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Practical natural language processing (NLP) tasks are commonly long-tailed
with noisy labels. Those problems challenge the generalization and robustness
of complex models such as Deep Neural Networks (DNNs). Some commonly used
resampling techniques, such as oversampling or undersampling, could easily lead
to overfitting. It is growing popular to learn the data weights leveraging a
small amount of metadata. Besides, recent studies have shown the advantages of
self-supervised pre-training, particularly to the under-represented data. In
this work, we propose a general framework to handle the problem of both
long-tail and noisy labels. The model is adapted to the domain of problems in a
contrastive learning manner. The re-weighting module is a feed-forward network
that learns explicit weighting functions and adapts weights according to
metadata. The framework further adapts weights of terms in the loss function
through a combination of the polynomial expansion of cross-entropy loss and
focal loss. Our extensive experiments show that the proposed framework
consistently outperforms baseline methods. Lastly, our sensitive analysis
emphasizes the capability of the proposed framework to handle the long-tailed
problem and mitigate the negative impact of noisy labels.
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We investigate various supersymmetric brane intersections. Motivated by the
recent results on supertubes, we investigate general constraints in which
parallel brane-antibrane configurations are supersymmetric. Dual descriptions
of these configurations involve systems of branes in relative motion. In
particular, we find new supersymmetric configurations which are not related to
a static brane intersection by a boost. In these new configurations, the
intersection point moves at the speed of light. These systems provide
interesting time dependent backgrounds for open strings.
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An orbital current can be generated whenever an object has a translational
and rotational degree of freedom. In condensed matter physics, intra-atomic
contributions to the transverse orbital transport, labeled orbital Hall effect,
rely on propagating wave packets that must consist of hybridized atomic
orbitals. However, inter-atomic contributions have to be considered as well
because they give rise to a new mechanism for generating orbital currents. As
we show, even wave packets consisting purely of s electrons can transport
orbital angular momentum if they move on a cycloid trajectory. We introduce the
kagome lattice with a single s orbital per atom as the minimal model for the
orbital Hall effect and observe the cycloid motion of the electrons in the
surface states.
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The presence of periodic modulation in graphene leads to a reconstruction of
the band structure and formation of minibands. In an external uniform magnetic
field, a fractal energy spectrum called Hofstadter butterfly is formed.
Particularly interesting in this regard are superlattices with tunable
modulation strength, such as electrostatically induced ones in graphene. We
perform quantum transport modeling in gate-induced square two-dimensional
superlattice in graphene and investigate the relation to the details of the
band structure. At low magnetic field the dynamics of carriers reflects the
semi-classical orbits which depend on the mini band structure. We theoretically
model transverse magnetic focusing, a ballistic transport technique by means of
which we investigate the minibands, their extent and carrier type. We find a
good agreement between the focusing spectra and the mini band structures
obtained from the continuum model, proving usefulness of this technique.
%positions of van Hove singularities at high magnetic field the calculated
four-probe resistance fit the Hofstadter butterfly spectrum obtained for our
superlattice. Our quantum transport modeling provides an insight into the mini
band structures, and can be applied to other superlattice geometries.
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The spatially-resolved laser-based high resolution ARPES measurements have
been performed on the optimally-doped $\mathrm{YBa_{2} Cu_{3} O_{7-\delta} }$
(Y123) superconductor. For the first time, we found the region from the cleaved
surface that reveals clear bulk electronic properties. The intrinsic Fermi
surface and band structures of Y123 are observed. The Fermi surface-dependent
and momentum-dependent superconducting gap is determined which is nodeless and
consistent with the d+is gap form.
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We propose a decentralized receiver for extra-large multiple-input
multiple-output (XL-MIMO) arrays. Our method operates with no central
processing unit (CPU) and all the signal detection tasks are done in
distributed nodes. We exploit a combined message-passing framework to design an
uncoordinated detection scheme that overcomes three major challenges in the
XL-MIMO systems: computational complexity, scalability and non-stationarities
in user energy distribution. Our numerical evaluations show a significant
performance improvement compared to benchmark distributed methods while
operating very close to the centralized receivers.
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Maximizing the performance potential of the modern day GPU architecture
requires judicious utilization of available parallel resources. Although
dramatic reductions can often be obtained through straightforward mappings,
further performance improvements often require algorithmic redesigns to more
closely exploit the target architecture. In this paper, we focus on efficient
molecular simulations for the GPU and propose a novel cell list algorithm that
better utilizes its parallel resources. Our goal is an efficient GPU
implementation of large-scale Monte Carlo simulations for the grand canonical
ensemble. This is a particularly challenging application because there is
inherently less computation and parallelism than in similar applications with
molecular dynamics. Consistent with the results of prior researchers, our
simulation results show traditional cell list implementations for Monte Carlo
simulations of molecular systems offer effectively no performance improvement
for small systems [5, 14], even when porting to the GPU. However for larger
systems, the cell list implementation offers significant gains in performance.
Furthermore, our novel cell list approach results in better performance for all
problem sizes when compared with other GPU implementations with or without cell
lists.
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Spin injection is a powerful experimental probe into a wealth of
nonequilibrium spin-dependent phenomena displayed by materials with spin-orbit
coupling (SOC). Here, we develop a theory of coupled spin-charge diffusive
transport in two-dimensional spin-valve devices. The theory describes a
realistic proximity-induced SOC with both spatially uniform and random
components of the SOC due to adatoms and imperfections, and applies to the two
dimensional electron gases found in two-dimensional materials and van der Walls
heterostructures. The various charge-to-spin conversion mechanisms known to be
present in diffusive metals, including the spin Hall effect and several
mechanisms contributing current-induced spin polarization are accounted for.
Our analysis shows that the dominant conversion mechanisms can be discerned by
analyzing the nonlocal resistance of the spin-valve for different polarizations
of the injected spins and as a function of the applied in-plane magnetic field.
|
Visual dialog (VisDial) is a task which requires an AI agent to answer a
series of questions grounded in an image. Unlike in visual question answering
(VQA), the series of questions should be able to capture a temporal context
from a dialog history and exploit visually-grounded information. A problem
called visual reference resolution involves these challenges, requiring the
agent to resolve ambiguous references in a given question and find the
references in a given image. In this paper, we propose Dual Attention Networks
(DAN) for visual reference resolution. DAN consists of two kinds of attention
networks, REFER and FIND. Specifically, REFER module learns latent
relationships between a given question and a dialog history by employing a
self-attention mechanism. FIND module takes image features and reference-aware
representations (i.e., the output of REFER module) as input, and performs
visual grounding via bottom-up attention mechanism. We qualitatively and
quantitatively evaluate our model on VisDial v1.0 and v0.9 datasets, showing
that DAN outperforms the previous state-of-the-art model by a significant
margin.
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The paper presents a general strategy to solve ordinary differential
equations (ODE), where some coefficient depend on the spatial variable and on
additional random variables. The approach is based on the application of a
recently developed dimension-incremental sparse fast Fourier transform. Since
such algorithms require periodic signals, we discuss periodization strategies
and associated necessary deperiodization modifications within the occuring
solution steps.
The computed approximate solutions of the ODE depend on the spatial variable
and on the random variables as well. Certainly, one of the crucial challenges
of the high dimensional approximation process is to rate the influence of each
variable on the solution as well as the determination of the relations and
couplings within the set of variables. The suggested approach meets these
challenges in a full automatic manner with reasonable computational costs,
i.e., in contrast to already existing approaches, one does not need to
seriously restrict the used set of ansatz functions in advance.
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Motivated by the problem of reconstructing dynamics from samples we revisit
the Conley index theory for discrete multivalued dynamical systems. We
introduce a new, less restrictive definition of the isolating neighbourhood. It
turns out that then the main tool for the construction of the index, i.e. the
index pair, is no longer useful. In order to overcome this obstacle we use the
concept of weak index pairs.
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The *reciprocal complement* $R(D)$ of an integral domain $D$ is the subring
of its fraction field generated by the reciprocals of its nonzero elements.
Many properties of $R(D)$ are determined when $D$ is a polynomial ring in
$n\geq 2$ variables over a field. In particular, $R(D)$ is an $n$-dimensional,
local, non-Noetherian, non-integrally closed, non-factorial, atomic G-domain,
with infinitely many prime ideals at each height other than $0$ and $n$.
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We study rigidly rotating strings in the $\varkappa$-deformed $AdS_3 \times
S^3$ background. We find out two classes of solutions corresponding to the
giant magnon and single spike solutions of the string rotating in two
$S^2_{\varkappa}$ subspace of rotations reduced along two different isometries.
We verify that the dispersion relations reduce to the well known relation in
the $\varkappa\rightarrow 0$ limit. We further study some oscillating string
solutions in the $S^3_{\varkappa}$ subspace.
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Motivated by the initial value problem in semiclassical gravity, we study the
initial value problem of a system consisting of a quantum scalar field weakly
interacting with a classical one. The quantum field obeys a Klein-Gordon
equation with a potential proportional to the classical field. The classical
field obeys an inhomogeneous Klein-Gordon equation sourced by the renormalised
expectation value of the squared quantum field in a Hadamard state, $\langle
\Psi| \Phi^2 \Psi \rangle$. Thus, the system of equations for the scalar fields
reminisces of the semi-classical Einstein field equations with a Klein-Gordon
field, where classical geometry is sourced by the renormalised stress-energy
tensor of the quantum field, and the Klein-Gordon equation depends on the
metric explicitly. We show that a unique asymptotic solution for the system can
be obtained perturbatively at any fixed finite order in the weak coupling from
initial data provided that the interaction is switched on and off smoothly in a
spacetime region to the future of the initial data surface. This allows one to
provide "free" initial data for the decoupled system that guarantees that the
Wightman function of the quantum field be of Hadamard form, and hence that the
renormalised $\langle \Psi| \Phi^2 \Psi \rangle$ exist (in a perturbative
sense) and be smooth. We comment on how to relax the switching of the
interaction, which might be relevant for the corresponding problem in
semiclassical gravity.
