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arxiv_dataset-88001708.04988 | Warp: a method for neural network interpretability applied to gene
expression profiles
q-bio.GN cs.AI
We show a proof of principle for warping, a method to interpret the inner
working of neural networks in the context of gene expression analysis. Warping
is an efficient way to gain insight to the inner workings of neural nets and
make them more interpretable. We demonstrate the ability of warping to recover
meaningful information for a given class on a samplespecific individual basis.
We found warping works well in both linearly and nonlinearly separable
datasets. These encouraging results show that warping has a potential to be the
answer to neural networks interpretability in computational biology.
| arxiv topic:q-bio.GN cs.AI |
arxiv_dataset-88011708.05088 | Stellar population of the superbubble N206 in the LMC I. Analysis of the
Of-type stars
astro-ph.SR astro-ph.GA
Massive stars are the key agents of feedback. Consequently, quantitative
analysis of massive stars are required to understand how the feedback of these
objects shapes/ creates the large scale structures of the ISM. The giant HII
region N206 in the Large Magellanic Cloud contains an OB association that
powers a X-ray superbubble, serving as an ideal laboratory in this context. We
obtained optical spectra with the muti-object spectrograph FLAMES at the
ESO-VLT. When possible, the optical spectroscopy was complemented by UV spectra
from the HST, IUE, and FUSE archives. Detailed spectral classifications are
presented for our sample Of-type stars. For the quantitative spectroscopic
analysis we use the Potsdam Wolf-Rayet (PoWR) model atmosphere code. The
physical parameters and nitrogen abundances of our sample stars are determined
by fitting synthetic spectra to the observations. The stellar and wind
parameters of nine Of-type stars are used to construct wind momentum,luminosity
relationship. We find that our sample follows a relation close to the
theoretical prediction, assuming clumped winds. The most massive star in the
N206 association is an Of supergiant which has a very high mass-loss rate. Two
objects in our sample reveal composite spectra, showing that the Of primaries
have companions of late O subtype. All stars in our sample have an evolutionary
age less than 4 million years, with the O2-type star being the youngest. All
these stars show a systematic discrepancy between evolutionary and
spectroscopic masses. All stars in our sample are nitrogen enriched. Nitrogen
enrichment shows a clear correlation with increasing projected rotational
velocities. The mechanical energy input from the Of stars alone is comparable
to the energy stored in the N206 superbubble as measured from the observed
X-ray and H alpha emission.
| arxiv topic:astro-ph.SR astro-ph.GA |
arxiv_dataset-88021708.05188 | Asymptotics for a Class of Meandric Systems, via the Hasse Diagram of
NC(n)
math.CO math.OA math.PR
We consider closed meandric systems, and their equivalent description in
terms of the Hasse diagrams of the lattices of non-crossing partitions $NC(n)$.
In this equivalent description, the number of components of a random meandric
system of order $n$ translates into the distance between two partitions in
$NC(n)$. We focus on a class of couples $(\pi,\rho)\in NC(n)^2$ -- namely the
ones where $\pi$ is conditioned to be an interval partition -- for which it
turns out to be tractable to study distances in the Hasse diagram. As a
consequence, we observe a non-trivial class of meanders (i.e. connected
meandric systems), which we call "meanders with shallow top", and which can be
explicitly enumerated. Moreover, the expected number of components for a random
"meandric system with shallow top", is asymptotically $(9n+28)/27$. Our
calculations concerning expected number of components are related to the idea
of taking the derivative at $t=1$ in a semigroup for the operation $\boxplus$
of free probability (but the underlying considerations are presented in a
self-contained way, and can be followed without assuming a free probability
background).
Let $c_{n}'$ denote the expected number of components of a general,
unconditioned, meandric system of order $n$. A variation of the methods used in
the shallow-top case allows us to prove that $\mathrm{lim\
inf}_{n\to\infty}c_{n}'/n\geq0.17$. We also note that, by a direct elementary
argument, one has $\mathrm{lim\ sup}_{n\to\infty}c_{n}'/n\leq0.5$. These bounds
support the conjecture that $c_{n}'$ follows a regime of "constant times $n$"
(where numerical experiments suggest that the constant should be
$\approx0.23$).
| arxiv topic:math.CO math.OA math.PR |
arxiv_dataset-88031708.05288 | Towards a theory of unbounded locally solid Riesz spaces
math.FA
We introduce the notion of unbounded locally solid Riesz spaces, and
investigate its fundamental properties.
| arxiv topic:math.FA |
arxiv_dataset-88041708.05388 | A Theoretical Model of X-ray Jets from Young Stellar Objects
astro-ph.SR astro-ph.EP
There is a subclass of the X-ray jets from young stellar objects which are
heated very close to the footpoint of the jets, particularly DG Tau jets.
Previous models attribute the strong heating to shocks in the jets. However,
the mechanism that localizes the heating at the footpoint remains puzzling. We
presented a different model of such X-ray jets, in which the disk atmosphere is
magnetically heated. Our disk corona model is based on the so-called nanoflare
model for the solar corona. We show that the magnetic heating near the disks
can result in the formation of a hot corona with a temperature of > 10^6 K even
if the average field strength in the disk is moderately weak, > 1 G. We
determine the density and the temperature at the jet base by considering the
energy balance between the heating and cooling. We derive the scaling relations
of the mass loss rate and terminal velocity of jets. Our model is applied to
the DG Tau jets. The observed temperature and estimated mass loss rate are
consistent with the prediction of our model in the case of the disk magnetic
field strength of ~20 G and the heating region of < 0.1 au. The derived scaling
relation of the temperature of X-ray jets could be a useful tool to estimate
the magnetic field strength. We also found that the jet X-ray can have a
significant impact on the ionization degree near the disk surface and the
dead-zone size.
| arxiv topic:astro-ph.SR astro-ph.EP |
arxiv_dataset-88051708.05488 | A Characterization of $(4,2)$-Choosable Graphs
math.CO
A graph $G$ is \emph{$(a,b)$-choosable} if given any list assignment $L$ with
$|L(v)|=a$ for each $v\in V(G)$ there exists a function $\varphi$ such that
$\varphi(v)\in L(v)$ and $|\varphi(v)|=b$ for all $v\in V(G)$, and whenever
vertices $x$ and $y$ are adjacent $\varphi(x)\cap \varphi(y)=\emptyset$. Meng,
Puleo, and Zhu conjectured a characterization of (4,2)-choosable graphs. We
prove their conjecture.
| arxiv topic:math.CO |
arxiv_dataset-88061708.05588 | On the Strichartz estimates for orthonormal systems of initial data with
regularity
math.FA
The classical Strichartz estimates for the free Schr\"odinger propagator have
recently been substantially generalised to estimates of the form \[
\bigg\|\sum_j\lambda_j|e^{it\Delta}f_j|^2\bigg\|_{L^p_tL^q_x}\lesssim\|\lambda\|_{\ell^\alpha}
\] for orthonormal systems $(f_j)_j$ of initial data in $L^2$, firstly in work
of Frank--Lewin--Lieb--Seiringer and later by Frank--Sabin. The primary
objective is identifying the largest possible $\alpha$ as a function of $p$ and
$q$, and in contrast to the classical case, for such estimates the critical
case turns out to be $(p,q) = (\frac{d+1}{d},\frac{d+1}{d-1})$. We consider the
case of orthonormal systems $(f_j)_j$ in the homogeneous Sobolev spaces
$\dot{H}^s$ for $s \in (0,\frac{d}{2})$ and we establish the sharp value of
$\alpha$ as a function of $p$, $q$ and $s$, except possibly an endpoint in
certain cases, at which we establish some weak-type estimates. Furthermore, at
the critical case $(p,q) = (\frac{d+1}{d-2s},\frac{d(d+1)}{(d-1)(d-2s)})$ for
general $s$, we show the veracity of the desired estimates when $\alpha = p$ if
we consider frequency localised estimates, and the failure of the
(non-localised) estimates when $\alpha = p$; this exhibits the difficulty of
upgrading from frequency localised estimates in this context, again in contrast
to the classical setting.
| arxiv topic:math.FA |
arxiv_dataset-88071708.05688 | Human Uncertainty and Ranking Error -- The Secret of Successful
Evaluation in Predictive Data Mining
cs.HC cs.AI
One of the most crucial issues in data mining is to model human behaviour in
order to provide personalisation, adaptation and recommendation. This usually
involves implicit or explicit knowledge, either by observing user interactions,
or by asking users directly. But these sources of information are always
subject to the volatility of human decisions, making utilised data uncertain to
a particular extent. In this contribution, we elaborate on the impact of this
human uncertainty when it comes to comparative assessments of different data
mining approaches. In particular, we reveal two problems: (1) biasing effects
on various metrics of model-based prediction and (2) the propagation of
uncertainty and its thus induced error probabilities for algorithm rankings.
For this purpose, we introduce a probabilistic view and prove the existence of
those problems mathematically, as well as provide possible solution strategies.
We exemplify our theory mainly in the context of recommender systems along with
the metric RMSE as a prominent example of precision quality measures.
| arxiv topic:cs.HC cs.AI |
arxiv_dataset-88081708.05788 | Computer Algebra for Microhydrodynamics
physics.flu-dyn cs.MS
I describe a method for computer algebra that helps with laborious
calculations typically encountered in theoretical microhydrodynamics. The
program mimics how humans calculate by matching patterns and making
replacements according to the rules of algebra and calculus. This note gives an
overview and walks through an example, while the accompanying code repository
contains the implementation details, a tutorial, and more examples. The code
repository is attached as supplementary material to this note, and maintained
at https://github.com/jeinarsson/matte
| arxiv topic:physics.flu-dyn cs.MS |
arxiv_dataset-88091708.05888 | An efficient distribution method for nonlinear two-phase flow in highly
heterogeneous multidimensional stochastic porous media
physics.flu-dyn
In the context of stochastic two-phase flow in porous media, we introduce a
novel and efficient method to estimate the probability distribution of the
wetting saturation field under uncertain rock properties in highly
heterogeneous porous systems, where streamline patterns are dominated by
permeability heterogeneity, and for slow displacement processes (viscosity
ratio close to unity). Our method, referred to as the frozen streamline
distribution method (FROST), is based on a physical understanding of the
stochastic problem. Indeed, we identify key random fields that guide the
wetting saturation variability, namely fluid particle times of flight and
injection times. By comparing saturation statistics against full-physics Monte
Carlo simulations, we illustrate how this simple, yet accurate FROST method
performs under the preliminary approximation of frozen streamlines. Further, we
inspect the performance of an accelerated FROST variant that relies on a
simplification about injection time statistics. Finally, we introduce how
quantiles of saturation can be efficiently computed within the FROST framework,
hence leading to robust uncertainty assessment.
| arxiv topic:physics.flu-dyn |
arxiv_dataset-88101708.05988 | Acoustic Macroscopic Rigid Body Levitation by Responsive Boundary
Hologram
physics.app-ph
Propagated acoustic waves, which generate radiation pressure, exert a
non-contact force on a remote object. By suitably designing the wave field,
remote tweezers are produced that stably levitate particles in the air without
any mechanical contact forces. Recent works have revealed that holographic
traps can levitate particles even with a single-sided wave source. However, the
levitatable objects in the previous studies were limited to particles smaller
than the wavelength, or flat parts placed near a rigid wall. Here, we achieve a
stable levitation of a macroscopic rigid body by a holographic design of
acoustic field without any dynamic control. The levitator models the acoustic
radiation force and torque applied to a rigid body by discretising the body's
surface, as well as the acoustic wave sources, and optimizes the acoustic field
on the body surface to achieve the Lyapunov stability so that the field can
properly respond to the fluctuation of the body position and rotation. In an
experiment, a 40 kHz (8.5 mm wavelength) ultrasonic phased array levitated a
polystyrene sphere and a regular octahedron with a size of ~50 mm located 200
mm away from acoustic elements in the air. This method not only expands the
variety of levitatable objects but also contributes to microscopic contexts,
such as in-vivo micromachines, since shorter-wavelength ultrasound than the
size of target objects can be used to achieve higher controllability and
stability.
| arxiv topic:physics.app-ph |
arxiv_dataset-88111708.06088 | Skew monoidal categories and skew multicategories
math.CT
We describe a perfect correspondence between skew monoidal categories and
certain generalised multicategories, called skew multicategories, that arise in
nature.
