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The ground state and magnetization process of an exactly solved spin-$1/2$
Ising-Heisenberg orthogonal-dimer chain with two different gyromagnetic factors
of the Ising and Heisenberg spins are investigated in detail. It is shown that
the investigated quantum spin chain exhibits up to seven possible ground states
depending on a mutual interplay of the magnetic field, intra- and inter-dimer
coupling constants. More specifically, the frustrated and modulated quantum
antiferromagnetic phases are responsible in zero-temperature magnetization
curves for a zero magnetization plateau. The intermediate 1/11- and
5/11-plateaus emerge due to the frustrated and modulated quantum ferrimagnetic
phases, while the intermediate 9/11- and 10/11-plateaus can be attributed to
the quantum and classical ferrimagnetic phases. It is conjectured that the
magnetization plateau experimentally observed in a high-field magnetization
curve of 3$d$-4$f$ heterobimetallic coordination polymer
[\{Dy(hfac)$_2$(CH$_3$OH)\}$_2$\{Cu(dmg)(Hdmg)\}$_2$]$_n$ (H$_2$dmg $=$
dimethylglyoxime; Hhfac $=$ 1,1,1,5,5,5-hexafluoropentane-2,4-dione) could be
attributed to the classical and quantum ferrimagnetic phases.
|
Traditional machine learning methods applied to the material sciences have
often predicted invariant, scalar properties of material systems to great
effect. Newer, coordinate equivariant models promise to provide a coordinate
system dependent output in a well defined manner, but recent applications often
neglect a direct prediction of directional (i.e. coordinate system dependent)
quantities and instead are used to predict still just invariant quantities.
This component-wise prediction of tensorial properties is achieved by
decomposing tensors into harmonic subspaces via a \textit{tensor spherical
harmonic decomposition}, by which we may also associate arbitrary tensors with
the irreducible representations of the rotation group. This essentially allows
us to read off tensors component-wise from the output representations of these
equivariant models. In this work, we present results for the prediction of
various material property tensors directly from crystalline structures. Namely,
given some material's crystalline structure, we may predict tensor components
of dielectric, piezoelectric, and elasticity tensors directly from the output
of a $SE(3)$ equivariant model.
|
We propose a probabilistic framework for interpreting and developing hard
thresholding sparse signal reconstruction methods and present several new
algorithms based on this framework. The measurements follow an underdetermined
linear model, where the regression-coefficient vector is the sum of an unknown
deterministic sparse signal component and a zero-mean white Gaussian component
with an unknown variance. We first derive an expectation-conditional
maximization either (ECME) iteration that guarantees convergence to a local
maximum of the likelihood function of the unknown parameters for a given signal
sparsity level. To analyze the reconstruction accuracy, we introduce the
minimum sparse subspace quotient (SSQ), a more flexible measure of the sampling
operator than the well-established restricted isometry property (RIP). We prove
that, if the minimum SSQ is sufficiently large, ECME achieves perfect or
near-optimal recovery of sparse or approximately sparse signals, respectively.
We also propose a double overrelaxation (DORE) thresholding scheme for
accelerating the ECME iteration. If the signal sparsity level is unknown, we
introduce an unconstrained sparsity selection (USS) criterion for its selection
and show that, under certain conditions, applying this criterion is equivalent
to finding the sparsest solution of the underlying underdetermined linear
system. Finally, we present our automatic double overrelaxation (ADORE)
thresholding method that utilizes the USS criterion to select the signal
sparsity level. We apply the proposed schemes to reconstruct sparse and
approximately sparse signals from tomographic projections and compressive
samples.
|
We study mechanisms for wavenumber selection in a minimal model for
run-and-tumble dynamics. We show that nonlinearity in tumbling rates induces
the existence of a plethora of traveling- and standing-wave patterns, as well
as a subtle selection mechanism for the wavenumbers of spatio-temporally
periodic waves. We comment on possible implications for rippling patterns
observed in colonies of myxobacteria.
|
We introduce the "partial-$p$" operation in a massive Euclidean
$\lambda\phi^{4}$ scalar field theory describing anisotropic Lifshitz critical
behavior. We then develop a minimal subtraction a la
$Bogoliubov-Parasyuk-Hepp-Zimmermann$ renormalization scheme. As an application
we compute critical exponents diagrammatically using the orthogonal
approximation at least up to two-loop order and show their equivalence with
other renormalization techniques. We discuss possible applications of the
method in other field-theoretic contexts.
|
Subgraph-enhanced graph neural networks (SGNN) can increase the expressive
power of the standard message-passing framework. This model family represents
each graph as a collection of subgraphs, generally extracted by random sampling
or with hand-crafted heuristics. Our key observation is that by selecting
"meaningful" subgraphs, besides improving the expressivity of a GNN, it is also
possible to obtain interpretable results. For this purpose, we introduce a
novel framework that jointly predicts the class of the graph and a set of
explanatory sparse subgraphs, which can be analyzed to understand the decision
process of the classifier. We compare the performance of our framework against
standard subgraph extraction policies, like random node/edge deletion
strategies. The subgraphs produced by our framework allow to achieve comparable
performance in terms of accuracy, with the additional benefit of providing
explanations.
|
Reconfigurable intelligent surfaces (RISs) have attracted wide interest from
industry and academia since they can shape the wireless environment into a
desirable form with a low cost. In practice, RISs have three types of
implementations: 1) reflective, where signals can be reflected to the users on
the same side of the base station (BS), 2) transmissive, where signals can
penetrate the RIS to serve the users on the opposite side of the BS, and 3)
hybrid, where the RISs have a dual function of reflection and transmission.
However, existing works focus on the reflective type RISs, and the other two
types of RISs are not well investigated. In this letter, a downlink multi-user
RIS-assisted communication network is considered, where the RIS can be one of
these types. We derive the system sum-rate, and discuss which type can yield
the best performance under a specific user distribution. Numerical results
verify our analysis.
|
Thermal atmospheric tides have a strong impact on the rotation of terrestrial
planets. They can lock these planets into an asynchronous rotation state of
equilibrium. We aim at characterizing the dependence of the tidal torque
resulting from the semidiurnal thermal tide on the tidal frequency, the planet
orbital radius, and the atmospheric surface pressure. The tidal torque is
computed from full 3D simulations of the atmospheric climate and mean flows
using a generic version of the LMDZ general circulation model (GCM) in the case
of a nitrogen-dominated atmosphere. Numerical results are discussed with the
help of an updated linear analytical framework. Power scaling laws governing
the evolution of the torque with the planet orbital radius and surface pressure
are derived. The tidal torque exhibits i) a thermal peak in the vicinity of
synchronization, ii) a resonant peak associated with the excitation of the Lamb
mode in the high frequency range, and iii) well defined frequency slopes
outside these resonances. These features are well explained by our linear
theory. Whatever the star-planet distance and surface pressure, the torque
frequency spectrum -- when rescaled with the relevant power laws -- always
presents the same behaviour. This allows us to provide a single and easily
usable empirical formula describing the atmospheric tidal torque over the whole
parameter space. With such a formula, the effect of the atmospheric tidal
torque can be implemented in evolutionary models of the rotational dynamics of
a planet in a computationally efficient, and yet relatively accurate way.
|
An expression is derived for the strain energy of a polymer chain under an
arbitrary three-dimensional deformation with finite strains. For a Gaussian
chain, this expression is reduced to the conventional Moony--Rivlin
constitutive law, while for non-Gaussian chains it implies novel constitutive
relations. Based on the three-chain approximation, explicit formulas are
developed for the strain energy of a chain modeled as a self-avoiding random
walk. In the case of self-avoiding chains with stretched-exponential
distribution function of end-to-end vectors, the strain energy density of a
network is described by the Ogden law with only two material constants. For the
des Cloizeaux distribution function, the constitutive equation involves three
adjustable parameters. The governing equations are verified by fitting
observations on uniaxial tension, uniaxial compression and biaxial tension of
elastomers. Good agreement is demonstrated between the experimental data and
the results of numerical analysis. An analytical formula is derived for the
ratio of the Young's modulus of a self-avoiding chain to that of a Gaussian
chain. It is found that the elastic modulus per chain in the Ogden network
exceeds that in a Gaussian network by a factor of three, whereas the elastic
modulus of a chain with the generalized stretched exponential distribution
function equals about half of the modulus of a Gaussian chain.
|
Currently, public-key compression of supersingular isogeny Diffie-Hellman
(SIDH) and its variant, supersingular isogeny key encapsulation (SIKE) involve
pairing computation and discrete logarithm computation. In this paper, we
propose novel methods to compute only 3 discrete logarithms instead of 4, in
exchange for computing a lookup table efficiently. The algorithms also allow us
to make a trade-off between memory and efficiency. Our implementation shows
that the efficiency of our algorithms is close to that of the previous work,
and our algorithms perform better in some special cases.
|
We introduce an algorithm which solves mean payoff games in polynomial time
on average, assuming the distribution of the games satisfies a flip invariance
property on the set of actions associated with every state. The algorithm is a
tropical analogue of the shadow-vertex simplex algorithm, which solves mean
payoff games via linear feasibility problems over the tropical semiring
$(\mathbb{R} \cup \{-\infty\}, \max, +)$. The key ingredient in our approach is
that the shadow-vertex pivoting rule can be transferred to tropical polyhedra,
and that its computation reduces to optimal assignment problems through
Pl\"ucker relations.
|
A novel splitting scheme to solve parametric multiconvex programs is
presented. It consists of a fixed number of proximal alternating minimisations
and a dual update per time step, which makes it attractive in a real-time
Nonlinear Model Predictive Control (NMPC) framework and for distributed
computing environments. Assuming that the parametric program is semi-algebraic
and that its KKT points are strongly regular, a contraction estimate is derived
and it is proven that the sub-optimality error remains stable if two key
parameters are tuned properly. Efficacy of the method is demonstrated by
solving a bilinear NMPC problem to control a DC motor.
|
The anomalous concentration of radiocarbon in 774/775 attracted intense
discussion on its origin, including the possible extreme solar event(s)
exceeding any events in observational history. Anticipating such extreme solar
events, auroral records were also surveyed in historical documents and those
including the red celestial sign after sunset in the Anglo-Saxon Chronicle
(ASC) were subjected to consideration. Usoskin et al. (2013: U13) interpreted
this record as an aurora and suggested enhanced solar activity around 774/775.