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We develop a Clifford algebra approach for 3D Ising model. By utilizing some
mathematical facts of the direct product of matrices and their trace, we expand
the dimension of the transfer matrices V of the 3D Ising system by adding unit
matrices I (with compensation of a factor) and adjusting their sequence, which
do not change the trace of the transfer matrices V (Theorem I: Trace Invariance
Theorem). It allows us to perform a linearization process on
sub-transfer-matrices (Theorem II: Linearization Theorem). It is found that
locally for each site j, the internal factor Wj in the transfer matrices can be
treated as a boundary factor, which can be dealt with by a procedure similar to
the Onsager-Kaufman approach for the boundary factor U in the 2D Ising model.
This linearization process splits each sub-transfer matrix into 2n sub-spaces
(and the whole system into 2nl sub-spaces). Furthermore, a local transformation
is employed on each of the sub-transfer matrices (Theorem III: Local
Transformation Theorem). The local transformation trivializes the non-trivial
topological structure, while it generalizes the topological phases on the
eigenvectors. This is induced by a gauge transformation in the Ising gauge
lattice that is dual to the original 3D Ising model. The non-commutation of
operators during the processes of linearization and local transformation can be
dealt with to be commutative in the framework of the Jordan-von Neumann-Wigner
procedure, in which the multiplication in Jordan algebras is applied instead of
the usual matrix multiplication AB (Theorem IV: Commutation Theorem).
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For any graph $G$, we define the power $\pi(G)$ as the minimum of the largest
number of neighbors in a $\gamma$-set of $G$, of any vertex, taken over all
$\gamma$-sets of $G$. We show that $\gamma(G\square H)\geq
\frac{\pi(G)}{2\pi(G) -1}\gamma(G)\gamma(H)$. This implies that for any graphs
$G$ and $H$, $\gamma(G\square H)\geq
\frac{\gamma(G)}{2\gamma(G)-1}\gamma(G)\gamma(H)$, and if $G$ is claw-free or
$P_4$-free, $\gamma(G\square H)\geq \frac{2}{3}\gamma(G)\gamma(H)$, where
$\gamma(G)$ is the domination number of $G$.
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We compute the eta function $\eta(s)$ and its corresponding $\eta$-invariant
for the Atiyah-Patodi-Singer operator $\mathcal{D}$ acting on an orientable
compact flat manifold of dimension $n =4h-1$, $h\ge 1$, and holonomy group
$F\simeq \mathbb{Z}_{2^r}$, $r\in \mathbb{N}$. We show that $\eta(s)$ is a
simple entire function times $L(s,\chi_4)$, the $L$-function associated to the
primitive Dirichlet character modulo 4. The $\eta$-invariant is 0 or equals
$\pm 2^k$ for some $k\ge 0$ depending on $r$ and $n$. Furthermore, we construct
an infinite family $\mathcal{F}$ of orientable $\mathbb{Z}_{2^r}$-manifolds
with $F\subset \mathrm{SO}(n,\mathbb{Z})$. For the manifolds $M\in \mathcal{F}$
we have $\eta(M)=-\tfrac{1}{2}|T|$, where $T$ is the torsion subgroup of
$H_1(M,\mathbb{Z})$, and that $\eta(M)$ determines the whole eta function
$\eta(s,M)$.
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Smoothed particle hydrodynamics (SPH) has been extensively studied in
computer graphics to animate fluids with versatile effects. However, SPH still
suffers from two numerical difficulties: the particle deficiency problem, which
will deteriorate the simulation accuracy, and the particle clumping problem,
which usually leads to poor stability of particle simulations. We propose to
solve these two problems by developing an approximate projection method for
incompressible free-surface flows under a variational staggered particle
framework. After particle discretization, we first categorize all fluid
particles into four subsets. Then according to the classification, we propose
to solve the particle deficiency problem by analytically imposing free surface
boundary conditions on both the Laplacian operator and the source term. To
address the particle clumping problem, we propose to extend the Taylor-series
consistent pressure gradient model with kernel function correction and
semi-analytical boundary conditions. Compared to previous approximate
projection method [1], our incompressibility solver is stable under both
compressive and tensile stress states, no pressure clumping or iterative
density correction (e.g., a density constrained pressure approach) is necessary
to stabilize the solver anymore. Motivated by the Helmholtz free energy
functional, we additionally introduce an iterative particle shifting algorithm
to improve the accuracy. It significantly reduces particle splashes near the
free surface. Therefore, high-fidelity simulations of the formation and
fragmentation of liquid jets and sheets are obtained for both the two-jets and
milk-crown examples.
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Fast and accurate anatomical landmark detection can benefit many medical
image analysis methods. Here, we propose a method to automatically detect
anatomical landmarks in medical images. Automatic landmark detection is
performed with a patch-based fully convolutional neural network (FCNN) that
combines regression and classification. For any given image patch, regression
is used to predict the 3D displacement vector from the image patch to the
landmark. Simultaneously, classification is used to identify patches that
contain the landmark. Under the assumption that patches close to a landmark can
determine the landmark location more precisely than patches farther from it,
only those patches that contain the landmark according to classification are
used to determine the landmark location. The landmark location is obtained by
calculating the average landmark location using the computed 3D displacement
vectors. The method is evaluated using detection of six clinically relevant
landmarks in coronary CT angiography (CCTA) scans: the right and left ostium,
the bifurcation of the left main coronary artery (LM) into the left anterior
descending and the left circumflex artery, and the origin of the right,
non-coronary, and left aortic valve commissure. The proposed method achieved an
average Euclidean distance error of 2.19 mm and 2.88 mm for the right and left
ostium respectively, 3.78 mm for the bifurcation of the LM, and 1.82 mm, 2.10
mm and 1.89 mm for the origin of the right, non-coronary, and left aortic valve
commissure respectively, demonstrating accurate performance. The proposed
combination of regression and classification can be used to accurately detect
landmarks in CCTA scans.
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Effects of non-Gaussian $\alpha-$stable L\'evy noise on the Gompertz tumor
growth model are quantified by considering the mean exit time and escape
probability of the cancer cell density from inside a safe or benign domain. The
mean exit time and escape probability problems are formulated in a
differential-integral equation with a fractional Laplacian operator. Numerical
simulations are conducted to evaluate how the mean exit time and escape
probability vary or bifurcates when $\alpha$ changes. Some bifurcation
phenomena are observed and their impacts are discussed.
|
Rising concerns about the impact of space weather-related disruptions demand
modelling and reliable forecasting of coronal mass ejection (CME) impacts. In
this study, we demonstrate the application of the modified Miller-Turner (mMT)
model implemented in EUropean Heliospheric FORecasting Information Asset
(EUHFORIA), to forecast the geo-effectiveness of observed coronal mass ejection
(CME) events in the heliosphere. The goal is to develop a model that not only
has a global geometry to improve overall forecasting but is also fast enough
for operational space weather forecasting. We test the original full torus
implementation and introduce a new three-fourth Torus version called the
Horseshoe CME model. This new model has a more realistic CME geometry, and it
overcomes the inaccuracies of the full torus geometry. We constrain the torus
geometrical and magnetic field parameters using observed signatures of the CMEs
before, during, and after the eruption. The assessment of the model's
capability to predict the most important Bz component is performed using the
advanced Dynamic Time Warping technique. The Horseshoe model prediction of CME
arrival time and geo-effectiveness for both validation events compare well to
the observations and are weighed with the results obtained with the spheromak
and FRi3D models that were already available in EUHFORIA. The runtime of the
Horseshoe model simulations is close to that of the spheromak model, which is
suitable for operational space weather forecasting. Yet, the capability of the
magnetic field prediction at 1~AU of the Horseshoe model is close to that of
the FRi3D model. In addition, we demonstrate that the Horseshoe CME model can
be used for simulating successive CMEs in EUHFORIA, overcoming a limitation of
the FRi3D model.
|
The cofactor conditions, introduced in James and Zhang, are conditions of
compatibility between phases in martensitic materials. They consist of three
subconditions: i) the condition that the middle principal stretch of the
transformation stretch tensor $\mathbf U$ is unity ($\lambda_2 = 1$), ii) the
condition $\mathbf a \cdot \mathbf U\, \cof (\mathbf U^2 - \mathbf I)\mathbf n
= 0$, where the vectors $\mathbf a$ and $\mathbf n$ are certain vectors arising
in the specification of the twin system, and iii) the inequality ${\rm tr}
\mathbf U^2 + \det \mathbf U^2 -(1/4) |\mathbf a|^2 |\mathbf n|^2\ge 2$.