| arxiv topic:math.CT |
arxiv_dataset-88121708.06188 | Numerical methods for SDEs with drift discontinuous on a set of positive
reach
math.NA math.PR
For time-homogeneous stochastic differential equations (SDEs) it is enough to
know that the coefficients are Lipschitz to conclude existence and uniqueness
of a solution, as well as the existence of a strongly convergent numerical
method for its approximation. Here we introduce a notion of piecewise Lipschitz
functions and study SDEs with a drift coefficient satisfying only this weaker
regularity condition. For these SDEs we can construct a strongly convergent
approximation scheme, if the set of discontinuities is a sufficiently smooth
hypersurface satisfying the geometrical property of being of positive reach. We
then arrive at similar conclusions as in the Lipschitz case. We will see that,
although SDEs are in the center of our interest, we will talk surprisingly
little about probability theory here.
| arxiv topic:math.NA math.PR |
arxiv_dataset-88131708.06288 | Comments on Higher Rank Wilson Loops in ${\cal N}=2^*$
hep-th
For ${\cal N}=2^*$ theory with $U(N)$ gauge group we evaluate expectation
values of Wilson loops in representations described by a rectangular Young
tableau with $n$ rows and $k$ columns. The evaluation reduces to a two-matrix
model and we explain, using a combination of numerical and analytical
techniques, the general properties of the eigenvalue distributions in various
regimes of parameters $(N,\lambda,n,k)$ where $\lambda$ is the 't Hooft
coupling. In the large $N$ limit we present analytic results for the leading
and sub-leading contributions. In the particular cases of only one row or one
column we reproduce previously known results for the totally symmetry and
totally antisymmetric representations. We also extensively discusss the ${\cal
N}=4$ limit of the ${\cal N}=2^*$ theory. While establishing these connections
we clarify aspects of various orders of limits and how to relax them; we also
find it useful to explicitly address details of the genus expansion. As a
result, for the totally symmetric Wilson loop we find new contributions that
improve the comparison with the dual holographic computation at one loop order
in the appropriate regime.
| arxiv topic:hep-th |
arxiv_dataset-88141708.06388 | Riccati-Ermakov systems and explicit solutions for variable coefficient
reaction-diffusion equations
math-ph math.MP
We present several families of nonlinear reaction diffusion equations with
variable coefficients including Fisher-KPP and Burgers type equations. Special
exact solutions such as traveling wave, rational, triangular wave and N-wave
type solutions are shown. By means of similarity transformations the variable
coefficients are conditioned to satisfy Riccati or Ermakov systems of
equations. When the Riccati system is used, conditions are established so that
finite-time singularities might occur. The solutions presented contain
multi-parameters providing a control on the dynamics of the solutions. In the
suplementary material, we provide a computer algebra verification of the
solutions and exemplify nontrivial dynamics of the solutions.
| arxiv topic:math-ph math.MP |
arxiv_dataset-88151708.06488 | Constraints on parameter space of BLMSSM from particle mass
hep-ph
To explaine the matter-antimatter asymmetry, a supersymmetric extention of
the standard model is proposed where baryon and lepton numbers are local
gauged(BLMSSM), and exotic superfields are introduced when gauge group is
enlarged to $SU(3)_C\otimes SU(2)_L\otimes U(1)_Y \otimes U(1)_B \otimes
U(1)_L$. As signals of new physics have not been observed on Large Hadron
Collider, the parameter space relevant to the masses of new particles is
stringently constrainted. By diagonalizing the mass squared matrices for
neutral scalar sectors and the mass matrices for exotic quarks, we plot the
masses of new particles varying with different parameters with some
assumptions, so the constraints on model parameter is obtained with different
lower limit on particle mass.
| arxiv topic:hep-ph |
arxiv_dataset-88161708.06588 | On the Fine Selmer Group
math.NT
Let $E/\mathbb{Q}$ be an elliptic curve, $p$ an odd prime and $K_{\infty}/K$
the anticyclotomic $\mathbb{Z}_p$-extension of a quadratic imaginary field $K$.
In a previous article the author conjectured that the fine $p^{\infty}$-Selmer
group $R_{p^{\infty}}(E/K_{\infty})$ is confinitely generated over
$\mathbb{Z}_p$. In this note we prove this conjecture assuming some hypotheses
on $E$ and $p$.
| arxiv topic:math.NT |
arxiv_dataset-88171708.06688 | A Symmetry Analysis of the $\infty$-Polylaplacian
math-ph math.AP math.MP
In this work we use Lie group theoretic methods and the theory of prolonged
group actions to study two fully nonlinear partial differential equations
(PDEs). First we consider a third order PDE in two spatial dimensions that
arises as the analogue of the Euler-Lagrange equations from a second order
variational principle in $L^{\infty}$. The equation, known as the
$\infty$-Polylaplacian, is a higher order generalisation of the
$\infty$-Laplacian, also known as Aronsson's equation. In studying this problem
we consider a reduced equation whose relation to the $\infty$-Polylaplacian can
be considered analogous to the relationship of the Eikonal to Aronsson's
equation. Solutions of the reduced equation are also solutions of the
$\infty$-Polylaplacian. For the first time we study the Lie symmetries admitted
by these two problems and use them to characterise and construct invariant
solutions under the action of one dimensional symmetry subgroups.
| arxiv topic:math-ph math.AP math.MP |
arxiv_dataset-88181708.06788 | Channel resolution enhancement through scalability of nano/micro-scale
thickness and width of SU-8 polymer based optical channels using UV
lithography
physics.app-ph physics.optics
This paper reports on an approach for fabrication of micro-channels with
nanometer thickness achieved by optimization of UV lithography processes.
Rectangular micro-channels with a staple edge are fabricated over the surface
of a silicon wafer substrate in which a sub-micron layer of diluted SU-8 thin
film has been coated. The optimization of the process parameters including the
duration of a two-step pre- and post-baking process, UV exposure dosage, and
finally chemical developing time with constant agitation produces
micro-channels with high contrast edges and thickness below 100 nm is achieved.
The dimensions achieved using this approach has potential applications in
sub-micron optical waveguides and nanoelectromechanical (NEMS) devices.
| arxiv topic:physics.app-ph physics.optics |
arxiv_dataset-88191708.06888 | Some Gruss type Inequalities using Pompeiu's mean value theorem on
Conformable Fractional Calculus
math.CA
The main objective of this paper is to obtain some Gruss Like Inequalities
using Pompeiu's mean value theorem on Conformable Fractional Calculus.
| arxiv topic:math.CA |
arxiv_dataset-88201708.06988 | Paving the Roadway for Safety of Automated Vehicles: An Empirical Study
on Testing Challenges
cs.SE cs.AI cs.RO
The technology in the area of automated vehicles is gaining speed and
promises many advantages. However, with the recent introduction of
conditionally automated driving, we have also seen accidents. Test protocols
for both, conditionally automated (e.g., on highways) and automated vehicles do
not exist yet and leave researchers and practitioners with different
challenges. For instance, current test procedures do not suffice for fully
automated vehicles, which are supposed to be completely in charge for the
driving task and have no driver as a back up. This paper presents current
challenges of testing the functionality and safety of automated vehicles
derived from conducting focus groups and interviews with 26 participants from
five countries having a background related to testing automotive safety-related
topics.We provide an overview of the state-of-practice of testing active safety
features as well as challenges that needs to be addressed in the future to
ensure safety for automated vehicles. The major challenges identified through
the interviews and focus groups, enriched by literature on this topic are
related to 1) virtual testing and simulation, 2) safety, reliability, and
quality, 3) sensors and sensor models, 4) required scenario complexity and
amount of test cases, and 5) handover of responsibility between the driver and
the vehicle.
| arxiv topic:cs.SE cs.AI cs.RO |
arxiv_dataset-88211708.07088 | Delay Analysis for Wireless D2D Caching with Inter-cluster Cooperation
cs.IT math.IT
Proactive wireless caching and D2D communication have emerged as promising
techniques for enhancing users' quality of service and network performance. In
this paper, we propose a new architecture for D2D caching with inter-cluster
cooperation. We study a cellular network in which users cache popular files and
share them with other users either in their proximity via D2D communication or
with remote users using cellular transmission. We characterize the network
average delay per request from a queuing perspective. Specifically, we
formulate the delay minimization problem and show that it is NP-hard.
Furthermore, we prove that the delay minimization problem is equivalent to
minimization of a non-increasing monotone super modular function subject to a
partition matroid constraint. A computationally efficient greedy algorithm is
proposed which is proven to be locally optimal within a factor 2 of the
optimum. Simulation results show more than 45% delay reduction compared to a
D2D caching system without inter-cluster cooperation.
| arxiv topic:cs.IT math.IT |
arxiv_dataset-88221708.07188 | Self-Organization in Traffic Lights: Evolution of Signal Control with
Advances in Sensors and Communications
cs.SY
Traffic signals are ubiquitous devices that first appeared in 1868. Recent
advances in information and communications technology (ICT) have led to
unprecedented improvements in such areas as mobile handheld devices (i.e.,
smartphones), the electric power industry (i.e., smart grids), transportation
infrastructure, and vehicle area networks. Given the trend towards
interconnectivity, it is only a matter of time before vehicles communicate with
one another and with infrastructure. In fact, several pilots of such
vehicle-to-vehicle and vehicle-to-infrastructure (e.g. traffic lights and
parking spaces) communication systems are already operational. This survey of
autonomous and self-organized traffic signaling control has been undertaken
with these potential developments in mind. Our research results indicate that,
while many sophisticated techniques have attempted to improve the scheduling of
traffic signal control, either real-time sensing of traffic patterns or a
priori knowledge of traffic flow is required to optimize traffic. Once this is
achieved, communication between traffic signals will serve to vastly improve
overall traffic efficiency.
| arxiv topic:cs.SY |
arxiv_dataset-88231708.07288 | Identifying Criticality in Higher Dimensions by Time Matrix Product
State
cond-mat.str-el
Characterizing criticality in quantum many-body systems of dimension $\ge 2$
is one of the most important challenges of the contemporary physics. In
principle, there is no generally valid theoretical method that could solve this
problem. In this work, we propose an efficient approach to identify the
criticality of quantum systems in higher dimensions. Departing from the
analysis of the numerical renormalization group flows, we build a general
equivalence between the higher-dimensional ground state and a one-dimensional
(1D) quantum state defined in the imaginary time direction in terms of the
so-called time matrix product state (tMPS). We show that the criticality of the
targeted model can be faithfully identified by the tMPS, using the mature
scaling schemes of correlation length and entanglement entropy in 1D quantum
theories. We benchmark our proposal with the results obtained for the
Heisenberg anti-ferromagnet on honeycomb lattice. We demonstrate critical
scaling relation of the tMPS for the gapless case, and a trivial scaling for
the gapped case with spatial anisotropy. The critical scaling behaviors are
insensitive to the system size, suggesting the criticality can be identified in
small systems. Our tMPS scheme for critical scaling shows clearly that the
spin-1/2 kagom\'e Heisenberg antiferromagnet has a gapless ground state. More
generally, the present study indicates that the 1D conformal field theories in
imaginary time provide a very useful tool to characterize the criticality of
higher dimensional quantum systems.
| arxiv topic:cond-mat.str-el |
arxiv_dataset-88241708.07388 | Symbol, Surface operators and $S$-duality
hep-th
We study rigid surface operators in the $N=4$ supersymmetric Yang-Mills
theories with gauge groups $SO(n)$ and $Sp(2n)$. Using maps $X_S$ and $Y_S$
between these two theories, Wyllard made explicit proposals for how the
$S$-duality map should act on certain subclasses of surface operators. We study
the maps $X_S$ and $Y_S$ further and simplify the construction of symbol
invariant of rigid surface operators by a convenient trick. By consistency
checks, we recover and extend the $S$-duality maps proposed by Wyllard. We find
new subclasses of rigid surface operators related by $S$-duality. We try to
explain the exceptions of $S$-duality maps. We also discuss the extension of
the techniques used in the $B_n/C_n$ theories to the $D_n$ theories.
| arxiv topic:hep-th |
arxiv_dataset-88251708.07488 | Off-axis short GRBs from structured jets as counterparts to GW events
astro-ph.HE
Binary neutron star mergers are considered to be the most favorable sources
that produce electromagnetic (EM) signals associated with gravitational waves
(GWs). These mergers are the likely progenitors of short duration gamma-ray
bursts (GRBs). The brief gamma-ray emission (the "prompt GRB" emission) is
produced by ultra-relativistic jets, as a result, this emission is strongly
beamed over a small solid angle along the jet. It is estimated to be a decade
or more before a short GRB jet within the LIGO volume points along our line of
sight. For this reason, the study of the prompt signal as an EM counterpart to
GW events has been sparse. We argue that for a realistic jet model, one whose
luminosity and Lorentz factor vary smoothly with angle, the prompt signal can
be detected for a significantly broader range of viewing angles. This can lead
to a new type of EM counterpart, an "off-axis" short GRB. Our estimates and
simulations show that it is feasible to detect these signals with the aid of
the temporal coincidence from a LIGO trigger, even if the observer is
substantially misaligned with respect to the jet.
