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With the great popularity of Graph Neural Networks (GNNs), their robustness
to adversarial topology attacks has received significant attention. Although
many attack methods have been proposed, they mainly focus on fixed-budget
attacks, aiming at finding the most adversarial perturbations within a fixed
budget for target node. However, considering the varied robustness of each
node, there is an inevitable dilemma caused by the fixed budget, i.e., no
successful perturbation is found when the budget is relatively small, while if
it is too large, the yielding redundant perturbations will hurt the
invisibility. To break this dilemma, we propose a new type of topology attack,
named minimum-budget topology attack, aiming to adaptively find the minimum
perturbation sufficient for a successful attack on each node. To this end, we
propose an attack model, named MiBTack, based on a dynamic projected gradient
descent algorithm, which can effectively solve the involving non-convex
constraint optimization on discrete topology. Extensive results on three GNNs
and four real-world datasets show that MiBTack can successfully lead all target
nodes misclassified with the minimum perturbation edges. Moreover, the obtained
minimum budget can be used to measure node robustness, so we can explore the
relationships of robustness, topology, and uncertainty for nodes, which is
beyond what the current fixed-budget topology attacks can offer.
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We study the galaxy stellar mass function in different environments in the
local Universe, considering both the total mass function and that of individual
galaxy morphological types. We compare the mass functions of galaxies with $\rm
log_{10} M_{\star}/M_{\odot} \geq 10.25$ in the general field and in galaxy
groups, binary and single galaxy systems from the Padova-Millennium Galaxy and
Group Catalogue at $z=0.04-0.1$ with the mass function of galaxy clusters of
the WIde-field Nearby Galaxy-Cluster Survey at $z=0.04-0.07$. Strikingly, the
variations of the mass function with global environment, overall, are small and
subtle. The shapes of the mass functions of the general field and clusters are
indistinguishable, and only small, statistically insignificant variations are
allowed in groups. Only the mass function of our single galaxies, representing
the least massive haloes and comprising less than a third of the general field
population, is proportionally richer in low-mass galaxies than other
environments. The most notable environmental effect is a progressive change in
the upper galaxy mass, with very massive galaxies found only in the most
massive environments. This environment-dependent mass cut-off is unable to
affect the Schechter parameters and the K-S test, and can only be revealed by
an ad-hoc analysis. Finally, we show how, in each given environment, the mass
function changes with morphological type, and that galaxies of the same
morphological type can have different mass functions in different environments.
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Point cloud registration is a fundamental problem in many domains.
Practically, the overlap between point clouds to be registered may be
relatively small. Most unsupervised methods lack effective initial evaluation
of overlap, leading to suboptimal registration accuracy. To address this issue,
we propose an unsupervised network Overlap Bias Matching Network (OBMNet) for
partial point cloud registration. Specifically, we propose a plug-and-play
Overlap Bias Matching Module (OBMM) comprising two integral components, overlap
sampling module and bias prediction module. These two components are utilized
to capture the distribution of overlapping regions and predict bias
coefficients of point cloud common structures, respectively. Then, we integrate
OBMM with the neighbor map matching module to robustly identify correspondences
by precisely merging matching scores of points within the neighborhood, which
addresses the ambiguities in single-point features. OBMNet can maintain
efficacy even in pair-wise registration scenarios with low overlap ratios.
Experimental results on extensive datasets demonstrate that our approach's
performance achieves a significant improvement compared to the state-of-the-art
registration approach.
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We introduce the notion of hyperfiniteness for permutation actions of
countable groups on countable sets and give a geometric and analytic
characterization, similar to the known characterizations for amenable actions.
We also answer a question of van Douwen on actions of the free group on two
generators on countable sets.
|
Higher-order connectivity patterns such as small induced sub-graphs called
graphlets (network motifs) are vital to understand the important components
(modules/functional units) governing the configuration and behavior of complex
networks. Existing work in higher-order clustering has focused on simple
homogeneous graphs with a single node/edge type. However, heterogeneous graphs
consisting of nodes and edges of different types are seemingly ubiquitous in
the real-world. In this work, we introduce the notion of typed-graphlet that
explicitly captures the rich (typed) connectivity patterns in heterogeneous
networks. Using typed-graphlets as a basis, we develop a general principled
framework for higher-order clustering in heterogeneous networks. The framework
provides mathematical guarantees on the optimality of the higher-order
clustering obtained. The experiments demonstrate the effectiveness of the
framework quantitatively for three important applications including (i)
clustering, (ii) link prediction, and (iii) graph compression. In particular,
the approach achieves a mean improvement of 43x over all methods and graphs for
clustering while achieving a 18.7% and 20.8% improvement for link prediction
and graph compression, respectively.
|
Solitonic scalar field configurations are studied in a theory coupled to
gravity. It is found that non-topological solitons, Q-balls, are present in the
theory. Properties of gravitationally self coupled Q-balls are studied by
analytical and numerical means. Analytical arguments show that, unlike in the
typical flat space scenario, the size of Q-balls is ultimately limited by
gravitational effects. Even though the largest Q-balls are very dense, their
radii are still much larger than the corresponding Schwarzschild radii. Gravity
can also act as a stabilising mechanism for otherwise energetically unstable
Q-balls.
|
Schnyder woods are a well-known combinatorial structure for plane
triangulations, which yields a decomposition into 3 spanning trees. We extend
here definitions and algorithms for Schnyder woods to closed orientable
surfaces of arbitrary genus. In particular, we describe a method to traverse a
triangulation of genus $g$ and compute a so-called $g$-Schnyder wood on the
way. As an application, we give a procedure to encode a triangulation of genus
$g$ and $n$ vertices in $4n+O(g \log(n))$ bits. This matches the worst-case
encoding rate of Edgebreaker in positive genus. All the algorithms presented
here have execution time $O((n+g)g)$, hence are linear when the genus is fixed.
|
We perform a systematic analysis of an extension of the Standard Model that
includes a complex singlet scalar field and is scale invariant at the tree
level. We call such a model the Minimal Scale Invariant extension of the
Standard Model (MSISM). The tree-level scale invariance of the model is
explicitly broken by quantum corrections, which can trigger electroweak
symmetry breaking and potentially provide a mechanism for solving the gauge
hierarchy problem. Even though the scale invariant Standard Model is not a
realistic scenario, the addition of a complex singlet scalar field may result
in a perturbative and phenomenologically viable theory. We present a complete
classification of the flat directions which may occur in the classical scalar
potential of the MSISM. After calculating the one-loop effective potential of
the MSISM, we investigate a number of representative scenarios and determine
their scalar boson mass spectra, as well as their perturbatively allowed
parameter space compatible with electroweak precision data. We discuss the
phenomenological implications of these scenarios, in particular, whether they
realize explicit or spontaneous CP violation, neutrino masses or provide dark
matter candidates. In particular, we find a new minimal scale-invariant model
of maximal spontaneous CP violation which can stay perturbative up to
Planck-mass energy scales, without introducing an unnaturally large hierarchy
in the scalar-potential couplings.
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In this work we present scattering functions of conjugates consisting of a
colloid particle and a self-avoiding polymer chain. This model is directly
derived from the two point correlation function with the inclusion of excluded
volume effects. The dependence of the calculated scattering function on the
geometric shapes of the colloid and polymer stiffness is investigated. In
comparison to existing experimental results, our model is found to be able to
describe the scattering signature of the colloid-polymer conjugates and provide
additional conformational information. This model explicitly elucidates the
link between the global conformation of a conjugate and the microstructure of
its constituent components.
|
In a recent computational campaign [Ng et al., Astrophys. J. 747, 109, 2012]
to investigate a three-dimensional model of coronal heating using reduced
magnetohydrodynamics (RMHD), we have obtained scaling results of heating rate
versus Lundquist number based on a series of runs in which random photospheric
motions are imposed for hundreds to thousands of Alfv\'en time in order to
obtain converged statistical values. Using this collection of numerical data,
we have performed additional statistical analysis related to the formation of
current sheets and heating events, or nanoflares [Parker, Astrophys. J. 330,
474, 1988]. While there have been many observations of the energy distribution
of solar flares, there have not been many results based on large-scale
three-dimensional direct simulations due to obvious numerical difficulties. We
will present energy distributions and other statistics based on our
simulations, calculated using a method employed in [Dmitruk & G\'omez,
Astrophys. J., 484, L83, 1997]. We will also make comparisons of our results
with observations.
|
The KdV hierarchy is a family of evolutions on a Schr\"odinger operator that
preserves its spectrum. Canonical systems are a generalization of Schr\"odinger
operators, that nevertheless share many features with Schr\"odinger operators.
Since this is a very natural generalization, one would expect that it would
also be straightforward to build a hierarchy of isospectral evolutions on
canonical systems analogous to the KdV hierarchy. Surprisingly, we show that
there are many obstructions to constructing a hierarchy of flows on canonical
systems that obeys the standard assumptions of the KdV hierarchy. This suggests
that we need a more sophisticated approach to develop such a hierarchy, if it
is indeed possible to do so.
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Differential equations with state-dependent delays define a semiflow of
continuously differentiable solution operators in general only on the
associated {\it solution manifold} in the Banach space
$C^1_n=C^1([-h,0],\mathbb{R}^n)$. For a prototypic example we develop a new
proof that its solution manifold is diffeomorphic to an open subset of the
subspace given by $\phi'(0)=0$, without recourse to a restrictive hypothesis
about the form of delays which is instrumental in earlier work on the nature of
solution manifolds. The new proof uses the framework of algebraic-delay
systems.
|
Projections of bipartite or two-mode networks capture co-occurrences, and are
used in diverse fields (e.g., ecology, economics, bibliometrics, politics) to
represent unipartite networks. A key challenge in analyzing such networks is
determining whether an observed number of co-occurrences between two nodes is
significant, and therefore whether an edge exists between them. One approach,
the fixed degree sequence model (FDSM), evaluates the significance of an edge's
weight by comparison to a null model in which the degree sequences of the
original bipartite network are fixed. Although the FDSM is an intuitive null
model, it is computationally expensive because it requires Monte Carlo
simulation to estimate each edge's $p$-value, and therefore is impractical for
large projections. In this paper, we explore four potential alternatives to
FDSM: fixed fill model (FFM), fixed row model (FRM), fixed column model (FCM),
and stochastic degree sequence model (SDSM). We compare these models to FDSM in
terms of accuracy, speed, statistical power, similarity, and ability to recover
known communities. We find that the computationally-fast SDSM offers a
statistically conservative but close approximation of the
computationally-impractical FDSM under a wide range of conditions, and that it
correctly recovers a known community structure even when the signal is weak.
