  The design of sparse linear arrays has proven instrumental in the
implementation of cost-effective and efficient automotive radar systems for
high-resolution imaging. This paper investigates the impact of coarse
quantization on measurements obtained from such arrays. To recover azimuth
angles from quantized measurements, we leverage the low-rank properties of the
constructed Hankel matrix. In particular, by addressing the one-bit Hankel
matrix completion problem through a developed singular value thresholding
algorithm, our proposed approach accurately estimates the azimuth angles of
interest. We provide comprehensive insights into recovery performance and the
required number of one-bit samples. The effectiveness of our proposed scheme is
underscored by numerical results, demonstrating successful reconstruction using
only one-bit data.


  In our work we investigate Witt equivalence of general function fields over
global fields. It is proven that for any two such fields K and L the Witt
equivalence induces a canonical bijection between Abhyankar valuations on K and
L having residue fields not finite of characteristic 2. The main tool used in
the proof is a method of constructing valuations due to Arason, Elman and
Jacob. Numerous applications are provided, in particular to Witt equivalence of
function fields over number fields: it is proven, among other things, that for
two number fields k and l the Witt equivalence between the fields
k(x_1,...,x_n) and l(x_1,...,x_n) implies that k and l are themselves Witt
equivalent and have equal 2-ranks of their ideal class groups.


  We present a comprehensive analysis of young stellar object (YSO) variability
within the M17 Southwest Extension (M17 SWex), using 3.5 years of monitoring
data from the JCMT Transient Survey at sub-millimeter (sub-mm) and 9 years from
the NEOWISE mission at mid-infrared (mid-IR). Our study encompasses
observations of 147 bright sub-mm peaks identified within our deep JCMT
co-added map as well as 156 YSOs in NEOWISE W1 and 179 in W2 that were
previously identified in Spitzer surveys. We find three robust sub-mm
variables: two are candidate YSOs and one is a likely extragalactic source. At
mid-IR wavelengths, our analysis reveals secular and stochastic variability in
47 YSOs, with the highest fraction of secular variability occurring at the
earliest evolutionary stage. This is similar to what has previously been
observed for low-mass YSO variability within the Gould Belt. However, we
observe less overall variability in M17SWex at both the sub-mm and mid-IR. We
suspect that this lower fraction is due to the greater distance to M17 SWex.
Our findings showcase the utility of multi-wavelength observations to better
capture the complex variability phenomena inherent to star formation processes
and demonstrate the importance of years-long monitoring of a diverse selection
of star-forming environments.


  Balmer recently showed that there is a general notion of a nilpotence theorem
for tensor triangulated categories through the use of homological residue
fields and the connection with the homological spectrum. The homological
spectrum (like the theory of $\pi$-points) can be viewed as a topological space
that provides an important realization of the Balmer spectrum.
  Let ${\mathfrak g}={\mathfrak g}_{\bar{0}}\oplus {\mathfrak g}_{\bar{1}}$ be
a classical Lie superalgebra over ${\mathbb C}$. In this paper, the authors
consider the tensor triangular geometry for the stable category of
finite-dimensional Lie superalgebra representations: $\text{stab}({\mathcal
F}_{({\mathfrak g},{\mathfrak g}_{\bar{0}})})$, The localizing subcategories
for the detecting subalgebra ${\mathfrak f}$ are classified which answers a
question of Boe, Kujawa, and Nakano. As a consequence of these results, the
authors prove a nilpotence theorem and determine the homological spectrum for
the stable module category of ${\mathcal F}_{({\mathfrak f},{\mathfrak
f}_{\bar{0}})}$. The authors verify Balmer's ``Nerves of Steel'' Conjecture for
${\mathcal F}_{({\mathfrak f},{\mathfrak f}_{\bar{0}})}$.
  Let $F$ (resp. $G$) be the associated supergroup (scheme) for ${\mathfrak f}$
(resp. ${\mathfrak g}$). Under the condition that $F$ is a splitting subgroup
for $G$, the results for the detecting subalgebra can be used to prove a
nilpotence theorem for $\text{stab}({\mathcal F}_{({\mathfrak g},{\mathfrak
g}_{\bar{0}})})$, and to determine the homological spectrum in this case. Now
using natural assumptions in terms of realization of supports, the authors
provide a method to explicitly realize the Balmer spectrum of
$\text{stab}({\mathcal F}_{({\mathfrak g},{\mathfrak g}_{\bar{0}})})$, and
prove the Nerves of Steel Conjecture in this case.


  A high-precision mass measurement for the pentaquark (5Q) Theta^+ in
J^P=3/2^{\pm} channel is performed in anisotropic quenched lattice QCD using a
large number of gauge configurations as N_{conf}=1000. We employ the standard
Wilson gauge action at beta=5.75 and the O(a) improved Wilson (clover) quark
action with kappa=0.1210(0.0010)0.1240 on a 12^3 \times 96 lattice with the
renormalized anisotropy as a_s/a_t = 4. The Rarita-Schwinger formalism is
adopted for the interpolating fields. Several types of the interpolating fields
with isospin I=0 are examined such as (a) the NK^*-type, (b) the
(color-)twisted NK^*-type, (c) a diquark-type. The chiral extrapolation leads
to only massive states, i.e., m_{5Q} \simeq 2.1-2.2 GeV in J^P=3/2^- channel,
and m_{5Q} = 2.4-2.6 GeV in J^P=3/2^+ channel. The analysis with the hybrid
boundary condition(HBC) is performed to investigate whether these states are
compact 5Q resonances or not. No low-lying compact 5Q resonance states are
found below 2.1GeV.