| arxiv topic:astro-ph.HE |
arxiv_dataset-88261708.07588 | Central Moment Analogues to Linear Optically Generated Cluster States
quant-ph
Two-mode squeezed states in the limit of small squeezing, Hong-Ou-Mandel
interference and post selection on coincidence counts are some of the staples
of linear quantum optics. We show that by using classical expectations on
central moments of intensities, we can remove the requirement of small
squeezing necessary for high fidelity coincidence detection. Utilizing existing
techniques to probabilistically generate a cluster state, we construct a
statistical analogue with deterministic generation at the cost of losing the
ability to feed forward and requiring statistical averaging.
| arxiv topic:quant-ph |
arxiv_dataset-88271708.07688 | Phase partitioning in a novel near equi-atomic AlCuFeMn alloy
cond-mat.mtrl-sci
A novel low cost, near equi-atomic alloy comprising of Al, Cu, Fe and Mn is
synthesized using arc-melting technique. The cast alloy possesses a dendritic
microstructure where the dendrites consist of disordered FCC and ordered FCC
phases. The inter-dendritic region is comprised of ordered FCC phase and
spinodally decomposed BCC phases. A Cu segregation is observed in the
inter-dendritic region while dendritic region is rich in Fe. The bulk hardness
of the alloy is ~ 380 HV, indicating significant yield strength.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-88281708.07788 | Stability of the Lanczos Method for Matrix Function Approximation
cs.DS cs.NA math.NA
The ubiquitous Lanczos method can approximate $f(A)x$ for any symmetric $n
\times n$ matrix $A$, vector $x$, and function $f$. In exact arithmetic, the
method's error after $k$ iterations is bounded by the error of the best
degree-$k$ polynomial uniformly approximating $f(x)$ on the range
$[\lambda_{min}(A), \lambda_{max}(A)]$. However, despite decades of work, it
has been unclear if this powerful guarantee holds in finite precision.
We resolve this problem, proving that when $\max_{x \in [\lambda_{min},
\lambda_{max}]}|f(x)| \le C$, Lanczos essentially matches the exact arithmetic
guarantee if computations use roughly $\log(nC\|A\|)$ bits of precision. Our
proof extends work of Druskin and Knizhnerman [DK91], leveraging the stability
of the classic Chebyshev recurrence to bound the stability of any polynomial
approximating $f(x)$.
We also study the special case of $f(A) = A^{-1}$, where stronger guarantees
hold. In exact arithmetic Lanczos performs as well as the best polynomial
approximating $1/x$ at each of $A$'s eigenvalues, rather than on the full
eigenvalue range. In seminal work, Greenbaum gives an approach to extending
this bound to finite precision: she proves that finite precision Lanczos and
the related CG method match any polynomial approximating $1/x$ in a tiny range
around each eigenvalue [Gre89].
For $A^{-1}$, this bound appears stronger than ours. However, we exhibit
matrices with condition number $\kappa$ where exact arithmetic Lanczos
converges in $polylog(\kappa)$ iterations, but Greenbaum's bound predicts
$\Omega(\kappa^{1/5})$ iterations. It thus cannot offer significant improvement
over the $O(\kappa^{1/2})$ bound achievable via our result. Our analysis raises
the question of if convergence in less than $poly(\kappa)$ iterations can be
expected in finite precision, even for matrices with clustered, skewed, or
otherwise favorable eigenvalue distributions.
| arxiv topic:cs.DS cs.NA math.NA |
arxiv_dataset-88291708.07888 | Active Expansion Sampling for Learning Feasible Domains in an Unbounded
Input Space
cs.LG stat.ML
Many engineering problems require identifying feasible domains under implicit
constraints. One example is finding acceptable car body styling designs based
on constraints like aesthetics and functionality. Current active-learning based
methods learn feasible domains for bounded input spaces. However, we usually
lack prior knowledge about how to set those input variable bounds. Bounds that
are too small will fail to cover all feasible domains; while bounds that are
too large will waste query budget. To avoid this problem, we introduce Active
Expansion Sampling (AES), a method that identifies (possibly disconnected)
feasible domains over an unbounded input space. AES progressively expands our
knowledge of the input space, and uses successive exploitation and exploration
stages to switch between learning the decision boundary and searching for new
feasible domains. We show that AES has a misclassification loss guarantee
within the explored region, independent of the number of iterations or labeled
samples. Thus it can be used for real-time prediction of samples' feasibility
within the explored region. We evaluate AES on three test examples and compare
AES with two adaptive sampling methods -- the Neighborhood-Voronoi algorithm
and the straddle heuristic -- that operate over fixed input variable bounds.
| arxiv topic:cs.LG stat.ML |
arxiv_dataset-88301708.07988 | Analytic model for tangential YORP
astro-ph.EP
The tangential YORP effect (TYORP) plays a significant role in the dynamical
evolution of asteroids, and up to now has only been studied numerically. This
paper describes the first analytic model of the TYORP effect. Although the
model rests on numerous physical and mathematical simplifications, the final
analytic expression for TYORP is found to be in agreement with the results of
rigorous numeric simulations to the accuracy of several tens per cent.
The obtained analytic expression is used to estimate the TYORP produced by
the non-flat surface of regolith, -- a contribution to TYORP that has never
been considered. It is found that the contribution to TYORP arising from
regolith can be comparable to the conventional TYORP produced by boulders.
Then, the analytic expression is fitted with a log-normal function and used
to integrate TYORP over all boulder sizes. The general trend of TYORP for
multiple boulders appears qualitatively similar to the trend of one boulder,
and also demonstrates a maximal TYORP at some particular rotation rate. The
obtained expression for integrated TYORP may be instrumental for simulations of
evolution of asteroids subject to TYORP.
To conclude, the physical origin of TYORP is discussed in light of the
constructed analytic model.
| arxiv topic:astro-ph.EP |
arxiv_dataset-88311708.08088 | Direct Photon Production and Azimuthal Anisotropy at Low Transverse
Momentum measured in PHENIX
nucl-ex
The PHENIX experiment discovered a large excess of low-$p_{T}$ direct photons
in Au+Au collisions at 200 GeV compared to reference p+p collisions, which has
been attributed to thermal radiation from the medium produced in the
collisions. At the same time the excess photons show a large azimuthal
anisotropy, expressed as Fourier coefficients $v_{2}$ and $v_{3}$. These
surprising results have not yet been fully described by theoretical models. We
will present the results obtained from real photons in the electromagnetic
calorimeter and photons converted on the outer shell of the Hadron Blind
Detector. PHENIX has also developed a new technique to identify conversion
photons without assuming the radius where the conversion happened. This method
greatly increases the available statistics and reduces systematic
uncertainties.
| arxiv topic:nucl-ex |
arxiv_dataset-88321708.08188 | Active Animations of Reduced Deformable Models with Environment
Interactions
cs.GR
We present an efficient spacetime optimization method to automatically
generate animations for a general volumetric, elastically deformable body. Our
approach can model the interactions between the body and the environment and
automatically generate active animations. We model the frictional contact
forces using contact invariant optimization and the fluid drag forces using a
simplified model. To handle complex objects, we use a reduced deformable model
and present a novel hybrid optimizer to search for the local minima
efficiently. This allows us to use long-horizon motion planning to
automatically generate animations such as walking, jumping, swimming, and
rolling. We evaluate the approach on different shapes and animations, including
deformable body navigation and combining with an open-loop controller for
realtime forward simulation.
| arxiv topic:cs.GR |
arxiv_dataset-88331708.08288 | Stylizing Face Images via Multiple Exemplars
cs.CV cs.GR cs.MM
We address the problem of transferring the style of a headshot photo to face
images. Existing methods using a single exemplar lead to inaccurate results
when the exemplar does not contain sufficient stylized facial components for a
given photo. In this work, we propose an algorithm to stylize face images using
multiple exemplars containing different subjects in the same style. Patch
correspondences between an input photo and multiple exemplars are established
using a Markov Random Field (MRF), which enables accurate local energy transfer
via Laplacian stacks. As image patches from multiple exemplars are used, the
boundaries of facial components on the target image are inevitably
inconsistent. The artifacts are removed by a post-processing step using an
edge-preserving filter. Experimental results show that the proposed algorithm
consistently produces visually pleasing results.
| arxiv topic:cs.CV cs.GR cs.MM |
arxiv_dataset-88341708.08388 | Random edge states on a finite lattice
cond-mat.dis-nn cond-mat.mes-hall
A finite photonic lattice with two bands and a random gap is considered.
Using a two-dimensional Dirac equation, the effect of a random sign of the
Dirac mass is studied numerically. The edge state at the sample boundary has a
strong influence on the electromagnetic field and its polarization inside the
sample. The creation of edge states through a randomly fluctuating sign of the
Dirac mass defeats Anderson localization and allows the electromagnetic field
to distribute over the entire sample. The width of the distribution increases
with an increasing gap due to increasing sharpness of the edge states. These
results are compared with those of a random one-band Helmholtz equation. In
contrast to the Dirac model, the one-band model displays a clear signature of
Anderson localization.
| arxiv topic:cond-mat.dis-nn cond-mat.mes-hall |
arxiv_dataset-88351708.08488 | The jet of the young star RW Aur A and related problems
astro-ph.SR
Comparing the images of the jet of the young star RW Aur A, separated by a
period of 21.3 years, we found that the outermost jet's knots have emerged
$\approx 350$ yr ago. We argue that at that moment the jet itself has appeared
and intensive accretion onto the star has began due to the rearrangement of its
protoplanetary disk structure caused by the tidal effect of the companion RW
Aur B. More precisely, we assume that the increase of accretion is a response
to changing conditions in the outer disk regions, which followed after the
sound wave, generated by these changes, crossed the disk in a radial direction.
The difference in the parameters of the blue and red lobes of the RW Aur A jet,
according to our opinion, is a result of the asymmetric distribution of the
circumstellar matter above and below the disk, due to a fly-by of the
companion. It was found from the analysis of RW Aur historical light curve that
deep and long $(\Delta t>150$ days) dimmings of RW Aur A observed after 2010
yr, had no analogues in the previous 110 years. We also associate the change in
the character of the photometric variability of the star with the rearrangement
of the structure of inner $(r<1$ a.u.) regions of its protoplanetary disk and
discuss why these changes began only 350 years after the beginning of the
active accretion phase.
| arxiv topic:astro-ph.SR |
arxiv_dataset-88361708.08588 | Analysis of high-harmonic generation in terms of complex Floquet
spectral analysis
quant-ph physics.optics
Recent developments on intense laser sources is opening a new field of
optical sciences. An intense coherent light beam strongly interacting with the
matter causes a coherent motion of a particle, forming a strongly dressed
excited particle. A photon emission from this dressed excited particle is a
strong nonlinear process causing high-harmonic generation(HHG), where the
perturbation analysis is broken down. In this work, we study a coherent photon
emission from a strongly dressed excited atom in terms of complex spectral
analysis in the extended Floquet-Hilbert-space. We have obtained the
eigenstates of the total Hamiltonian with use of Feshbach-Brilloiun-Wigner
projection method. In this extended space, the eigenstates of the total
Hamiltonian consisting of the radiation field and the atom system have complex
eigenvalues whose imaginary part represents the decay rate. Time evolution of
the system is represented by the complex eigenvector expansion so that the
correlation dynamics between the photon and the atom is fully taken into
account. The HHG is interpreted as the irreversible spontaneous photon emission
due to the resonance singularity in terms of the multiple Floquet states that
are generated by periodic external field. We have found that the interference
between the emitted photons over the different Floquet states causes spatial
pulse emission correlated with the decay process of the excited atom.
| arxiv topic:quant-ph physics.optics |
arxiv_dataset-88371708.08688 | Further Results on Size and Power of Heteroskedasticity and
Autocorrelation Robust Tests, with an Application to Trend Testing
math.ST stat.ME stat.TH
We complement the theory developed in Preinerstorfer and P\"otscher (2016)
with further finite sample results on size and power of heteroskedasticity and
autocorrelation robust tests. These allows us, in particular, to show that the
sufficient conditions for the existence of size-controlling critical values
recently obtained in P\"otscher and Preinerstorfer (2018) are often also
necessary. We furthermore apply the results obtained to tests for hypotheses on
deterministic trends in stationary time series regressions, and find that many
tests currently used are strongly size-distorted.
