2023-11-21 | Nonparametric variable importance for time-to-event outcomes with application to prediction of HIV infection | In survival analysis, complex machine learning algorithms have been
increasingly used for predictive modeling. Given a collection of features
available for inclusion in a predictive model, it may be of interest to
quantify the relative importance of a subset of features for the prediction
task at hand. In particular, in HIV vaccine trials, participant baseline
characteristics are used to predict the probability of infection over the
intended follow-up period, and investigators may wish to understand how much
certain types of predictors, such as behavioral factors, contribute toward
overall predictiveness. Time-to-event outcomes such as time to infection are
often subject to right censoring, and existing methods for assessing variable
importance are typically not intended to be used in this setting. We describe a
broad class of algorithm-agnostic variable importance measures for prediction
in the context of survival data. We propose a nonparametric efficient
estimation procedure that incorporates flexible learning of nuisance
parameters, yields asymptotically valid inference, and enjoys
double-robustness. We assess the performance of our proposed procedure via
numerical simulations and analyze data from the HVTN 702 study to inform
enrollment strategies for future HIV vaccine trials. | 2311.12726v2 |
2023-11-29 | Atmospheric Escape From Three Terrestrial Planets in the L 98-59 System | A critically important process affecting the climate evolution and potential
habitability of an exoplanet is atmospheric escape, in which high-energy
radiation from a star drives the escape of hydrogen atoms and other light
elements from a planet's atmosphere. L 98-59 is a benchmark system for studying
such atmospheric processes, with three transiting terrestrial-size planets
receiving Venus-like instellations (4-25 S$_\oplus$) from their M3 host star.
We use the VPLanet model to simulate the evolution of the L 98-59 system and
the atmospheric escape of its inner three small planets, given different
assumed initial water quantities. We find that, regardless of their initial
water content, all three planets accumulate significant quantities of oxygen
due to efficient water photolysis and hydrogen loss. All three planets also
receive enough XUV flux to drive rapid water loss, which considerably affects
their developing climates and atmospheres. Even in scenarios of low initial
water content, our results suggest that the James Webb Space Telescope (JWST)
will be sensitive to observations of retained oxygen on the L 98-59 planets in
its future scheduled observations, with planets b and c being the most likely
targets to possess an extended atmosphere. Our results constrain the
atmospheric evolution of these small rocky planets, and they provide context
for current and future observations of the L 98-59 system to generalize our
understanding of multi-terrestrial planet systems. | 2312.00062v1 |
2023-12-05 | A complex-projected Rayleigh quotient iteration for targeting interior eigenvalues | We introduce a new Projected Rayleigh Quotient Iteration aimed at improving
the convergence behaviour of classic Rayleigh Quotient iteration (RQI) by
incorporating approximate information about the target eigenvector at each
step. While classic RQI exhibits local cubic convergence for Hermitian
matrices, its global behaviour can be unpredictable, whereby it may converge to
an eigenvalue far away from the target, even when started with accurate initial
conditions. This problem is exacerbated when the eigenvalues are closely
spaced. The key idea of the new algorithm is at each step to add a
complex-valued projection to the original matrix (that depends on the current
eigenvector approximation), such that the unwanted eigenvalues are lifted into
the complex plane while the target stays close to the real line, thereby
increasing the spacing between the target eigenvalue and the rest of the
spectrum. Making better use of the eigenvector approximation leads to more
robust convergence behaviour and the new method converges reliably to the
correct target eigenpair for a significantly wider range of initial vectors
than does classic RQI. We prove that the method converges locally cubically and
we present several numerical examples demonstrating the improved global
convergence behaviour. In particular, we apply it to compute eigenvalues in a
band-gap spectrum of a Sturm-Liouville operator used to model photonic crystal
fibres, where the target and unwanted eigenvalues are closely spaced. The
examples show that the new method converges to the desired eigenpair even when
the eigenvalue spacing is very small, often succeeding when classic RQI fails. | 2312.02847v2 |
2023-12-14 | On statistical zonostrophic instability and the effect of magnetic fields | Zonal flows are mean flows in the east-west direction, which are ubiquitous
on planets, and can be formed through 'zonostrophic instability': within
turbulence or random waves, a weak large-scale zonal flow can grow
exponentially to become prominent. In this paper, we study the statistical
behaviour of the zonostrophic instability and the effect of magnetic fields. We
use a stochastic white noise forcing to drive random waves, and study the
growth of a mean flow in this random system. The dispersion relation for the
growth rate of the expectation of the mean flow is derived, and properties of
the instability are discussed. In the limits of weak and strong magnetic
diffusivity, the dispersion relation reduces to manageable expressions, which
provide clear insights into the effect of the magnetic field and scaling laws
for the threshold of instability. The magnetic field mainly plays a stabilising
role and thus impedes the formation of the zonal flow, but under certain
conditions it can also have destabilising effects. Numerical simulation of the
stochastic flow is performed to confirm the theory. Results indicate that the
magnetic field can significantly increase the randomness of the zonal flow. It
is found that the zonal flow of an individual realisation may behave very
differently from the expectation. For weak magnetic diffusivity and moderate
magnetic field strengths, this leads to considerable variation of the outcome,
that is whether zonostrophic instability takes place or not in individual
realisations. | 2312.08905v1 |
2023-12-19 | Towards a theta correspondence in families for type II dual pairs | Let $R$ be a commutative $\mathbb{Z}[1/p]$-algebra, let $m \leq n$ be
positive integers, and let $G_n=\text{GL}_n(F)$ and $G_m=\text{GL}_m(F)$ where
$F$ is a $p$-adic field. The Weil representation is the smooth $R[G_n\times
G_m]$-module $C_c^{\infty}(\text{Mat}_{n\times m}(F),R)$ with the action
induced by matrix multiplication. When $R=\mathbb{C}$ or is any algebraically
closed field of banal characteristic compared to $G_n$ and $G_m$, the local
theta correspondence holds by the work of Howe and M\'inguez. At the level of
supercuspidal support, we interpret the theta correspondence as a morphism of
varieties $\theta_R$, which we describe as an explicit closed immersion. For
arbitrary $R$, we construct a canonical ring homomorphism $\theta^\#_{R} :
\mathfrak{Z}_{R}(G_n)\to \mathfrak{Z}_{R}(G_m)$ that controls the action of the
center $\mathfrak{Z}_{R}(G_n)$ of the category of smooth $R[G_n]$-modules on
the Weil representation. We use the rank filtration of the Weil representation
to first obtain $\theta_{\mathbb{Z}[1/p]}^\#$, then obtain $\theta^\#_R$ for
arbitrary $R$ by proving $\mathfrak{Z}_R(G_n)$ is compatible with scalar
extension. In particular, the map $\text{Spec}(\mathfrak{Z}_R(G_m))\to
\text{Spec}(\mathfrak{Z}_R(G_n))$ induced by $\theta_R^\#$ recovers $\theta_R$
in the $R=\mathbb{C}$ case and in the banal case. We use gamma factors to prove
$\theta_R^\#$ is surjective for any $R$. Finally, we describe $\theta^\#_R$ in
terms of the moduli space of Langlands parameters and use this description to
give an alternative proof of surjectivity in the tamely ramified case. | 2312.12031v1 |
2023-12-19 | Microscopic theory of current-induced skyrmion transport and its application in disordered spin textures | Magnetic skyrmions hold great promise for realizing compact and stable memory
devices that can be manipulated at very low energy costs via electronic current
densities. In this work, we extend a recently introduced method to describe
classical skyrmion textures coupled to dynamical itinerant electrons. In this
scheme, the electron dynamics is described via nonequilibrium Green's functions
(NEGF) within the generalized Kadanoff-Baym ansatz, and the classical spins are
treated via the Landau-Lifshitz-Gilbert equation. The framework is here
extended to open systems, by the introduction of a non-interacting
approximation to the collision integral of NEGF. This, in turn, allows us to
perform computations of the real-time response of skyrmions to electronic
currents in large quantum systems coupled to electronic reservoirs, which
exhibit a linear scaling in the number of time steps. We use this approach to
investigate how electronic spin currents and dilute spin disorder affects
skyrmion transport and the skyrmion Hall drift. Our results show that the
skyrmion dynamics is sensitive to the specific form of spin disorder, such that
different disorder configurations leads to qualitatively different skyrmion
trajectories for the same applied bias. This sensitivity arises from the local
spin dynamics around the magnetic impurities, a feature that is expected not to
be well captured by phenomenological or spin-only descriptions. At the same
time, our findings illustrate the potential of engineering microscopic impurity
patterns to steer skyrmion trajectories. | 2312.12201v1 |
2024-01-09 | Characterization of two fast-turnaround dry dilution refrigerators for scanning probe microscopy | Low-temperature scanning probe microscopes (SPMs) are critical for the study
of quantum materials and quantum information science. Due to the rising costs
of helium, cryogen-free cryostats have become increasingly desirable. However,
they typically suffer from comparatively worse vibrations than cryogen-based
systems, necessitating the understanding and mitigation of vibrations for SPM
applications. Here we demonstrate the construction of two cryogen-free dilution
refrigerator SPMs with minimal modifications to the factory default and we
systematically characterize their vibrational performance. We measure the
absolute vibrations at the microscope stage with geophones, and use both
microwave impedance microscopy and a scanning single electron transistor to
independently measure tip-sample vibrations. Additionally, we implement
customized filtering and thermal anchoring schemes, and characterize the
cooling power at the scanning stage and the tip electron temperature. This work
serves as a reference to researchers interested in cryogen-free SPMs, as such
characterization is not standardized in the literature or available from
manufacturers. | 2401.04373v1 |
2024-01-11 | Micromagnetic simulations of the size dependence of the Curie temperature in ferromagnetic nanowires and nanolayers | We solve the Landau-Lifshitz-Gilbert equation in the finite-temperature
regime, where thermal fluctuations are modeled by a random magnetic field whose
variance is proportional to the temperature. By rescaling the temperature
proportionally to the computational cell size $\Delta x$ ($T \to T\,\Delta
x/a_{\text{eff}}$, where $a_{\text{eff}}$ is the lattice constant) [M. B. Hahn,
J. Phys. Comm., 3:075009, 2019], we obtain Curie temperatures $T_{\text{C}}$
that are in line with the experimental values for cobalt, iron and nickel. For
finite-sized objects such as nanowires (1D) and nanolayers (2D), the Curie
temperature varies with the smallest size $d$ of the system. We show that the
difference between the computed finite-size $T_{\text{C}}$ and the bulk
$T_{\text{C}}$ follows a power-law of the type: $(\xi_0/d)^\lambda$, where
$\xi_0$ is the correlation length at zero temperature, and $\lambda$ is a
critical exponent. We obtain values of $\xi_0$ in the nanometer range, also in
accordance with other simulations and experiments. The computed critical
exponent is close to $\lambda=2$ for all considered materials and geometries.
