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We compare two different implementations of fault-tolerant entangling gates
on logical qubits. In one instance, a twelve-qubit trapped-ion quantum computer
is used to implement a non-transversal logical CNOT gate between two five qubit
codes. The operation is evaluated with varying degrees of fault tolerance,
which are provided by including quantum error correction circuit primitives
known as flagging and pieceable fault tolerance. In the second instance, a
twenty-qubit trapped-ion quantum computer is used to implement a transversal
logical CNOT gate on two [[7,1,3]] color codes. The two codes were implemented
on different but similar devices, and in both instances, all of the quantum
error correction primitives, including the determination of corrections via
decoding, are implemented during runtime using a classical compute environment
that is tightly integrated with the quantum processor. For different
combinations of the primitives, logical state fidelity measurements are made
after applying the gate to different input states, providing bounds on the
process fidelity. We find the highest fidelity operations with the color code,
with the fault-tolerant SPAM operation achieving fidelities of 0.99939(15) and
0.99959(13) when preparing eigenstates of the logical X and Z operators, which
is higher than the average physical qubit SPAM fidelities of 0.9968(2) and
0.9970(1) for the physical X and Z bases, respectively. When combined with a
logical transversal CNOT gate, we find the color code to perform the
sequence--state preparation, CNOT, measure out--with an average fidelity
bounded by [0.9957,0.9963]. The logical fidelity bounds are higher than the
analogous physical-level fidelity bounds, which we find to be [0.9850,0.9903],
reflecting multiple physical noise sources such as SPAM errors for two qubits,
several single-qubit gates, a two-qubit gate and some amount of memory error.
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We present a path planning framework that takes into account the human's
safety perception in the presence of a flying robot. The framework addresses
two objectives: (i) estimation of the uncertain parameters of the proposed
safety perception model based on test data collected using Virtual Reality (VR)
testbed, and (ii) offline optimal control computation using the estimated
safety perception model. Due to the unknown factors in the human tests data, it
is not suitable to use standard regression techniques that minimize the mean
squared error (MSE). We propose to use a Hidden Markov model (HMM) approach
where human's attention is considered as a hidden state to infer whether the
data samples are relevant to learn the safety perception model. The HMM
approach improved log-likelihood over the standard least squares solution. For
path planning, we use Bernstein polynomials for discretization, as the
resulting path remains within the convex hull of the control points, providing
guarantees for deconfliction with obstacles at low computational cost. An
example of optimal trajectory generation using the learned human model is
presented. The optimal trajectory generated using the proposed model results in
reasonable safety distance from the human. In contrast, the paths generated
using the standard regression model have undesirable shapes due to overfitting.
The example demonstrates that the HMM approach has robustness to the unknown
factors compared to the standard MSE model.
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We investigate the photonic bands of an atomic Bose-Einstein condensate with
a triangular vortex lattice. Index contrast between the vortex cores and the
bulk of the condensate is achieved through the enhancement of the index via
atomic coherence. Frequency dependent dielectric function is used in the
calculations of the bands, resulting in photonic band gap widths of a few MHz.
|
The O vacancy (Ov) formation energy, $E_\textrm{Ov}$, is an important
property of a metal-oxide, governing its performance in applications such as
fuel cells or heterogeneous catalysis. These defects are routinely studied with
density functional theory (DFT). However, it is well-recognized that standard
DFT formulations (e.g. the generalized gradient approximation) are insufficient
for modeling the Ov, requiring higher levels of theory. The embedded cluster
method offers a promising approach to compute $E_\textrm{Ov}$ accurately,
giving access to all electronic structure methods. Central to this approach is
the construction of quantum(-mechanically treated) clusters placed within
suitable embedding environments. Unfortunately, current approaches to
constructing the quantum clusters either require large system sizes, preventing
application of high-level methods, or require significant manual input,
preventing investigations of multiple systems simultaneously. In this work, we
present a systematic and general quantum cluster design protocol that can
determine small converged quantum clusters for studying the Ov in metal-oxides
with accurate methods such as local coupled cluster with single, double and
perturbative triple excitations [CCSD(T)]. We apply this protocol to study the
Ov in the bulk and surface planes of rutile TiO2 and rocksalt MgO, producing
the first accurate and well-converged determinations of $E_\textrm{Ov}$ with
this method. These reference values are used to benchmark exchange-correlation
functionals in DFT and we find that all studied functionals underestimate
$E_\textrm{Ov}$, with the average error decreasing along the rungs of Jacob's
ladder. This protocol is automatable for high-throughput calculations and can
be generalized to study other point defects or adsorbates.
|
In this paper, we treat an open problem related to the number of periodic
orbits of Hamiltonian diffeomorphisms on closed symplectic manifolds, so-called
generic Conley conjecture. Generic Conley conjecture states that generically
Hamiltonian diffeomorphisms have infinitely many simple contractible periodic
orbits. We prove generic Conley conjecture for very wide classes of symplectic
manifolds.
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In 1999, Pitman and Stanley introduced the polytope bearing their name along
with a study of its faces, lattice points, and volume. The Pitman-Stanley
polytope is well-studied due to its connections to probability, parking
functions, the generalized permutahedra, and flow polytopes. Its lattice points
correspond to plane partitions of skew shape with entries 0 and 1. Pitman and
Stanley remarked that their polytope can be generalized so that lattice points
correspond to plane partitions of skew shape with entries $0,1, \ldots , m$.
Since then, this generalization has been untouched. We study this
generalization and show that it can also be realized as a flow polytope of a
grid graph. We give multiple characterizations of its vertices in terms of
plane partitions of skew shape and integer flows. For a fixed skew shape, we
show that the number of vertices of this polytope is a polynomial in $m$ whose
leading term, in certain cases, counts standard Young tableaux of a skew
shifted shape. Moreover, we give formulas for the number of faces, as well as
generating functions for the number of vertices.
|
As a step towards the structure theory of Lie algebras in symmetric monoidal
categories we establish results involving the Killing form. The proper
categorical setting for discussing these issues are symmetric ribbon
categories.
|
We theoretically analyze equilibrium fluctuations of persistent current (PC)
in nanorings. We demonstrate that these fluctuations persist down to zero
temperature provided the current operator does not commute with the total
Hamiltonian of the system. For a model of a quantum particle on a ring we
explicitly evaluate PC noise power which has the form of sharp peaks at
frequencies set by the corresponding interlevel distances. In rings with many
conducting channels a much smoother and broader PC noise spectrum is expected.
A specific feature of PC noise is that its spectrum can be tuned by an external
magnetic flux indicating the presence of quantum coherence in the system.
|
This paper studies problems on locally stopping distributed consensus
algorithms over networks where each node updates its state by interacting with
its neighbors and decides by itself whether certain level of agreement has been
achieved among nodes. Since an individual node is unable to access the states
of those beyond its neighbors, this problem becomes challenging. In this work,
we first define the stopping problem for generic distributed algorithms. Then,
a distributed algorithm is explicitly provided for each node to stop consensus
updating by exploring the relationship between the so-called local and global
consensus. Finally, we show both in theory and simulation that its
effectiveness depends both on the network size and the structure.
|
Entity relation extraction consists of two sub-tasks: entity recognition and
relation extraction. Existing methods either tackle these two tasks separately
or unify them with word-by-word interactions. In this paper, we propose HIORE,
a new method for unified entity relation extraction. The key insight is to
leverage the high-order interactions, i.e., the complex association among word
pairs, which contains richer information than the first-order word-by-word
interactions. For this purpose, we first devise a W-shape DNN (WNet) to capture
coarse-level high-order connections. Then, we build a heuristic high-order
graph and further calibrate the representations with a graph neural network
(GNN). Experiments on three benchmarks (ACE04, ACE05, SciERC) show that HIORE
achieves the state-of-the-art performance on relation extraction and an
improvement of 1.1~1.8 F1 points over the prior best unified model.
|
Modern AI techniques open up ever-increasing possibilities for autonomous
vehicles, but how to appropriately verify the reliability of such systems
remains unclear. A common approach is to conduct safety validation based on a
predefined Operational Design Domain (ODD) describing specific conditions under
which a system under test is required to operate properly. However, collecting
sufficient realistic test cases to ensure comprehensive ODD coverage is
challenging. In this paper, we report our practical experiences regarding the
utility of data simulation with deep generative models for scenario-based ODD
validation. We consider the specific use case of a camera-based rail-scene
segmentation system designed to support autonomous train operation. We
demonstrate the capabilities of semantically editing railway scenes with deep
generative models to make a limited amount of test data more representative. We
also show how our approach helps to analyze the degree to which a system
complies with typical ODD requirements. Specifically, we focus on evaluating
proper operation under different lighting and weather conditions as well as
while transitioning between them.
|
We present a theory of the thermal Hall effect in insulating quantum magnets,
where the heat current is totally carried by charge-neutral objects such as
magnons and spinons. Two distinct types of thermal Hall responses are
identified. For ordered magnets, the intrinsic thermal Hall effect for magnons
arises when certain conditions are satisfied for the lattice geometry and the
underlying magnetic order. The other type is allowed in a spin liquid which is
a novel quantum state since there is no order even at zero temperature. For
this case, the deconfined spinons contribute to the thermal Hall response due
to Lorentz force. These results offer a clear experimental method to prove the
existence of the deconfined spinons via a thermal transport phenomenon.
|
Venus has no known satellites, but has four known co-orbitals: (322756) 2001
CK32, 2002 VE68, 2012 XE133, and 2013 ND15. Here, we present numerical evidence
suggesting that 2015 WZ12 is a possible Venus co-orbital; it might have been
until recently a transient Trojan. Follow-up observations of this target in the
near future will be difficult, though.
