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arxiv_dataset-68001511.0682 | An Empirical Comparison of the Summarization Power of Graph Clustering
Methods
cs.IR cs.SI
How do graph clustering techniques compare with respect to their
summarization power? How well can they summarize a million-node graph with a
few representative structures? Graph clustering or community detection
algorithms can summarize a graph in terms of coherent and tightly connected
clusters. In this paper, we compare and contrast different techniques: METIS,
Louvain, spectral clustering, SlashBurn and KCBC, our proposed k-core-based
clustering method. Unlike prior work that focuses on various measures of
cluster quality, we use vocabulary structures that often appear in real graphs
and the Minimum Description Length (MDL) principle to obtain a graph summary
per clustering method. Our main contributions are: (i) Formulation: We propose
a summarization-based evaluation of clustering methods. Our method,
VOG-OVERLAP, concisely summarizes graphs in terms of their important structures
which lead to small edge overlap, and large node/edge coverage; (ii) Algorithm:
we introduce KCBC, a graph decomposition technique, in the heart of which lies
the k-core algorithm (iii) Evaluation: We compare the summarization power of
five clustering techniques on large real graphs, and analyze their compression
performance, summary statistics and runtimes.
| arxiv topic:cs.IR cs.SI |
arxiv_dataset-68011511.0692 | Cell assembly dynamics of sparsely-connected inhibitory networks: a
simple model for the collective activity of striatal projection neurons
q-bio.NC nlin.CD
Striatal projection neurons form a sparsely-connected inhibitory network, and
this arrangement may be essential for the appropriate temporal organization of
behavior. Here we show that a simplified, sparse inhibitory network of
Leaky-Integrate-and-Fire neurons can reproduce some key features of striatal
population activity, as observed in brain slices [Carrillo-Reid et al., J.
Neurophysiology 99 (2008) 1435{1450]. In particular we develop a new metric to
determine the conditions under which sparse inhibitory networks form
anti-correlated cell assemblies with time-varying activity of individual cells.
We found that under these conditions the network displays an input-specific
sequence of cell assembly switching, that effectively discriminates similar
inputs. Our results support the proposal [Ponzi and Wickens, PLoS Comp Biol 9
(2013) e1002954] that GABAergic connections between striatal projection neurons
allow stimulus-selective, temporally-extended sequential activation of cell
assemblies. Furthermore, we help to show how altered intrastriatal GABAergic
signaling may produce aberrant network-level information processing in
disorders such as Parkinson's and Huntington's diseases.
| arxiv topic:q-bio.NC nlin.CD |
arxiv_dataset-68021511.0702 | On a Natural Dynamics for Linear Programming
cs.DS math.DS math.OC physics.bio-ph
In this paper we study dynamics inspired by Physarum polycephalum (a slime
mold) for solving linear programs [NTY00, IJNT11, JZ12]. These dynamics are
arrived at by a local and mechanistic interpretation of the inner workings of
the slime mold and a global optimization perspective has been lacking even in
the simplest of instances. Our first result is an interpretation of the
dynamics as an optimization process. We show that Physarum dynamics can be seen
as a steepest-descent type algorithm on a certain Riemannian manifold.
Moreover, we prove that the trajectories of Physarum are in fact paths of
optimizers to a parametrized family of convex programs, in which the objective
is a linear cost function regularized by an entropy barrier. Subsequently, we
rigorously establish several important properties of solution curves of
Physarum. We prove global existence of such solutions and show that they have
limits, being optimal solutions of the underlying LP. Finally, we show that the
discretization of the Physarum dynamics is efficient for a class of linear
programs, which include unimodular constraint matrices. Thus, together, our
results shed some light on how nature might be solving instances of perhaps the
most complex problem in P: linear programming.
| arxiv topic:cs.DS math.DS math.OC physics.bio-ph |
arxiv_dataset-68031511.0712 | Oscillatory amplitude of stochastic gravitational wave spectrum
gr-qc
Primordial gravitational waves generated from early universe are placed in
the squeezed vacuum state and the resulting stochastic background is studied
for various models of the expanding universe. The quantum effect on the
stochastic gravitational waves leads to overall enhancement of the amplitude
and spectral energy density when compared to those in the absence of squeezing
effect with continued increase in the amplitude in the accelerating stage and
oscillatory behavior at higher frequency range of the spectrum in the
accelerating universe. Through the quantum effect, it is also found that the
reheating phenomenon affects the entire spectrum. The results of the present
study may be useful to test the possibility of detection of the stochastic
gravitational waves by current and future gravitational wave detectors and
whether these waves exist in the squeezed vacuum state.
| arxiv topic:gr-qc |
arxiv_dataset-68041511.0722 | Different kinds of chimera death states in nonlocally coupled
oscillators
nlin.CD nlin.AO
We investigate the significance of nonisochronicity parameter in a network of
nonlocally coupled Stuart-Landau oscillators with symmetry breaking form. We
observe that the presence of nonisochronicity parameter leads to structural
changes in the chimera death region while varying the strength of the
interaction. This gives rise to the existence of different types of chimera
death states such as multi-chimera death state, type-I periodic chimera death
(PCD) state and, type-II periodic chimera death (PCD) state. We also find that
the number of periodic domains in both the types of PCD states exponentially
decreases with an increase of coupling range and obeys a power law under
nonlocal coupling. Additionally, we also analyze the structural changes of
chimera death states by reducing the system of dynamical equations to a phase
model through the phase approximation. We also briefly study the role of
nonisochronicity parameter on chimera states, where the existence of
multi-chimera state with respect to the coupling range is pointed out.
Moreover, we also analyze the robustness of the chimera death state to
perturbations in the natural frequencies of the oscillators.
| arxiv topic:nlin.CD nlin.AO |
arxiv_dataset-68051511.0732 | A Dark Spot on a Massive White Dwarf
astro-ph.SR
We present the serendipitous discovery of eclipse-like events around the
massive white dwarf SDSS J152934.98+292801.9 (hereafter J1529+2928). We
selected J1529+2928 for time-series photometry based on its spectroscopic
temperature and surface gravity, which place it near the ZZ Ceti instability
strip. Instead of pulsations, we detect photometric dips from this white dwarf
every 38 minutes. Follow-up optical spectroscopy observations with Gemini
reveal no significant radial velocity variations, ruling out stellar and brown
dwarf companions. A disintegrating planet around this white dwarf cannot
explain the observed light curves in different filters. Given the short period,
the source of the photometric dips must be a dark spot that comes into view
every 38 min due to the rotation of the white dwarf. Our optical spectroscopy
does not show any evidence of Zeeman splitting of the Balmer lines, limiting
the magnetic field strength to B<70 kG. Since up to 15% of white dwarfs display
kG magnetic fields, such eclipse-like events should be common around white
dwarfs. We discuss the potential implications of this discovery on transient
surveys targeting white dwarfs, like the K2 mission and the Large Synoptic
Survey Telescope.
| arxiv topic:astro-ph.SR |
arxiv_dataset-68061511.0742 | A novel Randall-Sundrum model with $S_{3}$ flavor symmetry
hep-ph
We propose a simple and predictive model of fermion masses and mixing in a
warped extra dimension, with the smallest discrete non-Abelian group $S_{3}$
and the discrete symmetries $Z_{2}\otimes Z_{4}$. Standard Model fields
propagate in the bulk and the mass hierarchies and mixing angles are accounted
for the fermion zero modes localization profiles, similarly to the the
Randall-Sundrum (RS) model. To the best of our knowledge, this model is the
first implementation of an $S_{3}$ flavor symmetry in this type of warped extra
dimension framework. Our model successfully describes the fermion masses and
mixing pattern and is consistent with the current low energy fermion flavor
data. The discrete flavor symmetry in our model leads to predictive mixing
inspired textures, where the Cabbibo mixing arises from the down type quark
sector whereas up type quark sector contributes to the remaining mixing angles.
| arxiv topic:hep-ph |
arxiv_dataset-68071511.0752 | Magnetic domain walls in nanostrips of single-crystalline
$\mathrm{Fe}_4\mathrm{N}(001)$ thin films with fourfold in-plane magnetic
anisotropy
cond-mat.mtrl-sci cond-mat.mes-hall
We investigated head-to-head domain walls in nanostrips of epitaxial
$\mathrm{Fe}_4\mathrm{N}(001)$ thin films, displaying a fourfold magnetic
anisotropy. Magnetic force microscopy and micromagnetic simulations show that
the domain walls have specific properties, compared to soft magnetic materials.
In particular, strips aligned along a hard axis of magnetization are wrapped by
partial flux-closure concertina domains below a critical width, while
progressively transforming to zigzag walls for wider strips. Transverse walls
are favored upon initial application of a magnetic field transverse to the
strip, while transformation to a vortex walls is favored upon motion under a
longitudinal magnetic field. In all cases the magnetization texture of such
fourfold anisotropy domain walls exhibits narrow micro-domain walls, which may
give rise to peculiar spin-transfer features.
| arxiv topic:cond-mat.mtrl-sci cond-mat.mes-hall |
arxiv_dataset-68081511.0762 | Predicting Coronal Mass Ejections transit times to Earth with neural
network
astro-ph.SR
Predicting transit times of Coronal Mass Ejections (CMEs) from their initial
parameters is a very important subject, not only from the scientific
perspective, but also because CMEs represent a hazard for human technology. We
used a neural network to analyse transit times for 153 events with only two
input parameters: initial velocity of the CME, $v$, and Central Meridian
Distance, CMD, of its associated flare. We found that transit time dependence
on $v$ is showing a typical drag-like pattern in the solar wind. The results
show that the speed at which acceleration by drag changes to deceleration is
$v\approx$500 km s$^{-1}$. Transit times are also found to be shorter for CMEs
associated with flares on the western hemisphere than those originating on the
eastern side of the Sun. We attribute this difference to the eastward
deflection of CMEs on their path to 1 AU. The average error of the NN
prediction in comparison to observations is $\approx$12 hours which is
comparable to other studies on the same subject.
| arxiv topic:astro-ph.SR |
arxiv_dataset-68091511.0772 | Table-top setup for investigating the scintillation properties of liquid
argon
physics.ins-det astro-ph.IM
The spectral and temporal light emission properties of liquid argon have been
studied in the context of its use in large liquid rare-gas detectors for
detecting Dark Matter particles in astronomy. A table-top setup has been
developed. Continuous and pulsed low energy electron beam excitation is used to
stimulate light emission. A spectral range from 110 to 1000 nm in wavelength is
covered by the detection system with a time resolution on the order of 1 ns.
| arxiv topic:physics.ins-det astro-ph.IM |
arxiv_dataset-68101511.0782 | Planetary Candidates from the First Year of the K2 Mission
astro-ph.EP astro-ph.IM astro-ph.SR
The Kepler Space Telescope is currently searching for planets transiting
stars along the ecliptic plane as part of its extended K2 mission. We processed
the publicly released data from the first year of K2 observations (Campaigns 0,
1, 2, and 3) and searched for periodic eclipse signals consistent with
planetary transits. Out of 59,174 targets we searched, we detect 234 planetary
candidates around 208 stars. These candidates range in size from gas giants to
smaller than the Earth, and range in orbital periods from hours to over a
month. We conducted initial reconnaissance spectroscopy of 68 of the brighter
candidate host stars, and present high resolution optical spectra for these
stars. We make all of our data products, including light curves, spectra, and
vetting diagnostics available to users online.
| arxiv topic:astro-ph.EP astro-ph.IM astro-ph.SR |
arxiv_dataset-68111511.0792 | The minimum rank problem for circulants
math.CO
The minimum rank problem is to determine for a graph $G$ the smallest rank of
a Hermitian (or real symmetric) matrix whose off-diagonal zero-nonzero pattern
is that of the adjacency matrix of $G$. Here $G$ is taken to be a circulant
graph, and only circulant matrices are considered. The resulting graph
parameter is termed the minimum circulant rank of the graph. This value is
determined for every circulant graph in which a vertex neighborhood forms a
consecutive set, and in this case is shown to coincide with the usual minimum
rank. Under the additional restriction to positive semidefinite matrices, the
resulting parameter is shown to be equal to the smallest number of dimensions
in which the graph has an orthogonal representation with a certain symmetry
property, and also to the smallest number of terms appearing among a certain
family of polynomials determined by the graph. This value is then determined
when the number of vertices is prime. The analogous parameter over the reals is
also investigated.
| arxiv topic:math.CO |
arxiv_dataset-68121511.0802 | Authentication With a Guessing Adversary
cs.IT math.IT
In this paper, we consider the authentication problem where a candidate
measurement presented by an unidentified user is compared to a previously
stored measurement of the legitimate user, the enrollment, with respect to a
certain distortion criteria for authentication. An adversary wishes to
impersonate the legitimate user by guessing the enrollment until the system
authenticates him. For this setting, we study the minimum number of required
guesses (on average) by the adversary for a successful impersonation attack and
find the complete characterization of the asymptotic exponent of this metric,
referred to as the deception exponent. Our result is a direct application of
the results of the Guessing problem by Arikan and Merhav [19]. Paralleling the
work in [19] we also extend this result to the case where the adversary may
have access to additional side information correlated to the enrollment data.