Therefore, although each backbone model may have particular applications, we
recommend SDSM for extracting the backbone of bipartite projections when FDSM
is impractical.
|
This work combines three paradigms of image processing: i) the total
variation approach to denoising, ii) the superior structure of hexagonal
lattices, and iii) fast and exact graph cut optimization techniques. Although
isotropic in theory, numerical implementations of the $BV$ seminorm invariably
show anisotropic behaviour. Discretization of the image domain into a hexagonal
grid seems perfectly suitable to mitigate this undesirable effect. To this end,
we recast the continuous problem as a finite-dimensional one on an arbitrary
lattice, before focussing on the comparison of Cartesian and hexagonal
structures. Minimization is performed with well-established graph cut
algorithms, which are easily adapted to new spatial discretizations. Apart from
producing minimizers that are closer in the $\ell^1$ sense to the clean image
for sufficiently high degrees of regularization, our experiments suggest that
the hexagonal lattice also allows for a more effective reduction of two major
drawbacks of existing techniques: metrication artefacts and staircasing. For
the sake of practical relevance we address the difficulties that naturally
arise when dealing with non-standard images.
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Ultra-fast transmission electron microscopy (UTEM) combines sub-picosecond
time-resolution with the versatility of TEM spectroscopies. It allows one to
study the dynamics of materials properties combining complementary techniques.
However, until now, time-resolved cathodoluminescence, which is expected to
give access to the optical properties dynamics, was still unavailable in a
UTEM. In this paper, we report time-resolved cathodoluminescence measurements
in an ultrafast transmission electron microscope. We measured lifetime maps,
with a 12 nm spatial resolution and sub-nanoseconds resolution, of
nano-diamonds with a high density of NV center. This study paves the way to new
applications of UTEM and to correlative studies of optically active
nanostructures.
|
For an essentially small hereditary abelian category $\mathcal{A}$, we define
a new kind of algebra $\mathcal{H}_{\Delta}(\mathcal{A})$, called the
$\Delta$-Hall algebra of $\mathcal{A}$. The basis of
$\mathcal{H}_{\Delta}(\mathcal{A})$ is the isomorphism classes of objects in
$\mathcal{A}$, and the $\Delta$-Hall numbers calculate certain three-cycles of
exact sequences in $\mathcal{A}$. We show that the $\Delta$-Hall algebra
$\mathcal{H}_{\Delta}(\mathcal{A})$ is isomorphic to the 1-periodic derived
Hall algebra of $\mathcal{A}$. By taking suitable extension and twisting, we
can obtain the $\imath$Hall algebra and the semi-derived Hall algebra
associated to $\mathcal{A}$ respectively.
When applied to the the nilpotent representation category $\mathcal{A}={\rm
rep^{nil}}(\mathbf{k} Q)$ for an arbitrary quiver $Q$ without loops, the
(\emph{resp.} extended) $\Delta$-Hall algebra provides a new realization of the
(\emph{resp.} universal) $\imath$quantum group associated to $Q$.
|
In the paper we discuss the angular correlation present in hadron-hadron
collisions at large rapidity difference ($\bas\,y_{12}\,\gg\,1$). We find that
in the CGC/saturation approach the largest contribution stems from the density
variation mechanism. Our principal results are that the odd Fourier
harmonics($v_{2n+1}$), decrease substantially as function of $y_{12}$, while
the even harmonics ($v_{2n}$ ), increase considerably with a growth of
$y_{12}$.
|
Methods are developed for constructing spectral representations of cold
(barotropic) neutron-star equations of state. These representations are
faithful in the sense that every physical equation of state has a
representation of this type, and conversely every such representation satisfies
the minimal thermodynamic stability criteria required of any physical equation
of state. These spectral representations are also efficient, in the sense that
only a few spectral coefficients are generally required to represent
neutron-star equations of state quiet accurately. This accuracy and efficiency
is illustrated by constructing spectral fits to a large collection of
"realistic" neutron-star equations of state.
|
The laws of quantum physics can be studied under the mathematical operation T
that inverts the direction of time. Strong and electromagnetic forces are known
to be invariant under temporal inversion, however the weak force is not. The
BaBar experiment recently exploited the quantum-correlated production of pairs
of B0 mesons to show that T is a broken symmetry. Here we show that it is
possible to perform a wide range of tests of quark flavour changing processes
under T in order to validate the Standard Model of particle physics covering b
to u, d, s, and c transitions as well as c to u, d and s transitions using
entangled B and D pairs created in Y(4S) and psi(3770) decays. We also note
that pseudoscalar decays to two spin one particle final states provide an
additional set of CP filter bases to use for T violation tests.
|
Motivated by the thermal transport problem in the Kitaev spin liquids, we
consider a nearest-neighbor tight-binding model on the honeycomb lattice in the
presence of random uncorrelated $\pi$-fluxes. We employ different numerical
methods to study its transport properties near half-filling. The
zero-temperature DC conductivity away from the Dirac point is found to be
quadratic in Fermi momentum and inversely proportional to the flux density.
Localization due to the random $\pi$-fluxes is observed and the localization
length is extracted. Our results imply that, for realistic system size, the
thermal conductivity of a pure Kitaev spin liquid diverges as
$\kappa_\text{K}\sim T^3 e^{\Delta_v/k_BT}$ when $k_B T\ll \Delta_v$, and
suggest the possible occurrence of strong Majorana localization
$\kappa_\text{K}/T\ll k_B^2/2\pi\hbar$ when $k_B T\sim \Delta_v$, where
$\Delta_v$ is the vison gap.
|
We look at the magnetic field induced weak localisation peak of graphene
samples with different mobilities. At very low temperatures, low mobility
samples exhibit a very broad peak as a function of the magnetic field, in
contrast to higher mobility samples, where the weak localisation peak is very
sharp. We analyze the experimental data in the context of the localisation
length, which allows us to extract, both the localisation length and the phase
coherence length of the samples, regardless of their mobilities. This analysis
is made possible by the observation that the localisation length undergoes a
generic weak localisation dependence with striking universal properties.
|
Fractional differential (and difference) operators play a role in a number of
diverse settings: integrable systems, mirror symmetry, Hurwitz numbers, the
Bethe ansatz equations. We prove extensions of the three major results on
algebras of commuting (ordinary) differentials operators to the setting of
fractional differential operators: (1) the Burchnall-Chaundy theorem that a
pair of commuting differential operators is algebraically dependent, (2) the
classification of maximal commutative algebras of differential operators in
terms of Sato's theory and (3) the Krichever correspondence constructing those
of rank 1 in an algebro-geometric way. Unlike the available proofs of the
Burchnall-Chaundy theorem which use the action of one differential operator on
the kernel of the other, our extension to the fractional case uses bounds on
orders of fractional differential operators and growth of algebras, which also
presents a new and much shorter proof of the original result. The second main
theorem is achieved by developing a new tool of the spectral field of a point
in Sato's Grassmannian, which carries more information than the widely used
notion of spectral curve of a KP solution. Our Krichever type correspondence
for fractional differential operators is based on infinite jet bundles.
|
Based on the (3+1)-dimensional hydrodynamic model, the space-time evolution
of hot and dense nuclear matter produced in non-central relativistic heavy-ion
collisions is discussed. The elliptic flow parameter v_2 is obtained by Fourier
analysis of the azimuthal distribution of pions and protons which are emitted
from the freeze-out hypersurface. As a function of rapidity, the pion and
proton elliptic flow parameters both have a peak at midrapidity.
|
In this paper, we generalize Jordan-Lee-Preskill, an algorithm for simulating
flat-space quantum field theories, to 3+1 dimensional inflationary spacetime.
The generalized algorithm contains the encoding treatment, the initial state
preparation, the inflation process, and the quantum measurement of cosmological
observables at late time. The algorithm is helpful for obtaining predictions of
cosmic non-Gaussianities, serving as useful benchmark problems for quantum
devices, and checking assumptions made about interacting vacuum in the
inflationary perturbation theory.