| arxiv topic:math.ST stat.ME stat.TH |
arxiv_dataset-88381708.08788 | Electron and phonon properties of noncentrosymmetric RhGe from ab initio
calculations
cond-mat.mtrl-sci
Band structure, Fermi surface, and phonon dispersions of noncentrosymmetric
B20-type RhGe are calculated ab initio for the first time and their evolution
with increasing pressure is investigated. We consider in detail
symmetry-conditioned features of the band structure, as well as
pressure-induced changes in the Fermi surface topology, which are expected to
affect the thermopower of RhGe. We also report on special calculations of
electric field gradients on the Rh and Ge nuclei and compare these results with
a very recent 111 Cd-TDPAC study of B20-RhGe.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-88391708.08888 | Periodic solutions for the N-vortex problem via a superposition
principle
math.DS math-ph math.MP
We examine the $N$-vortex problem on general domains
$\Omega\subset\mathbb{R}^2$ concerning the existence of nonstationary
collision-free periodic solutions. The problem in question is a first order
Hamiltonian system of the form $$
\Gamma_k\dot{z}_k=J\nabla_{z_k}H(z_1,\ldots,z_N),\quad k=1,\ldots,N, $$ where
$\Gamma_k\in\mathbb{R}\setminus\{0\}$ is the strength of the $k$th vortex at
position $z_k(t)\in\Omega$, $J\in\mathbb{R}^{2\times 2}$ is the standard
symplectic matrix and $$ H(z_1,\ldots,z_N)=-\frac{1}{2\pi}\sum_{\underset{k\neq
j}{k,j=1}}^N\Gamma_j\Gamma_k\log|z_k-z_j|-\sum_{k,j=1}^N\Gamma_j\Gamma_k
g(z_k,z_j) $$ with some regular and symmetric, but in general not explicitely
known function $g:\Omega\times\Omega\rightarrow \mathbb{R}$. The investigation
relies on the idea to superpose a stationary solution of a system of less than
$N$ vortices and several clusters of vortices that are close to rigidly
rotating configurations of the whole-plane system. We establish general
conditions on both, the stationary solution and the configurations, under which
multiple $T$-periodic solutions are shown to exist for every $T>0$ small
enough. The crucial condition holds in generic bounded domains and is
explicitely verified for an example in the unit disc $\Omega=B_1(0)$. In
particular we therefore obtain various examples of periodic solutions in
$B_1(0)$ that are not rigidly rotating configurations.
| arxiv topic:math.DS math-ph math.MP |
arxiv_dataset-88401708.08988 | Dual-fisheye lens stitching for 360-degree imaging
cs.CV cs.MM
Dual-fisheye lens cameras have been increasingly used for 360-degree
immersive imaging. However, the limited overlapping field of views and
misalignment between the two lenses give rise to visible discontinuities in the
stitching boundaries. This paper introduces a novel method for dual-fisheye
camera stitching that adaptively minimizes the discontinuities in the
overlapping regions to generate full spherical 360-degree images. Results show
that this approach can produce good quality stitched images for Samsung Gear
360 -- a dual-fisheye camera, even with hard-to-stitch objects in the stitching
borders.
| arxiv topic:cs.CV cs.MM |
arxiv_dataset-88411708.09088 | A Comparative Study of Matrix Factorization and Random Walk with Restart
in Recommender Systems
cs.IR
Between matrix factorization or Random Walk with Restart (RWR), which method
works better for recommender systems? Which method handles explicit or implicit
feedback data better? Does additional information help recommendation?
Recommender systems play an important role in many e-commerce services such as
Amazon and Netflix to recommend new items to a user. Among various
recommendation strategies, collaborative filtering has shown good performance
by using rating patterns of users. Matrix factorization and random walk with
restart are the most representative collaborative filtering methods. However,
it is still unclear which method provides better recommendation performance
despite their extensive utility.
In this paper, we provide a comparative study of matrix factorization and RWR
in recommender systems. We exactly formulate each correspondence of the two
methods according to various tasks in recommendation. Especially, we newly
devise an RWR method using global bias term which corresponds to a matrix
factorization method using biases. We describe details of the two methods in
various aspects of recommendation quality such as how those methods handle
cold-start problem which typically happens in collaborative filtering. We
extensively perform experiments over real-world datasets to evaluate the
performance of each method in terms of various measures. We observe that matrix
factorization performs better with explicit feedback ratings while RWR is
better with implicit ones. We also observe that exploiting global popularities
of items is advantageous in the performance and that side information produces
positive synergy with explicit feedback but gives negative effects with
implicit one.
| arxiv topic:cs.IR |
arxiv_dataset-88421708.09188 | Molecular transitions as probes of the physical conditions of
extragalactic environments
astro-ph.GA
Ab initio grids of time dependent chemical models, varying in gas density,
temperature, cosmic ray ionization rate, and radiation field, are used as input
to RADEX calculations. Tables of abundances, column densities, theoretical line
intensities, and line ratios for some of the most used dense gas tracers are
provided. The degree of correlation as well as degeneracy inherent in molecular
ratios is discussed. Comparisons of the theoretical intensities with example
observations are also provided. We find that, within the parameters space
explored, chemical abundances can be constrained by a well defined set of gas
density-gas temperature-cosmic ray ionization rate for the species we
investigate here. However, line intensities, as well as, more importantly, line
ratios, from different chemical models can be very similar leading to a clear
degeneracy. We also find that the gas subjected to a galactic cosmic ray
ionization rate will not necessarily have reached steady state by 1 Myr. The
species most affected by time dependency effects are HCN and CS, both high
density tracers. We use our method to fit an example set of data from two
galaxies. We find that (i) molecular line ratios can be easily matched even
with erroneous individual line intensities; (ii) no set of species can be
matched by a one-component ISM; (iii) a species may be a good tracer of an
energetic process but only under specific density and temperature conditions.
We show that by taking into consideration the chemistry behind each species and
the individual line intensities, many degeneracies that arise by just using
molecular line ratios can be avoided. Finally we show that using a species or a
ratio as a tracer of an individual energetic process (e.g. cosmic rays, UV)
ought to be done with caution.
| arxiv topic:astro-ph.GA |
arxiv_dataset-88431708.09288 | Exploring Gender Differences in Graduation Proficiency in Mathematics
Education Using a Markov Chain Model: Implications for Economic Growth in
Nigeria
math.HO
This study employs an ex-post facto research design to explore the
fluctuations of gender difference in academic achievement among graduating
students of mathematics education. Graduation statistics for a total of 1106
graduating students of mathematics education (923 males and 183 females) from a
University in North Central Nigeria were used to design a discrete-time Markov
chain model for the movement of the difference (d) in graduating proficiency
from one range of values (states) to the other. Additional goodness of fit test
($\chi$ 2 = 1.731, p = 0.99924) and t-test (t = 0.4055, p = 0.6852) unveiled
that d has stayed much the same over the 12 graduation cycles used in the
study, and that whatever factors determine the difference in academic
achievement between male and female graduating students of mathematics
education on a graduation cycle basis have remained much the same over the
years. Further analysis of the model predicted the closure of the observed
gender gap in the next 15 graduation cycles (p 15). The results of this study
has specifically highlighted the fact that female graduates of mathematics
education are as proficient as their male counterparts in driving value added
services in and beyond the education sub-sector of the Nigerian economy. Based
on the findings of this study, it was recommended that future work may consider
an in-depth investigation of the sensitivity of parameters that may have
influenced specific probabilities given in the model.
| arxiv topic:math.HO |
arxiv_dataset-88441708.09388 | A Model of the Pulsating Extremely Low-Mass White Dwarf Precursor WASP
0247-25B
astro-ph.SR
We present an analysis of the evolutionary and pulsation properties of the
extremely low-mass white dwarf precursor (B) component of the double-lined
eclipsing system WASP 0247-25. Given that the fundamental parameters of that
star have been obtained previously at a unique level of precision, WASP
0247-25B represents the ideal case for testing evolutionary models of this
newly-found category of pulsators. Taking into account the known constraints on
the mass, orbital period, effective temperature, surface gravity, and
atmospheric composition, we present a model that is compatible with these
constraints and show pulsation modes that have periods very close to the
observed values. Importantly, these modes are predicted excited. Although the
overall consistency remains perfectible, the observable properties of WASP
0247-25B are closely reproduced. A key ingredient of our binary evolutionary
models is represented by rotational mixing as the main competitor against
gravitational settling. Depending on assumptions made about the values of the
degree index l for the observed pulsation modes, we found three possible
seismic solutions. We discuss two tests, rotational splitting and multicolor
photometry, that should readily identify the modes and discriminate between
these solutions. However, this will require improved temporal resolution and
higher S/N observations than currently available.
| arxiv topic:astro-ph.SR |
arxiv_dataset-88451708.09488 | On Scheduling a Photolithography Process Containing Cluster Tools
math.OC
Photolithography is typically the bottleneck process in semiconductor
manufacturing. In this paper, we present a model for optimizing the scheduling
of the photolithography process in the presence of both individual and cluster
tools. The combination of these individual and cluster tools that process
various layers (stages) of the semiconductor manufacturing process flow is a
special type of flexible flowshop. We seek separately to minimize total
weighted completion time and maximize on-time delivery performance.
Experimental results suggest that our solution algorithms show promise for real
world implementation as they can help to improve resource utilization, reduce
job completion times, and decrease unnecessary delays in a wafer fab.
| arxiv topic:math.OC |
arxiv_dataset-88461708.09588 | Joint Separation and Denoising of Noisy Multi-talker Speech using
Recurrent Neural Networks and Permutation Invariant Training
cs.SD eess.AS
In this paper we propose to use utterance-level Permutation Invariant
Training (uPIT) for speaker independent multi-talker speech separation and
denoising, simultaneously. Specifically, we train deep bi-directional Long
Short-Term Memory (LSTM) Recurrent Neural Networks (RNNs) using uPIT, for
single-channel speaker independent multi-talker speech separation in multiple
noisy conditions, including both synthetic and real-life noise signals. We
focus our experiments on generalizability and noise robustness of models that
rely on various types of a priori knowledge e.g. in terms of noise type and
number of simultaneous speakers. We show that deep bi-directional LSTM RNNs
trained using uPIT in noisy environments can improve the Signal-to-Distortion
Ratio (SDR) as well as the Extended Short-Time Objective Intelligibility
(ESTOI) measure, on the speaker independent multi-talker speech separation and
denoising task, for various noise types and Signal-to-Noise Ratios (SNRs).
Specifically, we first show that LSTM RNNs can achieve large SDR and ESTOI
improvements, when evaluated using known noise types, and that a single model
is capable of handling multiple noise types with only a slight decrease in
performance. Furthermore, we show that a single LSTM RNN can handle both
two-speaker and three-speaker noisy mixtures, without a priori knowledge about
the exact number of speakers. Finally, we show that LSTM RNNs trained using
uPIT generalize well to noise types not seen during training.
| arxiv topic:cs.SD eess.AS |
arxiv_dataset-88471708.09688 | The impact of the carrier envelope phase -- dependence on system and
laser parameters
physics.atm-clus
We investigate, from a theoretical perspective, photo-emission of electrons
induced by ultra-short infrared pulses covering only a few photon cycles. In
particular, we investigate the impact of the Carrier-Envelope Phase (CEP) of
the laser pulse which plays an increasingly large role for decreasing pulse
length. As key observable we look at the asymmetry of the angular distribution
as function of kinetic energy of the emitted electrons. The focus of the
present study lies on the system dependence of the reaction. To this end, we
study two very different systems in comparison, an Ar atom and the Na9+
cluster. The study employs a fully quantum-mechanical description of electron
dynamics at the level of Time-Dependent Density Functional Theory (TDDFT). We
find a sensitive dependence on the system which can be related to the different
spectral response properties. Results can be understood from an interplay of
the ponderomotive motion driven by the external photon field and dynamical
polarization of the system.
| arxiv topic:physics.atm-clus |
arxiv_dataset-88481708.09788 | Light Adaptation in Phycobilisome antennas: Influence on the Rod Length
and Structural Arrangement
physics.chem-ph physics.bio-ph
Phycobilisomes, the light-harvesting antennas of cyanobacteria, can adapt to
a wide range of environments thanks to a composition and function response to
stress conditions. We study how structural changes influence excitation
transfer in these super-complexes. Specifically, we show the influence of the
rod length on the photon absorption and subsequent excitation transport to the
core. Despite the fact that the efficiency of individual disks on the rod
decreases with increasing rod length, we find an optimal length for which the
average rod efficiency is maximal. Combining this study with experimental
structural measurements, we propose models for the arrangement of the
phycobiliproteins inside the thylakoid membranes, evaluate the importance of
rod length, and predict the corresponding transport properties for different
cyanobacterial species. This analysis, which links the functional and
structural properties of full phycobilisome complexes, thus provides further
rationals to help resolving their exact structure.