The paper is a revised version of a submission to IEEE WIFS 2015, with the
referencing to the paper [19] clarified compared with the conference version.
| arxiv topic:cs.IT math.IT |
arxiv_dataset-68131511.0812 | Heavy to light Higgs boson decays at NLO in the Singlet Extension of the
Standard Model
hep-ph
We study the decay of a heavy Higgs boson into a light Higgs pair at one loop
in the singlet extension of the Standard Model. To this purpose, we construct
several renormalization schemes for the extended Higgs sector of the model. We
apply these schemes to calculate the heavy-to-light Higgs decay width at
next-to-leading order electroweak accuracy, and demonstrate that certain
prescriptions lead to gauge-dependent results. We comprehensively examine how
the NLO predictions depend on the relevant singlet model parameters, with
emphasis on the trademark behavior of the quantum effects, and how these change
under different renormalization schemes and a variable renormalization scale.
Once all present constraints on the model are included, we find mild NLO
corrections, typically of few percent, and with small theoretical
uncertainties.
| arxiv topic:hep-ph |
arxiv_dataset-68141511.0822 | Covariant Action for Type IIB Supergravity
hep-th gr-qc
Taking clues from the recent construction of the covariant action for type II
and heterotic string field theories, we construct a manifestly Lorentz
covariant action for type IIB supergravity, and discuss its gauge fixing
maintaining manifest Lorentz invariance. The action contains a
(non-gravitating) free 4-form field besides the usual fields of type IIB
supergravity. This free field, being completely decoupled from the interacting
sector, has no physical consequence.
| arxiv topic:hep-th gr-qc |
arxiv_dataset-68151511.0832 | Improved topological conformity enhances heat conduction across metal
contacts on transferred graphene
cond-mat.mtrl-sci
Thermal conductance of metal contacts on transferred graphene (trG) could be
significantly reduced from the intrinsic value of similar contacts on as-grown
graphene (grG), due to additional resistance by increased roughness, residues,
oxides and voids. In this paper, we compare the thermal conductance (G) of
Al/trG/Cu interfaces with that of Al/grG/Cu interfaces to understand heat
transfer across metal contacts on transferred graphene. Our samples are
polycrystalline graphene grown on Cu foils by chemical vapor deposition (CVD)
and CVD-grown graphene transferred to evaporated Cu thin films. We find that
for the Al/grG/Cu interfaces of as-grown CVD graphene, G=31 MW m^{-2} K^{-1} at
room temperature, two orders of magnitude lower than that of Al/Cu interfaces.
For most as-transferred graphene on Cu films, G=20 MW m^{-2} K^{-1}, 35% lower
than that of as-grown CVD graphene. We carefully rule out the contributions of
residues, native oxides and interfaces roughness, and attribute the difference
in the thermal conductance of as-grown and as-transferred CVD graphene to
different degrees of conformity of graphene to the Cu substrates. We find that
a contact area of 50% only reduces the thermal conductance by 35%, suggesting
that a small amount of heat transfer occurs across voids at graphene
interfaces. We successfully improve the conformity of the as-transferred
graphene to the substrates by annealing the samples at 300{\deg}C, and thus
enhance the thermal conductance of the transferred graphene to the intrinsic
value. From the temperature dependence measurements of G of Al/trG/Cu and
Al/grG/Cu interfaces, we also confirm that phonons are the dominant heat
carries across the metal/graphene/metal interfaces despite a substantial
carrier concentration of 3x10^{12} cm^{-2} induced in the graphene.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-68161511.0842 | Orthogonal forms and orthogonality preservers on real function algebras
revisited
math.OA
In 2014, we determine the precise form of a continuous orthogonal form on a
commutative real C$^*$-algebra. We also describe the general form of a
(not-necessarily continuous) orthogonality preserving linear map between
commutative unital real C$^*$-algebras. Among the consequences, we show that
every orthogonality preserving linear bijection between commutative unital real
C$^*$-algebras is continuous. In this note we revisit these results and their
proofs with the idea of filling a gap in the arguments, and to extend the
original conclusions.
| arxiv topic:math.OA |
arxiv_dataset-68171511.0852 | Complete reducibility of subgroups of reductive algebraic groups over
nonperfect fields 1
math.GR math.AG
Let $k$ be a nonperfect field of characteristic $2$. Let $G$ be a $k$-split
simple algebraic group of type $E_6$ (or $G_2$) defined over $k$. In this
paper, we present the first examples of nonabelian non-$G$-completely reducible
$k$-subgroups of $G$ which are $G$-completely reducible over $k$. Our
construction is based on that of subgroups of $G$ acting non-separably on the
unipotent radical of a proper parabolic subgroup of $G$ in our previous work.
We also present examples with the same property for a non-connected reductive
group $G$. Along the way, several general results concerning complete
reducibility over nonperfect fields are proved using the recently proved Tits
center conjecture for spherical buildings. In particular, we show that under
mild conditions a $k$-subgroup of $G$ is pseudo-reductive if it is
$G$-completely reducible over $k$.
| arxiv topic:math.GR math.AG |
arxiv_dataset-68181511.0862 | Effect of interstitial-driven lattice expansion on the stacking fault
energy in austenitic steels
cond-mat.mtrl-sci
Interstitials (carbon and nitrogen) are crucial alloying elements for
optimizing the mechanical performance of the twinning-induced plasticity (TWIP)
steels in terms of the stacking fault energy (SFE). First-principles
calculations have been performed to study the effect of interstitial-induced
lattice expansion on the SFE. Comparing the predictions with the SFEs measured
for alloys containing C and N, our results suggest that the dominant effect of
these interstitials on the SFE is due to the lattice expansion effect.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-68191511.0872 | New mathematics for the non additive Tsallis' scenario
quant-ph cond-mat.stat-mech
In this manuscript we investigate quantum uncertainties in a Tsallis' non
additive scenario. To such an end we appeal to q-exponentials, that are the
cornerstone of Tsallis' theory. In this respect, it is found that some new
mathematics is needed and we are led to construct a set of novel special states
that are the q-exponential equivalents of the ordinary coherent states of the
harmonic oscillator. We then characterize these new Tsallis' special states by
obtaining the associated i) probability distributions for a state of momentum
$k$, ii) mean values for some functions of space an momenta, and iii)
concomitant quantum uncertainties. The latter are then compared to the usual
ones.
| arxiv topic:quant-ph cond-mat.stat-mech |
arxiv_dataset-68201511.0882 | D6-branes and axion monodromy inflation
hep-th astro-ph.CO
We develop new scenarios of large field inflation in type IIA string
compactifications in which the key ingredient is a D6-brane that creates a
potential for a B-field axion. The potential has the multi-branched structure
typical of F-term axion monodromy models and, near its supersymmetric minima,
it is described by a 4d supergravity model of chaotic inflation with a
stabiliser field. The same statement applies to the D6-brane Wilson line, which
can also be considered as an inflaton candidate. We analyse both cases in the
context of type IIA moduli stabilisation, finding an effective potential for
the inflaton system and a simple mechanism to lower the inflaton mass with
respect to closed string moduli stabilised by fluxes. Finally, we compute the
B-field potential for trans-Planckian field values by means of the DBI action.
The effect of Planck suppressed corrections is a flattened potential which, in
terms of the compactification parameters, interpolates between linear and
quadratic inflation. This renders the cosmological parameters of these models
compatible with current experimental bounds, with the tensor-to-scalar ratio
ranging as 0.08 < r < 0.12
| arxiv topic:hep-th astro-ph.CO |
arxiv_dataset-68211511.0892 | Computational Homogenization of Fresh Concrete Flow Around Reinforcing
Bars
cs.CE physics.flu-dyn
Motivated by casting of fresh concrete in reinforced concrete structures, we
introduce a numerical model of a steady-state non-Newtonian fluid flow through
a porous domain. Our approach combines homogenization techniques to represent
the reinforced domain by the Darcy law with an interface coupling of the Stokes
and Darcy flows through the Beavers-Joseph-Saffman conditions. The ensuing
two-scale problem is solved by the Finite Element Method with consistent
linearization and the results obtained from the homogenization approach are
verified against fully resolved direct numerical simulations.
| arxiv topic:cs.CE physics.flu-dyn |
arxiv_dataset-68221511.0902 | Eventually Positive Semigroups of Linear Operators
math.FA math.AP
We develop a systematic theory of eventually positive semigroups of linear
operators mainly on spaces of continuous functions. By eventually positive we
mean that for every positive initial condition the solution to the
corresponding Cauchy problem is positive for large enough time.
Characterisations of such semigroups are given by means of resolvent properties
of the generator and Perron--Frobenius type spectral conditions. We apply these
characterisations to prove eventual positivity of several examples of
semigroups including some generated by fourth order elliptic operators and a
delay differential equation. We also consider eventually positive semigroups on
arbitrary Banach lattices and establish several results for their spectral
bound which were previously only known for positive semigroups.
| arxiv topic:math.FA math.AP |
arxiv_dataset-68231511.0912 | Coresets for Kinematic Data: From Theorems to Real-Time Systems
cs.RO cs.CV
A coreset (or core-set) of a dataset is its semantic compression with respect
to a set of queries, such that querying the (small) coreset provably yields an
approximate answer to querying the original (full) dataset. In the last decade,
coresets provided breakthroughs in theoretical computer science for
approximation algorithms, and more recently, in the machine learning community
for learning "Big data". However, we are not aware of real-time systems that
compute coresets in a rate of dozens of frames per second. In this paper we
suggest a framework to turn theorems to such systems using coresets. We begin
with a proof of independent interest, that any set of $n$ matrices in
$\mathbb{R}^{d\times d}$ whose sum is $S$, has a positively weighted subset
whose sum has the same center of mass (mean) and orientation (left+right
singular vectors) as $S$, and consists of $O(dr)$ matrices (independent of
$n$), where $r\leq d$ is the rank of $S$. We provide an algorithm that computes
this (core) set in one pass over possibly infinite stream of matrices in
$d^{O(1)}$ time per matrix insertion. By maintaining such a coreset for
kinematic (moving) set of $n$ points, we can run pose-estimation algorithms,
such as Kabsch or PnP, on the small coresets, instead of the $n$ points, in
real-time using weak devices, while obtaining the same results. This enabled us
to implement a low-cost ($<\$100$) IoT wireless system that tracks a toy (and
harmless) quadcopter which guides guests to a desired room (in a hospital,
mall, hotel, museum, etc.) with no help of additional human or remote
controller. We hope that our framework will encourage researchers outside the
theoretical community to design and use coresets in future systems and papers.
