  In order to have a better understanding of ultrafast electrical control of
exchange interactions in multi-orbital systems, we study a two-orbital Hubbard
model at half filling under the action of a time-periodic electric field. Using
suitable projection operators and a generalized time-dependent canonical
transformation, we derive an effective Hamiltonian which describes two
different regimes. First, for a wide range of non-resonant frequencies, we find
a change of the bilinear Heisenberg exchange $J_{\textrm{ex}}$ that is
analogous to the single-orbital case. Moreover we demonstrate that also the
additional biquadratic exchange interaction $B_{\textrm{ex}}$ can be enhanced,
reduced and even change sign depending on the electric field. Second, for
special driving frequencies, we demonstrate a novel spin-charge coupling
phenomenon enabling coherent transfer between spin and charge degrees of
freedom of doubly ionized states. These results are confirmed by an exact
time-evolution of the full two-orbital Mott-Hubbard Hamiltonian.


  In theory, the Lanczos algorithm generates an orthogonal basis of the
corresponding Krylov subspace. However, in finite precision arithmetic, the
orthogonality and linear independence of the computed Lanczos vectors is
usually lost quickly. In this paper we study a class of matrices and starting
vectors having a special nonzero structure that guarantees exact computations
of the Lanczos algorithm whenever floating point arithmetic satisfying the IEEE
754 standard is used. Analogous results are formulated also for a variant of
the conjugate gradient method that produces then almost exact results. The
results are extended to the Arnoldi algorithm, the nonsymmetric Lanczos
algorithm, the Golub-Kahan bidiagonalization, the block-Lanczos algorithm and
their counterparts for solving linear systems.


  Extrasolar planets are expected to emit detectable low frequency radio
emission. In this paper we present results from new low frequency observations
of two extrasolar planetary systems (Epsilon Eridani and HD 128311) taken at
150 MHz with the Giant Metrewave Radio Telescope (GMRT). These two systems have
been chosen because the stars are young (with ages < 1 Gyr) and are likely to
have strong stellar winds, which will increase the expected radio flux. The
planets are massive (presumably) gas giant planets in longer period orbits, and
hence will not be tidally locked to their host star (as is likely to be the
case for short period planets) and we would expect them to have a strong
planetary dynamo and magnetic field. We do not detect either system, but are
able to place tight upper limits on their low frequency radio emission, at
levels comparable to the theoretical predictions for these systems. From these
observations we have a 2.5sigma limit of 7.8 mJy for Epsilon Eri and 15.5 mJy
for HD 128311. In addition, these upper limits also provide limits on the low
frequency radio emission from the stars themselves. These results are discussed
and also the prospects for the future detection of radio emission from
extrasolar planets.


  We provide a combinatorial study of split matroids, a class that was
motivated by the study of matroid polytopes from a tropical geometry point of
view. A nice feature of split matroids is that they generalize paving matroids,
while being closed under duality and taking minors. Furthermore, these matroids
proved to be useful in giving exact asymptotic bounds for the dimension of the
Dressian, and also implied new results on the rays of the tropical
Grassmannians.
  In the present paper, we introduce the notion of elementary split matroids, a
subclass of split matroids that contains all connected split matroids. We give
a hypergraph characterization of elementary split matroids in terms of
independent sets, and show that the proposed class is closed not only under
duality and taking minors but also truncation. We further show that, in
contrast to split matroids, the proposed class can be characterized by a single
forbidden minor. As an application, we provide a complete list of binary split
matroids.


  We show that some $q$-series such as universal mock theta functions are
linear sums of theta quotients and mock Jacobi forms of weight 1/2, which
become holomorphic parts of real analytic modular forms when they are
restricted to torsion points and multiplied by suitable powers of $q$. And we
prove that certain linear sums of $q$-series are weakly holomorphic modular
forms of weight 1/2 due to annihilation of mock Jacobi forms or completion by
mock Jacobi forms. As an application, we obtain a relation between the rank and
crank of a partition.


  4-dimensional optics is here introduced axiomatically as the space that
supports a Universal wave equation which is applied to the postulated Higgs
field. Self-guiding of this field is shown to produce all the modes necessary
to provide explanations for the known elementary particles. Forces are shown to
appear as evanescent fields due to waveguiding of the Higgs field, which
provide coupling between waveguides corresponding to different particles.
Carrier particles are also discussed and shown to correspond to waveguided
modes existing in 3-dimensional space.


  Integrating smart algorithms on neural devices presents significant
opportunities for various brain disorders. In this paper, we review the latest
advancements in the development of three categories of intelligent neural
prostheses featuring embedded signal processing on the implantable or wearable
device. These include: 1) Neural interfaces for closed-loop symptom tracking
and responsive stimulation; 2) Neural interfaces for emerging network-related
conditions, such as psychiatric disorders; and 3) Intelligent BMI SoCs for
movement recovery following paralysis.


  We investigate the problem of sentence-level supporting argument detection
from relevant documents for user-specified claims. A dataset containing claims
and associated citation articles is collected from online debate website
idebate.org. We then manually label sentence-level supporting arguments from
the documents along with their types as study, factual, opinion, or reasoning.
We further characterize arguments of different types, and explore whether
leveraging type information can facilitate the supporting arguments detection
task. Experimental results show that LambdaMART (Burges, 2010) ranker that uses
features informed by argument types yields better performance than the same
ranker trained without type information.


  During the last three decades, many papers have reported the existence of a
luminosity-metallicity or mass-metallicity (M-Z) relation for all kinds of
galaxies: The more massive galaxies are also the ones with more metal-rich
interstellar medium. We have obtained the mass-metallicity relation at
different lookback times for the same set of galaxies from the Sloan Digital
Sky Survey (SDSS), using the stellar metallicities estimated with our spectral
synthesis code STARLIGHT. Using stellar metallicities has several advantages:
We are free of the biases that affect the calibration of nebular metallicities;
we can include in our study objects for which the nebular metallicity cannot be
measured, such as AGN hosts and passive galaxies; we can probe metallicities at
different epochs of a galaxy evolution.
  We have found that the M-Z relation steepens and spans a wider range in both
mass and metallicity at higher redshifts for SDSS galaxies. We also have
modeled the time evolution of stellar metallicity with a closed-box chemical
evolution model, for galaxies of different types and masses. Our results
suggest that the M-Z relation for galaxies with present-day stellar masses down
to 10^10 solar masses is mainly driven by the star formation history and not by
inflows or outflows.


  We demonstrate direct evidence of possible surface superconductivity on
small, well-shaped MgB2 single crystals. Transport measurements in the range H
< 1.6 Hc2^c, where Hc2^c is the bulk upper critical field for the c axis, show
non-Ohmic and strongly angular dependent resistivity. Studies of the alignment
of H with selected crystal surfaces, transport and specific heat measurements
on the same crystal, and a physical sculpturing of the crystal surfaces using a
focused ion beam all support the conclusion. Similar, albeit less pronounced
results are obtained for fields in the basal plane.


  Non-analyticities in the logarithm of the Loschmidt echo, known as dynamical
quantum phase transitions [DQPTs], are a recently introduced attempt to
classify the myriad of possible phenomena which can occur in far from
equilibrium closed quantum systems. In this work, we analytically investigate
the Loschmidt echo in nonequilibrium $s$-wave and topological $p_x+ip_y$
fermionic superfluids. We find that the presence of non-analyticities in the
echo is not invariant under global rotations of the superfluid phase. We remedy
this deficiency by introducing a more general notion of a grand canonical
Loschmidt echo. Overall, our study shows that DQPTs are not a good indicator
for the long time dynamics of an interacting system. In particular, there are
no DQPTs to tell apart distinct dynamical phases of quenched BCS
superconductors. Nevertheless, they can signal a quench induced change in the
topology and also keep track of solitons emerging from unstable stationary
states of a BCS superconductor.


  Effectively predicting molecular interactions has the potential to accelerate
molecular dynamics by multiple orders of magnitude and thus revolutionize
chemical simulations. Graph neural networks (GNNs) have recently shown great
successes for this task, overtaking classical methods based on fixed molecular
kernels. However, they still appear very limited from a theoretical
perspective, since regular GNNs cannot distinguish certain types of graphs. In
this work we close this gap between theory and practice. We show that GNNs with
spherical representations are indeed universal approximators for predictions
that are invariant to translation, and equivariant to permutation and rotation.
We then discretize such GNNs via directed edge embeddings and two-hop message
passing, and incorporate multiple structural improvements to arrive at the
geometric message passing neural network (GemNet). We demonstrate the benefits
of the proposed changes in multiple ablation studies. GemNet outperforms
previous models on the COLL, MD17, and OC20 datasets by 34%, 41%, and 20%,
respectively, and performs especially well on the most challenging molecules.
Our implementation is available online.


  An $(r,w;d)$ cover-free family $(CFF)$ is a family of subsets of a finite set
such that the intersection of any $r$ members of the family contains at least
$d$ elements that are not in the union of any other $w$ members. The minimum
number of elements for which there exists an $(r,w;d)-CFF$ with $t$ blocks is
denoted by $N((r,w;d),t)$.
  In this paper, we show that the value of $N((r,w;d),t)$ is equal to the
$d$-biclique covering number of the bipartite graph $I_t(r,w)$ whose vertices
are all $w$- and $r$-subsets of a $t$-element set, where a $w$-subset is
adjacent to an $r$-subset if their intersection is empty. Next, we introduce
some new bounds for $N((r,w;d),t)$. For instance, we show that for $r\geq w$
and $r\geq 2$
  $$ N((r,w;1),t) \geq c{{r+w\choose w+1}+{r+w-1 \choose w+1}+ 3 {r+w-4 \choose
w-2} \over \log r} \log (t-w+1),$$ where $c$ is a constant satisfies the
well-known bound $N((r,1;1),t)\geq c\frac{r^2}{\log r}\log t$. Also, we
determine the exact value of $N((r,w;d),t)$ for some values of $d$. Finally, we
show that $N((1,1;d),4d-1)=4d-1$ whenever there exists a Hadamard matrix of
order 4d.


  Some simulations of Type Ia supernovae feature self-consistent thermonuclear
detonations. However, these detonations are not meaningful if the simulations
are not resolved, so it is important to establish the requirements for
achieving a numerically converged detonation. In this study we examine a test
detonation problem inspired by collisions of white dwarfs. This test problem
demonstrates that achieving a converged thermonuclear ignition requires spatial
resolution much finer than 1 km in the burning region. Current computational
resource constraints place this stringent resolution requirement out of reach
for multi-dimensional supernova simulations. Consequently, contemporary
simulations that self-consistently demonstrate detonations are possibly not
converged and should be treated with caution.