| arxiv topic:physics.chem-ph physics.bio-ph |
arxiv_dataset-88491709.00034 | One- and Two-Photon Scattering by Two Atoms in a Waveguide
quant-ph
We consider the interaction of one- and two-photon pulses in a waveguide with
two two-level systems (TLS) that are also able to interact directly either
through an exchange- or a dipole-type interaction. We focus on the system's
transport properties and show how the presence of a second TLS increases the
control options, especially when direct interactions are also allowed. We also
obtain, within a Markov (long pulse) approximation, exact results for the
nonlinear or entangled terms that arise in the two-photon case, and discuss
both their potential applications and ways to minimize their effects.
| arxiv topic:quant-ph |
arxiv_dataset-88501709.00134 | Universality of Logarithmic Loss in Lossy Compression
cs.IT math.IT
We establish two strong senses of universality of logarithmic loss as a
distortion criterion in lossy compression: For any fixed length lossy
compression problem under an arbitrary distortion criterion, we show that there
is an equivalent lossy compression problem under logarithmic loss. In the
successive refinement problem, if the first decoder operates under logarithmic
loss, we show that any discrete memoryless source is successively refinable
under an arbitrary distortion criterion for the second decoder.
| arxiv topic:cs.IT math.IT |
arxiv_dataset-88511709.00234 | Causality and c-completion of multiwarped spacetimes
gr-qc
In this paper a systematic study of the causal structure and global causality
properties of multiwarped spacetimes is developed. This analysis is used to
make a detailed description of the causal boundary of these spacetimes. Some
applications of our results in examples of physical interest, for instance, in
the context of Maldacena's conjecture, are considered.
| arxiv topic:gr-qc |
arxiv_dataset-88521709.00334 | Multiparton pp and pA collisions -- from geometry to parton-- parton
correlations
hep-ph hep-ex
We derive expressions for the cross section of the multiparton interactions
based on the analysis of the relevant Feynman diagrams. We express the cross
sections through the double (triple, ...) generalized parton distributions
(GPDs). In the mean field approximation for the double GPDs the answer is
expressed through the integral over two gluon form factor which was measured in
the exclusive DIS vector meson production.We explain under what conditions the
derived expressions correspond to an intuitive picture of hard interactions in
the impact parameter representation. The mean field approximation in which
correlations of the partons are neglected fail to explain the data, while pQCD
induced correlation enhance large $p_\perp$ and $ 0.001 < x < 0.1$ typically
enhance the cross section by a factor of 1.5 -- 2 explaining the current data.
We argue that in the small x kinematics ($10^{-4} \le x \le 10^{-3}$) where
effects of perturbative correlations diminish, the nonperturbative mechanism
kicks in and generates positive correlations comparable in magnitude with the
perturbative ones. We explain how our technique can be used for calculations of
MPI in the proton - nucleus scattering. The interplay of hard interactions and
underlying event is discussed, as well as different geometric pictures for each
of MPI mechanisms-pQCD, nonperturbative correlations and mean field.
Predictions for value of \effs for various processes and a wide range of
kinematics are given. We show that together different MPI mechanisms give good
description of experimental data, both at Tvatron, and LHC, including the
central kinematics studied by ATLAS and CMS detectors, and forward (heavy
flavors) kinematics studied by LHCb.
| arxiv topic:hep-ph hep-ex |
arxiv_dataset-88531709.00434 | Generalized dispersion of the edge plasmon modes of two-dimensional
Dirac materials
cond-mat.mes-hall
Here, the dispersion of edge surface plasmon polariton (SPP) modes is
expressed in terms of the elements of the conductivity tensor.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-88541709.00534 | Cubic Polynomials, Linear Shifts, and Ramanujan Cubics
math.NT
We show that every monic polynomial of degree three with complex coefficients
and no repeated roots is either a (vertical and horizontal) translation of
$y=x^3$ or can be composed with a linear function to obtain a Ramanujan cubic.
As a result, we gain some new insights into the roots of cubic polynomials.
| arxiv topic:math.NT |
arxiv_dataset-88551709.00634 | Two simple observations on representations of metaplectic groups
math.RT
M. Hanzer and I. Matic have proved that the genuine unitary principal series
representations of the metaplectic groups are irreducible. A simple consequence
of that paper is a criterion for the irreducibility of the non-unitary
principal series representations of the metaplectic groups that we give in this
paper.
| arxiv topic:math.RT |
arxiv_dataset-88561709.00734 | Worst-case approximability of functions on finite groups by
endomorphisms and affine maps
math.GR
We study the maximum Hamming distance (or rather, the complementary notion of
"minimum approximability") of a general function on a finite group $G$ to
either of the sets $\operatorname{End}(G)$ and $\operatorname{Aff}(G)$, of
group endomorphisms of $G$ and affine maps on $G$ respectively, the latter
being a certain generalization of endomorphisms. We give general bounds on
these two quantities and discuss an infinite class of extremal examples (where
each of the two Hamming distances can be made as large as generally possible).
Finally, we compute the precise values of the two quantities for all finite
groups $G$ with $|G|\leq15$.
| arxiv topic:math.GR |
arxiv_dataset-88571709.00834 | How does the cosmic web impact assembly bias?
astro-ph.CO
The mass, accretion rate and formation time of dark matter haloes near
proto-filaments (identified as saddle points of the potential) are analytically
predicted using a conditional version of the excursion set approach in its
so-called "upcrossing" approximation. The model predicts that at fixed mass,
mass accretion rate and formation time vary with orientation and distance from
the saddle, demonstrating that assembly bias is indeed influenced by the tides
imposed by the cosmic web. Starved, early forming haloes of smaller mass lie
preferentially along the main axis of filaments, while more massive and younger
haloes are found closer to the nodes. Distinct gradients for distinct tracers
such as typical mass and accretion rate occur because the saddle condition is
anisotropic, and because the statistics of these observables depend on both the
conditional means and their covariances. The theory is extended to other
critical points of the potential field. The response of the mass function to
variations of the matter density field (the so-called large scale bias) is
computed, and its trend with accretion rate is shown to invert along the
filament. The signature of this model should correspond at low redshift to an
excess of reddened galactic hosts at fixed mass along preferred directions, as
recently reported in spectroscopic and photometric surveys and in
hydrodynamical simulations. The anisotropy of the cosmic web emerges therefore
as a significant ingredient to describe jointly the dynamics and physics of
galaxies, e.g. in the context of intrinsic alignments or morphological
diversity.
| arxiv topic:astro-ph.CO |
arxiv_dataset-88581709.00934 | From random partitions to fractional Brownian sheets
math.PR
We propose discrete random-field models that are based on random partitions
of $\mathbb{N}^2$. The covariance structure of each random field is determined
by the underlying random partition. Functional central limit theorems are
established for the proposed models, and fractional Brownian sheets, with full
range of Hurst indices, arise in the limit. Our models could be viewed as
discrete analogues of fractional Brownian sheets, in the same spirit that the
simple random walk is the discrete analogue of the Brownian motion.
| arxiv topic:math.PR |
arxiv_dataset-88591709.01034 | Comparison of two hardware-based hit filtering methods for trackers in
high-pileup environments
physics.ins-det
As experiments in high energy physics aims to measure increasingly rare
processes, the experiments continually strive to increase the expected signal
yields. In the case of the High Luminosity upgrade of the LHC, the luminosity
is raised by increasing the number of simultaneous proton-proton interactions,
so-called pile-up. This increases the expected yields of signal and background
processes alike. The signal is embedded in a large background of processes that
mimic that of signal events. It is therefore imperative for the experiments to
develop new triggering methods to effectively distinguish the interesting
events from the background. We present a comparison of two methods for
filtering detector hits to be used for triggering on particle tracks: one based
on a pattern matching technique using Associative Memory (AM) chips and the
other based on the Hough transform. Their efficiency and hit rejection are
evaluated for proton-proton collisions with varying amounts of pile-up using a
simulation of a generic silicon tracking detector. It is found that, while both
methods are feasible options for an efficient track trigger, the AM based
pattern matching produces a lower number of hit combinations with respect to
the Hough transform whilst keeping more of the true signal hits. We also
present the effect on the two methods when increasing the amount of support
material in the detector and introducing inefficiencies by deactivating
detector modules. The increased support material has negligible effects on the
efficiency for both methods, while dropping 5% (10%) of the available modules
decreases the efficiency to about 95% (87%) for both methods, irrespectively of
the amount of pile-up.
| arxiv topic:physics.ins-det |
arxiv_dataset-88601709.01134 | WRPN: Wide Reduced-Precision Networks
cs.CV cs.LG cs.NE
For computer vision applications, prior works have shown the efficacy of
reducing numeric precision of model parameters (network weights) in deep neural
networks. Activation maps, however, occupy a large memory footprint during both
the training and inference step when using mini-batches of inputs. One way to
reduce this large memory footprint is to reduce the precision of activations.
However, past works have shown that reducing the precision of activations hurts
model accuracy. We study schemes to train networks from scratch using
reduced-precision activations without hurting accuracy. We reduce the precision
of activation maps (along with model parameters) and increase the number of
filter maps in a layer, and find that this scheme matches or surpasses the
accuracy of the baseline full-precision network. As a result, one can
significantly improve the execution efficiency (e.g. reduce dynamic memory
footprint, memory bandwidth and computational energy) and speed up the training
and inference process with appropriate hardware support. We call our scheme
WRPN - wide reduced-precision networks. We report results and show that WRPN
scheme is better than previously reported accuracies on ILSVRC-12 dataset while
being computationally less expensive compared to previously reported
reduced-precision networks.
| arxiv topic:cs.CV cs.LG cs.NE |
arxiv_dataset-88611709.01234 | Order Preserving Maps of Posets
math.CO
For any two finite posets $P$ and $Q$, let $\Hom(P,Q)$ be the hom-poset
consisting of all order preserving maps from $P$ to $Q$, and $J(Q)$ the
collection of all order ideals of $Q$. In this paper, we study some basic
properties of the hom-poset $\Hom(P,Q)$ and prove that $\Hom\big(P,J(Q)\big)$
is a distributive lattice and characterized by \[ \Hom\big(P,J(Q)\big)\cong
J(P^*\times Q), \] where $P^*$ is the dual of $P$. Consequently, we obtain that
$\Hom\big(P,J(Q)\big)$ and $\Hom\big(Q,J(P)\big)$ are dual isomorphic, i.e., \[
\Hom\big(P,J(Q)\big)\cong \Hom^{*}\big(Q,J(P)\big). \] As applications, we
calculate the number of order preserving maps from any poset to the boolean
algebra, and the characteristic polynomial of $\Hom\big(P,J(Q)\big)$.
| arxiv topic:math.CO |
arxiv_dataset-88621709.01334 | Optimal Power Allocation by Imperfect Hardware Analysis in Untrusted
Relaying Networks
cs.CR cs.IT math.IT
By taking a variety of realistic hardware imperfections into consideration,
we propose an optimal power allocation (OPA) strategy to maximize the
instantaneous secrecy rate of a cooperative wireless network comprised of a
source, a destination and an untrusted amplify-and-forward (AF) relay. We
assume that either the source or the destination is equipped with a large-scale
multiple antennas (LSMA) system, while the rest are equipped with a single
antenna. To prevent the untrusted relay from intercepting the source message,
the destination sends an intended jamming noise to the relay, which is referred
to as destination-based cooperative jamming (DBCJ). Given this system model,
novel closed-form expressions are presented in the high signal-to-noise ratio
(SNR) regime for the ergodic secrecy rate (ESR) and the secrecy outage
probability (SOP). We further improve the secrecy performance of the system by
optimizing the associated hardware design. The results reveal that by
beneficially distributing the tolerable hardware imperfections across the
transmission and reception radio-frequency (RF) front ends of each node, the
system's secrecy rate may be improved. The engineering insight is that equally
sharing the total imperfections at the relay between the transmitter and the
receiver provides the best secrecy performance. Numerical results illustrate
that the proposed OPA together with the most appropriate hardware design
significantly increases the secrecy rate.
| arxiv topic:cs.CR cs.IT math.IT |
arxiv_dataset-88631709.01434 | A Generic Approach for Escaping Saddle points
cs.LG cs.AI
A central challenge to using first-order methods for optimizing nonconvex
problems is the presence of saddle points. First-order methods often get stuck
at saddle points, greatly deteriorating their performance. Typically, to escape
from saddles one has to use second-order methods. However, most works on
second-order methods rely extensively on expensive Hessian-based computations,
making them impractical in large-scale settings. To tackle this challenge, we
introduce a generic framework that minimizes Hessian based computations while
at the same time provably converging to second-order critical points. Our
framework carefully alternates between a first-order and a second-order
subroutine, using the latter only close to saddle points, and yields
convergence results competitive to the state-of-the-art. Empirical results
suggest that our strategy also enjoys a good practical performance.
| arxiv topic:cs.LG cs.AI |
arxiv_dataset-88641709.01534 | Magnetic properties of Co doped Nb clusters
cond-mat.str-el
From magnetic deflection experiments on isolated Co doped Nb clusters we made
the interesting observation of some clusters being magnetic, while others
appear to be non-magnetic. There are in principle two explanations for this
behavior. Either the local moment at the Co site is completely quenched or it
is screened by the delocalized electrons of the cluster, i.e. the Kondo effect.