To this end, we provide extensive experimental results on both synthetic and
real data, as well as a link to the open code of our system and algorithms.
| arxiv topic:cs.RO cs.CV |
arxiv_dataset-68241511.0922 | Self-testing protocols based on the chained Bell inequalities
quant-ph
Self testing is a device-independent technique based on non-local
correlations whose aim is to certify the effective uniqueness of the quantum
state and measurements needed to produce these correlations. It is known that
the maximal violation of some Bell inequalities suffices for this purpose.
However, most of the existing self-testing protocols for two devices exploit
the well-known Clauser-Horne-Shimony-Holt Bell inequality or modifications of
it, and always with two measurements per party. Here, we generalize the
previous results by demonstrating that one can construct self-testing protocols
based on the chained Bell inequalities, defined for two devices implementing an
arbitrary number of two-output measurements. On the one hand, this proves that
the quantum state and measurements leading to the maximal violation of the
chained Bell inequality are unique. On the other hand, in the limit of a large
number of measurements, our approach allows one to self-test the entire plane
of measurements spanned by the Pauli matrices X and Z. Our results also imply
that the chained Bell inequalities can be used to certify two bits of perfect
randomness.
| arxiv topic:quant-ph |
arxiv_dataset-68251511.0932 | Pointed Hopf actions on fields, II
math.RA math.QA
This is a continuation of the authors' study of finite-dimensional pointed
Hopf algebras H which act inner faithfully on commutative domains. As mentioned
in Part I of this work, the study boils down to the case where H acts inner
faithfully on a field. These Hopf algebras are referred to as
Galois-theoretical.
In this work, we provide classification results for finite-dimensional
pointed Galois-theoretical Hopf algebras H of finite Cartan type. Namely, we
determine when such H of type A_1^{\times r} and some H of rank two possess the
Galois-theoretical property. Moreover, we provide necessary and sufficient
conditions for Reshetikhin twists of small quantum groups to be
Galois-theoretical.
| arxiv topic:math.RA math.QA |
arxiv_dataset-68261511.0942 | Relationship between Fujikawa's Method and the Background Field Method
for the Scale Anomaly
hep-th
We show the equivalence between Fujikawa's method for calculating the scale
anomaly and the diagrammatic approach to calculating the effective potential
via the background field method, for an $O(N)$ symmetric scalar field theory.
Fujikawa's method leads to a sum of terms, each one superficially in one-to-one
correspondence with a vacuum diagram of the 1-loop expansion. From the
viewpoint of the classical action, the anomaly results in a breakdown of the
Ward identities due to a scale-dependence of the couplings, whereas in terms of
the effective action, the anomaly is the result of the breakdown of Noether's
theorem due to explicit symmetry breaking terms of the effective potential.
| arxiv topic:hep-th |
arxiv_dataset-68271512.00048 | Arbitrary axisymmetric steady streaming: Flow, force and propulsion
physics.flu-dyn
A well-developed method to induce mixing on microscopic scales is to exploit
flows generated by steady streaming. Steady streaming is a classical fluid
dynamics phenomenon whereby a time-periodic forcing in the bulk or along a
boundary is enhanced by inertia to induce a non-zero net flow. Building on
classical work for simple geometrical forcing and motivated by the complex
shape oscillations of elastic capsules and bubbles, we develop the mathematical
framework to quantify the steady streaming of a spherical body with arbitrary
axisymmetric time-periodic boundary conditions. We compute the flow
asymptotically for small-amplitude oscillations of the boundary in the limit
where the viscous penetration length scale is much smaller than the body. In
that case, the flow has a boundary layer structure and the fluid motion is
solved by asymptotic matching. Our results, presented in the case of no-slip
boundary conditions and extended to include the motion of vibrating free
surfaces, recovers classical work as particular cases. We illustrate the flow
structure given by our solution and propose one application of our results for
small-scale force-generation and synthetic locomotion.
| arxiv topic:physics.flu-dyn |
arxiv_dataset-68281512.00148 | Field Emission properties of nanocomposites of conducting polymers
cond-mat.mtrl-sci
Nanocomposites based on graphene and carbon nanotubes dispersed in
polypyrrole or poly(3,4ethylenedioxy)thiophene have been prepared and their
performance as cold cathodes for field emission has been evaluated. It was
found that the polymer matrix will degrade during the field emission process
and result in unstable performance. Electropolymerization of the composites
results in significantly better field emission performance, but the stability
is still a major problem. Deposition of composites onto a stable membrane was
proposed as a strategy for improving the performance of electrodes. The field
emission data indicates that composites deposited on the surface of a membrane
can limit the emission surface and result in lower maximum emission and higher
Turn-On voltage. The lower emission current and consequently lower heat
generation, in addition to the possible heat dissipation by the AAO membrane,
can reduce the rate of the thermal degradation of the polymer. The membrane can
also act as a physical barrier that holds nanotubes in place and allows
electrons through. Thus, it can prevent shorting of the field emission cell. In
this way higher emission and longer life time can be achieved.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-68291512.00248 | Engineering Long-Lived Collective Dark States in Spin Ensembles
quant-ph cond-mat.mes-hall
Ensembles of electron spins in hybrid microwave systems are powerful and
versatile components for future quantum technologies. Quantum memories with
high storage capacities are one such example which require long-lived states
that can be addressed and manipulated coherently within the inhomogeneously
broadened ensemble. This broadening is essential for true multimode memories,
but induces a considerable spin dephasing and together with dissipation from a
cavity interface poses a constraint on the memory's storage time. In this work
we show how to overcome both of these limitations through the engineering of
long-lived dark states in an ensemble of electron spins hosted by
nitrogen-vacancy centres in diamond. By burning narrow spectral holes into a
spin ensemble strongly coupled to a superconducting microwave cavity, we
observe long-lived Rabi oscillations with high visibility and a decay rate that
is a factor of forty smaller than the spin ensemble linewidth and thereby a
factor of more than three below the pure cavity dissipation rate. This
significant reduction lives up to the promise of hybrid devices to perform
better than their individual subcomponents. To demonstrate the potential of our
approach we realise the first step towards a solid-state microwave spin
multiplexer by engineering multiple long-lived dark states. Our results show
that we can fully access the "decoherence free" subspace in our experiment and
selectively prepare protected states by spectral hole burning. This technique
opens up the way for truly long-lived quantum memories, solid-state microwave
frequency combs, optical to microwave quantum transducers and spin squeezed
states. Our approach also paves the way for a new class of cavity QED
experiments with dense spin ensembles, where dipole spin-spin interactions
become important and many-body phenomena will be directly accessible on a chip.
| arxiv topic:quant-ph cond-mat.mes-hall |
arxiv_dataset-68301512.00348 | Nonlinear contractions in metric spaces under locally T-transitive
binary relations
math.GN math.FA
In this paper, we present a variant of Boyd-Wong fixed point theorem in a
metric space equipped with a locally T-transitive binary relation, which under
universal relation reduces to Boyd-Wong (Proc. Amer. Math. Soc. 20 (1969)
458-464) and Jotic (Indian J. Pure Appl. Math. 26 (1995) 947-952) fixed point
theorems. Also, our results extend several other well-known fixed point
theorems such as: Alam and Imdad (J. Fixed Point Theory Appl. 17 (4) (2015)
693-702) and Karapinar and Roldan-Lopez-de-Hierro (J. Inequal. Appl. 2014:522
(2014) 12 pp) besides some others.
| arxiv topic:math.GN math.FA |
arxiv_dataset-68311512.00448 | Science Use in Regulatory Impact Analysis: The Effects of Political
Attention and Controversy
cs.DL cs.CY
Scholars, policymakers, and research sponsors have long sought to understand
the conditions under which scientific research is used in the policymaking
process. Recent research has identified a resource that can be used to trace
the use of science across time and many policy domains. US federal agencies are
mandated by executive order to justify all economically significant regulations
by regulatory impact analyses (RIAs), in which they present evidence of the
scientific underpinnings and consequences of the proposed rule. To gain new
insight into when and how regulators invoke science in their policy
justifications, we ask: does the political attention and controversy
surrounding a regulation affect the extent to which science is utilized in
RIAs? We examine scientific citation activity in all 101 economically
significant RIAs from 2008-2012 and evaluate the effects of attention -- from
the public, policy elites and the media -- on the degree of science use in
RIAs. Our main finding is that regulators draw more heavily on scientific
research when justifying rules subject to a high degree of attention from
outside actors. These findings suggest that scientific research plays an
important role in the justification of regulations, especially those that are
highly salient to the public and other policy actors.
| arxiv topic:cs.DL cs.CY |
arxiv_dataset-68321512.00548 | Extrapolation Technique Pitfalls in Asymmetry Measurements at Colliders
hep-ex hep-ph
Asymmetry measurements are common in collider experiments and can sensitively
probe particle properties. Typically, data can only be measured in a finite
region covered by the detector, so an extrapolation from the visible asymmetry
to the inclusive asymmetry is necessary. Often a constant multiplicative factor
is more than adequate for the extrapolation and this factor can be readily
determined using simulation methods. However, there is a potential, avoidable
pitfall involved in the determination of this factor when the asymmetry in the
simulated data sample is small. We find that to obtain a reliable estimate of
the extrapolation factor, the number of simulated events required rises as the
inverse square of the simulated asymmetry; this can mean that an unexpectedly
large sample size is required when determining its value.
| arxiv topic:hep-ex hep-ph |
arxiv_dataset-68331512.00648 | Four-dimensional system with torus attractor birth via saddle-node
bifurcation of limit cycles in content of family of blue sky catastrophes
nlin.CD
A new four-dimensional model with quasi-periodic dynamics is suggested. The
torus attractor originates via the saddle-node bifurcation, which may be
regarded as a member of a bifurcation family embracing different types of blue
sky catastrophes. Also the torus birth trough the Neimark-Sacker bifurcation
occurs in some other region of the parameter space.
| arxiv topic:nlin.CD |
arxiv_dataset-68341512.00748 | The Conversion of CESR to Operate as the Test Accelerator, CesrTA, Part
3: Electron Cloud Diagnostics
physics.acc-ph
Cornell's electron/positron storage ring (CESR) was modified over a series of
accelerator shutdowns beginning in May 2008, which substantially improves its
capability for research and development for particle accelerators. CESR's
energy span from 1.8 to 5.6 GeV with both electrons and positrons makes it
ideal for the study of a wide spectrum of accelerator physics issues and
instrumentation related to present light sources and future lepton damping
rings. Additionally a number of these are also relevant for the beam physics of
proton accelerators. This paper is the third in a series of four describing the
the conversion of CESR to the test accelerator, CesrTA. The first two papers
discuss the overall plan for the conversion of the storage ring to an
instrument capable of studying advanced accelerator physics issues and the
details of the vacuum system upgrades. This paper focusses on the necessary
development of new instrumentation, situated in four dedicated experimental
regions, capable of studying such phenomena as electron clouds (ECs) and
methods to mitigate EC effects. The fourth paper in this series describes the
vacuum system modifications of the superconducting wigglers to accommodate the
diagnostic instrumentation for the study of EC behavior within wigglers. While
the initial studies of CesrTA focussed on questions related to the
International Linear Collider damping ring design, CesrTA is a very versatile
storage ring, capable of studying a wide range of accelerator physics and
instrumentation questions.
| arxiv topic:physics.acc-ph |
arxiv_dataset-68351512.00848 | Understanding analog quantum simulation dynamics in coupled ion-trap
qubits
cond-mat.dis-nn quant-ph
We study numerically a disordered transverse-field Ising Hamiltonian with
long-range couplings. This model was recently investigated experimentally in a
trapped-ion quantum simulator and was found to exhibit features of many-body
localization at strong disorder. We use exact diagonalization to study the
collective state preservation and the eigenstate entanglement structure as a
function of both disorder strength and interaction range. Our numerical
results, using the same system sizes as the experiment, verify the observation
of many-body localization reported in the recent quantum simulation experiment,
and point to directions for future experiments.
| arxiv topic:cond-mat.dis-nn quant-ph |
arxiv_dataset-68361512.00948 | Besov spaces of self-affine lattice tilings and pointwise regularity
math.FA
We investigate Besov spaces of self-affine tilings of ${\Bbb R}^{n}$ and
discuss various characterizations of those Besov spaces. We see what is a
finite set of functions which generates the Besov spaces from a view of
multiresolution approximation on self-affine lattice tilings of ${\Bbb R}^{n}$.