  We prove that the cyclic chain complex of the categorical coalgebra of
singular chains on an arbitrary topological space $X$ is naturally
quasi-isomorphic to the $S^1$-equivariant chains of the free loop space of $X$.
This statement does not require any hypotheses on $X$ or on the commutative
ring of coefficients. Along the way, we introduce a family of polytopes, coined
as Goodwillie polytopes, that controls the combinatorics behind the
relationship of the coHochschild complex of a categorical coalgebra and the
Hochschild complex of its associated differential graded category.


  Excavation of irregular rigid objects in clutter, such as fragmented rocks
and wood blocks, is very challenging due to their complex interaction dynamics
and highly variable geometries. In this paper, we adopt reinforcement learning
(RL) to tackle this challenge and learn policies to plan for a sequence of
excavation trajectories for irregular rigid objects, given point clouds of
excavation scenes. Moreover, we separately learn a compact representation of
the point cloud on geometric tasks that do not require human labeling. We show
that using the representation reduces training time for RL, while achieving
similar asymptotic performance compare to an end-to-end RL algorithm. When
using a policy trained in simulation directly on a real scene, we show that the
policy trained with the representation outperforms end-to-end RL. To our best
knowledge, this paper presents the first application of RL to plan a sequence
of excavation trajectories of irregular rigid objects in clutter.


  We report our Raman studies of a new lead-free relaxor ferroelectrics,
Ba0.85Ca0.15Ti0.9Zr0.1O3 (BCTZO). The Raman modes of BCTZO are compared with
those of BaTi0.8Zr0.2O3 (BTZO), and BaTiO3 (BTO). Also, they are compared with
the eigenmodes of BTO calculated by using an ab-initio quantum-mechanical
frozen-phonon method. The sharp mode at 321 cm-1 of BTO, reported as a coupled
mode showing an interference effect, becomes progressively broader in BTZO and
BCTZO. This behavior, together with a broadening of the 527-cm-1 mode, suggests
that the mode-coupling is weakened in BTZO and BCTZO. The structural
transitions of BCTZO were investigated as functions of pressure at pressures
below 20 GPa and of temperature at temperatures below 600 K. Three
characteristic pressure-induced transitions, on each at 2.5, 5.0, and 13.0 GPa,
were found. The transitions are suggested by the drastic changes in phonon
modes (two softening modes, one each at ~ 300 and ~ 530 cm-1) and by the
transformation of the intensity profile. A temperature-induced transition was
found at a Curie temperature of ~ 380 K, where the average structure changes
from tetragonal to cubic. It is accompanied by a softening mode at ~ 530 cm-1.
The phonon spectrum of BCTZO suggests that its local environment is close to
that of BTZO. However, the characteristic pressures of BCTZO are close to those
of BTO. The sequence of pressure-induced transitions in both BCTZO and BTZO
illustrate rich interplay between the long-range averaged structure and the
short-range local order such that four distinguishable phases are suggested:
tetragonal, locally ordered but compensated cubic, disordered cubic, and ideal
cubic. We found that the critical pressures are plausibly related to the
average crystal lattice.


  The tunneling current and shot noise of the current between two Fractional
Quantum Hall (FQH) edges in the $ \nu=12/5 $ FQH state in electronic
Mach-Zehnder interferometer are studied. It is shown that the tunneling current
and shot noise can be used to probe the existence of $k=3 $ parafermion
statistics in the $ \nu=12/5 $ FQH state. More specifically, the dependence of
the current on the Aharonov-Bohm flux in the Read-Rezayi state is asymmetric
under the change of the sign of the applied voltage. This property is absent in
the Abelian Laughlin states. Moreover the Fano factor can exceed 12.7 electron
charges in the $ \nu=12/5 $ FQH state . This number well exceeds the maximum
possible Fano factor in all Laughlin states and the $ \nu=5/2 $ Moore-Read
state which was shown previously to be $ e $ and $ 3.2 e $ respectively.


  We consider a wireless device-to-device (D2D) caching network where n nodes
are placed on a regular grid of area A(n). Each node caches L_C*F (coded) bits
from a library of size L*F bits, where L is the number of files and F is the
size of each file. Each node requests a file from the library independently
according to a popularity distribution. Under a commonly used "physical model"
and Zipf popularity distribution, we characterize the optimal per-node capacity
scaling law for extended networks (i.e., A(n). Moreover, we propose a
cache-induced hierarchical cooperation scheme and associated cache content
placement optimization algorithm to achieve the optimal per-node capacity
scaling law. When the path loss exponent \alpha<3, the optimal per-node
capacity scaling law achieved by the cache-induced hierarchical cooperation can
be significantly better than that achieved by the existing state-of-the-art
schemes. To the best of our knowledge, this is the first work that completely
characterizes the per-node capacity scaling law for wireless caching networks
under the physical model and Zipf distribution with an arbitrary skewness
parameter \tau. While scaling law analysis yields clean results, it may not
accurately reflect the throughput performance of a large network with a finite
number of nodes. Therefore, we also analyze the throughput of the proposed
cache-induced hierarchical cooperation for networks of practical size. The
analysis and simulations verify that cache-induced hierarchical cooperation can
also achieve a large throughput gain over the cache-assisted multihop scheme
for networks of practical size.


  O and early B stars are at the apex of galactic ecology, but in the Milky
Way, only a minority of them may yet have been identified. We present the
results of a pilot study to select and parametrise OB star candidates in the
Southern Galactic plane, down to a limiting magnitude of $g=20$. A 2
square-degree field capturing the Carina Arm around the young massive star
cluster, Westerlund 2, is examined. The confirmed OB stars in this cluster are
used to validate our identification method, based on selection from the $(u-g,
g-r)$ diagram for the region. Our Markov Chain Monte Carlo fitting method
combines VPHAS+ $u, g, r, i$ with published $J, H, K$ photometry in order to
derive posterior probability distributions of the stellar parameters $\log(\rm
T_{\rm eff})$ and distance modulus, together with the reddening parameters
$A_0$ and $R_V$. The stellar parameters are sufficient to confirm OB status
while the reddening parameters are determined to a precision of
$\sigma(A_0)\sim0.09$ and $\sigma(R_V)\sim0.08$. There are 489 objects that fit
well as new OB candidates, earlier than $\sim$B2. This total includes 74
probable massive O stars, 5 likely blue supergiants and 32 reddened subdwarfs.
This increases the number of previously known and candidate OB stars in the
region by nearly a factor of 10. Most of the new objects are likely to be at
distances between 3 and 6 kpc. We have confirmed the results of previous
studies that, at these longer distances, these sight lines require non-standard
reddening laws with $3.5<R_V<4$.


  We adapt Luk's analysis of the characteristic initial value problem in
General Relativity to the asymptotic characteristic problem for the conformal
Einstein field equations to demonstrate the local existence of solutions in a
neighbourhood of the set on which the data are given. In particular, we obtain
existence of solutions along a narrow rectangle along null infinity which, in
turn, corresponds to an infinite domain in the asymptotic region of the
physical spacetime. This result generalises work by K\'ann\'ar on the local
existence of solutions to the characteristic initial value problem by means of
Rendall's reduction strategy. In analysing the conformal Einstein equations we
make use of the Newman-Penrose formalism and a gauge due to J. Stewart.


  Automation in construction has the potential to expand the technological
landscape of labor intensive tasks, and bring gains in efficiency and
productivity to sustain global competitiveness. In this paper we propose a
task-level approach for assembly of spiral brick columns. Our extensive
computational simulations using the generalized models of spiral brick columns
show the feasibility, the effectiveness and efficiency of our proposed
approach. Our results offer the potential to use robots in automated
construction of spiral brick columns with utmost efficiency.


  Stellar models have been computed for stars having [Fe/H] = 0.0 and -2.0 to
determine the effects of using boundary conditions derived from the latest
MARCS model atmospheres. The latter were fitted to the interior models at both
the photosphere and at tau = 100, and at least for the 0.8-1.0 solar mass stars
considered here, the resultant evolutionary tracks were found to be nearly
independent of the chosen fitting point. Particular care was taken to treat the
entire star as consistently as possible; i.e., both the interior and atmosphere
codes assumed the same abundances and the same treatment of convection. Tracks
were also computed using either the classical gray T(tau,T_eff) relation or
that derived by Krishna Swamy (1966) to derive the boundary pressure. The
latter predict warmer giant branches (by ~150 K) at solar abundances than those
based on gray or MARCS atmospheres, which happens to be in good agreement with
the inferred temperatures of giants in the open cluster M67 from the latest
(V-K)-T_eff relations. Most of the calculations assumed Z=0.0125 (Asplund et
al.), though a few models were computed for Z=0.0165 (Grevesse & Sauval) to
determine the dependence of the tracks on Z_\odot. Grids of "scaled solar,
differentially corrected" (SDC) atmospheres were also computed to try to
improve upon theoretical MARCS models. When they were used as boundary
conditions, the resultant tracks agreed very well with those based on a
standard scaled-solar (e.g., Krishna Swamy) T(tau,T_eff) relation,
independently of the assumed metal abundance. Fits of isochrones to the C-M
diagram of the [Fe/H] = -2 globular cluster M68 were examined, as was the
possibility that the mixing-length parameter varies with stellar parameters.


  We report on studies of the loss maps for particles travelling from the end
of the ThomX's linac along the transfer line to the end of the ring first turn
in preparation of the machine commissioning. ThomX is a 50-MeV-electron
accelerator prototype which will use Compton backscattering to generate a high
flux of hard X-rays. The accelerator tracking code MadX is used to simulate
electrons' propagation and compute losses. These maps may be projected at any
localisation along the bunch path or plotted along the bunch path. This
information is particularly relevant at the locations of the monitoring devices
(screens, position monitors,...) where loss predictions will be compared with
measurements.