This is the expected result for a mean-field approach, but slightly larger than
the values observed experimentally. | 2401.05722v1 |
2024-01-24 | How AI Ideas Affect the Creativity, Diversity, and Evolution of Human Ideas: Evidence From a Large, Dynamic Experiment | Exposure to large language model output is rapidly increasing. How will
seeing AI-generated ideas affect human ideas? We conducted an experiment (800+
participants, 40+ countries) where participants viewed creative ideas that were
from ChatGPT or prior experimental participants and then brainstormed their own
idea. We varied the number of AI-generated examples (none, low, or high
exposure) and if the examples were labeled as 'AI' (disclosure). Our dynamic
experiment design -- ideas from prior participants in an experimental condition
are used as stimuli for future participants in the same experimental condition
-- mimics the interdependent process of cultural creation: creative ideas are
built upon prior ideas. Hence, we capture the compounding effects of having
LLMs 'in the culture loop'. We find that high AI exposure (but not low AI
exposure) did not affect the creativity of individual ideas but did increase
the average amount and rate of change of collective idea diversity. AI made
ideas different, not better. There were no main effects of disclosure. We also
found that self-reported creative people were less influenced by knowing an
idea was from AI, and that participants were more likely to knowingly adopt AI
ideas when the task was difficult. Our findings suggest that introducing AI
ideas into society may increase collective diversity but not individual
creativity. | 2401.13481v1 |
2024-01-31 | Multimaterial Inkjet Printing of Mechanochromic Materials | Inkjet printing technology achieves the precise deposition of liquid-phase
materials via the digitally controlled formation of picoliter-sized droplets.
Beyond graphical printing, inkjet printing has been employed for the deposition
of separated drops on surfaces or the formation of continuous layers, which
allows to construct materials gradients or periodic features that provide
enhanced functionalities. Here, we explore the use of multinozzle,
drop-on-demand piezoelectric inkjet technology for the manufacturing of
mechanochromic materials, i.e., materials that change their color or
fluorescence in response to mechanical deformation. To accomplish this,
suitable polyurethane polymers of differing hardness grades were tested with a
range of organic solvents to formulate low-viscosity, inkjet-printable
solutions. Following their rheological characterization, two solutions
comprised of "soft" and "hard" polyurethanes were selected for in-depth study.
The solutions were imbibed with a mechanochromic additive to yield fluorescent
inks, which were either dropcast onto polymeric substrates or printed to form
checkerboard patterns of alternating hardness using a lab-built, multimaterial
inkjet platform. Fluorescence imaging and spectroscopy were used to identify
different hardness grades in the dropcast and printed materials, as well as to
monitor the responses of these gradient materials to mechanical deformation.
The insights gained in this study are expected to facilitate the development of
inkjet-printable, mechanochromic polymer materials for a wide range of
applications. | 2401.17758v2 |
2024-01-11 | Resonant inelastic x-ray scattering in warm-dense Fe compounds beyond the SASE FEL resolution limit | Resonant inelastic x-ray scattering (RIXS) is a widely used spectroscopic
technique, providing access to the electronic structure and dynamics of atoms,
molecules, and solids. However, RIXS requires a narrow bandwidth x-ray probe to
achieve high spectral resolution. The challenges in delivering an energetic
monochromated beam from an x-ray free electron laser (XFEL) thus limit its use
in few-shot experiments, including for the study of high energy density
systems. Here we demonstrate that by correlating the measurements of the
self-amplified spontaneous emission (SASE) spectrum of an XFEL with the RIXS
signal, using a dynamic kernel deconvolution with a neural surrogate, we can
achieve electronic structure resolutions substantially higher than those
normally afforded by the bandwidth of the incoming x-ray beam. We further show
how this technique allows us to discriminate between the valence structures of
Fe and Fe$_2$O$_3$, and provides access to temperature measurements as well as
M-shell binding energies estimates in warm-dense Fe compounds. | 2402.00039v1 |
2024-02-08 | Trustful Coopetitive Infrastructures for the New Space Exploration Era | In the new space economy, space agencies, large enterprises, and start-ups
aim to launch space multi-robot systems (MRS) for various in-situ resource
utilization (ISRU) purposes, such as mapping, soil evaluation, and utility
provisioning. However, these stakeholders' competing economic interests may
hinder effective collaboration on a centralized digital platform. To address
this issue, neutral and transparent infrastructures could facilitate
coordination and value exchange among heterogeneous space MRS. While related
work has expressed legitimate concerns about the technical challenges
associated with blockchain use in space, we argue that weighing its potential
economic benefits against its drawbacks is necessary. This paper presents a
novel architectural framework and a comprehensive set of requirements for
integrating blockchain technology in MRS, aiming to enhance coordination and
data integrity in space exploration missions. We explored distributed ledger
technology (DLT) to design a non-proprietary architecture for heterogeneous MRS
and validated the prototype in a simulated lunar environment. The analyses of
our implementation suggest global ISRU efficiency improvements for map
exploration, compared to a corresponding group of individually acting robots,
and that fostering a coopetitive environment may provide additional revenue
opportunities for stakeholders. | 2402.06014v1 |
2024-02-08 | Designing Trustful Cooperation Ecosystems is Key to the New Space Exploration Era | In the emerging space economy, autonomous robotic missions with specialized
goals such as mapping and mining are gaining traction, with agencies and
enterprises increasingly investing resources. Multirobot systems (MRS) research
has provided many approaches to establish control and communication layers to
facilitate collaboration from a technical perspective, such as granting more
autonomy to heterogeneous robotic groups through auction-based interactions in
mesh networks. However, stakeholders' competing economic interests often
prevent them from cooperating within a proprietary ecosystem. Related work
suggests that distributed ledger technology (DLT) might serve as a mechanism
for enterprises to coordinate workflows and trade services to explore space
resources through a transparent, reliable, non-proprietary digital platform. We
challenge this perspective by pointing to the core technical weaknesses of
blockchains, in particular, increased energy consumption, low throughput, and
full transparency through redundancy. Our objective is to advance the
discussion in a direction where the benefits of DLT from an economic
perspective are weighted against the drawbacks from a technical perspective. We
finally present a possible DLT-driven heterogeneous MRS for map exploration to
study the opportunities for economic collaboration and competitiveness. | 2402.06036v1 |
2024-02-29 | Magnon spectrum of altermagnets: Time-dependent matrix product states vs. linearized Holstein-Primakoff calculations unravelling spontaneous magnon decay | The energy-momentum dispersion of magnons, viewed as noninteracting and
infinitely long-lived quasiparticles describing collective low-energy
excitations of magnetic materials, is often presented as sharp bands obtained
from the effective quantum spin Hamiltonian, after being simplified via
linearized Holstein-Primakoff (HP) transformations. However, magnons are prone
to many-body interactions with other quasiparticles which can lead to their
spontaneous decay. The magnon-magnon interactions could affect newly classified
altermagnets. On the other hand, sharp bands of noninteracting chiral magnons
in RuO2, as the canonical example of altermagnets, have been very recently
predicted. Here, we employ nonperturbative numerically (quasi)exact quantum
many-body calculations, via time-dependent matrix product states (TDMPS), to
obtain magnon spectral function of RuO2. These calculations produce a broadened
magnon dispersion, which overlaps with linearized HP theory sharp bands only at
edges/center of the Brillouin zone. Substantially deviating otherwise.