Using this result we give a generalization of already known characterizations
of Besov spaces given by wavelet expansion and we apply to study the pointwise
H${\ddot {\rm o}}$lder space. Furthermore we give descriptions of scaling
exponents measured by Besov spaces, and estimations of a pointwise H${\ddot
{\rm o}}$lder exponent to compute the pointwise scaling exponent of several
oscillatory functions.
| arxiv topic:math.FA |
arxiv_dataset-68371512.01048 | Deterministic generation of bright single resonance fluorescence photons
from a Purcell-enhanced quantum dot-micropillar system
quant-ph cond-mat.mes-hall
We report on the observation of bright emission of single photons under
pulsed resonance fluorescence conditions from a single quantum dot (QD) in a
micropillar cavity. The brightness of the QD fluorescence is greatly enhanced
via the coupling to the fundamental mode of a micropillar, allowing us to
determine a single photon extraction efficiency of $(20.7\pm0.8)~\%$ per linear
polarization basis. This yields an overall extraction efficiency of
$(41.4\pm1.5)~\%$ in our device. We observe the first Rabi-oscillation in a
weakly coupled quantum dot-micropillar system under coherent pulsed optical
excitation, which enables us to deterministically populate the excited QD
state. In this configuration, we probe the single photon statistics of the
device yielding $g^{(2)}(0)=0.072\pm0.011$ at a QD-cavity detuning of
$75~\mu$eV.
| arxiv topic:quant-ph cond-mat.mes-hall |
arxiv_dataset-68381512.01148 | Bose Operators, Coherent States, Truncation, Spin Coherent States, Lie
Algebras and Spectrum
quant-ph math-ph math.MP
We study truncated Bose operators in finite dimensional Hilbert spaces. Spin
coherent states for the truncated Bose operators and canonical coherent states
for Bose operators are compared. The Lie algebra structure and the spectrum of
the truncated Bose operators are discussed.
| arxiv topic:quant-ph math-ph math.MP |
arxiv_dataset-68391512.01248 | Sisyphus Thermalization of Photons in a Cavity-Coupled Double Quantum
Dot
cond-mat.mes-hall quant-ph
We investigate the non-classical states of light that emerge in a microwave
resonator coupled to a periodically-driven electron in a nanowire double
quantum dot (DQD). Under certain drive configurations, we find that the
resonator approaches a thermal state at the temperature of the surrounding
substrate with a chemical potential given by a harmonic of the drive frequency.
Away from these thermal regions we find regions of gain and loss, where the
system can lase, or regions where the DQD acts as a single-photon source. These
effects are observable in current devices and have broad utility for quantum
optics with microwave photons.
| arxiv topic:cond-mat.mes-hall quant-ph |
arxiv_dataset-68401512.01348 | On the possible values of the entropy of undirected graphs
cs.IT cs.DM math.CO math.IT
The entropy of a digraph is a fundamental measure which relates network
coding, information theory, and fixed points of finite dynamical systems. In
this paper, we focus on the entropy of undirected graphs. We prove that for any
integer $k$ the number of possible values of the entropy of an undirected graph
up to $k$ is finite. We also determine all the possible values for the entropy
of an undirected graph up to the value of four.
| arxiv topic:cs.IT cs.DM math.CO math.IT |
arxiv_dataset-68411512.01448 | Maximum Rank and Asymptotic Rank of Finite Dynamical Systems
math.CO cs.DM math.DS
A finite dynamical system is a system of multivariate functions over a finite
alphabet used to model a network of interacting entities. The main feature of a
finite dynamical system is its interaction graph, which indicates which local
functions depend on which variables; the interaction graph is a qualitative
representation of the interactions amongst entities on the network. The rank of
a finite dynamical system is the cardinality of its image; the periodic rank is
the number of its periodic points. In this paper, we determine the maximum rank
and the maximum periodic rank of a finite dynamical system with a given
interaction graph over any non-Boolean alphabet. We also obtain a similar
result for Boolean finite dynamical systems (also known as Boolean networks)
whose interaction graphs are contained in a given digraph. We then prove that
the average rank is relatively close (as the size of the alphabet is large) to
the maximum. The results mentioned above only deal with the parallel update
schedule. We finally determine the maximum rank over all block-sequential
update schedules and the supremum periodic rank over all complete update
schedules.
| arxiv topic:math.CO cs.DM math.DS |
arxiv_dataset-68421512.01548 | Tensor Networks from Kinematic Space
hep-th
We point out that the MERA network for the ground state of a 1+1-dimensional
conformal field theory has the same structural features as kinematic
space---the geometry of CFT intervals. In holographic theories kinematic space
becomes identified with the space of bulk geodesics studied in integral
geometry. We argue that in these settings MERA is best viewed as a
discretization of the space of bulk geodesics rather than of the bulk geometry
itself. As a test of this kinematic proposal, we compare the MERA
representation of the thermofield-double state with the space of geodesics in
the two-sided BTZ geometry, obtaining a detailed agreement which includes the
entwinement sector. We discuss how the kinematic proposal can be extended to
excited states by generalizing MERA to a broader class of compression networks.
| arxiv topic:hep-th |
arxiv_dataset-68431512.01648 | Tur\'an Type Inequality for The Hahn-Exton $q$-Bessel Functions
math.CA
The aim of this paper is to establish Tur\'an -type inequality for the
Hahn-Exton $q$-Bessel functions. The result is obtained by the use of limit
transition.
| arxiv topic:math.CA |
arxiv_dataset-68441512.01748 | Restricted Low-Rank Approximation via ADMM
cs.NA cs.DS
The matrix low-rank approximation problem with additional convex constraints
can find many applications and has been extensively studied before. However,
this problem is shown to be nonconvex and NP-hard; most of the existing
solutions are heuristic and application-dependent. In this paper, we show that,
other than tons of application in current literature, this problem can be used
to recover a feasible solution for SDP relaxation. By some sophisticated
tricks, it can be equivalently posed in an appropriate form for the Alternating
Direction Method of Multipliers (ADMM) to solve. The two updates of ADMM
include the basic matrix low-rank approximation and projection onto a convex
set. Different from the general non-convex problems, the sub-problems in each
step of ADMM can be solved exactly and efficiently in spite of their
non-convexity. Moreover, the algorithm will converge exponentially under proper
conditions. The simulation results confirm its superiority over existing
solutions. We believe that the results in this paper provide a useful tool for
this important problem and will help to extend the application of ADMM to the
non-convex regime.
| arxiv topic:cs.NA cs.DS |
arxiv_dataset-68451512.01848 | Rank Pooling for Action Recognition
cs.CV
We propose a function-based temporal pooling method that captures the latent
structure of the video sequence data - e.g. how frame-level features evolve
over time in a video. We show how the parameters of a function that has been
fit to the video data can serve as a robust new video representation. As a
specific example, we learn a pooling function via ranking machines. By learning
to rank the frame-level features of a video in chronological order, we obtain a
new representation that captures the video-wide temporal dynamics of a video,
suitable for action recognition. Other than ranking functions, we explore
different parametric models that could also explain the temporal changes in
videos. The proposed functional pooling methods, and rank pooling in
particular, is easy to interpret and implement, fast to compute and effective
in recognizing a wide variety of actions. We evaluate our method on various
benchmarks for generic action, fine-grained action and gesture recognition.
Results show that rank pooling brings an absolute improvement of 7-10 average
pooling baseline. At the same time, rank pooling is compatible with and
complementary to several appearance and local motion based methods and
features, such as improved trajectories and deep learning features.
| arxiv topic:cs.CV |
arxiv_dataset-68461512.01948 | Interface induced high temperature superconductivity in single unit-cell
FeSe films on SrTiO3(110)
cond-mat.supr-con
We report high temperature superconductivity in one unit-cell (1-UC) FeSe
films grown on STO(110) substrate by molecular beam epitaxy. By in-situ
scanning tunneling spectroscopy measurement, we observed a superconducting gap
as large as 17 meV. Transport measurements on 1-UC FeSe/STO(110) capped with
FeTe layers reveal superconductivity with an onset TC of 31.6 K and an upper
critical magnetic field of 30.2 T. We also find that the TC can be further
increased by an external electric field, but the effect is smaller than that on
STO(001) substrate. The study points out the important roles of interface
related charge transfer and electron-phonon coupling in the high temperature
superconductivity of FeSe/STO.
| arxiv topic:cond-mat.supr-con |
arxiv_dataset-68471512.02048 | Homogenization Method, uncovered on 2 pages
math-ph math.MP
This note gives a brief and `crash' introduction to the method of
Homogenization with the use of wave equation and diffusion equation with
periodic in space coefficients as instructive examples. We expose the method
with the use of an approach, which appears in Vibrodynamics. The note can be
interesting for people who want to use the Homogenization method immediately.
| arxiv topic:math-ph math.MP |
arxiv_dataset-68481512.02148 | On homoclinic orbits to center manifolds of elliptic-hyperbolic
equilibria in Hamiltonian systems
math.DS
We consider a Hamiltonian system which has an elliptic-hyperbolic equilibrium
with a homoclinic loop. We identify the set of orbits which are homoclinic to
the center manifold of the equilibrium via a Lyapunov- Schmidt reduction
procedure. This leads to the study of a singularity which inherits certain
structure from the Hamiltonian nature of the system. Under non-degeneracy
assumptions, we classify the possible Morse indices of this singularity,
permitting a local description of the set of homoclinic orbits. We also
consider the case of time-reversible Hamiltonian systems.
| arxiv topic:math.DS |
arxiv_dataset-68491512.02248 | Frequency domain reduced order model of aligned-spin effective-one-body
waveforms with generic mass-ratios and spins
gr-qc
I provide a frequency domain reduced order model (ROM) for the aligned-spin
effective-one-body (EOB) model "SEOBNRv2" for data analysis with second and
third generation ground based gravitational wave (GW) detectors. SEOBNRv2
models the dominant mode of the GWs emitted by the coalescence of black hole
(BH) binaries. The large physical parameter space (dimensionless spins $-1 \leq
\chi_i \leq 0.99$ and symmetric mass-ratios $0.01 \leq \eta \leq 0.25$)
requires sophisticated reduced order modeling techniques, including patching in
the parameter space and in frequency. I find that the time window over which
the inspiral-plunge and the merger-ringdown waveform in SEOBNRv2 are connected
is discontinuous when the spin of the deformed Kerr BH $\chi=0.8$ or the
symmetric mass-ratio $\eta \sim 0.083$. This discontinuity increases resolution
requirements for the ROM. The ROM can be used for compact binary systems with
total masses of $2 M_\odot$ or higher for the advanced LIGO (aLIGO) design
sensitivity and a $10$ Hz lower cutoff frequency. The ROM has a worst mismatch
against SEOBNRv2 of $\sim 1\%$, but in general mismatches are better than $\sim
0.1\%$. The ROM is crucial for key data analysis applications for compact
binaries, such as GW searches and parameter estimation carried out within the
LIGO Scientific Collaboration (LSC).
| arxiv topic:gr-qc |
arxiv_dataset-68501512.02348 | A Hermite-Minkowski type theorem of varieties over finite fields
math.NT
As an application of P. Delgine's theorem (Esnault and Kerz in Acta Math.