  The most massive black holes in our Universe form binaries at the centre of
merging galaxies. The recent evidence for a gravitational-wave (GW) background
from pulsar timing may constitute the first observation that these supermassive
black hole binaries (SMBHBs) merge. Yet, the most massive SMBHBs are out of
reach of interferometric {GW} detectors and are exceedingly difficult to
resolve individually with pulsar timing. These limitations call for unexplored
strategies to detect individual SMBHBs in the uncharted frequency band
$\lesssim10^{-5}\,\rm Hz$ in order to establish their abundance and decipher
the coevolution with their host galaxies. Here we show that SMBHBs imprint
detectable long-term modulations on GWs from stellar-mass binaries residing in
the same galaxy. We determine that proposed deci-Hz GW interferometers
sensitive to numerous stellar-mass binaries could uncover modulations from
$\sim\mathscr{O}(10^{-1}$ - $10^4)$ SMBHBs with masses $\sim\mathscr{O}(10^7$ -
$10^8)\,\rm M_\odot$ out to redshift $z\sim3.5$. This offers a unique
opportunity to map the population of SMBHBs through cosmic time, which might
remain inaccessible otherwise.


  We present a survey of $z\sim3$ Ly$\alpha$ emitters (LAEs) within the fields
of the VLT LBG Redshift Survey. The data encompasses 5 independent survey
fields co-spatial with spectroscopic LBG data and covering a larger total area
than previously analysed for LAE number counts and clustering. This affords an
improved analysis over previous work by minimising the effects of cosmic
variance and allowing the cross-clustering analysis of LAEs and LBGs. Our
photometric sample consists of $\approx600$ LAE candidates, over an area of
1.07~deg$^2$, with equivalent widths of $\gtrsim65$~\AA\ and a flux limit of
$\approx2\times10^{-17}$~erg~cm$^{-2}$~s$^{-1}$. From spectroscopic follow-up,
we measured a success rate of $78\pm18\%$. We find the $R$-band continuum
luminosity function to be $\sim10\times$ lower than the luminosity function of
LBGs at this redshift, consistent with previous studies. Exploiting the large
area of the survey, we estimate the LAE auto-correlation function and find a
clustering length of $r_0=2.86\pm0.33~h^{-1}$~Mpc, low compared to the $z\sim3$
LBG population, but somewhat higher than previous LAE measurements. This
corresponds to a median halo mass of $M_{\rm
DM}=10^{11.0\pm0.3}~h^{-1}~$M$_{\odot}$. We present an analysis of clustering
length versus continuum magnitude and find that the measurements for LAEs and
LBGs are consistent at faint magnitudes. Our combined dataset of LAEs and LBGs
allows us to measure, for the first time, the LBG-LAE cross-correlation,
finding a clustering length of $r_0=3.29\pm0.57~h^{-1}$~Mpc and a LAE halo mass
of $10^{11.1\pm0.4}~h^{-1}$~M$_{\odot}$. Overall, we conclude that LAEs inhabit
primarily low mass halos, but form a relatively small proportion of the galaxy
population found in such halos.


  Pairwise quantum correlations in the ground state of a N-spins
antiferromagnetic chain described by the Heisenberg model with nearest neighbor
exchange coupling are investigated. By varying a single coupling between two
neighboring sites it is possible to drive spins from entangled to disentangled
states, reversibly. For even N the two-spin density matrix is written in the
form of a Werner state, allowing identification of the weight parameter with
the usual spin-spin correlation function $\langle S_i^z \, S_j^z \rangle =
\Gamma_{ij}$. The correlation functions show universal behavior in the
$\Gamma$-dependence. This study presents a concrete possibility for the
practical demonstration of entanglement control, opening alternatives for
probing non-classical correlations and the realization of Werner states in
familiar condensed matter systems. All required fabrication and measurement
ingredients are currently available.


  We consider a system with a discrete configuration space. We show that the
geometrical structures associated with such a system provide the tools
necessary for a reconstruction of discrete quantum mechanics once dynamics is
brought into the picture. We do this in three steps. Our starting point is
information geometry, the natural geometry of the space of probability
distributions. Dynamics requires additional structure. To evolve the
probabilities $P^k$, we introduce coordinates $S^k$ canonically conjugate to
the $P^k$ and a symplectic structure. We then seek to extend the metric
structure of information geometry, to define a geometry over the full space of
the $P^k$ and $S^k$. Consistency between the metric tensor and the symplectic
form forces us to introduce a K\"ahler geometry. The construction has notable
features. A complex structure is obtained in a natural way. The canonical
coordinates of the K\"ahler space are precisely the wave functions of quantum
mechanics. The full group of unitary transformations is obtained. Finally, one
may associate a Hilbert space with the K\"ahler space, which leads to the
standard version of quantum theory. We also show that the metric that we derive
here using purely geometrical arguments is precisely the one that leads to
Wootters' expression for the statistical distance for quantum systems.


  Low levels of inertia due to increasing renewable penetration bring several
challenges, such as the higher need for Primary Frequency Response (PFR). A
potential solution to mitigate this problem consists on reducing the largest
possible power loss in the grid. This paper develops a novel modelling
framework to analyse the benefits of such approach.
  A new frequency-constrained Stochastic Unit Commitment (SUC) is proposed
here, which allows to dynamically reduce the largest possible loss in the
optimisation problem. Furthermore, the effect of load damping is included by
means of an approximation, while its effect is typically neglected in previous
frequency-secured-UC studies. Through several case studies, we demonstrate that
reducing the largest loss could significantly decrease operational cost and
carbon emissions in the future Great Britain's grid.


  SUSY partnership between singular potentials often breaks down. Via
regularization it can be restored on certain ad hoc subspaces of Hilbert space
[Das and Pernice, Nucl. Phys. B 561 (1999) 357]. Within the naturally
complexified (so called PT symmetric) quantum mechanics we show how SUSY
between strongly singular harmonic oscillators can completely be
re-established. Our recipe leads to a new form of the bosonic creation and
annihilation operators and proves continuous near the usual regular (i.e.,
linear harmonic) limit.


  Urban transportation systems grow over time as city populations grow and move
and their transportation needs evolve. Typical network growth models, such as
preferential attachment, grow the network node by node whereas rail and metro
systems grow by adding entire lines with all their nodes. The objective of this
paper is to see if any canonical regular network forms such as stars or grids
capture the growth patterns of urban metro systems for which we have historical
data in terms of old maps. Data from these maps reveal that the systems'
Pearson degree correlation grows increasingly from initially negative values
toward positive values over time and in some cases becomes decidedly positive.
We have derived closed form expressions for degree correlation and clustering
coefficient for a variety of canonical forms that might be similar to metro
systems. Of all those examined, only a few types patterned after a wide area
network (WAN) with a "core-periphery" structure show similar positive-trending
degree correlation as network size increases. This suggests that large metro
systems either are designed or evolve into the equivalent of message carriers
that seek to balance travel between arbitrary node-destination pairs with
avoidance of congestion in the central regions of the network.
  Keywords: metro, subway, urban transport networks, degree correlation


  Imaging atmospheric Cherenkov telescope (IACT) arrays record images from air
showers initiated by gamma rays entering the atmosphere, allowing astrophysical
sources to be observed at very high energies. To maximize IACT sensitivity,
gamma-ray showers must be efficiently distinguished from the dominant
background of cosmic-ray showers using images from multiple telescopes. A
combination of convolutional neural networks (CNNs) with a recurrent neural
network (RNN) has been proposed to perform this task. Using CTLearn, an open
source Python package using deep learning to analyze data from IACTs, with
simulated data from the upcoming Cherenkov Telescope Array (CTA), we implement
a CNN-RNN network and find no evidence that sorting telescope images by total
amplitude improves background rejection performance.


  Ion-mobility spectrometry (IMS) is an analytical technique used to separate
and identify ionized gas molecules based on their mobility in a carrier buffer
gas. Such methods come in a large variety of versions that currently allow ion
identification at and above the millimeter scale. Here, we present a design for
a cross-flow-IMS method able to generate and detect ions at the sub-millimeter
scale. We propose a novel ion focusing strategy and tested it in a prototype
device using Nitrogen as a sample gas, and also with simulations using four
different sample gases. By introducing an original lobular ion generation
localized to a few ten of microns and substantially simplifying the design, our
device is able to keep constant laminar flow conditions for high flow rates. In
this way, it avoids the turbulences in the gas flow, which would occur in other
ion-focusing cross-flow methods limiting their performance at the
sub-millimeter scale. Scalability of the proposed design can contribute to
improve resolving power and resolution of currently available cross-flow
methods.


  In this article, we study the diameter two properties (D2Ps), the diametral
diameter two properties (diametral D2Ps), and the Daugavet property in
Orlicz-Lorentz spaces equipped with the Luxemburg norm. First, we characterize
the Radon-Nikod\'ym property of Orlicz-Lorentz spaces in full generality by
considering all finite real-valued Orlicz functions. To show this, the
fundamental functions of their K\"othe dual spaces defined by extended
real-valued Orlicz functions are computed. We also show that if an Orlicz
function does not satisfy the appropriate $\Delta_2$-condition, the
Orlicz-Lorentz space and its order-continuous subspace have the strong diameter
two property. Consequently, given that an Orlicz function is an N-function at
infinity, the same condition characterizes the diameter two properties of
Orlicz-Lorentz spaces as well as the octahedralities of their K\"othe dual
spaces. The Orlicz-Lorentz function spaces with the Daugavet property and the
diametral D2Ps are isometrically isomorphic to $L_1$ when the weight function
is regular. In the process, we observe that every locally uniformly nonsquare
point is not a $\Delta$-point. This fact provides another class of real Banach
spaces without $\Delta$-points. As another application, it is shown that for
Orlicz-Lorentz spaces equipped with the Luxemburg norm defined by an N-function
at infinity, their K\"othe dual spaces do not have the local diameter two
property, and so as other (diametral) diameter two properties and the Daugavet
property.


  Automatic Program Repair (APR) techniques can promisingly help reducing the
cost of debugging. Many relevant APR techniques follow the
generate-and-validate approach, that is, the faulty program is iteratively
modified with different change operators and then validated with a test suite
until a plausible patch is generated. In particular, Kali is a
generate-and-validate technique developed to investigate the possibility of
generating plausible patches by only removing code. Former studies show that
indeed Kali successfully addressed several faults. This paper addresses the
case of code-removal patches in automated program repair investigating the
reasons and the scenarios that make their creation possible, and the
relationship with patches implemented by developers. Our study reveals that
code-removal patches are often insufficient to fix bugs, and proposes a
comprehensive taxonomy of code-removal patches that provides evidence of the
problems that may affect test suites, opening new opportunities for researchers
in the field of automatic program repair.