  A fundamental challenge for wide-field imaging surveys is obtaining follow-up
spectroscopic observations: there are > $10^9$ photometrically cataloged
sources, yet modern spectroscopic surveys are limited to ~few x $10^6$ targets.
As we approach the Large Synoptic Survey Telescope (LSST) era, new algorithmic
solutions are required to cope with the data deluge. Here we report the
development of a machine-learning framework capable of inferring fundamental
stellar parameters (Teff, log g, and [Fe/H]) using photometric-brightness
variations and color alone. A training set is constructed from a systematic
spectroscopic survey of variables with Hectospec/MMT. In sum, the training set
includes ~9000 spectra, for which stellar parameters are measured using the
SEGUE Stellar Parameters Pipeline (SSPP). We employed the random forest
algorithm to perform a non-parametric regression that predicts Teff, log g, and
[Fe/H] from photometric time-domain observations. Our final, optimized model
produces a cross-validated root-mean-square error (RMSE) of 165 K, 0.39 dex,
and 0.33 dex for Teff, log g, and [Fe/H], respectively. Examining the subset of
sources for which the SSPP measurements are most reliable, the RMSE reduces to
125 K, 0.37 dex, and 0.27 dex, respectively, comparable to what is achievable
via low-resolution spectroscopy. For variable stars this represents a ~12-20%
improvement in RMSE relative to models trained with single-epoch photometric
colors. As an application of our method, we estimate stellar parameters for
~54,000 known variables. We argue that this method may convert photometric
time-domain surveys into pseudo-spectrographic engines, enabling the
construction of extremely detailed maps of the Milky Way, its structure, and
history.


  In this paper, we consider elliptic differential operators on compact
manifolds with a random perturbation in the 0th order term and show under
fairly weak additional assumptions that the large eigenvalues almost surely
distribute according to the Weyl law, well-known in the self-adjoint case.


  Cherkis bow varieties were introduced as ADHM type description of moduli
space of instantons on the Taub-NUT space equivariant under a cyclic group
action. They are also models of Coulomb branches of quiver gauge theories of
affine type A. In this paper, we realize each bow variety with torus fixed
points as a symplectic reduction of a cotangent bundle of a partial flag
variety by a unipotent group, and find a slice of this action. By this
description, we calculate the equivariant cohomology (and ordinary cohomology)
of some of them and answer some questions raisedbefore. This also uses a new
result about circle-equivariant cohomology proven in an appendix. We also give
an explicit generalized Mirkovic-Vybornov isomorphism for bow varieties in the
appendix.


  For rearranging objects on tabletops with overhand grasps, temporarily
relocating objects to some buffer space may be necessary. This raises the
natural question of how many simultaneous storage spaces, or "running buffers",
are required so that certain classes of tabletop rearrangement problems are
feasible. In this work, we examine the problem for both labeled and unlabeled
settings. On the structural side, we observe that finding the minimum number of
running buffers (MRB) can be carried out on a dependency graph abstracted from
a problem instance, and show that computing MRB is NP-hard. We then prove that
under both labeled and unlabeled settings, even for uniform cylindrical
objects, the number of required running buffers may grow unbounded as the
number of objects to be rearranged increases. We further show that the bound
for the unlabeled case is tight. On the algorithmic side, we develop effective
exact algorithms for finding MRB for both labeled and unlabeled tabletop
rearrangement problems, scalable to over a hundred objects under very high
object density. More importantly, our algorithms also compute a sequence
witnessing the computed MRB that can be used for solving object rearrangement
tasks. Employing these algorithms, empirical evaluations reveal that random
labeled and unlabeled instances, which more closely mimics real-world setups,
generally have fairly small MRBs. Using real robot experiments, we demonstrate
that the running buffer abstraction leads to state-of-the-art solutions for
in-place rearrangement of many objects in tight, bounded workspace.


  This paper proposes a new method that fuses acoustic measurements in the
reverberation field and low-accuracy inertial measurement unit (IMU) motion
reports for simultaneous localization and mapping (SLAM). Different from
existing studies that only use acoustic data for direction-of-arrival (DoA)
estimates, the source's distance from sensors is calculated with the
direct-to-reverberant energy ratio (DRR) and applied as a new constraint to
eliminate the nonlinear noise from motion reports. A particle filter is applied
to estimate the critical distance, which is key for associating the source's
distance with the DRR. A keyframe method is used to eliminate the deviation of
the source position estimation toward the robot. The proposed DoA-DRR acoustic
SLAM (D-D SLAM) is designed for three-dimensional motion and is suitable for
most robots. The method is the first acoustic SLAM algorithm that has been
validated on a real-world indoor scene dataset that contains only acoustic data
and IMU measurements. Compared with previous methods, D-D SLAM has acceptable
performance in locating the robot and building a source map from a real-world
indoor dataset. The average location accuracy is 0.48 m, while the source
position error converges to less than 0.25 m within 2.8 s. These results prove
the effectiveness of D-D SLAM in real-world indoor scenes, which may be
especially useful in search and rescue missions after disasters where the
environment is foggy, i.e., unsuitable for light or laser irradiation.


  In this paper we prove the following: (1) The basic error of time-dependent
perturbation theory is using the sum of first finite order of perturbed
solutions to substitute the exact solution in the divergent interval of the
series for calculating the transition probability. In addition quantum
mechanics neglects the influence of the normality condition in the continuous
case. In both cases Fermi golden rule is not a mathematically reasonable
deductive inference from the Schrodinger equation. (2) The transition
probability per unit time deduced from the exact solution of the Schrodinger
equation is zero, which cannot be used to describe the transition processes.


  We consider a market in which capacity-constrained generators compete in
scalar-parameterized supply functions to serve an inelastic demand spread
throughout a transmission constrained power network. The market clears
according to a locational marginal pricing mechanism, in which the independent
system operator (ISO) determines the generators' production quantities to
minimize the revealed cost of meeting demand, while ensuring that network
transmission and generator capacity constraints are met. Under the stylizing
assumption that both the ISO and generators choose their strategies
simultaneously, we establish the existence of Nash equilibria for the
underlying market, and derive an upper bound on the allocative efficiency loss
at Nash equilibrium relative to the socially optimal level. We also
characterize an upper bound on the markup of locational marginal prices at Nash
equilibrium above their perfectly competitive levels. Of particular relevance
to ex ante market power monitoring, these bounds reveal the role of certain
market structures---specifically, the \emph{market share} and \emph{residual
supply index} of a producer---in predicting the degree to which that producer
is able to exercise market power to influence the market outcome to its
advantage. Finally, restricting our attention to the simpler setting of a
two-node power network, we provide a characterization of market structures
under which a Braess-like paradox occurs due to the exercise of market
power---that is to say, we provide a necessary and sufficient condition on
market structure under which the strengthening of the network's transmission
line capacity results in the (counterintuitive) increase in the total cost of
generation at Nash equilibrium.