Conversely, Neuhauser and Neuhauser (2015a, 2015b: N15a and N15b) interpreted
"after sunset" as during sunset or twilight; they considered this sign as a
halo display and suggested a solar minimum around 774. However, so far these
records have not been discussed in comparison with eyewitness auroral records
during the known extreme space-weather events, although they were discussed in
relationship with potential extreme events in 774/775. Therefore, we
reconstruct the observational details based on the original records in the ASC
and philological references, compare them with eyewitness auroral observations
during known extreme space-weather events, and consider contemporary solar
activity. We clarify the observation was indeed "after sunset", reject the
solar halo hypothesis, define the observational time span between 25 Mar. 775
and 25 Dec. 777, and note the parallel halo drawing in 806 in the ASC shown in
N15b was not based on the original observation in England. We show examples of
eyewitness auroral observations during twilight in known space-weather events,
and this celestial sign does not contradict the observational evidence.
Accordingly, we consider this event happened after the onset of the event in
774/775, but shows relatively enhanced solar activity, with other historical
auroral records in the mid-770s, as also confirmed by the Be data from ice
cores.
|
We show that the existence of a well-known type of ideals on a regular
cardinal $\lambda$ implies a compactness property concerning the
specialisability of a tree of height $\lambda$ with no cofinal branches. We
also use Neeman's method of side conditions to show that the existence of such
ideals is consistent with stationarily many appropriate guessing models. These
objects suffice to extend the main theorem of \cite{mhpr_spe}: one can
generically specialise any branchless tree of height $\kappa^{++}$ with a
${<}\kappa$-closed, $\kappa^{+}$-proper, and $\kappa^{++}$-preserving forcing,
which has the $\kappa^+$-approximation property.
|
A general field-antifield BV formalism for antisymplectic first class
constraints is proposed. It is as general as the corresponding symplectic
BFV-BRST formulation and it is demonstrated to be consistent with a previously
proposed formalism for antisymplectic second class constraints through a
generalized conversion to corresponding first class constraints. Thereby the
basic concept of gauge symmetry is extended to apply to quite a new class of
gauge theories potentially possible to exist.
|
Analyzing data from multiple neuroimaging studies has great potential in
terms of increasing statistical power, enabling detection of effects of smaller
magnitude than would be possible when analyzing each study separately and also
allowing to systematically investigate between-study differences. Restrictions
due to privacy or proprietary data as well as more practical concerns can make
it hard to share neuroimaging datasets, such that analyzing all data in a
common location might be impractical or impossible. Meta-analytic methods
provide a way to overcome this issue, by combining aggregated quantities like
model parameters or risk ratios. Most meta-analytic tools focus on parametric
statistical models, and methods for meta-analyzing semi-parametric models like
generalized additive models have not been well developed. Parametric models are
often not appropriate in neuroimaging, where for instance age-brain
relationships may take forms that are difficult to accurately describe using
such models. In this paper we introduce meta-GAM, a method for meta-analysis of
generalized additive models which does not require individual participant data,
and hence is suitable for increasing statistical power while upholding privacy
and other regulatory concerns. We extend previous works by enabling the
analysis of multiple model terms as well as multivariate smooth functions. In
addition, we show how meta-analytic $p$-values can be computed for smooth
terms. The proposed methods are shown to perform well in simulation
experiments, and are demonstrated in a real data analysis on hippocampal volume
and self-reported sleep quality data from the Lifebrain consortium. We argue
that application of meta-GAM is especially beneficial in lifespan neuroscience
and imaging genetics. The methods are implemented in an accompanying R package
\verb!metagam!, which is also demonstrated.
|
We investigate four finiteness conditions related to residual finiteness:
complete separability, strong subsemigroup separability, weak subsemigroup
separability and monogenic subsemigroup separability. For each of these
properties we examine under which conditions the property is preserved under
direct products. We also consider if any of the properties are inherited by the
factors in a direct product. We give necessary and sufficient conditions for
finite semigroups to preserve the properties of strong subsemigroup
separability and monogenic subsemigroup separability in a direct product.
|
In the original Art Gallery Problem (AGP), one seeks the minimum number of
guards required to cover a polygon $P$. We consider the Chromatic AGP (CAGP),
where the guards are colored. As long as $P$ is completely covered, the number
of guards does not matter, but guards with overlapping visibility regions must
have different colors. This problem has applications in landmark-based mobile
robot navigation: Guards are landmarks, which have to be distinguishable (hence
the colors), and are used to encode motion primitives, \eg, "move towards the
red landmark". Let $\chi_G(P)$, the chromatic number of $P$, denote the minimum
number of colors required to color any guard cover of $P$. We show that
determining, whether $\chi_G(P) \leq k$ is \NP-hard for all $k \geq 2$. Keeping
the number of colors minimal is of great interest for robot navigation, because
less types of landmarks lead to cheaper and more reliable recognition.
|
An infinite family of irreducible homogeneous free divisors in $K[x, y, z]$
is constructed. Indeed, we identify sets of monomials $X$ such that the general
polynomial supported on $X$ is a free divisor.
|
We describe a construction of complex geometrical analysis which corresponds
to the classical theory of spherical harmonics.
|
The job of a physicist is to describe Nature. General features, hypotheses
and theories help to describe physics phenomena at a more abstract, fundamental
level, and are sometimes tacitly assigned some sort of real existence; doing so
appears to be of little harm in most of classical physics. However, missing any
tangible connection to everyday experience, one better always bears in mind the
descriptive nature of any efforts to grasp the quantum. And elementary
particles interact in the quantum world, of course. When communicating the
world of elementary particles to the general public, the Bayesian approach of
an ever ongoing updating of the depiction of reality turns out to be virtually
indispensable. The human experience of providing a series of increasingly
better descriptions generates plenty of personal pleasures, for researchers as
well as for amateurs. A suggestive analogy for improving our understanding of
the world, even the seemingly paradoxical quantum world, may be found in recent
insight into how congenitally blind children and young adults learn to see,
after having received successful eye surgery.
|
We provide a simple algorithm for recognizing and performing Reidemeister
moves in a Gauss diagram.
|
A formalism is introduced which may describe both standard linearized waves
and gravitational waves in Isaacson's high-frequency limit. After emphasizing
main differences between the two approximation techniques we generalize the
Isaacson method to non-vacuum spacetimes. Then we present three large explicit
classes of solutions for high-frequency gravitational waves in particular
backgrounds. These involve non-expanding (plane, spherical or hyperboloidal),
cylindrical, and expanding (spherical) waves propagating in various universes
which may contain a cosmological constant and electromagnetic field. Relations
of high-frequency gravitational perturbations of these types to corresponding
exact radiative spacetimes are described.
|
Single atoms or atom-like emitters are the purest source of on-demand single
photons, they are intrinsically incapable of multi-photon emission. To
demonstrate this degree of purity we have realized a tunable, on-demand source
of single photons using a single ion trapped at the common focus of high
numerical aperture lenses. Our trapped-ion source produces single-photon pulses
at a rate of 200 kHz with g$^2(0) = (1.9 \pm 0.2) \times 10^{-3}$, without any
background subtraction. The corresponding residual background is accounted for
exclusively by detector dark counts. We further characterize the performance of
our source by measuring the violation of a non-Gaussian state witness and show
that its output corresponds to ideal attenuated single photons. Combined with
current efforts to enhance collection efficiency from single emitters, our
results suggest that single trapped ions are not only ideal stationary qubits
for quantum information processing, but promising sources of light for scalable
optical quantum networks.
|
In the context of the recent COVID-19 outbreak, quarantine has been used to
"flatten the curve" and slow the spread of the disease. In this paper, we show
that this is not the only benefit of quarantine for the mitigation of an SIR
epidemic spreading on a graph. Indeed, human contact networks exhibit a
powerlaw structure, which means immunizing nodes at random is extremely
ineffective at slowing the epidemic, while immunizing high-degree nodes can
efficiently guarantee herd immunity. We theoretically prove that if quarantines
are declared at the right moment, high-degree nodes are disproportionately in
the Removed state, which is a form of targeted immunization. Even if
quarantines are declared too early, subsequent waves of infection spread slower
than the first waves. This leads us to propose an opening and closing strategy
aiming at immunizing the graph while infecting the minimum number of
individuals, guaranteeing the population is now robust to future infections. To
the best of our knowledge, this is the only strategy that guarantees herd
immunity without requiring vaccines. We extensively verify our results on
simulated and real-life networks.