  The temperature dependence of bottomonium states at temperatures above and
below $T_c$ is presented, using non-relativistic dynamics for the bottom quark
and full relativistic lattice QCD simulations for two light flavors on a highly
anisotropic lattice. We find that the S-waves ($\Upsilon$ and $\eta_b$) show
little temperature dependence in this range while the P wave propagators show a
crossover from the exponential decay characterizing the hadronic phase to a
power-law behavior consistent with nearly-free dynamics at approximately twice
the critical temperature.


  We present photometric and spectroscopic data sets for SN 2020pvb, a Type
IIn-P supernova (SN) similar to SNe 1994W, 2005cl, 2009kn and 2011ht, with a
precursor outburst detected (PS1 w-band ~ -13.8 mag) around four months before
the B-band maximum light. SN 2020pvb presents a relatively bright light curve
peaking at M_B = -17.95 +- 0.30 mag and a plateau lasting at least 40 days
before it went in solar conjunction. After this, the object is no longer
visible at phases > 150 days above -12.5 mag in the B-band, suggesting that the
SN 2020pvb ejecta interacts with a dense spatially confined circumstellar
envelope. SN 2020pvb shows in its spectra strong Balmer lines and a forest of
FeII lines with narrow P Cygni profiles. Using archival images from the Hubble
Space Telescope, we constrain the progenitor of SN 2020pvb to have a luminosity
of log(L/L_sun) <= 5.4, ruling out any single star progenitor over 50 M_sun.
All in all, SN 2020pvb is a Type IIn-P whose progenitor star had an outburst ~
0.5 yr before the final explosion, the material lost during this outburst is
probably playing a role in shaping the physical properties of the supernova.


  The mechanical performance of Directed Energy Deposition Additive
Manufactured (DED-AM) components can be highly material dependent. Through in
situ and operando synchrotron X-ray imaging we capture the underlying phenomena
controlling build quality of stainless steel (SS316) and titanium alloy (Ti6242
or Ti-6Al-2Sn-4Zr-2Mo). We reveal three mechanisms influencing the build
efficiency of titanium alloys compared to stainless steel: blown powder
sintering; reduced melt-pool wetting due to the sinter; and pore pushing in the
melt-pool. The former two directly increase lack of fusion porosity, while the
later causes end of track porosity. Each phenomenon influences the melt-pool
characteristics, wetting of the substrate and hence build efficacy and
undesirable microstructural feature formation. We demonstrate that porosity is
related to powder characteristics, pool flow, and solidification front
morphology. Our results clarify DED-AM process dynamics, illustrating why each
alloy builds differently, facilitating the wider application of additive
manufacturing to new materials.


  We demonstrate excitation-manifold resolved polarisation characterisation of
continuous-variable (CV) quantum states. In contrast to traditional
characterisation of polarisation that is based on the Stokes parameters, we
experimentally determine the Stokes vector of each excitation manifold
separately. Only for states with a given photon number does the methods
coincide. For states with an indeterminate photon number, for example Gaussian
states, the employed method gives a richer and more accurate description. We
apply the method both in theory and in experiment to some common states to
demonstrate its advantages.


  Probabilistic programming (PP) is a programming paradigm that allows for
writing statistical models like ordinary programs, performing simulations by
running those programs, and analyzing and refining their statistical behavior
using powerful inference engines. This paper takes a step towards leveraging PP
for reasoning about data-aware processes. To this end, we present a systematic
translation of Data Petri Nets (DPNs) into a model written in a PP language
whose features are supported by most PP systems. We show that our translation
is sound and provides statistical guarantees for simulating DPNs. Furthermore,
we discuss how PP can be used for process mining tasks and report on a
prototype implementation of our translation. We also discuss further analysis
scenarios that could be easily approached based on the proposed translation and
available PP tools.


  In one of the most important methods in Density Functional Theory - the
Full-Potential Linearized Augmented Plane Wave (FLAPW) method - dense
generalized eigenproblems are organized in long sequences. Moreover each
eigenproblem is strongly correlated to the next one in the sequence. We propose
a novel approach which exploits such correlation through the use of an
eigensolver based on subspace iteration and accelerated with Chebyshev
polynomials. The resulting solver, parallelized using the Elemental library
framework, achieves excellent scalability and is competitive with current dense
parallel eigensolvers.


  Since statistical guarantees for neural networks are usually restricted to
global optima of intricate objective functions, it is not clear whether these
theories really explain the performances of actual outputs of neural-network
pipelines. The goal of this paper is, therefore, to bring statistical theory
closer to practice. We develop statistical guarantees for simple neural
networks that coincide up to logarithmic factors with the global optima but
apply to stationary points and the points nearby. These results support the
common notion that neural networks do not necessarily need to be optimized
globally from a mathematical perspective. More generally, despite being limited
to simple neural networks for now, our theories make a step forward in
describing the practical properties of neural networks in mathematical terms.


  Let M be a compact hyperkaehler manifold, and W the coarse moduli of complex
deformations of M. Every positive integer class v in $H^2(M)$ defines a divisor
$D_v$ in W consisting of all algebraic manifolds polarized by v. We prove that
every connected component of this divisor is dense in W.


  Advantages of quantum effects in several technologies, such as computation
and communication, have already been well appreciated, and some devices, such
as quantum computers and communication links, exhibiting superiority to their
classical counterparts have been demonstrated. The close relationship between
information and energy motivates us to explore if similar quantum benefits can
be found in energy technologies. Investigation of performance limits for a
broader class of information-energy machines is the subject of the rapidly
emerging field of quantum thermodynamics. Extension of classical
thermodynamical laws to the quantum realm is far from trivial. This short
review presents some of the recent efforts in this fundamental direction and
focuses on quantum heat engines and their efficiency bounds when harnessing
energy from non-thermal resources, specifically those containing quantum
coherence and correlations.


  The dominant viewpoint on Jovian decametric S-burst emission neglects the
time delay of the radiation, although its base theory of electron cyclotron
maser instability allows a significant decreasing of X-mode group velocity near
the cutoff frequency at the bottom of source region. We searched for effects of
the frequency-related delay of radiation in broadband Jovian radio storms
consisting of periodic S-bursts (S-burst trains) at 16 to 30 MHz. It was found
that up to 1% of bursts in a train are of distorted meandering shape in dynamic
spectrum, where the emission from one radio source was observed at several
frequencies simultaneously. It is difficult to explain such spectra in terms of
radio waves beaming or causality without significant frequency-related delay of
radio emission. We found experimentally that the frequency drift rate of middle
lines of such events coincides with the drift rate of disturbances in common
S-bursts. This indicates a general distortion of the dynamic spectrum of
S-bursts. As a result, the correlation method for the measurement of the
spectral distortion is proposed. Using this method, we found the approximation
coefficients for the distortion in 32 spectra of 8 Io-B storms. The corrected
spectra formally show that S-burst trains do not move mainly outward from
Jupiter, as it is usually assumed, but fly in the opposite direction. Our
simulation confirms that the dispersion is capable in principle to reproduce
the found spectral distortion. Hence, the dispersion-like phenomena in Jovian
S-bursts deserve discussion because they have no satisfactory explanations in
terms of traditional approach.


  T- and S-duality rules among the gauge potentials in type II supergravities
are studied. In particular, by following the approach of arXiv:1909.01335, we
determine the T- and S-duality rules for certain mixed-symmetry potentials,
which couple to supersymmetric branes with tension $T\propto g_s^{-n}$ ($n\leq
4$). Although the T-duality rules are rather intricate, we find a certain
redefinition of potentials which considerably simplifies the duality rules.
After the redefinition, potentials are identified with components of the
T-duality-covariant potentials, which have been predicted by the $E_{11}$
conjecture. We also discuss the field strengths of the mixed-symmetry
potentials.


  Semi-Dirac semimetal is a material exhibiting linear band dispersion in one
direction and quadratic band dispersion in the orthogonal direction and,
therefore, hosts massless and massive fermions at the same point in the
momentum space. While a number of interesting physical properties have been
predicted in semi-Dirac semimetals, it has been rare to realize such materials
in condensed matters. Based on the fact that some honeycomb materials are
easily oxidized or chemically absorb other atoms, here, we theoretically
propose an approach of modifying their band structures by covalent addition of
group-VI elements and strain engineering. We predict a silicene oxide with
chemical formula of Si2O to be a candidate of semi-Dirac semimetal. Our
approach is backed by the analysis and understanding of the effect of p-orbital
frustration on the band structure of the graphene-like materials.


  Cognitive systems generally require a human to translate a problem definition
into some specification that the cognitive system can use to attempt to solve
the problem or perform the task. In this paper, we illustrate that large
language models (LLMs) can be utilized to map a problem class, defined in
natural language, into a semi-formal specification that can then be utilized by
an existing reasoning and learning system to solve instances from the problem
class. We present the design of LLM-enabled cognitive task analyst agent(s).
Implemented with LLM agents, this system produces a definition of problem
spaces for tasks specified in natural language. LLM prompts are derived from
the definition of problem spaces in the AI literature and general
problem-solving strategies (Polya's How to Solve It). A cognitive system can
then use the problem-space specification, applying domain-general problem
solving strategies ("weak methods" such as search), to solve multiple instances
of problems from the problem class. This result, while preliminary, suggests
the potential for speeding cognitive systems research via disintermediation of
problem formulation while also retaining core capabilities of cognitive
systems, such as robust inference and online learning.


  The conversion between different spherical image and video projection formats
requires highly accurate resampling techniques in order to minimize the
inevitable loss of information. Suitable resampling algorithms such as nearest
neighbor, linear or cubic resampling are readily available. However, no
generally applicable resampling technique exploits the special properties of
spherical images so far. Thus, we propose a novel viewport-adaptive resampling
(VAR) technique that takes the spherical characteristics of the underlying
resampling problem into account. VAR can be applied to any mesh-to-mesh capable
resampling algorithm and shows significant gains across all tested techniques.
In combination with frequency-selective resampling, VAR outperforms
conventional cubic resampling by more than 2 dB in terms of WS-PSNR. A visual
inspection and the evaluation of further metrics such as PSNR and SSIM support
the positive results.


  In this note we prove two results on the quantitative illumination parameter
f(d) of the unit ball of a d-dimensional normed space introduced by K. Bezdek
(1992). The first is that f(d) = O(2^d d^2 log d). The second involves Steiner
minimal trees. Let v(d) be the maximum degree of a vertex, and s(d) of a
Steiner point, in a Steiner minimal tree in a d-dimensional normed space, where
both maxima are over all norms. F. Morgan (1992) conjectured that s(d) <= 2^d,
and D. Cieslik (1990) conjectured v(d) <= 2(2^d-1). We prove that s(d) <= v(d)
<= f(d) which, combined with the above estimate of f(d), improves the
previously best known upper bound v(d) < 3^d.