  Small 3He-rich solar energetic particle (SEP) events have been commonly
associated with extreme-ultraviolet (EUV) jets and narrow coronal mass
ejections (CMEs) which are believed to be the signatures of magnetic
reconnection involving field lines open to interplanetary space. The elemental
and isotopic fractionation in these events are thought to be caused by
processes confined to the flare sites. In this study we identify 32 3He-rich
SEP events observed by the Advanced Composition Explorer near the Earth during
the solar minimum period 2007-2010 and examine their solar sources with the
high resolution Solar Terrestrial Relations Observatory (STEREO) EUV images.
Leading the Earth, STEREO-A provided for the first time a direct view on
3He-rich flares, which are generally located on the Sun's western hemisphere.
Surprisingly, we find that about half of the 3He-rich SEP events in this survey
are associated with large-scale EUV coronal waves. An examination of the wave
front propagation, the source-flare distribution and the coronal magnetic field
connections suggests that the EUV waves may affect the injection of 3He-rich
SEPs into interplanetary space.


  We demonstrate analytically and numerically that focusing of high harmonics
produced by the reflection of a few femtosecond laser pulse from a concave
plasma surface opens a new way towards unprecedentally high intensities. The
key features allowing for boosting of the focal intensity is the harmonic
coherency and the small exponent of the power-law decay of the harmonic
spectrum. Using the similarity theory and direct particle-in-cell simulations
we find that the intensity at the Coherent Harmonic Focus (CHF) scales as
$I_{\tiny CHF} \propto a_0^3 I_0$, where $a_0$ and $I_0\propto a_0^2$ are the
dimensionless relativistic amplitude and the intensity of the incident laser
pulse. The scaling suggests that due to the CHF, the Schwinger intensity limit
can be achieved using lasers with $I_0 \approx 10^{22}$ W/cm$^2$. The pulse
duration at the focus scales as $\tau_{\tiny CHF} \propto 1/a_0^2$ and reaches
the subattosecond range.


  In the recent past, a property of neural training trajectories in
weight-space had been isolated, that of "local elasticity" (denoted as $S_{\rm
rel}$). Local elasticity attempts to quantify the propagation of the influence
of a sampled data point on the prediction at another data. In this work, we
embark on a comprehensive study of the existing notion of $S_{\rm rel}$ and
also propose a new definition that addresses the limitations that we point out
for the original definition in the classification setting. On various
state-of-the-art neural network training on SVHN, CIFAR-10 and CIFAR-100 we
demonstrate how our new proposal of $S_{\rm rel}$, as opposed to the original
definition, much more sharply detects the property of the weight updates
preferring to make prediction changes within the same class as the sampled
data.
  In neural regression experiments we demonstrate that the original $S_{\rm
rel}$ reveals a $2-$phase behavior -- that the training proceeds via an initial
elastic phase when $S_{\rm rel}$ changes rapidly and an eventual inelastic
phase when $S_{\rm rel}$ remains large. We show that some of these properties
can be analytically reproduced in various instances of doing regression via
gradient flows on model predictor classes.


  The ratio $R_p$ between the electric and magnetic proton form factors has
been recently measured at JLab up to $Q^2=8.5 ~GeV^2$. We have extended the
calculation of the nucleon form factors with the hypercentral Constituent Quark
Model and compared them with the data on $R_p$ and on the $Q^2$ behavior of the
ratio $Q^2 F_2/F_1$. In both cases the theoretical curves agree with the
experimental points.


  Many password alternatives for web authentication proposed over the years,
despite having different designs and objectives, all predominantly rely on the
knowledge of some secret. This motivates us, herein, to provide the first
detailed exploration of the integration of a fundamentally different element of
defense into the design of web authentication schemes: a mimicry-resistance
dimension. We analyze web authentication mechanisms with respect to new
usability and security properties related to mimicry-resistance (augmenting the
UDS framework), and in particular evaluate invisible techniques (those
requiring neither user actions, nor awareness) that provide some
mimicry-resistance (unlike those relying solely on static secrets), including
device fingerprinting schemes, PUFs (physically unclonable functions), and a
subset of Internet geolocation mechanisms.


  In this short note, we study the geometry of the eigenvariety parametrising
p-adic automorphic forms for GL(1) over a number field K, as constructed by
Buzzard. We show that if K is not totally real and contains no CM subfield,
points in this space arising from classical automorphic forms (i.e. algebraic
Grossencharacters of K) are not Zariski-dense in the eigenvariety (as a rigid
space); but the eigenvariety posesses a natural formal scheme model, and the
set of classical points is Zariski-dense in the formal scheme.
  We also sketch the theory for GL(2) over an imaginary quadratic field,
following Calegari and Mazur, emphasising the strong formal similarity with the
case of GL(1) over a general number field.


  Automatically understanding the contents of an image is a highly relevant
problem in practice. In e-commerce and social media settings, for example, a
common problem is to automatically categorize user-provided pictures. Nowadays,
a standard approach is to fine-tune pre-trained image models with
application-specific data. Besides images, organizations however often also
collect collaborative signals in the context of their application, in
particular how users interacted with the provided online content, e.g., in
forms of viewing, rating, or tagging. Such signals are commonly used for item
recommendation, typically by deriving latent user and item representations from
the data. In this work, we show that such collaborative information can be
leveraged to improve the classification process of new images. Specifically, we
propose a multitask learning framework, where the auxiliary task is to
reconstruct collaborative latent item representations. A series of experiments
on datasets from e-commerce and social media demonstrates that considering
collaborative signals helps to significantly improve the performance of the
main task of image classification by up to 9.1%.