|
We introduce the theory of non-linear cosmological perturbations using the
correspondence limit of the Schr\"odinger equation. The resulting formalism is
equivalent to using the collisionless Boltzman (or Vlasov) equations which
remain valid during the whole evolution, even after shell crossing. Other
formulations of perturbation theory explicitly break down at shell crossing,
e.g. Eulerean perturbation theory, which describes gravitational collapse in
the fluid limit. This paper lays the groundwork by introducing the new
formalism, calculating the perturbation theory kernels which form the basis of
all subsequent calculations. We also establish the connection with conventional
perturbation theories, by showing that third order tree level results, such as
bispectrum, skewness, cumulant correlators, three-point function are exactly
reproduced in the appropriate expansion of our results. We explicitly show that
cumulants up to N=5 predicted by Eulerian perturbation theory for the dark
matter field $\delta$ are exactly recovered in the corresponding limit. A
logarithmic mapping of the field naturally arises in the Schr\"odinger context,
which means that tree level perturbation theory translates into (possibly
incomplete) loop corrections for the conventional perturbation theory. We show
that the first loop correction for the variance is $\sigma^2 = \sigma_L^2+
(-1.14+n)\sigma_L^4$ for a field with spectral index $n$. This yields 1.86 and
0.86 for $n=-3,-2$ respectively, and to be compared with the exact loop order
corrections 1.82, and 0.88. Thus our tree-level theory recovers the dominant
part of first order loop corrections of the conventional theory, while
including (partial) loop corrections to infinite order in terms of $\delta$.
|
Identifying the factors that determine academic performance is an essential
part of educational research. Existing research indicates that class attendance
is a useful predictor of subsequent course achievements. The majority of the
literature is, however, based on surveys and self-reports, methods which have
well-known systematic biases that lead to limitations on conclusions and
generalizability as well as being costly to implement. Here we propose a novel
method for measuring class attendance that overcomes these limitations by using
location and bluetooth data collected from smartphone sensors. Based on
measured attendance data of nearly 1,000 undergraduate students, we demonstrate
that early and consistent class attendance strongly correlates with academic
performance. In addition, our novel dataset allows us to determine that
attendance among social peers was substantially correlated ($>$0.5), suggesting
either an important peer effect or homophily with respect to attendance.
|
Let $R$ be the ring of $S$-integers in a number field $K$. Let
$\mathcal{B}=\{\beta, \beta^{\ast}\}$ be the multi-set of roots of a nonzero
quadratic polynomial over $R$. There are varieties $V(\mathcal{B})_{N,k}$
defined over $R$ parametrizing periodic continued fractions $[b_1,\ldots ,
b_N,\overline{a_1,\ldots ,a_k}]$ for $\beta$ or $\beta^{\ast}$. We study the
$R$-points on these varieties, finding contrasting behavior according to
whether groups of units are infinite or not. If $R$ is the rational integers or
the ring of integers in an imaginary quadratic field, we prove that the
$R$-points of $V(\mathcal{B})_{N,k}$ are not Zariski dense. On the other hand,
suppose that $\beta\not\in K\cup\{\infty\}$, $R^\times$ is infinite, and that
there are infinitely many units in the (left) order $R_\beta$ of $\beta
R+R\subseteq K(\beta)$ with norm to $K$ equal to $(-1)^k$. Then we prove that
the $R$-points on $V(\mathcal{B})_{1,k}$ are Zariski dense for $k\geq 8$ and
the $R$-points on $V(\mathcal{B})_{0,k}$ are Zariski dense for $k\geq 9$. We
also prove that $V(\mathcal{B})_{1,k}$ and $V(\mathcal{B})_{0,k}$ are
$K$-rational irreducible varieties for $k$ sufficiently large.
|
The aim of this article is to investigate the well-posedness, stability and
convergence of solutions to the time-dependent Maxwell's equations for electric
field in conductive media in continuous and discrete settings. The situation we
consider would represent a physical problem where a subdomain is emerged in a
homogeneous medium, characterized by constant dielectric permittivity and
conductivity functions. It is well known that in these homogeneous regions the
solution to the Maxwell's equations also solves the wave equation which makes
calculations very efficient. In this way our problem can be considered as a
coupling problem for which we derive stability and convergence analysis. A
number of numerical examples validate theoretical convergence rates of the
proposed stabilized explicit finite element scheme.
|
This is a pedagogical review of the recent observational data obtained from
type Ia supernova surveys that support the accelerating expansion of the
universe. The methods for the analysis of the data are reviewed and some of the
theoretical implications obtained from their analysis are discussed.
|
We report yes-go and no-go results on consistent cross-couplings for a
collection of gravitons. Motivated by the search of theories where multiplets
of massless spin-two fields cross-interact, we look for all the consistent
deformations of a positive sum of Pauli-Fierz actions. We also investigate the
problem of deforming a (positive and negative) sum of linearized Weyl gravity
actions and show explicitly that there exists multi-Weyl-graviton theories. As
the single-graviton Weyl theory, these theories do not have an energy bounded
from below.
|
We study the problem of computing optimal prices for a version of the
Product-Mix auction with budget constraints. In contrast to the ``standard''
Product-Mix auction, the objective is to maximize revenue instead of social
welfare. We prove correctness of an algorithm proposed by Paul Klemperer and
DotEcon which is sufficiently efficient in smaller markets.
|
Web crawling, snowball sampling, and respondent-driven sampling (RDS) are
three types of network sampling techniques used to contact individuals in
hard-to-reach populations. This paper studies these procedures as a Markov
process on the social network that is indexed by a tree. Each node in this tree
corresponds to an observation and each edge in the tree corresponds to a
referral. Indexing with a tree (instead of a chain) allows for the sampled
units to refer multiple future units into the sample. In survey sampling, the
design effect characterizes the additional variance induced by a novel sampling
strategy. If the design effect is some value $DE$, then constructing an
estimator from the novel design makes the variance of the estimator $DE$ times
greater than it would be under a simple random sample with the same sample size
$n$. Under certain assumptions on the referral tree, the design effect of
network sampling has a critical threshold that is a function of the referral
rate $m$ and the clustering structure in the social network, represented by the
second eigenvalue of the Markov transition matrix, $\lambda_2$. If $m <
1/\lambda_2^2$, then the design effect is finite (i.e. the standard estimator
is $\sqrt{n}$-consistent). However, if $m > 1/\lambda_2^2$, then the design
effect grows with $n$ (i.e. the standard estimator is no longer
$\sqrt{n}$-consistent). Past this critical threshold, the standard error of the
estimator converges at the slower rate of $n^{\log_m \lambda_2}$. The Markov
model allows for nodes to be resampled; computational results show that the
findings hold in without-replacement sampling. To estimate confidence intervals
that adapt to the correct level of uncertainty, a novel resampling procedure is
proposed. Computational experiments compare this procedure to previous
techniques.
|
A promising approach to overcome decoherence in quantum computing schemes is
to perform active quantum error correction using topology. Topological
subsystem codes incorporate both the benefits of topological and subsystem
codes, allowing for error syndrome recovery with only 2-local measurements in a
two-dimensional array of qubits. We study the error threshold for topological
subsystem color codes under very general external noise conditions. By
transforming the problem into a classical disordered spin model, we estimate
using Monte Carlo simulations that topological subsystem codes have an optimal
error tolerance of 5.5(2)%. This means there is ample space for improvement in
existing error-correcting algorithms that typically find a threshold of
approximately 2%.
|
Understanding how the birthplace of stars affects planet-forming discs is
important for a comprehensive theory of planet formation. Most stars are born
in dense star-forming regions where the external influence of other stars,
particularly the most massive stars, will affect the survival and enrichment of
their planet-forming discs. Simulations suggest that stellar dynamics play a
central role in regulating how external feedback affects discs, but comparing
models to observations requires an estimate of the initial stellar density in
star-forming regions. Structural analyses constrain the amount of dynamical
evolution a star-forming region has experienced; regions that maintain
substructure and do not show mass segregation are likely dynamically young, and
therefore close to their birth density. In this paper, we present a structural
analysis of two clusters in the Carina Nebula, Tr14 and Tr16. We show that
neither cluster shows evidence for mass segregation or a centrally concentrated
morphology, suggesting that both regions are dynamically young. This allows us
to compare to simulations from Nicholson et al. (2019) who predict disc
survival rates in star-forming regions of different initial densities. The
surviving disc fractions in Tr14 and Tr16 are consistent with their predictions
(both are $\sim 10$%), supporting a growing body of evidence that the
star-forming environment plays an important role in the survival and enrichment
of protoplanetary discs.
|
We use the Suita conjecture (now a theorem) to prove that for any domain
$\Omega \subset \mathbb{C}$ its Bergman kernel $K(\cdot, \cdot)$ satisfies
$K(z_0, z_0) = \hbox{Volume}(\Omega)^{-1}$ for some $z_0 \in \Omega$ if and
only if $\Omega$ is either a disk minus a (possibly empty) closed polar set or
$\mathbb{C}$ minus a (possibly empty) closed polar set. When $\Omega$ is
bounded with $C^{\infty}$-boundary, we provide a simple proof of this using the
zero set of the Szeg\"o kernel. Finally, we show that this theorem fails to
hold in $\mathbb{C}^n$ for $n > 1$ by constructing a bounded complete Reinhardt
domain (with algebraic boundary) which is strongly convex and not biholomorphic
to the unit ball $\mathbb{B}^n \subset \mathbb{C}^n$.
|
In this paper, we introduce a new extended version of the shallow water
equations with surface tension which is skew-symmetric with respect to the L2
scalar product and allows for large gradients of fluid height. This result is a
generalization of the results published by P. Noble and J.-P. Vila in [SIAM J.
Num. Anal. (2016)] and by D. Bresch, F. Couderc, P. Noble and J.P. Vila in
[C.R. Acad. Sciences Paris (2016)] which are restricted to quadratic forms of
the capillary energy respectively in the one dimensional and two dimensional
setting.This is also an improvement of the results by J. Lallement, P.
Villedieu et al. published in [AIAA Aviation Forum 2018] where the augmented
version is not skew-symetric with respect to the L2 scalar product. Based on
this new formulation, we propose a new numerical scheme and perform a nonlinear
stability analysis.Various numerical simulations of the shallow water equations
are presented to show differences between quadratic (w.r.t the gradient of the
height) and general surface tension energy when high gradients of the fluid
height occur.
|
Two main physical mechanisms are used to explain supernova explosions:
thermonuclear explosion of a white dwarf(Type Ia) and core collapse of a
massive star (Type II and Type Ib/Ic). Type Ia supernovae serve as distance
indicators that led to the discovery of the accelerating expansion of the
Universe. The exact nature of their progenitor systems however remain unclear.