|
This work discusses the numerical approximation of a nonlinear
reaction-advection-diffusion equation, which is a dimensionless form of the
Weertman equation. This equation models steadily-moving dislocations in
materials science. It reduces to the celebrated Peierls-Nabarro equation when
its advection term is set to zero. The approach rests on considering a
time-dependent formulation, which admits the equation under study as its
long-time limit. Introducing a Preconditioned Collocation Scheme based on
Fourier transforms, the iterative numerical method presented solves the
time-dependent problem, delivering at convergence the desired numerical
solution to the Weertman equation. Although it rests on an explicit
time-evolution scheme, the method allows for large time steps, and captures the
solution in a robust manner. Numerical results illustrate the efficiency of the
approach for several types of nonlinearities.
|
Using a microscopic numerical approach suitable to describe disordered
antiferromagnets, with application to $Fe_{x}Zn_{1-x}F_{2}$, it is shown that
the characteristics of the spin glass phase found for $x=0.25$ is much in
agreement with the scenario predicted by the scaling theory of the droplet
model.
|
We consider the gravity-capillary water waves problem in a domain $\Omega_t
\subset \mathbb{T} \times \mathbb{R}$ with substantial geometric features.
Namely, we consider a variable bottom, smooth obstacles in the flow and a
constant background current. We utilize a vortex sheet model introduced by
Ambrose, et. al. in arXiv:2108.01786. We show that the water waves problem is
locally-in-time well-posed in this geometric setting and study the lifespan of
solutions. We then add a damping term and derive evolution equations that
account for the damper. Ultimately, we show that the same well-posedness and
lifespan results apply to the damped system. We primarily utilize energy
methods.
|
The cohomology of the Hilbert schemes of points on smooth projective surfaces
can be approached both with vertex algebra tools and equivariant tools. Using
the first tool, we study the existence and the structure of universal formulas
for the Chern classes of the tangent bundle over the Hilbert scheme of points
on a projective surface. The second tool leads then to nice generating formulas
in the particular case of the Hilbert scheme of points on the affine plane.
|
The controlled creation of defect center---nanocavity systems is one of the
outstanding challenges for efficiently interfacing spin quantum memories with
photons for photon-based entanglement operations in a quantum network. Here, we
demonstrate direct, maskless creation of atom-like single silicon-vacancy (SiV)
centers in diamond nanostructures via focused ion beam implantation with $\sim
32$ nm lateral precision and $< 50$ nm positioning accuracy relative to a
nanocavity. Moreover, we determine the Si+ ion to SiV center conversion yield
to $\sim 2.5\%$ and observe a 10-fold conversion yield increase by additional
electron irradiation. We extract inhomogeneously broadened ensemble emission
linewidths of $\sim 51$ GHz, and close to lifetime-limited single-emitter
transition linewidths down to $126 \pm13$ MHz corresponding to $\sim 1.4$-times
the natural linewidth. This demonstration of deterministic creation of
optically coherent solid-state single quantum systems is an important step
towards development of scalable quantum optical devices.
|
We study the dynamics of gyrotactic swimmers in turbulence, whose orientation
is governed by gravitational torque and local fluid velocity gradient. The
gyrotaxis strength is measured by the ratio of the Kolmogorov time scale to the
reorientation time scale due to gravity, and a large value of this ratio means
the gyrotaxis is strong. By means of direct numerical simulations, we
investigate the effects of swimming velocity and gyrotactic stability on
spatial accumulation and alignment. Three-dimensional Vorono{\"\i} analysis is
used to study the spatial distribution and time evolution of the particle
concentration. We study spatial distribution by examing the overall
preferential sampling and where clusters and voids (subsets of particles that
have small and large Vorono{\"\i} volumes respectively) form. Compared with the
ensemble particles, the preferential sampling of clusters and voids is found to
be more pronounced. The clustering of fast swimmers lasts much longer than
slower swimmers when the gyrotaxis is strong and intermediate, but an opposite
trend emerges when the gyrotaxis is weak. In addition, we study the
preferential alignment with the Lagrangian stretching direction, with which
passive slender rods have been known to align. We show that the Lagrangian
alignment is reduced by the swimming velocity when the gyrotaxis is weak, while
the Lagrangian alignment is enhanced for the regime in which gyrotaxis is
strong.
|
We refine existing general network optimization techniques, give new
characterizations for the class of problems to which they can be applied, and
show that they can also be used to solve various two-player games in almost
linear time. Among these is a new variant of the network interdiction problem,
where the interdictor wants to destroy high-capacity paths from the source to
the destination using a vertex-wise limited budget of arc removals. We also
show that replacing the limit average in mean payoff games by the maximum
weight results in a class of games amenable to these techniques.
|
Railroad transportation plays a vital role in the future of sustainable
mobility. Besides building new infrastructure, capacity can be improved by
modern train control systems, e.g., based on moving blocks. At the same time,
there is only limited work on how to optimally route trains using the potential
gained by these systems. Recently, an initial approach for train routing with
moving block control has been proposed to address this demand. However,
detailed evaluations on so-called lazy constraints are missing, and no publicly
available implementation exists. In this work, we close this gap by providing
an extended approach as well as a flexible open-source implementation that can
use different solving strategies. Using that, we experimentally evaluate what
choices should be made when implementing a lazy constraint approach. The
corresponding implementation and benchmarks are publicly available as part of
the Munich Train Control Toolkit (MTCT) at https://github.com/cda-tum/mtct.
|
We present a scenario for efficient magnetization of very young galaxies
about 0.5 Gigayears after the Big-Bang by a cosmic ray-driven dynamo. These
objects experience a phase of strong star formation during this first $10^9$
years. We transfer the knowledge of the connection between star formation and
the production rate of cosmic rays by supernova remnants to such high redshift
objects. Since the supernova rate is a direct measure for the production rate
of cosmic rays we conclude that very young galaxies must be strong sources of
cosmic rays. The key argument of our model is the finding that magnetic fields
and cosmic rays are dynamically coupled, i.e. a strong cosmic ray source
contains strong magnetic fields since the relativistic particles drive an
efficient dynamo in a galaxy via their buoyancy. We construct a
phenomenological model of a dynamo driven by buoyancy of cosmic rays and show
that if azimuthal shearing is strong enough the dynamo amplification timescale
is close to the buoyancy timescale of the order of several $10^7 \div 10^8$ yr.
We predict that young galaxies are strongly magnetized and may contribute
significantly to the gamma-ray-background.
|
The polynomial $x^n+1$ over finite fields has been of interest due to its
applications in the study of negacyclic codes over finite fields. In this
paper, a rigorous treatment of the factorization of $x^n+1$ over finite fields
is given as well as its applications. Explicit and recursive methods for
factorizing $x^n+1$ over finite fields are provided together with the
enumeration formula. As applications, some families of negacyclic codes are
revisited with more clear and simpler forms.
|
We demonstrate that detection of the heavier minimal supersymmetric model
CP-even Higgs boson $H^0$ will be possible at the LHC via its $H^0\to h^0h^0\to
4b$ and/or $H^0\to A^0A^0\to 4b$ decay channels for significant portions of the
$( m_{A^0},\tan\beta)$ model parameter space. At low $ m_{A^0}$ ($\lsim
60\gev$), {\it both} the $H^0\to A^0A^0\to 4b$ and $H^0\to h^0h^0\to 4b$ modes
yield a viable signal for most $\tan\beta$ values; viability for the $h^0h^0$
channel extends up to $\mhh\sim 2\mt$ when the model parameter $\tan\beta$ is
not large. At the Tevatron, the $h^0h^0$ and $A^0A^0$ channels are both
potentially viable at low $ m_{A^0}$ for sufficiently good $b$-tagging
efficiency and purity.
|
We consider a classical overdamped Brownian particle moving in a symmetric
periodic potential. We show that a net particle flow can be produced by
adiabatically changing two external periodic potentials with a spatial and a
temporal phase difference. The classical pumped current is found to be
independent of the friction and to vanish both in the limit of low and high
temperature. Below a critical temperature, adiabatic pumping appears to be more
efficient than transport due to a constant external force.
|
The resolved mass assembly of Milky-Way-mass galaxies has been previously
studied in simulations, the local universe, and at higher redshifts using
infrared (IR) light profiles. To better characterize the mass assembly of Milky
Way Analogues (MWAs), as well as their changes in star-formation rate and color
gradients, we construct resolved stellar mass and star-formation rate maps of
MWA progenitors selected with abundance matching techniques up to z $\sim$ 2
using deep, multi-wavelength imaging data from the Hubble Frontier Fields. Our
results using stellar mass profiles agree well with previous studies that
utilize IR light profiles, showing that the inner 2 kpc of the galaxies and the
regions beyond 2 kpc exhibit similar rates of stellar mass growth. This
indicates the progenitors of MWAs from $z\sim 2$ to the present do not
preferentially grow their bulges or their disks. The evolution of the
star-formation rate (SFR) profiles indicate greater decrease in SFR density in
the inner regions versus the outer regions. S\'ersic parameters indicate modest
growth in the central regions at lower redshifts, perhaps indicating slight
bulge growth. However, the S\'ersic index does not rise above $n \sim 2$ until
$z < 0.5$, meaning these galaxies are still disk dominated systems. We find
that the half-mass radii of the MWA progenitors increase between $1.5 < z < 2$,
but remain constant at later epochs ($z < 1.5$). This implies mild bulge growth
since $z\sim 2$ in MWA progenitors, in line with previous MWA mass assembly
studies.