  We define and study a combinatorial Hopf algebra dRec with basis elements
indexed by diagonal rectangulations of a square. This Hopf algebra provides an
intrinsic combinatorial realization of the Hopf algebra tBax of twisted Baxter
permutations, which previously had only been described extrinsically as a sub
Hopf algebra of the Malvenuto-Reutenauer Hopf algebra of permutations. We
describe the natural lattice structure on diagonal rectangulations, analogous
to the Tamari lattice on triangulations, and observe that diagonal
rectangulations index the vertices of a polytope analogous to the
associahedron. We give an explicit bijection between twisted Baxter
permutations and the better-known Baxter permutations, and describe the
resulting Hopf algebra structure on Baxter permutations.


  On simply connected five manifolds Sasakian-Einstein metrics coincide with
Riemannian metrics admitting real Killing spinors which are of great interest
as models of near horizon geometry for three-brane solutions in superstring
theory [KW]. We expand on the recent work of Demailly and Koll\'ar [DK] and
Johnson and Koll\'ar [JK1] who give methods for constructing K\"ahler-Einstein
metrics on log del Pezzo surfaces. By [BG1] circle V-bundles over log del Pezzo
surfaces with K\"ahler-Einstein metrics have Sasakian-Einstein metrics on the
total space of the bundle. Here these simply connected 5-manifolds arise as
links of isolated hypersurface singularities which by the well known work of
Smale [Sm] together with [BG3] must be diffeomorphic to
$\scriptstyle{S^5#l(S^2\times S^3)}.$ More precisely, using methods from Mori
theory in algebraic geometry we prove the existence of 14 inequivalent
Sasakian-Einstein structures on $\scriptstyle{S^2\times S^3}$ and infinite
families of such structures on $\scriptstyle{#l(S^2\times S^3)}$ with
$\scriptstyle{2\leq l\leq7}$. We also discuss the moduli problem for these
Sasakian-Einstein structures.


  The proposed International Linear Collider (ILC) is well-suited for
discovering physics beyond the Standard Model and for precisely unravelling the
structure of the underlying physics. The physics return of the ILC can be
maximized by the use of polarized beams, in particular the simultaneous
polarization of the e- and the e+ beam. Ongoing physics studies are accompanied
by active R&D on the machine part for generating polarized beams and for
measuring the polarization with high precision at the ILC. Some new results on
the physics case and on the technical aspects of the polarization of both beams
are briefly summarized.


  With the emergence of Artificial Intelligent chatbot tools such as ChatGPT
and code writing AI tools such as GitHub Copilot, educators need to question
what and how we should teach our courses and curricula in the future. In
reality, automated tools may result in certain academic fields being deeply
reduced in the number of employable people. In this work, we make a case study
of cybersecurity undergrad education by using the lens of ``Understanding by
Design'' (UbD). First, we provide a broad understanding of learning objectives
(LOs) in cybersecurity from a computer science perspective. Next, we dig a
little deeper into a curriculum with an undergraduate emphasis on cybersecurity
and examine the major courses and their LOs for our cybersecurity program at
Miami University. With these details, we perform a thought experiment on how
attainable the LOs are with the above-described tools, asking the key question
``what needs to be enduring concepts?'' learned in this process. If an LO
becomes something that the existence of automation tools might be able to do,
we then ask ``what level is attainable for the LO that is not a simple query to
the tools?''. With this exercise, we hope to establish an example of how to
prompt ChatGPT to accelerate students in their achievements of LOs given the
existence of these new AI tools, and our goal is to push all of us to leverage
and teach these tools as powerful allies in our quest to improve human
existence and knowledge.


  We consider non-local currents in the context of quantized affine algebras,
following the construction introduced by Bernard and Felder. In the case of
$U_q(A_1^{(1)})$ and $U_q(A_2^{(2)})$, these currents can be identified with
configurations in the six-vertex and Izergin--Korepin nineteen-vertex models.
Mapping these to their corresponding Temperley--Lieb loop models, we directly
identify non-local currents with discretely holomorphic loop observables. In
particular, we show that the bulk discrete holomorphicity relation and its
recently derived boundary analogue are equivalent to conservation laws for
non-local currents.


  Recently, Capsule Networks (CapsNets) have shown improved performance
compared to the traditional Convolutional Neural Networks (CNNs), by encoding
and preserving spatial relationships between the detected features in a better
way. This is achieved through the so-called Capsules (i.e., groups of neurons)
that encode both the instantiation probability and the spatial information.
However, one of the major hurdles in the wide adoption of CapsNets is their
gigantic training time, which is primarily due to the relatively higher
complexity of their new constituting elements that are different from CNNs. In
this paper, we implement different optimizations in the training loop of the
CapsNets, and investigate how these optimizations affect their training speed
and the accuracy. Towards this, we propose a novel framework FasTrCaps that
integrates multiple lightweight optimizations and a novel learning rate policy
called WarmAdaBatch (that jointly performs warm restarts and adaptive batch
size), and steers them in an appropriate way to provide high training-loop
speedup at minimal accuracy loss. We also propose weight sharing for capsule
layers. The goal is to reduce the hardware requirements of CapsNets by removing
unused/redundant connections and capsules, while keeping high accuracy through
tests of different learning rate policies and batch sizes. We demonstrate that
one of the solutions generated by the FasTrCaps framework can achieve 58.6%
reduction in the training time, while preserving the accuracy (even 0.12%
accuracy improvement for the MNIST dataset), compared to the CapsNet by Google
Brain. The Pareto-optimal solutions generated by FasTrCaps can be leveraged to
realize trade-offs between training time and achieved accuracy. We have
open-sourced our framework on https://github.com/Alexei95/FasTrCaps.


  The (3+1)D relativistic hydrodynamics with chiral anomaly is used to obtain a
quantitative description of the chiral magnetic effect (CME) in heavy-ion
collisions. We find that the charge-dependent hadron azimuthal correlations are
sensitive to the CME, and that the experimental observations are consistent
with the presence of the effect.


