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In this Letter, both the manipulation of valley-polarized currents and the
optical-like behaviors of Dirac fermions are theoretically explored in
polycrystalline graphene. When strain is applied, the misorientation between
two graphene domains separated by a grain boundary can result in a mismatch of
their electronic structures. Such a discrepancy manifests itself in a strong
breaking of the inversion symmetry, leading to perfect valley polarization in a
wide range of transmission directions. In addition, these graphene domains act
as different media for electron waves, offering the possibility to modulate and
obtain negative refraction indexes.
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Partial observability and uncertainty are common problems in sequential
decision-making that particularly impede the use of formal models such as
Markov decision processes (MDPs). However, in practice, agents may be able to
employ costly sensors to measure their environment and resolve partial
observability by gathering information. Moreover, imprecise transition
functions can capture model uncertainty. We combine these concepts and extend
MDPs to robust active-measuring MDPs (RAM-MDPs). We present an active-measure
heuristic to solve RAM-MDPs efficiently and show that model uncertainty can,
counterintuitively, let agents take fewer measurements. We propose a method to
counteract this behavior while only incurring a bounded additional cost. We
empirically compare our methods to several baselines and show their superior
scalability and performance.
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In this paper we present an algorithm, called conauto-2.0, that can
efficiently compute a set of generators of the automorphism group of a graph,
and test whether two graphs are isomorphic, finding an isomorphism if they are.
This algorithm uses the basic individualization/refinement technique, and is an
improved version of the algorithm conauto, which has been shown to be very fast
for random graphs and several families of hard graphs. In this paper, it is
proved that, under some circumstances, it is not only possible to prune the
search space (using already found generators of the automorphism group), but
also to infer new generators without the need of explicitly finding an
automorphism of the graph. This result is especially suited for graphs with
regularly connected components, and can be applied in any isomorphism testing
and canonical labeling algorithm (that use the individualization/refinement
technique) to significantly improve its performance. Additionally, a dynamic
target cell selection function is used to adapt to different graphs. The
resulting algorithm preserves all the nice features of conauto, but reduces the
time for testing graphs with regularly connected components and other hard
graph families. We run extensive experiments, which show that the most popular
algorithms (namely, nauty, bliss, Traces, and saucy) are slower than
conauto-2.0, among others, for the graph families based on components.
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Silicon photonics enables wafer-scale integration of optical functionalities
on chip. A silicon-based laser frequency combs could significantly expand the
applications of silicon photonics, by providing integrated sources of mutually
coherent laser lines for terabit-per-second transceivers, parallel coherent
LiDAR, or photonics-assisted signal processing. Here, we report on
heterogeneously integrated laser soliton microcombs combining both InP/Si
semiconductor lasers and ultralow-loss silicon nitride microresonators on
monolithic silicon substrate. Thousands of devices are produced from a single
wafer using standard CMOS techniques. Using on-chip electrical control of the
microcomb-laser relative optical phase, these devices can output single-soliton
microcombs with 100 GHz repetition rate. Our approach paves the way for
large-volume, low-cost manufacturing of chip-based frequency combs for
next-generation high-capacity transceivers, datacenters, space and mobile
platforms.
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Synchronization is the process of achieving identical dynamics among coupled
identical units. If the units are different from each other, their dynamics
cannot become identical; yet, after transients, there may emerge a functional
relationship between them -- a phenomenon termed "generalized synchronization."
Here, we show that the concept of transient uncoupling, recently introduced for
synchronizing identical units, also supports generalized synchronization among
nonidentical chaotic units. Generalized synchronization can be achieved by
transient uncoupling even when it is impossible by regular coupling. We
furthermore demonstrate that transient uncoupling stabilizes synchronization in
the presence of common noise. Transient uncoupling works best if the units stay
uncoupled whenever the driven orbit visits regions that are locally diverging
in its phase space. Thus, to select a favorable uncoupling region, we propose
an intuitive method that measures the local divergence at the phase points of
the driven unit's trajectory by linearizing the flow and subsequently
suppresses the divergence by uncoupling.
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We examine the sensitivity of flavor changing neutral current (FCNC)
processes to anomalous triple gauge boson couplings. We show that in the
non-linear realization of the electroweak symmetry breaking sector these
processes are very sensitive to two CP conserving anomalous couplings. A clean
separation of their effects is possible in the next round of experiments
probing $b\to s\gamma$ and $b\to s\ell^+\ell^-$ processes, as well as kaon
decays such as $K^+\to\pi^+\nu\bar\nu$. The obtained sensitivity is found to be
competitive with that of direct measurements at high energy colliders. In
particular, for one of the $WWZ$ couplings the one-loop FCNC effects are
enhanced by a logarithmic dependence on the scale of new physics. We also
explore the potential signals of CP violating anomalous triple gauge boson
couplings in rare $B$ decays.
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This letter establishes a novel relationship between a class of recurrent
neural networks and certain evolutionary dynamics that emerge in the context of
population games. Specifically, it is shown that the output of a recurrent
neural network, in the context of classification problems, coincides with the
evolution of the population state in a population game. This connection is
established with dynamic payoffs and under replicator evolutionary dynamics.
The connection provides insights into the neural network's behavior from both
dynamical systems and game-theoretical perspectives, aligning with recent
literature that suggests that neural network outputs may resemble the Nash
equilibria of suitable games. It also uncovers potential connections between
the neural network classification problem and mechanism design. To illustrate
our results, we present different numerical experiments in the context of
classification problems.
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Signed distance field (SDF) is a prominent implicit representation of 3D
meshes. Methods that are based on such representation achieved state-of-the-art
3D shape reconstruction quality. However, these methods struggle to reconstruct
non-convex shapes. One remedy is to incorporate a constructive solid geometry
framework (CSG) that represents a shape as a decomposition into primitives. It
allows to embody a 3D shape of high complexity and non-convexity with a simple
tree representation of Boolean operations. Nevertheless, existing approaches
are supervised and require the entire CSG parse tree that is given upfront
during the training process. On the contrary, we propose a model that extracts
a CSG parse tree without any supervision - UCSG-Net. Our model predicts
parameters of primitives and binarizes their SDF representation through
differentiable indicator function. It is achieved jointly with discovering the
structure of a Boolean operators tree. The model selects dynamically which
operator combination over primitives leads to the reconstruction of high
fidelity. We evaluate our method on 2D and 3D autoencoding tasks. We show that
the predicted parse tree representation is interpretable and can be used in CAD
software.
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We show that if g is a generic (in the sense of Baire category) isometry of a
generic subspace of the Urysohn metric space U, then g does not extend to a
full isometry of U. The same holds for the Urysohn sphere S. Let M be a Fraisse
L-structure, where L is a relational countable language and M has no
algebraicity. We provide necessary and sufficient conditions for the following
to hold: for a generic substructure A of M, every automorphism f in Aut(A)
extends to a full automorphism f in Aut(M). From our analysis, a dichotomy
arises and some structural results are derived that, in particular, apply to
omega-stable Fraisse structures without algebraicity.
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We realize Leavitt ultragraph path algebras as partial skew group rings.
Using this realization we characterize artinian ultragraph path algebras and
give simplicity criteria for these algebras.
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In this article we briefly discuss the finite generation of fiber rings of
invariant k-jets of holomorphic curves in a complex projective manifold, using
differential Galois theory.
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We analyze the effects of an in-medium broadening of nucleon resonances on
the exclusive photoproduction of mesons on nuclei as well as on the total
photoabsorption cross sections in a transport calculation. We show that the
resonance widths observed in semi-inclusive photoproduction on nuclei are
insensitive to an in-medium broadening of nucleon resonances. This is due to a
simple effect: the sizeable width of the nuclear surface and Fermi motion.
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Previous analyses of mid-infrared water spectra from young protoplanetary
disks observed with the Spitzer-IRS found an anti-correlation between water
luminosity and the millimeter dust disk radius observed with ALMA. This trend
was suggested to be evidence for a fundamental process of inner disk water
enrichment, used to explain properties of the Solar System 40 years ago, in
which icy pebbles drift inward from the outer disk and sublimate after crossing
the snowline. Previous analyses of IRS water spectra, however, were uncertain
due to the low spectral resolution that blended lines together. We present new
JWST-MIRI spectra of four disks, two compact and two large with multiple radial
gaps, selected to test the scenario that water vapor inside the snowline is
regulated by pebble drift. The higher spectral resolving power of MIRI-MRS now
yields water spectra that separate individual lines, tracing upper level
energies from 900 K to 10,000 K. These spectra clearly reveal excess emission
in the low-energy lines in compact disks, compared to the large disks,
demonstrating an enhanced cool component with $T \approx$ 170-400 K and
equivalent emitting radius $R_{\rm{eq}}\approx$ 1-10 au. We interpret the cool
water emission as ice sublimation and vapor diffusion near the snowline,
suggesting that there is indeed a higher inwards mass flux of icy pebbles in
compact disks. Observation of this process opens up multiple exciting prospects
to study planet formation chemistry in inner disks with JWST.
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Pulsars are special objects whose positions can be determined independently
from timing, radio interferometric, and Gaia astrometry at sub-milliarcsecond
(mas) precision; thus, they provide a unique way to monitor the link between
dynamical and kinematic reference frames. We aimed to assess the orientation
consistency between the dynamical reference frame represented by the planetary
ephemeris and the kinematic reference frames constructed by Gaia and VLBI
through pulsar positions. We identified 49 pulsars in Gaia Data Release 3 and
62 pulsars with very long baseline interferometry (VLBI) positions from the
PSR$\pi$ and MSPSR$\pi$ projects and searched for the published timing
solutions of these pulsars. We then compared pulsar positions measured by
timing, VLBI, and Gaia to estimate the orientation offsets of the ephemeris
frames with respect to the Gaia and VLBI reference frames by iterative fitting.