Vietnam. 37:531-562, 2012) on a finiteness of $l$-adic sheaves on a variety
over a finite field, we show the finiteness of \'etale coverings of such a
variety with given degree whose ramification bounded along an effective Cartier
divisor. This can be thought of a higher dimensional analogue of the classical
Hermite-Minkowski theorem.
| arxiv topic:math.NT |
arxiv_dataset-68511512.02448 | Characters of the Norm-One Units of Local Division Algebras of Prime
Degree
math.RT
We give an explicit construction of all complex continuous irreducible
characters of the group ${\rm SL}_1(D)$, where $D$ is a division algebra of
prime degree $\ell$ over a local field of odd residual characteristic different
than $\ell$. For $\ell$ odd, we show that all such characters of ${\rm
SL}_1(D)$ are induced from linear characters of compact-open subgroups of ${\rm
SL}_1(D)$. We also compute an explicit formula for the representation zeta
function of ${\rm SL}_1(D)$.
| arxiv topic:math.RT |
arxiv_dataset-68521512.02548 | A Stabilised Nodal Spectral Element Method for Fully Nonlinear Water
Waves
physics.comp-ph cs.CE math.NA
We present an arbitrary-order spectral element method for general-purpose
simulation of non-overturning water waves, described by fully nonlinear
potential theory. The method can be viewed as a high-order extension of the
classical finite element method proposed by Cai et al (1998)
\cite{CaiEtAl1998}, although the numerical implementation differs greatly.
Features of the proposed spectral element method include: nodal Lagrange basis
functions, a general quadrature-free approach and gradient recovery using
global $L^2$ projections. The quartic nonlinear terms present in the Zakharov
form of the free surface conditions can cause severe aliasing problems and
consequently numerical instability for marginally resolved or very steep waves.
We show how the scheme can be stabilised through a combination of
over-integration of the Galerkin projections and a mild spectral filtering on a
per element basis. This effectively removes any aliasing driven instabilities
while retaining the high-order accuracy of the numerical scheme. The additional
computational cost of the over-integration is found insignificant compared to
the cost of solving the Laplace problem. The model is applied to several
benchmark cases in two dimensions. The results confirm the high order accuracy
of the model (exponential convergence), and demonstrate the potential for
accuracy and speedup. The results of numerical experiments are in excellent
agreement with both analytical and experimental results for strongly nonlinear
and irregular dispersive wave propagation. The benefit of using a high-order --
possibly adapted -- spatial discretization for accurate water wave propagation
over long times and distances is particularly attractive for marine
hydrodynamics applications.
| arxiv topic:physics.comp-ph cs.CE math.NA |
arxiv_dataset-68531512.02648 | Free loci of matrix pencils and domains of noncommutative rational
functions
math.RA math.RT
Consider a monic linear pencil $L(x) = I - A_1x_1 - \cdots - A_gx_g$ whose
coefficients $A_j$ are $d \times d$ matrices. It is naturally evaluated at
$g$-tuples of matrices $X$ using the Kronecker tensor product, which gives rise
to its free locus $Z(L) = \{ X: \det L(X) = 0 \}$. In this article it is shown
that the algebras $A$ and $A'$ generated by the coefficients of two linear
pencils $L$ and $L'$, respectively, with equal free loci are isomorphic up to
radical. Furthermore, $Z(L) \subseteq Z(L')$ if and only if the natural map
sending the coefficients of $L'$ to the coefficients of $L$ induces a
homomorphism $A'/{\rm rad} A' \to A/{\rm rad} A$. Since linear pencils are a
key ingredient in studying noncommutative rational functions via realization
theory, the above results lead to a characterization of all noncommutative
rational functions with a given domain. Finally, a quantum version of
Kippenhahn's conjecture on linear pencils is formulated and proved: if
hermitian matrices $A_1, \dots, A_g$ generate $M_d(\mathbb{C})$ as an algebra,
then there exist hermitian matrices $X_1, \dots, X_g$ such that $\sum_i A_i
\otimes X_i$ has a simple eigenvalue.
| arxiv topic:math.RA math.RT |
arxiv_dataset-68541512.02748 | Ziegler Spectrum and Krull Gabriel Dimension
math.RA math.RT
These notes are based on a talk given at the Summer School
"Infinite-dimensional representations of finite-dimensional algebras" held at
the University of Manchester in September 2015. They intend to provide a brief
introduction to the notion of Ziegler Spectrum and Krull-Gabriel dimension.
| arxiv topic:math.RA math.RT |
arxiv_dataset-68551512.02848 | Standard model of the rare-earths, analyzed from the Hubbard I
approximation
cond-mat.str-el cond-mat.mtrl-sci physics.comp-ph
In this work we examine critically the electronic structure of the rare-earth
elements by use of the so-called Hubbard I approximation. From the theoretical
side all measured features of both occupied and unoccupied states are
reproduced, without significant deviations between observations and theory. We
also examine cohesive properties like the equilibrium volume and bulk modulus,
where we find, in general, a good agreement between theory and measurements. In
addition we have reproduced the spin and orbital moments of these elements, as
they are reflected from measurements of the saturation moment. We have also
employed the Hubbard I approximation to extract the interatomic exchange
parameters of an effective spin Hamiltonian for the heavy rare earths. We show
that the Hubbard I approximation gives results which are consistent with
calculations where $4f$ electrons are treated as core states for Gd. The latter
approach was also used to address the series of the heavy/late rare-earths. Via
Monte Carlo simulations we obtained ordering temperatures which reproduce
measurements within about $20\%$. We have further illustrated the accuracy of
these exchange parameters by comparing measured and calculated magnetic
configurations for the heavy rare earths and the magnon dispersion for Gd. The
Hubbard I approximation is compared to other theories of the electronic
structure, and we argue that it is superior. We discuss the relevance of our
results in general, and how this makes it possible to treat the electronic
structure of materials containing rare-earth elements, such as permanent
magnets, magnetostrictive compounds, photovoltaics, optical fibers, topological
insulators, and molecular magnets.
| arxiv topic:cond-mat.str-el cond-mat.mtrl-sci physics.comp-ph |
arxiv_dataset-68561512.02948 | Emergent Weak Scale from Cosmological Evolution and Dimensional
Transmutation
hep-ph hep-th
In this note we present a framework in which the weak scale appears
dynamically technically natural with no new physics up to the Planck scale. The
mixing between the massless Higgs and the R^2 metric theory induces, in
canonical parametrization of the Einstein frame, an effective field-dependent
Higgs mass parameter. It is a dynamical variable which in the course of cosmic
evolution scans a wide range of values and eventually stabilizes at a low
scale. The one-loop effective potential has an electroweak symmetry breaking
vacuum and the hierarchy is explained by dimensional transmutation and
cosmological relaxation mechanisms. Furthermore, by evaluating the
renormalization group improved effective potential we find that the electroweak
vacuum is the global minimum of the effective potential.
| arxiv topic:hep-ph hep-th |
arxiv_dataset-68571512.03048 | On perfect codes that do not contain Preparata-like codes
cs.IT math.IT
We show that for every length of form $4^k-1$, there exists a binary
$1$-perfect code that does not include any Preparata-like code.
| arxiv topic:cs.IT math.IT |
arxiv_dataset-68581512.03148 | Coefficient estimates of analytic endomorphisms of the unit disk fixing
a point with applications to concave functions
math.CV
In this note, we discuss the coefficient regions of analytic self-maps of the
unit disk with a prescribed fixed point. As an application, we solve the
Fekete-Szeg\H{o} problem for normalized concave functions with a prescribed
pole in the unit disk.
| arxiv topic:math.CV |
arxiv_dataset-68591512.03248 | Sealed operation, and circulation and purification of gas in the HARPO
TPC
physics.ins-det astro-ph.IM
HARPO is a time projection chamber (TPC) demonstrator of a gamma-ray
telescope and polarimeter in the MeV-GeV range, for a future space mission. We
present the evolution of the TPC performance over a five month sealed-mode
operation, by the analysis of cosmic-ray data, followed by the fast and
complete recovery of the initial gas properties using a lightweight gas
circulation and purification system.
| arxiv topic:physics.ins-det astro-ph.IM |
arxiv_dataset-68601512.03348 | Calculation of expectation values of operators in the Complex Scaling
method
nucl-th physics.atom-ph
The complex scaling method (CSM) provides with a way to obtain resonance
parameters of particle unstable states by rotating the coordinates and momenta
of the original Hamiltonian. It is convenient to use an L$^2$ integrable basis
to resolve the complex rotated or complex scaled Hamiltonian H$_{\theta}$, with
$\theta$ being the angle of rotation in the complex energy plane. Within the
CSM, resonance and scattering solutions do not exhibit an outgoing or
scattering wave asymptotic behavior, but rather have decaying asymptotics. One
of the consequences is that, expectation values of operators in a resonance or
scattering complex scaled solution are calculated by complex rotating the
operators. In this work we are exploring applications of the CSM on
calculations of expectation values of quantum mechanical operators by
retrieving the Gamow asymptotic character of the decaying state and calculating
hence the expectation value using the unrotated operator. The test cases
involve a schematic two-body Gaussian model and also applications using
realistic interactions.
| arxiv topic:nucl-th physics.atom-ph |
arxiv_dataset-68611512.03448 | Two Roads to the Null Energy Condition
hep-th gr-qc
The null energy condition has sweeping consequences in general relativity. I
argue here that it has been misunderstood as a property exclusively of matter,
when in fact it arises only in a theory of both matter and gravity. I then
derive an equivalent geometric formulation of the null energy condition from
worldsheet string theory, where it arises beautifully as simply Einstein's
equations in two dimensions. But further, I show that this condition also has a
thermodynamic origin, following from a local version of the second law of
thermodynamics, applied to gravitational entropy. Thus, far from being an
incidental property of matter, the validity of the null energy condition hints
at the deep dual origins of gravity.
| arxiv topic:hep-th gr-qc |
arxiv_dataset-68621512.03548 | Proposal for Quantum Sensing Based on Two-Dimensional Dynamical
Decoupling: NMR Correlation Spectroscopy of Single Molecules
quant-ph
Nuclear magnetic resonance (NMR) has enormous applications. Two-dimensional
NMR is an essential technique to characterize correlations between nuclei and,
hence, molecule structures. Towards the ultimate goal of single-molecule NMR,
dynamical-decoupling- (DD) enhanced diamond quantum sensing enables the
detection of single nuclear spins and nanoscale NMR. However, there is still
the lack of a standard method in DD-based quantum sensing to characterize
correlations between nuclear spins in single molecules. Here we present a
scheme of two-dimensional DD-based quantum sensing, as a universal method for
correlation spectroscopy of single molecules. We design two-dimensional DD
sequences composed of two sets of periodic DD sequences with different periods,
which can be independently set to match two different transition frequencies
for resonant DD. We find that under the resonant DD condition the sensor
coherence patterns, as functions of the two independent pulse numbers of DD
subsequences, can fully determine different types of correlations between
nuclear spin transitions. This work offers a systematic approach to correlation
spectroscopy for single-molecule NMR.
| arxiv topic:quant-ph |
arxiv_dataset-68631512.03648 | On two conjectures concerning squarefree numbers in arithmetic
progressions
math.NT
We prove upper bounds for the error term of the distribution of squarefree
numbers up to $X$ in arithmetic progressions modulo $q$ making progress towards
two well-known conjectures concerning this distribution and improving upon
earlier results by Hooley. We make use of recent estimates for short
exponential sums by Bourgain-Garaev and for exponential sums twisted by the
M\"obius function by Bourgain and Fouvry-Kowalski-Michel.
| arxiv topic:math.NT |
arxiv_dataset-68641512.03748 | Semi-Stable Chow-Hall Algebras of Quivers and Quantized Donaldson-Thomas
Invariants
math.RT math.AG
The semi-stable ChowHa of a quiver with stability is defined as an analog of
the Cohomological Hall algebra of Kontsevich and Soibelman via convolution in
equivariant Chow groups of semi-stable loci in representation varieties of
quivers. We prove several structural results on the semi-stable ChowHa, namely
isomorphism of the cycle map, a tensor product decomposition, and a
tautological presentation. For symmetric quivers, this leads to an
identification of their quantized Donaldson-Thomas invariants with the
Chow-Betti numbers of moduli spaces.
| arxiv topic:math.RT math.AG |
arxiv_dataset-68651512.03848 | Directed Unions of Local Quadratic Transforms of a Regular Local Ring
math.AC
We consider the directed union S of an infinite sequence {(R_n, m_n)} of
successive local quadratic transforms of a regular local ring (R, m). If dim R
= 2, Abhyankar proves that S is a valuation ring. If dim R > 2, Shannon gives
necessary and sufficient conditions for S to be a rank 1 valuation domain and
Granja gives necessary and sufficient conditions that S be a rank 2 rational
rank 2 valuation domain. Granja observes that these are the only cases where S
is a valuation domain. If the sequence is along a rank 1 valuation ring V with
valuation v, Granja, Martinez, and Rodriguez show that if the infinite sum of
the values v(m_n) diverges, then S = V. We prove that this infinite sum is
finite if V has rational rank at least 2. We present an example of a sequence
whose union S is a rank 2 valuation domain, but whose value group is not Z^2.