  The Colin de Verdiere number of graph G, denoted by \mu(G), is a spectral
invariant of G that is related to some of its topological properties. For
example, \mu(G) \leq 3 iff G is planar. A penny graph is the contact graph of
equal-radii disks with disjoint interiors in the plane. In this note we prove
lower bounds on \mu(G) when the complement \bar{G} is a penny graph.


  It is known that all $\tau$ functions of the Painlev\'{e} equations satisfy
the fourth-order quadratic differential equation. Among them, for the III, V,
and VI equations, it is possible to express the formal series solutions
explicitly by using combinatorics. In this paper, we show the convergence of
the formal series, including the solutions of more general equations. And by
the absolute convergence of $\tau $ series, the convergence of the conformal
block function ($c=1$) also follows since it is a partial sum of the $\tau $
series. We also characterized the form of a homogeneous quadratic equation with
a series solution similar to the tau functions of the Painlev\'{e} equations.
The Painlev\'{e} equations are classified into six types, and it is known that
they can be obtained by sequentially degenerating from type VI to type I.


  We present the VVV-SkZ_pipeline, a DAOPHOT-based photometric pipeline,
created to perform PSF-fitting photometry of "VISTA Variables in the V\'ia
L\'actea" (VVV) ESO Public Survey data. The pipeline replaces the user avoiding
repetitive interaction in all the operations, retaining all of the benefits of
the power and accuracy of the DAOPHOT suite. The pipeline provides an
astrometrized photometric catalog reliable up to more than 2 magnitudes
brighter than the saturation limit, where other techniques fail. It also
produces deeper and more accurate photometry. These achievements allow the
VVV-SkZ_pipeline to produce data well anchored to the selected standard
photometric system and analyze important phenomena (i.e. TRGB, RGB slope, HB
morphology, RR Lyrae), that other methods are not able to manage.


  Cluster states are useful in many quantum information processing
applications. In particular, universal measurement-based quantum computation
(MBQC) utilizes 2D cluster states, and topologically fault-tolerant MBQC
requires cluster states with three or higher dimensions. This work proposes a
protocol to deterministically generate multidimensional photonic cluster states
using a single atom-cavity system and time-delay feedback. The dimensionality
of the cluster state increases linearly with the number of time-delay feedback.
We firstly give a diagrammatic derivation of the tensor network states, which
is valuable in simulating matrix product states and projected entangled pair
states generated from sequential photons. Our method also provides a simple way
to bridge and analyze the experimental imperfections and the logical errors of
the generated states. In this method, we analyze the generated cluster states
under realistic experimental conditions and address both one-qubit and
two-qubit errors. Through numerical simulation, we observe an optimal
atom-cavity cooperativity for the fidelity of the generated states, which is
surprising given the prevailing assumption that higher cooperativity systems
are inherently better for photonic applications.


  We optimize multilayered anti-reflective coatings for photovoltaic devices,
using modern evolutionary algorithms. We apply a rigorous methodology to show
that a given structure, which is particularly regular, emerge spontaneously in
a very systematical way for a very broad range of conditions. The very
regularity of the structure allows for a thorough physical analysis of how the
designs operate. This allows to understand that the central part is a photonic
crystal utilized as a buffer for light, and that the external layers have the
purpose of reducing the impedance mismatch between the outer media and the
Bloch mode supported by the photonic crystal. This shows how optimization can
suggest new design rules and be considered as a source of inspiration. Finally,
we fabricate these structures with easily deployable techniques.


  Michael Farber introduced the Lusternik-Schnirelmann category cat$(M,\xi)$
for the pair of finite CW complex $M$ and first-order cohomology $\xi$. It is
inspired by the Morse-Novikov theory, which is a closed 1-form version of the
Morse theory. An important result of this theory is that if the number of zeros
of a closed 1-form $\omega$ on a closed manifold is less than
cat$(M,[\omega])$, then any gradient flows of $\omega$ has at least one
homoclinic cycle. This paper begins with an explanation of
Lusternik-Schnirelmann theory of closed 1-form, and extends Farber's results to
general non-compact manifolds. We will also explain that Farber's results hold
equally well on non compact manifolds, and explain the new phenomena related
gradient flows of $\omega$ that occurs on non compact manifolds.


  We study the quantization of a model proposed by Newton to explain
centripetal force namely, that of a particle moving on a regular polygon. The
exact eigenvalues and eigenfunctions are obtained. The quantum mechanics of a
particle moving on a circle and in an infinite potential well are derived as
limiting cases.


  We study the machine learning task for models with operators mapping between
the Wasserstein space of probability measures and a space of functions, like
e.g. in mean-field games/control problems. Two classes of neural networks,
based on bin density and on cylindrical approximation, are proposed to learn
these so-called mean-field functions, and are theoretically supported by
universal approximation theorems. We perform several numerical experiments for
training these two mean-field neural networks, and show their accuracy and
efficiency in the generalization error with various test distributions.
Finally, we present different algorithms relying on mean-field neural networks
for solving time-dependent mean-field problems, and illustrate our results with
numerical tests for the example of a semi-linear partial differential equation
in the Wasserstein space of probability measures.


  The solution of the axial U(1) problem, the role of the topology of the gauge
group in forcing the breaking of axial symmetry in any irreducible
representation of the observable algebra and the theta vacua structure are
revisited in the temporal gauge with attention to the mathematical consistency
of the derivations. Both realizations with strong and weak Gauss law are
discussed; the control of the general mechanisms and structures is obtained on
the basis of the localization of the (large) gauge transformations and the
local generation of the chiral symmetry. The Schwinger model in the temporal
gauge exactly reproduces the general results.


  This work shows how a secure Internet can be implemented through a fast key
distribution system that uses physical noise to protect the transmitted
information. Starting from a shared random sequence $K_0$ between two (or more)
users, longsequences $R$ of random bits can be shared. The signals sent over
the Internet are deterministic but have a built-in Nature-made uncertainty that
protects the shared sequences. After privacy amplification the shared $R$
random bits --encrypted by noise-- are subsequently utilized in one-time-pad
data ciphering.


  We define a type of Niebrzydowski tribracket we call $\Delta$-tribrackets and
show that their counting invariants are invariants of link-homotopy. We further
identify several classes of tribrackets whose counting invariants for oriented
classical knots and links are trivial, including vertical tribrackets
satisfying the center-involutory condition and horizontal tribrackets
satisfying the late-commutativity condition. We provide examples and end with
questions for future research.


  We consider the online transportation problem set in a metric space
containing parking garages of various capacities. Cars arrive over time, and
must be assigned to an unfull parking garage upon their arrival. The objective
is to minimize the aggregate distance that cars have to travel to their
assigned parking garage. We show that the natural greedy algorithm, augmented
with garages of $k\ge3$ times the capacity, is $\left(1 +
\frac{2}{k-2}\right)$-competitive.


  We prove that a single-layer neural network trained with the online actor
critic algorithm converges in distribution to a random ordinary differential
equation (ODE) as the number of hidden units and the number of training steps
$\rightarrow \infty$. In the online actor-critic algorithm, the distribution of
the data samples dynamically changes as the model is updated, which is a key
challenge for any convergence analysis. We establish the geometric ergodicity
of the data samples under a fixed actor policy. Then, using a Poisson equation,
we prove that the fluctuations of the model updates around the limit
distribution due to the randomly-arriving data samples vanish as the number of
parameter updates $\rightarrow \infty$. Using the Poisson equation and weak
convergence techniques, we prove that the actor neural network and critic
neural network converge to the solutions of a system of ODEs with random
initial conditions. Analysis of the limit ODE shows that the limit critic
network will converge to the true value function, which will provide the actor
an asymptotically unbiased estimate of the policy gradient. We then prove that
the limit actor network will converge to a stationary point.


  In this paper we show how to recover a spectral approximations to broad
classes of structured matrices using only a polylogarithmic number of adaptive
linear measurements to either the matrix or its inverse. Leveraging this result
we obtain faster algorithms for variety of linear algebraic problems. Key
results include:
  $\bullet$ A nearly linear time algorithm for solving the inverse of symmetric
$M$-matrices, a strict superset of Laplacians and SDD matrices.
  $\bullet$ An $\tilde{O}(n^2)$ time algorithm for solving $n \times n$ linear
systems that are constant spectral approximations of Laplacians or more
generally, SDD matrices.
  $\bullet$ An $\tilde{O}(n^2)$ algorithm to recover a spectral approximation
of a $n$-vertex graph using only $\tilde{O}(1)$ matrix-vector multiplies with
its Laplacian matrix.
  The previous best results for each problem either used a trivial number of
queries to exactly recover the matrix or a trivial $O(n^\omega)$ running time,
where $\omega$ is the matrix multiplication constant.
  We achieve these results by generalizing recent semidefinite programming
based linear sized sparsifier results of Lee and Sun (2017) and providing
iterative methods inspired by the semistreaming sparsification results of
Kapralov, Lee, Musco, Musco and Sidford (2014) and input sparsity time linear
system solving results of Li, Miller, and Peng (2013). We hope that by
initiating study of these natural problems, expanding the robustness and scope
of recent nearly linear time linear system solving research, and providing
general matrix recovery machinery this work may serve as a stepping stone for
faster algorithms.


  The field of Machine Learning research is divided into subject areas, where
each area tries to solve a specific problem, using specific methods. In recent
years, borders have almost been erased, and many areas inherit methods from
other areas. This trend leads to better results and the number of papers in the
field is growing every year. The problem is that the amount of information is
also growing, and many methods remain unknown in a large number of papers. In
this work, we propose the concept of inheritance between machine learning
models, which allows conducting research, processing much less information, and
pay attention to previously unnoticed models. We hope that this project will
allow researchers to find ways to improve their ideas. In addition, it can be
used by researchers to publish their methods too. Project is available by link:
https://www.infornopolitan.xyz/backronym


  Simple applications of a principle of minimum energy and the property of
monotonicity for the corresponding non-local operator, have allowed a direct
proof of the G-compactness in a weak sense, as well as in the strong sense. The
definitions of H-convergence and G-convergence, weak or strong, have been
proved to be equivalent.