|
Although Casimir forces are inseparable from their fluctuations, little is
known about these fluctuations in soft matter systems. We use the membrane
stress tensor to study the fluctuations of the membrane-mediated Casimir-like
force. This method enables us to recover the Casimir force between two
inclusions and to calculate its variance. We show that the Casimir force is
dominated by its fluctuations. Furthermore, when the distance d between the
inclusions is decreased from infinity, the variance of the Casimir force
decreases as -1/d^2. This distance dependence shares a common physical origin
with the Casimir force itself.
|
In particle physics, semi-supervised machine learning is an attractive option
to reduce model dependencies searches beyond the Standard Model. When utilizing
semi-supervised techniques in training machine learning models in the search
for bosons at the Large Hadron Collider, the over-training of the model must be
investigated. Internal fluctuations of the phase space and bias in training can
cause semi-supervised models to label false signals within the phase space due
to over-fitting. The issue of false signal generation in semi-supervised models
has not been fully analyzed and therefore utilizing a toy Monte Carlo model,
the probability of such situations occurring must be quantified. This
investigation of $Z\gamma$ resonances is performed using a pure background
Monte Carlo sample. Through unique pure background samples extracted to mimic
ATLAS data in a background-plus-signal region, multiple runs enable the
probability of these fake signals occurring due to over-training to be
thoroughly investigated.
|
We consider the stochastic background of gravitational waves produced during
the radiation-dominated hot big bang as a constraint on the primordial density
perturbation on comoving length scales much smaller than those directly probed
by the cosmic microwave background or large-scale structure. We place weak
upper bounds on the primordial density perturbation from current data. Future
detectors such as BBO and DECIGO will place much stronger constraints on the
primordial density perturbation on small scales.
|
We probe the gravitational force perpendicular to the Galactic plane at the
position of the Sun based on a sample of red giants, with measurements taken
from the DR3 Gaia catalogue. Measurements far out of the Galactic plane up to
3.5 kpc allow us to determine directly the total mass density, where dark
matter is dominant and the stellar and gas densities are very low. In a
complementary way, we have also used a new determination of the local baryonic
mass density to help determine the density of dark matter in the Galactic plane
at the solar position. For the local mass density of dark matter, we obtained
$\rho_\mathrm{dm}$=0.0128$\pm $0.0008= 0.486 $\pm$0.030 Gev cm$^{-3}$. For the
flattening of the gravitational potential of the dark halo, it is
$q_\mathrm{\phi,h}$=0.843$\pm0.035$. For its density,
$q_\mathrm{\rho,h}$=0.781$\pm$0.055.
|
In present work, we discuss some topological features of charged particles
interacting a uniform magnetic field in a finite volume. The edge state
solutions are presented, as a signature of non-trivial topological systems, the
energy spectrum of edge states show up in the gap between allowed energy bands.
By treating total momentum of two-body system as a continuous distributed
parameter in complex plane, the analytic properties of solutions of finite
volume system in a magnetic field is also discussed.
|
Preliminary results of identical-particle correlations probing the geometric
substructure of the particle-emitting source at RHIC are presented. An
$m_T$-independent scaling of pion HBT radii from large (central Au+Au) to small
(p+p) collision systems naively suggests comparable flow strength in all of
them. Multidimensional correlation functions are studied in detail using a
spherical decomposition method. In the light systems, the presence of
significant long-range non-femtoscopic correlations complicates the extraction
of HBT radii.
|
We reconsider the moments of the reduced density matrix of two disjoint
intervals and of its partial transpose with respect to one interval for
critical free fermionic lattice models. It is known that these matrices are
sums of either two or four Gaussian matrices and hence their moments can be
reconstructed as computable sums of products of Gaussian operators. We find
that, in the scaling limit, each term in these sums is in one-to-one
correspondence with the partition function of the corresponding conformal field
theory on the underlying Riemann surface with a given spin structure. The
analytical findings have been checked against numerical results for the Ising
chain and for the XX spin chain at the critical point.
|
Floquet Majorana edge modes capture the topological features of periodically
driven superconductors. We present a Kitaev chain with multiple time periodic
driving and demonstrate how the avoidance of bands crossing is altered, which
gives rise to new regions supporting Majorana edge modes. A one dimensional
generalized method was proposed to predict Majorana edge modes via the Zak
phase of the Floquet bands. We also study the time independent effective
Hamiltonian at high frequency limit and introduce diverse index to characterize
topological phases with different relative phase between the multiple driving.
Our work enriches the physics of driven system and paves the way for locating
Majorana edge modes in larger parameter space.
|
The Noisy Max mechanism and its variations are fundamental private selection
algorithms that are used to select items from a set of candidates (such as the
most common diseases in a population), while controlling the privacy leakage in
the underlying data. A recently proposed extension, Noisy Top-k with Gap,
provides numerical information about how much better the selected items are
compared to the non-selected items (e.g., how much more common are the selected
diseases). This extra information comes at no privacy cost but crucially relies
on infinite precision for the privacy guarantees. In this paper, we provide a
finite-precision secure implementation of this algorithm that takes advantage
of integer arithmetic.
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An entropy-bounded Discontinuous Galerkin (EBDG) scheme is proposed in which
the solution is regularized by constraining the entropy. The resulting scheme
is able to stabilize the solution in the vicinity of discontinuities and
retains the optimal accuracy for smooth solutions. The properties of the
limiting operator according to the entropy-minimum principle are proofed
analytically, and an optimal CFL-criterion is derived. We provide a rigorous
description for locally imposing entropy constraints to capture multiple
discontinuities. Significant advantages of the EBDG-scheme are the general
applicability to arbitrary high-order elements and its simple implementation
for two- and three-dimensional configurations. Numerical tests confirm the
properties of the scheme, and particular focus is attributed to the robustness
in treating discontinuities on arbitrary meshes.
|
We take an argument of G\"odel's from his ground-breaking 1931 paper,
generalize it, and examine its validity. The argument in question is this: the
sentence $G$ says about itself that it is not provable, and $G$ is indeed not
provable; therefore, $G$ is true.
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In this paper we focus on a feedback mechanism for unsourced random access
(URA) communications. We propose an algorithm to construct feedback packets
broadcasted to the users by the base station (BS) as well as the feedback
packet format that allows the users to estimate their channels and infer
positive or negative feedback based on the presented thresholding algorithm. We
demonstrate that the proposed feedback imposes a much smaller complexity burden
on the users compared to the feedback that positively acknowledges all
successful or negatively acknowledges all undecoded users. We also show that
the proposed feedback technique can lead to a substantial reduction in the
packet error rates and signal-to-noise ratios (SNR)s required to support
various numbers of active users in the system.
|
Let $G$ and $\tilde G$ be Kleinian groups whose limit sets $S$ and $\tilde
S$, respectively, are homeomorphic to the standard Sierpi\'nski carpet, and
such that every complementary component of each of $S$ and $\tilde S$ is a
round disc. We assume that the groups $G$ and $\tilde G$ act cocompactly on
triples on their respective limit sets. The main theorem of the paper states
that any quasiregular map (in a suitably defined sense) from an open connected
subset of $S$ to $\tilde S$ is the restriction of a M\"obius transformation
that takes $S$ onto $\tilde S$, in particular it has no branching. This theorem
applies to the fundamental groups of compact hyperbolic 3-manifolds with
non-empty totally geodesic boundaries.
One consequence of the main theorem is the following result. Assume that $G$
is a torsion-free hyperbolic group whose boundary at infinity $\dee_\infty G$
is a Sierpi\'nski carpet that embeds quasisymmetrically into the standard
2-sphere. Then there exists a group $H$ that contains $G$ as a finite index
subgroup and such that any quasisymmetric map $f$ between open connected
subsets of $\dee_\infty G$ is the restriction of the induced boundary map of an
element $h\in H$.
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The CZTI (Cadmium Zinc Telluride Imager) onboard AstroSat is a high energy
coded mask imager and spectrometer in the energy range of 20 - 100 keV. Above
100 keV, the dominance of Compton scattering cross-section in CZTI results in a
significant number of 2-pixel Compton events and these have been successfully
utilized for polarization analysis of Crab pulsar and nebula (and transients
like Gamma-ray bursts) in 100 - 380 keV. These 2-pixel Compton events can also
be used to extend the spectroscopic energy range of CZTI up to 380 keV for
bright sources. However, unlike the spectroscopy in primary energy range, where
simultaneous background measurement is available from masked pixels, Compton
spectroscopy requires blank sky observation for background measurement.