Together, these conditions are necessary and sufficient for the equations of
the crystallographic theory of martensite to be satisfied for the given twin
system but for any volume fraction f of the twins, $0 \le f \le 1$. This
contrasts sharply with the generic solutions of the crystallographic theory
which have at most two such volume fractions for a given twin system of the
form $f^*$ and $1-f^*$. In this paper we simplify the form of the cofactor
conditions, we give their specific forms for various symmetries and twin types,
we clarify the extent to which the satisfaction of the cofactor conditions for
one twin system implies its satisfaction for other twin systems. In particular,
we prove that the satisfaction of the cofactor conditions for either Type I or
Type II twins implies that there are solutions of the crystallographic theory
using these twins that have no elastic transition layer. We show that the
latter further implies macroscopically curved, transition-layer-free
austenite/martensite interfaces for Type I twins, and planar
transition-layer-free interfaces for Type II twins which nevertheless permit
significant flexibility of the martensite. We identify some real material
systems nearly satisfying the cofactor conditions.
|
We consider a class of diffusion equations with the Caputo time-fractional
derivative $\partial_t^\alpha u=L u$ subject to the homogeneous Dirichlet
boundary conditions. Here, we consider a fractional order $0<\alpha < 1$ and a
second-order operator $L$ which is elliptic and non-symmetric. In this paper,
we show that the logarithmic convexity extends to this non-symmetric case
provided that the drift coefficient is given by a gradient vector field. Next,
we perform some numerical experiments to validate the theoretical results in
both symmetric and non-symmetric cases. Finally, some conclusions and open
problems will be mentioned.
|
Option pricing is mainly based on ideal market conditions which are well
represented by the Geometric Brownian Motion (GBM) as market model. We study
the effect of non-ideal market conditions on the price of the option. We focus
our attention on two crucial aspects appearing in real markets: The influence
of heavy tails and the effect of colored noise. We will see that both effects
have opposite consequences on option pricing.
|
We prove closure properties for the class of C*-algebras that are inductive
limits of semiprojective C*-algebras. Most importantly, we show that this class
is closed under shape domination, and so in particular under shape and homotopy
equivalence. It follows that the considered class is quite large. It contains
for instance the stable suspension of any nuclear C*-algebra satisfying the UCT
and with torsion-free $K_0$-group. In particular, the stabilized C*-algebra of
continuous functions on the pointed sphere is isomorphic to an inductive limit
of semiprojectives.
|
We reveal multiple components of an interacting galaxy system at
$z\approx3.35$ through a detailed analysis of the exquisite high-resolution
Keck/HIRES spectrum of the afterglow of a gamma-ray burst (GRB). Through
Voigt-profile fitting of absorption lines from the Lyman-series, we constrain
the neutral hydrogen column density to $N_{\mathrm{HI}} \leq 10^{18.35}$
cm$^{-2}$ for the densest of four distinct systems at the host redshift of
GRB~080810, among the lowest $N_{\mathrm{HI}}$ ever observed in a GRB host,
despite the line of sight passing within a projected 5 kpc of the galaxy
centres. By detailed analysis of the corresponding metal absorption lines, we
derive chemical, ionic and kinematic properties of the individual absorbing
systems, and thus build a picture of the host as a whole. Striking differences
between the systems imply that the line of sight passes through several phases
of gas: the star-forming regions of the GRB host; enriched material in the form
of a galactic outflow; the hot and ionised halo of a second, interacting galaxy
falling towards the host at a line-of-sight velocity of 700 km s$^{-1}$; and a
cool, metal-poor cloud which may represent one of the best candidates yet for
the inflow of metal-poor gas from the intergalactic medium.
|
The graph model checking problem consists in testing whether an input graph
satisfies a given logical formula. In this paper, we study this problem in a
distributed setting, namely local certification. The goal is to assign labels
to the nodes of a network to certify that some given property is satisfied, in
such a way that the labels can be checked locally.
We first investigate which properties can be locally certified with small
certificates. Not surprisingly, this is almost never the case, except for not
very expressive logic fragments. Following the steps of Courcelle-Grohe, we
then look for meta-theorems explaining what happens when we parameterize the
problem by some standard measures of how simple the graph classes are. In that
direction, our main result states that any MSO formula can be locally certified
on graphs with bounded treedepth with a logarithmic number of bits per node,
which is the golden standard in certification.
|
In this work we study the problem of constructing stochastic processes with a
predetermined covariance decay by parameterizing its marginals and a given
family of copulas. We show that the proposed methodology is compatibility-free
and present several examples to illustrate the theory, including the important
Gaussian and Euclidean families of copulas. We associate the theory to common
applied time series models.
|
We propose an all-electronic technique to manipulate and control interacting
quantum systems by unitary single-jump feedback conditioned on the outcome of a
capacitively coupled electrometer and in particular a single-electron
transistor. We provide a general scheme to stabilize pure states in the quantum
system and employ an effective Hamiltonian method for the quantum master
equation to elaborate on the nature of stabilizable states and the conditions
under which state purification can be achieved. The state engineering within
the quantum feedback scheme is shown to be linked with the solution of an
inverse eigenvalue problem. Two applications of the feedback scheme are
presented in detail: (i) stabilization of delocalized pure states in a single
charge qubit and (ii) entanglement stabilization in two coupled charge qubits.
In the latter example we demonstrate the stabilization of a maximally entangled
Bell state for certain detector positions and local feedback operations.
|
In this paper we construct a wide class of Gribov copies in Coulomb gauge
SU(2) gauge theory. Infinitesimal copies are studied in some detail and their
non-perturbative nature is made manifest. As an application it is shown that
the copies prevent a non-perturbative definition of colour charge.
|
Two-photon E1M1 transition rates are evaluated for heliumlike ions with
nuclear charges in the range Z = 50-94. The two-photon rates modify previously
published lifetimes/transition rates of 2 3P0 states. For isotopes with nuclear
spin I not equal 0, where hyperfine quenching dominates the 2 3P0 decay,
two-photon contributions are significant; for example, in heliumlike 187 Os the
two-photon correction is 3% of the total rate. For isotopes with I= 0, where
the 2 3P0 decay is unquenched, the E1M1 corrections are even more important
reaching 60% for Z=94. Therefore, to aid in the interpretation of experiments
on hyperfine quenching in heliumlike ions and to provide a more complete
database for unquenched transitions, a knowledge of E1M1 rates is important.
|
Despite the significant progress that depth-based 3D hand pose estimation
methods have made in recent years, they still require a large amount of labeled
training data to achieve high accuracy. However, collecting such data is both
costly and time-consuming. To tackle this issue, we propose a semi-supervised
method to significantly reduce the dependence on labeled training data. The
proposed method consists of two identical networks trained jointly: a teacher
network and a student network. The teacher network is trained using both the
available labeled and unlabeled samples. It leverages the unlabeled samples via
a loss formulation that encourages estimation equivariance under a set of
affine transformations. The student network is trained using the unlabeled
samples with their pseudo-labels provided by the teacher network. For inference
at test time, only the student network is used. Extensive experiments
demonstrate that the proposed method outperforms the state-of-the-art
semi-supervised methods by large margins.
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A tropical version of the Schauder fixed point theorem for compact subsets of
tropical linear spaces is proved.
|
We present the first extensive and detailed theoretical scenario for the
interpretation of Cepheid properties observed in the SDSS filters. Three sets
of nonlinear convective pulsation models, corresponding to the chemical
compositions of Cepheids in the Milky Way, the Large Magellanic Cloud and the
Small Magellanic Cloud respectively, are transformed into the SDSS bands by
relying on updated model atmospheres. The resulting observables, namely the
instability strip boundaries and the light curves, as well as the
Period-Luminosity, the Wesenheit and the Period-Luminosity-Colour relations,
are discussed as a function of the metal content, for both the fundamental and
the first overtone mode. The fundamental PL relations are found to deviate from
linear relations when computed over the whole observed Cepheid period range,
especially at the shorter wavelenghts, confirming previous findings in the
Johnson-Cousins bands. The obtained slopes are found to be mildly steeper than
the ones of the semiempirical and the empirical relations available in the
literature and covering roughly the same period range, with the discrepancy
ranging from about 13% in u-band to about 3% in z.
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Content Delivery Networks (CDNs) deliver content (e.g. Web pages, videos) to
geographically distributed end-users over the Internet. Some contents do
sometimes attract the attention of a large group of end-users. This often leads
to flash crowds which can cause major issues such as outage in the CDN.
Microservice architectural style aims at decomposing monolithic systems into
smaller components which can be independently deployed, upgraded and disposed.
Network Function Virtualization (NFV) is an emerging technology that aims to
reduce costs and bring agility by decoupling network functions from the
underlying hardware. This paper leverages the NFV and microservice
architectural style to propose an architecture for on-the-fly CDN component
provisioning to tackle issues such as flash crowds. In the proposed
architecture, CDN components are designed as sets of microservices which
interact via RESTFul Web services and are provisioned as Virtual Network
Functions (VNFs), which are deployed and orchestrated on-the-fly. We have built
a prototype in which a CDN surrogate server, designed as a set of
microservices, is deployed on-the-fly. The prototype is deployed on SAVI, a
Canadian distributed test bed for future Internet applications. The performance
is also evaluated.
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Laser metal deposition (LMD) is an additive manufacturing technique, whose
performances can be influenced by several factors and parameters. Monitoring
their evolution allows for a better comprehension and control of the process,
hence enhancing the deposition quality. In particular, the deposition height is
an important variable that, if it does not match the process growth, can bring
to defects and geometrical inaccuracies in the deposited structures. The
current work presents a system based on optical triangulation for the height
monitoring, implemented on a LMD setup composed of a fiber laser, a deposition
head, and an anthropomorphic robot. Its coaxial and non-intrusive configuration
allows for flexibility in the deposition strategy and direction. A measurement
laser beam is launched through the powder nozzle and hits the melt pool. A
coaxial camera acquires the probe spot, whose position is converted to relative
height. The device has been demonstrated for monitoring the deposition of a
stainless steel cylinder. The measurements allowed to reconstruct a spatial map
of the height variation, highlighting a transient in the deposition growth
which can be explained in terms of a self-regulating mechanism for the layer
thickness.
|
A single spherical antenna is capable of measuring the direction and
polarization of a gravitational wave. It is possible to solve the inverse
problem using only linear algebra even in the presence of noise. The simplicity
of this solution enables one to explore the error on the solution using
standard techniques. In this paper we derive the error on the direction and
polarization measurements of a gravitational wave. We show that the solid angle
error and the uncertainty on the wave amplitude are direction independent. We
also discuss the possibility of determining the polarization amplitudes with
isotropic sensitivity for any given gravitational wave source.