We found orientation offsets of $\sim$10 mas in the DE200 frame with respect to
the Gaia and VLBI frame. Our results depend strongly on the subset used in the
comparison and could be biased by underestimated errors in the archival timing
data, reflecting the limitation of using the literature timing solutions to
determine the frame rotation.
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In previous theoretical research, we inferred that cancer stem cells (CSCs),
the cells that presumably drive tumor growth and resistance to conventional
cancer treatments, are not uniformly distributed in the bulk of a tumorsphere.
To confirm this theoretical prediction, we cultivated tumorspheres enriched in
CSCs, and performed immunofluorecent detection of the stemness marker SOX2
using a confocal microscope.
In this article, we present a method developed to process the images that
reconstruct the amount and location of the CSCs in the tumorspheres. Its
advantage is the use of a statistical criterion to classify the cells in stem
and differentiated instead of setting an arbitrary threshold. From the analysis
of the results of the methods using graph theory and computational modeling, we
concluded that the distribution of Cancer Stem Cells in an experimental
tumorsphere is non-homogeneous. This method is independent of the tumorsphere
assay being useful for analyzing images in which several different kinds of
cells are stained with different markers.
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The future of 3D printing utilizing unmanned aerial vehicles (UAVs) presents
a promising capability to revolutionize manufacturing and to enable the
creation of large-scale structures in remote and hard- to-reach areas e.g. in
other planetary systems. Nevertheless, the limited payload capacity of UAVs and
the complexity in the 3D printing of large objects pose significant challenges.
In this article we propose a novel chunk-based framework for distributed 3D
printing using UAVs that sets the basis for a fully collaborative aerial 3D
printing of challenging structures. The presented framework, through a novel
proposed optimisation process, is able to divide the 3D model to be printed
into small, manageable chunks and to assign them to a UAV for partial printing
of the assigned chunk, in a fully autonomous approach. Thus, we establish the
algorithms for chunk division, allocation, and printing, and we also introduce
a novel algorithm that efficiently partitions the mesh into planar chunks,
while accounting for the inter-connectivity constraints of the chunks. The
efficiency of the proposed framework is demonstrated through multiple physics
based simulations in Gazebo, where a CAD construction mesh is printed via
multiple UAVs carrying materials whose volume is proportionate to a fraction of
the total mesh volume.
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Superconductivity forms out of the condensation of Cooper pairs of electrons.
The mechanism by which Cooper pairs are created in non-conventional
superconductors is often elusive because experimental signatures that connect a
specific pairing mechanism to the properties of superconducting state are rare.
The recently discovered superconducting oxide-insulator/KTaO$_3$ interface may
offer clues about its origins. Here we observe distinct dependences of the
superconducting transition temperature Tc on carrier density n$_{2D}$ for
electron gases formed at KTaO$_3$ (111), (001) and (110) interfaces. For the
KTaO$_3$ (111) interface, a remarkable linear dependence of Tc on n$_{2D}$ is
observed over a range of nearly one order of magnitude. Further, our study of
the dependence of superconductivity on gate electric fields reveals the role of
the interface in mediating superconductivity, which also allows for a
reversible electric switching of superconductivity at T = 2 K. We found that
the extreme sensitivity of superconductivity to crystallographic orientation
can be explained by Cooper pairing via inter-orbital interactions induced by
the inversion-breaking transverse optical (TO1) phonons and quantum
confinement. This mechanism is also consistent with the dependence of Tc on
n$_{2D}$ at the KTaO$_3$ (111) interface. Our study may shed light on the
pairing mechanism in other superconducting quantum-paraelectrics.
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By using a method, previously established to calculate electromagnetic
fields, we compute the force of light upon a metallic particle. This procedure
is based on both Maxwell's Stress Tensor and the Couple Dipole Method. With
these tools, we study the force when the particle is over a flat dielectric
surface. The multiple interaction of light between the particle and the surface
is fully taken into account. The wave illuminating the particle is either
evanescent or propagating depending an whether or not total internal reflection
takes place. We analyze the behaviour of this force on either a small or a
large particle in terms of the wavelength. A remarkable result obtained for
evanescent field illumination, is that the force on a small silver particle can
be either attractive or repulsive depending on the wavelength. This behaviour
also varies as the particle becomes larger.
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Except for Koshy who devotes seven pages to applications of Fibonacci Numbers
to electric circuits, most books and the Fibonacci Quarterly have been
relatively silent on applications of graphs and electric circuits to Fibonacci
numbers. This paper continues a recent trend of papers studying the interplay
of graphs, circuits, and Fibonacci numbers by presenting and studying the
Circuit Array, an infinite 2-dimensional array whose entries are electric
resistances labelling edge values of circuits associated with a family of
graphs. The Circuit Array has several features distinguishing it from other
more familiar arrays such as the Binomial Array and Wythoff Array. For example,
it can be proven modulo a strongly supported conjecture that the numerators of
its left-most diagonal do not satisfy any linear, homogeneous, recursion, with
constant coefficients (LHRCC). However, we conjecture with supporting numerical
evidence an asymptotic formula involving $\pi$ satisfied by the left-most
diagonal of the Circuit Array.
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We present a multilevel Monte Carlo (MLMC) method for the uncertainty
quantification of variably saturated porous media flow that are modeled using
the Richards' equation. We propose a stochastic extension for the empirical
models that are typically employed to close the Richards' equations. This is
achieved by treating the soil parameters in these models as spatially
correlated random fields with appropriately defined marginal distributions. As
some of these parameters can only take values in a specific range, non-Gaussian
models are utilized. The randomness in these parameters may result in path-wise
highly nonlinear systems, so that a robust solver with respect to the random
input is required. For this purpose, a solution method based on a combination
of the modified Picard iteration and a cell-centered multigrid method for
heterogeneous diffusion coefficients is utilized. Moreover, we propose a
non-standard MLMC estimator to solve the resulting high-dimensional stochastic
Richards' equation. The improved efficiency of this multilevel estimator is
achieved by parametric continuation that allows us to incorporate simpler
nonlinear problems on coarser levels for variance reduction while the target
strongly nonlinear problem is solved only on the finest level. Several
numerical experiments are presented showing computational savings obtained by
the new estimator compared to the original MC estimator.
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The Fanaroff-Riley class II radio galaxy Cygnus A hosts jets which produce
radio emission, X-ray cavities, cocoon shocks, and X-ray hotspots where the jet
interacts with the ICM. Surrounding one hotspot is a peculiar "hole" feature
which appears as a deficit in X-ray emission. We use relativistic hydrodynamic
simulations of a collimated jet interacting with an inclined interface between
lobe and cluster plasma to model the basic processes which may lead to such a
feature. We find that the jet reflects off of the interface into a broad,
turbulent flow back out into the lobe, which is dominated by gas stripped from
the interface at first and from the intracluster medium itself at later times.
We produce simple models of X-ray emission from the ICM, the hotspot, and the
reflected jet to show that a hole of emission surrounding the hotspot as seen
in Cygnus A may be produced by Doppler de-boosting of the emission from the
reflected jet as seen by an observer with a sight line nearly along the axis of
the outgoing material.
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As crowdsourcing emerges as an efficient and cost-effective method for
obtaining labels for machine learning datasets, it is important to assess the
quality of crowd-provided data, so as to improve analysis performance and
reduce biases in subsequent machine learning tasks. Given the lack of ground
truth in most cases of crowdsourcing, we refer to data quality as annotators'
consistency and credibility. Unlike the simple scenarios where Kappa
coefficient and intraclass correlation coefficient usually can apply, online
crowdsourcing requires dealing with more complex situations. We introduce a
systematic method for evaluating data quality and detecting spamming threats
via variance decomposition, and we classify spammers into three categories
based on their different behavioral patterns. A spammer index is proposed to
assess entire data consistency and two metrics are developed to measure crowd
worker's credibility by utilizing the Markov chain and generalized random
effects models. Furthermore, we showcase the practicality of our techniques and
their advantages by applying them on a face verification task with both
simulation and real-world data collected from two crowdsourcing platforms.
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This paper concerns the dynamical behavior of weakly reversible,
deterministically modeled population processes near the facets (codimension-one
faces) of their invariant manifolds and proves that the facets of such systems
are "repelling." It has been conjectured that any population process whose
network graph is weakly reversible (has strongly connected components) is
persistent. We prove this conjecture to be true for the subclass of weakly
reversible systems for which only facets of the invariant manifold are
associated with semilocking sets, or siphons. An important application of this
work pertains to chemical reaction systems that are complex-balancing. For
these systems it is known that within the interior of each invariant manifold
there is a unique equilibrium. The Global Attractor Conjecture states that each
of these equilibria is globally asymptotically stable relative to the interior
of the invariant manifold in which it lies. Our results pertaining to weakly
reversible systems imply that this conjecture holds for all complex-balancing
systems whose boundary equilibria lie in the relative interior of the boundary
facets. As a corollary, we show that the Global Attractor Conjecture holds for
those systems for which the associated invariant manifolds are two-dimensional.