Components of our work also include a detailed discussion about the lattice
regularization of the cosmic perturbation theory, a detailed discussion about
the in-in formalism, a discussion about encoding using the HKLL-type formula
that might apply for both dS and AdS spacetimes, a discussion about bounding
curvature perturbations, a description of the three-party Trotter simulation
algorithm for time-dependent Hamiltonians, a ground state projection algorithm
for simulating gapless theories, a discussion about the quantum-extended
Church-Turing Thesis, and a discussion about simulating cosmic reheating in
quantum devices.
|
We demonstrate a monolithic III-V photonic circuit combining a heralded
single photon source with a beamsplitter, at room temperature and telecom
wavelength. Pulsed parametric down-conversion in an AlGaAs waveguide generates
counterpropagating photons, one of which is used to herald the injection of its
twin into the beamsplitter. We use this configuration to implement an
integrated Hanbury-Brown and Twiss experiment, yielding a heralded second-order
correlation $g^{(2)}_{\rm her}(0)=0.10 \pm 0.02$ that confirms single-photon
operation. The demonstrated generation and manipulation of quantum states on a
single III-V semiconductor chip opens promising avenues towards real-world
applications in quantum information.
|
Van der Waals (vdW) layered materials have drawn tremendous interests due to
their unique properties. Atom intercalation in the vdW gap of layered materials
can tune their electronic structure and generate unexpected properties. Here we
report a chemical-scissor mediated method that enables metal intercalation into
transition metal dichalcogenides (TMDCs) in molten salts. By using this
approach, various guest metal atoms (Mn, Fe, Co, Ni, Cu, and Ag) were
intercalated into various TMDCs hosts (such as TiS2, NbS2, TaS2, TiSe2, NbSe2,
TaSe2 and Ti0.5V0.5S2). The structure of the intercalated compound and
intercalation mechanism was investigated. The results indicate that the vdW gap
and valence state of TMDCs can be modified through metal intercalation, and the
intercalation behavior is dictated by the electron work function. Such a
chemical-scissor mediated intercalation provides an approach to tune the
physical and chemical properties of TMDCs, which may open an avenue in
functional application ranging from energy conversion to electronics.
|
This paper addresses the problem of exponential practical stabilization of
linear time-invariant systems with disturbances using event-triggered control
and bounded communication bit rate. We consider both the case of instantaneous
communication with finite precision data at each transmission and the case of
non-instantaneous communication with bounded communication rate. Given a
prescribed rate of convergence, the proposed event-triggered control
implementations opportunistically determine the transmission instants and the
finite precision data to be transmitted on each transmission. We show that our
design exponentially practically stabilizes the origin while guaranteeing a
uniform positive lower bound on the inter-transmission and inter-reception
times, ensuring that the number of bits transmitted on each transmission is
upper bounded uniformly in time, and allowing for the possibility of
transmitting fewer bits at any given time if more bits than prescribed were
transmitted earlier. We also characterize the necessary and sufficient average
data rate for exponential practical stabilization. Several simulations
illustrate the results.
|
The {\em overlap number} of a finite $(d+1)$-uniform hypergraph $H$ is
defined as the largest constant $c(H)\in (0,1]$ such that no matter how we map
the vertices of $H$ into $\R^d$, there is a point covered by at least a
$c(H)$-fraction of the simplices induced by the images of its hyperedges.
In~\cite{Gro2}, motivated by the search for an analogue of the notion of graph
expansion for higher dimensional simplicial complexes, it was asked whether or
not there exists a sequence $\{H_n\}_{n=1}^\infty$ of arbitrarily large
$(d+1)$-uniform hypergraphs with bounded degree, for which $\inf_{n\ge 1}
c(H_n)>0$. Using both random methods and explicit constructions, we answer this
question positively by constructing infinite families of $(d+1)$-uniform
hypergraphs with bounded degree such that their overlap numbers are bounded
from below by a positive constant $c=c(d)$. We also show that, for every $d$,
the best value of the constant $c=c(d)$ that can be achieved by such a
construction is asymptotically equal to the limit of the overlap numbers of the
complete $(d+1)$-uniform hypergraphs with $n$ vertices, as
$n\rightarrow\infty$. For the proof of the latter statement, we establish the
following geometric partitioning result of independent interest. For any $d$
and any $\epsilon>0$, there exists $K=K(\epsilon,d)\ge d+1$ satisfying the
following condition. For any $k\ge K$, for any point $q \in \mathbb{R}^d$ and
for any finite Borel measure $\mu$ on $\mathbb{R}^d$ with respect to which
every hyperplane has measure $0$, there is a partition $\mathbb{R}^d=A_1 \cup
\ldots \cup A_{k}$ into $k$ measurable parts of equal measure such that all but
at most an $\epsilon$-fraction of the $(d+1)$-tuples
$A_{i_1},\ldots,A_{i_{d+1}}$ have the property that either all simplices with
one vertex in each $A_{i_j}$ contain $q$ or none of these simplices contain
$q$.
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Although the Large Hadron Collider (LHC) has not observed supersymmetric
(SUSY) partners of the Standard Model particles, their existence is not ruled
out yet. One recently explored scenario in which there are light SUSY partners
that have evaded current bounds from the LHC is that of a light long-lived stop
quark. In this paper we consider light stop pair production at the LHC when the
stop mass is between 200 and 400 GeV. If the stops are long-lived they can form
a bound state, stoponium, which then undergoes two-body decays to Standard
Model particles. By considering the near-threshold production of such a pair
through the gluon-gluon fusion process and taking into account the strong
Coulombic interactions responsible for the formation of this bound state, we
obtain factorization theorems for the stop pair inclusive and differential
production cross sections. We also perform a resummation of large threshold
logarithms up to next-to-next-to-leading logarithmic accuracy using
well-established renormalization group equations in an effective field theory
methodology. These results are used to calculate the invariant mass
distributions of two photons or two Z bosons coming from the decay of the
stoponium at the LHC. For our choices of SUSY model parameters, the stoponium
is not detectable above Standard Model backgrounds in \gamma \gamma or ZZ at 8
TeV, but will be visible with 400 fb^(-1) of accumulated data if its mass is
below 500 GeV when the LHC runs at 14 TeV.
|
In January 3, 2009, Satoshi Nakamoto gave rise to the "Bitcoin Block Chain"
creating the first block of the chain hashing on his computers central
processing unit (CPU). Since then, the hash calculations to mine Bitcoin have
been getting more and more complex, and consequently the mining hardware
evolved to adapt to this increasing difficulty. Three generations of mining
hardware have followed the CPU's generation. They are GPU's, FPGA's and ASIC's
generations. This work presents an agent based artificial market model of the
Bitcoin mining process and of the Bitcoin transactions. The goal of this work
is to model the economy of the mining process, starting from GPU's generation,
the first with economic significance. The model reproduces some "stylized
facts" found in real time price series and some core aspects of the mining
business. In particular, the computational experiments performed are able to
reproduce the unit root property, the fat tail phenomenon and the volatility
clustering of Bitcoin price series. In addition, under proper assumptions, they
are able to reproduce the price peak at the end of November 2013, its next fall
in April 2014, the generation of Bitcoins, the hashing capability, the power
consumption, and the mining hardware and electrical energy expenses of the
Bitcoin network.
|
In the coming years a new insight into galaxy formation and the thermal
history of the Universe is expected to come from the detection of the highly
redshifted cosmological 21 cm line. The cosmological 21 cm line signal is
buried under Galactic and extragalactic foregrounds which are likely to be a
few orders of magnitude brighter. Strategies and techniques for effective
subtraction of these foreground sources require a detailed knowledge of their
structure in both intensity and polarization on the relevant angular scales of
1-30 arcmin. We present results from observations conducted with the Westerbork
telescope in the 140-160 MHz range with 2 arcmin resolution in two fields
located at intermediate Galactic latitude, centred around the bright quasar
3C196 and the North Celestial Pole. They were observed with the purpose of
characterizing the foreground properties in sky areas where actual observations
of the cosmological 21 cm line could be carried out. The polarization data were
analysed through the rotation measure synthesis technique. We have computed
total intensity and polarization angular power spectra. Total intensity maps
were carefully calibrated, reaching a high dynamic range, 150000:1 in the case
of the 3C196 field. [abridged]
|
Fluorescence resonance energy transfer (FRET) is widely used as a
'spectroscopic ruler' to measure fluctuations in macromolecules because of the
strong dependence of the rate on the separation (R) between the donor (D) and
acceptor (A). However, the well-known Forster rate expression that predicts an
$R^{-6}$ dependence, is limited by several approximations. Notable among them
is the neglect of the vibronic relaxation in the reactant (donor) and product
(acceptor) manifolds. Vibronic relaxation can play an important role when the
energy transfer rate is faster than the vibronic relaxation rate. Under such
conditions, donor to acceptor energy transfer can occur from the excited
vibronic states. This phenomenon is not captured by the usual formulation based
on the overlap of donor emission and acceptor absorption spectra. Here, we
attempt to eliminate this lacuna, by allowing relaxation in the vibronic energy
levels and adopting a relaxation model to account for vibronic cascading down
in the donor manifold. We develop a Green's function based generalized
formalism and provide an exact solution for the excited state population
relaxation and the rate of energy transfer in the presence of vibronic
relaxation. We find and verify that the neglect of vibronic relaxations can
significantly alter the energy transfer rate and overestimates the distance
between D and A.
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We investigate the possibility of constructing Kochen-Specker uncolorable
sets of idempotent matrices whose entries lie in various rings, including the
rational numbers, the integers, and finite fields. Most notably, we show that
there is no Kochen-Specker coloring of the $n \times n$ idempotent integer
matrices for $n \geq 3$, thereby illustrating that Kochen-Specker contextuality
is an inherent feature of pure matrix algebra. We apply this to generalize
recent no-go results on noncommutative spectrum functors, showing that any
contravariant functor from rings to sets (respectively, topological spaces or
locales) that restricts to the Zariski prime spectrum functor for commutative
rings must assign the empty set (respectively, empty space or locale) to the
matrix ring $M_n(R)$ for any integer $n \geq 3$ and any ring $R$. An appendix
by Alexandru Chirvasitu shows that Kochen-Specker colorings of idempotents in
partial subalgebras of $M_3(F)$ for a perfect field $F$ can be extended to
partial algebra morphisms into the algebraic closure of $F$.
|
For Verizon MediaDemand Side Platform(DSP), forecasting of ad campaign
performance not only feeds key information to the optimization server to allow
the system to operate on a high-performance mode, but also produces actionable
insights to the advertisers. In this paper, the forecasting problem for CPA
lines in the middle of the flight is investigated by taking the bidding
mechanism into account. The proposed methodology generates relationships
between various key performance metrics and optimization signals. It can also
be used to estimate the sensitivity of ad campaign performance metrics to the
adjustments of optimization signal, which is important to the design of a
campaign management system. The relationship between advertiser spends and
effective Cost Per Action(eCPA) is also characterized, which serves as a
guidance for mid-flight line adjustment to the advertisers. Several practical
issues in implementation, such as downsampling of the dataset, are also
discussed in the paper. At last, the forecasting results are validated against
actual deliveries and demonstrates promising accuracy.