Artificially making exchange interaction within two sublattices of RuO2 closer
in value forces these two spectra to overlap, thereby explaining the origin of
the failure of linearized HP theory. Such features translate into the
difference between their respective density of states, which we also compute
and which could be tested by Raman scattering experiments. Finally, we employ
popular Landau-Lifshitz-Gilbert (LLG) equation-based classical atomistic spin
dynamics (ASD) simulations to obtain dynamical structure factor and extract
magnon spectrum from it at finite temperature. Despite including magnon-magnon
interactions via nonlinearity of LLG equation, ASD simulations cannot fully
match the TDMPS-computed magnon spectrum due to nonclassical effects harbored
by altermagnets. | 2402.19433v1 |
2024-03-07 | Controllable Skyrmion Islands in a Moiré Magnet | Antiferromagnetic(AFM) skyrmions have been in the spotlight as ideal
topological magnetic bits. Although they are topologically protected, they do
not exhibit the skyrmion Hall effect unlike the ferromagnetic ones. Thus, AFM
skyrmions are considered to provide a better control of the skyrmion's motion
due to the absence of the skyrmion Magnus effect. In this work, we propose a
possible realization of controllable AFM skyrmions in a twisted Moir\'e magnet.
The tunability of Moir\'e materials is not only a good platform for the
provision of rich phases, but also for the stabilization of skyrmion phase. We
investigate the ground state of twisted bilayer AFM system by solving the
Landau-Lifshitz-Gilbert equation in a continuum model. We show that the AFM
skyrmions are stabilized even in the absence of the external/dipolar magnetic
field, as a consequence of the interplay of interlayer coupling,
Dzyaloshinskii-Moriya (DM) interaction and Ising anisotropy. More
interestingly, due to the magnetoelectric effect, the application of an
external electric field locally stabilizes the skyrmions in the twisted bilayer
AFM systems, even in the absence of DM interaction. It also allows the skyrmion
helicity to change continuously when both the DM interaction and an electric
field are present. We show the phase diagram with respect to the strength of
interlayer coupling, the DM interaction and an electric field. Our results
suggest the possibility of using AFM skyrmions as stable, controllable
topological magnetic bits. | 2403.04208v1 |
2024-03-08 | A Data Augmentation Pipeline to Generate Synthetic Labeled Datasets of 3D Echocardiography Images using a GAN | Due to privacy issues and limited amount of publicly available labeled
datasets in the domain of medical imaging, we propose an image generation
pipeline to synthesize 3D echocardiographic images with corresponding ground
truth labels, to alleviate the need for data collection and for laborious and
error-prone human labeling of images for subsequent Deep Learning (DL) tasks.
The proposed method utilizes detailed anatomical segmentations of the heart as
ground truth label sources. This initial dataset is combined with a second
dataset made up of real 3D echocardiographic images to train a Generative
Adversarial Network (GAN) to synthesize realistic 3D cardiovascular Ultrasound
images paired with ground truth labels. To generate the synthetic 3D dataset,
the trained GAN uses high resolution anatomical models from Computed Tomography
(CT) as input. A qualitative analysis of the synthesized images showed that the
main structures of the heart are well delineated and closely follow the labels
obtained from the anatomical models. To assess the usability of these synthetic
images for DL tasks, segmentation algorithms were trained to delineate the left
ventricle, left atrium, and myocardium. A quantitative analysis of the 3D
segmentations given by the models trained with the synthetic images indicated
the potential use of this GAN approach to generate 3D synthetic data, use the
data to train DL models for different clinical tasks, and therefore tackle the
problem of scarcity of 3D labeled echocardiography datasets. | 2403.05384v1 |
2024-03-10 | Dynamical generation of skyrmion and bimeron crystals by a circularly polarized electric field in frustrated magnets | A skyrmion crystal (SkX) has attracted much attention in condensed matter
physics, since topologically nontrivial structures induce fascinating physical
phenomena. The SkXs have been experimentally observed in a variety of
materials, where the Zeeman coupling to the static magnetic field plays an
important role in the formation of the SkXs. In this study, we theoretically
propose another route to generate the SkXs by using a circularly polarized
electric field. We investigate a non-equilibrium steady state in a classical
frustrated Heisenberg magnet under the circularly polarized electric field,
where the electric field is coupled to the electric polarization via the
spin-current mechanism. By numerically solving the Landau-Lifshitz-Gilbert
equation at zero temperature, we show that the electric field radiation
generates a SkX with a high topological number in the high-frequency regime,
where the sign of the skyrmion number is fixed to be negative (positive) under
the left (right) circularly polarized field. The intense electric field melts
these SkXs and generates isolated skyrmions. We clarify that the microscopic
origin is effective electric-field-induced three-spin interactions by adopting
the high-frequency expansion in the Floquet formalism. Furthermore, we find
that the electric field radiation generates another type of SkXs, a bimeron
crystal, in the low-frequency regime. Our results provide a way to generate the
SkXs and control the topology by the circularly polarized electric field. | 2403.06118v1 |
2024-03-12 | Flexible Non-intrusive Dynamic Instrumentation for WebAssembly | A key strength of managed runtimes over hardware is the ability to gain
detailed insight into the dynamic execution of programs with instrumentation.
Analyses such as code coverage, execution frequency, tracing, and debugging,
are all made easier in a virtual setting. As a portable, low-level bytecode,
WebAssembly offers inexpensive in-process sandboxing with high performance. Yet
to date, Wasm engines have not offered much insight into executing programs,
supporting at best bytecode-level stepping and basic source maps, but no
instrumentation capabilities. In this paper, we show the first non-intrusive
dynamic instrumentation system for WebAssembly in the open-source Wizard
Research Engine. Our innovative design offers a flexible, complete hierarchy of
instrumentation primitives that support building high-level, complex analyses
in terms of low-level, programmable probes. In contrast to emulation or machine
code instrumentation, injecting probes at the bytecode level increases
expressiveness and vastly simplifies the implementation by reusing the engine's
JIT compiler, interpreter, and deoptimization mechanism rather than building
new ones. Wizard supports both dynamic instrumentation insertion and removal
while providing consistency guarantees, which is key to composing multiple
analyses without interference. We detail a fully-featured implementation in a
high-performance multi-tier Wasm engine, show novel optimizations specifically
designed to minimize instrumentation overhead, and evaluate performance
characteristics under load from various analyses. This design is well-suited
for production engine adoption as probes can be implemented to have no impact
on production performance when not in use. | 2403.07973v1 |
2024-03-13 | Highly confined epsilon-near-zero- and surface-phonon polaritons in SrTiO3 membranes | Recent theoretical studies have suggested that transition metal perovskite
oxide membranes can enable surface phonon polaritons in the infrared range with
low loss and much stronger subwavelength confinement than bulk crystals. Such
modes, however, have not been experimentally observed so far. Here, using a
combination of far-field Fourier-transform infrared (FTIR) spectroscopy and
near-field synchrotron infrared nanospectroscopy (SINS) imaging, we study the
phonon-polaritons in a 100 nm thick freestanding crystalline membrane of SrTiO3
transferred on metallic and dielectric substrates. We observe a
symmetric-antisymmetric mode splitting giving rise to epsilon-near-zero and
Berreman modes as well as highly confined (by a factor of 10) propagating
phonon polaritons, both of which result from the deep-subwavelength thickness
of the membranes. Theoretical modeling based on the analytical finite-dipole
model and numerical finite-difference methods fully corroborate the
experimental results. Our work reveals the potential of oxide membranes as a
promising platform for infrared photonics and polaritonics. | 2403.08500v1 |
2024-03-18 | Lattice QCD estimates of thermal photon production from the QGP | Thermal photons produced in heavy-ion collision experiments are an important
observable for understanding quark-gluon plasma (QGP). The thermal photon rate
from the QGP at a given temperature can be calculated from the spectral
function of the vector current correlator. Extraction of the spectral function
from the lattice correlator is known to be an ill-conditioned problem, as there
is no unique solution for a spectral function for a given lattice correlator
with statistical errors. The vector current correlator, on the other hand,
receives a large ultraviolet contribution from the vacuum, which makes the
extraction of the thermal photon rate difficult from this channel. We therefore
consider the difference between the transverse and longitudinal part of the
spectral function, only capturing the thermal contribution to the current
correlator, simplifying the reconstruction significantly. The lattice
correlator is calculated for light quarks in quenched QCD at $T=470~$MeV ($\sim
1.5\, T_c$), as well as in 2+1 flavor QCD at $T=220~$MeV ($\sim 1.2 \, T_{pc}$)
with $m_{\pi}=320$ MeV. In order to quantify the non-perturbative effects, the
lattice correlator is compared with the corresponding
$\text{NLO}+\text{LPM}^{\text{LO}}$ estimate of correlator. The reconstruction
of the spectral function is performed in several different frameworks, ranging
from physics-informed models of the spectral function to more general models in
the Backus-Gilbert method and Gaussian Process regression. We find that the
resulting photon rates agree within errors. | 2403.11647v1 |
2024-03-20 | Optimal Risk-Sensitive Scheduling Policies for Remote Estimation of Autoregressive Markov Processes | We design scheduling policies that minimize a risk-sensitive cost criterion
for a remote estimation setup. Since risk-sensitive cost objective takes into
account not just the mean value of the cost, but also higher order moments of
its probability distribution, the resulting policy is robust to changes in the
underlying system's parameters. The setup consists of a sensor that observes a
discrete-time autoregressive Markov process, and at each time $t$ decides
whether or not to transmit its observations to a remote estimator using an
unreliable wireless communication channel after encoding these observations
into data packets. We model the communication channel as a Gilbert-Elliott
channel \cite{10384144}. Sensor probes the channel \cite{laourine2010betting}
and hence knows the channel state at each time $t$ before making scheduling
decision. The scheduler has to minimize the expected value of the exponential
of the finite horizon cumulative cost that is sum of the following two
quantities (i) the cumulative transmission power consumed, (ii) the cumulative
squared estimator error. We pose this dynamic optimization problem as a Markov
decision process (MDP), in which the system state at time $t$ is composed of
(i) the instantaneous error $\Delta(t):= x(t)-a\hat{x}(t-1)$, where
$x(t),\hat{x}(t-1)$ are the system state and the estimate at time $t,t-1$
respectively, and (ii) the channel state $c(t)$. We show that there exists an
optimal policy that has a threshold structure, i.e., at each time $t$, for each
possible channel state $c$, there is a threshold $\D\ust(c)$ such that if the
current channel state is $c$, then it transmits only when the error $\D(t)$
exceeds $\D\ust(c)$. | 2403.13898v1 |
2024-03-27 | The Correlations of Scene Complexity, Workload, Presence, and Cybersickness in a Task-Based VR Game | This investigation examined the relationships among scene complexity,
workload, presence, and cybersickness in virtual reality (VR) environments.