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Hierarchical models of galaxy formation now provide a much closer match to
observations than they did a few years ago. The progress has been achieved by
adjusting the description of baryonic processes such as star formation and
supernova/AGN feedback, while leaving the evolution of the underlying dark
matter (DM) halos the same. Being most results very sensitive to the input
baryonic physics, the ultimate vindication of the hierarchical paradigm should
come from observational tests probing more directly the merging history of DM
halos rather than the history of star formation. Two questions may start
addressing this deeper level: is the predicted halo merging rate consistent
with the observed galaxy merging rate? and, are predicted and observed
evolution of the galaxy mass function consistent with each other. The current
status of these issues is briefly reviewed.
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The knowledge of isotopic and elemental abundances of the pristine solar
system material provides a fundamental test of galactic chemical evolution
models, while the composition of the solar photosphere is a reference pattern
to understand stellar abundances. However, spectroscopic or meteoritic
abundance determinations are only possible for an incomplete sample of the 83
elements detected in the solar system. Therefore, only relative abundances are
experimentally determined, with respect to H or to Si for spectroscopic or
meteoritic measurements, respectively. For this reason, the available
compilations of solar abundances are obtained by combining spectroscopic and
meteoritic determinations, a procedure requiring the knowledge of the chemical
modification occurred in the solar photosphere. We provide a method to derive
the mass fractions of all the 83 elements (and their most abundant isotopes) in
the early solar system material and in the present-day solar surface.
Calculations are repeated by adopting the most widely adopted compilations of
solar abundances. Since for a given [Fe/H], the total metallicity depends on
solar (Z/X), a 30% reduction of Z is found when passing from the classical
Anders&Grevesse to the most recent Lodders compilation. Some implications are
discussed, as, in particular, an increase of about 700 Myr of the estimated age
of Globular Clusters. Within the experimental errors, the complete set of
relative solar abundances, as obtained by combining meteoritic and photospheric
measurements, are consistent with the variations implied by the quoted physical
processes. Few deviations can be easily attributed to the decay of long-lived
radioactive isotopes. The huge lithium depletion is only partially explained by
introducing a rotational-induced mixing in the tachocline.
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There has been growing interest in the use of multi-robot systems in various
tasks and scenarios. The main attractiveness of such systems is their
flexibility, robustness, and scalability. An often overlooked yet promising
feature is system modularity, which offers the possibility to harness agent
specialization, while also enabling system-level upgrades. However, altering
the agents' capacities can change the exploration-exploitation balance required
to maximize the system's performance. Here, we study the effect of a swarm's
heterogeneity on its exploration-exploitation balance while tracking multiple
fast-moving evasive targets under the Cooperative Multi-Robot Observation of
Multiple Moving Targets framework. To this end, we use a decentralized search
and tracking strategy with adjustable levels of exploration and exploitation.
By indirectly tuning the balance, we first confirm the presence of an optimal
balance between these two key competing actions. Next, by substituting slower
moving agents with faster ones, we show that the system exhibits a performance
improvement without any modifications to the original strategy. In addition,
owing to the additional amount of exploitation carried out by the faster
agents, we demonstrate that a heterogeneous system's performance can be further
improved by reducing an agent's level of connectivity, to favor the conduct of
exploratory actions. Furthermore, in studying the influence of the density of
swarming agents, we show that the addition of faster agents can counterbalance
a reduction in the overall number of agents while maintaining the level of
tracking performance. Finally, we explore the challenges of using
differentiated strategies to take advantage of the heterogeneous nature of the
swarm.
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A new topology is proposed on the space of holonomy equivalence classes of
loops, induced by the topology of the space $\Sigma$ in which the loops are
embedded. The possible role for the new topology in the context of the work by
Ashtekar et al. is discussed.
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The Graph Convolutional Network (GCN) model and its variants are powerful
graph embedding tools for facilitating classification and clustering on graphs.
However, a major challenge is to reduce the complexity of layered GCNs and make
them parallelizable and scalable on very large graphs -- state-of the art
techniques are unable to achieve scalability without losing accuracy and
efficiency. In this paper, we propose novel parallelization techniques for
graph sampling-based GCNs that achieve superior scalable performance on very
large graphs without compromising accuracy. Specifically, our GCN guarantees
work-efficient training and produces order of magnitude savings in computation
and communication. To scale GCN training on tightly-coupled shared memory
systems, we develop parallelization strategies for the key steps in training:
For the graph sampling step, we exploit parallelism within and across multiple
sampling instances, and devise an efficient data structure for concurrent
accesses that provides theoretical guarantee of near-linear speedup with number
of processing units. For the feature propagation step within the sampled graph,
we improve cache utilization and reduce DRAM communication by data
partitioning. We prove that our partitioning strategy is a 2-approximation for
minimizing the communication time compared to the optimal strategy. We
demonstrate that our parallel graph embedding outperforms state-of-the-art
methods in scalability (with respect to number of processors, graph size and
GCN model size), efficiency and accuracy on several large datasets. On a
40-core Xeon platform, our parallel training achieves $64\times$ speedup (with
AVX) in the sampling step and $25\times$ speedup in the feature propagation
step, compared to the serial implementation, resulting in a net speedup of
$21\times$.
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The method of separation of variables is significant, it has been applied to
physics, engineering , chemistry and other fields. It allows to reduce the
diffculity of problems by separating the variables from partial differential
equation system into ordinary differential equations system. However, this
method has complexity in higher order partial differential equations. In this
reserach, we generalize this method by using multinomial theorem of n-harmonic
equation to solve n-harmonic equation with $m$ dimension and then solving an
important class of partial differential equations with unbounded boundary
conditions. Additionaly, application of convolution.
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We consider the exact continuous relaxation model of matrix rank minimization
problem proposed by Yu and Zhang (Comput.Optim.Appl. 1-20, 2022). Motivated by
the inertial techinique, we propose a general inertial smoothing proximal
gradient algorithm(GIMSPG) for this kind of problems. It is shown that the
singular values of any accumulation point have a common support set and the
nonzero singular values have a unified lower bound. Besides, the zero singular
values of the accumulation point can be achieved within finite iterations.
Moreover, we prove that any accumulation point of the sequence generated by the
GIMSPG algorithm is a lifted stationary point of the continuous relaxation
model under the flexible parameter constraint. Finally, we carry out numerical
experiments on random data and image data respectively to illustrate the
efficiency of the GIMSPG algorithm.
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We study a one-dimensional reaction-diffusion system which describes an
isothermal autocatalytic chemical reaction involving both a quadratic (A + B ->
2B) and a cubic (A + 2B -> 3B) autocatalysis. The parameters of this system are
the ratio D = D_B/D_A of the diffusion constants of the reactant A and the
autocatalyst B, and the relative activity k of the cubic reaction. First, for
all values of D > 0 and k >= 0, we prove the existence of a family of
propagating fronts (or travelling waves) describing the advance of the
reaction. In particular, in the quadratic case k=0, we recover the results of
Billingham and Needham [BN]. Then, if D is close to 1 and k is sufficiently
small, we prove using energy functionals that these propagating fronts are
stable against small perturbations in exponentially weighted Sobolev spaces.
This extends to our system part of the stability results which are known for
the scalar Fisher equation.
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The handling of weak networks with asymmetric loads and disturbances implies
the accurate handling of the second-harmonic component that appears in an
unbalanced network. This paper proposes a classic vector control approach using
a PI-based controller with superior decoupling capabilities for operation in
weak networks with unbalanced phase voltages. A synchronization method for weak
unbalanced networks is detailed, with dedicated dimensioning rules. The use of
a double-frame controller allows a current symmetry or controlled imbalance to
be forced for compensation of power oscillations by controlling the negative
current sequence. This paper also serves as a useful reminder of the proper way
to cancel the inherent coupling effect due to the transformation to the
synchronous rotating reference frame, and of basic considerations of the
relationship between switching frequency and control bandwidth.
|
A new analysis is presented of the angular correlation function $C(\Theta)$
of cosmic microwave background (CMB) temperature at large angular separation,
based on published maps derived from {\sl WMAP} and {\sl Planck} satellite
data, using different models of astrophysical foregrounds. It is found that
using a common analysis, the results from the two satellites are very similar.
In particular, it is found that previously published differences between
measured values of $C(\Theta)$ near $\Theta=90^\circ$ arise mainly from
different choices of masks in regions of largest Galactic emissions, and that
demonstrated measurement biases are reduced by eliminating masks altogether.
Maps from both satellites are shown to agree with $C(90^\circ)=0$ to within
estimated statistical and systematic errors, consistent with an exact symmetry
predicted in a new holographic quantum model of inflation.
|
Safe and secure electric vehicle charging stations (EVCSs) are important in
smart transportation infrastructure. The prevalence of EVCSs has rapidly
increased over time in response to the rising demand for EV charging. However,
developments in information and communication technologies (ICT) have made the
cyber-physical system (CPS) of EVCSs susceptible to cyber-attacks, which might
destabilize the infrastructure of the electric grid as well as the environment
for charging. This study suggests a 5Ws \& 1H-based investigation approach to
deal with cyber-attack-related incidents due to the incapacity of the current
investigation frameworks to comprehend and handle these mishaps. Also, a
stochastic anomaly detection system (ADS) is proposed to identify the
anomalies, abnormal activities, and unusual operations of the station entities
as a post cyber event analysis.
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Throughout cosmological simulations, the properties of the matter density
field in the initial conditions have a decisive impact on the features of the
structures formed today. In this paper we use a random-forest classification
algorithm to infer whether or not dark matter particles, traced back to the
initial conditions, would end up in dark matter halos whose masses are above
some threshold. This problem might be posed as a binary classification task,
where the initial conditions of the matter density field are mapped into
classification labels provided by a halo finder program. Our results show that
random forests are effective tools to predict the output of cosmological
simulations without running the full process. These techniques might be used in
the future to decrease the computational time and to explore more efficiently
the effect of different dark matter/dark energy candidates on the formation of
cosmological structures.