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Active learning (AL) techniques reduce labeling costs for training neural
machine translation (NMT) models by selecting smaller representative subsets
from unlabeled data for annotation. Diversity sampling techniques select
heterogeneous instances, while uncertainty sampling methods select instances
with the highest model uncertainty. Both approaches have limitations -
diversity methods may extract varied but trivial examples, while uncertainty
sampling can yield repetitive, uninformative instances. To bridge this gap, we
propose HUDS, a hybrid AL strategy for domain adaptation in NMT that combines
uncertainty and diversity for sentence selection. HUDS computes uncertainty
scores for unlabeled sentences and subsequently stratifies them. It then
clusters sentence embeddings within each stratum using k-MEANS and computes
diversity scores by distance to the centroid. A weighted hybrid score that
combines uncertainty and diversity is then used to select the top instances for
annotation in each AL iteration. Experiments on multi-domain German-English
datasets demonstrate the better performance of HUDS over other strong AL
baselines. We analyze the sentence selection with HUDS and show that it
prioritizes diverse instances having high model uncertainty for annotation in
early AL iterations.
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This thesis investigates the quality of randomly collected data by employing
a framework built on information-based complexity, a field related to the
numerical analysis of abstract problems. The quality or power of gathered
information is measured by its radius which is the uniform error obtainable by
the best possible algorithm using it. The main aim is to present progress
towards understanding the power of random information for approximation and
integration problems.
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We show that large language models (LLMs) are remarkably good at working with
interpretable models that decompose complex outcomes into univariate
graph-represented components. By adopting a hierarchical approach to reasoning,
LLMs can provide comprehensive model-level summaries without ever requiring the
entire model to fit in context. This approach enables LLMs to apply their
extensive background knowledge to automate common tasks in data science such as
detecting anomalies that contradict prior knowledge, describing potential
reasons for the anomalies, and suggesting repairs that would remove the
anomalies. We use multiple examples in healthcare to demonstrate the utility of
these new capabilities of LLMs, with particular emphasis on Generalized
Additive Models (GAMs). Finally, we present the package $\texttt{TalkToEBM}$ as
an open-source LLM-GAM interface.
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We propose a multi-criteria Composite Index Method (CIM) to compare the
performance of alternative approaches to solving an optimization problem. The
CIM is convenient in those situations when neither approach dominates the other
when tested on different sizes of problem instances. The CIM takes problem
instance size and multiple performance criteria into consideration within a
weighting scheme to produce a single number that measures the relative
improvement of one alternative over the other. Different weights are given to
each dimension based on their relative importance as determined by the end
user. We summarize the successful application of the CIM to an NP-hard
combinatorial optimization problem known as the backhaul profit maximization
problem (BPMP). Using the CIM we tested a series of eleven techniques for
improving solution time using CPLEX to solve two different BPMP models proposed
in the literature.
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In this paper, we study Markov dynamics on unitary duals of compact quantum
groups. We construct such dynamics from characters of quantum groups. Then we
show that the dynamics have generators, and we give an explicit formula of the
generators using the representation theory. Moreover, we construct Markov
dynamics on the unitary dual of an inductive limit of compact quantum groups.
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We report on the status of a variety of radiative B decays studied by the
CLEO detector with $9.7\times 10^6$ $B\bar{B}$ pairs.
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In this paper we investigate solvability of a partial integral equation in
the space $L_2(\Omega\times\Omega),$ where $\Omega=[a,b]^\nu.$ We define a
determinant for the partial integral equation as a continuous function on
$\Omega$ and for a continuous kernels of the partial integral equation we give
explicit description of the solution.
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We propose a new, unifying framework that yields an array of cryptographic
primitives with certified deletion. These primitives enable a party in
possession of a quantum ciphertext to generate a classical certificate that the
encrypted plaintext has been information-theoretically deleted, and cannot be
recovered even given unbounded computational resources.
- For X \in {public-key, attribute-based, fully-homomorphic, witness,
timed-release}, our compiler converts any (post-quantum) X encryption to X
encryption with certified deletion. In addition, we compile
statistically-binding commitments to statistically-binding commitments with
certified everlasting hiding. As a corollary, we also obtain
statistically-sound zero-knowledge proofs for QMA with certified everlasting
zero-knowledge assuming statistically-binding commitments.
- We also obtain a strong form of everlasting security for two-party and
multi-party computation in the dishonest majority setting. While simultaneously
achieving everlasting security against all parties in this setting is known to
be impossible, we introduce everlasting security transfer (EST). This enables
any one party (or a subset of parties) to dynamically and certifiably
information-theoretically delete other participants' data after protocol
execution. We construct general-purpose secure computation with EST assuming
statistically-binding commitments, which can be based on one-way functions or
pseudorandom quantum states.
We obtain our results by developing a novel proof technique to argue that a
bit b has been information-theoretically deleted from an adversary's view once
they output a valid deletion certificate, despite having been previously
information-theoretically determined by the ciphertext they held in their view.
This technique may be of independent interest.
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We propose generalizations of a number of standard network models, including
the classic random graph, the configuration model, and the stochastic block
model, to the case of time-varying networks. We assume that the presence and
absence of edges are governed by continuous-time Markov processes with rate
parameters that can depend on properties of the nodes. In addition to computing
equilibrium properties of these models, we demonstrate their use in data
analysis and statistical inference, giving efficient algorithms for fitting
them to observed network data. This allows us, for instance, to estimate the
time constants of network evolution or infer community structure from temporal
network data using cues embedded both in the probabilities over time that node
pairs are connected by edges and in the characteristic dynamics of edge
appearance and disappearance. We illustrate our methods with a selection of
applications, both to computer-generated test networks and real-world examples.
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We study the interplay between coherent transport by tunneling and diffusive
transport through classically chaotic phase-space regions, as it is reflected
in the Floquet spectrum of the periodically driven quartic double well. The
tunnel splittings in the semiclassical regime are determined with high
numerical accuracy, and the association of the corresponding doublet states to
either chaotic or regular regions of the classical phase space is quantified in
terms of the overlap of the Husimi distribution with the chaotic layer along
the separatrix. We find a strong correlation between both quantities. They show
an increase by orders of magnitude as chaotic diffusion between the wells
starts to dominate the classical dynamics. We discuss semiclassical
explanations for this correlation.
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The possible origin of the R-parity violating interactions in the minimal
supersymmetric standard model and its connection to the radiative symmetry
breaking mechanism (RSBM) is investigated. In the context of the simplest model
where the implementation of the RSBM is possible, we find that in the majority
of the parameter space R-parity is spontaneously broken at the low-scale. These
results hint at the possibility that R-parity violating processes will be
observed at the Large Hadron Collider, if Supersymmetry is realized in nature.
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Using a model heat engine, we show that neural network-based reinforcement
learning can identify thermodynamic trajectories of maximal efficiency. We
consider both gradient and gradient-free reinforcement learning. We use an
evolutionary learning algorithm to evolve a population of neural networks,
subject to a directive to maximize the efficiency of a trajectory composed of a
set of elementary thermodynamic processes; the resulting networks learn to
carry out the maximally-efficient Carnot, Stirling, or Otto cycles. When given
an additional irreversible process, this evolutionary scheme learns a
previously unknown thermodynamic cycle. Gradient-based reinforcement learning
is able to learn the Stirling cycle, whereas an evolutionary approach achieves
the optimal Carnot cycle. Our results show how the reinforcement learning
strategies developed for game playing can be applied to solve physical problems
conditioned upon path-extensive order parameters.
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We investigate the unusual properties of quasirelativistic massless fermions
under a magnetic or electric field by means of nonminimal couplings. Within
this approach, the spin-orbit coupling (SOC) effects are properly generated in
the energy spectrum of the quasiparticles. By including a magnetic field, $B$,
we show that the spin splitting of Landau Levels (LL) obeys a $\sqrt{B}$ linear
dependence with SOC, typical of relativistic particles. Moreover, our
calculated spectrum of LLs resembles the behavior of the three-dimensional (3D)
massless Kane fermions. Using a nonminimal coupling with an external electric
field, we demonstrate that a Rashba-like SOC naturally appears into the
relativistic equations and apply to the case of two-dimensional (2D) massless
Dirac fermions. Still considering our proposed approach, the Hall conductivity
is also computed for the 2D case under transverse electric field both at zero
and finite temperatures for a general chemical potential. The results feature a
typical quantization of the Hall conductivity at low temperatures, when the
absolute value of the gap opened by the electric field is larger than the
considered chemical potential.
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The electronic structure of a vortex line trapped by an insulating columnar
defect in a type-II superconductor is analysed within the Bogolubov-de Gennes
theory. For quasiparticle trajectories with small impact parameters defined
with respect to the vortex axis the normal reflection of electrons and holes at
the defect surface results in the formation of an additional subgap spectral
branch. The increase in the impact parameter at this branch is accompanied by
the decrease of the excitation energy. When the impact parameter exceeds the
radius of the defect this branch transforms into the Caroli--de
Gennes--Matricon one. As a result, the minigap in the quasiparticle spectrum
increases with the increase in the defect radius. The scenario of the spectrum
transformation is generalized for the case of arbitrary vorticity.
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Using a nonlinear Schr\"odinger equation including short-range two-body
attraction and three-body repulsion, we investigate the spatial distribution of
indirect excitons in semiconductor coupled quantum wells. The results obtained
can interpret the experimental phenomenon that annular exciton cloud first
contracts then expands when the number of confined excitons is increased in
impurity potential well, as observed by Lai \emph{et al.} [Lai $et al.$,
Science \textbf{303}, 503 (2004)]. In particular, the model reconciles the
patterns of exciton rings reported by Butov \emph{et al.} [Butov $et al.$,
Nature \textbf{418}, 751 (2002)]. At higher densities, the model predicts much
richer patterns, which could be tested by future experiments.