We also consider sequences of monomial local quadratic transforms and give
necessary and sufficient conditions that the union be a rank 1 valuation
domain. If it is, it has rational rank d. We string together finite sequences
of monomial local quadratic transforms to construct examples where S is a rank
1 valuation domain with rational rank < d.
| arxiv topic:math.AC |
arxiv_dataset-68661512.03948 | Deforming the Window of a Gabor Frame: the Ellipsoid Method
math.FA math-ph math.MP quant-ph
In a recent paper in Appl. Comput. Harmon. Anal. 38(2), 196--221 (2014) we
have introduced and studied the notion of weak Hamiltonian deformation of a
Gabor (=Weyl-Heisenberg) frame. In this Note we use these results to prove that
one can modify the window of a Gabor frame using certain metaplectic operators
provided that one modifies only a finite number of points of the frame lattice.
| arxiv topic:math.FA math-ph math.MP quant-ph |
arxiv_dataset-68671512.04048 | $B^0 \to D^0 \bar D^0 K^0$, $B^+ \to D^0 \bar D^0 K^+$ and the scalar $D
\bar D$ bound state
hep-ph nucl-th
We study the $B^0$ decay to $D^0 \bar D^0 K^0$ based on the chiral unitary
model that generates the X(3720) resonance, and make predictions for the $D^0
\bar D^0$ invariant mass distribution. From the shape of the distribution, the
existence of the resonance below threshold could be induced. We also predict
the rate of production of the X(3720) resonance to the $D^0 \bar D^0$ mass
distribution with no free parameters.
| arxiv topic:hep-ph nucl-th |
arxiv_dataset-68681512.04148 | ALMA Observation of the 658 GHz Vibrationally Excited H$_{2}$O Maser in
Orion KL Source I
astro-ph.SR
We present an observational study of the vibrationally excited H$_{2}$O line
at 658 GHz ($\nu_{2}$=1, 1$_{1, 0}$-1$_{0, 1}$) toward Orion KL using the
Atacama Large Millimeter/Submillimeter Array (ALMA). This line is clearly
detected at the position of the massive protostar candidate, the Source I. The
spatial structure is compact with a size of about 100 AU and is elongated along
the northeast-southwest low-velocity (18 km s$^{-1}$) bipolar outflow traced by
22 GHz H$_{2}$O masers, SiO masers, and thermal SiO lines. A velocity gradient
can be seen perpendicular to the bipolar outflow. Overall spatial and velocity
structure seems analogous to that of the 321 GHz H$_{2}$O maser line previously
detected with ALMA and vibrationally excited SiO maser emission. The brightness
temperature of the 658 GHz H$_{2}$O line is estimated to be higher than
2$\times$10$^{4}$ K, implying that it is emitted via maser action. Our results
suggest that the 658 GHz H$_{2}$O maser line is emitted from the base of the
outflow from a rotating and expanding accretion disk as observed for the SiO
masers and the 321 GHz H$_{2}$O maser. We also search for two other H$_{2}$O
lines at 646 GHz (9$_{7, 3}$-8$_{8, 0}$ and 9$_{7, 2}$-8$_{8, 1}$), but they
are not detected in Orion KL.
| arxiv topic:astro-ph.SR |
arxiv_dataset-68691512.04248 | Non-compact Newton boundary and Whitney equisingularity for non-isolated
singularities
math.AG
In an unpublished lecture note, J. Brian\c{c}on observed that if $\{f_t\}$ is
a family of isolated complex hypersurface singularities such that the Newton
boundary of $f_t$ is independent of $t$ and $f_t$ is non-degenerate, then the
corresponding family of hypersurfaces $\{f_t^{-1}(0)\}$ is Whitney equisingular
(and hence topologically equisingular). A first generalization of this
assertion to families with non-isolated singularities was given by the second
author under a rather technical condition. In the present paper, we give a new
generalization under a simpler condition.
| arxiv topic:math.AG |
arxiv_dataset-68701512.04348 | Automated Model Generation for Analysis of Large-scale Interconnected
Uncertain Systems
math.OC
The first challenge in robustness analysis of large-scale interconnected
uncertain systems is to provide a model of such systems in a standard-form that
is required within different analysis frameworks. This becomes particularly
important for large-scale systems, as analysis tools that can handle such
systems heavily rely on the special structure within such model descriptions.
We here propose an automated framework for providing such models of large-scale
interconnected uncertain systems that are used in Integral Quadratic Constraint
(IQC) analysis. Specifically, in this paper we put forth a methodological way
to provide such models from a block-diagram and nested description of
interconnected uncertain systems. We describe the details of this automated
framework using an example.
| arxiv topic:math.OC |
arxiv_dataset-68711512.04448 | Magnetic critical properties and basal-plane anisotropy of Sr$_2$IrO$_4$
cond-mat.str-el
The anisotropic magnetic properties of Sr$_2$IrO$_4$ are investigated, using
longitudinal and torque magnetometry. The critical scaling across $T_c$ of the
longitudinal magnetization is the one expected for the 2D XY universality
class. Modeling the torque for a magnetic field in the basal-plane, and taking
into account all in-plane and out-of-plane magnetic couplings, we derive the
effective 4-fold anisotropy $K_4 \approx$ 1 10$^5$ erg mole$^{-1}$. Although
larger than for the cuprates, it is found too small to account for a
significant departure from the isotropic 2D XY model. The in-plane torque also
allows us to put an upper bound for the anisotropy of a field-induced shift of
the antiferromagnetic ordering temperature.
| arxiv topic:cond-mat.str-el |
arxiv_dataset-68721512.04548 | Properties of Resonantly Produced Sterile Neutrino Dark Matter Subhalos
astro-ph.CO
The anomalous 3.55 keV X-ray line recently detected towards a number of
massive dark matter objects may be interpreted as the radiative decays of 7.1
keV mass sterile neutrino dark matter. Depending on its parameters, the sterile
neutrino can range from cold to warm dark matter with small-scale suppression
that differs in form from commonly-adopted thermal warm dark matter. Here, we
numerically investigate the subhalo properties for 7.1 keV sterile neutrino
dark matter produced via the resonant Shi-Fuller mechanism. Using accurate
matter power spectra, we run cosmological zoom-in simulations of a Milky
Way-sized halo and explore the abundance of massive subhalos, their radial
distributions, and their internal structure. We also simulate the halo with
thermal 2.0 keV warm dark matter for comparison and discuss quantitative
differences. We find that the resonantly produced sterile neutrino model for
the 3.55 keV line provides a good description of structures in the Local Group,
including the number of satellite dwarf galaxies and their radial distribution,
and largely mitigates the too-big-to-fail problem. Future searches for
satellite galaxies by deep surveys, such as the Dark Energy Survey, Large
Synoptic Survey Telescope, and Wide Field Infrared Survey Telescope, will be a
strong direct test of warm dark matter scenarios.
| arxiv topic:astro-ph.CO |
arxiv_dataset-68731512.04648 | Admissible colourings of 3-manifold triangulations for Turaev-Viro type
invariants
cs.CG math.CO math.GT
Turaev Viro invariants are amongst the most powerful tools to distinguish
3-manifolds: They are implemented in mathematical software, and allow practical
computations. The invariants can be computed purely combinatorially by
enumerating colourings on the edges of a triangulation T.
These edge colourings can be interpreted as embeddings of surfaces in T. We
give a characterisation of how these embedded surfaces intersect with the
tetrahedra of T. This is done by characterising isotopy classes of simple
closed loops in the 3-punctured disk. As a direct result we obtain a new system
of coordinates for edge colourings which allows for simpler definitions of the
tetrahedron weights incorporated in the Turaev-Viro invariants.
Moreover, building on a detailed analysis of the colourings, as well as
classical work due to Kirby and Melvin, Matveev, and others, we show that
considering a much smaller set of colourings suffices to compute Turaev-Viro
invariants in certain significant cases. This results in a substantial
improvement of running times to compute the invariants, reducing the number of
colourings to consider by a factor of $2^n$. In addition, we present an
algorithm to compute Turaev-Viro invariants of degree four -- a problem known
to be #P-hard -- which capitalises on the combinatorial structure of the input.
The improved algorithms are shown to be optimal in the following sense: There
exist triangulations admitting all colourings the algorithms consider.
Furthermore, we demonstrate that our new algorithms to compute Turaev-Viro
invariants are able to distinguish the majority of $\mathbb{Z}$-homology
spheres with complexity up to $11$ in $O(2^n)$ operations in $\mathbb{Q}$.
| arxiv topic:cs.CG math.CO math.GT |
arxiv_dataset-68741512.04748 | Cubic Graphs with Total Domatic Number at Least Two
math.CO cs.DM
Let $G$ be a graph. A total dominating set of $G$ is a set $S$ of vertices of
$G$ such that every vertex is adjacent to at least one vertex in $S$. The total
domatic number of a graph is the maximum number of total dominating sets which
partition the vertex set of $G$. In this paper we would like to characterize
the cubic graphs with total domatic number at least two.
| arxiv topic:math.CO cs.DM |
arxiv_dataset-68751512.04848 | Data Driven Resource Allocation for Distributed Learning
cs.LG cs.DS stat.ML
In distributed machine learning, data is dispatched to multiple machines for
processing. Motivated by the fact that similar data points often belong to the
same or similar classes, and more generally, classification rules of high
accuracy tend to be "locally simple but globally complex" (Vapnik & Bottou
1993), we propose data dependent dispatching that takes advantage of such
structure. We present an in-depth analysis of this model, providing new
algorithms with provable worst-case guarantees, analysis proving existing
scalable heuristics perform well in natural non worst-case conditions, and
techniques for extending a dispatching rule from a small sample to the entire
distribution. We overcome novel technical challenges to satisfy important
conditions for accurate distributed learning, including fault tolerance and
balancedness. We empirically compare our approach with baselines based on
random partitioning, balanced partition trees, and locality sensitive hashing,
showing that we achieve significantly higher accuracy on both synthetic and
real world image and advertising datasets. We also demonstrate that our
technique strongly scales with the available computing power.
| arxiv topic:cs.LG cs.DS stat.ML |
arxiv_dataset-68761512.04948 | APOGEE Kinematics I: Overview of the Kinematics of the Galactic Bulge as
Mapped by APOGEE
astro-ph.GA
We present the stellar kinematics across the Galactic bulge and into the disk
at positive longitudes from the SDSS-III APOGEE spectroscopic survey of the
Milky Way. APOGEE includes extensive coverage of the stellar populations of the
bulge along the mid-plane and near-plane regions. From these data, we have
produced kinematic maps of 10,000 stars across longitudes 0 deg < l < 65 deg,
and primarily across latitudes of |b| < 5 deg in the bulge region. The APOGEE
data reveal that the bulge is cylindrically rotating across all latitudes and
is kinematically hottest at the very centre of the bulge, with the smallest
gradients in both kinematic and chemical space inside the inner-most region
(l,|b|) < (5,5) deg. The results from APOGEE show good agreement with data from
other surveys at higher latitudes and a remarkable similarity to the rotation
and dispersion maps of barred galaxies viewed edge on. The thin bar that is
reported to be present in the inner disk within a narrow latitude range of |b|
< 2 deg appears to have a corresponding signature in [Fe/H] and [alpha/Fe].