In order to reveal the physical origin, we conducted a combined theoretical and
experimental investigation. First, we established the ground state geometry of
the clusters by comparing the experimental vibrational spectra with those
obtained from a density functional theory study. Then, we performed an analyses
based on the Anderson impurity model. It appears that the non-magnetic clusters
are due to a complete quenching of the local Co moment and not due to the Kondo
effect. In addition, the magnetic behavior of the clusters can be understood
from an inspection of their electronic structure. Here magnetism is favored
when the effective hybridization around the chemical potential is small, while
the absence of magnetism is signalled by a large effective hybridization around
the chemical potential.
| arxiv topic:cond-mat.str-el |
arxiv_dataset-88651709.01634 | The Voynich Manuscript is Written in Natural Language: The Pahlavi
Hypothesis
cs.CL
The late medieval Voynich Manuscript (VM) has resisted decryption and was
considered a meaningless hoax or an unsolvable cipher. Here, we provide
evidence that the VM is written in natural language by establishing a relation
of the Voynich alphabet and the Iranian Pahlavi script. Many of the Voynich
characters are upside-down versions of their Pahlavi counterparts, which may be
an effect of different writing directions. Other Voynich letters can be
explained as ligatures or departures from Pahlavi with the intent to cope with
known problems due to the stupendous ambiguity of Pahlavi text. While a
translation of the VM text is not attempted here, we can confirm the
Voynich-Pahlavi relation at the character level by the transcription of many
words from the VM illustrations and from parts of the main text. Many of the
transcribed words can be identified as terms from Zoroastrian cosmology which
is in line with the use of Pahlavi script in Zoroastrian communities from
medieval times.
| arxiv topic:cs.CL |
arxiv_dataset-88661709.01734 | Investigation of the inner structures around HD169142 with VLT/SPHERE
astro-ph.EP
We present observations of the Herbig Ae star HD169142 with VLT/SPHERE
instruments InfraRed Dual-band Imager and Spectrograph (IRDIS) ($K1K2$ and
$H2H3$ bands) and the Integral Field Spectrograph (IFS) ($Y$, $J$ and $H$
bands). We detect several bright blobs at $\sim$180 mas separation from the
star, and a faint arc-like structure in the IFS data. Our reference
differential imaging (RDI) data analysis also finds a bright ring at the same
separation. We show, using a simulation based on polarized light data, that
these blobs are actually part of the ring at 180 mas. These results demonstrate
that the earlier detections of blobs in the $H$ and $K_S$ bands at these
separations in Biller et al. as potential planet/substellar companions are
actually tracing a bright ring with a Keplerian motion. Moreover, we detect in
the images an additional bright structure at $\sim$93 mas separation and
position angle of 355$^{\circ}$, at a location very close to previous
detections. It appears point-like in the $YJ$ and $K$ bands but is more
extended in the $H$ band. We also marginally detect an inner ring in the RDI
data at $\sim$100 mas. Follow-up observations are necessary to confirm the
detection and the nature of this source and structure.
| arxiv topic:astro-ph.EP |
arxiv_dataset-88671709.01834 | Electromagnetic trace anomaly in a generalized linear sigma model
hep-ph
We build the electromagnetic trace anomaly effective term for a generalized
linear sigma model with two chiral nonets, one with a quark-antiquark
structure, the other one with a four quark content. In the leading order of
this framework, we study the decays into two photons of the lowest isosinglet
scalar mesons. We find that the direct inclusion of underlying mixing among
two- and four-quark components in the trace anomaly term is essential in order
for the model prediction to agree with the available experimental data on decay
width of $f_0(980)$ to two photons. Consequently, this sets a lower bound of
0.5 KeV on the decay with of $f_0(500)$ to two photons.
| arxiv topic:hep-ph |
arxiv_dataset-88681709.01934 | Stellar streams as gravitational experiments II. Asymmetric tails of
globular cluster streams
astro-ph.GA
Kinematically cold tidal streams of globular clusters (GC) are excellent
tracers of the Galactic gravitational potential at moderate Galactocentric
distances, and can also be used as probes of the law of gravity on Galactic
scales. Here, we compare for the first time the generation of such streams in
Newtonian and Milgromian gravity (MOND). We first compute analytical results to
investigate the expected shape of the GC gravitational potential in both
frameworks, and we then run N-body simulations with the Phantom of Ramses code.
We find that the GCs tend to become lopsided in MOND. This is a consequence of
the external field effect which breaks the strong equivalence principle. When
the GC is filling its tidal radius the lopsidedness generates a strongly
asymmetric tidal stream. In Newtonian dynamics, such markedly asymmetric
streams can in general only be the consequence of interactions with dark matter
subhalos, giant molecular clouds, or interaction with the Galactic bar. In
these Newtonian cases, the asymmetry is the consequence of a very large gap in
the stream, whilst in MOND it is a true asymmetry. This should thus allow us in
the future to distinguish these different scenarios by making deep observations
of the environment of the asymmetric stellar stream of Palomar 5. Moreover, our
simulations indicate that the high internal velocity dispersion of Palomar 5
for its small stellar mass would be natural in MOND.
| arxiv topic:astro-ph.GA |
arxiv_dataset-88691709.02034 | String Matching: Communication, Circuits, and Learning
cs.CC
String matching is the problem of deciding whether a given $n$-bit string
contains a given $k$-bit pattern. We study the complexity of this problem in
three settings.
Communication complexity. For small $k$, we provide near-optimal upper and
lower bounds on the communication complexity of string matching. For large $k$,
our bounds leave open an exponential gap; we exhibit some evidence for the
existence of a better protocol.
Circuit complexity. We present several upper and lower bounds on the size of
circuits with threshold and DeMorgan gates solving the string matching problem.
Similarly to the above, our bounds are near-optimal for small $k$.
Learning. We consider the problem of learning a hidden pattern of length at
most $k$ relative to the classifier that assigns 1 to every string that
contains the pattern. We prove optimal bounds on the VC dimension and sample
complexity of this problem.
| arxiv topic:cs.CC |
arxiv_dataset-88701709.02134 | Data Aggregation and Packet Bundling of Uplink Small Packets for
Monitoring Applications in LTE
cs.IT cs.NI math.IT
In cellular massive Machine-Type Communications (MTC), a device can transmit
directly to the base station (BS) or through an aggregator (intermediate node).
While direct device-BS communication has recently been in the focus of 5G/3GPP
research and standardization efforts, the use of aggregators remains a less
explored topic. In this paper we analyze the deployment scenarios in which
aggregators can perform cellular access on behalf of multiple MTC devices. We
study the effect of packet bundling at the aggregator, which alleviates
overhead and resource waste when sending small packets. The aggregators give
rise to a tradeoff between access congestion and resource starvation and we
show that packet bundling can minimize resource starvation, especially for
smaller numbers of aggregators. Under the limitations of the considered model,
we investigate the optimal settings of the network parameters, in terms of
number of aggregators and packet-bundle size. Our results show that, in
general, data aggregation can benefit the uplink massive MTC in LTE, by
reducing the signalling overhead.
| arxiv topic:cs.IT cs.NI math.IT |
arxiv_dataset-88711709.02234 | Stable Ground States for the HMF Poisson Model
math.AP
In this paper we prove the nonlinear orbital stability of a large class of
steady states solutions to the Hamiltonian Mean Field (HMF) system with a
Poisson interaction potential. These steady states are obtained as minimizers
of an energy functional under one, two or infinitely many constraints. The
singularity of the Poisson potential prevents from a direct run of the general
strategy in [20, 16] which was based on generalized rearrangement techniques,
and which has been recently extended to the case of the usual (smooth) cosine
potential [17]. Our strategy is rather based on variational techniques.
However, due to the boundedness of the space domain, our variational problems
do not enjoy the usual scaling invariances which are, in general, very
important in the analysis of variational problems. To replace these scaling
arguments, we introduce new transformations which, although specific to our
context, remain somehow in the same spirit of rearrangements tools introduced
in the references above. In particular, these transformations allow for the
incorporation of an arbitrary number of constraints, and yield a stability
result for a large class of steady states.
| arxiv topic:math.AP |
arxiv_dataset-88721709.02334 | Nearest Embedded and Embedding Self-Nested Trees
cs.DS
Self-nested trees present a systematic form of redundancy in their subtrees
and thus achieve optimal compression rates by DAG compression. A method for
quantifying the degree of self-similarity of plants through self-nested trees
has been introduced by Godin and Ferraro in 2010. The procedure consists in
computing a self-nested approximation, called the nearest embedding self-nested
tree, that both embeds the plant and is the closest to it. In this paper, we
propose a new algorithm that computes the nearest embedding self-nested tree
with a smaller overall complexity, but also the nearest embedded self-nested
tree. We show from simulations that the latter is mostly the closest to the
initial data, which suggests that this better approximation should be used as a
privileged measure of the degree of self-similarity of plants.
| arxiv topic:cs.DS |
arxiv_dataset-88731709.02434 | New limits on cosmic strings from gravitational wave observation
astro-ph.CO gr-qc
We combine new analysis of the stochastic gravitational wave background to be
expected from cosmic strings with the latest pulsar timing array (PTA) limits
to give an upper bound on the energy scale of the possible cosmic string
network, $G\mu < 1.5\times 10^{-11}$ at the 95% confidence level. We also show
bounds from LIGO and to be expected from LISA and BBO.
Current estimates for the gravitational wave background from supermassive
black hole binaries are at the level where a PTA detection is expected. But if
PTAs do observe a background soon, it will be difficult in the short term to
distinguish black holes from cosmic strings as the source, because the spectral
indices from the two sources happen to be quite similar.
If PTAs do not observe a background, then the limits on $G\mu$ will improve
somewhat, but a string network with $G\mu$ substantially below $10^{-11}$ will
produce gravitational waves primarily at frequencies too high for PTA
observation, so significant further progress will depend on
intermediate-frequency observatories such as LISA, DECIGO and BBO.
| arxiv topic:astro-ph.CO gr-qc |
arxiv_dataset-88741709.02534 | Biological Cell Resonators
physics.optics physics.bio-ph
This thesis develops the theory of whispering gallery modes, exploring under
what conditions a micro or nanoscale device can sustain these resonances, and
for which physical criteria the resonance conditions deteriorate. The study is
then extended to consider the biological cell in which modes are definitively
sustained without artificial assistance. The properties of resonators and their
emitted energy spectra are studied within the general framework of the Finite
Difference Time Domain method, requiring supercomputing resources to probe the
transient behaviour and interactions among the electromagnetic fields. The
formal theory of Mie scattering is also extended to develop a cutting-edge,
computationally efficient model for general, multilayer microspheres, which
represents a valuable achievement for the scientific community in its own
right. The model unifies the approaches in the field of mathematical modelling
to express the energy spectrum in a single encompassing equation, which is then
applied in a range of contexts. The gulf between modelling and biological
resonators is bridged by an in-depth study of the physical characteristics of a
range of biological cells, and the selection criteria for viable resonator
candidates are developed through a number of detailed feasibility studies. The
bovine embryo is consequently selected as the optimal choice for this
investigation. Evidence is established for the ability of a bovine embryo to
sustain whispering gallery modes. The ability of a cell to sustain modes on its
own represents a conceptually elegant paradigm for new technologies involving
on-site cell interrogation and reporting of the status and health of a
biological cell in the future. The methodological and technological
developments contained herein thus become a vital asset for the future
realisation of autonomous biological cell sensors.
| arxiv topic:physics.optics physics.bio-ph |
arxiv_dataset-88751709.02634 | Additive energy and the metric Poissonian property
math.NT math.CO
Let $A$ be a set of natural numbers. Recent work has suggested a strong link
between the additive energy of $A$ (the number of solutions to $a_1 + a_2 = a_3
+ a_4$ with $a_i \in A$) and the metric Poissonian property, which is a
fine-scale equidistribution property for dilates of $A$ modulo $1$. There
appears to be reasonable evidence to speculate a sharp Khintchine-type
threshold, that is, to speculate that the metric Poissonian property should be
completely determined by whether or not a certain sum of additive energies is
convergent or divergent. In this article, we primarily address the convergence
theory, in other words the extent to which having a low additive energy forces
a set to be metric Poissonian.
| arxiv topic:math.NT math.CO |
arxiv_dataset-88761709.02734 | Could the low braking index pulsar PSR J1734-3333 evolve into a
magnetar?
astro-ph.HE
The low braking-index pulsar PSR J1734$-$3333 could be born with superhigh
internal magnetic fields $B_{\rm in}\sim10^{15}-10^{16}$ G, and undergo a
supercritical accretion soon after its formation in a supernova explosion. The
buried multipole magnetic fields will merger into a dipole magnetic field.