Radio emission from the interaction between the explosion shock front and its
surrounding CSM or ISM provides an important probe into the progenitor star's
last evolutionary stage. No radio emission has yet been detected from Type Ia
supernovae by current telescopes. The SKA will hopefully detect radio emission
from Type Ia supernovae due to its much better sensitivity and resolution.
There is a 'supernovae rate problem' for the core collapse supernovae because
the optically dim ones are missed due to being intrinsically faint and/or due
to dust obscuration. A number of dust-enshrouded optically hidden supernovae
should be discovered via SKA1-MID/survey, especially for those located in the
innermost regions of their host galaxies. Meanwhile, the detection of
intrinsically dim SNe will also benefit from SKA1. The detection rate will
provide unique information about the current star formation rate and the
initial mass function. A supernova explosion triggers a shock wave which expels
and heats the surrounding CSM and ISM, and forms a supernova remnant (SNR). It
is expected that more SNRs will be discovered by the SKA. This may decrease the
discrepancy between the expected and observed numbers of SNRs. Several SNRs
have been confirmed to accelerate protons, the main component of cosmic rays,
to very high energy by their shocks. This brings us hope of solving the
Galactic cosmic ray origin's puzzle by combining the low frequency (SKA) and
very high frequency (Cherenkov Telescope Array: CTA) bands' observations of
SNRs.
|
This paper will review a new technique of detecting companion stars in LMXBs
and X-ray transients in outburst using the Bowen fluorescence lines at
4634-4640 Angs. These lines are very efficiently reprocessed in the atmospheres
of the companion stars, and thereby provide estimates of the K2 velocities and
mass functions. The method has been applied to Sco X-1, X1822-371 and GX339-4
which, in the latter case, provides the first dynamical evidence for the
presence of an accreting black hole. Preliminary results from a VLT campaign on
V801 Ara, V926 Sco and XTE J1814-338 are also presented.
|
We demonstrate a systematic method for solving the Hamilton-Jacobi equation
for general relativity with the inclusion of matter fields. The generating
functional is expanded in a series of spatial gradients. Each term is
manifestly invariant under reparameterizations of the spatial coordinates
(``gauge-invariant''). At each order we solve the Hamiltonian constraint using
a conformal transformation of the 3-metric as well as a line integral in
superspace. This gives a recursion relation for the generating functional which
then may be solved to arbitrary order simply by functionally differentiating
previous orders. At fourth order in spatial gradients, we demonstrate solutions
for irrotational dust as well as for a scalar field. We explicitly evolve the
3-metric to the same order. This method can be used to derive the Zel'dovich
approximation for general relativity.
|
The goal of this paper is to lay the foundations for a combinatorial study,
via orthogonal functions and intertwining operators, of category O for the
rational Cherednik algebra of type G(r,p,n). As a first application, we give a
self-contained and elementary proof of the analog for the groups G(r,p,n), with
r>1, of Gordon's theorem (previously Haiman's conjecture) on the diagonal
coinvariant ring. We impose no restriction on p; the result for p<r has been
proved by Vale using a technique analogous to Gordon's. Because of the
combinatorial application to Haiman's conjecture, the paper is logically
self-contained except for standard facts about complex reflection groups. The
main results should be accessible to mathematicians working in algebraic
combinatorics who are unfamiliar with the impressive range of ideas used in
Gordon's proof of his theorem.
|
A multisymplectic setting for classical field theories subjected to
non-holonomic constraints is presented. The infinite dimensional setting in the
space of Cauchy data is also given.
|
The Hamiltonian structures of several hybrid kinetic-fluid models are
identified explicitly, upon considering collisionless Vlasov dynamics for the
hot particles interacting with a bulk fluid. After presenting different
pressure-coupling schemes for an ordinary fluid interacting with a hot gas, the
paper extends the treatment to account for a fluid plasma interacting with an
energetic ion species. Both current-coupling and pressure-coupling MHD schemes
are treated extensively. In particular, pressure-coupling schemes are shown to
require a transport-like term in the Vlasov kinetic equation, in order for the
Hamiltonian structure to be preserved. The last part of the paper is devoted to
studying the more general case of an energetic ion species interacting with a
neutralizing electron background (hybrid Hall-MHD). Circulation laws and
Casimir functionals are presented explicitly in each case.
|
We describe regularized methods for image reconstruction and focus on the
question of hyperparameter and instrument parameter estimation, i.e.
unsupervised and myopic problems. We developed a Bayesian framework that is
based on the \post density for all unknown quantities, given the observations.
This density is explored by a Markov Chain Monte-Carlo sampling technique based
on a Gibbs loop and including a Metropolis-Hastings step. The numerical
evaluation relies on the SPIRE instrument of the Herschel observatory. Using
simulated and real observations, we show that the hyperparameters and
instrument parameters are correctly estimated, which opens up many perspectives
for imaging in astrophysics.
|
We prove a formula for the speed of distance stationary random sequences. A
particular case is the classical formula for the largest Lyapunov exponent of
an i.i.d. product of two by two matrices in terms of a stationary measure on
projective space. We apply this result to Poisson-Delaunay random walks on
Riemannian symmetric spaces. In particular, we obtain sharp estimates for the
asymptotic behavior of the speed of hyperbolic Poisson-Delaunay random walks
when the intensity of the Poisson point process goes to zero. This allows us to
prove that a dimension drop phenomena occurs for the harmonic measure
associated to these random walks. With the same technique we give examples of
co-compact Fuchsian groups for which the harmonic measure of the simple random
walk has dimension less than one.
|
The Vietnamese Power system is expected to expand considerably in upcoming
decades. However, pathways towards higher shares of renewables ought to be
investigated. In this work, we investigate a highly renewable Vietnamese power
system by jointly optimising the expansion of renewable generation facilities
and the transmission grid. We show that in the cost-optimal case, highest
amounts of wind capacities are installed in southern Vietnam and solar
photovoltaics (PV) in central Vietnam. In addition, we show that transmission
has the potential to reduce levelised cost of electricity by approximately 10%.
|
Though the truths of logic and pure mathematics are objective and independent
of any contingent facts or laws of nature, our knowledge of these truths
depends entirely on our knowledge of the laws of physics. Recent progress in
the quantum theory of computation has provided practical instances of this, and
forces us to abandon the classical view that computation, and hence
mathematical proof, are purely logical notions independent of that of
computation as a physical process. Henceforward, a proof must be regarded not
as an abstract object or process but as a physical process, a species of
computation, whose scope and reliability depend on our knowledge of the physics
of the computer concerned.
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Convective processes are crucial in shaping exoplanetary atmospheres but are
computationally expensive to simulate directly. A novel technique of simulating
moist convection on tidally locked exoplanets is to use a global 3D model with
a stretched mesh. This allows us to locally refine the model resolution to 4.7
km and resolve fine-scale convective processes without relying on
parameterizations. We explore the impact of mesh stretching on the climate of a
slowly rotating TRAPPIST-1e-like planet, assuming it is 1:1 tidally locked. In
the stretched-mesh simulation with explicit convection, the climate is 5 K
colder and 25% drier than that in the simulations with parameterized convection
(with both stretched and quasi-uniform meshes)}. This is due to the increased
cloud reflectivity - because of an increase of low-level cloudiness - and
exacerbated by the diminished greenhouse effect due to less water vapor. At the
same time, our stretched-mesh simulations reproduce the key characteristics of
the global climate of tidally locked rocky exoplanets, without any noticeable
numerical artifacts. Our methodology opens an exciting and computationally
feasible avenue for improving our understanding of 3D mixing in exoplanetary
atmospheres. Our study also demonstrates the feasibility of a global stretched
mesh configuration for LFRic-Atmosphere, the next-generation Met Office climate
and weather model.
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The novel weak-value-amplification (WVA) scheme of precision metrology is
deeply rooted in the quantum nature of destructive interference between the
pre- and post-selection states. And, an alternative version, termed as joint
WVA (JWVA), which employs the difference-signal from the post-selection
accepted and rejected results, has been found possible to achieve even better
sensitivity (two orders of magnitude higher) under some technical limitations
(e.g. misalignment errors). In this work, after erasing the quantum coherence,
we analyze the difference-signal amplification (DSA) technique, which serves as
a classical counterpart of the JWVA, and show that similar amplification effect
can be achieved. We obtain a simple expression for the amplified signal, carry
out characterization of precision, and point out the optimal working regime. We
also discuss how to implement the post-selection of a classical mixed state.
The proposed classical DSA technique holds similar technical advantages of the
JWVA and may find interesting applications in practice.
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In this note, we consider the observational constraints on some cosmological
models by using the 307 Union type Ia supernovae (SNIa), the 32 calibrated
Gamma-Ray Bursts (GRBs) at $z>1.4$, the updated shift parameter $R$ from WMAP
5-year data (WMAP5), and the distance parameter $A$ of the measurement of the
baryon acoustic oscillation (BAO) peak in the distribution of SDSS luminous red
galaxies with the updated scalar spectral index $n_s$ from WMAP5. The tighter
constraints obtained here update the ones obtained previously in the
literature.
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This paper describes a method for scheduling the events of a switched system
to achieve an optimal performance. The approach has guarantees on convergence
and computational complexity that parallel derivative-based iterative
optimization but in the infinite dimensional, integer constrained setting of
mode scheduling. In comparison to methods relying on mixed integer programming,
the presented approach does not require a priori discretizations of time or
state. Furthermore, in comparison to embedding and relaxation methods, every
iteration of the algorithm returns a dynamically feasible solution. A large
class of problems call for optimal mode scheduling. This paper considers a
vehicle tracking problem and a high dimensional multimachine power network
synchronization problem. For the power network example, both single horizon and
receding horizon approaches prevent instability of the network, and the
receding horizon approach does so at near real-time speeds on a single
processor.
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In this work, we have examined how the multi-vacancy defects induced in the
horizontal direction change the energetics and the electronic structure of
semiconducting Single-Walled Carbon Nanotubes (SWCNTs). The electronic
structure of SWCNTs is computed for each deformed configuration by means of
real space, Order(N) Tight Binding Molecular Dynamic (O(N) TBMD) simulations.