  We give an evidence of the Big Fix. The theory of wormholes and multiverse
suggests that the parameters of the Standard Model are fixed in such a way that
the total entropy at the late stage of the universe is maximized, which we call
the maximum entropy principle. In this paper, we discuss how it can be
confirmed by the experimental data, and we show that it is indeed true for the
Higgs vacuum expectation value $v_{h}$. We assume that the baryon number is
produced by the sphaleron process, and that the current quark masses, the gauge
couplings and the Higgs self coupling are fixed when we vary $v_{h}$. It turns
out that the existence of the atomic nuclei plays a crucial role to maximize
the entropy. This is reminiscent of the anthropic principle, however it is
required by the fundamental low in our case.


  A topological space $X$ is called Piotrowski if every quasicontinuous map
$f:Z\to X$ from a Baire space $Z$ to $X$ has a continuity point. In this paper
we survey known results on Piotrowski spaces and investigate the relation of
Piotrowski spaces to strictly fragmentable, Stegall, and game determined
spaces. Also we prove that a Piotrowski Tychonoff space $X$ contains a dense
(completely) metrizable Baire subspace if and only if $X$ is Baire (Choquet).


  In this paper, we propose a distributed reinforcement learning (RL) technique
called distributed power control using Q-learning (DPC-Q) to manage the
interference caused by the femtocells on macro-users in the downlink. The DPC-Q
leverages Q-Learning to identify the sub-optimal pattern of power allocation,
which strives to maximize femtocell capacity, while guaranteeing macrocell
capacity level in an underlay cognitive setting. We propose two different
approaches for the DPC-Q algorithm: namely, independent, and cooperative. In
the former, femtocells learn independently from each other while in the latter,
femtocells share some information during learning in order to enhance their
performance. Simulation results show that the independent approach is capable
of mitigating the interference generated by the femtocells on macro-users.
Moreover, the results show that cooperation enhances the performance of the
femtocells in terms of speed of convergence, fairness and aggregate femtocell
capacity.


  In this work we study genus one fibrations in Calabi-Yau three-folds with a
non-trivial first fundamental group. The manifolds under consideration are
constructed as smooth quotients of complete intersection Calabi-Yau three-folds
(CICYs) by a freely acting, discrete automorphism. By probing the compatibility
of symmetries with genus one fibrations (that is, discrete group actions which
preserve a local decomposition of the manifold into fiber and base) we find
fibrations that are inherited from fibrations on the covering spaces. Of the
7,890 CICY three-folds, 195 exhibit known discrete symmetries, leading to a
total of 1,695 quotient manifolds. By scanning over 20,700 fiber/symmetry pairs
on the covering spaces we find 17,161 fibrations on the quotient Calabi-Yau
manifolds. It is found that the vast majority of the non-simply connected
manifolds studied exhibit multiple different genus one fibrations - echoing a
similar ubiquity of such structures that has been observed in other data sets.
The results are available at http://www1.phys.vt.edu/quotientdata/. The
possible base manifolds are all singular and are catalogued. These Calabi-Yau
fibrations generically exhibit multiple fibers and are of interest in F-theory
as backgrounds leading to theories with superconformal loci and discretely
charged matter.


  The power method and block Lanczos method are popular numerical algorithms
for computing the truncated singular value decomposition (SVD) and eigenvalue
decomposition problems. Especially in the literature of randomized numerical
linear algebra, the power method is widely applied to improve the quality of
randomized sketching, and relative-error bounds have been well established.
Recently, Musco & Musco (2015) proposed a block Krylov subspace method that
fully exploits the intermediate results of the power iteration to accelerate
convergence. They showed spectral gap-independent bounds which are stronger
than the power method by order-of-magnitude. This paper offers novel error
analysis techniques and significantly improves the bounds of both the
randomized power method and the block Lanczos method. This paper also
establishes the first gap-independent bound for the warm-start block Lanczos
method.


  Moir\'e materials, and in particular twisted bilayer graphene (TBG), exhibit
a range of fascinating phenomena, that emerge from the interplay of band
topology and interactions. We show that the non-linear second-order
photoresponse is an appealing probe of this rich interplay. A dominant part of
the photoresponse is the shift-current, which is determined by the geometry of
the electronic wavefunctions and carrier properties, and thus becomes strongly
modified by electron-electron interactions. We analyze its dependence on the
twist angle and doping, and investigate the role of interactions. In the
absence of interactions, the response of the system is dictated by two energy
scales: the mean energy of direct transitions between the hole and electron
flat bands, and the gap between flat and dispersive bands. Including
electron-electron interactions, both enhance the response at the
non-interacting characteristic frequencies as well as produce new resonances.
We attribute these changes to the filling-dependent band renormalization in
TBG. Our results highlight the connection between non-trivial geometric
properties of TBG and its optical response, as well as demonstrate how optical
probes can access the role of interactions in moi\'re materials.


  In this paper, we discuss long-time behavior of sample paths for a wide range
of regime-switching diffusions. Firstly, almost sure asymptotic stability is
concerned (i) for regime-switching diffusions with finite state spaces by the
Perron-Frobenius theorem, and, with regard to the case of reversible Markov
chain, via the principal eigenvalue approach; (ii) for regime-switching
diffusions with countable state spaces by means of a finite partition trick and
an M-Matrix theory. We then apply our theory to study the stabilization for
linear switching models. Several examples are given to demonstrate our theory.


  The case experience of anesthesiologists is one of the leading causes of
accidental dural punctures and failed epidurals - the most common complications
of epidural analgesia used for pain relief during delivery. We designed a
bimanual haptic simulator to train anesthesiologists and optimize epidural
analgesia skill acquisition. We present an assessment study conducted with 22
anesthesiologists of different competency levels from several Israeli
hospitals. Our simulator emulates the forces applied to the epidural (Touhy)
needle, held by one hand, and those applied to the Loss of Resistance (LOR)
syringe, held by the other one. The resistance is calculated based on a model
of the epidural region layers parameterized by the weight of the patient. We
measured the movements of both haptic devices and quantified the results' rate
(success, failed epidurals, and dural punctures), insertion strategies, and the
participants' answers to questionnaires about their perception of the
simulation realism. We demonstrated good construct validity by showing that the
simulator can distinguish between real-life novices and experts. Face and
content validity were examined by studying users' impressions regarding the
simulator's realism and fulfillment of purpose. We found differences in
strategies between different level anesthesiologists, and suggest trainee-based
instruction in advanced training stages.