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We study the velocity dispersion profiles of the nuclei of NGC 1326, 2685,
5273 and 5838 in the CO first overtone band. There is evidence for a black hole
(BH) in NGC 1326 and 5838. Gas is seen flowing out of the nuclear region of NGC
5273. We put upper limits on the nuclear BHs responsible for its activity and
that of NGC 2685.
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In this paper, we investigate the effect of TDD, as compared to a non-TDD
approach, as well as its retainment (or retention) over a time span of (about)
six months. To pursue these objectives, we conducted a (quantitative)
longitudinal cohort study with 30 novice developers (i.e., third-year
undergraduate students in Computer Science). We observed that TDD affects
neither the external quality of software products nor developers' productivity.
However, we observed that the participants applying TDD produced significantly
more tests, with a higher fault-detection capability than those using a non-TDD
approach. As for the retainment of TDD, we found that TDD is retained by novice
developers for at least six months.
|
Two approximations of the integral of a class of sinusoidal composite
functions, for which an explicit form does not exist, are derived. Numerical
experiments show that the proposed approximations yield an error that does not
depend on the width of the integration interval. Using such approximations,
definite integrals can be computed in almost real-time.
|
The proposed stochastic model for pedestrian dynamics is based on existing
approaches using cellular automata, combined with substantial extensions, to
compensate the deficiencies resulting of the discrete grid structure. This
agent motion model is extended by both a grid-based path planning and mid-range
agent interaction component. The stochastic model proves its capabilities for a
quantitative reproduction of the characteristic shape of the common fundamental
diagram of pedestrian dynamics. Moreover, effects of self-organizing behavior
are successfully reproduced. The stochastic cellular automata approach is found
to be adequate with respect to uncertainties in human motion patterns, a
feature previously held by artificial noise terms alone.
|
We prove, using the celebrated result by Spitzer about winding of planar
Brownian motion, and the existence of harmonic morphisms $f:M\to{\mathbb S}^1$
representing cohomology classes in $\text{H}^1(M,\mathbb Z)$, that there is a
stochastic process $H_t:{\mathcal C}(M)\to{\text{Hom}(\text{H}^1(M;\mathbb R),
\mathbb R)}\simeq{\text{H}_1(M;\mathbb R)}$ ($t\in[0,\infty)$), where
${\mathcal C}(M)= \{ \alpha:[0, \infty) \to M :\alpha \,\, \text{is continuous}
\}$, which has a multivariate Cauchy distribution i.e. such that for each
nontrivial cohomology class $[\omega]\in{\text{H}^1(M;\mathbb R), \mathbb R)}$,
represented by a closed 1-form $\omega$, in the de Rham cohomology, the process
$A^\omega_t:{\mathcal C}(M)\to\mathbb R\,$ ($t\in[0,\infty)$) with
$A^\omega_t(B)=H_t(B)([\omega]),\, B\in{\mathcal C}(M)$ converges in
distribution, with respect to Wiener measure on ${\mathcal C}(M)$, to a
Cauchy's distribution, with parameter 1. The process describes the
``homological winding" of the Brownian paths in $M$, thus it can be regarded as
a generalization of Spitzer result. The last section discusses the asymptotic
behavior of holonomy along Brownian paths.
|
We present a systematic study of how vortices in superfluid films interact
with the spatially varying Gaussian curvature of the underlying substrate. The
Gaussian curvature acts as a source for a geometric potential that attracts
(repels) vortices towards regions of negative (positive) Gaussian curvature
independently of the sign of their topological charge. Various experimental
tests involving rotating superfluid films and vortex pinning are first
discussed for films coating gently curved substrates that can be treated in
perturbation theory from flatness. An estimate of the experimental regimes of
interest is obtained by comparing the strength of the geometrical forces to the
vortex pinning induced by the varying thickness of the film which is in turn
caused by capillary effects and gravity. We then present a non-perturbative
technique based on conformal mappings that leads an exact solution for the
geometric potential as well as the geometric correction to the interaction
between vortices. The conformal mapping approach is illustrated by means of
explicit calculations of the geometric effects encountered in the study of some
strongly curved surfaces and by deriving universal bounds on their strength.
|
We define cryptographic assumptions applicable to two mistrustful parties who
each control two or more separate secure sites between which special relativity
guarantees a time lapse in communication. We show that, under these
assumptions, unconditionally secure coin tossing can be carried out by
exchanges of classical information. We show also, following Mayers, Lo and
Chau, that unconditionally secure bit commitment cannot be carried out by
finitely many exchanges of classical or quantum information. Finally we show
that, under standard cryptographic assumptions, coin tossing is strictly weaker
than bit commitment. That is, no secure classical or quantum bit commitment
protocol can be built from a finite number of invocations of a secure coin
tossing black box together with finitely many additional information exchanges.
|
We investigate the logical structure of intuitionistic Kripke-Platek set
theory IKP, and show that the first-order logic of IKP is intuitionistic
first-order logic IQC.
|
The purpose of this paper is to present some functionalities of the HyperPro
System. HyperPro is a hypertext tool which allows to develop Constraint Logic
Programming (CLP) together with their documentation. The text editing part is
not new and is based on the free software Thot. A HyperPro program is a Thot
document written in a report style. The tool is designed for CLP but it can be
adapted to other programming paradigms as well. Thot offers navigation and
editing facilities and synchronized static document views. HyperPro has new
functionalities such as document exportations, dynamic views (projections),
indexes and version management. Projection is a mechanism for extracting and
exporting relevant pieces of code program or of document according to specific
criteria. Indexes are useful to find the references and occurrences of a
relation in a document, i.e., where its predicate definition is found and where
a relation is used in other programs or document versions and, to translate
hyper-texts links into paper references. It still lack importation facilities.
|
The interest in active matter stimulates the need to generalize thermodynamic
description and relations to active matter systems, which are intrinsically out
of equilibrium. One important example is the Jarzynski relation, which links
the exponential average of work done in an arbitrary process connecting two
equilibrium states with the difference of the free energies of these states.
Using a simple model system, a single thermal active Ornstein-Uhlenbeck
particle in a harmonic potential, we show that if the standard stochastic
thermodynamics definition of work is used, the Jarzynski relation is not
generally valid for processes between stationary states of active matter
systems.
|
We propose a new factorization pattern for tree-level Yang-Mills (YM)
amplitudes, where they decompose into a sum of products of two lower-point
amplitudes by setting specific two-point non-planar Mandelstam variables within
a rectangular configuration to zero. This approach manifests the hidden zeros
of YM amplitudes recently identified. Furthermore, by setting specific Lorentz
products involving polarization vectors to zero, the amplitudes further reduce
to a sum of products of three currents. These novel factorizations provide a
fresh perspective on the structure of YM amplitudes, potentially enhancing our
understanding and calculation of these fundamental quantities.
|
In this report, we report some fundamental results and bounds on the number
of messages and storage required to implement barriers using futuristic on-chip
optical and RF networks. We prove that it is necessary to maintain a count to
at least N (number of threads) in memory, broadcast the barrier id at least
once, and if we elect a co-ordinator, we can reduce the number of messages by a
factor of O(N ).
|
We draw an explicit connection between the statistical properties of an
entangled two-mode continuous variable (CV) resource and the amount of
entanglement that can be dynamically transferred to a pair of non-interacting
two-level systems. More specifically, we rigorously reformulate entanglement
transfer process by making use of covariance matrix formalism. When the
resource state is Gaussian, our method makes the approach to the transfer of
quantum correlations much more flexible than in previously considered schemes
and allows the straightforward inclusion of the effects of noise affecting the
CV system. Moreover, the proposed method reveals that the use of de-Gaussified
two-mode states is almost never advantageous for transferring entanglement with
respect to the full Gaussian picture, despite the entanglement in the
non-Gaussian resource can be much larger than in its Gaussian counterpart. We
can thus conclude that the entanglement-transfer map overthrows the "ordering"
relations valid at the level of CV resource states.
|
We present an extensive study of the radiative transfer in dusty galaxies
based on Monte Carlo simulations. The main output of these simulations are the
attenuation curves ${\cal A}_\lambda$ (i.e. the ratio between the observed,
dust extinguished, total intensity to the intrinsic unextinguished one of the
galaxy as a function of wavelength). We have explored the dependence of ${\cal
A}_\lambda$ on a conspicuous set of quantities (Hubble type, inclination, dust
optical thickness, dust distribution and extinction properties) for a large
wavelength interval, ranging from 1250\AA to the K band, thus finally providing
a comprehensive atlas of dust extinction in galaxies, which is electronically
available. This study is particularly suitable for inclusion into galaxy
formation evolution models and to directly interpret observational data on high
redshift galaxies.
|
Despite no new physics so far at the LHC, a $Z'$ boson with $m_{Z'} \sim 100$
GeV could still emerge via Drell-Yan (DY) production, $q \bar q \to Z' \to
\mu^+ \mu^-$, in the next few years. To unravel the nature of the $Z'$
coupling, we utilize the $c$- and $b$-tagging algorithms developed by ATLAS and
CMS to investigate $cg \to c Z'$ at 14 TeV LHC. While light-jet contamination
can be eliminated, mistagged $b$-jets cannot be rejected in any of the tagging
schemes we adopt. On the other hand, for nonzero $bbZ'$ coupling, far superior
$b$-tagging could discover the $bg \to b Z'$ process, where again light-jet
mistag can be ruled out, but mistagged $c$-jets cannot yet be excluded.