Energy band gap is obtained in real space through the behavior of electronic
density of states (eDOS) near the Fermi level. Vacancies can effectively change
the energetics and hence the electronic structure of SWCNTs. In this study, we
choose three different kinds of semiconducting zigzag SWCNTs and determine the
band gap modifications. We have selected (12,0), (13,0) and (14,0) zigzag
SWCNTs according to n (mod 3) = 0, n (mod 3) = 1 and n (mod 3) = 2
classification. (12,0) SWCNT is metallic in its pristine state. The application
of vacancies opens the electronic band gap and it goes up to 0.13 eV for a di-
vacancy defected tube. On the other hand (13,0) and (14,0) SWCNTs are
semiconductors with energy band gap values of 0.44 eV and 0.55 eV in their
pristine state, respectively. Their energy band gap values decrease to 0.07 eV
and 0.09 eV when mono-vacancy defects are induced in their horizontal
directions. Then the di-vacancy defects open the band gap again. So in both
cases, the semiconducting-metallic - semiconducting transitions occur. It is
also shown that the band gap modification exhibits irreversible
characteristics, which means that band gap values of the nanotubes do not reach
their pristine values with increasing number of vacancies.
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There are several works \cite{De} (and \cite{St}), \cite{En}, \cite{Co} and
\cite{Va} enumerating four-dimensional parallelotopes. In this work we give a
new enumeration showing that any four-dimensional parallelotope is either a
zonotope or the Minkowski sum of a zonotope with the regular 24-cell
$\{3,4,3\}$. Each zonotopal parallelotope is the Minkowski sum of segments
whose generating vectors form a unimodular system. There are exactly 17
four-dimensional unimodular systems. Hence, there are 17 four-dimensional
zonotopal parallelotopes. Other 35 four-dimensional parallelotopes are: the
regular 24-cell $\{3,4,3\}$ and 34 sums of the regular parallelotope with
non-zero zonotopal parallelotopes. For the nontrivial enumerating of the 34
sums we use a theorem discribing necessary and sufficient conditions when the
Minkowski sum of a parallelotope with a segment is a parallelotope.
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Coherent superpositions of the 49s and 48s Rydberg states of cold Rb atoms
were studied near the surface of an atom chip. The superpositions were created
and manipulated using microwaves resonant with the two-photon 49s-48s
transition. Coherent behavior was observed using Rabi flopping, Ramsey
sequences, spin-echo and spin-locking. These results are discussed in the
context of Rydberg atoms as electric field noise sensors. We consider the
coherence of systems quadratically coupled to noise fields with 1/f^k power
spectral densities (k \approx 1).
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In this paper we argue that when gauge invariance is taken into
consideration, there is no consistent geometric framework of Finsler class that
can accommodate Randers type spaces. In this context, an alternative
non-Finslerian framework for Randers spacetimes compatible with gauge
invariance is introduced.
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Individually addressed Er$^{3+}$ ions in solid-state hosts are promising
resources for quantum repeaters, because of their direct emission in the
telecom band and compatibility with silicon photonic devices. While the
Er$^{3+}$ electron spin provides a spin-photon interface, ancilla nuclear spins
could enable multi-qubit registers with longer storage times. In this work, we
demonstrate coherent coupling between the electron spin of a single Er$^{3+}$
ion and a single $I=1/2$ nuclear spin in the solid-state host crystal, which is
a fortuitously located proton ($^1$H). We control the nuclear spin using
dynamical decoupling sequences applied to the electron spin, implementing one-
and two-qubit gate operations. Crucially, the nuclear spin coherence time
exceeds the electron coherence time by several orders of magnitude, because of
its smaller magnetic moment. These results provide a path towards combining
long-lived nuclear spin quantum registers with telecom-wavelength emitters for
long-distance quantum repeaters.
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A subset $S$ of a group $G$ invariably generates $G$ if, when each element of
$S$ is replaced by an arbitrary conjugate, the resulting set generates $G.$ An
invariable generating set $X$ of $G$ is called minimal if no proper subset of
$X$ invariably generates $G.$ We will address several questions related to the
behaviour of minimal invariable generating sets of a finite group.
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A domain wall separating two oppositely magnetized regions in a ferromagnetic
semiconductor exhibits, under appropriate conditions, strongly nonlinear I-V
characteristics similar to those of a p-n diode. We study these characteristics
as functions of wall width and temperature. As the width increases or the
temperature decreases, direct tunneling between the majority spin bands
decreases the effectiveness of the diode. This has important implications for
the zero-field quenched resistance of magnetic semiconductors and for the
design of a recently proposed spin transistor.
|
New results are reported from a measurement of $\pi^0$ electroproduction near
threshold using the $p(e,e^{\prime} p)\pi^0$ reaction. The experiment was
designed to determine precisely the energy dependence of $s-$ and $p-$wave
electromagnetic multipoles as a stringent test of the predictions of Chiral
Perturbation Theory (ChPT). The data were taken with an electron beam energy of
1192 MeV using a two-spectrometer setup in Hall A at Jefferson Lab. For the
first time, complete coverage of the $\phi^*_{\pi}$ and $\theta^*_{\pi}$ angles
in the $p \pi^0$ center-of-mass was obtained for invariant energies above
threshold from 0.5 MeV up to 15 MeV. The 4-momentum transfer $Q^2$ coverage
ranges from 0.05 to 0.155 (GeV/c)$^2$ in fine steps. A simple phenomenological
analysis of our data shows strong disagreement with $p-$wave predictions from
ChPT for $Q^2>0.07$ (GeV/c)$^2$, while the $s-$wave predictions are in
reasonable agreement.
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In 2007 an interesting phenomenon was discovered: a thread of water, the
so-called water bridge (WB), can hang between two glass beakers filled with
deionized water if voltage is applied to them. We analyze the available
explanations of the WB stability and propose a completely different one: the
force that supports the WB is the surface tension of water and the role of
electric field is not to allow the WB to reduce its surface energy by means of
breaking into separate drops.
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Accurate short-term traffic prediction plays a pivotal role in various smart
mobility operation and management systems. Currently, most of the
state-of-the-art prediction models are based on graph neural networks (GNNs),
and the required training samples are proportional to the size of the traffic
network. In many cities, the available amount of traffic data is substantially
below the minimum requirement due to the data collection expense. It is still
an open question to develop traffic prediction models with a small size of
training data on large-scale networks. We notice that the traffic states of a
node for the near future only depend on the traffic states of its localized
neighborhoods, which can be represented using the graph relational inductive
biases. In view of this, this paper develops a graph network (GN)-based deep
learning model LocaleGN that depicts the traffic dynamics using localized data
aggregating and updating functions, as well as the node-wise recurrent neural
networks. LocaleGN is a light-weighted model designed for training on few
samples without over-fitting, and hence it can solve the problem of few-sample
traffic prediction. The proposed model is examined on predicting both traffic
speed and flow with six datasets, and the experimental results demonstrate that
LocaleGN outperforms existing state-of-the-art baseline models. It is also
demonstrated that the learned knowledge from LocaleGN can be transferred across
cities. The research outcomes can help to develop light-weighted traffic
prediction systems, especially for cities lacking historically archived traffic
data.
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We theoretically study electromagnetically induced transparency (EIT) in
reflection spectra of V-type system at the gas-solid interface. In addition to
a narrow dip arising from the EIT effect, we find the other particular
saturation effect induced by pump field, which does not exist in $\Lambda$ or
$\Xi$ -type system reflection spectra. The saturation effect only induces an
intensity decrement in the reflection spectra, and there is no influence on the
narrow dip arising from the EIT effect. We detailedly calculate and analyze the
dependence of V-type system reflection spectra on probe field intensity, pump
field intensity, coherent decay rate, and the initial population after the
collision between atoms and the interface.
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Magnons are viewed as local deviations from the ordered state. Usually, the
spin magnetic moment of magnons is considered. In a 3D-confined structure of a
magnetic insulator with magnetodipolar mode (MDM) oscillations, an orbital
angular momentum (OAM) as well as a spin angular momentum (SAM) can be observed
along a static magnetic field. In such a confined structure as quasi-2D ferrite
disk, energy levels of MDM oscillations are quantized. Quantum confinement is
characterized by a half-integer internal OAM, which is also associated with a
circulating energy flow. The observation of MDM resonances in the 3D-confined
structure of a magnetic insulator is due to the interaction of two subsystems:
ferromagnetic and electric polarization orders. The coupling states of these
two concurrent orders, caused by OAMs, are considered as magnetoelectric (ME)
states. The fields in the vicinity of MDM resonators are characterized by
simultaneous violation of time reversal and inversion symmetry. This plays a
significant role in the problems of strong light-matter interaction regime and
quantum atmosphere. The analysis of SAM and OAM in 3D-confined magnetic
insulators becomes very important for the realization of ME meta-atomic
structures. Current interest lies in considering such artificial systems as
subwavelength ME quantum emitters of electromagnetic radiation.
|
We define dynamic striping as the ability to assign different Lustre striping
characteristics to contiguous segments of a file as it grows. In this paper, we
evaluate the effects of dynamic striping using a watermark-based strategy where
the stripe count or width is increased once a file's size exceeds one of the
chosen watermarks. To measure the performance of this strategy we used a
modified version of the IOR benchmark, a netflow analysis workload, and the
blastn algorithm from NCBI BLAST. The results indicate that dynamic striping is
beneficial to tasks with unpredictable data file size and large sequential
reads, but are less conclusive for workloads with significant random read
phases.
|
The effective action for gravity at high curvatures is likely to contain
higher derivative terms. These corrections may have profound consequences for
the singularity structure of space-time and for early Universe cosmology. In
this contribution, recent work is reviewed which demonstrates that it is
possible to construct a class of effective gravitational actions for which all
solutions with sufficient symmetries have limited curvature and are
nonsingular. Near the limiting curvature, the coupling between matter and
gravity goes to zero and in this sense the theory is asymptotically free.