  One core goal of the Kepler mission was to determine the frequency of
Earth-like planets that orbit Sun-like stars. Accurately estimating this planet
occurrence rate requires both a well-vetted list of planets and a clear
understanding of the stars searched for planets. Previous ground-based
follow-up observations have, through a variety of methods, sought to improve
our knowledge of stars that are known to host planets. Kepler targets without
detected planets, however, have not been subjected to the same intensity of
follow-up observations. In this paper, we better constrain stellar multiplicity
for stars around which Kepler could have theoretically detected a transiting
Earth-sized planet in the habitable zone. We subsequently aim to improve
estimates of the exoplanet search completeness -- the fraction of exoplanets
that were detected by Kepler -- with our analysis. By obtaining adaptive optics
observations of 71 Kepler target stars from the Shane 3-m telescope at Lick
Observatory, we detected 14 candidate stellar companions within 4'' of 13
target stars. Of these 14 candidate stellar companions, we determine through
multiple independent methods that 3 are likely to be bound to their
corresponding target star. We then assess the impact of our observations on
exoplanet occurrence rate calculations, finding an increase in occurrence of 6%
(0.9 $\sigma$) for various estimates of the frequency of Earth-like planets and
an increase of 26% (4.5 $\sigma$) for super-Earths and sub-Neptunes. These
occurrence increases are not entirely commensurate with theoretical
predictions, though this discrepancy may be due to differences in the treatment
of stellar binarity.


  Existing investigations of the anomalous Hall effect i.e. a current flowing
transverse to the electric field in the absence of an external magnetic field)
are concerned with the transport current. However, for many applications one
needs to know the total current, including its pure magnetization part. In this
paper, we employ the two-dimensional massive Dirac equation to find the exact
universal total current flowing along a potential step of arbitrary shape. For
a spatially slowly varying potential we find the current density
$\mathbf{j}(\vec r)$ and the energy distribution of the current density
$\mathbf{j}^\varepsilon(\vec r)$. The latter turns out to be unexpectedly
nonuniform, behaving like a $\delta$-function at the border of the classically
accessible area at energy~$\varepsilon$. To demonstrate explicitly the
difference between the magnetization and transport currents we consider the
transverse shift of an electron ray in an electric field.


  A critical feature in signal processing is the ability to interpret
correlations in time series signals, such as speech. Machine learning systems
process this contextual information by tracking internal states in recurrent
neural networks (RNNs), but these can cause memory and processor bottlenecks in
applications from edge devices to data centers, motivating research into new
analog inference architectures. But whereas photonic accelerators, in
particular, have demonstrated big leaps in uni-directional feedforward deep
neural network (DNN) inference, the bi-directional architecture of RNNs
presents a unique challenge: the need for a short-term memory that (i)
programmably transforms optical waveforms with phase coherence , (ii) minimizes
added noise, and (iii) enables programmable readily scales to large neuron
counts. Here, we address this challenge by introducing an optoacoustic
recurrent operator (OREO) that simultaneously meets (i,ii,iii). Specifically,
we experimentally demonstrate an OREO that contextualizes and computes the
information carried by a sequence of optical pulses via acoustic waves. We show
that the acoustic waves act as a link between the different optical pulses,
capturing the optical information and using it to manipulate the subsequent
operations. Our approach can be controlled completely optically on a
pulse-by-pulse basis, offering simple reconfigurability for a use case-specific
optimization. We use this feature to demonstrate a recurrent drop-out, which
excludes optical input pulses from the recurrent operation. We furthermore
apply OREO as an acceptor to recognize up-to $27$ patterns in a sequence of
optical pulses. Finally, we introduce a DNN architecture that uses the OREO as
bi-directional perceptrons to enable new classes of DNNs in coherent optical
signal processing.


  Hitchin pairs on Riemann surfaces are generalizations of Higgs bundles,
allowing the Higgs field to be twisted by an arbitrary line bundle. We consider
this generalization in the context of $G$-Higgs bundles for a real reductive
Lie group $G$. We outline the basic theory and review some selected results,
including recent results by Nozad and the author arXiv:1602.02712 [math.AG] on
Hitchin pairs for the unitary group of indefinite signature $\mathrm{U}(p,q)$.


  We address the problem of estimating the state of a differentially flat
system from measurements that may be corrupted by an adversarial attack. In
cyber-physical systems, malicious attacks can directly compromise the system's
sensors or manipulate the communication between sensors and controllers. We
consider attacks that only corrupt a subset of sensor measurements. We show
that the possibility of reconstructing the state under such attacks is
characterized by a suitable generalization of the notion of s-sparse
observability, previously introduced by some of the authors in the linear case.
We also extend our previous work on the use of Satisfiability Modulo Theory
solvers to estimate the state under sensor attacks to the context of
differentially flat systems. The effectiveness of our approach is illustrated
on the problem of controlling a quadrotor under sensor attacks.


  Gaussian elimination with partial pivoting (GEPP) has long been among the
most widely used methods for computing the LU factorization of a given matrix.
However, this method is also known to fail for matrices that induce large
element growth during the factorization process. In this paper, we propose a
new scheme, Gaussian elimination with randomized complete pivoting (GERCP) for
the efficient and reliable LU factorization of a given matrix. GERCP satisfies
GECP (Gaussian elimination with complete pivoting) style element growth bounds
with high probability, yet costs only marginally higher than GEPP. Our
numerical experimental results strongly suggest that GERCP is as reliable as
GECP and as efficient as GEPP for computing the LU factorization.