|
We consider the effect of parametric uncertainty on properties of Linear Time
Invariant systems. Traditional approaches to this problem determine the
worst-case gains of the system over the uncertainty set. Whilst such approaches
are computationally tractable, the upper bound obtained is not necessarily
informative in terms of assessing the influence of the parameters on the system
performance. We present theoretical results that lead to simple, convex
algorithms producing parametric bounds on the $\mathcal{L}_2$-induced
input-to-output and state-to-output gains as a function of the uncertain
parameters. These bounds provide quantitative information about how the
uncertainty affects the system.
|
A high level polarizable force field is used to study the temperature
dependence of hydrophobic hydration of small-sized molecules from computer
simulations. Molecular dynamics (MD) simulations of liquid water at various
temperatures form the basis of free energy perturbation calculations that
consider the onset and growth of a repulsive sphere. This repulsive sphere acts
as a model construct for the hydrophobic species. In the present study, an
extension is pursued for seven independent target temperatures, ranging from
close to the freezing point almost up to the boiling point of liquid water
under standard conditions. Care is taken to maintain proper physico-chemical
model descriptions by cross-checking with experimental water densities at the
selected target temperatures. The polarizable force field description of
molecular water turns out to be suitable throughout the entire temperature
domain considered. Derivatives of the computed free energies of hydrophobic
hydration with respect to the temperature give access to the changes in
entropy. In practice the entropy differential is determined from the negative
of the slope of tangential lines formed at a certain target temperature in the
free energy profile. The obtained changes in entropy are negative for
small-sized cavities, and hence reconfirm the basic ideas of the Lum Chandler
Weeks theory on hydrophobic hydration of small-sized solutes.
|
Let X_t be a totally disconnected subset of the real line R for each t in R.
We construct a partition {Y_t | t in R} of R into nowhere dense Lebesgue null
sets Y_t such that for every t in R there exists an increasing homeomorphism
from X_t onto Y_t. In particular, the real line can be partitioned into
2^{aleph_0} Cantor sets and also into 2^{aleph_0} mutually non-homeomorphic
compact subspaces. Furthermore we prove that for every cardinal number k with 2
\leq k \leq 2^{aleph_0} the real line (as well as the Baire space R\Q) can be
partitioned into exactly k homeomorphic Bernstein sets and also into exactly k
mutually non-homeomorphic Bernstein sets. We also investigate partitions of R
into Marczewski sets, including the possibility that they are Luzin sets or
Sierpinski sets.
|
The capability to switch electrically between superconducting and insulating
states of matter represents a novel paradigm in the state-of-the-art
engineering of correlated electronic systems. An exciting possibility is to
turn on superconductivity in a topologically non-trivial insulator, which
provides a route to search for non-Abelian topological states. However,
existing demonstrations of superconductor-insulator switches have involved only
topologically trivial systems, and even those are rare due to the stringent
requirement to tune the carrier density over a wide range. Here we report
reversible, in-situ electrostatic on off switching of superconductivity in a
recently established quantum spin Hall insulator, namely monolayer tungsten
ditelluride (WTe2). Fabricated into a van der Waals field effect transistor,
the monolayer's ground state can be continuously gate-tuned from the
topological insulating to the superconducting state, with critical temperatures
Tc up to ~ 1 Kelvin. The critical density for the onset of superconductivity is
estimated to be ~ 5 x 10^12 cm^-2, among the lowest for two-dimensional (2D)
superconductors. Our results establish monolayer WTe2 as a material platform
for engineering novel superconducting nanodevices and topological phases of
matter.
|
We consider the eigenvalue problem for one-dimensional linear Schr\"odinger
lattices (tight-binding) with an embedded few-sites linear or nonlinear,
Hamiltonian or non-conservative defect (an oligomer). Such a problem arises
when considering scattering states in the presence of (generally complex)
impurities as well as in the stability analysis of nonlinear waves. We describe
a general approach based on a matching of solutions of the linear portions of
the lattice at the location of the oligomer defect. As specific examples we
discuss both linear and nonlinear, Hamiltonian and $\cP \cT$-symmetric dimers
and trimers. In the linear case, this approach provides us a handle for
semi-analytically computing the spectrum [this amounts to the solution of a
polynomial equation]. In the nonlinear case, it enables the computation of the
linearization spectrum around the stationary solutions. The calculations
showcase the oscillatory instabilities that strongly nonlinear states typically
manifest.
|
We introduce a new representation concept for lattices by boolean matrices,
and utilize it to prove that any matroid is boolean representable. We show that
such a representation can be easily extracted from a representation of the
associated lattice of flats of the matroid, leading also to a tighter bound on
the representation's size. Consequently, we obtain a linkage of boolean
representations with geometry in a very natural way.
|
Certified defense methods against adversarial perturbations have been
recently investigated in the black-box setting with a zeroth-order (ZO)
perspective. However, these methods suffer from high model variance with low
performance on high-dimensional datasets due to the ineffective design of the
denoiser and are limited in their utilization of ZO techniques. To this end, we
propose a certified ZO preprocessing technique for removing adversarial
perturbations from the attacked image in the black-box setting using only model
queries. We propose a robust UNet denoiser (RDUNet) that ensures the robustness
of black-box models trained on high-dimensional datasets. We propose a novel
black-box denoised smoothing (DS) defense mechanism, ZO-RUDS, by prepending our
RDUNet to the black-box model, ensuring black-box defense. We further propose
ZO-AE-RUDS in which RDUNet followed by autoencoder (AE) is prepended to the
black-box model. We perform extensive experiments on four classification
datasets, CIFAR-10, CIFAR-10, Tiny Imagenet, STL-10, and the MNIST dataset for
image reconstruction tasks. Our proposed defense methods ZO-RUDS and ZO-AE-RUDS
beat SOTA with a huge margin of $35\%$ and $9\%$, for low dimensional
(CIFAR-10) and with a margin of $20.61\%$ and $23.51\%$ for high-dimensional
(STL-10) datasets, respectively.
|
Polyakov loops $L_a(T), a=3,8,...$ are shown to give the most important
nonperturbative contribution to the thermodynamic potentials. Derived from the
gluonic field correlators they enter as factors into free energy. It is shown
in the $SU(3)$ case that $L_a (T)$ define to a large extent the behavior of the
free energy and the trace anomaly $I(T)$, most sensitive to nonperturbative
effects.
|
Physical Unclonable Function (PUF) has recently attracted interested from
both industry and academia as a potential alternative approach to secure
Internet of Things (IoT) devices from the more traditional computational based
approach using conventional cryptography. PUF is promising solution for
lightweight security, where the manufacturing fluctuation process of IC is used
to improve the security of IoT as it provides low complexity design and
preserves secrecy. It provides less cost of computational resources which
prevent high power consumption and can be implemented in both Field
Programmable Gate Arrays (FPGA) and Application-Specific Integrated Circuits
(ASICs). In this survey we provide a comprehensive review of the
state-of-the-art of PUF, its architectures, protocols and security for IoT.
|
Recent advances in optimization methods used for training convolutional
neural networks (CNNs) with kernels, which are normalized according to
particular constraints, have shown remarkable success. This work introduces an
approach for training CNNs using ensembles of joint spaces of kernels
constructed using different constraints. For this purpose, we address a problem
of optimization on ensembles of products of submanifolds (PEMs) of convolution
kernels. To this end, we first propose three strategies to construct ensembles
of PEMs in CNNs. Next, we expound their geometric properties (metric and
curvature properties) in CNNs. We make use of our theoretical results by
developing a geometry-aware SGD algorithm (G-SGD) for optimization on ensembles
of PEMs to train CNNs. Moreover, we analyze convergence properties of G-SGD
considering geometric properties of PEMs. In the experimental analyses, we
employ G-SGD to train CNNs on Cifar-10, Cifar-100 and Imagenet datasets. The
results show that geometric adaptive step size computation methods of G-SGD can
improve training loss and convergence properties of CNNs. Moreover, we observe
that classification performance of baseline CNNs can be boosted using G-SGD on
ensembles of PEMs identified by multiple constraints.
|
Observation of the Fano line shapes is essential to understand properties of
the Fano resonance in different physical systems. We explore a tunable Fano
resonance by tuning the phase shift in a Mach-Zehnder interferometer (MZI)
based on a single-mode nano-optomechanical cavity. The Fano resonance is
resulted from the optomechanically induced transparency caused by a
nano-mechanical resonator and can be tuned by applying an optomechanical MZI.
By tuning the phase shift in one arm of the MZI, we can observe the
periodically varying line shapes of the Fano resonance, which represents an
elaborate manipulation of the Fano resonance in the nanoscale optomechanics.
|
We present SetExpander, a corpus-based system for expanding a seed set of
terms into amore complete set of terms that belong to the same semantic class.