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A single-sort continuum Curie-Weiss system of interacting particles is
studied. The particles are placed in the space $\mathbb{R}^d$ divided into
congruent cubic cells. For a region $V\subset \mathbb{R}^d$ consisting of $N\in
\mathbb{N}$ cells, every two particles contained in $V$ attract each other with
intensity $J_1/N$. The particles contained in the same cell are subjected to
binary repulsion with intensity $J_2>J_1$. For fixed values of the temperature,
the interaction intensities, and the chemical potential the thermodynamic phase
is defined as a probability measure on the space of occupation numbers of
cells, determined by a condition typical of Curie-Weiss theories. It is proved
that the half-plane $J_1\,\times\,$\textit{chemical potential} contains phase
coexistence points at which there exist two thermodynamic phases of the system.
An equation of state for this system is obtained.
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Using the 3D smoothed particle hydrodynamics code PHANTOM, we investigate the
evolution of the orbital properties of massive black hole binaries embedded in
massive discs where gravitational instabilities (GIs) triggered by the disc
self-gravity are the only source of angular momentum transport. In particular,
we investigate the evolution of binaries with different initial eccentricities
$e_0=0.05,\,0.5,\,0.8$ and mass ratios $q=0.1,\,0.3,\,0.9$. Our simulations
suggest that there might not be a unique value of critical eccentricity. We
find initially more eccentric binaries to tend to higher asymptotic
eccentricity values than more circular ones. This implies that there is a range
of critical eccentricity values, that depends on the initial condition of the
system. In particular, we find the width of this range to be narrower for more
unequal binaries. We furthermore measure preferential accretion onto our
binaries, finding more accretion onto the primary only for mass ratio $q=0.3$
and eccentricity $e=0.8$. We discuss how this might have implications for the
amplitude of the gravitational wave background detected by Pulsar Timing Arrays
(PTA) experiments. We finally measure the corresponding value of the viscosity
parameter $\alpha$ in our simulations and discuss how this depends on the
binary properties.
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We describe a phase transition for long-range entanglement in a
three-dimensional cluster state affected by noise. The partially decohered
state is modeled by the thermal state of a suitable Hamiltonian. We find that
the temperature at which the entanglement length changes from infinite to
finite is nonzero. We give an upper and lower bound to this transition
temperature.
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An outstanding problem in gravitation theory and relativistic astrophysics
today is to understand the final outcome of an endless gravitational collapse.
Such a continual collapse would take place when stars more massive than few
times the mass of the sun collapse under their own gravity on exhausting their
nuclear fuel. According to the general theory of relativity, this results
either in a black hole, or a naked singularity- which can communicate with
faraway observers in the universe. While black holes are (almost) being
detected and are increasingly used to model high energy astrophysical
phenomena, naked singularities have turned into a topic of active discussion,
aimed at understanding their structure and implications. Recent developments
here are reviewed, indicating future directions.
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We use representation theory to construct integral formulas for solutions to
the quantum Toda lattice in general type. This result generalizes work of
Givental for SL(n)/B in a uniform way to arbitrary type and can be interpreted
as a kind of mirror theorem for the full flag variety G/B. We also prove the
existence of a totally positive critical point of the 'superpotential' in every
mirror fiber.
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We study the nature of tunneling phase time for various quantum mechanical
structures such as networks and rings having potential barriers in their arms.
We find the generic presence of Hartman effect, with superluminal velocities as
a consequence, in these systems. In quantum networks it is possible to control
the `super arrival' time in one of the arms by changing the parameters on
another arm which is spatially separated from it. This is yet another quantum
nonlocal effect. Negative time delays (time advancement) and `ultra Hartman
effect' with negative saturation times have been observed in some parameter
regimes. In presence and absence of Aharonov-Bohm (AB) flux quantum rings show
Hartman effect. We obtain the analytical expression for the saturated phase
time. In the opaque barrier regime this is independent of even the AB flux
thereby generalizing the Hartman effect. We also briefly discuss the concept of
"space collapse or space destroyer" by introducing a free space in between two
barriers covering the ring. Further we show in presence of absorption the
reflection phase time exhibits Hartman effect in contrast to the transmission
phase time.
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Autonomous mobile robot competitions judge based on a robot's ability to
quickly and accurately navigate the game field. This means accurate
localization is crucial for creating an autonomous competition robot. Two
common localization methods are odometry and computer vision landmark
detection. Odometry provides frequent velocity measurements, while landmark
detection provides infrequent position measurements. The state can also be
predicted with a physics model. These three types of localization can be
"fused" to create a more accurate state estimate using an Extended Kalman
Filter (EKF). The EKF is a nonlinear full-state estimator that approximates the
state estimate with the lowest covariance error when given the sensor
measurements, the model prediction, and their variances. In this paper, we
demonstrate the effectiveness of the EKF by implementing it on a 4-wheel
mecanum-drive robot simulation. The position and velocity accuracy of fusing
together various combinations of these three data sources are compared. We also
discuss the assumptions and limitations of an EKF.
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In real-world video surveillance applications, person re-identification
(ReID) suffers from the effects of occlusions and detection errors. Despite
recent advances, occlusions continue to corrupt the features extracted by
state-of-art CNN backbones, and thereby deteriorate the accuracy of ReID
systems. To address this issue, methods in the literature use an additional
costly process such as pose estimation, where pose maps provide supervision to
exclude occluded regions. In contrast, we introduce a novel Holistic Guidance
(HG) method that relies only on person identity labels, and on the distribution
of pairwise matching distances of datasets to alleviate the problem of
occlusion, without requiring additional supervision. Hence, our proposed
student-teacher framework is trained to address the occlusion problem by
matching the distributions of between- and within-class distances (DCDs) of
occluded samples with that of holistic (non-occluded) samples, thereby using
the latter as a soft labeled reference to learn well separated DCDs. This
approach is supported by our empirical study where the distribution of between-
and within-class distances between images have more overlap in occluded than
holistic datasets. In particular, features extracted from both datasets are
jointly learned using the student model to produce an attention map that allows
separating visible regions from occluded ones. In addition to this, a joint
generative-discriminative backbone is trained with a denoising autoencoder,
allowing the system to self-recover from occlusions. Extensive experiments on
several challenging public datasets indicate that the proposed approach can
outperform state-of-the-art methods on both occluded and holistic datasets
|
The incomplete beta function is an important special function in statistics.
In modern theory of hypergeometric functions, we regard hypergeometric
functions as pairings of twisted cycles and twisted cocycles. However, the
incomplete beta function cannot be understood in this scheme; in other words,
the domain of the integration is not cycle (incomplete). We will generalize the
theory of A-hypergeometric systems for incomplete functions. We give a general
study as well as a detailed study on an incomplete Gauss hypergeometric
function.
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We analyze the pattern formation in systems of active particles with chiral
forces in the context of pedestrian dynamics. To describe the interparticle
interactions, we use the standard social force model and supplement it with a
new type of force that reflects chirality. We perform numerical simulations of
two pedestrian flows moving in opposite directions along a corridor. We observe
two dynamic phase transitions that occur for varying number densities of
particles and strengths of the chirality force: one from disordered motion to
multi-lane motion and another from multi-lane to two-lane motion. We develop a
qualitative theory that describes the demarcation lines for these phase
transitions in the phase diagram chirality-density. The results of our analysis
agree fairly well with the simulation data. A comparison with previously
reported experimental data has been provided. Our findings may find
applications in urban and transportation-planning problems.
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Laboratory formation of large carbon clusters with m C atoms where m could be
up to few thousand, in carbonaceous plasma, has been studied by using an
especially designed ion source. Carbon is introduced into the glow discharge
plasma by sputtering of the graphite electrode. Soot dominated plasma is
created whose constituents are carbon clusters. It produces and recycles
cluster containing plasma. Regenerative sooting plasma creates the environment
in which the entire spectrum of clusters that contain the linear chains, rings
and fullerenes. Velocity spectra of the extracted clusters have been measured
with an ExB filter. These spectra indicate and identify the mechanisms
operating in the soot.
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Existing 3D pose datasets of object categories are limited to generic object
types and lack of fine-grained information. In this work, we introduce a new
large-scale dataset that consists of 409 fine-grained categories and 31,881
images with accurate 3D pose annotation. Specifically, we augment three
existing fine-grained object recognition datasets (StanfordCars, CompCars and
FGVC-Aircraft) by finding a specific 3D model for each sub-category from
ShapeNet and manually annotating each 2D image by adjusting a full set of 7
continuous perspective parameters. Since the fine-grained shapes allow 3D
models to better fit the images, we further improve the annotation quality by
initializing from the human annotation and conducting local search of the pose
parameters with the objective of maximizing the IoUs between the projected mask
and the segmentation reference estimated from state-of-the-art deep
Convolutional Neural Networks (CNNs). We provide full statistics of the
annotations with qualitative and quantitative comparisons suggesting that our
dataset can be a complementary source for studying 3D pose estimation. The
dataset can be downloaded at http://users.umiacs.umd.edu/~wym/3dpose.html.
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Multi-dimensional distributions of discrete data that resemble ellipsoids
arise in numerous areas of science, statistics, and computational geometry. We
describe a complete algebraic algorithm to determine the quadratic form
specifying the equation of ellipsoid for the boundary of such multi-dimensional
discrete distribution. In this approach, the equation of ellipsoid is
reconstructed using a set of matrix equations from low-dimensional projections
of the input data. We provide a Mathematica program realizing the full
implementation of the ellipsoid reconstruction algorithm in an arbitrary number
of dimensions. To demonstrate its many potential uses, the fast reconstruction
method is applied to quasi-Gaussian statistical distributions arising in
elementary particle production at the Large Hadron Collider.
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This paper looks in detail at how an evolutionary algorithm attempts to solve
instances from the multimodal problem generator. The paper shows that in order
to consistently reach the global optimum, an evolutionary algorithm requires a
population size that should grow at least linearly with the number of peaks. It
is also shown a close relationship between the supply and decision making
issues that have been identified previously in the context of population sizing
models for additively decomposable problems.