Numerous factors can influence the overall VR experience, and existing research
on this matter is not yet conclusive, warranting further investigation. In this
between-subjects experimental setup, 44 participants engaged in the Pendulum
Chair game, with half exposed to a simple scene with lower optic flow and lower
familiarity, and the remaining half to a complex scene characterized by higher
optic flow and greater familiarity. The study measured the dependent variables
workload, presence, and cybersickness and analyzed their correlations.
Equivalence testing was also used to compare the simple and complex
environments. Results revealed that despite the visible differences between the
environments, within the 10% boundaries of the maximum possible value for
workload and presence, and 13.6% of the maximum SSQ value, a statistically
significant equivalence was observed between the simple and complex scenes.
Additionally, a moderate, negative correlation emerged between workload and SSQ
scores. The findings suggest two key points: (1) the nature of the task can
mitigate the impact of scene complexity factors such as optic flow and
familiarity, and (2) the correlation between workload and cybersickness may
vary, showing either a positive or negative relationship. | 2403.19019v1 |
2024-03-28 | Long-range Phase Coherence and Tunable Second Order $φ_0$-Josephson Effect in a Dirac Semimetal $1T-PtTe_2$ | Superconducting diode effects have recently attracted much attention for
their potential applications in superconducting logic circuits. Several
mechanisms such as magneto-chiral effects, finite momentum Cooper pairing,
asymmetric edge currents have been proposed to give rise to a supercurrent
diode effect in different materials. In this work, we establish the presence of
a large intrinsic Josephson diode effect in a type-II Dirac semimetal
$1T-PtTe_2$ facilitated by its helical spin-momentum locking and distinguish it
from other extrinsic effects. The magnitude of the Josephson diode effect is
shown to be directly correlated to the large second-harmonic component of the
supercurrent that is induced by the significant contribution of the topological
spin-momentum locked states that promote coherent Andreev processes in the
junction. We denote such junctions, where the relative phase between the two
harmonics corresponding to charge transfers of $2e$ and $4e$ can be tuned by a
magnetic field, as second order ${\phi}_0$-junctions. The direct correspondence
between the second harmonic supercurrent component and the diode effect in
$1T-PtTe_2$ junctions makes topological semimetals with high transparency an
ideal platform to study and implement the Josephson diode effect, while also
enabling further research on higher order supercurrent transport in Josephson
junctions. | 2403.19445v1 |
1997-04-08 | A complementary group technique for the resolution of the outer multiplicity problem of SU(n): (II) A recoupling approach to the solution of SU(3)\supset U(2) reduced Wigner coefficients | A general procedure for the derivation of SU(3)\supset U(2) reduced Wigner
coefficients for the coupling (\lambda_{1}\mu_{1})\times
(\lambda_{2}\mu_{2})\downarrow (\lambda\mu)^{\eta}, where \eta is the outer
multiplicity label needed in the decomposition, is proposed based on a
recoupling approach according to the complementary group technique given in
(I). It is proved that the non-multiplicity-free reduced Wigner coefficients of
SU(n) are not unique with respect to canonical outer multiplicity labels, and
can be transformed from one set of outer multiplicity labels to another. The
transformation matrices are elements of SO(m), where m is the number of
occurrence of the corresponding irrep (\lambda\mu) in the decomposition
(\lambda_{1}\mu_{1})\times (\lambda_{2}\mu_{2})\downarrow (\lambda\mu). Thus, a
kind of the reduced Wigner coefficients with multiplicity is obtained after a
special SO(m) transformation. New features of this kind of reduced Wigner
coefficients and the differences from the reduced Wigner coefficients with
other choice of the multiplicity label given previously are discussed. The
method can also be applied to the derivation of general SU(n) Wigner or reduced
Wigner coefficients with multiplicity. Algebraic expression of another kind of
reduced Wigner coefficients, the so-called reduced auxiliary Wigner
coefficients for SU(3)\supset U(2), are also obtained. | 9704015v1 |
2008-11-03 | Modeling the evolution of Gini coefficient for personal incomes in the USA between 1947 and 2005 | The evolution of Gini coefficient for personal incomes in the USA between
1947 and 2005 is analyzed and modeled. There are several versions of personal
income distribution (PID) provided by the US Census Bureau (US CB) for this
period with various levels of resolution. Effectively, these PIDs result in
different Gini coefficients due to the differences between discrete and
continuous representations. When all persons of 15 years of age and over are
included in the PIDs, Gini coefficient drops from 0.64 in 1947 to 0.54 in 1990.
This effect is observed due to a significant decrease in the portion of people
without income. For the PIDs not including persons without income, Gini
coefficient is varying around 0.51 between 1960 and 2005 with standard
deviation of 0.004, i.e. is in fact constant. This Gini coefficient is
practically independent on the portion of population included in the PIDs
according to any revision of income definitions. The driving force of the model
describing the evolution of individual incomes (microeconomic level) and their
aggregate value (macroeconomic level) is the change in nominal GDP per capita.
The model accurately predicts the evolution of Gini coefficient for the PIDs
for people with income. The model gives practically unchanged (normalized) PIDs
and Gini coefficient between 1947 and 2005. The empirical Gini curves converge
to the predicted one when the number of people without income decreases.
Asymptotically, the empirical curves should collapse to the theoretical one
when all the working age population obtains an appropriate definition of
income. Therefore the model Gini coefficient potentially better describes true
behavior of inequality in the USA because the definitions of income used by the
US Census Bureau apparently fail to describe true income distribution. | 0811.0356v1 |
2009-09-30 | Granular gas of viscoelastic particles in a homogeneous cooling state | Kinetic properties of a granular gas of viscoelastic particles in a
homogeneous cooling state are studied analytically and numerically. We employ
the most recent expression for the velocity-dependent restitution coefficient
for colliding viscoelastic particles, which allows to describe systems with
large inelasticity. In contrast to previous studies, the third coefficient a3
of the Sonine polynomials expansion of the velocity distribution function is
taken into account. We observe a complicated evolution of this coefficient.
Moreover, we find that a3 is always of the same order of magnitude as the
leading second Sonine coefficient a2; this contradicts the existing hypothesis
that the subsequent Sonine coefficients a2, a3 ..., are of an ascending order
of a small parameter, characterizing particles inelasticity. We analyze
evolution of the high-energy tail of the velocity distribution function. In
particular, we study the time dependence of the tail amplitude and of the
threshold velocity, which demarcates the main part of the velocity distribution
and the high-energy part. We also study evolution of the self-diffusion
coefficient D and explore the impact of the third Sonine coefficient on the
self-diffusion. Our analytical predictions for the third Sonine coefficient,
threshold velocity and the self-diffusion coefficient are in a good agreement
with the numerical finding. | 0909.5563v2 |
2013-11-30 | Polynomial properties of Jack connection coefficients and generalization of a result by Dénes | This article is devoted to the computation of Jack connection coefficients, a
generalization of the connection coefficients of two classical commutative
subalgebras of the group algebra of the symmetric group: the class algebra and
the double coset algebra. The connection coefficients of these two algebraic
structures are of significant interest in the study of Schur and zonal
polynomials as well as the irreducible characters of the symmetric group and
the zonal spherical functions. Furthermore they play an important role in
combinatorics as they give the number of factorizations of a permutation into a
product of permutations with given cyclic properties. Usually studied
separately, these two families of coefficients share strong similar properties.