SetExpander implements an iterative end-to-end workflow. It enables users to
easily select a seed set of terms, expand it, view the expanded set, validate
it, re-expand the validated set and store it, thus simplifying the extraction
of domain-specific fine-grained semantic classes.SetExpander has been used
successfully in real-life use cases including integration into an automated
recruitment system and an issues and defects resolution system. A video demo of
SetExpander is available at
https://drive.google.com/open?id=1e545bB87Autsch36DjnJHmq3HWfSd1Rv (some images
were blurred for privacy reasons)
|
W. Thurston proved that to a triangulation of the sphere of non-negative
combinatorial curvature, one can associate an element in a certain lattice over
the Eisenstein integers such that its orbit is a complete invariant of the
triangulation. In this paper, we show that this association can be obtained
naturally by using Type III degenerations of K3 surfaces.
|
In-plane and out-of-plane thermal conductivities (\kappa_{ab} and \kappa_{c})
are measured on single crystals of pure, 1%-hole-doped, and 1%-Zn-doped
La_{2}CuO_{4}. The roles of magnons and the spin stripes in the heat transport
in these samples are discussed. Comparison with the heat transport in
CuGeO_{3}, which shows similar \kappa(T) behavior as that of La_{2}CuO_{4},
gives us a lesson of how the heat transport can probe the difference in the
spin ground state.
|
In this paper, we show how to incorporate cubic and hexagonal anisotropies in
interfacial energies in phase field models; this incorporation is achieved by
including upto sixth rank tensor terms in the free energy expansion, assuming
that the free energy is only a function of coarse grained composition, its
gradient, curvature and aberration. We derive the number of non-zero and
independent components of these tensors. Further, by demanding that the
resultant interfacial energy is positive definite for inclusion of each of the
tensor terms individually, we identify the constraints imposed on the
independent components of these tensors. The existing results in the invariant
group theory literature can be used to simplify the process of construction of
some (but not all) of the higher order tensors. Finally, we derive the relevant
phase field evolution equations.
|
We show that a general purpose clusterization algorithm, Deterministic
Annealing, can be adapted to the problem of jet identification in particle
production by high energy collisions. In particular we consider the problem of
jet searching in events generated at hadronic colliders. Deterministic
Annealing is able to reproduce the results obtained by traditional jet
algorithms and to exhibit a higher degree of flexibility.
|
We study the global existence of classical solutions to volume-surface
reaction-diffusion systems with control of mass. Such systems appear naturally
from modeling evolution of concentrations or densities appearing both in a
volume domain and its surface, and therefore have attracted considerable
attention. Due to the characteristic volume-surface coupling, global existence
of solutions to general systems is a challenging issue. In particular, the
duality method, which is powerful in dealing with mass conserved systems in
domains, is not applicable on its own. In this paper, we introduce a new family
of $L^p$-energy functions and combine them with a suitable duality method for
volume-surface systems, to ultimately obtain global existence of classical
solutions under a general assumption called the \textit{intermediate sum
condition}. For systems that conserve mass, but do not satisfy this condition,
global solutions are shown under a quasi-uniform condition, that is, under the
assumption that the diffusion coefficients are close to each other. In the case
of mass dissipation, we also show that the solution is bounded uniformly in
time by studying the system on each time-space cylinder of unit size, and
showing that the solution is sup-norm bounded independently of the cylinder.
Applications of our results include global existence and boundedness for
systems arising from membrane protein clustering or activation of Cdc42 in cell
polarization.
|
We present an analog model for the Ba\~nados, Teitelboim, Zanelli (BTZ) black
hole based on a hydrodynamical flow. We numerically solve the fully nonlinear
hydrodynamic equations of motion and observe the excitation and decay of the
analog BTZ quasinormal modes in the process. We consider both a small
perturbation in the steady state configuration of the fluid and a large
perturbation; the latter could be regarded as an example of formation of the
analog (acoustic) BTZ black hole.
|
Four different ways of obtaining low-density parity-check codes from expander
graphs are considered. For each case, lower bounds on the minimum stopping set
size and the minimum pseudocodeword weight of expander (LDPC) codes are
derived. These bounds are compared with the known eigenvalue-based lower bounds
on the minimum distance of expander codes. Furthermore, Tanner's
parity-oriented eigenvalue lower bound on the minimum distance is generalized
to yield a new lower bound on the minimum pseudocodeword weight. These bounds
are useful in predicting the performance of LDPC codes under graph-based
iterative decoding and linear programming decoding.
|
The accuracy and precision of current atom-interferometric inertialsensors
rival state-of-the-art conventional devices using artifact-based test masses .
Atomic sensors are well suited for fundamental measurements of gravito-inertial
fields. The sensitivity required to test gravitational theories can be achieved
by extending the baseline of the interferometer. The I.C.E.
(Interf\'erom\'etrie Coh\'erente pour l'Espace) interferometer aims to achieve
long interrogation times in compact apparatus via reduced gravity. We have
tested a cold-atom source during airplane parabolic flights. We show that this
environment is compatible with free-fall interferometric measurements using up
to 4 second interrogation time. We present the next-generation apparatus using
degenerate gases for low release-velocity atomic sources in space-borne
experiments.
|
We use the {\it Gaia} EDR3 to explore the Galactic supernova remnant SNR
G272.2-3.2, produced by the explosion of a Type Ia supernova (SNIa), about
7,500 years ago, to search for a surviving companion. From the abundances in
the SNR ejecta, G272.2-3.2 is a normal SN Ia. The {\it Gaia} parallaxes allow
to select the stars located within the estimated distance range of the SNR, and
the {\it Gaia} proper motions to study their kinematics. From the {\it Gaia}
EDR3 photometry, we construct the HR diagram of the selected sample, which we
compare with the theoretical predictions for the evolution of possible star
companions of SNIa. We can discard several proposed types of companions by
combining kinematics and photometry. We can also discard hypervelocity stars.
We focus our study on the kinematically most peculiar star, {\it Gaia} EDR3
5323900215411075328 (hereafter MV-G272), a 8.9 $\sigma$ outlier in proper
motion. It is of M1-M2 stellar type. Its trajectory on the sky locates it at
the center of the SNR, 6,000--8,000 years ago, a unique characteristic among
the the sample. Spectra allow a stellar parameters determination and a chemical
abundance analysis. In conclusion, we have a candidate to be the surviving
companion of the SN Ia that resulted in SNR G272.2-3.2. It is supported by its
kinematical characteristics and its trajectory within the SNR. This opens the
possibility of a single-degenerate scenario for a SN Ia with an M-type dwarf
companion.
|
The autocorrelation function of the force acting on a slow classical system,
resulting from interaction with a fast quantum system is calculated following
Berry-Robbins and Jarzynski within the leading order correction to the
adiabatic approximation. The time integral of the autocorrelation function is
proportional to the rate of dissipation. The fast quantum system is assumed to
be chaotic in the classical limit for each configuration of the slow system. An
analytic formula is obtained for the finite time integral of the correlation
function, in the framework of random matrix theory (RMT), for a specific
dependence on the adiabatically varying parameter. Extension to a wider class
of RMT models is discussed. For the Gaussian unitary and symplectic ensembles
for long times the time integral of the correlation function vanishes or falls
off as a Gaussian with a characteristic time that is proportional to the
Heisenberg time, depending on the details of the model. The fall off is
inversely proportional to time for the Gaussian orthogonal ensemble. The
correlation function is found to be dominated by the nearest neighbor level
spacings. It was calculated for a variety of nearest neighbor level spacing
distributions, including ones that do not originate from RMT ensembles. The
various approximate formulas obtained are tested numerically in RMT. The
results shed light on the quantum to classical crossover for chaotic systems.
The implications on the possibility to experimentally observe deterministic
friction are discussed.
|
In this paper, we study the geometry associated with Schroedinger operator
via Hamiltonian and Lagrangian formalism. Making use of a multiplier technique,
we construct the heat kernel with the coefficient matrices of the operator both
diagonal and non-diagonal. For applications, we compute the heat kernel of a
Schroedinger operator with terms of lower order, and obtain a globally closed
solution to a matrix Riccati equations as a by-product. Besides, we finally
recover and generalise several classical results on some celebrated operators.
|
We present IRAM 30m observations of molecular lines of CO and its
isotopologues from the massive spiral galaxy NGC 5908 selected from the
CGM-MASS sample. $^{12}$CO $J=1-0$, $^{12}$CO $J=2-1$, and $^{13}$CO $J=1-0$
lines have been detected in most of the positions along the galactic disk. The
total molecular gas mass of NGC 5908 is $\sim7\times10^9\rm~M_\odot$ and the
total cool gas mass adding atomic hydrogen is
$\sim1.3\times10^{10}\rm~M_\odot$, comparable to the upper limit of the mass of
the X-ray emitting hot gas in the halo. Modeling the rotation curves
constructed with all three CO lines indicates that NGC 5908 has a dark matter
halo mass of $M_{\rm vir}\sim10^{13}\rm~M_{\rm \odot}$, putting it among the
most massive isolated spiral galaxies. The $^{12}$CO/$^{13}$CO $J=1-0$,
$^{12}$CO $J=2-1$/$J=1-0$ line ratios and the estimated molecular gas
temperature all indicate normal but non-negligible star formation in this
fairly gas-rich massive isolated spiral galaxy, consistent with the measured
star formation intensity and surface densities. The galaxy is probably at an
early evolutionary stage after a fast growth stage with mergers and/or
starbursts, with plenty of leftover cool gas, relatively high SFR, low hot CGM
cooling rate, and low X-ray emissivity.
|
In this work, the sharp interface limit of the degenerate Cahn-Hilliard
equation (in two space dimensions) with a polynomial double well free energy
and a quadratic mobility is derived via a matched asymptotic analysis involving
exponentially large and small terms and multiple inner layers. In contrast to
some results found in the literature, our analysis reveals that the interface
motion is driven by a combination of surface diffusion flux proportional to the
surface Laplacian of the interface curvature and an additional contribution
from nonlinear, porous-medium type bulk diffusion, For higher degenerate
mobilities, bulk diffusion is subdominant. The sharp interface models are
corroborated by comparing relaxation rates of perturbations to a radially
symmetric stationary state with those obtained by the phase field model.
|
Let K be a subfield of the real field, D be a discrete subset of K and f :
D^n -> K be a function such that f(D^n) is somewhere dense. Then (K,f) defines
the set of integers. We present several applications of this result. We show
that K expanded by predicates for different cyclic multiplicative subgroups
defines the set of integers. Moreover, we prove that every definably complete
expansion of a subfield of the real field satisfies an analogue of the Baire
Category Theorem.
|
A primary goal of numerical relativity is to provide estimates of the wave
strain, $h$, from strong gravitational wave sources, to be used in detector
templates. The simulations, however, typically measure waves in terms of the
Weyl curvature component, $\psi_4$. Assuming Bondi gauge, transforming to the
strain $h$ reduces to integration of $\psi_4$ twice in time. Integrations
performed in either the time or frequency domain, however, lead to secular
non-linear drifts in the resulting strain $h$. These non-linear drifts are not
explained by the two unknown integration constants which can at most result in
linear drifts. We identify a number of fundamental difficulties which can arise
from integrating finite length, discretely sampled and noisy data streams.