The most important result of the paper, however, is that solving an instance
of the multimodal problem generator is like solving a peak-in-a-haystack, and
it is argued that evolutionary algorithms are not the best algorithms for such
a task. Finally, and as opposed to what several researchers have been doing, it
is our strong belief that the multimodal problem generator is not adequate for
assessing the performance of evolutionary algorithms.
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Using a perturbation approach, we make rigorous the formal boundary layer
asymptotic analysis of Turcotte, Spence and Bau from the early eighties for the
vertical flow of an internally heated Boussinesq fluid in a vertical channel
with viscous dissipation and pressure work. A key point in our proof is to
establish the non-degeneracy of a special solution of the Painlev\'{e}-I
transcendent. To this end, we relate this problem to recent studies for the
ground states of the focusing nonlinear Schr\"{o}dinger equation in an annulus.
We also relate our result to a particular case of the well known Lazer-McKenna
conjecture from nonlinear analysis.
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This paper explores the use of Large Language Models (LLMs) and in particular
ChatGPT in programming, source code analysis, and code generation. LLMs and
ChatGPT are built using machine learning and artificial intelligence
techniques, and they offer several benefits to developers and programmers.
While these models can save time and provide highly accurate results, they are
not yet advanced enough to replace human programmers entirely. The paper
investigates the potential applications of LLMs and ChatGPT in various areas,
such as code creation, code documentation, bug detection, refactoring, and
more. The paper also suggests that the usage of LLMs and ChatGPT is expected to
increase in the future as they offer unparalleled benefits to the programming
community.
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Codes for rank modulation have been recently proposed as a means of
protecting flash memory devices from errors. We study basic coding theoretic
problems for such codes, representing them as subsets of the set of
permutations of $n$ elements equipped with the Kendall tau distance. We derive
several lower and upper bounds on the size of codes. These bounds enable us to
establish the exact scaling of the size of optimal codes for large values of
$n$. We also show the existence of codes whose size is within a constant factor
of the sphere packing bound for any fixed number of errors.
|
The $\eta'$ mass reduction in the nuclear medium is expected from the
degeneracy of the pseudoscalar-singlet and octet mesons when chiral symmetry is
manifest. In this study, we investigate the $\eta'N$ 2body interaction which is
the foundation of the in-medium $\eta'$ properties using the linear sigma model
as a chiral effective model. The $\eta'N$ interaction in the linear sigma model
comes from the scalar meson exchange with U$_A$(1) symmetry effect and is found
to be fairly strong attraction. Moreover, the $\eta N$ transition is included
in our calculation, and is important for the imaginary part of the
$\eta'$-optical potential. The transition amplitude of $\eta'N$ to the $\eta N$
channel is relatively small compared to that of elastic channel. From the
analysis of the $\eta'N$ 2body system, we find a $\eta'N$ bound state with the
binding energy $12.3-3.3i$MeV. We expect that this strongly attractive two body
interaction leads to a deep and attractive optical potential.
|
Online reinforcement learning (RL) algorithms are increasingly used to
personalize digital interventions in the fields of mobile health and online
education. Common challenges in designing and testing an RL algorithm in these
settings include ensuring the RL algorithm can learn and run stably under
real-time constraints, and accounting for the complexity of the environment,
e.g., a lack of accurate mechanistic models for the user dynamics. To guide how
one can tackle these challenges, we extend the PCS (Predictability,
Computability, Stability) framework, a data science framework that incorporates
best practices from machine learning and statistics in supervised learning (Yu
and Kumbier, 2020), to the design of RL algorithms for the digital
interventions setting. Further, we provide guidelines on how to design
simulation environments, a crucial tool for evaluating RL candidate algorithms
using the PCS framework. We illustrate the use of the PCS framework for
designing an RL algorithm for Oralytics, a mobile health study aiming to
improve users' tooth-brushing behaviors through the personalized delivery of
intervention messages. Oralytics will go into the field in late 2022.
|
Sea-level rise and associated flood hazards pose severe risks to the millions
of people globally living in coastal zones. Models representing coastal
adaptation and impacts are important tools to inform the design of strategies
to manage these risks. Representing the often deep uncertainties influencing
these risks poses nontrivial challenges. A common uncertainty characterization
approach is to use a few benchmark cases to represent the range and relative
probabilities of the set of possible outcomes. This has been done in coastal
adaptation studies, for example, by using low, moderate, and high percentiles
of an input of interest, like sea-level changes. A key consideration is how
this simplified characterization of uncertainty influences the distributions of
estimated coastal impacts. Here, we show that using only a few benchmark
percentiles to represent uncertainty in future sea-level change can lead to
overconfident projections and underestimate high-end risks as compared to using
full ensembles for sea-level change and socioeconomic parametric uncertainties.
When uncertainty in future sea level is characterized by low, moderate, and
high percentiles of global mean sea-level rise, estimates of high-end (95th
percentile) damages are underestimated by between 18% (SSP1-2.6) and 46%
(SSP5-8.5). Additionally, using the 5th and 95th percentiles of sea-level
scenarios underestimates the 5-95% width of the distribution of adaptation
costs by a factor ranging from about two to four, depending on SSP-RCP pathway.
The resulting underestimation of the uncertainty range in adaptation costs can
bias adaptation and mitigation decision-making.
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We use three strong lensing clusters to constrain the cosmological parameters
Omega_m and Omega_lambda. Recent HST observations of galaxy clusters reveal a
large number of multiple images, which are predicted to be at different
redshifts. We showed in a previous work that if it is possible to measure
spectroscopically the redshift of many multiple images then one can constrain
(Omega_m,Omega_lambda) through ratios of angular diameter distances
independently of any external assumptions. Using three strong lensing clusters,
our combined results lead to tight constraints.
|
We have investigated the magnetic behavior of the nanocrystalline form of a
well-known Laves phase compound, ErCo2 - the bulk form of which has been known
to undergo an interesting first-order ferrimagnetic ordering near 32 K -
synthesized by high-energy ball-milling. It is found that, in these
nanocrystallites, Co exhibits ferromagnetic order at room temperature as
inferred from the magnetization data. However, the magnetic transition
temperature for Er sublattice remains essentially unaffected as though the
(Er)4f-Co(3d) coupling is weak on Er magnetism. The net magnetic moment as
measured at high fields, sat at 120 kOe, is significantly reduced with respect
to that for the bulk in the ferrimagnetically ordered state and possible
reasons are outlined. We have also compared the magnetocaloric behavior for the
bulk and the nano particles.
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Here, we provide a simple Hubbard-like model of spin-$1/2$ fermions that
gives rise to the SU(2) symmetric Thirring model that is equivalent, in the
low-energy limit, to Yang-Mills-Chern-Simons model. First, we identify the
regime that simulates the SU(2) Yang-Mills theory. Then, we suitably extend
this model so that it gives rise to the SU(2) level $k$ Chern-Simons theory
with $k\geq2$ that can support non-Abelian anyons. This is achieved by
introducing multiple fermionic species and modifying the Thirring interactions,
while preserving the SU(2) symmetry. Our proposal provides the means to
theoretically and experimentally probe non-Abelian SU(2) level $k$ topological
phases.
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In this thesis, we settle the computational complexity of some fundamental
questions in polynomial optimization. These include the questions of (i)
finding a local minimum, (ii) testing local minimality of a point, and (iii)
deciding attainment of the optimal value. Our results characterize the
complexity of these three questions for all degrees of the defining polynomials
left open by prior literature.
Regarding (i) and (ii), we show that unless P=NP, there cannot be a
polynomial-time algorithm that finds a point within Euclidean distance $c^n$
(for any constant $c$) of a local minimum of an $n$-variate quadratic program.
By contrast, we show that a local minimum of a cubic polynomial can be found
efficiently by semidefinite programming (SDP). We prove that second-order
points of cubic polynomials admit an efficient semidefinite representation,
even though their critical points are NP-hard to find. We also give an
efficiently-checkable necessary and sufficient condition for local minimality
of a point for a cubic polynomial.
Regarding (iii), we prove that testing whether a quadratically constrained
quadratic program with a finite optimal value has an optimal solution is
NP-hard. We also show that testing coercivity of the objective function,
compactness of the feasible set, and the Archimedean property associated with
the description of the feasible set are all NP-hard. We also give a new
characterization of coercive polynomials that lends itself to a hierarchy of
SDPs.
In our final chapter, we present an SDP relaxation for finding approximate
Nash equilibria in bimatrix games. We show that for a symmetric game, a
$1/3$-Nash equilibrium can be efficiently recovered from any rank-2 solution to
this relaxation. We also propose SDP relaxations for NP-hard problems related
to Nash equilibria, such as that of finding the highest achievable welfare
under any Nash equilibrium.
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The far-from-equilibrium low-temperature dynamics of ultra-thin magnetic
films is analyzed by using Monte Carlo numerical simulations on a two
dimensional Ising model with competing exchange ($J_0$) and dipolar ($J_d$)
interactions. In particular, we focus our attention on the low temperature
region of the $(\delta,T)$ phase diagram (where $\delta= J_0/J_d$) for the
range of values of $\delta$ where striped phases with widths $h=1$ ($h1$) and
$h=2$ ($h2$) are present. The presence of metastable states of the phase $h2$
in the region where the phase $h1$ is the thermodynamically stable one and
viceversa was established recently. In this work we show that the presence of
these metastable states appears as a blocking mechanism that slows the dynamics
of magnetic domains growth when the system is quenched from a high temperature
state to a low temperature state in the region of metastability.
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The patterns of R violation resulting from imposition of a gauged U(1)
horizontal symmetry, on the minimal supersymmetric standard model are
systematically analyzed. We concentrate on a class of models with integer U(1)
charges chosen to reproduce the quark masses and mixings as well as charged
lepton masses exactly or approximately. The U(1) charges are further restricted
from the requirement that very large bilinear lepton number violating terms
should not be allowed in the super-potential. It is shown that all the
trilinear $\lambda'_{ijk}$ and all but at most two trilinear $\lambda_{ijk}$
couplings vanish or are enormously suppressed.