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In this paper we will give a similar factorization as in \cite{4}, \cite{5},
where the autors Svrtan and Meljanac examined certain matrix factorizations on
Fock-like representation of a multiparametric quon algebra on the free
associative algebra of noncommuting polynomials equiped with multiparametric
partial derivatives. In order to replace these matrix factorizations (given
from the right) by twisted algebra computation, we first consider the natural
action of the symmetric group $S_{n}$ on the polynomial ring $R_{n}$ in $n^2$
commuting variables $X_{a\,b}$ and also introduce a twisted group algebra
(defined by the action of $S_{n}$ on $R_{n}$) which we denote by
${\mathcal{A}(S_{n})}$. Here we consider some factorizations given from the
left because they will be more suitable in calculating the constants (= the
elements which are annihilated by all multiparametric partial derivatives) in
the free algebra of noncommuting polynomials.
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Breast cancer is one of the most common and dangerous cancers in women, while
it can also afflict men. Breast cancer treatment and detection are greatly
aided by the use of histopathological images since they contain sufficient
phenotypic data. A Deep Neural Network (DNN) is commonly employed to improve
accuracy and breast cancer detection. In our research, we have analyzed
pre-trained deep transfer learning models such as ResNet50, ResNet101, VGG16,
and VGG19 for detecting breast cancer using the 2453 histopathology images
dataset. Images in the dataset were separated into two categories: those with
invasive ductal carcinoma (IDC) and those without IDC. After analyzing the
transfer learning model, we found that ResNet50 outperformed other models,
achieving accuracy rates of 90.2%, Area under Curve (AUC) rates of 90.0%,
recall rates of 94.7%, and a marginal loss of 3.5%.
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In this paper, we model a real-time feasible rosette imager, consisting of a
rosette scanner, an optical sensor and a deterministic image reconstruction
algorithm. We fine-tune the rosette imager through selecting the appropriate
sensor field of view and rosette pattern. The sensor field of view is
determined through a greedy approach using uniform random sampling.
Furthermore, the optimal rosette pattern is selected by determining which
pattern best covers the imaging area uniformly.
We explore image sparsity, image decimation and Gaussian filtering in a
well-known natural data set and dead leaves data set using the PSNR,
Peak-Signal-to-Noise Ratio. This exploration helps to establish a connection
between PSNR and image sparsity. Furthermore, we compare various rosette imager
configurations in a Bayesian framework. We also conclude that the rosette
imager does not outperform a focal-plane array of equivalent samples in terms
of image quality but can match the performance.
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Recent years have seen the rapid development of miniaturized reconstructive
spectrometers (RSs), yet they still confront a range of technical challenges,
such as bandwidth/resolution ratio, sensing speed, and/or power efficiency.
Reported RS designs often suffer from insufficient decorrelation between
sampling channels, which results in limited compressive sampling efficiency, in
essence, due to inadequate engineering of sampling responses. This in turn
leads to poor spectral-pixel-to-channel ratios (SPCRs), typically restricted at
single digits. So far, there lacks a general guideline for manipulating RS
sampling responses for the effectiveness of spectral information acquisition.
In this study, we shed light on a fundamental parameter from the compressive
sensing theory - the average mutual correlation coefficient v - and provide
insight into how it serves as a critical benchmark in RS design with regards to
the SPCR and reconstruction accuracy. To this end, we propose a novel RS design
with multi-resonant cavities, consisting of a series of partial reflective
interfaces. Such multi-cavity configuration offers an expansive parameter
space, facilitating the superlative optimization of sampling matrices with
minimized v. As a proof-of-concept demonstration, a single-shot, dual-band RS
is implemented on a SiN platform, tailored for capturing signature spectral
shapes across different wavelength regions, with customized photonic crystal
nanobeam mirrors. Experimentally, the device demonstrates an overall operation
bandwidth of 270 nm and a <0.5 nm resolution with only 15 sampling channels per
band, leading to a record high SPCR of 18.0. Moreover, the proposed
multi-cavity design can be readily adapted to various photonic platforms. For
instance, we showcase that by employing multi-layer coatings, an
ultra-broadband RS can be optimized to exhibit a 700 nm bandwidth with an SPCR
of over 100.
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Using the new state-of-the-art core-collapse supernova (CCSN) code
F{\sc{ornax}}, we have simulated the three-dimensional dynamical evolution of
the cores of 9-, 10-, 11-, 12-, and 13-M$_{\odot}$ stars from the onset of
collapse. Stars from 8-M$_{\odot}$ to 13-M$_{\odot}$ constitute roughly 50% of
all massive stars, so the explosive potential for this mass range is important
to the overall theory of CCSNe. We find that the 9-, 10-, 11-, and
12-M$_{\odot}$ models explode in 3D easily, but that the 13-M$_{\odot}$ model
does not. From these findings, and the fact that slightly more massive
progenitors seem to explode \citep{vartanyan2019}, we suggest that there is a
gap in explodability near 12-M$_{\odot}$ to 14-M$_{\odot}$ for non-rotating
progenitor stars. Factors conducive to explosion are turbulence behind the
stalled shock, energy transfer due to neutrino-matter absorption and
neutrino-matter scattering, many-body corrections to the neutrino-nucleon
scattering rate, and the presence of a sharp silicon-oxygen interface in the
progenitor. Our 3D exploding models frequently have a dipolar structure, with
the two asymmetrical exploding lobes separated by a pinched waist where matter
temporarily continues to accrete. This process maintains the driving neutrino
luminosty, while partially shunting matter out of the way of the expanding
lobes, thereby modestly facilitating explosion. The morphology of all 3D
explosions is characterized by multiple bubble structures with a range of
low-order harmonic modes. Though much remains to be done in CCSN theory, these
and other results in the literature suggest that, at least for these lower-mass
progenitors, supernova theory is converging on a credible solution.
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A neural network consisting of piecewise affine building blocks, such as
fully-connected layers and ReLU activations, is itself a piecewise affine
function supported on a polyhedral complex. This complex has been previously
studied to characterize theoretical properties of neural networks, but, in
practice, extracting it remains a challenge due to its high combinatorial
complexity. A natural idea described in previous works is to subdivide the
regions via intersections with hyperplanes induced by each neuron. However, we
argue that this view leads to computational redundancy. Instead of regions, we
propose to subdivide edges, leading to a novel method for polyhedral complex
extraction. A key to this are sign-vectors, which encode the combinatorial
structure of the complex. Our approach allows to use standard tensor operations
on a GPU, taking seconds for millions of cells on a consumer grade machine.
Motivated by the growing interest in neural shape representation, we use the
speed and differentiability of our method to optimize geometric properties of
the complex. The code is available at
https://github.com/arturs-berzins/relu_edge_subdivision .
|
It is shown that the stochastic model of Fenyes and Nelson can be generalized
in such a way that the diffusion constant of the Markov theory becomes a free
parameter. This extra freedom allows one to identify quantum mechanics with a
class of Markov processes with diffusion constants varying from zero to
infinity.
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Machine learning has recently emerged as a powerful tool for generating new
molecular and material structures. The success of state-of-the-art models stems
from their ability to incorporate physical symmetries, such as translation,
rotation, and periodicity. Here, we present a novel generative method called
Response Matching (RM), which leverages the fact that each stable material or
molecule exists at the minimum of its potential energy surface. Consequently,
any perturbation induces a response in energy and stress, driving the structure
back to equilibrium. Matching to such response is closely related to score
matching in diffusion models. By employing the combination of a machine
learning interatomic potential and random structure search as the denoising
model, RM exploits the locality of atomic interactions, and inherently respects
permutation, translation, rotation, and periodic invariances. RM is the first
model to handle both molecules and bulk materials under the same framework. We
demonstrate the efficiency and generalization of RM across three systems: a
small organic molecular dataset, stable crystals from the Materials Project,
and one-shot learning on a single diamond configuration.
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We introduce a family of ideals $I_{n,\lambda,s}$ in
$\mathbb{Q}[x_1,\dots,x_n]$ for $\lambda$ a partition of $k\leq n$ and an
integer $s \geq \ell(\lambda)$. This family contains both the Tanisaki ideals
$I_\lambda$ and the ideals $I_{n,k}$ of Haglund-Rhoades-Shimozono as special
cases. We study the corresponding quotient rings $R_{n,\lambda,s}$ as symmetric
group modules. When $n=k$ and $s$ is arbitrary, we recover the Garsia-Procesi
modules, and when $\lambda=(1^k)$ and $s=k$, we recover the generalized
coinvariant algebras of Haglund-Rhoades-Shimozono. We give a monomial basis for
$R_{n,\lambda,s}$, unifying the monomial bases studied by Garsia-Procesi and
Haglund-Rhoades-Shimozono, and realize the $S_n$-module structure of
$R_{n,\lambda,s}$ in terms of an action on $(n,\lambda,s)$-ordered set
partitions. We also prove formulas for the Hilbert series and graded Frobenius
characteristic of $R_{n,\lambda,s}$. We then connect our work with
Eisenbud-Saltman rank varieties using results of Weyman. As an application of
our work, we give a monomial basis, Hilbert series formula, and graded
Frobenius characteristic formula for the coordinate ring of the
scheme-theoretic intersection of a rank variety with diagonal matrices.
|
We present a data set from a first-principles study of amino-methylated and
acetylated (capped) dipeptides of the 20 proteinogenic amino acids - including
alternative possible side chain protonation states and their interactions with
selected divalent cations (Ca$^{2+}$, Mg$^{2+}$ and Ba$^{2+}$). The data covers
21,909 stationary points on the respective potential-energy surfaces in a wide
relative energy range of up to 4 eV (390 kJ/mol). Relevant properties of
interest, like partial charges, were derived for the conformers. The motivation
was to provide a solid data basis for force field parameterization and further
applications like machine learning or benchmarking. In particular the process
of creating all this data on the same first-principles footing, i.e.
density-functional theory calculations employing the generalized gradient
approximation with a van der Waals correction, makes this data suitable for
data-driven force field development. To make the data accessible across domain
borders and to machines, we formalized the metadata in an ontology.