First (partially) introduced by Goulden and Jackson in 1996, Jack connection
coefficients provide a natural unified approach closely related to the theory
of Jack polynomials, a family of bases in the ring of symmetric functions
indexed by a parameter \alpha that generalizes both Schur (case \alpha = 1) and
zonal polynomials (case \alpha = 2). Jack connection coefficients are also
directly linked to Jack characters, a general view of the characters of the
symmetric group and the zonal spherical functions. Goulden and Jackson
conjectured that these coefficients are polynomials in \alpha with nice
combinatorial properties, the so-called Matchings-Jack conjecture. In this
paper, we use the theory of Jack symmetric functions and the Laplace Beltrami
operator to show the polynomial properties of Jack connection coefficients in
some important cases. We also provide explicit formulations including notably a
generalization of a classical formula of D\'enes for the number of minimal
factorizations of a permutation into transpositions. | 1312.0120v3 |
2019-02-14 | A Consistent Reduced Network for HCN Chemistry in Early Earth and Titan Atmospheres: Quantum Calculations of Reaction Rate Coefficients | HCN is a key ingredient for synthesizing biomolecules such as nucleobases and
amino acids. We calculate 42 reaction rate coefficients directly involved with
or in competition with the production of HCN in the early Earth or Titan
atmospheres. These reactions are driven by methane and nitrogen radicals
produced via UV photodissociation or lightning. For every reaction in this
network, we calculate rate coefficients at 298 K using canonical variational
transition state theory (CVT) paired with computational quantum chemistry
simulations at the BHandHLYP/augcc-pVDZ level of theory. We also calculate the
temperature dependence of the rate coefficients for the reactions that have
barriers from 50 to 400 K. We present 15 new reaction rate coefficients with no
previously known value; 93% of our calculated coefficients are within an order
of magnitude of the nearest experimental or recommended values. Above 320 K,
the rate coefficient for the new reaction H2CN -> HCN + H dominates. Contrary
to experiments, we find the HCN reaction pathway, N + CH3 -> HCN + H2, to be
inefficient and suggest that the experimental rate coefficient actually
corresponds to an indirect pathway, through the H2CN intermediate. We present
CVT using energies computed with density functional theory as a feasible and
accurate method for calculating a large network of rate coefficients of
small-molecule reactions. | 1902.05574v1 |
2019-05-22 | Holographic OPE Coefficients from AdS Black Holes with Matters | We study the OPE coefficients $c_{\Delta, J}$ for heavy-light scalar
four-point functions, which can be obtained holographically from the two-point
function of a light scalar of some non-integer conformal dimension $\Delta_L$
in an AdS black hole. We verify that the OPE coefficient $c_{d,0}=0$ for pure
gravity black holes, consistent with the tracelessness of the holographic
energy-momentum tensor. We then study the OPE coefficients from black holes
involving matter fields. We first consider general charged AdS black holes and
we give some explicit low-lying examples of the OPE coefficients. We also
obtain the recursion formula for the lowest-twist OPE coefficients with at most
two current operators. For integer $\Delta_L$, although the OPE coefficients
are not fully determined, we set up a framework to read off the coefficients
$\gamma_{\Delta,J}$ of the $\log(z\bar{z})$ terms that are associated with the
anomalous dimensions of the exchange operators and obtain a general formula for
$\gamma_{\Delta,J}$. We then consider charged AdS black holes in gauged
supergravity STU models in $D=5$ and $D=7$, and their higher-dimensional
generalizations. The scalar fields in the STU models are conformally massless,
dual to light operators with $\Delta_L=d-2$. We derive the linear perturbation
of such a scalar in the STU charged AdS black holes and obtain the explicit OPE
coefficient $c_{d-2,0}$. Finally, we analyse the asymptotic properties of
scalar hairy AdS black holes and show how $c_{d,0}$ can be nonzero with
exchanging scalar operators in these backgrounds. | 1905.09302v2 |
2020-11-10 | The improved model of user similarity coefficients computation For recommendation systems | The subject matter of the article is a model of calculating the user
similarity coefficients of the recommendation systems. The goal is the
development of the improved model of user similarity coefficients calculation
for recommendation systems to optimize the time of forming recommendation
lists. The tasks to be solved are: to investigate the probability of changing
user preferences of a recommendation system by comparing their similarity
coefficients in time, to investigate which distribution function describes the
changes of similarity coefficients of users in time. The methods used are:
graph theory, probability theory, radioactivity theory, algorithm theory.
Conclusions. In the course of the researches, the model of user similarity
coefficients calculating for the recommendation systems has been improved. The
model differs from the known ones in that it takes into account the
recalculation period of similarity coefficients for the individual user and
average recalculation period of similarity coefficients for all users of the
system or a specific group of users. The software has been developed, in which
a series of experiments was conducted to test the effectiveness of the
developed method. The conducted experiments showed that the developed method in
general increases the quality of the recommendation system without significant
fluctuations of Precision and Recall of the system. Precision and Recall can
decrease slightly or increase, depending on the characteristics of the incoming
data set. The use of the proposed solutions will increase the application
period of the previously calculated similarity coefficients of users for the
prediction of preferences without their recalculation and, accordingly, it will
shorten the time of formation and issuance of recommendation lists up to 2
times. | 2011.05057v1 |
2021-08-03 | Generalized coefficients of the Dirichlet series | The paper considers a method for converting a divergent Dirichlet series into
a convergent Dirichlet series by directly converting the coefficients of the
original series $1\rightarrow\delta_{n}(s)$ for the Riemann Zeta function. In
the first part of the paper, we study the properties of the coefficients
${\delta}^*_n$ of a finite Dirichlet series for approximating the Riemann Zeta
function on the interval $\Delta{H}$. In general, the coefficients
${\delta}^*_n$ of a finite Dirichlet series are complex numbers. The dependence
of the coefficients ${\delta}^*_n$ of a finite Dirichlet series on the ordinal
number of the coefficient $n$ is established, which can be set by a sigmoid,
and for each $N$ there is a single sigmoid $\hat{\delta}_n$ and a single
interval $\Delta{H}$ for which the condition is satisfied
$$\Big|\sum\limits_{n}^{N}\{{\delta}^*_n- \hat\delta_n\}\Big| < \epsilon;$$ The
second part of the paper presents the results of using the sigmoid to calculate
the values of the generalized coefficients $\delta_{n}(s)$ of the Dirichlet
series for the Riemann Zeta function. For the accuracy of the calculation,
$\log_{10}(1/\epsilon)$ values of the Riemann Zeta Function by summing the
resulting convergent Dirichlet series, the power of the imaginary part
$t=Im(s)$ is established. Presumably, the sigmoid can be used to asymptotically
calculate the values of the analytical continuation of any function defined by
the Dirichlet series. Presumably, for any divergent series to which the
generalized summation method is applicable, it is possible to find a direct
transformation of the coefficients of the divergent series, so that the
resulting series with the transformed coefficients will converge to the same
function as the series of transformed partial sums. | 2108.01270v1 |
2022-04-26 | Coefficient Mutation in the Gene-pool Optimal Mixing Evolutionary Algorithm for Symbolic Regression | Currently, the genetic programming version of the gene-pool optimal mixing
evolutionary algorithm (GP-GOMEA) is among the top-performing algorithms for
symbolic regression (SR). A key strength of GP-GOMEA is its way of performing
variation, which dynamically adapts to the emergence of patterns in the
population. However, GP-GOMEA lacks a mechanism to optimize coefficients. In
this paper, we study how fairly simple approaches for optimizing coefficients
can be integrated into GP-GOMEA. In particular, we considered two variants of
Gaussian coefficient mutation. We performed experiments using different
settings on 23 benchmark problems, and used machine learning to estimate what
aspects of coefficient mutation matter most. We find that the most important
aspect is that the number of coefficient mutation attempts needs to be
commensurate with the number of mixing operations that GP-GOMEA performs. We
applied GP-GOMEA with the best-performing coefficient mutation approach to the
data sets of SRBench, a large SR benchmark, for which a ground-truth underlying
equation is known. We find that coefficient mutation can help re-discovering
the underlying equation by a substantial amount, but only when no noise is
added to the target variable. In the presence of noise, GP-GOMEA with
coefficient mutation discovers alternative but similarly-accurate equations. | 2204.12159v1 |
2023-09-01 | Interpretation of High-Dimensional Linear Regression: Effects of Nullspace and Regularization Demonstrated on Battery Data | High-dimensional linear regression is important in many scientific fields.
This article considers discrete measured data of underlying smooth latent
processes, as is often obtained from chemical or biological systems.