Provided that DY production is discovered soon enough, we find that a
simultaneous search for $c g \to c Z'$ and $b g \to b Z'$ can conclusively
discern the nature of $Z'$ couplings involved.
|
We demonstrate that two-time correlation functions, which are generalizations
of out-of-time-ordered correlators (OTOCs), can show 'false-flags' of chaos by
exhibiting behaviour predicted by random matrix theory even in a system with
classically regular dynamics. In particular, we analyze a system of bosons
trapped in a double-well potential and probed by a quantum dot which is coupled
to the bosons dispersively. This is an integrable system (considered both as
separate parts and in total). Despite the continuous time evolution generated
by the actual Hamiltonian, we find that the n-fold two-time correlation
function for the probe describes an effective stroboscopic or Floquet dynamics
whereby the bosons appear to be alternately driven by two different
non-commuting Hamiltonians in a manner reminiscent of the Trotterized time
evolution that occurs in digital quantum simulation. The classical limit of
this effective dynamics can have a nonzero Lyapunov exponent, while the
effective level statistics and return probability show traditional signatures
of chaotic behaviour. In line with several other recent studies, this work
highlights the fact that the behavior of OTOCs and their generalizations must
be interpreted with some care.
|
Growth and roughness of the interface of deposited polymer chains driven by a
field onto an impenetrable adsorbing surface are studied by computer
simulations in (2+1) dimensions. The evolution of the interface width W shows a
crossover from short-time growth described by the exponent beta1 to a long-time
growth with exponent beta2 (>beta1). The saturated width increases, i.e., the
interface roughens, with the molecular weight Lc, but the roughness exponent
alpha (from Ws~L^alpha) becomes negative in contrast to models for particle
deposition; alpha depends on the chain length--a nonuniversal scaling with the
substrate length L. Roughening and deroughening occur as the field E and the
temperature T compete such that Ws=(A+BT)E^-1/2.
|
We consider the generalization of a matrix integral with arbitrary spectral
curve $\rho_0(E)$ to a 0+1D theory of matrix quantum mechanics (MQM). Using
recent techniques for 1D quantum systems at large-$N$, we formulate a
hydrodynamical effective theory for the eigenvalues. The result is a simple 2D
free boson BCFT on a curved background, describing the quantum fluctuations of
the eigenvalues around $\rho_0(E)$, which is now the large-$N$ limit of the
quantum expectation value of the eigenvalue density operator $\hat{\rho}(E)$.
The average over the ensemble of random matrices becomes a quantum expectation
value. Equal-time density correlations reproduce the results (including
non-perturbative corrections) of random matrix theory. This suggests an
interpretation of JT gravity as dual to a $\textit{one-time-point}$ reduction
of MQM. As an application, we compute the R\'enyi entropy associated to a
bipartition of the eigenvalues. We match a previous result by Hartnoll and
Mazenc for the $c=1$ matrix model dual to two-dimensional string theory and
extend it to arbitrary $\rho_0(E)$. The hydrodynamical theory provides a clear
picture of the emergence of spacetime in two dimensional string theory. The
entropy is naturally finite and displays a large amount of short range
entanglement, proportional to the microcanonical entropy. We also compute the
reduced density matrix for a subset of $n<N$ eigenvalues.
|
We argue that an ensemble of backgrounds best understands hydrodynamic
dispersion relations in a medium with few degrees of freedom and is therefore
subject to strong thermal fluctuations. In the linearized regime, dispersion
relations become describeable by polynomials with random coefficients. We give
a short review of this theory and perform a numerical study of the distribution
of the roots of polynomials whose coefficients are of the order of a Knudsen
series but fluctuate in accordance with canonical fluctuations of temperature.
We find that, remarkably, the analytic structure of the poles of fluctuating
dispersion relations is very different from deterministic ones, particularly
regarding the distribution of imaginary parts with respect to real components.
We argue that this provides evidence that hydrodynamic behavior persists, and
is enhanced, by non-perturbative background fluctuations.
|
Considered are the large $N$, or large intensity, forms of the distribution
of the length of the longest increasing subsequences for various models.
Earlier work has established that after centring and scaling, the limit laws
for these distributions relate to certain distribution functions at the hard
edge known from random matrix theory. By analysing the hard to soft edge
transition, we supplement and extend results of Baik and Jenkins for the
Hammersley model and symmetrisations, which give that the leading correction is
proportional to $z^{-2/3}$, where $z^2$ is the intensity of the Poisson rate,
and provides a functional form as derivates of the limit law. Our methods give
the functional form both in terms of Fredholm operator theoretic quantities,
and in terms of Painlev\'e transcendents. For random permutations and their
symmetrisations, numerical analysis of exact enumerations and simulations gives
compelling evidence that the leading corrections are proportional to
$N^{-1/3}$, and moreover provides an approximation to their graphical forms.
|
Domain Generalization (DG) endeavors to create machine learning models that
excel in unseen scenarios by learning invariant features. In DG, the prevalent
practice of constraining models to a fixed structure or uniform
parameterization to encapsulate invariant features can inadvertently blend
specific aspects. Such an approach struggles with nuanced differentiation of
inter-domain variations and may exhibit bias towards certain domains, hindering
the precise learning of domain-invariant features. Recognizing this, we
introduce a novel method designed to supplement the model with domain-level and
task-specific characteristics. This approach aims to guide the model in more
effectively separating invariant features from specific characteristics,
thereby boosting the generalization. Building on the emerging trend of visual
prompts in the DG paradigm, our work introduces the novel \textbf{H}ierarchical
\textbf{C}ontrastive \textbf{V}isual \textbf{P}rompt (HCVP) methodology. This
represents a significant advancement in the field, setting itself apart with a
unique generative approach to prompts, alongside an explicit model structure
and specialized loss functions. Differing from traditional visual prompts that
are often shared across entire datasets, HCVP utilizes a hierarchical prompt
generation network enhanced by prompt contrastive learning. These generative
prompts are instance-dependent, catering to the unique characteristics inherent
to different domains and tasks. Additionally, we devise a prompt modulation
network that serves as a bridge, effectively incorporating the generated visual
prompts into the vision transformer backbone. Experiments conducted on five DG
datasets demonstrate the effectiveness of HCVP, outperforming both established
DG algorithms and adaptation protocols.
|
Fuzzy implication functions have been widely investigated, both in
theoretical and practical fields. The aim of this work is to continue previous
works related to fuzzy implications constructed by means of non necessarily
associative aggregation functions. In order to obtain a more general and
flexible context, we extend the class of implications derived by fuzzy
negations and t-norms, replacing the latter by general overlap functions. We
also investigate their properties, characterization and intersections with
other classes of fuzzy implication functions.
|
The world-sheet S-matrix of the string in AdS5 x S5 has been shown to admit a
q-deformation that relates it to the S-matrix of a generalization of the
sine-Gordon theory, which arises as the Pohlmeyer reduction of the superstring.
Whilst this is a fascinating development the resulting S-matrix is not
explicitly unitary. The problem has been known for a long time in the context
of S-matrices related to quantum groups. A braiding relation often called
"unitarity" actually only corresponds to quantum field theory unitarity when
the S-matrix is Hermitian analytic and quantum group S-matrices manifestly
violate this. On the other hand, overall consistency of the S-matrix under the
bootstrap requires that the deformation parameter is a root of unity and
consequently one is forced to perform the "vertex" to IRF, or SOS,
transformation on the states to truncate the spectrum consistently. In the IRF
formulation unitarity is now manifest and the string S-matrix and the S-matrix
of the generalised sine-Gordon theory are recovered in two different limits. In
the latter case, expanding the Yang-Baxter equation we find that the tree-level
S-matrix of the Pohlmeyer-reduced string should satisfy a modified classical
Yang-Baxter equation explaining the apparent anomaly in the perturbative
computation. We show that the IRF form of the S-matrix meshes perfectly with
the bootstrap equations.
|
The Higgs boson of 125 GeV requires large stop masses, leading to the large
$\mu$-parameter in most cases of gauge mediation. On the other hand, the
explanation for the muon $g-2$ anomaly needs small slepton and
neutralino/chargino masses. Such disparity in masses may be obtained from a
mass splitting of colored and non-colored messenger fields. However, even if
the required small slepton and neutralino/chargino masses are realized, all
parameter regions consistent with the muon g-2 are excluded by the recent
updated ATLAS result on the wino search in the case that the messenger fields
are in ${\bf 5}+\bar {\bf 5}$ representations of SU(5). It is also revealed
that the messenger fields in ${\bf 10} + \overline{\bf 10}$ or ${\bf 24}$
representation can not explain the muon g-2 anomaly. We show, giving a simple
example model, that the above confliction is solved if there is an additional
contribution to the Higgs soft mass which makes the $\mu$-parameter small. We
also show that the required Higgs B-term for the electroweak symmetry breaking
is consistently generated by radiative corrections from gaugino loops.
|
We use sensitivity analysis to design $\textit{optimality-based}$
discretization (cutting-plane) methods for the global optimization of nonconvex
semi-infinite programs (SIPs). We begin by formulating the optimal
discretization of SIPs as a max-min problem and propose variants that are more
computationally tractable. We then use parametric sensitivity theory to design
an efficient method for solving these max-min problems to local optimality and
argue this yields valid discretizations without sacrificing global optimality
guarantees. Finally, we formulate optimality-based $\textit{generalized}$
discretization of SIPs as max-min problems and design efficient local
optimization algorithms to solve them approximately. Numerical experiments on
test instances from the literature demonstrate that our new optimality-based
discretization methods can significantly reduce the number of iterations for
convergence relative to the classical feasibility-based method.