Background subtraction, in this case, is non-trivial because of the presence of
both short-term and long-term temporal variations in the data, which depend on
multiple factors like earth rotation and the effect of South Atlantic Anomaly
(SAA) regions etc. We have developed a methodology of background selection and
subtraction that takes into account for these effects. Here, we describe these
background selection and subtraction techniques and validate them using
spectroscopy of Crab in the extended energy range of 30 - 380 keV region, and
compare the obtained spectral parameters with the INTEGRAL results. This new
capability allows for the extension of the energy range of AstroSat
spectroscopy and will also enable the simultaneous spectro-polarimetric study
of other bright sources like Cygnus X-1.
|
Because closed timelike curves are consistent with general relativity, many
have asserted that time travel into the past is physically possible if not
technologically infeasible. However, the possibility of time travel into the
past rests on the unstated and false assumption that zero change to the past
implies zero change to the present. I show that this assumption is logically
inconsistent; as such, it renders time travel into the past both unscientific
and pseudoscientific.
|
Metasurfaces have received a lot of attentions recently due to their
versatile capability in manipulating electromagnetic wave. Advanced designs to
satisfy multiple objectives with non-linear constraints have motivated
researchers in using machine learning (ML) techniques like deep learning (DL)
for accelerated design of metasurfaces. For metasurfaces, it is difficult to
make quantitative comparisons between different ML models without having a
common and yet complex dataset used in many disciplines like image
classification. Many studies were directed to a relatively constrained datasets
that are limited to specified patterns or shapes in metasurfaces. In this
paper, we present our SUTD polarized reflection of complex metasurfaces
(SUTD-PRCM) dataset, which contains approximately 260,000 samples of complex
metasurfaces created from electromagnetic simulation, and it has been used to
benchmark our DL models. The metasurface patterns are divided into different
classes to facilitate different degree of complexity, which involves
identifying and exploiting the relationship between the patterns and the
electromagnetic responses that can be compared in using different DL models.
With the release of this SUTD-PRCM dataset, we hope that it will be useful for
benchmarking existing or future DL models developed in the ML community. We
also propose a classification problem that is less encountered and apply neural
architecture search to have a preliminary understanding of potential
modification to the neural architecture that will improve the prediction by DL
models. Our finding shows that convolution stacking is not the dominant element
of the neural architecture anymore, which implies that low-level features are
preferred over the traditional deep hierarchical high-level features thus
explains why deep convolutional neural network based models are not performing
well in our dataset.
|
Thin films of silicon oxide (SiOx) are mixtures of semiconductive c-Si
nanoclusters (NC) embedded in an insulating g-SiO2 matrix. Tour et al. have
shown that a trenched thin film geometry enables the NC to form semiconductive
filamentary arrays when driven by an applied field. The field required to form
reversible nanoscale switching networks (NSN) decreases rapidly within a few
cycles, or by annealing at 600 C in even fewer cycles, and is stable to 700C.
Here we discuss an elastic mechanism that explains why a vertical edge across
the planar Si-SiOx interface is necessary to form NSN. The discussion shows
that the formation mechanism is intrinsic and need not occur locally at the
edge, but can occur anywhere in the SiOx film, given the unpinned nanoscale
vertical edge geometry.
|
Controlling the type and density of charge carriers by doping is the key step
for developing graphene electronics. However, direct doping of graphene is
rather a challenge. Based on first-principles calculations, a concept of
overcoming doping difficulty in graphene via substrate is reported.We find that
doping could be strongly enhanced in epitaxial graphene grown on silicon
carbide substrate. Compared to free-standing graphene, the formation energies
of the dopants can decrease by as much as 8 eV. The type and density of the
charge carriers of epitaxial graphene layer can be effectively manipulated by
suitable dopants and surface passivation. More importantly, contrasting to the
direct doping of graphene, the charge carriers in epitaxial graphene layer are
weakly scattered by dopants due to the spatial separation between dopants and
the conducting channel. Finally, we show that a similar idea can also be used
to control magnetic properties, for example, induce a half-metallic state in
the epitaxial graphene without magnetic impurity doping.
|
We present Karl G. Jansky Very Large Array (VLA) observations of 44 GHz
continuum and CO J=2-1 line emission in BR1202-0725 at z=4.7 (a starburst
galaxy and quasar pair) and BRI1335-0417 at z=4.4 (also hosting a quasar). With
the full 8 GHz bandwidth capabilities of the upgraded VLA, we study the
(rest-frame) 250 GHz thermal dust continuum emission for the first time along
with the cold molecular gas traced by the Low-J CO line emission. The measured
CO J=2-1 line luminosities of BR1202-0725 are L'(CO) = (8.7+/-0.8)x10^10 K km/s
pc^2 and L'(CO) = (6.0+/-0.5)x10^10 K km/s pc^2 for the submm galaxy (SMG) and
quasar, which are equal to previous measurements of the CO J=5-4 line
luminosities implying thermalized line emission and we estimate a combined cold
molecular gas mass of ~9x10^10 Msun. In BRI1335-0417 we measure L'(CO) =
(7.3+/-0.6)x10^10 K km/s pc^2. We detect continuum emission in the SMG
BR1202-0725 North (S(44GHz) = 51+/-6 microJy), while the quasar is detected
with S(44GHz) = 24+/-6 microJy and in BRI1335-0417 we measure S(44GHz) = 40+/-7
microJy. Combining our continuum observations with previous data at
(rest-frame) far-infrared and cm-wavelengths, we fit three component models in
order to estimate the star-formation rates. This spectral energy distribution
fitting suggests that the dominant contribution to the observed 44~GHz
continuum is thermal dust emission, while either thermal free-free or
synchrotron emission contributes less than 30%.
|
Backward terahertz radiation can be produced by a high-intensity laser
normally incident upon an underdense plasma. It is found that terahertz
radiation is generated by electrons refluxing along the bubble shell. These
shell electrons have similar dynamic trajectories and emit backward radiations
to vacuum. This scheme has been proved through electron dynamic calculations as
well as by using an ionic sphere model. In addition, the bubble shape is found
to influence the radiation frequency, and this scheme can be implemented in
both uniform and up-ramp density gradient plasma targets. The terahertz
radiation may be used for diagnosing the electron bubble shape in the
interaction between an intense laser and plasma. All results are presented via
2.5 dimensional particle-in-cell simulations.
|
The discovery of gravitational waves and black holes has started a new era of
gravitational wave astronomy that allows us to probe the underpinning features
of gravity and astrophysics in extreme environments of the universe. In this
article, we investigate one such study with an extreme mass-ratio inspiral
system where the primary object is a spherically symmetric static black hole
immersed in a dark matter halo governed by the Hernquist density distribution.
We consider the eccentric equatorial orbital motion of the steller-mass object
orbiting around the primary and compute measurable effects. We examine the
behaviour of dark matter mass and halo radius in generated gravitational wave
fluxes and the evolution of eccentric orbital parameters -- eccentricity and
semi-latus rectum. We further provide an estimate of gravitational wave
dephasing and find the seminal role of low-frequency detectors in the
observational prospects of such an astrophysical environment.
|
We consider fully nonlinear Hamilton-Jacobi-Bellman equations associated to
diffusion control problems involving a finite set-valued (or switching) control
and possibly a continuum-valued control. In previous works (Akian, Fodjo, 2016
and 2017), we introduced a lower complexity probabilistic numerical algorithm
for such equations by combining max-plus and numerical probabilistic
approaches. The max-plus approach is in the spirit of the one of McEneaney,
Kaise and Han (2011), and is based on the distributivity of monotone operators
with respect to suprema. The numerical probabilistic approach is in the spirit
of the one proposed by Fahim, Touzi and Warin (2011). A difficulty of the
latter algorithm was in the critical constraints imposed on the Hamiltonian to
ensure the monotonicity of the scheme, hence the convergence of the algorithm.
Here, we present new probabilistic schemes which are monotone under rather weak
assumptions, and show error estimates for these schemes. These estimates will
be used in further works to study the probabilistic max-plus method.
|
We present results on the production of high transverse momentum charm mesons
in collisions of 515 GeV/c negative pions with beryllium and copper targets.
The experiment recorded a large sample of events containing high transverse
momentum showers detected in an electromagnetic calorimeter. From these data, a
sample of charm mesons has been reconstructed via their decay into the fully
charged K pi pi mode. A measurement of the single inclusive transverse momentum
distribution of charged D mesons from 1 to 8 GeV/c is presented. An
extrapolation of the measured differential cross section yields an integrated
charged D cross section of 11.4+-2.7(stat)+-3.3(syst) microbarns per nucleon
for charged D mesons with Feynman x greater than zero. The data are compared
with expectations based upon next-to-leading order perturbative QCD, as well as
with results from PYTHIA. We also compare our integrated charged D cross
section with measurements from other experiments.
|
In this paper we develop a general method for constructing 3-point functions
in conformal field theory with affine Lie group symmetry, continuing our recent
work on 2-point functions. The results are provided in terms of triangular
coordinates used in a wave function description of vectors in highest weight
modules. In this framework, complicated couplings translate into ordinary
products of certain elementary polynomials. The discussions pertain to all
simple Lie groups and arbitrary integrable representation. An interesting
by-product is a general procedure for computing tensor product coefficients,
essentially by counting integer solutions to certain inequalities. As an
illustration of the construction, we consider in great detail the three cases
SL(3), SL(4) and SO(5).