These issues are an artifact of post-processing data. They are independent of
the characteristics of the original simulation, such as gauge or numerical
method used. We suggest, however, a simple procedure for integrating numerical
waveforms in the frequency domain, which is effective at strongly reducing
spurious secular non-linear drifts in the resulting strain.
|
In this paper, we establish equiform differential geometry of space and
timelike curves in 4-dimensional Minkowski space. We obtain some conditions for
these curves. Also, general helices with respect to their equiform curvatures
are characterized.
|
After recalling briefly the main properties of the amalgamated duplication of
a ring $R$ along an ideal $I$, denoted by $R\JoinI$, we restrict our attention
to the study of the properties of $R\JoinI$, when $I$ is a multiplicative
canonical ideal of $R$ \cite{hhp}. In particular, we study when every regular
fractional ideal of $R\Join I$ is divisorial.
|
We consider real symmetric and complex Hermitian random matrices with the
additional symmetry $h_{xy}=h_{N-x,N-y}$. The matrix elements are independent
(up to the fourfold symmetry) and not necessarily identically distributed. This
ensemble naturally arises as the Fourier transform of a Gaussian orthogonal
ensemble (GOE). It also occurs as the flip matrix model - an approximation of
the two-dimensional Anderson model at small disorder. We show that the density
of states converges to the Wigner semicircle law despite the new symmetry type.
We also prove the local version of the semicircle law on the optimal scale.
|
We report observations of a stellar occultation by the classical Kuiper belt
object (50000) Quaoar occurred on 28 June 2019. A single-chord high-cadence (2
Hz) photometry dataset was obtained with the Tomo-e Gozen CMOS camera mounted
on the 1.05 m Schmidt telescope at Kiso Observatory. The obtained ingress and
egress data do not show any indication of atmospheric refraction and allow to
set new $1\sigma$ and $3\sigma$ upper limits of 6 and 16 nbar, respectively,
for the surface pressure of a pure methane atmosphere. These upper limits are
lower than the saturation vapor pressure of methane at Quaoar's expected mean
surface temperature ($T \sim 44$ K) and imply the absence of a $\sim$10
nbar-level global atmosphere formed by methane ice on Quaoar's surface.
|
We present new upper and lower bounds on the number of learner mistakes in
the `transductive' online learning setting of Ben-David, Kushilevitz and
Mansour (1997). This setting is similar to standard online learning, except
that the adversary fixes a sequence of instances $x_1,\dots,x_n$ to be labeled
at the start of the game, and this sequence is known to the learner.
Qualitatively, we prove a trichotomy, stating that the minimal number of
mistakes made by the learner as $n$ grows can take only one of precisely three
possible values: $n$, $\Theta\left(\log (n)\right)$, or $\Theta(1)$.
Furthermore, this behavior is determined by a combination of the VC dimension
and the Littlestone dimension. Quantitatively, we show a variety of bounds
relating the number of mistakes to well-known combinatorial dimensions. In
particular, we improve the known lower bound on the constant in the $\Theta(1)$
case from $\Omega\left(\sqrt{\log(d)}\right)$ to $\Omega(\log(d))$ where $d$ is
the Littlestone dimension. Finally, we extend our results to cover multiclass
classification and the agnostic setting.
|
We propose a very simple physical mechanism responsible for the formation of
the Low Ionization Line part of the Broad Line Region in Active Galactic
Nuclei. It explains the scaling of the Broad Line Region size with the
monochromatic luminosity, including the exact slope and the proportionality
constant, seen in the reverberation studies of nearby sources. The scaling is
independent from the mass and accretion rate of an active nucleus. The
mechanism predicts the formation of a dust-driven wind in the disk region where
the local effective temperature of a non-illuminated accretion disk drops below
1000 K and allows for dust formation. We explore now the predictive power of
the model with the aim to differentiate between this model and the previously
proposed mechanisms of the formation of the Broad Line Region. We discuss the
expected departures from the universal scaling at long wavelength, and the role
of the inclination angle of the accretion disk in the source. We compare the
expected line profiles with Mg II line profiles in the quasars observed by us
with the SALT telescope. We also discuss the tests based on the presence or
absence of the broad emission lines in low luminosity active galaxies. Finally,
we discuss the future tests of the model to be done with expected ground-based
observations and satellite missions.
|
Augmented Zagreb Index is a newly defined degree based topological invariant
which has been well established for its better correlation properties and is
defined as $AZI(G)= \sum_{uv\in E(G)}(\frac{d_G (u)d_G (v)}{d_G (u)+ d_G
(v)-2})^3 $, where $E(G)$ is the edge set of graph $G$ and $d(u),\,\,d(v)$ are
the degrees of the end vertices $u$ and $v$ of edge $uv$, respectively. It has
outperformed many well known degree based topological indices. In this article
we give closed formulae for the augmented Zagreb index of arm-chair polyhex and
zigzag edge polyhex nanotubes.
|
We address the correlations of black hole (BH) mass with four different
host-galaxy properties from eleven existing data sets. To guide theoretical
understanding, we first try to quantify the tightness of the intrinsic
correlations. Given the estimated measurement errors, we evaluate the
probability distribution of the residual variance in excess of that expected
from the measurement errors. Our central result is that the current data sets
do not allow definite conclusions regarding the quality of the true
correlations because the obtained probability distributions for the residual
variance overlap for most quantities. We then consider which of the relations
offer the best inferences of BH mass when there is no direct measurement
available. As with the residual variances, we find that the probability
distribution of expected uncertainty in inferred BH masses overlaps
significantly for most of the relations. Photometric methods would then be
preferred because the data are easier to obtain, as long as bulge-disk
decomposition or detailed modeling of the photometric profile (as in
\citet{graham:01}) do not present problems. Determining which correlation
offers the best inferences requires reducing the uncertainty in the expected
error in the inferred BH masses (the ``error on the error''). This uncertainty
is currently limited by uncertainty in the residual variance for all of the
relations.
|
Dynamic movement primitives are widely used for learning skills which can be
demonstrated to a robot by a skilled human or controller. While their
generalization capabilities and simple formulation make them very appealing to
use, they possess no strong guarantees to satisfy operational safety
constraints for a task. In this paper, we present constrained dynamic movement
primitives (CDMP) which can allow for constraint satisfaction in the robot
workspace. We present a formulation of a non-linear optimization to perturb the
DMP forcing weights regressed by locally-weighted regression to admit a Zeroing
Barrier Function (ZBF), which certifies workspace constraint satisfaction. We
demonstrate the proposed CDMP under different constraints on the end-effector
movement such as obstacle avoidance and workspace constraints on a physical
robot. A video showing the implementation of the proposed algorithm using
different manipulators in different environments could be found here
https://youtu.be/hJegJJkJfys.
|
We study to what extent Lieb--Thirring inequalities are extendable from
self-adjoint to general (possibly non-self-adjoint) Jacobi and Schr\"{o}dinger
operators. Namely, we prove the conjecture of Hansmann and Katriel from
[Complex Anal. Oper. Theory 5, No. 1 (2011), 197-218] and answer another open
question raised therein. The results are obtained by means of asymptotic
analysis of eigenvalues of discrete Schr\"{o}dinger operators with rectangular
barrier potential and complex coupling. Applying the ideas in the continuous
setting, we also solve a similar open problem for one-dimensional
Schr\"{o}dinger operators with complex-valued potentials published by Demuth,
Hansmann, and Katriel in [Integral Equations Operator Theory 75, No. 1 (2013),
1-5].
|
We investigate the predictive power of Collins, Soper, and Sterman's
$b$-space QCD resummation formalism for transverse momentum ($Q_T$)
distributions of heavy boson production in hadronic collisions. We show that
the predictive power of the resummation formalism has a strong dependence on
the collision energy $\sqrt{S}$ in addition to its well-known $Q^2$ dependence,
and the $\sqrt{S}$ dependence improves the predictive power at collider
energies. We demonstrate that at Tevatron and the LHC energies, the $Q_T$
distributions derived from $b$-space resummation are not sensitive to the
nonperturbative input at large $b$, and give good descriptions of the $Q_T$
distributions of heavy boson production at all transverse momenta $Q_T \leq Q$.
|
For a planar directed graph G, Postnikov's boundary measurement map sends
positive weight functions on the edges of G onto the appropriate totally
nonnegative Grassmann cell. We establish an explicit formula for Postnikov's
map by expressing each Pluecker coordinate as a ratio of two combinatorially
defined polynomials in the edge weights, with positive integer coefficients. In
the non-planar setting, we show that a similar formula holds for special
choices of Pluecker coordinates.
|
Let $\g$ be an affine Kac-Moody Lie algebra. Let $\U^+$ be the positive part
of the Drinfeld-Jimbo quantum enveloping algebra associated to $\g$. We
construct a basis of $\U^+$ which is related to the Kashiwara-Lusztig global
crystal basis (or canonical basis) by an upper triangular matrix (with respect
to an explicitly defined ordering) with 1's on the diagonal and with above
diagonal entries in $q_s^{-1} \Z[q_s^{-1}]$. Using this construction we study
the global crystal basis $\B(\Um)$ of the modified quantum enveloping algebra
defined by Lusztig. We obtain a Peter-Weyl like decomposition of the crystal
$\B(\Um)$ (Theorem 4.18), as well as an explicit description of two-sided cells
of $\B(\Um)$ and the limit algebra of $\Um$ at $q=0$ (Theorem 6.45).