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We proposed in "Functional Constraint Extraction From Register Transfer Level
for ATPG" that is currently submitted to TVLSI, an automatic functional
constraint extractor that can be applied on the RT level. These functional
constraints are used to generate pseudo functional test patterns with ATPG
tools. The patterns are then used to improve the verification process. This
technical report complements the work proposed as it contains the
implementation details of the proposed methodology and shows the detailed
intermediate and final results of the application of this methodology on a
concrete example.
|
In an earlier paper (Class. Quantum Grav. 19 (2002) p.259) the author wrote
the homothetic equations for vacuum solutions in a first order formalism
allowing for arbitrary alignment of the dyad. This paper generalises that
method to conformal vectors in non-vacuum spaces. The method is applied to
metrics admitting a three parameter motion group on non-null orbits.
|
We study the planar front solution for a class of reaction diffusion
equations in multidimensional space in the case when the essential spectrum of
the linearization in the direction of the front touches the imaginary axis. At
the linear level, the spectrum is stabilized by using an exponential weight.
A-priori estimates for the nonlinear terms of the equation governing the
evolution of the perturbations of the front are obtained when perturbations
belong to the intersection of the exponentially weighted space with the
original space without a weight. These estimates are then used to show that in
the original norm, initially small perturbations to the front remain bounded,
while in the exponentially weighted norm, they algebraically decay in time.
|
Liouville space search algorithm [Bruschweiler, Phys. Rev. Lett. {\bf 85},
4815(2000).] utilizes mixed initial states of the ensemble, and has been
successfully implemented earlier in weakly coupled spins, in which a spin can
be identified as a qubit. It has recently been demonstrated that n-strongly
coupled spins can be collectively treated as an n-qubit system. Application of
algorithms in such systems, requires new approaches using transition selective
pulses rather than qubit selective pulses. This work develops a modified
version of Liouville space search algorithm, which is applicable for strongly
as well as weakly coupled spins. All the steps of the algorithm, can be
implemented by using transition selective pulses. Experimental implementation
is carried out on a strongly dipolar coupled four qubit system.
|
We study the propagation of tension caused by an external force along a long
polymeric molecule in two different settings, namely along a free polymer in 3d
space being pulled from one end, and along a pre-stretched circular polymer,
confined in a narrow circular tube. We show that in both cases, the tension
propagation is governed by a diffusion equation, and in particular, the tension
front propagates as $t^{1/2}$ along the contour of the chain. The results are
confirmed numerically, and by molecular dynamics simulations in the case of the
3d polymer. We also compare our results with the previously suggested ones for
the translocation setting, and discuss why tension propagation is slower in
that case.
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In this paper we study the combinatorics of free Borel actions of the group
$\mathbb Z^d$ on Polish spaces. Building upon recent work by Chandgotia and
Meyerovitch, we introduce property $F$ on $\mathbb Z^d$-shift spaces $X$ under
which there is an equivariant map from any free Borel action to the free part
of $X$. Under further entropic assumptions, we prove that any subshift $Y$
(modulo the periodic points) can be Borel embedded into $X$. Several examples
satisfy property $F$ including, but not limited to, the space of proper
$3$-colourings, tilings by rectangles (under a natural arithmetic condition),
proper $2d$-edge colourings of $\mathbb Z^d$ and the space of bi-infinite
Hamiltonian paths. This answers questions raised by Seward, and Gao-Jackson,
and recovers a result by Weilacher and some results announced by
Gao-Jackson-Krohne-Seward.
|
Accurate measurement of institutional research productivity should account
for the real contribution of the research staff to the output produced in
collaboration with other organizations. In the framework of bibliometric
measurement, this implies accounting for both the number of co-authors and each
individual's real contribution to scientific publications. Common practice in
the life sciences is to indicate such contribution through the order of author
names in the byline. In this work, we measure the distortion introduced to
university-level bibliometric productivity rankings when the number of
co-authors or their position in the byline is ignored. The field of observation
consists of all Italian universities active in the life sciences (Biology and
Medicine). The analysis is based on the research output of the university staff
over the period 2004-2008. Based on the results, we recommend against the use
of bibliometric indicators that ignore co-authorship and real contribution of
each author to research outputs.
|
The spectroscopic response of and structural dynamics around all
azido-modified alanine residues (AlaN$_3$) in Lysozyme is characterized. It is
found that AlaN$_3$ is a positionally sensitive probe for the local dynamics,
covering a frequency range of $\sim 15$ cm$^{-1}$ for the center frequency of
the line shape. This is consistent with findings from selective replacements of
amino acids in PDZ2 which reported a frequency span of $\sim 10$ cm$^{-1}$ for
replacements of Val, Ala, or Glu by azidohomoalanine (AHA). For the frequency
fluctuation correlation functions (FFCFs) the long-time decay constants
$\tau_2$ range from $\sim 1$ to $\sim 10$ ps which compares with experimentally
measured correlation times of 3 ps. Attaching azide to alanine residues can
yield dynamics that decays to zero on the few ps time scale (i.e. static
component $\Delta_0 \sim 0$ ps$^{-1}$) or to a remaining, static contribution
of $\sim 0.5$ ps$^{-1}$ (corresponding to 2.5 cm$^{-1}$), depending on the
local environment on the 10 ps time scale. The magnitude of the static
component correlates qualitatively with the degree of hydration of the
spectroscopic probe. Although attaching azide to alanine residues is found to
be structurally minimally invasive with respect to the overall protein
structure, analysis of the local hydrophobicity indicates that the hydration
around the modification site differs for modified and unmodified alanine
residues, respectively.
|
We review Foyle et al. (2011) previous results, by applying a Fourier
intensity phases method to a nine object sample of galaxies. It was found that
two of the objects (NGC 628 and NGC 5194), with strong two-arm patterns,
present positive evidence for long-lived spirals. Only one of the objects (NGC
3627) shows the contrary evidence. As determined by an analysis of resolved
mass maps, the rest of the objects can not be included in the analysis because
they belong to flocculent and multi-arm type of spiral arms, which are not
described by density wave theory.
|
The spin-dependent Berry force is a genuine effect of Berry curvature in
molecular dynamics, which can dramatically result in spatial spin separation
and change of reaction pathways. However, the way to probe the effect of Berry
force remains challenging, because the time-reversal (TR) symmetry required for
opposite Berry forces conflicts with TR symmetry breaking spin alignment needed
to observe the effect, and the net effect could be transient for a molecular
wave packet. We demonstrate that in molecular photodissociation, the
dissociation rates can be different for molecules with opposite initial spin
directions due to Berry force. We showcase that the spatially separated spin
density, which is transiently induced by Berry force as the molecular wave
packet passes through conical intersection, can be reconstructed from the
circular dichroism (CD) of ultrafast non-resonant magnetic x-ray scattering
using free electron lasers.
|
Organic Electrochemical Transistors are considered today as a key technology
to interact with biological medium through their intrinsic ionic-electronic
coupling. In this paper, we show how this coupling can be finely tuned (in
operando) post-microfabrication via electropolymerization technique. This
strategy exploits the concept of adaptive sensing where both transconductance
and impedance are tunable and can be modified on-demand to match different
sensing requirements. Material investigation through Raman spectroscopy, atomic
force microscopy and scanning electron microscopy reveals that
electropolymerization can lead to a fine control of PEDOT microdomains
organization, which directly affect the iono-electronic properties of OECTs. We
further highlight how volumetric capacitance and effective mobility of
PEDOT:PSS influence distinctively the transconductance and impedance of OECTs.
This approach shows to improve the transconductance by 150% while reducing
their variability by 60% in comparison with standard spin-coated OECTs.
Finally, we show how to the technique can influence voltage spike rate hardware
classificationwith direct interest in bio-signals sorting applications.
|
In the absence of any additional assumption it is natural to conjecture that
sizeable flavour-mixing mass entries, $\Delta m^2$, may appear in the mass
matrices of the scalars of the MSSM, i.e. $\Delta m^2\sim O(m^2)$. This flavour
violation can still be reconciled with the experiment if the gaugino mass,
$M_{1/2}$, is large enough, leading to a {\em gaugino dominance} framework
(i.e. $M_{1/2}^2\gg m^2$), which permits a remarkably model--independent
analysis. We study this possibility focussing our attention on the
$\mu\rightarrow e,\gamma$ decay. In this way we obtain very strong and general
constraints, in particular $\frac{M_{1/2}^2}{\Delta m}\simgt 34\ {\rm TeV}$. On
the other hand, we show that our analysis and results remain valid for values
of $m^2$ much larger than $\Delta m^2$, namely for $\frac{\Delta
m^2}{m^2}\simgt \frac{m^2} {10\ {\rm TeV^2}}$, thus extending enormously their
scope of application. Finally, we discuss the implications for superstring
scenarios.