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We show the results of a study using the spectral synthesis technique study
for the full MaNGA sample showing their Chemical Enrichment History (ChEH) as
well as the evolution of the stellar mass-metallicity relation (MZR) over
cosmic time. We find that the more massive galaxies became enriched first and
the lower mass galaxies did so later, producing a change in the MZR which
becomes shallower in time. Separating the sample into morphology and
star-forming status bins some particularly interesting results appear: The mass
dependency of the MZR becomes less relevant for later morphological types, to
the extent that it inverts for Sd/Irr galaxies, suggesting that morphology is
at least as important a factor as mass in chemical evolution. The MZR for the
full sample shows a flattening at the high-mass end and another at the low-mass
range, but the former only appears for retired galaxies while the latter only
appears for star-forming galaxies. We also find that the average metallicity
gradient is currently negative for all mass bins but for low mass galaxies it
was inverted at some point in the past, before which all galaxies had a
positive gradient. We also compare how diverse the ChEHs are in the different
bins considered as well as what primarily drives the diversity: How much
galaxies become enriched or how quickly they do so.
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Labeling neural network submodules with human-legible descriptions is useful
for many downstream tasks: such descriptions can surface failures, guide
interventions, and perhaps even explain important model behaviors. To date,
most mechanistic descriptions of trained networks have involved small models,
narrowly delimited phenomena, and large amounts of human labor. Labeling all
human-interpretable sub-computations in models of increasing size and
complexity will almost certainly require tools that can generate and validate
descriptions automatically. Recently, techniques that use learned models
in-the-loop for labeling have begun to gain traction, but methods for
evaluating their efficacy are limited and ad-hoc. How should we validate and
compare open-ended labeling tools? This paper introduces FIND (Function
INterpretation and Description), a benchmark suite for evaluating the building
blocks of automated interpretability methods. FIND contains functions that
resemble components of trained neural networks, and accompanying descriptions
of the kind we seek to generate. The functions span textual and numeric
domains, and involve a range of real-world complexities. We evaluate methods
that use pretrained language models (LMs) to produce descriptions of function
behavior in natural language and code. Additionally, we introduce a new
interactive method in which an Automated Interpretability Agent (AIA) generates
function descriptions. We find that an AIA, built from an LM with black-box
access to functions, can infer function structure, acting as a scientist by
forming hypotheses, proposing experiments, and updating descriptions in light
of new data. However, AIA descriptions tend to capture global function behavior
and miss local details. These results suggest that FIND will be useful for
evaluating more sophisticated interpretability methods before they are applied
to real-world models.
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Motivated by the physics of coherently coupled, ultracold atom-molecule
mixtures, we investigate a classical model possessing the same symmetry --
namely a $U(1)\times \mathbb{Z}_2$ symmetry, associated with the mass
conservation in the mixture ($U(1)$ symmetry), times the $\mathbb{Z}_2$
symmetry in the phase relationship between atoms and molecules. In two spatial
dimensions the latter symmetry can lead to a finite-temperature Ising
transition, associated with (quasi) phase locking between the atoms and the
molecules. On the other hand, the $U(1)$ symmetry has an associated
Berezinskii-Kosterlitz-Thouless (BKT) transition towards quasi-condensation of
atoms or molecules. The existence of the two transitions is found to depend
crucially on the population imbalance (or detuning) between atoms and
molecules: when the molecules are majority in the system, their BKT
quasi-condensation transition occurs at a higher temperature than that of the
atoms; the latter has the unconventional nature of an Ising (quasi)
phase-locking transition, lacking a finite local order parameter below the
critical temperature. When the balance is gradually biased towards the atoms,
the two transitions merge together to leave out a unique BKT transition, at
which both atoms and molecules acquire quasi-long-range correlations, but only
atoms exhibit conventional BKT criticality, with binding of vortex-antivortex
pairs into short-range dipoles. The molecular vortex-antivortex excitations
bind as well, but undergo a marked crossover from a high-temperature regime in
which they are weakly bound, to a low-temperature regime of strong binding,
reminiscent of their transition in the absence of atom-molecule coupling.
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Building prediction models from mass-spectrometry data is challenging due to
the abundance of correlated features with varying degrees of zero-inflation,
leading to a common interest in reducing the features to a concise predictor
set with good predictive performance. In this study, we formally established
and examined regularized regression approaches, designed to address
zero-inflated and correlated predictors. In particular, we describe a novel
two-stage regularized regression approach (ridge-garrote) explicitly modelling
zero-inflated predictors using two component variables, comprising a ridge
estimator in the first stage and subsequently applying a nonnegative garrote
estimator in the second stage. We contrasted ridge-garrote with one-stage
methods (ridge, lasso) and other two-stage regularized regression approaches
(lasso-ridge, ridge-lasso) for zero-inflated predictors. We assessed the
predictive performance and predictor selection properties of these methods in a
comparative simulation study and a real-data case study to predict kidney
function using peptidomic features derived from mass-spectrometry. In the
simulation study, the predictive performance of all assessed approaches was
comparable, yet the ridge-garrote approach consistently selected more
parsimonious models compared to its competitors in most scenarios. While
lasso-ridge achieved higher predictive accuracy than its competitors, it
exhibited high variability in the number of selected predictors. Ridge-lasso
exhibited slightly superior predictive accuracy than ridge-garrote but at the
expense of selecting more noise predictors. Overall, ridge emerged as a
favourable option when variable selection is not a primary concern, while
ridge-garrote demonstrated notable practical utility in selecting a
parsimonious set of predictors, with only minimal compromise in predictive
accuracy.
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There is a long-standing controversy about the convergence of the dipole
moment of the galaxy angular distribution (the so-called clustering dipole). We
study the growth of the clustering dipole of galaxies as a function of the
limiting flux of the sample from the Two Micron All Sky Survey (2MASS).
Contrary to some earlier claims, we find that the dipole does not converge
before the completeness limit of the 2MASS Extended Source Catalog, i.e. up to
13.5 mag in the near-infrared K_s band (equivalent to an effective distance of
300 Mpc/h). We compare the observed growth of the dipole with the theoretically
expected, conditional one (i.e., given the velocity of the Local Group relative
to the CMB), for the LambdaCDM power spectrum and cosmological parameters
constrained by WMAP. The observed growth turns out to be within 1-sigma
confidence level of its theoretical counterpart once the proper observational
window of the 2MASS flux-limited catalog is included. For a contrast, if the
adopted window is a top-hat, then the predicted dipole grows significantly
faster and converges to its final value for a distance of about 300 Mpc/h. By
comparing the observational windows, we show that for a given flux limit and a
corresponding distance limit, the 2MASS flux-weighted window passes less
large-scale signal than the top-hat one. We conclude that the growth of the
2MASS dipole for effective distances greater than 200 Mpc/h is only apparent.
On the other hand, for a distance of 80 Mpc/h (mean depth of the 2MASS Redshift
Survey) and the LambdaCDM power spectrum, the true dipole is expected to reach
only ~80% of its final value. Eventually, since for the window function of
2MASS the predicted growth is consistent with the observed one, we can compare
the two to evaluate beta = (Omega_m)^0.55 / b. The result is beta = 0.38+-0.04,
which leads to an estimate of the density parameter Omega_m = 0.20+-0.08.
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Efficiently and accurately translating a corpus into a low-resource language
remains a challenge, regardless of the strategies employed, whether manual,
automated, or a combination of the two. Many Christian organizations are
dedicated to the task of translating the Holy Bible into languages that lack a
modern translation. Bible translation (BT) work is currently underway for over
3000 extremely low resource languages. We introduce the eBible corpus: a
dataset containing 1009 translations of portions of the Bible with data in 833
different languages across 75 language families. In addition to a BT
benchmarking dataset, we introduce model performance benchmarks built on the No
Language Left Behind (NLLB) neural machine translation (NMT) models. Finally,
we describe several problems specific to the domain of BT and consider how the
established data and model benchmarks might be used for future translation
efforts. For a BT task trained with NLLB, Austronesian and Trans-New Guinea
language families achieve 35.1 and 31.6 BLEU scores respectively, which spurs
future innovations for NMT for low-resource languages in Papua New Guinea.
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This work introduces a model of Future Technology Transformations for the
power sector (FTT:Power), a representation of global power systems based on
market competition, induced technological change (ITC) and natural resource use
and depletion. It is the first component of a family of sectoral bottom-up
models of technology, designed for integration into the global macroeconometric
model E3MG. ITC occurs as a result of technological learning produced by
cumulative investment and leads to highly nonlinear, irreversible and path
dependent technological transitions. The model uses a dynamic coupled set of
logistic differential equations. As opposed to traditional bottom-up energy
models based on systems optimisation, such differential equations offer an
appropriate treatment of the times and structure of change involved in sectoral
technology transformations, as well as a much reduced computational load.
Resource use and depletion are represented by local cost-supply curves, which
give rise to different regional energy landscapes. The model is explored for a
single global region using two simple scenarios, a baseline and a mitigation
case where the price of carbon is gradually increased. While a constant price
of carbon leads to a stagnant system, mitigation produces successive technology
transitions leading towards the gradual decarbonisation of the global power
sector.
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Semi-supervised learning by self-training heavily relies on pseudo-label
selection (PLS). The selection often depends on the initial model fit on
labeled data. Early overfitting might thus be propagated to the final model by
selecting instances with overconfident but erroneous predictions, often
referred to as confirmation bias. This paper introduces BPLS, a Bayesian
framework for PLS that aims to mitigate this issue. At its core lies a
criterion for selecting instances to label: an analytical approximation of the
posterior predictive of pseudo-samples. We derive this selection criterion by
proving Bayes optimality of the posterior predictive of pseudo-samples. We
further overcome computational hurdles by approximating the criterion
analytically. Its relation to the marginal likelihood allows us to come up with
an approximation based on Laplace's method and the Gaussian integral. We
empirically assess BPLS for parametric generalized linear and non-parametric
generalized additive models on simulated and real-world data. When faced with
high-dimensional data prone to overfitting, BPLS outperforms traditional PLS
methods.
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In a recent paper (Phys. Rev. Lett. 109, 160501 (2012). arXiv:1201.0849), it
is claimed that any quantum protocol for classical two-sided computation
between Alice and Bob can be proven completely insecure for Alice if it is
secure against Bob. Here we show that the proof is not sufficiently general,
because the security definition it based on is only a sufficient condition but
not a necessary condition.