|
We investigate symmetry properties of the Bethe ansatz wave functions for the
Heisenberg $XXZ$ spin chain. The $XXZ$ Hamiltonian commutes simultaneously with
the shift operator $T$ and the lattice inversion operator $V$ in the space of
$\Omega=\pm 1$ with $\Omega$ the eigenvalue of $T$. We show that the Bethe
ansatz solutions with normalizable wave functions cannot be the eigenstates of
$T$ and $V$ with quantum number $(\Omega,\Upsilon)=(\pm 1,\mp 1)$ where
$\Upsilon$ is the eigenvalue of $V$. Therefore the Bethe ansatz wave functions
should be singular for nondegenerate eigenstates of the Hamiltonian with
quantum number $(\Omega,\Upsilon)=(\pm 1,\mp 1)$. It is also shown that such
states exist in any nontrivial down-spin number sector and that the number of
them diverges exponentially with the chain length.
|
Using a combination of incentive modeling and empirical meta-analyses, this
paper provides a pointed critique at the incentive systems that drive venture
capital firms to optimize their practices towards activities that increase
General Partner utility yet are disjoint from improving the underlying asset of
startup equity. We propose a "distributed venture firm" powered by software
automations and governed by a set of functional teams called "Pods" that carry
out specific tasks with immediate and long-term payouts given on a deal-by-deal
basis. Avenues are provided for further research to validate this model and
discover likely paths to implementation.
|
We present a numerical model which describes the propagation of a single
femtosecond laser pulse in a medium of which the optical properties dynamically
change within the duration of the pulse. We use a Finite Difference Time Domain
(FDTD) method to solve the Maxwell's equations coupled to equations describing
the changes in the material properties. We use the model to simulate the
self-reflectivity of strongly focused femtosecond laser pulses on silicon and
gold under laser ablation condition. We compare the simulations to experimental
results and find excellent agreement.
|
We study nonlinear resolvents of holomorphic generators of one-parameter
semigroups acting in the open unit disk. The class of nonlinear resolvents can
be studied in the framework of geometric function theory because it consists of
univalent functions.
In this paper we establish distortion and covering results, find order of
starlikeness and of strong starlikeness of resolvents. This provides that any
resolvent admits quasiconformal extension to the complex plane $\C$. In
addition, we obtain some characteristics of semigroups generated by these
resolvents.
|
We study an information design problem with two informed senders and a
receiver in which, in contrast to traditional Bayesian persuasion settings,
senders do not have commitment power. In our setting, a trusted
mediator/platform gathers data from the senders and recommends the receiver
which action to play. We characterize the set of implementable action
distributions that can be obtained in equilibrium, and provide an $O(n \log n)$
algorithm (where $n$ is the number of states) that computes the optimal
equilibrium for the senders. Additionally, we show that the optimal equilibrium
for the receiver can be obtained by a simple revelation mechanism.
|
Moser & Tardos have developed a powerful algorithmic approach (henceforth
"MT") to the Lovasz Local Lemma (LLL); the basic operation done in MT and its
variants is a search for "bad" events in a current configuration. In the
initial stage of MT, the variables are set independently. We examine the
distributions on these variables which arise during intermediate stages of MT.
We show that these configurations have a more or less "random" form, building
further on the "MT-distribution" concept of Haeupler et al. in understanding
the (intermediate and) output distribution of MT. This has a variety of
algorithmic applications; the most important is that bad events can be found
relatively quickly, improving upon MT across the complexity spectrum: it makes
some polynomial-time algorithms sub-linear (e.g., for Latin transversals, which
are of basic combinatorial interest), gives lower-degree polynomial run-times
in some settings, transforms certain super-polynomial-time algorithms into
polynomial-time ones, and leads to Las Vegas algorithms for some coloring
problems for which only Monte Carlo algorithms were known.
We show that in certain conditions when the LLL condition is violated, a
variant of the MT algorithm can still produce a distribution which avoids most
of the bad events. We show in some cases this MT variant can run faster than
the original MT algorithm itself, and develop the first-known criterion for the
case of the asymmetric LLL. This can be used to find partial Latin transversals
-- improving upon earlier bounds of Stein (1975) -- among other applications.
We furthermore give applications in enumeration, showing that most applications
(where we aim for all or most of the bad events to be avoided) have many more
solutions than known before by proving that the MT-distribution has "large"
min-entropy and hence that its support-size is large.
|
The pervasive use of information and communication technology (ICT) in modern
societies enables countless opportunities for individuals, institutions,
businesses and scientists, but also raises difficult ethical and social
problems. In particular, ICT helped to make societies more complex and thus
harder to understand, which impedes social and political interventions to avoid
harm and to increase the common good. To overcome this obstacle, the
large-scale EU flagship proposal FuturICT intends to create a platform for
accessing global human knowledge as a public good and instruments to increase
our understanding of the information society by making use of ICT-based
research. In this contribution, we outline the ethical justification for such
an endeavor. We argue that the ethical issues raised by FuturICT research
projects overlap substantially with many of the known ethical problems emerging
from ICT use in general. By referring to the notion of Value Sensitive Design,
we show for the example of privacy how this core value of responsible ICT can
be protected in pursuing research in the framework of FuturICT. In addition, we
discuss further ethical issues and outline the institutional design of FuturICT
allowing to address them.
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In this note, we propose several unsolved problems concerning the
irrotational oscillation of a water droplet under zero gravity. We will derive
the governing equation of this physical model, and convert it to a quasilinear
dispersive partial differential equation defined on the sphere, which formally
resembles the capillary water waves equation but describes oscillation defined
on curved manifold instead. Three types of unsolved mathematical problems
related to this model will be discussed in observation of hydrodynamical
experiments under zero gravity: (1) Strichartz type inequalities for the
linearized problem (2) existence of periodic solutons (3) normal form reduction
and generic lifespan estimate. It is pointed out that all of these problems are
closely related to certain Diophantine equations, especially the third one.
|
For any regular cardinal $\kappa$ and ordinal $\eta<\kappa^{++}$ it is
consistent that $2^{\kappa}$ is as large as you wish, and every function
$f:\eta \to [\kappa,2^{\kappa}]\cap Card$ with $f(\alpha)=\kappa$ for
$cf(\alpha)<\kappa$ is the cardinal sequence of some locally compact scattered
space.
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The kinematic plane of stars near the Sun has proven an indispensable tool
for untangling the complexities of the structure of our Milky Way (MW). With
ever improving data, numerous kinematic "moving groups" of stars have been
better characterized and new ones continue to be discovered. Here we present an
improved method for detecting these groups using MGwave, a new open-source 2D
wavelet transformation code that we have developed. Our code implements similar
techniques to previous wavelet software; however, we include a more robust
significance methodology and also allow for the investigation of underdensities
which can eventually provide further information about the MW's
non-axisymmetric features. Applying MGwave to the latest data release from Gaia
(DR3), we detect 47 groups of stars with coherent velocities. We reproduce the
majority of the previously detected moving groups in addition to identifying
three additional significant candidates: one within Arcturus, and two in
regions without much substructure at low $V_R$. Finally, we have followed these
associations of stars beyond the solar neighborhood, from Galactocentric radius
of 6.5 to 10 kpc. Most detected groups are extended throughout radius
indicating that they are streams of stars possibly due to non-axisymmetric
features of the MW.
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Finding nearest neighbors in high-dimensional spaces is a fundamental
operation in many diverse application domains. Locality Sensitive Hashing (LSH)
is one of the most popular techniques for finding approximate nearest neighbor
searches in high-dimensional spaces. The main benefits of LSH are its
sub-linear query performance and theoretical guarantees on the query accuracy.
In this survey paper, we provide a review of state-of-the-art LSH and
Distributed LSH techniques. Most importantly, unlike any other prior survey, we
present how Locality Sensitive Hashing is utilized in different application
domains.
|
In this work, we explore a class of compact charged spheres that have been
tested against experimental and observational constraints with some known
compact stars candidates. The study is performed by considering the
self-gravitating, charged, isotropic fluids which is more pliability in solving
the Einstein-Maxwell equations. In order to determine the interior geometry, we
utilize the Vaidya-Tikekar geometry for the metric potential with
Riessner-Nordstrom metric as an exterior solution. In this models, we determine
constants after selecting some particular values of M and R, for the compact
objects SAX J1808.4-3658, Her X-1 and 4U 1538-52. The most striking consequence
is that hydrostatic equilibrium is maintained for different forces, and the
situation is clarified by using the generalized Tolman-Oppenheimer-Volkoff
(TOV) equation. In addition to this, we also present the energy conditions,
speeds of sound and compactness of stars that are very much compatible to that
for a physically acceptable stellar model. Arising solutions are also compared
with graphical representations that provide strong evidences for more realistic
and viable models, both at theoretical and astrophysical scale.