Since the magnetic flow transfers from the core to the crust of the pulsar, its
surface dipole field grows quickly at a power-law form assumed until it
saturates at the level of internal dipole field. The increase in surface dipole
magnetic field results in the observed low braking index of $n=0.9(2)$. Keeping
an average field growth index $\varepsilon=1.34(6)$, this pulsar will become a
magnetar with surface dipole magnetic field at the equator $B_{\rm d}\sim
2.6(1)\times 10^{14}$\,G and $\sim 5.3(2)\times 10^{14}$\,G after next 50\,kyrs
and 100\,kys, respectively.
| arxiv topic:astro-ph.HE |
arxiv_dataset-88771709.02834 | Large-scale structure perturbation theory without losing stream crossing
astro-ph.CO
We suggest an approach to perturbative calculations of large-scale clustering
in the Universe that includes from the start the stream crossing (multiple
velocities for mass elements at a single position) that is lost in traditional
calculations. Starting from a functional integral over displacement, the
perturbative series expansion is in deviations from (truncated) Zel'dovich
evolution, with terms that can be computed exactly even for stream-crossed
displacements. We evaluate the one-loop formulas for displacement and density
power spectra numerically in 1D, finding dramatic improvement in agreement with
N-body simulations compared to the Zel'dovich power spectrum (which is exact in
1D up to stream crossing). Beyond 1D, our approach could represent an
improvement over previous expansions even aside from the inclusion of stream
crossing, but we have not investigated this numerically. In the process we show
how to achieve effective-theory-like regulation of small-scale fluctuations
without free parameters.
| arxiv topic:astro-ph.CO |
arxiv_dataset-88781709.02934 | Insertion Sort with Self-reproducing Comparator P System
cs.ET
We present in this paper a self-reproducing comparator P~system that
simulates insertion sort. The comparator $\Pi_c$ is a degree-2 membrane and
structured as $\mu = [_{h_0} [_{h_1}]_{h_1} [_{h_2}]_{h_2} ]_{h_0}$. A
maximizing $\Pi_c$ compares two multisets $a$ and $b$ where $\min(|a|,|b|)$ is
stored in compartment $h_1$ while $\max(|a|,|b|)$ is stored in compartment
$h_2$. A conditional reproduction rule triggers $\Pi_c$ to clone itself out via
compartment division followed by endocytosis of the cloned compartment. We
present the process of sorting as a collection of transactions implemented in
hierarchical levels where each level has different concurrent or serialized
steps.
| arxiv topic:cs.ET |
arxiv_dataset-88791709.03034 | Connectivity in Interdependent Networks
cs.DM cs.NI cs.SI
We propose and analyze a graph model to study the connectivity of
interdependent networks. Two interdependent networks of arbitrary topologies
are modeled as two graphs, where every node in one graph is supported by supply
nodes in the other graph, and a node fails if all of its supply nodes fail.
Such interdependence arises in cyber-physical systems and layered network
architectures.
We study the \emph{supply node connectivity} of a network: namely, the
minimum number of supply node removals that would disconnect the network. We
develop algorithms to evaluate the supply node connectivity given arbitrary
network topologies and interdependence between two networks. Moreover, we
develop interdependence assignment algorithms that maximize the supply node
connectivity. We prove that a random assignment algorithm yields a supply node
connectivity within a constant factor from the optimal for most networks.
| arxiv topic:cs.DM cs.NI cs.SI |
arxiv_dataset-88801709.03134 | Switch between critical percolation modes in city traffic dynamics
physics.soc-ph
Percolation transition is widely observed in networks ranging from biology to
engineering. While much attention has been paid to network topologies, studies
rarely focus on critical percolation phenomena driven by network dynamics.
Using extensive real data, we study the critical percolation properties in city
traffic dynamics. Our results suggest that two modes of different critical
percolation behaviors are switching in the same network topology under
different traffic dynamics. One mode of city traffic (during nonrush hours or
days off) has similar critical percolation characteristics as small world
networks, while the other mode (during rush hours on working days) tends to
behave as a 2D lattice. This switching behavior can be understood by the fact
that the high-speed urban roads during nonrush hours or days off (that are
congested during rush hours) represent effective long-range connections, like
in small world networks. Our results might be useful for understanding and
improving traffic resilience.
| arxiv topic:physics.soc-ph |
arxiv_dataset-88811709.03234 | Fast construction of efficient composite likelihood equations
math.ST stat.TH
Growth in both size and complexity of modern data challenges the
applicability of traditional likelihood-based inference. Composite likelihood
(CL) methods address the difficulties related to model selection and
computational intractability of the full likelihood by combining a number of
low-dimensional likelihood objects into a single objective function used for
inference. This paper introduces a procedure to combine partial likelihood
objects from a large set of feasible candidates and simultaneously carry out
parameter estimation. The new method constructs estimating equations balancing
statistical efficiency and computing cost by minimizing an approximate distance
from the full likelihood score subject to a L1-norm penalty representing the
available computing resources. This results in truncated CL equations
containing only the most informative partial likelihood score terms. An
asymptotic theory within a framework where both sample size and data dimension
grow is developed and finite-sample properties are illustrated through
numerical examples.
| arxiv topic:math.ST stat.TH |
arxiv_dataset-88821709.03334 | Single-particle shot noise at non-zero temperature
cond-mat.mes-hall
The state of a single particle injected onto the surface of the Fermi sea is
a pure state if the temperature is zero and is a mixed state if the temperature
is finite. Moreover, the state of an injected particle is orthogonal to the
state of the Fermi sea at zero temperature, while it is not orthogonal at
non-zero temperature. These changes in the quantum state of the injected
particles can be detected using the temperature dependence of the shot noise
that is generated when the particles one by one pass through a semitransparent
quantum point contact. Namely, the shot noise produced by the mixed state is
suppressed in comparison with the noise of the pure state. In addition, the
correlations between the injected particles and the underlying Fermi sea,
present at non-zero temperature, do enhance the shot noise. Furthermore,
antibunching of injected particles with possible thermal excitations coming
from another input channel of a quantum point contact does suppress shot noise.
Here I analyze in detail these three effects, which are responsible for the
temperature dependence of the shot noise, and discuss how to distinguish them
experimentally.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-88831709.03434 | Neutrino Interferometry for High-Precision Tests of Lorentz Symmetry
with IceCube
hep-ex hep-ph
Lorentz symmetry is a fundamental space-time symmetry underlying the Standard
Model of particle physics and gravity. However, unified theories, such as
string theory, allow for violation of this symmetry. Thus, the discovery of
Lorentz symmetry violation could be the first hint of these theories. Here, we
use high-energy atmospheric neutrinos observed at the IceCube Neutrino
Observatory to search for anomalous neutrino oscillations as signals of Lorentz
violation. The large range of neutrino energies and propagation baselines,
together with high statistics, let us perform the most precise test of
space-time symmetry in the neutrino sector to date. We find no evidence for
Lorentz violation. This allows us to constrain the size of the dimension-four
operator in the Standard-Model Extension for Lorentz violation to the
$10^{-28}$ level and to set limits on higher dimensional operators of that
theory. These are among the most stringent limits on Lorentz violation across
all fields of physics.
| arxiv topic:hep-ex hep-ph |
arxiv_dataset-88841709.03534 | Disrupted Globular Clusters and the Gamma-Ray Excess in the Galactic
Centre
astro-ph.GA astro-ph.HE
The Fermi Large Area Telescope has provided the most detailed view toward the
Galactic Centre (GC) in high-energy gamma rays. Besides the interstellar
emission and point-source contributions, the data suggest a residual diffuse
gamma-ray excess. The similarity of its spatial distribution with the expected
profile of dark matter has led to claims that this may be evidence for dark
matter particle annihilation. Here, we investigate an alternative explanation
that the signal originates from millisecond pulsars (MSPs) formed in dense
globular clusters and deposited at the GC as a consequence of cluster inspiral
and tidal disruption. We use a semi-analytical model to calculate the
formation, migration, and disruption of globular clusters in the Galaxy. Our
model reproduces the mass of the nuclear star cluster and the present-day
radial and mass distribution of globular clusters. For the first time, we
calculate the evolution of MSPs from disrupted globular clusters throughout the
age of the Galaxy and consistently include the effect of the MSP spin-down due
to magnetic-dipole breaking. The final gamma-ray amplitude and spatial
distribution are in good agreement with the Fermi observations and provide a
natural astrophysical explanation for the GC excess.
| arxiv topic:astro-ph.GA astro-ph.HE |
arxiv_dataset-88851709.03634 | A Gronwall inequality and the Cauchy-type problem by means of
$\psi$-Hilfer operator
math.CA
In this paper, we propose a generalized Gronwall inequality through the
fractional integral with respect to another function. The Cauchy-type problem
for a nonlinear differential equation involving the $\psi$-Hilfer fractional
derivative and the existence and uniqueness of solutions are discussed.
Finally, through generalized Gronwall inequality, we prove the continuous
dependence of data on the Cauchy-type problem.
| arxiv topic:math.CA |
arxiv_dataset-88861709.03734 | Enhanced Random Access and Beam Training for mmWave Wireless Local
Networks with High User Density
cs.NI
As low frequency band becomes more and more crowded, millimeter-wave (mmWave)
has attracted significant attention recently. IEEE has released the 802.11ad
standard to satisfy the demand of ultra-high-speed communication. It adopts
beamforming technology that can generate directional beams to compensate for
high path loss. In the Association Beamforming Training (A-BFT) phase of
beamforming (BF) training, a station (STA) randomly selects an A-BFT slot to
contend for training opportunity. Due to the limited number of A-BFT slots,
A-BFT phase suffers high probability of collisions in dense user scenarios,
resulting in inefficient training performance. Based on the evaluation of the
IEEE 802.11ad standard and 802.11ay draft in dense user scenarios of mmWave
wireless networks, we propose an enhanced A-BFT beam training and random access
mechanism, including the Separated A-BFT (SA-BFT) and Secondary Backoff A-BFT
(SBA-BFT). The SA-BFT can provide more A-BFT slots and divide A-BFT slots into
two regions by defining a new `E-A-BFT Length' field compared to the legacy
802.11ad A-BFT, thereby maintaining compatibility when 802.11ay devices are
mixed with 802.11ad devices. It can also reduce the collision probability in
dense user scenarios greatly. The SBA-BFT performs secondary backoff with very
small overhead of transmission opportunities within one A-BFT slot, which not
only further reduces collision probability, but also improves the A-BFT slots
utilization. Furthermore, we propose a three-dimensional Markov model to
analyze the performance of the SBA-BFT. The analytical and simulation results
show that both the SA-BFT and the SBA-BFT can significantly improve BF training
efficiency, which are beneficial to the optimization design of dense user
wireless networks based on the IEEE 802.11ay standard and mmWave technology.
| arxiv topic:cs.NI |
arxiv_dataset-88871709.03834 | Stanley-Reisner rings for quasi-arithmetic matroids
math.CO math.AC
In this note we define a Stanley-Reisner ring for quasi-arithmetic matroids
and more general structures. To this end, we define two types of CW complexes
associated with a quasi-arithmetic matroid that generalize independence
complexes of matroids. Then we use Stanley's construction of Stanley-Reisner
rings for simplicial posets.
| arxiv topic:math.CO math.AC |
arxiv_dataset-88881709.03934 | Residual-based variational multiscale modeling in a discontinuous
Galerkin framework
math.NA
We develop the general form of the variational multiscale method in a
discontinuous Galerkin framework. Our method is based on the decomposition of
the true solution into discontinuous coarse-scale and discontinuous fine-scale
parts. The obtained coarse-scale weak formulation includes two types of
fine-scale contributions. The first type corresponds to a fine-scale volumetric
term, which we formulate in terms of a residual-based model that also takes
into account fine-scale effects at element interfaces. The second type consists
of independent fine-scale terms at element interfaces, which we formulate in
terms of a new fine-scale "interface model". We demonstrate for the
one-dimensional Poisson problem that existing discontinuous Galerkin
formulations, such as the interior penalty method, can be rederived by choosing
particular fine-scale interface models. The multiscale formulation thus opens
the door for a new perspective on discontinuous Galerkin methods and their
numerical properties. This is demonstrated for the one-dimensional
advection-diffusion problem, where we show that upwind numerical fluxes can be
interpreted as an ad hoc remedy for missing volumetric fine-scale terms.