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In the first part of this thesis we study baryonic U(1) symmetries dual to
Betti multiplets in the AdS_4/CFT_3 correspondence for M2 branes at Calabi-Yau
4-fold singularities. We begin by focusing on isolated toric singularities
without vanishing 6-cycles, which we classify, and propose for them field
theory duals. We then study in detail the cone over Q^111 and find agreement
between the spectrum of baryonic operators in this theory and M5 branes
wrapping 5-cycles in the Q^111 space. The physics of vacua in which these
symmetries are spontaneously broken precisely matches a dual gravity analysis
involving resolutions of the singularity, where we are able to match
condensates, Goldstone bosons and global strings. We then study the
implications of turning on a torsion 4-form flux. This flux non-trivially
affects the supergravity dual of Higgsing, and we show that the supergravity
and field theory analyses precisely match in an example based on Y^12(CP^2). We
then explain how the choice of M-theory circle can result in exotic
renormalization group flows. We also argue that theories where the resolutions
have 6-cycles are expected to receive non-perturbative corrections from M5
instantons. We give a general formula relating the instanton action to
normalizable harmonic 2-forms.
In the second part of this thesis we study the breaking of baryonic
symmetries in the AdS_5/CFT_4 correspondence. This leads, for particular vacuum
expectation values, to the emergence of baryonic symmetries during the
renormalization group flow. We identify these vacuum expectation values with
critical values of the B-field moduli in the dual supergravity backgrounds. We
study in detail the C^3/Z_3 orbifold theory and the dual supergravity
backgrounds that correspond to the breaking of the emerging baryonic
symmetries, and identify the expected Goldstone bosons and global strings in
the IR.
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Both symmetry and organized breaking of symmetry have a pivotal r\^ole in our
understanding of structure and pattern formation in physical systems, including
the origin of mass in the Universe and the chiral structure of biological
macromolecules. Here we report on a new symmetry breaking phenomenon that takes
place in all biologically active proteins, thus this symmetry breaking relates
to the inception of life. The unbroken symmetry determines the covalent bond
geometry of a sp3 hybridized carbon atom. It dictates the tetrahedral
architecture of atoms around the central carbon of an amino acid. Here we show
that in a biologically active protein this symmetry becomes broken. Moreover,
we show that the pattern of symmetry breaking is in a direct correspondence
with the local secondary structure of the folded protein.
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The inference of topological principles is a key problem in structured
reconstruction. We observe that wrongly predicted topological relationships are
often incurred by the lack of holistic geometry clues in low-level features.
Inspired by the fact that massive signals can be compactly described with
frequency analysis, we experimentally explore the efficiency and tendency of
learning structure geometry in the frequency domain. Accordingly, we propose a
frequency-domain feature learning strategy (F-Learn) to fuse scattered
geometric fragments holistically for topology-intact structure reasoning.
Benefiting from the parsimonious design, the F-Learn strategy can be easily
deployed into a deep reconstructor with a lightweight model modification.
Experiments demonstrate that the F-Learn strategy can effectively introduce
structure awareness into geometric primitive detection and topology inference,
bringing significant performance improvement to final structured
reconstruction. Code and pre-trained models are available at
https://github.com/Geo-Tell/F-Learn.
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We continue our study of BPS equations and supersymmetric configurations in
the Bagger-Lambert theory. The superalgebra allows three different types of
central extensions which correspond to compounds of various M-theory objects:
M2-branes, M5-branes, gravity waves and Kaluza-Klein monopoles which intersect
or have overlaps with the M2-branes whose dynamics is given by the
Bagger-Lambert action. As elementary objects they are all 1/2-BPS, and multiple
intersections of $n$-branes generically break the supersymmetry into $1/2^n$,
as it is well known. But a particular composite of M-branes can preserve from
1/16 up to 3/4 of the original ${\cal N}=8$ supersymmetries as previously
discovered. In this paper we provide the M-theory interpretation for various
BPS equations, and also present explicit solutions to some 1/2-BPS equations.
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We present a straightforward integration method to compute the abundance and
temperature evolution in explosive scenarios. In this approach the thermal
equation is implicitely coupled with chemical equations in order to avoid
instabilities and ensure a gentle transition from the normal combustion regime
to the quasi (QSE) and complete nuclear statistical equilibrium (NSE). Two
nuclear networks, with 14 nuclei (alpha-network) and 86 nuclei (including
protons and neutrons) respectively, have been considered. The scheme is
suitable to cope with a variety of explosive burning regimes.
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The ability to design the control of heat flow has innumerable benefits in
the design of electronic systems such as thermoelectric energy harvesters,
solid-state lighting, and thermal imagers, where the thermal design plays a key
role in performance and device reliability. However, to realize one advanced
control function of thermal flux, one needs to design one sophisticated,
multilayered and inhomogeneous thermal structure with different
composition/shape at different regions of one device. In this work, we employ
one identical sensu-unit with facile natural composition to experimentally
realize a new class of thermal metamaterials for controlling thermal conduction
(e.g., thermal concentrator, focusing/resolving, uniform heating), only
resorting to positioning and locating the same unit element of sensu-shape
structure. The thermal metamaterial unit and the proper arrangement of multiple
identical units are capable of transferring, redistributing and managing
thermal energy in a versatile fashion. It is also shown that our sensu-shape
unit elements can be used in manipulating dc currents without any change in the
layout for the thermal counterpart. The proposed scheme can also be applied to
control dc electric currents and dc magnetic fields that governed by Laplace
equation. These could markedly enhance the capabilities in thermal sensing,
thermal imaging, thermal-energy storage, thermal packaging, thermal therapy,
and more domains beyond.
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We set up a framework of 2-Hilbert bundles, which allows to rigorously define
the "stringor bundle", a higher differential geometric object anticipated by
Stolz and Teichner in an unpublished preprint about 20 years ago. Our framework
includes an associated bundle construction, allowing us to associate a
2-Hilbert bundle with a principal 2-bundle and a unitary representation of its
structure 2-group. We prove that the Stolz-Teichner stringor bundle is
canonically isomorphic to the 2-Hilbert bundle obtained from applying our
associated bundle construction to a string structure on a manifold and the
stringor representation of the string 2-group that we discovered in earlier
work. This establishes a perfect analogy to spin manifolds, representations of
the spin groups, and spinor bundles.
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This thesis examines some of the applications of scaling relations in
understanding non linear structure formation.
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We present a phenomenological study of photon-initiated (PI) lepton
production at the LHC, as implemented in the structure function (SF) approach.
We provide detailed predictions for multi-differential lepton pair production,
and show that the impact on observables sensitive to the the weak mixing angle,
$\sin^2 \theta_W$, and $W$ boson mass, $M_W$, as well as PDFs can be
non-negligible, in particular given the high precision being aimed for. The SF
calculation can provide percent level precision in the corresponding production
cross sections, and is therefore well positioned to account for LHC precision
requirements. We consider the pure $\gamma\gamma$ channel, and compare in
detail to the NLO collinear calculation. We in addition include initial-state
$Z$ as well as mixed $\gamma /Z + q$ contributions, and assess their impact. We
also consider photon-initiated lepton-lepton scattering, and again find the SF
approach can provide high precision predictions for this process in way that
can straightforwardly account for any fiducial cuts imposed. Finally, we
provide a publicly available Monte Carlo generator, SFGen, for PI lepton pair
production and lepton-lepton scattering within the SF approach, for use by the
community.
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The doped perovskite cobaltite La1-xSrxCoO3 (LSCO) has been advanced as a
model system for studying intrinsic magnetic phase separation. We have employed
a first-order reversal curve (FORC) method to probe the amount of irreversible
switching in bulk polycrystalline LSCO as a function of Sr doping, field
cooling procedure, and temperature. The value of the FORC distribution, rho, is
used as a measure of the extent of irreversible switching. For x < 0.18, the
small values of rho and its ridge-like distribution along local coercivity (Hc)
and zero bias (Hb), are characteristic of non-interacting single domain
particles. This is consistent with the formation of an array of isolated
nanoscopic ferromagnetic clusters, as observed in previous work. For x >= 0.18,
the much larger values of rho, the tilting of its distribution towards negative
bias field, and the emergence of regions with negative rho, are consistent with
increased long-range ferromagnetic ordering. The FORC distributions display
little dependence on the cooling procedure. With increasing temperature, the
fraction of irreversible switching determined from the FORC distribution
follows closely the ferromagnetic phase fraction measured by La nuclear
magnetic resonance. Our results furthermore demonstrate that the FORC method is
a valuable first-pass characterization tool for magnetic phase separation.
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The two most fundamental processes describing change in biology, development
and evolu-tion, occur over drastically different timescales, difficult to
reconcile within a unified framework. Development involves temporal sequences
of cell states controlled by hierarchies of regulatory structures. It occurs
over the lifetime of a single individual, and is associated to the gene
expression level change of a given genotype. Evolution, by contrast entails
genotypic change through the acquisition/loss of genes and changes in the
network topology of interactions among genes. It involves the emergence of new,
environmentally selected phenotypes over the lifetimes of many individuals.
Here we present a model of regulatory network evolution that accounts for both
timescales. We extend the framework of Boolean models of gene regulatory
networks (GRN)-currently only applicable to describing development to include
evolutionary processes. As opposed to one-to-one maps to specific attractors,
we identify the phenotypes of the cells as the relevant macrostates of the GRN.
A phenotype may now correspond to multiple attractors, and its formal
definition no longer requires a fixed size for the genotype. This opens the
possibility for a quantitative study of the phenotypic change of a genotype,
which is itself changing over evolutionary timescales. We show how the
realization of specific phenotypes can be controlled by gene duplication events
(used here as an archetypal evolutionary event able to change the genotype),
and how successive events of gene duplication lead to new regulatory structures
via selection. At the same time, we show that our generalized framework does
not inhibit network controllability and the possibility for network control
theory to describe epigenetic signaling during development.
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A introduction to the syntax and Semantics of Answer Set Programming intended
as an handout to [under]graduate students taking Artificial Intlligence or
Logic Programming classes.
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Subsets and Splits