|
We have shown in detail that the low-temperature expansion for the
non-perturbative gluon pressure has the Hagedorn-type structure. Its
exponential spectrum of all the effective gluonic excitations are expressed in
terms of the mass gap. It is this which is responsible for the large-scale
dynamical structure of the QCD ground state. The non-perturbative gluon
pressure properly scaled has a maximum at some characteristic temperature
$T=T_c = 266.5 \ \MeV$, separating the low- and high temperature regions. It is
exponentially suppressed in the $T \rightarrow 0$ limit. In the $T \rightarrow
T_c$ limit it demonstrates an exponential rise in the number of dynamical
degrees of freedom. Its exponential increase behavior with temperature is valid
only up to $T_c$. This makes it possible to identify $T_c$ with the
Hagedorn-type transition temperature $T_h$, i.e., to put $T_h=T_c$ within the
mass gap approach to QCD at finite temperature. The non-perturbative gluon
pressure has a complicated dependence on the mass gap and temperature near
$T_c$ and up to approximately $(4-5)T_c$. In the limit of very high
temperatures $T \rightarrow \infty$ its polynomial character is confirmed,
containing the terms proportional to $T^2$ and $T$, multiplied by the
corresponding powers of the mass gap. \end{abstract}
|
We prove a version of the Stokes formula for differential forms on locally
convex spaces. The main tool used for proving this formula is the surface layer
theorem proved in another paper by the author. Moreover, for differential forms
of a Sobolev-type class relative to a differentiable measure, we compute the
operator adjoint to the exterior differential in terms of standard operations
of calculus of differential forms and the logarithmic derivative. Previously,
this connection was established under essentially stronger assumptions.
|
Extremely red quasars (ERQs) are an interesting sample of quasars in the
Baryon Oscillation Spectroscopic Sample (BOSS) in the redshift range of $2.0 -
3.4$ and have extreme red colours of $i-W3\ge4.6$. Core ERQs have strong CIV
emission lines with rest equivalent width of $\ge100$\AA. Many core ERQs also
have CIV line profiles with peculiar boxy shapes which distinguish them from
normal blue quasars. We show, using a combination of kernel density estimation
and local outlier factor analyses on a space of the $i-W3$ colour, CIV rest
equivalent width and line kurtosis, that core ERQs likely represent a
separate population rather than a smooth transition between normal
blue quasars and the quasars in the tail of the colour-REW distribution. We
apply our analyses to find new criteria for selecting ERQs in this 3D parameter
space. Our final selection produces $133$ quasars, which are \emph{three} times
more likely to have a visually verified CIV broad absorption line feature than
the previous core ERQ sample. We further show that our newly selected sample
are extreme objects in the intersection of the WISE AGN catalogue with the
MILLIQUAS quasar catalogue in the colour-colour space of ($W1-W2$, $W2-W3$).
This paper validates an improved selection method for red quasars which can be
applied to future datasets such as the quasar catalogue from the Dark Energy
Spectroscopic Instrument (DESI).
|
The problem of sorting with priced information was introduced by [Charikar,
Fagin, Guruswami, Kleinberg, Raghavan, Sahai (CFGKRS), STOC 2000]. In this
setting, different comparisons have different (potentially infinite) costs. The
goal is to find a sorting algorithm with small competitive ratio, defined as
the (worst-case) ratio of the algorithm's cost to the cost of the cheapest
proof of the sorted order.
The simple case of bichromatic sorting posed by [CFGKRS] remains open: We are
given two sets $A$ and $B$ of total size $N$, and the cost of an $A-A$
comparison or a $B-B$ comparison is higher than an $A-B$ comparison. The goal
is to sort $A \cup B$. An $\Omega(\log N)$ lower bound on competitive ratio
follows from unit-cost sorting. Note that this is a generalization of the
famous nuts and bolts problem, where $A-A$ and $B-B$ comparisons have infinite
cost, and elements of $A$ and $B$ are guaranteed to alternate in the final
sorted order.
In this paper we give a randomized algorithm InversionSort with an
almost-optimal w.h.p. competitive ratio of $O(\log^{3} N)$. This is the first
algorithm for bichromatic sorting with a $o(N)$ competitive ratio.
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The anomalous Hall effect is mainly used to probe the magnetization
orientation in ferromagnetic materials. A less explored aspect is the torque
acting back on magnetization, an effect that can be important at high currents.
The spin-orbit coupling of the conduction electrons causes spin-up and
spin-down electrons to scatter to opposite sides when a charge current flows in
the sample. This is equivalent to a spin current with orientation and flow
perpendicular to the driving charge current, leading to a non-equilibrium spin
accumulation that exerts a torque on the bulk magnetization through the s-d
exchange interaction. The symmetry of this toque is that of an uniaxial
anisotropy along the driving current. The large screening currents generated
with laser pulses in all-optical magnetic switching experiments make for
practical uses of this torque.
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The low-complexity assumption in linear systems can often be expressed as
rank deficiency in data matrices with generalized Hankel structure. This makes
it possible to denoise the data by estimating the underlying structured
low-rank matrix. However, standard low-rank approximation approaches are not
guaranteed to perform well in estimating the noise-free matrix. In this paper,
recent results in matrix denoising by singular value shrinkage are reviewed. A
novel approach is proposed to solve the low-rank Hankel matrix denoising
problem by using an iterative algorithm in structured low-rank approximation
modified with data-driven singular value shrinkage. It is shown numerically in
both the input-output trajectory denoising and the impulse response denoising
problems, that the proposed method performs the best in terms of estimating the
noise-free matrix among existing algorithms of low-rank matrix approximation
and denoising.
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CVSO 30 is a young, active, weak-line T Tauri star; it possibly hosts the
only known planetary system with both a transiting hot-Jupiter and a
cold-Jupiter candidate (CVSO 30 b and c). We analyzed archival ROSAT, Chandra,
and XMM-Newton data to study the coronal emission in the system. According to
our modeling, CVSO 30 shows a quiescent X-ray luminosity of about 8e29 erg/s.
The X-ray absorbing column is consistent with interstellar absorption.
XMM-Newton observed a flare, during which a transit of the candidate CVSO 30 b
was expected, but no significant transit-induced variation in the X-ray flux is
detectable. While the hot-Jupiter candidate CVSO 30 b has continuously been
undergoing mass loss powered by the high-energy irradiation, we conclude that
its evaporation lifetime is considerably longer than the estimated stellar age
of 2.6 Myr.
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We study the effective behavior of random, heterogeneous, anisotropic, second
order phase transitions energies that arise in the study of pattern formations
in physical-chemical systems. Specifically, we study the asymptotic behavior,
as $\epsilon$ goes to zero, of random heterogeneous anisotropic functionals in
which the second order perturbation competes not only with a double well
potential but also with a possibly negative contribution given by the first
order term. We prove that, under suitable growth conditions and under a
stationarity assumption, the functionals $\Gamma$-converge almost surely to a
surface energy whose density is independent of the space variable. Furthermore,
we show that the limit surface density can be described via a suitable cell
formula and is deterministic when ergodicity is assumed.
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We present a control approach for autonomous vehicles based on deep
reinforcement learning. A neural network agent is trained to map its estimated
state to acceleration and steering commands given the objective of reaching a
specific target state while considering detected obstacles. Learning is
performed using state-of-the-art proximal policy optimization in combination
with a simulated environment. Training from scratch takes five to nine hours.
The resulting agent is evaluated within simulation and subsequently applied to
control a full-size research vehicle. For this, the autonomous exploration of a
parking lot is considered, including turning maneuvers and obstacle avoidance.
Altogether, this work is among the first examples to successfully apply deep
reinforcement learning to a real vehicle.
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Mobile augmented reality (MAR) blends a real scenario with overlaid virtual
content, which has been envisioned as one of the ubiquitous interfaces to the
Metaverse. Due to the limited computing power and battery life of MAR devices,
it is common to offload the computation tasks to edge or cloud servers in close
proximity. However, existing offloading solutions developed for MAR tasks
suffer from high migration overhead, poor scalability, and short-sightedness
when applied in provisioning multi-user MAR services. To address these issues,
a MAR service-oriented task offloading scheme is designed and evaluated in
edge-cloud computing networks. Specifically, the task interdependency of MAR
applications is firstly analyzed and modeled by using directed acyclic graphs.
Then, we propose a look-ahead offloading scheme based on a modified Monte Carlo
tree (MMCT) search, which can run several multi-step executions in advance to
get an estimate of the long-term effect of immediate action. Experiment results
show that the proposed offloading scheme can effectively improve the quality of
service (QoS) in provisioning multi-user MAR services, compared to four
benchmark schemes. Furthermore, it is also shown that the proposed solution is
stable and suitable for applications in a highly volatile environment.
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Pedestrian detection has achieved great improvements with the help of
Convolutional Neural Networks (CNNs). CNN can learn high-level features from
input images, but the insufficient spatial resolution of CNN feature channels
(feature maps) may cause a loss of information, which is harmful especially to
small instances. In this paper, we propose a new pedestrian detection
framework, which extends the successful RPN+BF framework to combine handcrafted
features and CNN features. RoI-pooling is used to extract features from both
handcrafted channels (e.g. HOG+LUV, CheckerBoards or RotatedFilters) and CNN
channels. Since handcrafted channels always have higher spatial resolution than
CNN channels, we apply RoI-pooling with larger output resolution to handcrafted
channels to keep more detailed information. Our ablation experiments show that
the developed handcrafted features can reach better detection accuracy than the
CNN features extracted from the VGG-16 net, and a performance gain can be
achieved by combining them. Experimental results on Caltech pedestrian dataset
with the original annotations and the improved annotations demonstrate the
effectiveness of the proposed approach. When using a more advanced RPN in our
framework, our approach can be further improved and get competitive results on
both benchmarks.