Interpretation in high dimensions is challenging because the nullspace and its
interplay with regularization shapes regression coefficients. The data's
nullspace contains all coefficients that satisfy $\mathbf{Xw}=\mathbf{0}$, thus
allowing very different coefficients to yield identical predictions. We
developed an optimization formulation to compare regression coefficients and
coefficients obtained by physical engineering knowledge to understand which
part of the coefficient differences are close to the nullspace. This nullspace
method is tested on a synthetic example and lithium-ion battery data. The case
studies show that regularization and z-scoring are design choices that, if
chosen corresponding to prior physical knowledge, lead to interpretable
regression results. Otherwise, the combination of the nullspace and
regularization hinders interpretability and can make it impossible to obtain
regression coefficients close to the true coefficients when there is a true
underlying linear model. Furthermore, we demonstrate that regression methods
that do not produce coefficients orthogonal to the nullspace, such as fused
lasso, can improve interpretability. In conclusion, the insights gained from
the nullspace perspective help to make informed design choices for building
regression models on high-dimensional data and reasoning about potential
underlying linear models, which are important for system optimization and
improving scientific understanding. | 2309.00564v2 |
2024-03-06 | Inverse resolution of spatially varying diffusion coefficient using Physics-Informed neural networks | Resolving the diffusion coefficient is a key element in many biological and
engineering systems, including pharmacological drug transport and fluid
mechanics analyses. Additionally, these systems often have spatial variation in
the diffusion coefficient which must be determined, such as for injectable
drug-eluting implants into heterogeneous tissues. Unfortunately, obtaining the
diffusion coefficient from images in such cases is an inverse problem with only
discrete data points. The development of a robust method that can work with
such noisy and ill-posed datasets to accurately determine spatially-varying
diffusion coefficients is of great value across a large range of disciplines.
Here, we developed an inverse solver that uses physics informed neural networks
(PINNs) to calculate spatially-varying diffusion coefficients from numerical
and experimental image data in varying biological and engineering applications.
The residual of the transient diffusion equation for a concentration field is
minimized to find the diffusion coefficient. The robustness of the method as an
inverse solver was tested using both numerical and experimental datasets. The
predictions show good agreement with both the numerical and experimental
benchmarks; an error of less than 6.31% was obtained against all numerical
benchmarks, while the diffusion coefficient calculated in experimental datasets
matches the appropriate ranges of other reported literature values. Our work
demonstrates the potential of using PINNs to resolve spatially-varying
diffusion coefficients, which may aid a wide-range of applications, such as
enabling better-designed drug-eluting implants for regenerative medicine or
oncology fields. | 2403.03970v1 |
1997-10-02 | Single-Particle Diffusion-Coefficient on Surfaces with Ehrlich-Schwoebel-Barriers | The diffusion coefficient of single particles in the presence of
Ehrlich-Schwoebel barriers (ESB)is considered. An exact expression is given for
the diffusion coefficient on linear chains with random arrangements of ESB. The
results are extended to surfaces having ESB with uniform extension in one or
both directions. All results are verified by Monte Carlo simulations. | 9710026v1 |
2001-06-19 | Antitrace maps and light transmission coefficients for a generalized Fibonacci multilayers | By using antitrace map method, we investigate the light transmission for a
generalized Fibonacci multilayers. Analytical results are obtained for
transmission coefficients in some special cases. We find that the transmission
coefficients possess two-cycle property or six-cycle property. The cycle
properties of the trace and antitrace are also obtained. | 0106378v1 |
2005-10-01 | $κ$-generalization of Stirling approximation and multinominal coefficients | Stirling approximation of the factorials and multinominal coefficients are
generalized based on the one-parameter ($\kappa$) deformed functions introduced
by Kaniadakis [Phys. Rev. E \textbf{66} (2002) 056125]. We have obtained the
relation between the $\kappa$-generalized multinominal coefficients and the
$\kappa$-entropy by introducing a new $\kappa$-product operation. | 0510018v1 |
1998-09-29 | Computation of the improvement coefficient $c_{sw}$ to 1-loop with improved gluon actions | The clover coefficient $\csw$ is computed at one loop order of perturbation
theory for improved gluon actions including six-link loops. The O(a)
improvement coefficients for the dimension three isovector composite operators
bilinear in the quark fields are also calculated. | 9809179v1 |
2001-02-12 | Resummed coefficient function for the shape function | We present a leading evaluation of the resummed coefficient function for the
shape function. It is also shown that the coefficient function is
short-distance-dominated. Our results allow relating the shape function
computed on the lattice to the physical QCD distributions. | 0102138v1 |
2007-02-21 | Transport coefficients of Relativistic Causal Hydrodynamics for Hadrons | We investigate coefficients in the Israel-Stewart's causal hydrodynamics and
discuss the way to calculate them with a microscopic theory. Based on the
hadro-molecular simulation based on an event generator URASiMA, we evaluate the
coefficients for a hot and dense hadronic fluid. | 0702220v2 |
1992-05-25 | Operator Coefficients for Composite Operators in the $(φ^4)_4$ Theory | In a previous paper we derived a relation between the operator product
coefficients and anomalous dimensions. We explore this relation in the
$(\phi^4)_4$ theory and compute the coefficient functions in the products of
$\phi^2$ and $\phi^4$ to first order in the parameter $\lambda$. The
calculation results in two-loop beta functions. | 9205084v1 |
1995-01-10 | The Heat Kernel Coefficients to the Matrix Schrödinger Operator | The heat kernel coefficients $H_k$ to the Schr\"odinger operator with a
matrix potential are investigated. We present algorithms and explicit
expressions for the Taylor coefficients of the $H_k$. Special terms are
discussed, and for the one-dimensional case some improved algorithms are
derived. | 9501026v1 |
1995-01-16 | Heat-kernel coefficients of the Laplace operator on the 3-dimensional ball | We consider the heat-kernel expansion of the massive Laplace operator on the
three dimensional ball with Dirichlet boundary conditions. Using this example,
we illustrate a very effective scheme for the calculation of an (in principle)
arbitrary number of heat-kernel coefficients for the case where the basis
functions are known. New results for the coefficients $B_{\frac 5 2},...,B_5$
are presented. | 9501064v1 |
2000-11-10 | Asymptotic expansion coefficients of the heat kernel in Riemann-Cartan space | By applying the covariant Taylor expansion method, the fifth lower
coefficients the asymptotic expansion of the heat kernel associated with a
fermion of spin 1/2 in Riemann-Cartan space are manifestly given. These
coefficients in Riemann-Cartan space is derived from those obtained in
Riemannian space by simple replacements. | 0011082v1 |
2006-02-22 | Eliminating the CPT-Odd f Coefficient from the Lorentz-Violating Standard Model Extension | The fermionic f coefficient in the Lorentz-violating standard model extension
presents a puzzle. Thus far, no observable quantity that depends upon f has
ever been found. We show that this is because f is actually unnecessary. It has
absolutely no effects at leading order and can be completely absorbed into
other coefficients of the theory by a redefinition of the field. | 0602235v1 |
2006-11-22 | Friction Coefficient for Quarks in Supergravity Duals | We study quarks moving in strongly-coupled plasmas that have supergravity
duals. We compute the friction coefficient of strings dual to such quarks for
general static supergravity backgrounds near the horizon. Our results also show
that a previous conjecture on the bound has to be modified and higher friction
coefficients can be achieved. | 0611235v1 |
1995-02-09 | A generalization of the binomial coefficients | We pose the question of what is the best generalization of the factorial and
the binomial coefficient. We give several examples, derive their combinatorial
properties, and demonstrate their interrelationships.