  We present a numerical study of the impact of AGN accretion and feedback on
the star formation history of barred disc galaxies. Our goal is to determine
whether the effect of feedback is positive (enhanced star formation) or
negative (quenched star formation), and to what extent. We performed a series
of 12 hydrodynamical simulations of disc galaxies, 10 barred and 2 unbarred,
with various initial gas fractions and AGN feedback prescriptions. In barred
galaxies, gas is driven toward the centre of the galaxy and causes a starburst,
followed by a slow decay, while in unbarred galaxies the SFR increases slowly
and steadily. AGN feedback suppresses star formation near the central black
hole. Gas is pushed away from the black hole, and collides head-on with
inflowing gas, forming a dense ring at a finite radius where star formation is
enhanced. We conclude that both negative and positive feedback are present, and
these effects mostly cancel out. There is no net quenching or enhancement in
star formation, but rather a displacement of the star formation sites to larger
radii. In unbarred galaxies, where the density of the central gas is lower,
quenching of star formation near the black hole is more efficient, and
enhancement of star formation at larger radii is less efficient. As a result,
negative feedback dominates. Lowering the gas fraction reduces the star
formation rate at all radii, whether or not there is a bar or an AGN.


  The design of novel devices with specific technical interests through
modulating structural properties and bonding characteristics promotes the
vigorous development of materials informatics. Herein, we propose a synergy
strategy of component reconstruction by combining geometric configuration and
bonding characteristics. With the synergy strategy, we designed a novel
two-dimensional (2D) graphene-like borides, e.g. g-B3N5, which possesses
counter-intuitive ultra-low thermal conductivity of 21.08 W/mK despite the
small atomic mass. The ultra-low thermal conductivity is attributed to the
synergy effect of electronics and geometry on thermal transport due to the
combining reconstruction of g-BN and nitrogene. With the synergy effect, the
dominant acoustic branches are strongly softened, and the scattering absorption
and Umklapp process are simultaneously suppressed. Thus, the thermal
conductivity is significantly lowered. To verify the component reconstruction
strategy, we further constructed g-B3P5 and g-B3As5, and uncovered the
ultra-low thermal conductivity of 2.50 and 1.85 W/mK, respectively. The synergy
effect and the designed ultra-low thermal conductivity materials with
lightweight atomic mass cater to the demand for light development of momentum
machinery and heat protection, such as aerospace vehicles, high-speed rail,
automobiles.


  We study brane matter in the ekpyrotic scenario and observe that in order to
obtain standard gravity on the visible brane, the tension of the visible brane
should be positive. If the sizes of both the fifth dimension and the Calabi-Yau
threefold are fixed, the Israel junction conditions do not allow time-dependent
brane matter. Relaxing this constraint, it is possible to obtain approximately
standard cosmology on the visible brane, with small corrections due to possible
time-dependence of the Calabi-Yau threefold.


  We continue the investigation of the spectral theory and exponential
asymptotics of Markov processes, following Kontoyiannis and Meyn (2003). We
introduce a new family of nonlinear Lyapunov drift criteria, characterizing
distinct subclasses of geometrically ergodic Markov processes in terms of
inequalities for the nonlinear generator. We concentrate on the class of
"multiplicatively regular" Markov processes, characterized via conditions
similar to (but weaker than) those of Donsker-Varadhan. For any such process
{Phi(t)} with transition kernel P on a general state space, the following are
obtained. 1. SPECTRAL THEORY: For a large class of functionals F, the kernel
Phat(x,dy) = e^{F(x)}P(x,dy) has a discrete spectrum in an appropriately
defined Banach space. There exists a "maximal" solution to the "multiplicative
Poisson equation," defined as the eigenvalue problem for Phat. Regularity
properties are established for \Lambda(F) = \log(\lambda), where \lambda is the
maximal eigenvalue, and for its convex dual. 2. MULTIPLICATIVE MEAN ERGODIC
THEOREM: The normalized mean E_x[\exp(S_t)] of the exponential of the partial
sums {S_t} of the process with respect to any one of the above functionals F,
converges to the maximal eigenfunction. 3. MULTIPLICATIVE REGULARITY: The drift
criterion under which our results are derived is equivalent to the existence of
regeneration times with finite exponential moments for {S_t}. 4. LARGE
DEVIATIONS: The sequence of empirical measures of {Phi(t)} satisfies an LDP in
a topology finer than the \tau-topology. The rate function is \Lambda^* and it
coincides with the Donsker-Varadhan rate function. 5. EXACTR LARGE DEVIATIONS:
The partial sums {S_t} satisfy an exact LD expansion, analogous to that
obtained for independent random variables.


  The classification results for the extreme characters of two basic "big"
groups, the infinite symmetric group S(infinity) and the infinite-dimensional
unitary group U(infinity), are remarkably similar. It does not seem to be
possible to explain this phenomenon using a suitable extension of the
Schur-Weyl duality to infinite dimension. We suggest an explanation of a
different nature that does not have analogs in the classical representation
theory.
  We start from the combinatorial/probabilistic approach to characters of "big"
groups initiated by Vershik and Kerov. In this approach, the space of extreme
characters is viewed as a boundary of a certain infinite graph. In the cases of
S(infinity) and U(infinity), those are the Young graph and the Gelfand-Tsetlin
graph, respectively. We introduce a new related object that we call the Young
bouquet. It is a poset with continuous grading whose boundary we define and
compute. We show that this boundary is a cone over the boundary of the Young
graph, and at the same time it is also a degeneration of the boundary of the
Gelfand-Tsetlin graph.
  The Young bouquet has an application to constructing infinite-dimensional
Markov processes with determinantal correlation functions.


  This note analyzed the angle-distribution of the probabilities of two-photon
states come out of a single-photon's stimulated emission amplification, show
that one can exploit EPR photon pairs combined with stimulated emission to
realize superluminal signaling.


  The upcoming Sixth Generation (6G) network is projected to grapple with a
range of security concerns, encompassing access control, authentication, secure
connections among 6G Core (6GC) entities, and trustworthiness. Classical
Virtual Private Networks (VPNs), extensively deployed in Evolved Packet Core
(EPC) network infrastructure, are notoriously susceptible to a variety of
attacks, including man-in-the-middle incursions, Domain Name System (DNS)
hijacking, Denial of Service (DoS) attacks, port scanning, and persistent
unauthorized access attempts. This paper introduces the concept of Software
Defined Perimeter (SDP) as an innovative solution, providing an alternative to
VPNs with the goal of fostering a secure zero-trust milieu within the 6G Core
networks. We capitalize on the SDP controller-based authentication and
authorization mechanisms to secure the EPC network's control and data plane
functions, conceiving an architecture that is expansible to the 6G network.
Further, we augment the SDP zero-trust capabilities via the incorporation of a
dynamic component, the Moving Target Defense (MTD). This enhances the network's
resilience against attacks targeting traditionally static network environments
established via VPNs. Following rigorous testbed analysis, our proposed
framework manifests superior resilience against DoS and port scanning attacks
when juxtaposed with traditional VPN methodologies.


  Soliton microcombs offer the prospect of advanced optical metrology and
timing systems in compact form factors. In these applications, pumping of
microcombs directly from a semiconductor laser without amplification or
triggering components is desirable for reduced power operation and to simplify
system design. At the same time, low repetition rate microcombs are required in
many comb applications for interface to detectors and electronics, but their
increased mode volume makes them challenging to pump at low power. Here, 10 GHz
repetition rate soliton microcombs are directly pumped by low-power (< 20 mW)
diode lasers. High-Q silica microresonators are used for this low power
operation and are packaged into fiber-connectorized modules that feature
temperature control for improved long-term frequency stability.


  This communication reports the formation of complex Langmuir monolayer at the
air-water interface by charge transfer types of interaction with the water
soluble N- cetyl N, N, N trimethyl ammonium bromide (CTAB) molecules doped with
rosebengal (RB), with the stearic acid (SA) molecules of a preformed SA
Langmuir monolayer. The reaction kinetics of the formation of RB-CTAB-SA
complex monolayer was monitored by observing the increase in surface pressure
with time while the barrier was kept fixed. Completion of interaction kinetics
was confirmed by FTIR study. This complex Langmuir films at the air-water
interface was transferred onto solid substrates at a desired surface pressure
to form multilayered Langmuir-Blodgett films. Spectroscopic characterizations
reveal some molecular level interactions as well as formation of
microcrystalline aggregates depending upon the molar ratios of CTAB and RB
within the complex LB films. Presence of two types of species in the complex LB
films was confirmed by fluorescence spectroscopy.


  The dynamics of an expanding hadron fluid at temperatures below the chiral
transition is studied in the framework of AdS/CFT correspondence. We establish
a correspondence between the asymptotic AdS geometry in the 4+1-dimensional
bulk with the analog spacetime geometry on its 3+1 dimensional boundary with
the background fluid undergoing a spherical Bjorken type expansion. The analog
metric tensor on the boundary depends locally on the soft pion dispersion
relation and the four-velocity of the fluid. The AdS/CFT correspondence
provides a relation between the pion velocity and the critical temperature of
the chiral phase transition.


  We present WebGLM, a web-enhanced question-answering system based on the
General Language Model (GLM). Its goal is to augment a pre-trained large
language model (LLM) with web search and retrieval capabilities while being
efficient for real-world deployments. To achieve this, we develop WebGLM with
strategies for the LLM-augmented retriever, bootstrapped generator, and human
preference-aware scorer. Specifically, we identify and address the limitations
of WebGPT (OpenAI), through which WebGLM is enabled with accuracy, efficiency,
and cost-effectiveness advantages. In addition, we propose systematic criteria
for evaluating web-enhanced QA systems. We conduct multi-dimensional human
evaluation and quantitative ablation studies, which suggest the outperformance
of the proposed WebGLM designs over existing systems. WebGLM with the
10-billion-parameter GLM (10B) is shown to perform better than the
similar-sized WebGPT (13B) and even comparably to WebGPT (175B) in human
evaluation. The code, demo, and data are at
\url{https://github.com/THUDM/WebGLM}.


  A large body of literature reports that both bismuth vanadate and haematite
photoanodes are semiconductors with an extremely high doping density between
10^18-10^21 cm^-3. Such values are obtained from Mott-Schottky plots by
assuming that the measured capacitance is dominated by the capacitance of the
depletion layer formed by the doping density within the photoanode. In this
work, we show that such an assumption is erroneous in many cases because the
injection of electrons from the collecting contact creates a ubiquitous
capacitance step that is very difficult to distinguish from that of the
depletion layer. Based on this reasoning, we derive an analytical resolution
limit that is independent of the assumed active area and surface roughness of
the photoanode, below which doping densities cannot be measured in a
capacitance measurement. We find that the reported doping densities in
literature lie very close to this value and therefore conclude that there is no
credible evidence from capacitance measurements that confirms that bismuth
vanadate and haematite photoanodes contain high doping densities.