|
We present Jordan-Brans-Dicke and general scalar-tensor gravitational theory
in extra dimensions in an asymptotically flat or anti de Sitter spacetime. We
consider a special gravitating, boson field configuration, a $q$-star, in 3, 4,
5 and 6 dimensions, within the framework of the above gravitational theory and
find that the parameters of the stable stars are a few per cent different from
the case of General Relativity.
|
Microresonator-based frequency combs (microcombs or Kerr-combs) can
potentially miniaturize the numerous applications of conventional frequency
combs. A priority is the realization of broad-band (ideally octave spanning)
spectra at detectable repetition rates for comb self referencing. However,
access to these rates involves pumping larger mode volumes and hence higher
threshold powers. Moreover, threshold power sets both the scale for power per
comb tooth and also the optical pump. Along these lines, it is shown that a
class of resonators having surface-loss-limited Q factors can operate over a
wide range of repetition rates with minimal variation in threshold power. A
new, surface-loss-limited resonator illustrates the idea. Comb generation on
mode spacings ranging from 2.6 GHz to 220 GHz with overall low threshold power
(as low as 1 mW) is demonstrated. A record number of comb lines for a microcomb
(around 1900) is also observed with pump power of 200 mW. The ability to
engineer a wide range of repetition rates with these devices is also used to
investigate a recently observed mechanism in microcombs associated with
dispersion of subcomb offset frequencies. We observe high-coherence,
phase-locking in cases where these offset frequencies are small enough so as to
be tuned into coincidence. In these cases, a record-low microcomb phase noise
is reported at a level comparable to an open-loop, high-performance microwave
oscillator.
|
In 2003, H\'{e}thelyi and K\"{u}lshammer proposed that if $G$ is a finite
group and $p$ is a prime dividing the group order, then $k(G)\geq 2\sqrt{p-1}$,
and they proved this conjecture for solvable $G$ and showed that it is sharp
for those primes $p$ for which $\sqrt{p-1}$ is an integer. This initiated a
flurry of activity, leading to many generalizations and variations of the
result; in particular, today the conjecture is known to be true for all finite
groups. In this note, we put forward a natural new and stronger conjecture,
which is sharp for all primes $p$, and we prove it for solvable groups, and
when $p$ is large, also for arbitrary groups.
|
The superconducting instability in a non-Fermi liquid in $ d>1$ is
considered. For a particular form of the single particle spectral function with
homogeneous scaling $A(\Lambda k, \Lambda \omega) = \Lambda^{\alpha} A(k,
\omega)$ it is shown that the pair susceptibility is also a scaling function of
temperature with power defined by $\alpha$. We find three different regimes
depending on the scaling constant. The BCS result is recovered for $\alpha =
-1$ and it corresponds to a marginal scaling of the coupling constant. For
$\alpha > -1$ the superconducting transition happens above some critical
coupling. In the opposite case of $\alpha < -1$ for any fixed coupling the
system undergoes a transition at low temperatures. Possible implications for
theories of high-$T_c$ with a superconducting transition driven by the
interlayer Josephson tunneling are discussed. 1 ps file for fig is attached at
the bottom of the tex file.
|
Let $S_g$ be the closed oriented surface of genus g and let
$\text{Mod}^{\pm}(S_g)$ be the extended mapping class group of $S_g$. When the
genus is at least 5, we prove that $\text{Mod}^{\pm}(S_g)$ can be generated by
two torsion elements. One of these generators is an order 2 element, and the
other one is an order 4g+2 element.
|
The challenge of understanding the collective behaviors of social systems can
benefit from methods and concepts from physics [1-6], not because humans are
similar to electrons, but because certain large-scale behaviors can be
understood without an understanding of the small-scale details [7], in much the
same way that sound waves can be understood without an understanding of atoms.
Democratic elections are one such behavior. Over the past few decades,
physicists have explored scaling patterns in voting and the dynamics of
political opinion formation, e.g. [8-13]. Here, we define the concepts of
negative representation, in which a shift in electorate opinions produces a
shift in the election outcome in the opposite direction, and electoral
instability, in which an arbitrarily small change in electorate opinions can
dramatically swing the election outcome, and prove that unstable elections
necessarily contain negatively represented opinions. Furthermore, in the
presence of low voter turnout, increasing polarization of the electorate can
drive elections through a transition from a stable to an unstable regime,
analogous to the phase transition by which some materials become ferromagnetic
below their critical temperatures. Empirical data suggest that United States
presidential elections underwent such a phase transition in the 1970s and have
since become increasingly unstable.
|
Electron captures by atomic nuclei in dense matter are among the most
important processes governing the late evolution of stars, limiting in
particular the stability of white dwarfs. Despite considerable progress in the
determination of the equation of state of dense Coulomb plasmas, the threshold
electron Fermi energies are still generally estimated from the corresponding
$Q$ values in vacuum. Moreover, most studies have focused on nonmagnetized
matter. However, some white dwarfs are endowed with magnetic fields reaching
$10^9$ G. Even more extreme magnetic fields might exist in super Chandrasekhar
white dwarfs, the progenitors of overluminous type Ia supernovae like SN 2006gz
and SN 2009dc. The roles of the dense stellar medium and magnetic fields on the
onset of electron captures and on the structure of white dwarfs are briefly
reviewed. New analytical formulas are derived to evaluate the threshold density
for the onset of electron captures for arbitrary magnetic fields. Their
influence on the structure of white dwarfs is illustrated by simple analytical
formulas and numerical calculations.
|
We present radiation hydrodynamics simulations of the collapse of massive
pre-stellar cores. We treat frequency dependent radiative feedback from stellar
evolution and accretion luminosity at a numerical resolution down to 1.27 AU.
In the 2D approximation of axially symmetric simulations, it is possible for
the first time to simulate the whole accretion phase (up to the end of the
accretion disk epoch) for the forming massive star and to perform a broad scan
of the parameter space. Our simulation series show evidently the necessity to
incorporate the dust sublimation front to preserve the high shielding property
of massive accretion disks. While confirming the upper mass limit of
spherically symmetric accretion, our disk accretion models show a persistent
high anisotropy of the corresponding thermal radiation field. This yields to
the growth of the highest-mass stars ever formed in multi-dimensional radiation
hydrodynamics simulations, far beyond the upper mass limit of spherical
accretion. Non-axially symmetric effects are not necessary to sustain
accretion. The radiation pressure launches a stable bipolar outflow, which
grows in angle with time as presumed from observations. For an initial mass of
the pre-stellar host core of 60, 120, 240, and 480 Msun the masses of the final
stars formed in our simulations add up to 28.2, 56.5, 92.6, and at least 137.2
Msun respectively.
|
X-ray timing observations of accreting stellar mass black holes have shown
that they can produce signals with such short time scales that we must be
probing very close to the innermost stable circular orbit that is predicted by
the theory of General Relativity (GR). These signals are quasi-periodic
oscillations (QPOs), and both the high-frequency variety (HFQPOs, which have
frequencies in the 40-450 Hz range) as well as the 0.1-10 Hz low-frequency type
have the potential to provide tests of GR in the strong field limit. An
important step on the path to GR tests is to constrain the physical black hole
properties, and the straightforward frequency measurements that are possible
with X-ray timing may provide one of the cleanest measurements of black hole
spins. While current X-ray satellites have uncovered these phenomenona, the
HFQPOs are weak signals, and future X-ray timing missions with larger effective
area are required for testing the candidate theoretical QPO mechanisms. Another
main goal in the study of accreting black holes is to understand the production
of relativistic jets. Here, we have also made progress during the past decade
by finding clear connections between the radio emission that traces the
strength of the jet and the properties of the X-ray emission. With new radio
capabilities just coming on-line, continuing detailed X-ray studies of
accreting black holes is crucial for continuing to make progress.
|
We discuss the application of various concepts from the theory of topological
dynamical systems to Delone sets and tilings. We consider in particular, the
maximal equicontinuous factor of a Delone dynamical system, the proximality
relation and the enveloping semigroup of such systems.
|
We analyze divergencies in 2-point and 3-point functions for noncommutative
$\theta$-expanded SU(2)-gauge theory with massless fermions. We show that,
after field redefinition and renormalization of couplings, one divergent term
remains.
|
We study the a, b and c coefficients of the isobaric-multiplet mass equation
using a macroscopic-microscopic approach developed by P. Moeller and his
collaborators in ADNDT 59, 185 (1995) and ADNDT 109-110, 1 (2016). We show that
already the macroscopic part of the finite-range liquid-drop model (FRLDM)
describes the general trend of the a and b coefficients relatively well, while
the staggering behavior of b coefficients for doublets and quartets can be
understood in terms of the difference of average proton and neutron pairing
energies. The sets of isobaric masses, predicted by the full
macroscopic-microscopic approaches, are used to explore the general trends of
IMME coefficients up to A=100. We conclude that while the agreement for a
coefficients is quite satisfactory, the global approaches have less sensitivity
to predict the staggering pattern observed for b coefficients of doublets and
quartets. The best set of theoretical b coefficients for multiplets up to about
A=100 is used to predict masses of proton-rich nuclei based on the known
experimental masses of neutron-rich mirror partners, and subsequently to
investigate their one- and two-proton separation energies. The estimated
position of the proton-drip line is in fair agreement with known experimental
data. These masses are important for simulations of the astrophysical
rp-process.
|
Behavior prediction in dynamic, multi-agent systems is an important problem
in the context of self-driving cars, due to the complex representations and
interactions of road components, including moving agents (e.g. pedestrians and
vehicles) and road context information (e.g. lanes, traffic lights). This paper
introduces VectorNet, a hierarchical graph neural network that first exploits
the spatial locality of individual road components represented by vectors and
then models the high-order interactions among all components. In contrast to
most recent approaches, which render trajectories of moving agents and road
context information as bird-eye images and encode them with convolutional
neural networks (ConvNets), our approach operates on a vector representation.