On cherche ici \`a d\'eterminer est la meilleure g\'en\'eralisation possible
des factorielles et des coefficients du bin\^oome. On s'interesse \`a plusieurs
exemples, \`a leurs propri\'et\'es combinatoires, et aux differentes relations
qu'ils mettent en jeu. | 9502218v1 |
2001-03-27 | Symbolic Evaluation of Coefficients in Airy-type Asymptotic Expansions | Computer algebra algorithms are developed for evaluating the coefficients in
Airy-type asymptotic expansions that are obtained from integrals with a large
parameter. The coefficients are defined from recursive schemes obtained from
integration by parts. An application is given for the Weber parabolic cylinder
function. | 0103184v1 |
2001-05-17 | A Characterization of the Heat Kernel Coefficients | We consider the asymptotic expansion of the heat kernel of a generalized
Laplacian for $t\to 0^+$ and characterize the coefficients $a_k$ of this
expansion by a natural intertwining property. In particular we will give a
closed formula for the infinite order jet of these coefficients on the diagonal
in terms of the local expressions of the powers of the given generalized
Laplacian in normal coordinates. | 0105144v1 |
2004-01-30 | The leading coefficient of certain Kazhdan-Lusztig polynomials of the permutation group $S_n$ | In this paper we show that the leading coefficient $\mu(y,w)$ of certain
Kazhdan-Lusztig polynomials $P_{y,w}$ of the permutation group $\mathfrak S_n$
of 1,2,...,n are not greater than 1. More precisely, we show that the leading
coefficients $\mu(y,w)$ are not greater than 1 whenever $a(y)< a(w)$, where $a:
\mathfrak S_n\to\mathbf N$ is the function defined by Lusztig. | 0401430v1 |
2005-01-12 | A q-Analog of Dual Sequences with Applications | In the present paper combinatorial identities involving q-dual sequences or
polynomials with coefficients q-dual sequences are derived. Further,
combinatorial identities for q-binomial coefficients(Gaussian coefficients),
q-Stirling numbers and q-Bernoulli numbers and polynomials are deduced. | 0501186v4 |
2005-06-14 | Combinatorial Interpretations of the q-Faulhaber and q-Salie Coefficients | Recently, Guo and Zeng discovered two families of polynomials featuring in a
q-analogue of Faulhaber's formula for the sums of powers and a q-analogue of
Gessel-Viennot's formula involving Salie's coefficients for the alternating
sums of powers. In this paper, we show that these are polynomials with
symmetric, nonnegative integral coefficients by refining Gessel-Viennot's
combinatorial interpretations. | 0506274v1 |
2005-06-22 | Linearization coefficients of Bessel polynomials | We prove positivity results about linearization and connection coefficients
for Bessel polynomials. The proof is based on a recursion formula and explicit
formulas for the coefficients in special cases. The result implies that the
distribution of a convex combination of independent Student-t random variables
with arbitrary odd degrees of freedom has a density which is a convex
combination of certain Student-t densities with odd degrees of freedom. | 0506458v1 |
2005-12-06 | Two-scale extensions for non-periodic coefficients | We consider non-homogeneous media with properties which can be characterized
by rapidly oscillated coefficients. For such coefficients we define a notion of
two-scale extension, present several ways to construct two-scale extensions,
discuss their properties and relation to homogenization | 0512123v1 |
2006-01-08 | Khovanov homology for virtual links with arbitrary coefficients | We construct explicitly the Khovanov homology theory for virtual links with
arbitrary coefficients by using the twisted coefficients method. This method
also works for constructing Khovanov homology for ``non-oriented virtual
knots'' in the sense of Viro, in particular, for knots in ${\bf R}P^{3}$. | 0601152v3 |
2006-03-03 | Orthogonal polynomials with exponentially decaying recursion coefficients | We review recent results on necessary and sufficient conditions for measures
on $\mathbb{R}$ and $\partial\mathbb{D}$ to yield exponential decay of the
recursion coefficients of the corresponding orthogonal polynomials. We include
results on the relation of detailed asymptotics of the recursion coefficients
to detailed analyticity of the measures. We present an analog of Carmona's
formula for OPRL. A major role is played by the Szego and Jost functions. | 0603099v1 |
2006-06-28 | Some characterizations of the spherical harmonics coefficients for isotropic random fields | In this paper we provide some simple characterizations for the spherical
harmonics coefficients of an isotropic random field on the sphere. The main
result is a characterization of isotropic gaussian fields through independence
of the coefficients of their development in spherical harmonics. | 0606709v1 |
2007-01-31 | Irreducibility of hypersurfaces | Given a polynomial P in several variables over an algebraically closed field,
we show that except in some special cases that we fully describe, if one
coefficient is allowed to vary, then the polynomial is irreducible for all but
at most deg(P)^2-1 values of the coefficient. We more generally handle the
situation where several specified coefficients vary. | 0701919v1 |
2007-03-19 | Meromorphic differentials with twisted coefficients on compact Riemann surfaces | This note is to concern a generalization to the case of twisted coefficients
of the classical theory of Abelian differentials on a compact Riemann surface.
We apply the Dirichlet's principle to a modified energy functional to show the
existence of differentials with twisted coefficients of the second and third
kinds under a suitable assumption on residues. | 0703542v1 |
1999-12-23 | Fundamental solutions to elliptic equations with discontinuous senior coefficients and an inequlity for these solutions | Asymptotic formula is derived for the behavior of the fundamental solution of
the second-order elliptic self-adjoint operator with a piecewise-smooth
coefficient in front of the senior derivatives near the discontinuity surface
of the coefficient. Applications to inverse problems are discussed. | 9912017v1 |
2006-08-28 | Coefficients and terms of the liquid drop model and mass formula | The coefficients of different combinations of terms of the liquid drop model
have been determined by a least square fitting procedure to the experimental
atomic masses. The nuclear masses can also be reproduced using a Coulomb radius
taking into account the increase of the ratio $R\_0/A^{1/3}$ with increasing
mass, the fitted surface energy coefficient remaining around 18 MeV. | 0608064v1 |
2001-02-12 | High-precision calculations of van der Waals coefficients for heteronuclear alkali-metal dimers | Van der Waals coefficients for the heteronuclear alkali-metal dimers of Li,
Na, K, Rb, Cs, and Fr are calculated using relativistic ab initio methods
augmented by high-precision experimental data. We argue that the uncertainties
in the coefficients are unlikely to exceed about 1%. | 0102030v1 |
2002-11-11 | Recursive Weak- and Strong Coupling Expansions in a Cosine Potential | For the Cos(2x)-Potential the coefficients of the weak- and strong coupling
perturbation series of the ground state energy are constructed recursively.
They match the well-known expansion coefficients of the Mathieu equation's
characteristic values. However presently there is no physically intuitive
method to extract the coefficients of the strong coupling series from those of
the weak one. The standard rule while giving exellent results for the
anharmonic oscillator fails completely in this case. | 0211057v1 |
2007-05-25 | Parabolic equations with measurable coefficients in $L_p$-spaces with mixed norms | The unique solvability of parabolic equations in Sobolev spaces with mixed
norms is presented. The second order coefficients (except $a^{11}$) are assumed
to be only measurable in time and one spatial variable, and VMO in the other
spatial variables. The coefficient $a^{11}$ is measurable in one spatial
variable and VMO in the other variables. | 0705.3808v1 |
2007-05-29 | About construction of orthogonal wavelets with compact support and with scaling coefficient N | In this paper a simple method of construction of scaling function $\phi (x)$
and orthogonal wavelets with the compact support for any natural coefficient of
scaling $N\ge 2$ is given. Examples of construction of wavelets for
coefficients of scaling N=2 and N=3 are produced. | 0705.4150v1 |
2007-08-24 | Experiments with a Positivity Preserving Operator | We consider some multivariate rational functions which have (or are
conjectured to have) only positive coefficients in their series expansion. We
consider an operator that preserves positivity of series coefficients, and
apply the inverse of this operator to the rational functions. We obtain new
rational functions which seem to have only positive coefficients, whose
positivity would imply positivity of the original series, and which, in a
certain sense, cannot be improved any further. | 0708.3286v1 |
2007-10-31 | A version of Fabry's theorem for power series with regularly varying coefficients | For real power series whose non-zero coefficients satisfy $|a_m|^{1/m}\to~1$
we prove a stronger version of Fabry theorem relating the frequency of sign
changes in the coefficients and analytic continuation of the sum of the power
series. | 0710.5894v2 |
2008-05-03 | Alternatives to Pearson's and Spearman's Correlation Coefficients | This article presents several alternatives to Pearson's correlation
coefficient and many examples. In the samples where the rank in a discrete
variable counts more than the variable values, the mixtures that we propose of
Pearson's and Spearman's correlation coefficients give better results. | 0805.0383v1 |
2008-06-02 | Hopf-cyclic homology with contramodule coefficients | A new class of coefficients for the Hopf-cyclic homology of module algebras
and coalgebras is introduced. These coefficients, termed stable
anti-Yetter-Drinfeld contramodules, are both modules and contramodules of a
Hopf algebra that satisfy certain compatibility conditions. | 0806.0389v2 |
2008-07-06 | Second-order elliptic equations with variably partially VMO coefficients | The solvability in $W^{2}_{p}(\bR^{d})$ spaces is proved for second-order
elliptic equations with coefficients which are measurable in one direction and
VMO in the orthogonal directions in each small ball with the direction
depending on the ball. This generalizes to a very large extent the case of
equations with continuous or VMO coefficients. | 0807.0926v2 |
2008-11-13 | The p-adic valuation of k-central binomial coefficients | The coefficients c(n,k) defined by (1-k^2x)^(-1/k) = sum c(n,k) x^n reduce to
the central binomial coefficients for k=2. Motivated by a question of H.