  In this article, we introduce a new cohomology theory associated to a Lie
2-algebras. This cohomology theory is shown to extend the classical cohomology
theory of Lie algebras; in particular, we show that the second cohomology group
classifies an appropriate type of extensions.


  In a recent PRL, Gonze et al claim that the density functional theory in
Hohenberg-Kohn formulation is not valid for crystalline solids in a homogenious
electric field. They introduce another theory, density-and-polarization
functional theory, which has to substitute the DFT in the calculations of the
long-wave dielectric response. We show that the theorem proven by Gonzo et al
holds in addition to, and not instead of, the Hohenberg-Kohn theorem.


  Tunneling between two-dimensional electron layers with mutually correlated
disorder potentials is studied theoretically. Due to this correlation, the
diffusive eigenstates in different layers are almost orthogonal to each other.
As a result, a peak in the tunnel I-V characteristics shifts towards small
bias, V. This "protects" the peak against the interaction-induced smearing,
since the relaxation rate near the Fermi level is low. If the correlation in
disorder potentials is complete, the peak position and width are governed by
the spin-orbit coupling in the layers; this coupling lifts the orthogonality of
the eigenstates. Possibility to use inter-layer tunneling for experimental
determination of weak intrinsic spin-orbit splitting of the Fermi surface is
discussed.


  From a group action on a space, define a variant of the configuration space
by insisting that no two points inhabit the same orbit. When the action is
almost free, this "orbit configuration space" is the complement of an
arrangement of subvarieties inside the cartesian product, and we use this
structure to study its topology. We give an abstract combinatorial description
of its poset of layers (connected components of intersections from the
arrangement) which turns out to be of much independent interest as a
generalization of partition and Dowling lattices. The close relationship to
these classical posets is then exploited to give explicit cohomological
calculations.


  The immersion of a single ion confined by a radiofrequency trap in an
ultracold atomic gas extends the concept of buffer gas cooling to a new
temperature regime. The steady state energy distribution of the ion is
determined by its kinetics in the radiofrequency field rather than the
temperature of the buffer gas. Moreover, the finite size of the ultracold gas
facilitates the observation of back-action of the ion onto the buffer gas. We
numerically investigate the system's properties depending on atom-ion mass
ratio, trap geometry, differential cross-section, and non-uniform neutral atom
density distribution. Experimental results are well reproduced by our model
considering only elastic collisions. We identify excess micromotion to set the
typical scale for the ion energy statistics and explore the applicability of
the mobility collision cross-section to the ultracold regime.


  Although language models (LMs) have boosted the performance of Question
Answering, they still need plenty of data. Data annotation, in contrast, is a
time-consuming process. This especially applies to Question Answering, where
possibly large documents have to be parsed and annotated with questions and
their corresponding answers. Furthermore, Question Answering models often only
work well for the domain they were trained on. Since annotation is costly, we
argue that domain-agnostic knowledge from LMs, such as linguistic
understanding, is sufficient to create a well-curated dataset. With this
motivation, we show that using large language models can improve Question
Answering performance on various datasets in the few-shot setting compared to
state-of-the-art approaches. For this, we perform data generation leveraging
the Prompting framework, suggesting that language models contain valuable
task-agnostic knowledge that can be used beyond the common
pre-training/fine-tuning scheme. As a result, we consistently outperform
previous approaches on few-shot Question Answering.


  Our primary result is that a demi-normal quasi-projective variety can be
embedded in a demi-normal projective variety. Recall that a demi-normal variety
$X$ is a variety with properties $S_2$, $G_1$, and seminormality. Equivalently,
$X$ has Serre's $S_2$ property and there is an open subvariety $U$ with
complement of codimension at least 2 in $X$, such that the only singularities
of $U$ are (analytically) double normal crossings. The term demi-normal was
coined by Koll\'ar in \cite{Kol13}. As a consequence of this embedding theorem,
we prove a semi-smooth Grauert-Riemenschneider vanishing theorem for
quasi-projective varieties, the projective case having been settled in
\cite{Berq14}. The original form of this vanishing result appears in
\cite{GR70}. We prove an analogous result for semi-rational singularities. The
definition of semi-rationality requires that the choice of a semi-resolution is
immaterial. This also has been established in the projective case in
\cite{Berq14}. The analogous result for quasi-projective varieties is settled
here. Semi-rational surface singularities have also been studied in
\cite{vS87}.


  We study the joint image of lines incident to points, meaning the set of
image tuples obtained from fixed cameras observing a varying 3D point-line
incidence. We prove a formula for the number of complex critical points of the
triangulation problem that aims to compute a 3D point-line incidence from noisy
images. Our formula works for an arbitrary number of images and measures the
intrinsic difficulty of this triangulation. Additionally, we conduct numerical
experiments using homotopy continuation methods, comparing different approaches
of triangulation of such incidences. In our setup, exploiting the incidence
relations gives both a faster point reconstruction and in three views more
accurate.


  We present an all-sky 90\% confidence level upper limit on the cosmic flux of
relativistic magnetic monopoles using 2886 days of IceCube data. The analysis
was optimized for monopole speeds between 0.750$c$ and 0.995$c$, without any
explicit restriction on the monopole mass. We constrain the flux of
relativistic cosmic magnetic monopoles to a level below $2.0\times 10^{-19}
{\textrm{cm}}^{-2} {\textrm{s}}^{-1} {\textrm{sr}}^{-1}$ over the majority of
the targeted speed range. This result constitutes the most strict upper limit
to date for magnetic monopoles above the Cherenkov threshold and up to $\beta
\sim 0.995$ and fills the gap between existing limits on the cosmic flux of
non-relativistic and ultrarelativistic magnetic monopoles


  The utility of chiral effective field theory, constructed in a manner in
which loop contributions are suppressed as one moves outside the power-counting
regime, is explored for baryon magnetic moments. Opportunities for the study of
significant chiral curvature in valence and full QCD and the nontrivial
behavior of strange- and light-quark contributions to the magnetic moment of
the Lambda baryon are highlighted.


  We calculate using loop expansion the effect of fluctuations on the structure
function and magnetization of the vortex lattice and compare it with existing
MC results. In addition to renormalization of the height of the Bragg peaks of
the structure function, there appears a characteristic saddle shape ''halos''
around the peaks. The effect of disorder on magnetization is also calculated.
All the infrared divergencies related to soft shear cancel.


  Studies suggest that one in three US adults use the Internet to diagnose or
learn about a health concern. However, such access to health information online
could exacerbate the disparities in health information availability and use.
Health information seeking behavior (HISB) refers to the ways in which
individuals seek information about their health, risks, illnesses, and
health-protective behaviors. For patients engaging in searches for health
information on digital media platforms, health literacy divides can be
exacerbated both by their own lack of knowledge and by algorithmic
recommendations, with results that disproportionately impact disadvantaged
populations, minorities, and low health literacy users. This study reports on
an exploratory investigation of the above challenges by examining whether
responsible and representative recommendations can be generated using advanced
analytic methods applied to a large corpus of videos and their metadata on a
chronic condition (diabetes) from the YouTube social media platform. The paper
focusses on biases associated with demographic characters of actors using
videos on diabetes that were retrieved and curated for multiple criteria such
as encoded medical content and their understandability to address patient
education and population health literacy needs. This approach offers an immense
opportunity for innovation in human-in-the-loop, augmented-intelligence,
bias-aware and responsible algorithmic recommendations by combining the
perspectives of health professionals and patients into a scalable and
generalizable machine learning framework for patient empowerment and improved
health outcomes.


  MET protein overexpression is a targetable event in non-small cell lung
cancer (NSCLC) and is the subject of active drug development. Challenges in
identifying patients for these therapies include lack of access to validated
testing, such as standardized immunohistochemistry (IHC) assessment, and
consumption of valuable tissue for a single gene/protein assay. Development of
pre-screening algorithms using routinely available digitized hematoxylin and
eosin (H&E)-stained slides to predict MET overexpression could promote testing
for those who will benefit most. While assessment of MET expression using IHC
is currently not routinely performed in NSCLC, next-generation sequencing is
common and in some cases includes RNA expression panel testing. In this work,
we leveraged a large database of matched H&E slides and RNA expression data to
train a weakly supervised model to predict MET RNA overexpression directly from
H&E images. This model was evaluated on an independent holdout test set of 300
over-expressed and 289 normal patients, demonstrating an ROC-AUC of 0.70 (95th
percentile interval: 0.66 - 0.74) with stable performance characteristics
across different patient clinical variables and robust to synthetic noise on
the test set. These results suggest that H&E-based predictive models could be
useful to prioritize patients for confirmatory testing of MET protein or MET
gene expression status.


  The prediction of stellar ($\gamma$,$\alpha$) reaction rates for heavy nuclei
is based on the calculation of ($\alpha$,$\gamma$) cross sections at
sub-Coulomb energies. These rates are essential for modeling the
nucleosynthesis of so-called $p$-nuclei. The standard calculations in the
statistical model show a dramatic sensitivity to the chosen $\alpha$-nucleus
potential. The present study explains the reason for this dramatic sensitivity
which results from the tail of the imaginary $\alpha$-nucleus potential in the
underlying optical model calculation of the total reaction cross section. As an
alternative to the optical model, a simple barrier transmission model is
suggested. It is shown that this simple model in combination with a well-chosen
$\alpha$-nucleus potential is able to predict total $\alpha$-induced reaction
cross sections for a wide range of heavy target nuclei above $A \gtrsim 150$
with uncertainties below a factor of two. The new predictions from the simple
model do not require any adjustment of parameters to experimental reaction
cross sections whereas in previous statistical model calculations all
predictions remained very uncertain because the parameters of the
$\alpha$-nucleus potential had to be adjusted to experimental data. The new
model allows to predict the reaction rate of the astrophysically important
$^{176}$W($\alpha$,$\gamma$)$^{180}$Os reaction with reduced uncertainties,
leading to a significantly lower reaction rate at low temperatures. The new
approach could also be validated for a broad range of target nuclei from $A
\approx 60$ up to $A \gtrsim 200$.


  We determine three invariants: Arnold's $J^+$-invariant as well as
$\mathcal{J}_1$ and $\mathcal{J}_2$ invariants, which were introduced by
Cieliebak-Frauenfelder-van Koert, of periodic orbits of the second kind near
the heavier primary in the restricted three-body problem, provided that the
mass ratio is sufficiently small.