By operating on the vectorized high definition (HD) maps and agent
trajectories, we avoid lossy rendering and computationally intensive ConvNet
encoding steps. To further boost VectorNet's capability in learning context
features, we propose a novel auxiliary task to recover the randomly masked out
map entities and agent trajectories based on their context. We evaluate
VectorNet on our in-house behavior prediction benchmark and the recently
released Argoverse forecasting dataset. Our method achieves on par or better
performance than the competitive rendering approach on both benchmarks while
saving over 70% of the model parameters with an order of magnitude reduction in
FLOPs. It also outperforms the state of the art on the Argoverse dataset.
|
A procedure of solving nonstationary Schredinger equations in the exact
analytic form is elaborated on the basis of exactly solvable stationary models.
The exact solutions are employed to study the nonadiabatic geometric phase.
|
An accurate understanding of a user's query intent can help improve the
performance of downstream tasks such as query scoping and ranking. In the
e-commerce domain, recent work in query understanding focuses on the query to
product-category mapping. But, a small yet significant percentage of queries
(in our website 1.5% or 33M queries in 2019) have non-commercial intent
associated with them. These intents are usually associated with non-commercial
information seeking needs such as discounts, store hours, installation guides,
etc. In this paper, we introduce Joint Query Intent Understanding (JointMap), a
deep learning model to simultaneously learn two different high-level user
intent tasks: 1) identifying a query's commercial vs. non-commercial intent,
and 2) associating a set of relevant product categories in taxonomy to a
product query. JointMap model works by leveraging the transfer bias that exists
between these two related tasks through a joint-learning process. As curating a
labeled data set for these tasks can be expensive and time-consuming, we
propose a distant supervision approach in conjunction with an active learning
model to generate high-quality training data sets. To demonstrate the
effectiveness of JointMap, we use search queries collected from a large
commercial website. Our results show that JointMap significantly improves both
"commercial vs. non-commercial" intent prediction and product category mapping
by 2.3% and 10% on average over state-of-the-art deep learning methods. Our
findings suggest a promising direction to model the intent hierarchies in an
e-commerce search engine.
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We give a quasi-complete solution of the (\Delta,N) problem for two
well-known families of digraphs used as good models for large interconnection
networks. In our study we also relate both families, the New Amsterdam and
Manhattan digraphs, with the double-step graphs (or circulant graphs with
degree two).
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Neutron stars, and magnetars in particular, are known to host the strongest
magnetic fields in the Universe. The origin of these strong fields is a matter
of controversy. In this preliminary work, via numerical simulations, we study,
for the first time in non-ideal general relativistic magnetohydrodynamic
(GRMHD) regime, the growth of the magnetic field due to the action of the
mean-field dynamo due to sub-scale, unresolved turbulence. The dynamo process,
combined with the differential rotation of the (proto-)star, is able to produce
an exponential growth of any initial magnetic seed field up to the values
required to explain the observations. By varying the dynamo coefficient we
obtain different growth rates. We find a quasi-linear dependence of the growth
rates on the intensity of the dynamo. Furthermore, the time interval in which
exponential growth occurs and the growth rates also seems to depend on the
initial configuration of the magnetic field.
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We investigate non-standard interaction effects in antineutrino-electron
scattering experiments with baselines short enough to ignore standard
oscillation phenomena. The setup is free of ambiguities from the interference
between new physics and oscillation effects and is sensitive to both
semileptonic new physics at the source and purely leptonic new physics in the
weak interaction scattering at the detector. We draw on the TEXONO experiment
as the model system, extending its analysis of non-standard interaction effects
at the detector to include the generally allowed non-standard interaction phase
at the detector and both non-universal and flavor changing new physics at the
reactor source. We confirm that the current data allows for new physics
constraints at the detector of the same order as those currently published, but
we find that constraints on the source new physics are at least an order of
magnitude weaker. The new physics phase effects are at the 5% level, noticeable
in the 90% C.L. contour plots but not significantly affecting the conclusions.
Based on projected increase in sensitivity with an upgraded TEXONO experiment,
we estimate the improvement of sensitivity to both source and detector
non-standard interactions. We find that the bounds on source parameters improve
by an order of magnitude, but do not reach parameter space beyond current
limits. On the other hand, the detector new physics sensitivity would push
current limits by factors 5 to 10 smaller.
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Safety-critical systems with neural network components require strong
guarantees. While existing neural network verification techniques have shown
great progress towards this goal, they cannot prove the absence of software
faults in the network implementation. This paper presents NeuroCodeBench - a
verification benchmark for neural network code written in plain C. It contains
32 neural networks with 607 safety properties divided into 6 categories: maths
library, activation functions, error-correcting networks, transfer function
approximation, probability density estimation and reinforcement learning. Our
preliminary evaluation shows that state-of-the-art software verifiers struggle
to provide correct verdicts, due to their incomplete support of the standard C
mathematical library and the complexity of larger neural networks.
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By means of fixed point index theory for multi-valued maps, we provide an
analogue of the classical Birkhoff--Kellogg Theorem in the context of
discontinuous operators acting on affine wedges in Banach spaces. Our theory is
fairly general and can be applied, for example, to eigenvalues and parameter
problems for ordinary differential equations with discontinuities. We
illustrate in details this fact for a class of second order boundary value
problem with deviated arguments and discontinuous terms. In a specific example,
we explicitly compute the terms that occur in our theory.
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Microbial colonies cultured on agar Petri dishes have become a model system
to study biological evolution in populations expanding in space. Processes such
as clonal segregation and gene surfing have been shown to be affected by
interactions between microbial cells and their environment. In this work we
investigate the role of mechanical interactions such as cell-surface adhesion.
We compare two strains of the bacterium E. coli: a wild-type strain and a
"shaved" strain that adheres less to agar. We show that the shaved strain has a
selective advantage over the wild type: although both strains grow with the
same rate in liquid media, the shaved strain produces colonies that expand
faster on agar. This allows the shaved strain outgrow the wild type when both
strains compete for space. We hypothesise that, in contrast to a more common
scenario in which selective advantage results from increased growth rate, the
higher fitness of the shaved strain is caused by reduced adhesion and friction
with the agar surface.
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We have monitored a Type II outburst of the Be/X-ray binary MXB 0656-072 in a
series of pointed RXTE observations during October through December 2003. The
source spectrum shows a cyclotron resonance scattering feature at 32.8 +/- 0.5
keV, corresponding to a magnetic field strength of (3.67 +/- 0.06) x 10^12 G
and is stable through the outburst and over the pulsar spin phase. The pulsar,
with an average pulse period of 160.4 +/- 0.4 s, shows a spin-up of 0.45 s over
the duration of the outburst. From optical data, the source distance is
estimated to be 3.9 +/- 0.1 kpc and this is used to estimate the X-ray
luminosity and a theoretical prediction of the pulsar spin-up during the
outburst.
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We revisit the two-site Hubbard-Holstein model by using extended phonon
coherent states. The nontrivial singlet bipolaron is studied exactly in the
whole coupling regime. The ground-state (GS) energy and the double occupancy
probability are calculated. The linear entropy is exploited successfully to
quantify bipartite entanglement between electrons and their environment
phonons, displaying a maximum entanglement of the singlet-bipolaron in strong
coupling regime. A dramatic drop in the crossover regime is observed in the GS
fidelity and its susceptibility. The bipolaron properties is also characterized
classically by correlation functions. It is found that the crossover from a
two-site to single-site bipolaron is more abrupt and shifts to a larger
electron-phonon coupling strength as electron-electron Coulomb repulsion
increases.
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A novel quickest detection setting is proposed which is a generalization of
the well-known Bayesian change-point detection model. Suppose
\{(X_i,Y_i)\}_{i\geq 1} is a sequence of pairs of random variables, and that S
is a stopping time with respect to \{X_i\}_{i\geq 1}. The problem is to find a
stopping time T with respect to \{Y_i\}_{i\geq 1} that optimally tracks S, in
the sense that T minimizes the expected reaction delay E(T-S)^+, while keeping
the false-alarm probability P(T<S) below a given threshold \alpha \in [0,1].
This problem formulation applies in several areas, such as in communication,
detection, forecasting, and quality control.
Our results relate to the situation where the X_i's and Y_i's take values in
finite alphabets and where S is bounded by some positive integer \kappa. By
using elementary methods based on the analysis of the tree structure of
stopping times, we exhibit an algorithm that computes the optimal average
reaction delays for all \alpha \in [0,1], and constructs the associated optimal
stopping times T. Under certain conditions on \{(X_i,Y_i)\}_{i\geq 1} and S,
the algorithm running time is polynomial in \kappa.
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We consider random walks in Dirichlet environment (RWDE) on $\Z ^d$, for $ d
\geq 3 $, in the sub-ballistic case. We associate to any parameter $ (\alpha_1,
..., \alpha_{2d}) $ of the Dirichlet law a time-change to accelerate the walk.
We prove that the continuous-time accelerated walk has an absolutely continuous
invariant probability measure for the environment viewed from the particle.
This allows to characterize directional transience for the initial RWDE. It
solves as a corollary the problem of Kalikow's 0-1 law in the Dirichlet case in
any dimension. Furthermore, we find the polynomial order of the magnitude of
the original walk's displacement.