Montgomery and H. Shapiro for the case k=3, we prove that c(n,k) are integers
and study their divisibility properties. | 0811.2028v1 |
2008-12-08 | Commutativity and Ideals in Category Crossed Products | In order to simultaneously generalize matrix rings and group graded crossed
products, we introduce category crossed products. For such algebras we describe
the center and the commutant of the coefficient ring. We also investigate the
connection between on the one hand maximal commutativity of the coefficient
ring and on the other hand nonemptyness of intersections of the coefficient
ring by nonzero twosided ideals. | 0812.1468v1 |
2009-02-27 | Estimation in nonstationary random coefficient autoregressive models | We investigate the estimation of parameters in the random coefficient
autoregressive model. We consider a nonstationary RCA process and show that the
innovation variance parameter cannot be estimated by the quasi-maximum
likelihood method. The asymptotic normality of the quasi-maximum likelihood
estimator for the remaining model parameters is proven so the unit root problem
does not exist in the random coefficient autoregressive model. | 0903.0022v1 |
2009-03-04 | SPDEs in divergence form with VMO coefficients and filtering theory of partially observable diffusion processes with Lipschitz coefficients | We present several results on the smoothness in $L_{p}$ sense of filtering
densities under the Lipschitz continuity assumption on the coefficients of a
partially observable diffusion processes. We obtain them by rewriting in
divergence form filtering equation which are usually considered in terms of
formally adjoint to operators in nondivergence form. | 0903.0877v1 |
2009-03-25 | Coefficients of the poles of local zeta functions and their applications to oscillating integrals | We introduce a new method which enables us to calculate the coefficients of
the poles of local zeta functions very precisely and prove some explicit
formulas. Some vanishing theorems for the candidate poles of local zeta
functions will be also given. Moreover we apply our method to oscillating
integrals and obtain an explicit formula for the coefficients of their
asymptotic expansions. | 0903.4265v1 |
2009-04-06 | Hall Coefficient of Dirac Fermions in Graphene under Charged Impurity Scatterings | With a conserving formalism within the self-consistent Born approximation, we
study the Hall conductivity of Dirac fermions in graphene under charged
impurity scatterings. The calculated inverse Hall coefficient is compared with
the experimental data. It is shown that the present calculations for the Hall
coefficient and the electric conductivity are in good agreement with the
experimental measurements. | 0904.0959v1 |
2009-05-26 | The image of the coefficient space in the universal deformation space | The coefficient space is a kind of resolution of singularities of the
universal flat deformation space for a given Galois representation of some
local field. It parameterizes (in some sense) the finite flat models for the
Galois representation. The aim of this note is to determine the image of the
coefficient space in the universal deformation space. | 0905.4289v2 |
2009-06-13 | Comments on "Slip coefficient in nanoscale pore flow" (arXiv:0805.1666) | We make some remarks on Sokhan and Quirke's [{\it Phys. Rev. E} 78, 015301(R)
(2008)] paper (arXiv:0805.1666). Sokhan and Quirke mentioned that, considering
their main result, {the slip coefficient is independent of the external force
(flux)} which is not consistent with previous measurements and approaches. We
also discuss the sudden changes of the slip coefficient for larger Knudsen
numbers or smaller nanopores. | 0906.2436v1 |
2009-07-14 | On divergence form SPDEs with growing coefficients in $W^{1}_{2}$ spaces without weights | We consider divergence form uniformly parabolic SPDEs with bounded and
measurable leading coefficients and possibly growing lower-order coefficients
in the deterministic part of the equations. We look for solutions which are
summable to the second power with respect to the usual Lebesgue measure along
with their first derivatives with respect to the spatial variable. | 0907.2467v2 |
2009-09-29 | On divergence form second-order PDEs with growing coefficients in $W^{1}_{p}$ spaces without weights | We consider second-order divergence form uniformly parabolic and elliptic
PDEs with bounded and $VMO_{x}$ leading coefficients and possibly linearly
growing lower-order coefficients. We look for solutions which are summable to
the $p$th power with respect to the usual Lebesgue measure along with their
first derivatives with respect to the spatial variables. | 0909.5248v1 |
2009-10-15 | $p$-adic properties of coefficients of weakly holomorphic modular forms | We examine the Fourier coefficients of modular forms in a canonical basis for
the spaces of weakly holomorphic modular forms of weights 4, 6, 8, 10, and 14,
and show that these coefficients are often highly divisible by the primes 2, 3,
and 5. | 0910.2997v1 |
2009-10-22 | On some functionals associated with certain coefficient problems | Under certain conditions, we obtain sharp bounds on some functionals defined
in the coefficient space of starlike functions. It has been found that the
functionals are closely associated with certain coefficient problems, which are
of independent interest. | 0910.4310v1 |
2009-11-16 | Optimal Quadrature Formulas with Positive Coefficients in $L_2^{(m)}(0,1)$ Space | In the Sobolev space $L_2^{(m)}(0,1)$ optimal quadrature formulas with the
nodes (1.5) are investigated. For optimal coefficients explicit form are
obtained and norm of the error functional is calculated. In particular, by
choosing parameter $\eta_0$ in (1.5) the optimal quadrature formulas with
positive coefficients are obtained and compared with well known optimal
formulas. | 0911.2896v1 |
2009-12-03 | Supercongruences satisfied by coefficients of 2F1 hypergeometric series | Recently, Chan, Cooper and Sica conjectured two congruences for coefficients
of classical 2F1 hypergeometric series which also arise from power series
expansions of modular forms in terms of modular functions. We prove these two
congruences using combinatorial properties of the coefficients. | 0912.0620v1 |
2009-12-22 | On the Basis Property of the Root Functions of Differential Operators with Matrix Coefficients | We obtain asymptotic formulas for eigenvalues and eigenfunctions of the
operator generated by a system of ordinary differential equations with summable
coefficients and periodic or antiperiodic boundary conditions. Then using these
asymptotic formulas, we find necessary and sufficient conditions on the
coefficients for which the system of eigenfunctions and associated functions of
the operator under consideration forms a Riesz basis. | 0912.4340v1 |
2010-04-20 | On the successive coefficients of certain univalent functions | The object of this paper is to study relationship between successive
coefficients of some subclasses of the class of univalent functions in the unit
disk. the result obtained is sharp, and is used to provide a new, short proof
of the well-known conjecture of Robertson on the coefficients of
close-to-convex functions. | 1004.3383v1 |
2010-07-15 | Certain Binomial Sums with recursive coefficients | In this short note, we establish some identities containing sums of binomials
with coefficients satisfying third order linear recursive relations. As a
result and in particular, we obtain general forms of earlier identities
involving binomial coefficients and Fibonacci type sequences. | 1007.2676v1 |
2010-09-30 | Polynomial differential equations with piecwise linear coefficients | Cubic and quartic non-autonomous differential equations with continuous
piecewise linear coefficients are considered. The main concern is to find the
maximum possible multiplicity of periodic solutions. For many classes, we show
that the mutiplicity is the same when the coefficients are polynomial functions
of degree n or piecewise linear functions with n segments. | 1009.6019v1 |
2010-10-11 | Clebsch--Gordan Coefficients of the Quaternion Group | The Clebsch--Gordan coefficients of the Kronecker products of the irreducible
representations of the Quaternion Group Q8, of the Generalized Quaternion
Groups Q16 and Q32, and of the factor group (Q32 X Q32)/{(1,1),(-1,-1)} are
computed as eigenvectors of a well-known matrix of triple-products of the
irreducible representations. | 1010.2249v1 |
2010-10-17 | Stochastic Homeomorphism Flows of SDEs with Singular Drifts and Sobolev Diffusion Coefficients | In this paper we prove the stochastic homeomorphism flow property and the
strong Feller property for stochastic differential equations with sigular time
dependent drifts and Sobolev diffusion coefficients. Moreover, the local well
posedness under local assumptions are also obtained. In particular, we extend
Krylov and R\"ockner's results in \cite{Kr-Ro} to the case of non-constant
diffusion coefficients. | 1010.3403v2 |
2011-01-14 | Cohomology with coefficients in stacks of Picard categories | Cohomology of a topological space with coefficients in stacks of abelian
2-groups is considered. A 2-categorical analog of the theorem of Grothendieck
is proved, relating cohomology of the space with coefficients in a 2-stage
spectrum and the Ext groups of appropriate stacks. | 1101.2918v2 |
2011-04-04 | A Note on The Positivity of the Coefficients of Some Power Series Expansions | In this short note, a general result concerning the positivity, under some
conditions, of the coefficients of a power series is proved. This allows us to
answer positively a question raised by Guo (2010) about the sign of the
coefficients of a power series relating the residual errors in Halley's
iterations for the $p$th root. | 1104.0470v1 |
2011-05-02 | Elliptic equations with singular BMO coefficients in Reifenberg domains | $W^{1, p}$ estimate for the solutions of elliptic equations whose coefficient
matrix can have large jump along the boundary of subdomains is obtained. The
principal coefficients are supposed to be in the John-Nirenberg space with
small BMO seminorms. The domain and subdomains are Reifenberg flat domains and
moreover, it has been shown that the estimates are uniform with respect to the
distance between the subdomains. | 1105.0228v1 |
2011-05-06 | The subgroup growth spectrum of virtually free groups | For a finitely generated group $\Gamma$ denote by $\mu(\Gamma)$ the growth
coefficient of $\Gamma$, that is, the infimum over all real numbers $d$ such
that $s_n(\Gamma)<n!^d$. We show that the growth coefficient of a virtually
free group is always rational, and that every rational number occurs as growth
coefficient of some virtually free group. Moreover, we describe an algorithm to
compute $\mu$. | 1105.1297v1 |
2011-06-06 | Divisibility Properties of Coefficients of Level $p$ Modular Functions for Genus Zero Primes | Lehner's 1949 results on the $j$-invariant showed high divisibility of the
function's coefficients by the primes $p\in\{2,3,5,7\}$. Expanding his results,
we examine a canonical basis for the space of level $p$ modular functions
holomorphic at the cusp 0. We show that the Fourier coefficients of these
functions are often highly divisible by these same primes. | 1106.1188v1 |
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