  We report results from HST-NICMOS imaging of the extremely dense core of the
globular cluster Terzan 5. This highly obscured bulge cluster has been
estimated to have one of the highest collision rates of any galactic globular
cluster, making its core a particularly conducive environment for the
production of interacting binary systems. We have reconstructed high-resolution
images of the central 19"x19" region of Terzan 5 by application of the drizzle
algorithm to dithered NIC2 images in the F110W, F187W, and F187N near-infrared
filters. We have used a DAOPHOT/ALLSTAR analysis of these images to produce the
deepest color-magnitude diagram (CMD) yet obtained for the core of Terzan 5. We
have also analyzed the parallel 11"X11" NIC1 field, centered 30" from the
cluster center and imaged in F110W and F160W, and an additional NIC2 field that
is immediately adjacent to the central field. This imaging results in a clean
detection of the red-giant branch and horizontal branch in the central NIC2
field, and the detection of these plus the main-sequence turnoff and the upper
main sequence in the NIC1 field. We have constructed an H versus J-H CMD for
the NIC1 field. We obtain a new distance estimate of 8.7 kpc, which places
Terzan 5 within less than 1 kpc of the galactic center. We have also determined
a central surface-density profile which results in a maximum likelihood
estimate of 7.9" +/- 0.6" for the cluster core radius. We discuss the
implications of these results for the dynamical state of Terzan 5.


  3D scene flow estimation from point clouds is a low-level 3D motion
perception task in computer vision. Flow embedding is a commonly used technique
in scene flow estimation, and it encodes the point motion between two
consecutive frames. Thus, it is critical for the flow embeddings to capture the
correct overall direction of the motion. However, previous works only search
locally to determine a soft correspondence, ignoring the distant points that
turn out to be the actual matching ones. In addition, the estimated
correspondence is usually from the forward direction of the adjacent point
clouds, and may not be consistent with the estimated correspondence acquired
from the backward direction. To tackle these problems, we propose a novel
all-to-all flow embedding layer with backward reliability validation during the
initial scene flow estimation. Besides, we investigate and compare several
design choices in key components of the 3D scene flow network, including the
point similarity calculation, input elements of predictor, and predictor &
refinement level design. After carefully choosing the most effective designs,
we are able to present a model that achieves the state-of-the-art performance
on FlyingThings3D and KITTI Scene Flow datasets. Our proposed model surpasses
all existing methods by at least 38.2% on FlyingThings3D dataset and 24.7% on
KITTI Scene Flow dataset for EPE3D metric. We release our codes at
https://github.com/IRMVLab/3DFlow.


  The close relationship between the nature of the Triangulum-Andromeda
(TriAnd) overdensity and the Galactic disk has become increasingly evident in
recent years. However, the chemical pattern of this overdensity (R$_{GC}$ = 20
- 30 kpc) is unique and differs from what we know of the local disk. In this
study, we analyze the chemical abundances of five $\alpha$ elements (Mg, O, Si,
Ca, and Ti) in a sample of stars belonging to the TriAnd overdensity, including
stars with [Fe/H] $<$ $-$1.2, to investigate the evolution of the $\alpha$
elements with metallicity. High-resolution spectra from Gemini North with
GRACES were analyzed. Overall, the TriAnd population presents an
$\alpha$-element pattern that differs from that of the local disk; the TriAnd
stars fall in between the local disk and the dwarf galaxies in the [X/Fe] vs.
[Fe/H] plane. The high [Mg/Fe] ratios obtained for the lower metallicity TriAnd
stars may indicate a roughly parallel sequence to the Milky Way local disk at
lower values of [Fe/H], revealing a 'knee' shifted towards lower metallicities
for the TriAnd population. Similar behavior is also exhibited in the [Ca/Fe]
and [Si/Fe] ratios. However, for O and Ti the behavior of the [X/Fe] ratios
shows a slight decay with decreasing metallicity. Our results reinforce the
TriAnd overdensity as a unique stellar population of the Milky Way, with an
abundance pattern that is different from all stellar populations studied to
date. The complete understanding of the complex TriAnd population will require
high-resolution spectroscopic observations of a larger sample of TriAnd stars.


  An inclusive search for supersymmetric processes that produce final states
with jets and missing transverse energy is performed in pp collisions at a
centre-of-mass energy of 8 TeV. The data sample corresponds to an integrated
luminosity of 11.7 inverse femtobarns collected by the CMS experiment at the
LHC. In this search, a dimensionless kinematic variable, AlphaT, is used to
discriminate between events with genuine and misreconstructed missing
transverse energy. The search is based on an examination of the number of
reconstructed jets per event, the scalar sum of transverse energies of these
jets, and the number of these jets identified as originating from bottom
quarks. No significant excess of events over the standard model expectation is
found. Exclusion limits are set in the parameter space of simplified models,
with a special emphasis on both compressed-spectrum scenarios and direct or
gluino-induced production of third-generation squarks. For the case of
gluino-mediated squark production, gluino masses up to 950-1125 GeV are
excluded depending on the assumed model. For the direct pair-production of
squarks, masses up to 450 GeV are excluded for a single light first- or
second-generation squark, increasing to 600\GeV for bottom squarks.


  Sonoluminescence is a process in which a strong sound field is used to
produce light in liquids. We explain sonoluminescence as a phase transition
from ordinary fluorescence to a superradiant phase. We consider a spin-boson
model composed of a single bosonic mode and an ensemble of $N$ identical
two-level atoms. We assume that the whole system is in thermal equilibrium with
a reservoir at temperature $\beta^{-1}$. We show that, in a
ultrastrong-coupling regime, between the two-level atoms and the
electromagnetic field it is possible to have a cooperative interaction of the
molecules of the gas in the interior of the bubble with the field, generating
sonoluminescence.


  Let $s_2$ be the sum-of-digits function in base $2$, which returns the number
of non-zero binary digits of a nonnegative integer $n$. We study $s_2$ alon g
arithmetic subsequences and show that --- up to a shift --- the set of
$m$-tuples of integers that appear as an arithmetic subsequence of $s_2$ has
full complexity.


  In this paper, we solve the long standing open problem on exact
dimensionality of self-affine measures on the plane. We show that every
self-affine measure on the plane is exact dimensional regardless of the choice
of the defining iterated function system. In higher dimensions, under certain
assumptions, we prove that self-affine and quasi self-affine measures are exact
dimensional. In both cases, the measures satisfy the Ledrappier-Young formula.


  We study the effect of two Modified Gravity (MG) theories, $f(R)$ and nDGP,
on three probes of large-scale structure, the real space power spectrum
estimator $Q_0$, bispectrum and voids, and validate fast approximate COLA
simulations against full $N$-body simulations for the prediction of these
probes. We find that using the first three even multipoles of the redshift
space power spectrum to estimate $Q_0$ is enough to reproduce the MG boost
factors of the real space power spectrum for both halo and galaxy catalogues.
By analysing the bispectrum and reduced bispectrum of Dark Matter (DM), we show
that the strong MG signal present in the DM bispectrum is mainly due to the
enhanced power spectrum. We warn about adopting screening approximations in
simulations as this neglects non-linear contributions that can source a
significant component of the MG bispectrum signal at the DM level, but we argue
that this is not a problem for the bispectrum of galaxies in redshift space
where the signal is dominated by the non-linear galaxy bias. Finally, we
perform void-finding on our galaxy mock catalogues by the ZOBOV watershed
algorithm. To apply a linear model for Redshift-Space Distortion (RSD) in the
void-galaxy cross-correlation function, we first examine the effects of MG on
the void profiles entering into the RSD model. We find relevant MG signals in
the integrated-density, velocity dispersion and radial velocity profiles in the
nDGP theory. Fitting the RSD model for the linear growth rate, we recover the
linear theory prediction in an nDGP model, which is larger than the
$\Lambda$CDM prediction at the $3 \sigma$ level. In $f(R)$ theory we cannot
naively compare the results of the fit with the linear theory prediction as
this is scale-dependent, but we obtain results that are consistent with the
$\Lambda$CDM prediction.


  Single photons from a coherent input are efficiently redirected to a separate
output by way of a fiber-coupled microtoroidal cavity interacting with
individual Cesium atoms. By operating in an overcoupled regime for the
input-output to a tapered fiber, our system functions as a quantum router with
high efficiency for photon sorting. Single photons are reflected and excess
photons transmitted, as confirmed by observations of photon antibunching
(bunching) for the reflected (transmitted) light. Our photon router is robust
against large variations of atomic position and input power, with the observed
photon antibunching persisting for intracavity photon number 0.03 \lesssim n
\lesssim 0.7.


  Given two colorings of a graph, we consider the following problem: can we
recolor the graph from one coloring to the other through a series of elementary
changes, such that the graph is properly colored after each step?
  We introduce the notion of distributed recoloring: The input graph represents
a network of computers that needs to be recolored. Initially, each node is
aware of its own input color and target color. The nodes can exchange messages
with each other, and eventually each node has to stop and output its own
recoloring schedule, indicating when and how the node changes its color. The
recoloring schedules have to be globally consistent so that the graph remains
properly colored at each point, and we require that adjacent nodes do not
change their colors simultaneously.
  We are interested in the following questions: How many communication rounds
are needed (in the LOCAL model of distributed computing) to find a recoloring
schedule? What is the length of the recoloring schedule? And how does the
picture change if we can use extra colors to make recoloring easier?
  The main contributions of this work are related to distributed recoloring
with one extra color in the following graph classes: trees, $3$-regular graphs,
and toroidal grids.


  The rigidity theorems of Llarull and Marques-Neves, which show two different
ways scalar curvature can characterize the sphere, have associated stability
conjectures. Here we produce the first examples related to these stability
conjectures. The first set of examples demonstrates the necessity of including
a condition on the minimum area of all minimal surfaces to prevent bubbling
along the sequence. The second set of examples constructs sequences that do not
converge in the Gromov-Hausdorff sense but do converge in the volume preserving
intrinsic flat sense. In order to construct such sequences, we improve the
Gromov-Lawson tunnel construction so that one can attach wells and tunnels to a
manifold with scalar curvature bounded below and only decrease the scalar
curvature by an arbitrarily small amount. Moreover, we are able to generalize
both the sewing construction of Basilio, Dodziuk, and Sormani, and the
construction due to Basilio, Kazaras, and Sormani of an intrinsic flat limit
with no geodesics.