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We show that the Euler system is not exactly controllable by a
finite-dimensional external force. The proof is based on the comparison of the
Kolmogorov epsilon-entropy for Holder spaces and for the class of functions
that can be obtained by solving the 2D Euler equations with various right-hand
sides.
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The theory of small-amplitude waves propagating across a blood vessel
junction has been well established with linear analysis. In this study we
consider the propagation of large-amplitude, nonlinear waves (i.e. shocks and
rarefactions) through a junction from a parent vessel into two (identical)
daughter vessels using a combination of three approaches: numerical
computations using a Godunov method with patching across the junction, analysis
of a nonlinear Riemann problem in the neighbourhood of the junction and an
analytical theory which extends the linear analysis to the following order in
amplitude. A unified picture emerges: an abrupt (prescribed) increase in
pressure at the inlet to the parent vessel generates a propagating shock wave
along the parent vessel which interacts with the junction. For modest driving,
this shock wave divides into propagating shock waves along the two daughter
vessels and reflects a rarefaction wave back towards the inlet. However, for
larger driving the reflected rarefaction wave becomes transcritical, generating
an additional shock wave. Just beyond criticality this new shock wave has zero
speed, pinned to the junction, but for further increases in driving this
additional shock divides into two new propagating shock waves in the daughter
vessels.
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We present optical spectroscopic and Swift UVOT/XRT observations of the X-ray
and UV/optical bright tidal disruption event (TDE) AT 2018fyk/ASASSN-18ul
discovered by ASAS-SN. The Swift lightcurve is atypical for a TDE, entering a
plateau after $\sim$40 days of decline from peak. After 80 days the UV/optical
lightcurve breaks again to decline further, while the X-ray emission becomes
brighter and harder. In addition to broad H, He and potentially O/Fe lines,
narrow emission lines emerge in the optical spectra during the plateau phase.
We identify both high ionisation (O III) and low ionisation (Fe II) lines,
which are visible for $\sim$45 days. We similarly identify Fe II lines in
optical spectra of ASASSN-15oi 330 d after discovery, indicating that a class
of Fe-rich TDEs exists. The spectral similarity between AT 2018fyk, narrow-line
Seyfert 1 galaxies and some extreme coronal line emitters suggests that TDEs
are capable of creating similar physical conditions in the nuclei of galaxies.
The Fe II lines can be associated with the formation of a compact accretion
disk, as the emergence of low ionisation emission lines requires optically
thick, high density gas. Taken together with the plateau in X-ray and
UV/optical luminosity this indicates that emission from the central source is
efficiently reprocessed into UV/optical wavelengths. Such a two-component
lightcurve is very similar to that seen in the TDE candidate ASASSN-15lh, and
is a natural consequence of a highly relativistic orbital pericenter.
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Janus colloids propelled by light, e.g., thermophoretic particles, offer
promising prospects as artificial microswimmers. However, their swimming
behavior and its dependence on fluid properties and fluid-colloid interactions
remain poorly understood. Here, we investigate the behavior of a thermophoretic
Janus colloid in its own temperature gradient using numerical simulations. The
dissipative particle dynamics method with energy conservation is used to
investigate the behavior in non-ideal and ideal-gas like fluids for different
fluid-colloid interactions, boundary conditions, and temperature-controlling
strategies. The fluid-colloid interactions appear to have a strong effect on
the colloid behavior, since they directly affect heat exchange between the
colloid surface and the fluid. The simulation results show that a reduction of
the heat exchange at the fluid-colloid interface leads to an enhancement of
colloid's thermophoretic mobility. The colloid behavior is found to be
different in non-ideal and ideal fluids, suggesting that fluid compressibility
plays a significant role. The flow field around the colloid surface is found to
be dominated by a source-dipole, in agreement with the recent theoretical and
simulation predictions. Finally, different temperature-control strategies do
not appear to have a strong effect on the colloid's swimming velocity.
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The physical characterization of exoplanets will require to take spectra at
several orbital positions. For that purpose, a direct imaging capability is
necessary. Direct imaging requires an efficient stellar suppression mechanism,
associated with an ultrasmooth telescope. We show that before future large
space missions (interferometer, 4-8 m class coronograph, external occulter or
Fresnel imager), direct imaging of giant planets and close-by super-Earth are
at the cross-road of a high scientific interest and a reasonable feasibility.
The scientific interest lies in the fact that super-Earths share common
geophysical attributes with Earths. They already begin to be detected by radial
velocity (RV) and, together with giant planets, they have a larger area than
Earths, making them detectable with a 1.5-2 m class telescope in reflected
light. We propose such a (space) telescope be a first step before large direct
imaging missions.
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Motivated by recent questions about the extension of Courant's nodal domain
theorem, we revisit a theorem published by C. Sturm in 1836, which deals with
zeros of linear combination of eigenfunctions of Sturm-Liouville problems.
Although well known in the nineteenth century, this theorem seems to have been
ignored or forgotten by some of the specialists in spectral theory since the
second half of the twentieth-century. Although not specialists in History of
Sciences, we have tried to put these theorems into the context of nineteenth
century mathematics.
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Mounts and hills played a predominant role in all pre-Hispanic Andean
cultures, especially for the Inca culture. Through the use of georeferenced
orthophotography, we found that the Inca site, Ruinas de Chada, represents the
origin of a radial ceque system with alignments connecting, at one end high
peaks of mounts at the Andes, and on the other end the summit of small hills in
which important shrines were built. These alignments extend over two hundred
kilometers, thus we propose that the information codified on this shrine was
based on an ancient geodetic science. A sacred geometric relationship is
encrypted in the pattern formed by the position of all shrines with high
accuracy, in which the Andean Chakana symbol is represented. These findings
suggest that the valley of Chada could have been the sacred center of
Collasuyu.
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Of the roughly 3000 neutron stars known, only a handful have sub-stellar
companions. The most famous of these are the low-mass planets around the
millisecond pulsar B1257+12. New evidence indicates that observational biases
could still hide a wide variety of planetary systems around most neutron stars.
We consider the environment and physical processes relevant to neutron star
planets, in particular the effect of X-ray irradiation and the relativistic
pulsar wind on the planetary atmosphere. We discuss the survival time of planet
atmospheres and the planetary surface conditions around different classes of
neutron stars, and define a neutron star habitable zone. Depending on as-yet
poorly constrained aspects of the pulsar wind, both Super-Earths around
B1257+12 could lie within its habitable zone.
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Speech quality in online conferencing applications is typically assessed
through human judgements in the form of the mean opinion score (MOS) metric.
Since such a labor-intensive approach is not feasible for large-scale speech
quality assessments in most settings, the focus has shifted towards automated
MOS prediction through end-to-end training of deep neural networks (DNN).
Instead of training a network from scratch, we propose to leverage the speech
representations from the pre-trained wav2vec-based XLS-R model. However, the
number of parameters of such a model exceeds task-specific DNNs by several
orders of magnitude, which poses a challenge for resulting fine-tuning
procedures on smaller datasets. Therefore, we opt to use pre-trained speech
representations from XLS-R in a feature extraction rather than a fine-tuning
setting, thereby significantly reducing the number of trainable model
parameters. We compare our proposed XLS-R-based feature extractor to a
Mel-frequency cepstral coefficient (MFCC)-based one, and experiment with
various combinations of bidirectional long short term memory (Bi-LSTM) and
attention pooling feedforward (AttPoolFF) networks trained on the output of the
feature extractors. We demonstrate the increased performance of pre-trained
XLS-R embeddings in terms a reduced root mean squared error (RMSE) on the
ConferencingSpeech 2022 MOS prediction task.
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The recent paper by Byrd & Lipton (2019), based on empirical observations,
raises a major concern on the impact of importance weighting for the
over-parameterized deep learning models. They observe that as long as the model
can separate the training data, the impact of importance weighting diminishes
as the training proceeds. Nevertheless, there lacks a rigorous characterization
of this phenomenon. In this paper, we provide formal characterizations and
theoretical justifications on the role of importance weighting with respect to
the implicit bias of gradient descent and margin-based learning theory. We
reveal both the optimization dynamics and generalization performance under deep
learning models. Our work not only explains the various novel phenomenons
observed for importance weighting in deep learning, but also extends to the
studies where the weights are being optimized as part of the model, which
applies to a number of topics under active research.
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This study introduces Polyp-DDPM, a diffusion-based method for generating
realistic images of polyps conditioned on masks, aimed at enhancing the
segmentation of gastrointestinal (GI) tract polyps. Our approach addresses the
challenges of data limitations, high annotation costs, and privacy concerns
associated with medical images. By conditioning the diffusion model on
segmentation masks-binary masks that represent abnormal areas-Polyp-DDPM
outperforms state-of-the-art methods in terms of image quality (achieving a
Frechet Inception Distance (FID) score of 78.47, compared to scores above
83.79) and segmentation performance (achieving an Intersection over Union (IoU)
of 0.7156, versus less than 0.6694 for synthetic images from baseline models
and 0.7067 for real data). Our method generates a high-quality, diverse
synthetic dataset for training, thereby enhancing polyp segmentation models to
be comparable with real images and offering greater data augmentation
capabilities to improve segmentation models. The source code and pretrained
weights for Polyp-DDPM are made publicly available at
https://github.com/mobaidoctor/polyp-ddpm.
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We show that any $n$-bit string can be recovered with high probability from
$\exp(\widetilde{O}(n^{1/5}))$ independent random subsequences.
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