Stars with [Fe/H] > -0.5 have dispersion and rotation profiles that are similar
to that of N-body models of boxy/peanut bulges. There is a smooth kinematic
transition from the thin bar and boxy bulge (l,|b|) < (15,12) deg out into the
disk for stars with [Fe/H] > -1.0, and the chemodynamics across (l,b) suggests
the stars in the inner Galaxy with [Fe/H] > -1.0 have an origin in the disk.
| arxiv topic:astro-ph.GA |
arxiv_dataset-68771512.05048 | Graph-theoretic strengths of contextuality
quant-ph
Cabello-Severini-Winter and Abramsky-Hardy (building on the framework of
Abramsky-Brandenburger) both provide classes of Bell and contextuality
inequalities for very general experimental scenarios using vastly different
mathematical techniques. We review both approaches, carefully detail the links
between them, and give simple, graph-theoretic methods for finding
inequality-free proofs of nonlocality and contextuality and for finding states
exhibiting strong nonlocality and/or contextuality. Finally, we apply these
methods to concrete examples in stabilizer quantum mechanics relevant to
understanding contextuality as a resource in quantum computation.
| arxiv topic:quant-ph |
arxiv_dataset-68781512.05148 | Can photonic crystals be homogenized in higher bands?
physics.optics
We consider conditions under which photonic crystals (PCs) can be homogenized
in the higher photonic bands and, in particular, near the $\Gamma$-point. By
homogenization we mean introducing some effective local parameters
$\epsilon_{\rm eff}$ and $\mu_{\rm eff}$ that describe reflection, refraction
and propagation of electromagnetic waves in the PC adequately. The parameters
$\epsilon_{\rm eff}$ and $\mu_{\rm eff}$ can be associated with a hypothetical
homogeneous effective medium. In particular, if the PC is homogenizable, the
dispersion relations and isofrequency lines in the effective medium and in the
PC should coincide to some level of approximation. We can view this requirement
as a necessary condition of homogenizability. In the vicinity of a
$\Gamma$-point, real isofrequency lines of two-dimensional PCs can be close to
mathematical circles, just like in the case of isotropic homogeneous materials.
Thus, one may be tempted to conclude that introduction of an effective medium
is possible and, at least, the necessary condition of homogenizability holds in
this case. We, however, show that this conclusion is incorrect: complex
dispersion points must be included into consideration even in the case of
strictly non-absorbing materials. By analyzing the complex dispersion relations
and the corresponding isofrequency lines, we have found that two-dimensional
PCs with $C_4$ and $C_6$ symmetries are not homogenizable in the higher
photonic bands. We also draw a distinction between spurious $\Gamma$-point
frequencies that are due to Brillouin-zone folding of Bloch bands and "true"
$\Gamma$-point frequencies that are due to multiple scattering. Understanding
of the physically different phenomena that lead to the appearance of spurious
and "true" $\Gamma$-point frequencies is important for the theory of
homogenization.
| arxiv topic:physics.optics |
arxiv_dataset-68791512.05248 | A practical theorem on using interferometry to measure the global 21-cm
signal
astro-ph.IM astro-ph.CO
The sky-averaged, or global, background of redshifted $21$ cm radiation is
expected to be a rich source of information on cosmological reheating and
reionizaton. However, measuring the signal is technically challenging: one must
extract a small, frequency-dependent signal from under much brighter spectrally
smooth foregrounds. Traditional approaches to study the global signal have used
single antennas, which require one to calibrate out the frequency-dependent
structure in the overall system gain (due to internal reflections, for example)
as well as remove the noise bias from auto-correlating a single amplifier
output. This has motivated proposals to measure the signal using
cross-correlations in interferometric setups, where additional calibration
techniques are available. In this paper we focus on the general principles
driving the sensitivity of the interferometric setups to the global signal. We
prove that this sensitivity is directly related to two characteristics of the
setup: the cross-talk between readout channels (i.e. the signal picked up at
one antenna when the other one is driven) and the correlated noise due to
thermal fluctuations of lossy elements (e.g. absorbers or the ground) radiating
into both channels. Thus in an interferometric setup, one cannot suppress
cross-talk and correlated thermal noise without reducing sensitivity to the
global signal by the same factor -- instead, the challenge is to characterize
these effects and their frequency dependence. We illustrate our general theorem
by explicit calculations within toy setups consisting of two short dipole
antennas in free space and above a perfectly reflecting ground surface, as well
as two well-separated identical lossless antennas arranged to achieve zero
cross-talk.
| arxiv topic:astro-ph.IM astro-ph.CO |
arxiv_dataset-68801512.05348 | The Effelsberg-Bonn HI Survey: Milky Way gas. First data release
astro-ph.IM astro-ph.GA
The Effelsberg-Bonn HI Survey (EBHIS) is a new 21-cm survey performed with
the 100-m telescope at Effelsberg. It covers the whole northern sky out to a
redshift of z~0.07 and comprises HI line emission from the Milky Way and the
Local Volume. We aim to substitute the northern-hemisphere part of the
Leiden/Argentine/Bonn Milky Way HI survey (LAB) with this first EBHIS data
release, which presents the HI gas in the Milky Way regime. The use of a
seven-beam L-band array made it feasible to perform this all-sky survey with a
100-m class telescope in a reasonable amount of observing time.
State-of-the-art fast-Fourier-transform spectrometers provide the necessary
data read-out speed, dynamic range, and spectral resolution to apply software
radio-frequency interference mitigation. EBHIS is corrected for stray radiation
and employs frequency-dependent flux-density calibration and sophisticated
baseline-removal techniques to ensure the highest possible data quality.
Detailed analyses of the resulting data products show that EBHIS is not only
outperforming LAB in terms of sensitivity and angular resolution, but also
matches the intensity-scale of LAB extremely well, allowing EBHIS to be used as
a drop-in replacement for LAB. Data products are made available to the public
in a variety of forms. Most important, we provide a properly gridded Milky Way
HI column density map in HEALPix representation. To maximize the usefulness of
EBHIS data, we estimate uncertainties in the HI column density and brightness
temperature distributions, accounting for systematic effects.
| arxiv topic:astro-ph.IM astro-ph.GA |
arxiv_dataset-68811512.05448 | ADMM for the SDP relaxation of the QAP
math.OC cs.DS math.CO
The semidefinite programming (SDP) relaxation has proven to be extremely
strong for many hard discrete optimization problems. This is in particular true
for the quadratic assignment problem (QAP), arguably one of the hardest NP-hard
discrete optimization problems. There are several difficulties that arise in
efficiently solving the SDP relaxation, e.g.,~increased dimension; inefficiency
of the current primal-dual interior point solvers in terms of both time and
accuracy; and difficulty and high expense in adding cutting plane constraints.
We propose using the alternating direction method of multipliers (ADMM) to
solve the SDP relaxation. This first order approach allows for inexpensive
iterations, a method of cheaply obtaining low rank solutions, as well a trivial
way of adding cutting plane inequalities. When compared to current approaches
and current best available bounds we obtain remarkable robustness, efficiency
and improved bounds.
| arxiv topic:math.OC cs.DS math.CO |
arxiv_dataset-68821512.05548 | Semi-doubled Sigma Models for Five-branes
hep-th
We study two-dimensional ${\cal N}=(2,2)$ gauge theory and its dualized
system in terms of complex (linear) superfields and their alternatives.
Although this technique itself is not new, we can obtain a new model, the
so-called "semi-doubled" GLSM. Similar to doubled sigma model, this involves
both the original and dual degrees of freedom simultaneously, whilst the latter
only contribute to the system via topological interactions. Applying this to
the ${\cal N}=(4,4)$ GLSM for H-monopoles, i.e., smeared NS5-branes, we obtain
its T-dualized systems in quite an easy way. As a bonus, we also obtain the
semi-doubled GLSM for an exotic $5^3_2$-brane whose background is locally
nongeometric. In the low energy limit, we construct the semi-doubled NLSM which
also generates the conventional string worldsheet sigma models. In the case of
the NLSM for $5^3_2$-brane, however, we find that the Dirac monopole equation
does not make sense any more because the physical information is absorbed into
the divergent part via the smearing procedure. This is nothing but the signal
which indicates that the nongeometric feature emerges in the considering model.
| arxiv topic:hep-th |
arxiv_dataset-68831512.05648 | Curves in $\mathbb{R}^4$ and two-rich points
math.CO cs.CG
We obtain a new bound on the number of two-rich points spanned by an
arrangement of low degree algebraic curves in $\mathbb{R}^4$. Specifically, we
show that an arrangement of $n$ algebraic curves determines at most $C_\epsilon
n^{4/3+3\epsilon}$ two-rich points, provided at most $n^{2/3+2\epsilon}$ curves
lie in any low degree hypersurface and at most $n^{1/3+\epsilon}$ curves lie in
any low degree surface. This result follows from a structure theorem about
arrangements of curves that determine many two-rich points.
| arxiv topic:math.CO cs.CG |
arxiv_dataset-68841512.05748 | Measurement of nuclear effects in neutrino interactions with minimal
dependence on neutrino energy
nucl-th hep-ex hep-ph nucl-ex
We present a phenomenological study of nuclear effects in neutrino
charged-current interactions, using transverse kinematic imbalances in
exclusive measurements. Novel observables with minimal dependence on neutrino
energy are proposed to study quasielastic scattering, and especially resonance
production. They should be able to provide direct constraints on nuclear
effects in neutrino- and antineutrino-nucleus interactions.
| arxiv topic:nucl-th hep-ex hep-ph nucl-ex |
arxiv_dataset-68851512.05848 | Shrinking Targets for Semisimple Groups
math.DS math.NT
We study the shrinking target problem for actions of semisimple groups on
homogeneous spaces, with applications to logarithm laws and Diophantine
approximation.
| arxiv topic:math.DS math.NT |
arxiv_dataset-68861512.05948 | Algorithmic aspects of branched coverings
cs.CC math.DS math.GR
This is the announcement, and the long summary, of a series of articles on
the algorithmic study of Thurston maps. We describe branched coverings of the
sphere in terms of group-theoretical objects called bisets, and develop a
theory of decompositions of bisets.
We introduce a canonical "Levy" decomposition of an arbitrary Thurston map
into homeomorphisms, metrically-expanding maps and maps doubly covered by torus
endomorphisms. The homeomorphisms decompose themselves into finite-order and
pseudo-Anosov maps, and the expanding maps decompose themselves into rational
maps.