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We discover a break in the GRB 011121 afterglow light curve after 1.3 days,
which implies an initial jet opening angle of about 9 deg. The SED during the
first four days is achromatic, and supports the jet origin of this break. The
SED during the supernova bump can be best represented by a black body with a
temperature of 6000 K. The deduced parameters for the decay slope as well as
the spectral index favor a wind scenario, i.e. an outflow into a circum-burst
environment shaped by the stellar wind of a massive GRB progenitor. Due to its
low redshift of z=0.36, GRB 011121 has been the best example for the
GRB-supernova connection until GRB 030329, and provides compelling evidence for
a circum-burster wind region expected to exist if the progenitor was a massive
star.
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Let $X$ be a smooth, complete and connected curve and $G$ be a simple and
simply connected algebraic group over $\comp$. We calculate the Picard group of
the moduli stack of quasi-parabolic $G$-bundles and identify the spaces of
sections of its members to the conformal blocs of Tsuchiya, Ueno and Yamada. We
describe the canonical sheaf on these stacks and show that they admit a unique
square root, which we will construct explicitly. Finally we show how the
results on the stacks apply to the coarse moduli spaces and recover (and
extend) the Drezet-Narasimhan theorem. We show moreover that the coarse moduli
spaces of semi-stable $SO_r$-bundles are not locally factorial for $r\geq 7$.
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The magnetic phases induced by the interplay between disorder acting only on
particles with a given spin projection ("spin-dependent disorder") and a local
repulsive interaction is explored. To this end the magnetic ground state phase
diagram of the Hubbard model at half-filling is computed within dynamical
mean-field theory combined with the geometric average over disorder, which is
able to describe Anderson localization. Five distinct phases are identified: a
ferromagnetically polarized metal, two types of insulators, and two types of
spin-selective localized phases. The latter four phases possess different
long-range order of the spins. The predicted phase diagram may be tested
experimentally using cold fermions in optical lattices subject to
spin-dependent random potentials.
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In this survey, we review some of the low energy quantum predictions of
General Relativity which are independent of details of the yet unknown
high-energy completion of the gravitational interaction. Such predictions can
be extracted using the techniques of effective field theory.
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We present an investigation of the near-surface tetragonal phase transition
in SrTiO3, using the complementary techniques of beta-detected nuclear magnetic
resonance and grazing-incidence X-ray diffraction. The results show a clear
depth dependence of the phase transition on scales of a few microns. The
measurements support a model in which there are tetragonal domains forming in
the sample at temperatures much higher than the bulk phase transition
temperature. Moreover, we find that these domains tend to form at higher
temperatures preferentially near the free surface of the crystal. The details
of the tetragonal domain formation and their depth/lateral dependencies are
discussed.
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We introduce a new class of division algebras, the hyperpolyadic algebras,
which correspond to the binary division algebras $\mathbb{R}$, $\mathbb{C}$,
$\mathbb{H}$, $\mathbb{O}$ without considering new elements. First, we use the
matrix polyadization procedure proposed earlier which increases the dimension
of the algebra. The algebras obtained in this way obey binary addition and a
nonderived n-ary multiplication and their subalgebras are division n-ary
algebras. For each invertible element we define a new norm which is
polyadically multiplicative, and the corresponding map is a $n$-ary
homomorphism. We define a polyadic analog of the Cayley-Dickson construction
which corresponds to the consequent embedding of monomial matrices from the
polyadization procedure. We then obtain another series of n-ary algebras
corresponding to the binary division algebras which have a higher dimension,
that is proportional to the intermediate arities. Second, a new polyadic
product of vectors in any vector space is defined. Endowed with this product
the vector space becomes a polyadic algebra which is a division algebra under
some invertibility conditions, and its structure constants are computed. Third,
we propose a new iterative process ("imaginary tower"), which leads to
nonunital nonderived ternary division algebras of half the dimension, which we
call "half-quaternions" and "half-octonions". The latter are not subalgebras of
the binary division algebras, but subsets only, since they have different
arity. Nevertheless, they are actually ternary division algebras, because they
allow division, and their nonzero elements are invertible. From the
multiplicativity of the introduced "half-quaternion" norm we obtain the ternary
analog of the sum of two squares identity. We show that the ternary division
algebra of imaginary "half-octonions" is unitless and totally associative.
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We investigate the level spacing distribution for the quantum spectrum of the
square billiard. Extending work of Connors--Keating, and Smilansky, we
formulate an analog of the Hardy--Littlewood prime $k$-tuple conjecture for
sums of two squares, and show that it implies that the spectral gaps, after
removing degeneracies and rescaling, are Poisson distributed. Consequently, by
work of Rudnick and Uebersch\"ar, the level spacings of arithmetic toral point
scatterers, in the weak coupling limit, are also Poisson distributed. We also
give numerical evidence for the conjecture and its implications.
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We develop a new approach to the computation of the Hausdorff dimension of
the invariant set of an iterated function system or IFS. In the one dimensional
case, our methods require only C^3 regularity of the maps in the IFS. The key
idea, which has been known in varying degrees of generality for many years, is
to associate to the IFS a parametrized family of positive, linear,
Perron-Frobenius operators L_s. The operators L_s can typically be studied in
many different Banach spaces. Here, unlike most of the literature, we study L_s
in a Banach space of real-valued, C^k functions, k >= 2; and we note that L_s
is not compact, but has a strictly positive eigenfunction v_s with positive
eigenvalue lambda_s equal to the spectral radius of L_s. Under appropriate
assumptions on the IFS, the Hausdorff dimension of the invariant set of the IFS
is the value s=s_* for which lambda_s =1. This eigenvalue problem is then
approximated by a collocation method using continuous piecewise linear
functions (in one dimension) or bilinear functions (in two dimensions). Using
the theory of positive linear operators and explicit a priori bounds on the
derivatives of the strictly positive eigenfunction v_s, we give rigorous upper
and lower bounds for the Hausdorff dimension s_*, and these bounds converge to
s_* as the mesh size approaches zero.
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We have computed the fourth-order nf^2 contributions to all three non-singlet
quark-quark splitting functions and their four nf^3 flavour-singlet
counterparts for the evolution of the parton distributions of hadrons in
perturbative QCD with nf effectively massless quark flavours. The analytic form
of these functions is presented in both Mellin N-space and momentum-fraction
x-space; the large-x and small-x limits are discussed. Our results agree with
all available predictions derived from lower-order information. The large-x
limit of the quark-quark cases provides the complete nf^2 part of the four-loop
cusp anomalous dimension which agrees with two recent partial computations.
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In this paper we study a Neumann problem for the fractional Laplacian, namely
\begin{equation}\left\{ \begin{array}{rcll} \varepsilon^{2s}(- \Delta)^{s}u + u
&=& f(u) \ \ &\mbox{in} \ \ \Omega \\ \mathcal{N}_{s}u &=& 0 , \,\, &\text{in}
\,\, \mathbb{R}^{N}\backslash \Omega \end{array}\right. \end{equation} where
$\Omega \subset \mathbb{R}^{N}$ is a smooth bounded domain, $N>2s$, $s \in
(0,1)$, $\varepsilon > 0$ is a parameter and $\mathcal{N}_{s}$ is the nonlocal
normal derivative introduced by Dipierro, Ros-Oton, and Valdinoci. We establish
the existence of a nonnegative, non-constant small energy solution
$u_{\varepsilon}$, and we use the Moser-Nash iteration procedure to show that
$u_{\varepsilon} \in L^{\infty}(\Omega)$.
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We study the minimum connected sensor cover problem (MIN-CSC) and the
budgeted connected sensor cover (Budgeted-CSC) problem, both motivated by
important applications (e.g., reduce the communication cost among sensors) in
wireless sensor networks. In both problems, we are given a set of sensors and a
set of target points in the Euclidean plane. In MIN-CSC, our goal is to find a
set of sensors of minimum cardinality, such that all target points are covered,
and all sensors can communicate with each other (i.e., the communication graph
is connected). We obtain a constant factor approximation algorithm, assuming
that the ratio between the sensor radius and communication radius is bounded.
In Budgeted-CSC problem, our goal is to choose a set of $B$ sensors, such that
the number of targets covered by the chosen sensors is maximized and the
communication graph is connected. We also obtain a constant approximation under
the same assumption.
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We give a brief overview of recent results obtained through the gauge/gravity
correspondence, concerning the propagation of a heavy quark in strongly-coupled
conformal field theories (such as N=4 super-Yang-Mills), both at zero and
finite temperature. In the vacuum, we discuss energy loss, radiation damping,
signal propagation and radiation-induced fluctuations. In the presence of a
thermal plasma, our emphasis is on early-time energy loss, screening and
quark-antiquark evolution after pair creation. Throughout, quark dynamics is
seen to be efficiently encapsulated in the usual string worldsheet dynamics.
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We study how the relationship between non-equivalent width parameters changes
once we restrict to some special graph class. As width parameters, we consider
treewidth, clique-width, twin-width, mim-width, sim-width and tree-independence
number, whereas as graph classes we consider $K_{t,t}$-subgraph-free graphs,
line graphs and their common superclass, for $t \geq 3$, of $K_{t,t}$-free
graphs.
We first provide a complete comparison when restricted to
$K_{t,t}$-subgraph-free graphs, showing in particular that treewidth,
clique-width, mim-width, sim-width and tree-independence number are all
equivalent. This extends a result of Gurski and Wanke (2000) stating that
treewidth and clique-width are equivalent for the class of
$K_{t,t}$-subgraph-free graphs.
Next, we provide a complete comparison when restricted to line graphs,
showing in particular that, on any class of line graphs, clique-width,
mim-width, sim-width and tree-independence number are all equivalent, and
bounded if and only if the class of root graphs has bounded treewidth. This
extends a result of Gurski and Wanke (2007) stating that a class of graphs
${\cal G}$ has bounded treewidth if and only if the class of line graphs of
graphs in ${\cal G}$ has bounded clique-width.