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A robust prediction model invoking the Takens embedding theorem, whose
\textit{working hypothesis} is obtained via an inference procedure based on the
minimum Fisher information principle, is presented. The coefficients of the
ansatz, central to the \textit{working hypothesis} satisfy a time independent
Schr\"{o}dinger-like equation in a vector setting. The inference of i) the
probability density function of the coefficients of the \textit{working
hypothesis} and ii) the establishing of constraint driven pseudo-inverse
condition for the modeling phase of the prediction scheme, is made, for the
case of normal distributions, with the aid of the quantum mechanical virial
theorem. The well-known reciprocity relations and the associated Legendre
transform structure for the Fisher information measure (FIM, hereafter)-based
model in a vector setting (with least square constraints) are self-consistently
derived. These relations are demonstrated to yield an intriguing form of the
FIM for the modeling phase, which defines the \textit{working hypothesis},
solely in terms of the observed data. Cases for prediction employing time
series' obtained from the: $(i)$ the Mackey-Glass delay-differential equation,
$(ii)$ one ECG sample from the MIT-Beth Israel Deaconess Hospital (MIT-BIH)
cardiac arrhythmia database, and $(iii)$ one ECG from the Creighton University
ventricular tachyarrhythmia database. The ECG samples were obtained from the
Physionet online repository. These examples demonstrate the efficiency of the
prediction model. Numerical examples for exemplary cases are provided.
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In this paper we extend the concept of Competitivity Graph to compare series
of rankings with ties ({\em partial rankings}). We extend the usual method used
to compute Kendall's coefficient for two partial rankings to the concept of
evolutive Kendall's coefficient for a series of partial rankings. The
theoretical framework consists of a four-layer multiplex network. Regarding the
treatment of ties, our approach allows to define a tie between two values when
they are close {\em enough}, depending on a threshold. We show an application
using data from the Spanish Stock Market; we analyse the series of rankings
defined by $25$ companies that have contributed to the IBEX-35 return and
volatility values over the period 2003 to 2013.
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The $(P, w)$-partition generating function $K_{(P,w)}(x)$ is a quasisymmetric
function obtained from a labeled poset. Recently, Liu and Weselcouch gave a
formula for the coefficients of $K_{(P,w)}(x)$ when expanded in the
quasisymmetric power sum function basis. This formula generalizes the classical
Murnaghan--Nakayama rule for Schur functions.
We extend this result to weighted $(P, w)$-partitions and provide a short
combinatorial proof, avoiding the Hopf algebra machinery used by
Liu-Weselcouch.
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In a recent publication [Phys. Rev. Lett. 97, 227402 (2006),
cond-mat/0611411], it has been demonstrated numerically that a long-range
disorder potential in semiconductor quantum wells can be reconstructed reliably
via single-photon interferometry of spontaneously emitted light.
In the present paper, a simplified analytical model of independent two-level
systems is presented in order to study the reconstruction procedure in more
detail. With the help of this model, the measured photon correlations can be
calculated analytically and the influence of parameters such as the disorder
length scale, the wavelength of the used light, or the spotsize can be
investigated systematically. Furthermore, the relation between the proposed
angle-resolved single-photon correlations and the disorder potential can be
understood and the measured signal is expected to be closely related to the
characteristic strength and length scale of the disorder.
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The OZI rule have been tested in a number of experiments in a wide interval
of energies. It was found that the rule is fulfilled well, within few percent
of accuracy. The results of experiments with stopped antiprotons at LEAR
(CERN), where unexpected large violation (by a factor 3-70) of the OZI rule was
found, were quite surprising. Later experiments found strong violation of the
OZI rule not only in antiproton annihilation but also in reactions with protons
and pions.
In the review we consider the phenomenology of the OZI rule, to what extent
it is valid in the hadron interactions. The experimental evidences of the large
OZI violation are discussed. The polarized strangeness model and its
explanation of the large OZI violation is discussed, the review of other
theoretical models is given.
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We define convex-geometric counterparts of divided difference (or Demazure)
operators from the Schubert calculus and representation theory. These operators
are used to construct inductively polytopes that capture Demazure characters of
representations of reductive groups. In particular, Gelfand-Zetlin polytopes
and twisted cubes of Grossberg-Karshon are obtained in a uniform way.
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A parameterization is described for quantifying translational motion of a
point in three-dimensional Euclidean space. The parameterization is similar to
well-known parameterizations such as spherical coordinates in that both
position and velocity are decoupled into magnitude and orientation components.
Unlike these standard parameterizations, where principal rotation sequences are
employed, the method presented in this research employs Euler parameters. By
using Euler parameters instead of Euler angles, singularities and trigonometric
functions are removed from the equations of motion. The parameterization is
demonstrated on two examples, where it is found that the new parameterization
offers both mathematical and computational advantages over other commonly used
parameterizations.
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Let $\sR$ be an epireflective category of $\topo$ and let $F_\sR$\, be the
epireflective functor associated with $\sR$. If $\sA$ denotes a
(semi)topological algebraic subcategory of $\topo$, we study when $F_\sR\,(A)$
is an epireflective subcategory of $\sA$. We prove that this is always the case
for semi-topological structures and we find some sufficient conditions for
topological algebraic structures. We also study when the epireflective functor
preserves products, subspaces and other properties. In particular, we solve an
open question about the coincidence of epireflections proposed by Echi and
Lazar in \cite[Question 1.6]{Echi:MPRIA} and repeated in \cite[Question
1.9]{Echi:TP}. Finally, we apply our results in different specific topological
algebraic structures.
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We present spectra of 32 previously unpublished confirmed and candidate
Wolf-Rayet ([WR]) and weak emission-line (WELS) central stars of planetary
nebulae (CSPNe). Eighteen stars have been discovered in the
Macquarie/AAO/Strasbourg H-Alpha (MASH) PN survey sample, and we have also
uncovered 14 confirmed and candidate [WR]s and WELS among the CSPNe of
previously known PNe. Spectral classifications have been undertaken using both
the Acker & Neiner and Crowther, De Marco & Barlow schemes. Twenty-two members
in this sample are identified as probable [WR]s; the remaining 10 appear to be
WELS. Observations undertaken as part of the MASH spectroscopic survey have now
increased the number of known [WR]s by ~30 per cent. This will permit a better
analysis of [WR] subclass distribution, metallicity effects, and evolutionary
sequences in these uncommon objects.
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We study a model of scalars which includes both the SM Higgs and a scalar
singlet as composites of heavy vector-like fermions. The vector-like fermions
are bounded by the super-strong four-fermion interactions. The scalar singlet
decays to SM vector bosons through loop of heavy vector-like fermions. We show
that the surprisingly large production cross section of di-photon events at 750
GeV resonance and the odd decay properties can all be explained. This model
serves as a good model for both SM Higgs and a scalar resonance at 750 GeV.
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Using Monte Carlo simulation, we studied fractionalized phases in a model of
exciton bose condensate and found evidence for an emergent photon in a finite
size system. The fractionalized phase is a meta-stable Coulomb phase where an
emergent photon arises as a gapless collective excitation of the excitons. We
also studied a possibility of spiral* phase where fractionalization and long
range spiral order of the exciton condensate coexist.
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In the coset model based on (A_{N-1}^{(1)} \oplus A_{N-1}^{(1)},
A_{N-1}^{(1)}) at level (N, N; 2N), it is known that the N=2 superconformal
algebra can be realized by the two kinds of adjoint fermions. Each Kac-Moody
current of spin-1 is given by the product of fermions with structure constant
(f symbols) as usual. One can construct the spin-1 current by combining the
above two fermions with the structure constant and the spin-1 current by
multiplying these two fermions with completely symmetric SU(N) invariant tensor
of rank 3 (d symbols). The lowest higher spin-2 current with nonzero U(1)
charge (corresponding to the zeromode eigenvalue of spin-1 current of N=2
superconformal algebra) can be obtained from these four spin-1 currents in
quadratic form. Similarly, the other type of lowest higher spin-2 current,
whose U(1) charge is opposite to the above one, can be obtained also. Four
higher spin-5/2 currents can be constructed from the operator product
expansions (OPEs) between the spin-3/2 currents of N=2 superconformal algebra
and the above two higher spin-2 currents. The two higher spin-3 currents can be
determined by the OPEs between the above spin-3/2 currents and the higher
spin-5/2 currents. Finally, the ten N=2 OPEs between the four N=2 higher spin
multiplets (2, 5/2, 5/2, 3), (2, 5/2, 5/2, 3), (7/2, 4, 4, 9/2) and (7/2, 4, 4,
9/2) are obtained explicitly for generic N.
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We consider general Morse-Smale diffeomorphisms on a closed orientable
two-dimentional surface. In this paper it is proved that the complete
topological invariant of Morse-Smale diffeomorphisms is finite, the algorithm
of the construction of the complete topological invariant in explicit form is
given and necessary and sufficient conditions of topological conjugacy of
Morse-Smale diffeomorphisms is obtained.
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A linear group G<GL(n) acts on d-tuples of n x n matrices by simultaneous
conjugation. In [Adv. Math. 19 (1976), 306-381] Procesi established generators
and relations between them for G-invariants, where G is GL(n), O(n), and Sp(n)
and the characteristic of base field is zero. We continue generalization of the
mentioned results to the case of positive characteristic originated by Donkin
in [Invent. Math. 110 (1992), 389-401]. We investigate relations between
generators for O(n)-invariants.
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We recently formulated the canonical boundary-value problem of propagation of
surface plasmon-polariton (SPP) waves along the direction of periodicity of a
one-dimensional photonic crystal. Here we present the general formulation of
that canonical problem supporting the oblique propagation of SPP waves in the
interface plane. The general dispersion equation has been obtained using the
rigorous coupled-wave approach for the oblique propagation and numerically
solved using the Muller's method. A periodicity in the wavenumbers of the SPP
waves was observed. Furthermore, the regions of high losses for the SPP waves,
dubbed as plasmonic bandgaps, were observed in the photonic band diagram of the
SPP waves. These plasmonic bandgaps can be used to construct optical filters
for the SPP waves.