As an outcome, we prove that it is decidable when two Thurston maps are
equivalent. We also show that the decompositions above are computable, both in
theory and in practice.
| arxiv topic:cs.CC math.DS math.GR |
arxiv_dataset-68871512.06048 | Cardy-Verlinde entropy in Ho\v{r}ava-Lifshitz gravity
gr-qc
We investigate homogeneous cosmological models with perfect-fluid sources in
the framework of the Ho\v rava-Lifshitz model for quantum gravity. We show that
the Hamiltonian constraint of such spacetimes can be rewritten as the Cardy
formula for the entropy in conformal field theory. The Cardy entropy is shown
to depend explicitly on the value of the Ho\v rava parameter $\lambda$ so that
it can be interpreted as determining the entropy and the gravitational
interaction of the theory. Moreover, we show that Verlinde's Pythagorean
representation of the Hamiltonian constraint is also valid in the case of
homogeneous Ho\v rava-Lifshitz spacetimes. We interpret these results as a
further indication of a deep relationship between gravity, thermodynamics and
holography in the quantum regime.
| arxiv topic:gr-qc |
arxiv_dataset-68881512.06148 | Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino
Experiment (DUNE) Conceptual Design Report Volume 2: The Physics Program for
DUNE at LBNF
physics.ins-det hep-ex
The Physics Program for the Deep Underground Neutrino Experiment (DUNE) at
the Fermilab Long-Baseline Neutrino Facility (LBNF) is described.
| arxiv topic:physics.ins-det hep-ex |
arxiv_dataset-68891512.06248 | Spatially Periodic Cells Are Neither Formed From Grids Nor Poor
Isolation
q-bio.NC
Grid cells recorded in the parahippocampal formation of freely moving rodents
provide a strikingly periodic representation of self-location whose underlying
mechanism has been the subject of intense interest. Our previous work(1) showed
that grid cells represent the most stable subset of a larger continuum of
spatially periodic cells (SPCs) which deviate from the hexagonal symmetry
observed in grid cells. Recently Navratilova et al(2) suggested that our
findings reflected poor isolation of the spikes from multiple grid cells,
rather than the existence of actual non-grid SPCs. Here we refute this
suggestion by showing that: (i) most SPCs cannot be formed from hexagonal
grids; (ii) all standard cluster isolation measures are similar between
recorded grid cells and non-grid SPCs, and are comparable to those reported in
other laboratories; (iii) the spikes from different fields of band-like SPCs do
not differ. Thus the theoretical implications of the presence of cells with
spatially periodic firing patterns that diverge from perfect hexagonality need
to be taken seriously, rather than explained away on the basis of hopeful but
unjustified assumptions.
| arxiv topic:q-bio.NC |
arxiv_dataset-68901512.06348 | Link prediction based on path entropy
physics.soc-ph cs.SI physics.data-an
Information theory has been taken as a prospective tool for quantifying the
complexity of complex networks. In this paper, we first study the information
entropy or uncertainty of a path using the information theory. Then we apply
the path entropy to the link prediction problem in real-world networks.
Specifically, we propose a new similarity index, namely Path Entropy (PE)
index, which considers the information entropies of shortest paths between node
pairs with penalization to long paths. Empirical experiments demonstrate that
PE index outperforms the mainstream link predictors.
| arxiv topic:physics.soc-ph cs.SI physics.data-an |
arxiv_dataset-68911512.06448 | SourcererCC: Scaling Code Clone Detection to Big Code
cs.SE
Despite a decade of active research, there is a marked lack in clone
detectors that scale to very large repositories of source code, in particular
for detecting near-miss clones where significant editing activities may take
place in the cloned code. We present SourcererCC, a token-based clone detector
that targets three clone types, and exploits an index to achieve scalability to
large inter-project repositories using a standard workstation. SourcererCC uses
an optimized inverted-index to quickly query the potential clones of a given
code block. Filtering heuristics based on token ordering are used to
significantly reduce the size of the index, the number of code-block
comparisons needed to detect the clones, as well as the number of required
token-comparisons needed to judge a potential clone.
We evaluate the scalability, execution time, recall and precision of
SourcererCC, and compare it to four publicly available and state-of-the-art
tools. To measure recall, we use two recent benchmarks, (1) a large benchmark
of real clones, BigCloneBench, and (2) a Mutation/Injection-based framework of
thousands of fine-grained artificial clones. We find SourcererCC has both high
recall and precision, and is able to scale to a large inter-project repository
(250MLOC) using a standard workstation.
| arxiv topic:cs.SE |
arxiv_dataset-68921512.06548 | Interferometric radio transient reconstruction in compressed sensing
framework
astro-ph.IM
Imaging by aperture synthesis from interferometric data is a well-known, but
is a strong ill-posed inverse problem. Strong and faint radio sources can be
imaged unambiguously using time and frequency integration to gather more
Fourier samples of the sky. However, these imagers assumes a steady sky and the
complexity of the problem increases when transients radio sources are also
present in the data. Hopefully, in the context of transient imaging, the
spatial and temporal information are separable which enable extension of an
imager fit for a steady sky. We introduce independent spatial and temporal
wavelet dictionaries to sparsely represent the transient in both spatial domain
and temporal domain. These dictionaries intervenes in a new reconstruction
method developed in the Compressed Sensing (CS) framework and using a
primal-dual splitting algorithm. According to the preliminary tests in
different noise regimes, this new "Time-agile" (or 2D-1D) method seems to be
efficient in detecting and reconstructing the transients temporal dependence.
| arxiv topic:astro-ph.IM |
arxiv_dataset-68931512.06648 | Generating functions for K-theoretic Donaldson invariants and Le
Potier's strange duality
math.AG
K-theoretic Donaldson invariants are holomorphic Euler characteristics of
determinant line bundles on moduli spaces of sheaves on surfaces. We compute
generating functions of K-theoretic Donaldson invariants on the projective
plane and rational ruled surfaces. We apply this result to prove some cases of
Le Potier's strange duality.
| arxiv topic:math.AG |
arxiv_dataset-68941512.06748 | Imaging Prominence Eruptions Out to 1 AU
astro-ph.SR physics.space-ph
Views of two bright prominence eruptions trackable all the way to 1AU are
here presented, using the heliospheric imagers on the Solar TErrestrial
RElations Observatory (STEREO) spacecraft. The two events first erupted from
the Sun on 2011 June 7 and 2012 August 31, respectively. Only these two
examples of clear prominence eruptions observable this far from the Sun could
be found in the STEREO image database, emphasizing the rarity of prominence
eruptions this persistently bright. For the 2011 June event, a time-dependent
3-D reconstruction of the prominence structure is made using point-by-point
triangulation. This is not possible for the August event due to a poor viewing
geometry. Unlike the coronal mass ejection (CME) that accompanies it, the 2011
June prominence exhibits little deceleration from the Sun to 1 AU, as a
consequence moving upwards within the CME. This demonstrates that prominences
are not necessarily tied to the CME's magnetic structure far from the Sun. A
mathematical framework is developed for describing the degree of
self-similarity for the prominence's expansion away from the Sun. This analysis
suggests only modest deviations from self-similar expansion, but close to the
Sun the prominence expands radially somewhat more rapidly than self-similarity
would predict.
| arxiv topic:astro-ph.SR physics.space-ph |
arxiv_dataset-68951512.06848 | Euler characteristics of Hilbert schemes of points on simple surface
singularities
math.AG math.CO math.RT
We study the geometry and topology of Hilbert schemes of points on the
orbifold surface [C^2/G], respectively the singular quotient surface C^2/G,
where G is a finite subgroup of SL(2,C) of type A or D. We give a decomposition
of the (equivariant) Hilbert scheme of the orbifold into affine space strata
indexed by a certain combinatorial set, the set of Young walls. The generating
series of Euler characteristics of Hilbert schemes of points of the singular
surface of type A or D is computed in terms of an explicit formula involving a
specialized character of the basic representation of the corresponding affine
Lie algebra; we conjecture that the same result holds also in type E. Our
results are consistent with known results in type A, and are new for type D.
| arxiv topic:math.AG math.CO math.RT |
arxiv_dataset-68961512.06948 | Scaling theory for anomalous semiclassical quantum transport
cond-mat.mes-hall nlin.CD
Quantum transport through devices coupled to electron reservoirs can be
described in terms of the full counting statistics (FCS) of charge transfer.
Transport observables, such as conductance and shot-noise power are just
cumulants of FCS and can be obtained from the sample's average density of
transmission eigenvalues, which in turn can be obtained from a finite element
representation of the saddle-point equation of the Keldysh (or supersymmetric)
non-linear sigma-model, known as quantum circuit theory. Normal universal
metallic behavior in the semiclassical regime is controlled by the presence of
a Fabry-Perot singularity in the average density of transmission eigenvalues.
We present general conditions for the suppression of Fabry-Perot modes in the
semiclassical regime in a sample of arbitrary shape, a disordered conductor or
a network of ballistic quantum dots, which leads to an anomalous metallic
phase. Through a double-scaling limit, we derive a scaling equation for
anomalous metallic transport, in the form of a nonlinear differential equation,
which generalizes the ballistic-diffusive scaling equation of a normal metal.
The two-parameter stationary solution of our scaling equation generalizes
Dorokhov's universal single-parameter distribution of transmission eigenvalues.
We provide a simple interpretation of the stationary solution using a
thermodynamic analogy with a spin-glass system. As an application, we consider
a system formed by a diffusive wire coupled via a barrier to
normal-superconductor (NS) reservoirs. We observe anomalous reflectionless
tunneling, when all perfectly transmitting channels are suppressed, which
cannot be explained by the usual mechanism of disorder-induced opening of
tunneling channels.
| arxiv topic:cond-mat.mes-hall nlin.CD |
arxiv_dataset-68971512.07048 | Beauty and Brains: Detecting Anomalous Pattern Co-Occurrences
cs.AI
Our world is filled with both beautiful and brainy people, but how often does
a Nobel Prize winner also wins a beauty pageant? Let us assume that someone who
is both very beautiful and very smart is more rare than what we would expect
from the combination of the number of beautiful and brainy people. Of course
there will still always be some individuals that defy this stereotype; these
beautiful brainy people are exactly the class of anomaly we focus on in this
paper. They do not posses intrinsically rare qualities, it is the unexpected
combination of factors that makes them stand out.
In this paper we define the above described class of anomaly and propose a
method to quickly identify them in transaction data. Further, as we take a
pattern set based approach, our method readily explains why a transaction is
anomalous. The effectiveness of our method is thoroughly verified with a wide
range of experiments on both real world and synthetic data.
| arxiv topic:cs.AI |
arxiv_dataset-68981512.07148 | Spontaneous symmetry breaking and phase coherence of a photon
Bose-Einstein condensate coupled to a reservoir
cond-mat.quant-gas
We examine the phase evolution of a Bose-Einstein condensate of photons
generated in a dye microcavity by temporal interference with a phase reference.
The photo-excitable dye molecules constitute a reservoir of variable size for
the condensate particles, allowing for grand canonical statistics with photon
bunching, as in a lamp-type source. We directly observe phase jumps of the
condensate associated with the large statistical number fluctuations and find a
separation of correlation timescales. For large systems, our data reveals phase
coherence and a spontaneously broken symmetry, despite the statistical
fluctuations.
| arxiv topic:cond-mat.quant-gas |
arxiv_dataset-68991512.07248 | A Sharp Condition for Exact Support Recovery of with Orthogonal Matching
Pursuit
cs.IT math.IT
Support recovery of sparse signals from noisy measurements with orthogonal
matching pursuit (OMP) has been extensively studied. In this paper, we show
that for any $K$-sparse signal $\x$, if a sensing matrix $\A$ satisfies the
restricted isometry property (RIP) with restricted isometry constant (RIC)
$\delta_{K+1} < 1/\sqrt {K+1}$, then under some constraints on the minimum
magnitude of nonzero elements of $\x$, OMP exactly recovers the support of $\x$
from its measurements $\y=\A\x+\v$ in $K$ iterations, where $\v$ is a noise
vector that is $\ell_2$ or $\ell_{\infty}$ bounded. This sufficient condition
is sharp in terms of $\delta_{K+1}$ since for any given positive integer $K$
and any $1/\sqrt{K+1}\leq \delta<1$, there always exists a matrix $\A$
satisfying the RIP with $\delta_{K+1}=\delta$ for which OMP fails to recover a
$K$-sparse signal $\x$ in $K$ iterations. Also, our constraints on the minimum
magnitude of nonzero elements of $\x$ are weaker than existing ones. Moreover,
we propose worst-case necessary conditions for the exact support recovery of
$\x$, characterized by the minimum magnitude of the nonzero elements of $\x$.
| arxiv topic:cs.IT math.IT |
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