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In this paper, we propose a spectral method for deriving functions that are
jointly smooth on multiple observed manifolds. This allows us to register
measurements of the same phenomenon by heterogeneous sensors, and to reject
sensor-specific noise. Our method is unsupervised and primarily consists of two
steps. First, using kernels, we obtain a subspace spanning smooth functions on
each separate manifold. Then, we apply a spectral method to the obtained
subspaces and discover functions that are jointly smooth on all manifolds. We
show analytically that our method is guaranteed to provide a set of orthogonal
functions that are as jointly smooth as possible, ordered by increasing
Dirichlet energy from the smoothest to the least smooth. In addition, we show
that the extracted functions can be efficiently extended to unseen data using
the Nystr\"{o}m method. We demonstrate the proposed method on both simulated
and real measured data and compare the results to nonlinear variants of the
seminal Canonical Correlation Analysis (CCA). Particularly, we show superior
results for sleep stage identification. In addition, we show how the proposed
method can be leveraged for finding minimal realizations of parameter spaces of
nonlinear dynamical systems.
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Given an initial matching and a policy objective on the distribution of agent
types to institutions, we study the existence of a mechanism that weakly
improves the distributional objective and satisfies constrained efficiency,
individual rationality, and strategy-proofness. We show that such a mechanism
need not exist in general. We introduce a new notion of discrete concavity,
which we call pseudo M$^{\natural}$-concavity, and construct a mechanism with
the desirable properties when the distributional objective satisfies this
notion. We provide several practically relevant distributional objectives that
are pseudo M$^{\natural}$-concave.
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In this paper we study the Nevanlinna-Pick matrix interpolation problem in
the Carath\'eodory class with infinite data (both in the nondegenerate and
degenerate cases). We develop the Sz\"okefalvi-Nagy and Kor\'anyi operator
approach to obtain an analytic description of all solutions of the problem.
Simple necessary and sufficient conditions for the determinacy of the problem
are given.
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A new trigger for NEMO Phase 2 tower based on the time differences of the PMT
hits has been studied. Such a trigger uses only a fixed number of PMT hits in a
chosen time windows. The background trigger rate is drastically reduced
requiring hits from different PMTs. A 87% trigger efficiency was estimated by
Montecarlo simulation for muon tracks with at least 5 PMT hits. The trigger
rate estimated by Montecarlo was also measured on raw data. The results from
Montecarlo simulations and raw data are reported.
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We show that the dispersionless limits of the Pfaff-KP (also known as the DKP
or Pfaff lattice) and the Pfaff-Toda hierarchies admit a reformulation through
elliptic functions. In the elliptic form they look like natural elliptic
deformations of the KP and 2D Toda hierarchy respectively.
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A two-type version of the frog model on $\mathbb{Z}^d$ is formulated, where
active type $i$ particles move according to lazy random walks with probability
$p_i$ of jumping in each time step ($i=1,2$). Each site is independently
assigned a random number of particles. At time 0, the particles at the origin
are activated and assigned type 1 and the particles at one other site are
activated and assigned type 2, while all other particles are sleeping. When an
active type $i$ particle moves to a new site, any sleeping particles there are
activated and assigned type $i$, with an arbitrary tie-breaker deciding the
type if the site is hit by particles of both types in the same time step. We
show that the event $G_i$ that type $i$ activates infinitely many particles has
positive probability for all $p_1,p_2\in(0,1]$ ($i=1,2$). Furthermore, if
$p_1=p_2$, then the types can coexist in the sense that $\mathbb{P}(G_1\cap
G_2)>0$. We also formulate several open problems. For instance, we conjecture
that, when the initial number of particles per site has a heavy tail, the types
can coexist also when $p_1\neq p_2$.
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Density-functional theory for superfluid systems is developed in the
framework of the functional renormalization group based on the effective action
formalism. We introduce the effective action for the particle-number and
nonlocal pairing densities and demonstrate that the Hohenberg-Kohn theorem for
superfluid systems is established in terms of the effective action. The flow
equation for the effective action is then derived, where the flow parameter
runs from $0$ to $1$, corresponding to the non-interacting and interacting
systems. From the flow equation and the variational equation that the
equilibrium density satisfies, we obtain the exact expression for the Kohn-Sham
potential generalized to including the pairing potentials. The resultant
Kohn-Sham potential has a nice feature that it expresses the microscopic
formulae of the external, Hartree, pairing, and exchange-correlation terms,
separately. It is shown that our Kohn-Sham potential gives the ground-state
energy of the Hartree-Fock-Bogoliubov theory by neglecting the correlations. An
advantage of our exact formalism lies in the fact that it provides ways to
systematically improve the correlation part.
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In this paper we first provide a general formula of inclusion for the
Dini-Hadamard epsilon-subdifferential of the difference of two functions and
show that it becomes equality in case the functions are directionally
approximately starshaped at a given point and a weak topological assumption is
fulfilled. To this end we give a useful characterization of the Dini-Hadamard
epsilon-subdifferential by means of sponges. The achieved results are employed
in the formulation of optimality conditions via the Dini-Hadamard
subdifferential for cone-constrained optimization problems having the
difference of two functions as objective.
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The medical datasets are usually faced with the problem of scarcity and data
imbalance. Moreover, annotating large datasets for semantic segmentation of
medical lesions is domain-knowledge and time-consuming. In this paper, we
propose a new object-blend method(short in soft-CP) that combines the
Copy-Paste augmentation method for semantic segmentation of medical lesions
offline, ensuring the correct edge information around the lession to solve the
issue above-mentioned. We proved the method's validity with several datasets in
different imaging modalities. In our experiments on the KiTS19[2] dataset,
Soft-CP outperforms existing medical lesions synthesis approaches. The Soft-CP
augementation provides gains of +26.5% DSC in the low data regime(10% of data)
and +10.2% DSC in the high data regime(all of data), In offline training data,
the ratio of real images to synthetic images is 3:1.
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The Optimal Filtering (OF) reconstruction of the sampled signals from a
particle detector such as a liquid ionization calorimeter relies on the
knowledge of the normalized pulse shapes. This knowledge is always imprecise,
since there are residual differences between the true ionization pulse shapes
and the predicted ones, whatever the method used to model or fit the
particle--induced signals. The systematic error introduced by the residuals on
the signal amplitude estimate is analyzed, as well as the effect on the quality
factor provided by the OF reconstruction. An analysis method to evaluate the
residuals from a sample of signals is developed and tested with a simulation
tool. The correction obtained is showed to preserve the original amplitude
normalization, while restoring the expected $\chi^2 $--like behavior of the
quality factor.
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To support future 6G mobile applications, the mobile edge computing (MEC)
network needs to be jointly optimized for computing, pushing, and caching to
reduce transmission load and computation cost. To achieve this, we propose a
framework based on deep reinforcement learning that enables the dynamic
orchestration of these three activities for the MEC network. The framework can
implicitly predict user future requests using deep networks and push or cache
the appropriate content to enhance performance. To address the curse of
dimensionality resulting from considering three activities collectively, we
adopt the soft actor-critic reinforcement learning in continuous space and
design the action quantization and correction specifically to fit the discrete
optimization problem. We conduct simulations in a single-user single-server MEC
network setting and demonstrate that the proposed framework effectively
decreases both transmission load and computing cost under various
configurations of cache size and tolerable service delay.
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Entropy generation in a chemical reaction is analyzed without using the
general formalism of non-equilibrium thermodynamics at a level adequate for
advanced undergraduates. In a first approach to the problem, the
phenomenological kinetic equation of an elementary first order reaction is used
to show that entropy production is always positive. A second approach assumes
that the reaction is near equilibrium to prove that the entropy generated is
always greater than zero, without any reference to the kinetics of the
reaction. Finally, it is shown that entropy generation is related to
fluctuations in the number of particles at equilibrium, i.e. it is associated
to a microscopic process.
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We study the dynamics of clusters of Active Brownian Disks generated by
Motility-Induced Phase Separation, by applying an algorithm that we devised to
track cluster trajectories. We identify an aggregation mechanism that goes
beyond Ostwald ripening but also yields $z=3$. Active clusters of mass $M$
self-propel with enhanced diffusivity $D\sim$ Pe$^2/\sqrt{M}$. Their fast
motion drives aggregation into large fractal structures, which are patchworks
of diverse hexatic orders, and coexist with regular, orientationally uniform,
smaller ones. To bring out the impact of activity, we perform a comparative
study of a passive system that evidences major differences with the active
case.
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We study $2d$ conformal field theory (CFT) at large central charge $c$ and
finite temperature $T$ with heavy operators inserted at spatial infinity. The
heavy operators produce a nearly thermalized steady state at an effective
temperature $T_{\rm eff}\leq T$. Under some assumptions, we find an effective
Schwarzian-like description of these states and, when they exist, their gravity
duals. We use this description to compute the Lyapunov exponents for light
operators to be $2\pi T_{\rm eff}$, so that scrambling is suppressed by the
heavy insertions.
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We systematically study how the integrality of the conformal characters
shapes the space of fermionic rational conformal field theories in two
dimensions. The integrality suggests that conformal characters on torus with a
given choice of spin structures should be invariant under a principal
congruence subgroup of $\mathrm{PSL}(2,\mathbb{Z})$. The invariance strongly
constrains the possible values of the central charge as well as the conformal
weights in both Neveu-Schwarz and Ramond sectors, which improves the
conventional holomorphic modular bootstrap method in a significant manner. This
allows us to make much progress on the classification of fermionic rational
conformal field theories with the number of independent characters less than
five.
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