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In this letter we present an analytical theory of Extraordinary optical
transmission (EOT) through semi-transparent screens, such as thin metallic
plates or high permittivity dielectric slabs. Using this theory we show that
EOT appears not only for screens perforated by holes or slits, but also for
screens loaded by any defects, including opaque defects. These results widen
the scope of EOT concept, opening up the way to the study of new physical
effects.
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The streaming instability provides an efficient way of overcoming the growth
barriers in the initial stages of the planet formation process. Considering the
realistic case of a particle size distribution, the dynamics of the system is
altered compared to the outcome of single size models. In order to understand
the outcome of the multi-species streaming instability in detail, we perform a
large parameter study in terms of particle number, particle size distribution,
particle size range, initial metallicity and initial particle scale height. We
study vertically stratified systems and determine the metallicity threshold for
filament formation. We compare these with a system where the initial particle
distribution is unstratified and find that its evolution follows that of its
stratified counterpart. We find that change in particle number does not result
in significant variation in the efficiency and timing of filament formation. We
also see that there is no clear trend for how varying the size distribution in
combination with particle size range changes the outcome of the multi-species
streaming instability. Finally, we find that an initial metallicity of
$Z_{\rm{init}}=0.005$ and $Z_{\rm{init}}=0.01$ both result in similar critical
metallicity values for the start of filament formation. Our results show that
the inclusion of a particle size distribution into streaming instability
simulations, while changing the dynamics as compared to mono-disperse systems,
does not result in overall unfavorable conditions for solid growth. We
attribute the sub-dominant role of multiple species to the high-density
conditions in the midplane, conditions under which also linear stability
analysis predict little difference between single and multiple species.
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We consider semi-inclusive unpolarized DIS for the production of charged
kaons and the different possibilities to test the conventionally used
assumptions s-\bar=0 and D_d^{K^+-K^-}=0. The considered tests have the
advantage that they do not require any knowledge of the fragmentation
functions. We also show that measurements of both charged and neutral kaons
would allow the determination of the kaon FFs D_q^{K^++K^-} solely from SIDIS
measurements, and discuss the comparison of (D_u-D_d)^{K^+-K^-} obtained
independently in SIDIS and e+e- reactions. All analysis are performed in LO and
NLO in QCD. The feasibility of the tests to HERMES SIDIS data is considered.
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We propose a new method for proving lower bounds on quantum query algorithms.
Instead of a classical adversary that runs the algorithm with one input and
then modifies the input, we use a quantum adversary that runs the algorithm
with a superposition of inputs. If the algorithm works correctly, its state
becomes entangled with the superposition over inputs. We bound the number of
queries needed to achieve a sufficient entanglement and this implies a lower
bound on the number of queries for the computation.
Using this method, we prove two new $\Omega(\sqrt{N})$ lower bounds on
computing AND of ORs and inverting a permutation and also provide more uniform
proofs for several known lower bounds which have been previously proven via
variety of different techniques.
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The quasistatic approach is used to analyze the criterion of ferromagnetism
for two-dimensional (2D) systems with the Fermi level near Van Hove (VH)
singularities of the electron spectrum. It is shown that the spectrum of spin
excitations (paramagnons) is positively defined when the interaction between
electrons and paramagnons, determined by the Hubbard on-site repulsion U, is
sufficiently large. Due to incommensurate spin fluctuations near the
ferromagnetic quantum phase transition, the critical interaction Uc remains
finite at VH filling and exceeds considerably its value obtained from the
Stoner criterion. A comparison with the functional renormalization group
results and mean-field approximation which yields a phase separation is also
performed.
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The authors have recently obtained a lower bound of the Hausdorff dimension
of the sets of vectors $(x_1, \ldots, x_d)\in [0,1)^d$ with large Weyl sums,
namely of vectors for which $$ \left| \sum_{n=1}^{N}\exp(2\pi i (x_1 n+\ldots
+x_d n^{d})) \right| \ge N^{\alpha} $$ for infinitely many integers $N \ge 1$.
Here we obtain an upper bound for the Hausdorff dimension of these exceptional
sets.
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Many-body ground states can be prepared via unitary evolution in cold atomic
systems. Given the initial state and a fixed time for the evolution, how close
can we get to a desired ground state if we can tune the Hamiltonian in time?
Here we study this optimal control problem focusing on Luttinger liquids with
tunable interactions. We show that the optimal protocol can be obtained by
simulated annealing. We find that the optimal interaction strength of the
Luttinger liquid can have a nonmonotonic time dependence. Moreover, the system
exhibits a marked transition when the ratio $\tau/L$ of the preparation time to
the system size exceeds a critical value. In this regime, the optimal protocols
can prepare the states with almost perfect accuracy. The optimal protocols are
robust against dynamical noise.
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This paper explores a method of localization and navigation of indoor mobile
robots using a node graph of landmarks that are based on fiducial markers. The
use of ArUco markers and their 2D orientation with respect to the camera of the
robot and the distance to the markers from the camera is used to calculate the
relative position of the robot as well as the relative positions of other
markers. The proposed method combines aspects of beacon-based navigation and
Simultaneous Localization and Mapping based navigation. The implementation of
this method uses a depth camera to obtain the distance to the marker. After
calculating the required orientation of the marker, it relies on odometry
calculations for tracking the position after localization with respect to the
marker. Using the odometry and the relative position of one marker, the robot
is then localized with respect to another marker. The relative positions and
orientation of the two markers are then calculated. The markers are represented
as nodes and the relative distances and orientations are represented as edges
connecting the nodes and a node graph can be generated that represents a map
for the robot. The method was tested on a wheeled humanoid robot with the
objective of having it autonomously navigate to a charging station inside a
room. This objective was successfully achieved and the limitations and future
improvements are briefly discussed.
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In order to understand the rates and properties of Type Ia and Type Ib/c
supernovae, X-ray binaries, gravitational wave sources, and gamma ray bursts as
a function of galactic environment and cosmic age, it is imperative that we
measure how the close binary properties of O and B-type stars vary with
metallicity. We have studied eclipsing binaries with early-B main-sequence
primaries in three galaxies with different metallicities: the Large and Small
Magellanic Clouds (LMC and SMC, respectively) as well as the Milky Way (MW).
The observed fractions of early-B stars which exhibit deep eclipses 0.25 <
Delta(m) (mag) < 0.65 and orbital periods 2 < P (days) < 20 in the MW, LMC, and
SMC span a narrow range of (0.7-1.0)%, which is a model independent result.
After correcting for geometrical selection effects and incompleteness toward
low-mass companions, we find for early-B stars in all three environments: (1) a
close binary fraction of (22+/-5)% across orbital periods 2 < P (days) < 20 and
mass ratios q = M_2/M_1 > 0.1, (2) an intrinsic orbital period distribution
slightly skewed toward shorter periods relative to a distribution that is
uniform in log P, (3) a mass-ratio distribution weighted toward low-mass
companions, and (4) a small, nearly negligible excess fraction of twins with q
> 0.9. Our fitted parameters derived for the MW eclipsing binaries match the
properties inferred from nearby, early-type spectroscopic binaries, which
further validates our results. There are no statistically significant trends
with metallicity, demonstrating that the close binary properties of massive
stars do not vary across metallicities -0.7 < log(Z/Z_sun) < 0.0 beyond the
measured uncertainties.
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Manifestations of dipole-dipole interactions in dilute thermal gases are
difficult to sense because of strong inhomogeneous broadening. Recent
experiments reported signatures of such interactions in fluorescence
detection-based measurements of multiple quantum coherence (MQC) signals, with
many characteristic features hitherto unexplained. We develop an original open
quantum systems theory of MQC in dilute thermal gases, which allows us to
resolve this conundrum. Our theory accounts for the vector character of the
atomic dipoles as well as for driving laser pulses of arbitrary strength,
includes the far-field coupling between the dipoles, which prevails in dilute
ensembles, and effectively incorporates atomic motion via a disorder average.
We show that collective decay processes -- which were ignored in previous
treatments employing the electrostatic form of dipolar interactions -- play a
key role in the emergence of MQC signals.
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The substrate temperature required for synthesis of graphene in an arc
discharge plasma was studied. It was shown that an increase of copper substrate
temperature up to the melting point leads to an increase in the amount of
graphene production and the quality of graphene sheets. Favorable range of
substrate temperatures for arc-based graphene synthesis was determined, and it
is in a relatively narrow range of about 1210-1340 K.
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A lamination of a graph embedded on a surface is a collection of pairwise
disjoint non-contractible simple closed curves drawn on the graph. In the case
when the surface is a sphere with three punctures (a.k.a. a pair of pants), we
first identify the lamination space of a graph embedded on that surface as a
lattice polytope, then we characterize the polytopes that arise as the
lamination space of some graph on a pair of pants. This characterizes the image
of a purely topological version of the spectral map for the vector bundle
Laplacian for a flat connection on a pair of pants. The proof uses a graph
exploration technique akin to the peeling of planar maps.
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While the periodic Anderson model (PAM) has been recognized as a good model
for various heavy f-electron systems, here we design a purely organic polymer
whose low-energy physics can be captured by PAM. By means of the spin density
functional calculation, we show that polymer of dimethylaminopyrrole is a
candidate, where its ground state can indeed be magnetic depending on the
doping. We discuss the factors favoring ferromagnetic ground state.
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Let $F$ be a locally compact non-Archimedean field, and let $B/F$ be a
division algebra of dimension 4. The Jacquet-Langlands correspondence provides
a bijection between smooth irreducible representations of $B^\times$ of
dimension $>1$ and irreducible cuspidal representations of $GL_2(F)$. We
present a new construction of this bijection in which the preservation of
epsilon factors is automatic.
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