  We consider the discrete, time-varying broadcast channel with memory under
the assumption that the channel states belong to a set of finite cardinality.
We first define the physically degraded finite-state broadcast channel for
which we derive the capacity region. We then define the stochastically degraded
finite-state broadcast channel and derive the capacity region for this scenario
as well. In both scenarios we consider the non-indecomposable finite-state
channel as well as the indecomposable one.


  The Mermin-Klyshko inequality for n spin-1/2 particles and two dichotomic
observables is generalized to n spin-s particles and two maximal observables.
It is shown that some multiparty multilevel Greenberger-Horne-Zeilinger states
[A. Cabello, Phys. Rev. A 63, 022104 (2001)] maximally violate this inequality
for any s. For a fixed n, the magnitude of the violation is constant for any s,
which provides a simple demonstration and generalizes the conclusion reached by
Gisin and Peres for two spin-s particles in the singlet state [Phys. Lett. A
162, 15 (1992)]. For a fixed s, the violation grows exponentially with n, which
provides a generalization to any s of Mermin's conclusion for n spin-1/2
particles [Phys. Rev. Lett. 65, 1838 (1990)].


  Exact solvability of brane equations is studied, and a new $U(1)\times
U(1)\times... \times U(1)$ invariant anzats for the solution of $p$-brane
equations in $D=(2p+1)$-dimensional Minkowski space is proposed. The reduction
of the $p$-brane Hamiltonian to the Hamiltonian of $p$-dimensional relativistic
anharmonic oscillator with the monomial potential of the degree equal to $2p$
is revealed. For the case of degenerate p-torus with equal radii it is shown
that the $p$-brane equations are integrable and their solutions are expressed
in terms of elliptic ($p=2$) or hyperelliptic ($p>2$) functions. The solution
describes contracting $p$-brane with the contraction time depending on $p$ and
the brane energy density. The toroidal brane elasticity is found to break down
linear Hooke law as it takes place for the anharmonic elasticity of smectic
liquid crystals.


  We propose a platform for robust and tunable nonreciprocal phonon transport
based on arrays of optomechanical microtoroids. In our approach, time-reversal
symmetry is broken by the interplay of photonic spin-orbit coupling, engineered
using a state-of-the-art geometrical approach, and the optomechanical
interaction. We demonstrate the topologically protected nature of this system
by investigating its robustness to imperfections. This type of system could
find application in phonon-based information storage and signal processing
devices.


  We analyze theoretically the bound state spectrum of an Aharonov Bohm (AB)
ring in a two-dimensional topological insulator using the four-band model of
HgTe-quantum wells as a concrete example. We calculate analytically the
circular helical edge states and their spectrum as well as the bound states
evolving out of the bulk spectrum as a function of the applied magnetic flux
and dimension of the ring. We also analyze the spin-dependent persistent
currents, which can be used to measure the spin of single electrons. We further
take into account the Rashba spin-orbit interaction which mixes the spin states
and derive its effect on the ring spectrum. The flux tunability of the ring
states allows for coherent mixing of the edge- and the spin degrees of freedom
of bound electrons which could be exploited for quantum information processing
in topological insulator rings.


  Whitehead's 1922 theory of gravitation continues to attract the attention of
philosophers, despite evidence presented in 1971 that it violates experiment.
We demonstrate that the theory strongly fails five quite different experimental
tests, and conclude that, notwithstanding its meritorious philosophical
underpinnings, Whitehead's theory is truly dead.


  The unfolding of detector effects is crucial for the comparison of data to
theory predictions. While traditional methods are limited to representing the
data in a low number of dimensions, machine learning has enabled new unfolding
techniques while retaining the full dimensionality. Generative networks like
invertible neural networks~(INN) enable a probabilistic unfolding, which map
individual events to their corresponding unfolded probability distribution. The
accuracy of such methods is however limited by how well simulated training
samples model the actual data that is unfolded. We introduce the iterative
conditional INN~(IcINN) for unfolding that adjusts for deviations between
simulated training samples and data. The IcINN unfolding is first validated on
toy data and then applied to pseudo-data for the $pp \to Z \gamma \gamma$
process.


  Bias in computer vision systems can perpetuate or even amplify discrimination
against certain populations. Considering that bias is often introduced by
biased visual datasets, many recent research efforts focus on training fair
models using such data. However, most of them heavily rely on the availability
of protected attribute labels in the dataset, which limits their applicability,
while label-unaware approaches, i.e., approaches operating without such labels,
exhibit considerably lower performance. To overcome these limitations, this
work introduces FLAC, a methodology that minimizes mutual information between
the features extracted by the model and a protected attribute, without the use
of attribute labels. To do that, FLAC proposes a sampling strategy that
highlights underrepresented samples in the dataset, and casts the problem of
learning fair representations as a probability matching problem that leverages
representations extracted by a bias-capturing classifier. It is theoretically
shown that FLAC can indeed lead to fair representations, that are independent
of the protected attributes. FLAC surpasses the current state-of-the-art on
Biased MNIST, CelebA, and UTKFace, by 29.1%, 18.1%, and 21.9%, respectively.
Additionally, FLAC exhibits 2.2% increased accuracy on ImageNet-A consisting of
the most challenging samples of ImageNet. Finally, in most experiments, FLAC
even outperforms the bias label-aware state-of-the-art methods.


  In this work we prove a new Northcott property for the Faltings height.
Namely we show, assuming the Colmez Conjecture and the Artin Conjecture, that
there are finitely many CM abelian varieties over the complex numbers of a
fixed dimension which have bounded Faltings height. The technique developed
uses new tools from integral p-adic Hodge theory to study the variation of
Faltings height within an isogeny class of CM abelian varieties. In special
cases, we are moreover able to use the technique to develop new Colmez-type
formulas for the Faltings height.


  We study the dipole moments, electric dipole moment, weak electric dipole
moment, anomalous magnetic moment, anomalous weak magnetic moment, of fermions
in the noncommutative extension of the SM. We observe that the noncommutative
effects are among the possible candidates to explain the electric and weak
electric dipole moment of fermions. Furthermore, the upper bounds for the
parameters which carry space-time and space-space noncommutativity can be
obtained by using the theoretical and experimental results of the fermion
dipole moments.