| arxiv topic:math.NA |
arxiv_dataset-88891709.04034 | Gamma-ray Observatory INTEGRAL reloaded
physics.pop-ph astro-ph.HE
A new lease on life was given to ESA's International Gamma-ray Astrophysics
Laboratory, because of its unique capability to identify electromagnetic
counterparts to sources of gravitational waves and ultra-high energy neutrinos.
| arxiv topic:physics.pop-ph astro-ph.HE |
arxiv_dataset-88901709.04134 | Exploring the expansion dynamics of the universe from galaxy cluster
surveys
astro-ph.CO gr-qc hep-ph
To understand the expansion dynamics of the universe from galaxy cluster
scales, using the angular diameter distance (ADD) data from two different
galaxy cluster surveys, we constrain four cosmological models to explore the
underlying value of $H_0$ and employ the model-independent Gaussian Processes
to investigate the evolution of the equation of state of dark energy. The ADD
data in the X-ray bands consists of two samples covering the redshift ranges
[0.023, 0.784] and [0.14, 0.89], respectively. We find that: (i) For these two
samples, the obtained values of $H_0$ are more consistent with the recent local
observation by Riess et al. than the global measurement by the Plank
Collaboration, and the $\Lambda$CDM model is still preferred utilizing the
information criterions; (ii) For the first sample, there is no evidence of
dynamical dark energy (DDE) at the $2\sigma$ confidence level (CL); (iii) For
the second one, the reconstructed equation of state of dark energy exhibits a
phantom-crossing behavior in the relatively low redshift range over the
$2\sigma$ CL, which gives a hint that the late-time universe may be actually
dominated by the DDE from galaxy cluster scales; (iv) By adding a combination
of Type Ia Supernovae, cosmic chronometers and Planck-2015 shift parameter and
HII galaxy measurements into both ADD samples, the DDE exists evidently over
the $2\sigma$ CL.
| arxiv topic:astro-ph.CO gr-qc hep-ph |
arxiv_dataset-88911709.04234 | Borel subsets of the real line and continuous reducibility
math.LO
We study classes of Borel subsets of the real line $\mathbb{R}$ such as
levels of the Borel hierarchy and the class of sets that are reducible to the
set $\mathbb{Q}$ of rationals, endowed with the Wadge quasi-order of
reducibility with respect to continuous functions on $\mathbb{R}$. Notably, we
explore several structural properties of Borel subsets of $\mathbb{R}$ that
diverge from those of Polish spaces with dimension zero. Our first main result
is on the existence of embeddings of several posets into the restriction of
this quasi-order to any Borel class that is strictly above the classes of open
and closed sets, for instance the linear order $\omega_1$, its reverse
$\omega_1^\star$ and the poset $\mathcal{P}(\omega)/\mathsf{fin}$ of inclusion
modulo finite error. As a consequence of its proof, it is shown that there are
no complete sets for these classes. We further extend the previous theorem to
targets that are reducible to $\mathbb{Q}$. These non-structure results
motivate the study of further restrictions of the Wadge quasi-order. In our
second main theorem, we introduce a combinatorial property that is shown to
characterize those $F_\sigma$ sets that are reducible to $\mathbb{Q}$. This is
applied to construct a minimal set below $\mathbb{Q}$ and prove its uniqueness
up to Wadge equivalence. We finally prove several results concerning gaps and
cardinal characteristics of the Wadge quasi-order and thereby answer questions
of Brendle and Geschke.
| arxiv topic:math.LO |
arxiv_dataset-88921709.04334 | Realising Interactions Between Dark Matter and Dark Energy Using
$k$-essence Cosmology
gr-qc
In this paper we exploit dynamics of a $k-$essence scalar field to realise
interactions between dark components of universe resulting in a evolution
consistent with observed features of late time phase of cosmic evolution.
Stress energy tensor corresponding to a $k-$essence Lagrangian $L=V( \phi)F(X)$
(where $X=\frac{1}{2}g^{\mu\nu}\nabla_\mu\phi \nabla_\nu\phi$) is shown to be
equivalent to an ideal fluid with two components having same equation of state.
Stress energy tensor of one of the components may be generated from a constant
potential $k-$essence Lagrangian of form $L_1=V_0F(X)$ ($V_0$ constant) and
that of other from another Lagrangian of form $L_2=V_1(\phi)F(X)$ with $V=V_0 +
V_1(\phi)$.
We have shown that, the unified dynamics of dark matter and dark energy
described by a single scalar field $\phi$ driven by a $k-$essence Lagrangian
$L= V(\phi)F(X)$ may be viewed in terms of diffusive interactions between the
two hypothetical fluid components `1' and `2' with stress energy tensors
equivalent to that of Lagrangians $L_1$ and $L_2$ respectively. The energy
transfer between the fluid components is determined by functions $V(\phi)$,
$F(X)$ and their derivatives. Such a realisation is shown to be consistent with
the Supernova Ia data with certain constraints on the temporal behaviour of
$k-$essence potential $V(\phi)$. We have described a methodology to obtain such
constraints.
| arxiv topic:gr-qc |
arxiv_dataset-88931709.04434 | Ultra-Stretchable Interconnects for High-Density Stretchable Electronics
physics.ins-det physics.app-ph
The exciting field of stretchable electronics (SE) promises numerous novel
applications, particularly in-body and medical diagnostics devices. However,
future advanced SE miniature devices will require high-density, extremely
stretchable interconnects with micron-scale footprints, which calls for proven
standardized (complementary metal-oxide semiconductor (CMOS)-type) process
recipes using bulk integrated circuit (IC) microfabrication tools and
fine-pitch photolithography patterning. Here, we address this combined
challenge of microfabrication with extreme stretchability for high-density SE
devices by introducing CMOS-enabled, free-standing, miniaturized interconnect
structures that fully exploit their 3D kinematic freedom through an interplay
of buckling, torsion, and bending to maximize stretchability. Integration with
standard CMOS-type batch processing is assured by utilizing the Flex-to-Rigid
(F2R) post-processing technology to make the back-end-of-line interconnect
structures free-standing, thus enabling the routine microfabrication of
highly-stretchable interconnects. The performance and reproducibility of these
free-standing structures is promising: an elastic stretch beyond 2000% and
ultimate (plastic) stretch beyond 3000%, with <0.3% resistance change, and >10
million cycles at 1000% stretch with <1% resistance change. This generic
technology provides a new route to exciting highly-stretchable miniature
devices.
| arxiv topic:physics.ins-det physics.app-ph |
arxiv_dataset-88941709.04534 | Modeling a Propagating Sawtooth Flare Ribbon Structure as a Tearing Mode
in the Presence of Velocity Shear
astro-ph.SR
On April 18, 2014 (SOL2014-04-18T13:03) an M-class flare was observed by
IRIS. The associated flare ribbon contained a quasi-periodic sawtooth pattern
that was observed to propagate along the ribbon, perpendicular to the IRIS
spectral slit, with a phase velocity of $\sim 15$ km s$^{-1}$. This motion
resulted in periodicities in both intensity and Doppler velocity along the
slit. These periodicities were reported to be approximately $\pm0.5$ arcseconds
in position and $\pm20$ km s$^{-1}$ in velocity and were measured to be
$\sim180^{\circ}$ out of phase with one another. This quasi-periodic behavior
has been attributed by others to bursty or patchy reconnection and slipping
occurring during three-dimensional magnetic reconnection. While able to account
for periodicities in both intensity and Doppler velocity these suggestions do
not explicitly account for the phase velocity of the entire sawtooth structure,
or for the relative phasing of the oscillations. Here we propose that the
observations can be explained by a tearing mode instability occurring at a
current sheet across which there is also a velocity shear. Using a linear model
of this instability we reproduce the relative phase of the oscillations, as
well as the phase velocity of the sawtooth structure. We suggest a geometry and
local plasma parameters for the April 18 flare which would support our
hypothesis. Under this proposal the combined spectral and spatial IRIS
observations of this flare may provide the most compelling evidence to date of
a tearing mode occurring in the solar magnetic field.
| arxiv topic:astro-ph.SR |
arxiv_dataset-88951709.04634 | Observations of red-giant variable stars by Aboriginal Australians
physics.hist-ph
Aboriginal Australians carefully observe the properties and positions of
stars, including both overt and subtle changes in their brightness, for
subsistence and social application. These observations are encoded in oral
tradition. I examine two Aboriginal oral traditions from South Australia that
describe the periodic changing brightness in three pulsating, red-giant
variable stars: Betelgeuse (Alpha Orionis), Aldebaran (Alpha Tauri), and
Antares (Alpha Scorpii). The Australian Aboriginal accounts stand as the only
known descriptions of pulsating variable stars in any Indigenous oral tradition
in the world. Researchers examining these oral traditions over the last
century, including anthropologists and astronomers, missed the description of
these stars as being variable in nature as the ethnographic record contained
several misidentifications of stars and celestial objects. Arguably,
ethnographers working on Indigenous Knowledge Systems should have academic
training in both the natural and social sciences.
| arxiv topic:physics.hist-ph |
arxiv_dataset-88961709.04734 | Perspectives for Evaluating Conversational AI
cs.AI
Conversational AI systems are becoming famous in day to day lives. In this
paper, we are trying to address the following key question: To identify whether
design, as well as development efforts for search oriented conversational AI
are successful or not.It is tricky to define 'success' in the case of
conversational AI and equally tricky part is to use appropriate metrics for the
evaluation of conversational AI. We propose four different perspectives namely
user experience, information retrieval, linguistic and artificial intelligence
for the evaluation of conversational AI systems. Additionally, background
details of conversational AI systems are provided including desirable
characteristics of personal assistants, differences between chatbot and an AI
based personal assistant. An importance of personalization and how it can be
achieved is explained in detail. Current challenges in the development of an
ideal conversational AI (personal assistant) are also highlighted along with
guidelines for achieving personalized experience for users.
| arxiv topic:cs.AI |
arxiv_dataset-88971709.04834 | Linear perturbations in spherically symmetric dust cosmologies including
a cosmological constant
astro-ph.CO gr-qc
We study the dynamical behaviour of gauge-invariant linear perturbations in
spherically symmetric dust cosmologies including a cosmological constant. In
contrast to spatially homogeneous FLRW models, the reduced degree of spatial
symmetry causes a non-trivial dynamical coupling of gauge-invariant quantities
already at first order perturbation theory and the strength and influence of
this coupling on the spacetime evolution is investigated here. We present
results on the underlying dynamical equations augmented by a cosmological
constant and integrate them numerically. We also present a method to derive
cosmologically relevant initial variables for this setup. Estimates of angular
power spectra for each metric variable are computed and evaluated on the
central observer's past null cone. By comparing the full evolution to the
freely evolved initial profiles, the coupling strength will be determined for a
best fit radially inhomogeneous patch obtained in previous works (see Redlich
et. al. (2014)). We find that coupling effects are not noticeable within the
cosmic variance limit and can therefore safely be neglected for a relevant
cosmological scenario. On the contrary, we find very strong coupling effects in
a best fit spherical void model matching the distance redshift relation of SNe
which is in accordance with previous findings using parametric void models.
| arxiv topic:astro-ph.CO gr-qc |
arxiv_dataset-88981709.04934 | Sensitivity analysis on imaging the calcaneus using microwaves
physics.med-ph
The bone quality is asociated with changes in its dielectric properties
(permittivity and conductivity). The feasibility of detecting changes in these
properties is evaluated using a tomographic array of 16 monopole antennas with
z-polarized microwaves at 1.3GHz. The direct problem was evaluated
computationally with the Finite-Difference-Time-Domain (FDTD) method. Local and
global sensitivity analysis were considered for identifiyng the parameters that
most affect the detection. We observed that the direct problem is highly
sensitive to the conductivity of the tissues that surround the calcaneus and
the one of the calcaneus itself. Global and local sensitivity methods have
shown evidences for feasible detection of variation in dielectric properties of
bone.
| arxiv topic:physics.med-ph |
arxiv_dataset-88991709.05034 | Radially distributed values and normal families
math.CV
Let $L_0$ and $L_1$ be two distinct rays emanating from the origin and let
${\mathcal F}$ be the family of all functions holomorphic in the unit disk
${\mathbb D}$ for which all zeros lie on $L_0$ while all $1$-points lie on
$L_1$. It is shown that ${\mathcal F}$ is normal in ${\mathbb
D}\backslash\{0\}$. The case where $L_0$ is the positive real axis and $L_1$ is
the negative real axis is studied in more detail.
| arxiv topic:math.CV |
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