We then provide an almost-complete comparison for $K_{t,t}$-free graphs,
leaving one missing case. Our main result is that $K_{t,t}$-free graphs of
bounded mim-width have bounded tree-independence number. This result has
structural and algorithmic consequences. In particular, it proves a special
case of a conjecture of Dallard, Milani\v{c} and \v{S}torgel.
Finally, we consider the question of whether boundedness of a certain width
parameter is preserved under graph powers. We show that the question has a
positive answer for sim-width precisely in the case of odd powers.
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We investigate the connection between highly frustrated kagome based
Hamiltonians and a recently synthesized family of materials containing Ti3+
S=1/2 ions. Employing a combination of all electron density functional theory
and numerical diagonalization techniques, we establish the Heisenberg
Hamiltonians for the distorted kagome antiferromagnets Rb2NaTi3F12, Cs2NaTi3F12
and Cs2KTi3F12. We determine magnetization curves in excellent agreement with
experimental observations. Our calculations successfully clarify the
relationship between the experimental observations and the
magnetization-plateau behavior at 1/3 height of the saturation and predict
characteristic behaviors under fields that are higher than the experimentally
measured region. We demonstrate that the studied Ti(III) family of materials
interpolates between kagome strip and kagome lattice.
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The measurements of intensity of ultrasonic resonances below the transition
to the superconducting state in a tetragonal metal cannot distinguish between
the magnetic and nonmagnetic superconducting states with two-component order
parameters.
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A variety of "strange metals" exhibit resistivity that decreases linearly
with temperature as $T\rightarrow 0$, in contrast with conventional metals
where resistivity decreases as $T^2$. This $T$-linear resistivity has been
attributed to charge carriers scattering at a rate given by $\hbar/\tau=\alpha
k_{\rm B} T$, where $\alpha$ is a constant of order unity. This simple
relationship between the scattering rate and temperature is observed across a
wide variety of materials, suggesting a fundamental upper limit on
scattering---the "Planckian limit"---but little is known about the underlying
origins of this limit. Here we report a measurement of the angle-dependent
magnetoresistance (ADMR) of Nd-LSCO---a hole-doped cuprate that displays
$T$-linear resistivity down to the lowest measured temperatures. The ADMR
unveils a well-defined Fermi surface that agrees quantitatively with
angle-resolved photoemission spectroscopy (ARPES) measurements and reveals a
$T$-linear scattering rate that saturates the Planckian limit, namely $\alpha =
1.2 \pm 0.4$. Remarkably, we find that this Planckian scattering rate is
isotropic, i.e. it is independent of direction, in contrast with expectations
from "hot-spot" models. Our findings suggest that $T$-linear resistivity in
strange metals emerges from a momentum-independent inelastic scattering rate
that reaches the Planckian limit.
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Recently, non-regular three-quarter sampling has shown to deliver an
increased image quality of image sensors by using differently oriented L-shaped
pixels compared to the same number of square pixels. A three-quarter sampling
sensor can be understood as a conventional low-resolution sensor where one
quadrant of each square pixel is opaque. Subsequent to the measurement, the
data can be reconstructed on a regular grid with twice the resolution in both
spatial dimensions using an appropriate reconstruction algorithm. For this
reconstruction, local joint sparse deconvolution and extrapolation (L-JSDE) has
shown to perform very well. As a disadvantage, L-JSDE requires long computation
times of several dozen minutes per megapixel. In this paper, we propose a
faster version of L-JSDE called recurrent L-JSDE (RL-JSDE) which is a
reformulation of L-JSDE. For reasonable recurrent measurement patterns, RL-JSDE
provides significant speedups on both CPU and GPU without sacrificing image
quality. Compared to L-JSDE, 20-fold and 733-fold speedups are achieved on CPU
and GPU, respectively.
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Resonant metasurfaces have received extensive attention due to their sharp
spectral feature and extraordinary field enhancement. In this work, by breaking
the in-plane symmetry of silicon nanopillars, we achieve a sharp Fano
resonance. The far-field radiation and near-field distribution of metasurfaces
are calculated and analyzed to further uncover the resonant performance of
metasurfaces. Moreover, the theoretical derivation and simulation exhibit an
inverse quadratic dependence of Q-factors on asymmetry parameters, revealing
that the resonance is governed by the symmetry-protected bound states in the
continuum. Finally we experimentally demonstrate the sharp resonance, and
employ it to effciently boost the third-harmonic generation. This enhancement
can be attributed to the strong optical intensity enhancement inside the
metasurface.
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We introduce PH-STAT, a comprehensive Matlab toolbox designed for performing
a wide range of statistical inferences on persistent homology. Persistent
homology is a prominent tool in topological data analysis (TDA) that captures
the underlying topological features of complex data sets. The toolbox aims to
provide users with an accessible and user-friendly interface for analyzing and
interpreting topological data. The package is distributed in
https://github.com/laplcebeltrami/PH-STAT.
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We report the experimental demonstration of a quantum teleportation protocol
with a semiconductor single photon source. Two qubits, a target and an ancilla,
each defined by a single photon occupying two optical modes (dual-rail qubit),
were generated independently by the single photon source. Upon measurement of
two modes from different qubits and postselection, the state of the two
remaining modes was found to reproduce the state of the target qubit. In
particular, the coherence between the target qubit modes was transferred to the
output modes to a large extent. The observed fidelity is 80 %, a figure which
can be explained quantitatively by the residual distinguishability between
consecutive photons from the source. An improved version of this teleportation
scheme using more ancillas is the building block of the recent KLM proposal for
efficient linear-optics quantum computation \cite{ref:klm}.
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We propose a particle production mechanism analogous to the particle
photoproduction processes, arising from the gluon-nucleon interactions in
relativistic heavy ion collisions. The comparison is made on the effect of the
gluon-nucleon interactions on the photon production in Au+Au collisions at
$\sqrt{s_{NN}}=$200 GeV and Pb+Pb collisions at $\sqrt{s_{NN}}=$2.76 TeV. The
numerical results indicate that as the collision energy increases, the
contribution of gluon-nucleon interactions becomes more prominent.
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In this article, we propose a way of seeing the noncommutative tori in the
category of noncommutative motives. As an algebra, the noncommutative torus is
lack the smoothness property required to define a noncomutative motive. Thus,
instead of working with the algebra, we work with the category of holomorphic
bundles. It is known that these are related to the coherent sheaves of an
elliptic curve. We describe the cyclic homology of the category of holomorphic
bundle on a noncommutative torus. We then introduce a notion of (weak)
t-structure in dg categories. By applying the t-structure to a noncommutative
torus, we show that it induces a decomposition of the motivic Galois group of
the Tannakian subcategory generated by the auxiliary elliptic curve.
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We investigate the presence of spatial localization in nuclei using a method
that maps the nucleon same-spin pair probability and is based on the
density-matrix. The method is used to study spatial localization of light
nuclei within the Hartree-Fock approximation. We show that the method provides
an alternative tool for studying spatial localization in comparison to the
localization observed from maxima in the nuclear mass density.
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I summarize here the results of a global fit to the full data set
corresponding to 535 days of data of the Super-Kamiokande experiment as well as
to all other experiments in order to compare the two most likely solutions to
the atmospheric neutrino anomaly in terms of oscillations in the $\nu_\mu \to
\nu_\tau$ and $\nu_\mu \to \nu_s$ channels.
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Massive spin s>=3/2 fields can become partially massless in cosmological
backgrounds. In the plane spanned by m^2 and \Lambda, there are lines where new
gauge invariances permit intermediate sets of higher helicities, rather than
the usual flat space extremes of all 2s+1 massive or just 2 massless
helicities. These gauge lines divide the (m^2,\Lambda) plane into unitarily
allowed or forbidden intermediate regions where all 2s+1 massive helicities
propagate but lower helicity states can have negative norms. We derive these
consequences for s=3/2,2 by studying both their canonical (anti)commutators and
the transmutation of massive constraints to partially massless Bianchi
identities. For s=2, a Hamiltonian analysis exhibits the absence of zero
helicity modes in the partially massless sector. For s=5/2,3 we derive Bianchi
identities and their accompanying gauge invariances for the various partially
massless theories with propagating helicities (+/-5/2,+/-3/2) and (+/-3,+/-2),
(+/-3,+/-2,+/-1), respectively. Of these, only the s=3 models are unitary. To
these ends, we also provide the half integer generalization of the integer spin
wave operators of Lichnerowicz. Partial masslessness applies to all higher
spins in (A)dS as seen by their degree of freedom counts. Finally a derivation
of massive d=4 constraints by dimensional reduction from their d=5 massless
Bianchi identity ancestors is given.
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Line-graph (LG) lattices are known for having flat bands (FBs) from the
destructive interference of Bloch wavefunctions encoded in pure lattice
symmetry. Here, we develop a generic atomic/molecular orbital design principle
for FBs in non-LG lattices. Based on linear-combination-of-atomic-orbital
(LCAO) theory, we demonstrate that the underlying wavefunction symmetry of FBs
in a LG lattice can be transformed into the atomic/molecular orbital symmetry
in a non-LG lattice. We illustrate such orbital-designed topological FBs in
three 2D non-LG, square, trigonal, and hexagonal lattices, where the designed
orbitals faithfully reproduce the corresponding lattice symmetries of
checkerboard, Kagome, and diatomic-Kagome lattices, respectively.
Interestingly, systematic design of FBs with a high Chern number is also
achieved based on the same principle. Fundamentally our theory enriches the FB
physics; practically it significantly expands the scope of FB materials, since
most materials have multiple atomic/molecular orbitals at each lattice site,
rather than a single s orbital mandated in graph theory and generic lattice
models.
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Subsets and Splits