  Proteins with nontrivial topology, containing knots and slipknots, have the
ability to fold to their native states without any additional external forces
invoked. A mechanism is suggested for folding of these proteins, such as YibK
and YbeA, which involves an intermediate configuration with a slipknot. It
elucidates the role of topological barriers and backtracking during the folding
event. It also illustrates that native contacts are sufficient to guarantee
folding in around 1-2% of the simulations, and how slipknot intermediates are
needed to reduce the topological bottlenecks. As expected, simulations of
proteins with similar structure but with knot removed fold much more
efficiently, clearly demonstrating the origin of these topological barriers.
Although these studies are based on a simple coarse-grained model, they are
already able to extract some of the underlying principles governing folding in
such complex topologies.


  Given a matrix $A\in \mathbb{R}^{n\times d}$ and a vector $b\in
\mathbb{R}^n$, we consider the regression problem with $\ell_\infty$
guarantees: finding a vector $x'\in \mathbb{R}^d$ such that $ \|x'-x^*\|_\infty
\leq \frac{\epsilon}{\sqrt{d}}\cdot \|Ax^*-b\|_2\cdot \|A^\dagger\|$ where
$x^*=\arg\min_{x\in \mathbb{R}^d}\|Ax-b\|_2$. One popular approach for solving
such $\ell_2$ regression problem is via sketching: picking a structured random
matrix $S\in \mathbb{R}^{m\times n}$ with $m\ll n$ and $SA$ can be quickly
computed, solve the ``sketched'' regression problem $\arg\min_{x\in
\mathbb{R}^d} \|SAx-Sb\|_2$. In this paper, we show that in order to obtain
such $\ell_\infty$ guarantee for $\ell_2$ regression, one has to use sketching
matrices that are dense. To the best of our knowledge, this is the first user
case in which dense sketching matrices are necessary. On the algorithmic side,
we prove that there exists a distribution of dense sketching matrices with
$m=\epsilon^{-2}d\log^3(n/\delta)$ such that solving the sketched regression
problem gives the $\ell_\infty$ guarantee, with probability at least
$1-\delta$. Moreover, the matrix $SA$ can be computed in time $O(nd\log n)$.
Our row count is nearly-optimal up to logarithmic factors, and significantly
improves the result in [Price, Song and Woodruff, ICALP'17], in which a
super-linear in $d$ rows, $m=\Omega(\epsilon^{-2}d^{1+\gamma})$ for
$\gamma=\Theta(\sqrt{\frac{\log\log n}{\log d}})$ is required. We also develop
a novel analytical framework for $\ell_\infty$ guarantee regression that
utilizes the Oblivious Coordinate-wise Embedding (OCE) property introduced in
[Song and Yu, ICML'21]. Our analysis is arguably much simpler and more general
than [Price, Song and Woodruff, ICALP'17], and it extends to dense sketches for
tensor product of vectors.


  Optimizing the morphologies and the controllers that adapt to various tasks
is a critical issue in the field of robot design, aka. embodied intelligence.
Previous works typically model it as a joint optimization problem and use
search-based methods to find the optimal solution in the morphology space.
However, they ignore the implicit knowledge of task-to-morphology mapping which
can directly inspire robot design. For example, flipping heavier boxes tends to
require more muscular robot arms. This paper proposes a novel and general
differentiable task-inspired framework for contact-aware robot design called
Task2Morph. We abstract task features highly related to task performance and
use them to build a task-to-morphology mapping. Further, we embed the mapping
into a differentiable robot design process, where the gradient information is
leveraged for both the mapping learning and the whole optimization. The
experiments are conducted on three scenarios, and the results validate that
Task2Morph outperforms DiffHand, which lacks a task-inspired morphology module,
in terms of efficiency and effectiveness.


  We propose RemixIT, a simple and novel self-supervised training method for
speech enhancement. The proposed method is based on a continuously
self-training scheme that overcomes limitations from previous studies including
assumptions for the in-domain noise distribution and having access to clean
target signals. Specifically, a separation teacher model is pre-trained on an
out-of-domain dataset and is used to infer estimated target signals for a batch
of in-domain mixtures. Next, we bootstrap the mixing process by generating
artificial mixtures using permuted estimated clean and noise signals. Finally,
the student model is trained using the permuted estimated sources as targets
while we periodically update teacher's weights using the latest student model.
Our experiments show that RemixIT outperforms several previous state-of-the-art
self-supervised methods under multiple speech enhancement tasks. Additionally,
RemixIT provides a seamless alternative for semi-supervised and unsupervised
domain adaptation for speech enhancement tasks, while being general enough to
be applied to any separation task and paired with any separation model.


  Entanglement is the defining characteristic of quantum mechanics. Bipartite
entanglement is characterized by the von Neumann entropy. Entanglement is not
just described by a number, however; it is also characterized by its level of
complexity. The complexity of entanglement is at the root of the onset of
quantum chaos, universal distribution of entanglement spectrum statistics,
hardness of a disentangling algorithm and of the quantum machine learning of an
unknown random circuit, and universal temporal entanglement fluctuations. In
this paper, we numerically show how a crossover from a simple pattern of
entanglement to a universal, complex pattern can be driven by doping a random
Clifford circuit with $T$ gates. This work shows that quantum complexity and
complex entanglement stem from the conjunction of entanglement and
non-stabilizer resources, also known as magic.


  The paper discusses extensions of the renormalization group (RG) formalism
for 3D incompressible Euler equations, which can be used for describing
singularities developing in finite (blowup) or infinite time from smooth
initial conditions of finite energy. In this theory, time evolution is
substituted by the equivalent evolution for renormalized solutions governed by
the RG equations. A fixed point attractor of the RG equations, if it exists,
describes universal self-similar form of observable singularities. This
universality provides a constructive criterion for interpreting results of
numerical experiments. In this paper, renormalization schemes with multiple
spatial scales are developed for the cases of power law and exponential
scaling. The results are compared with the numerical simulations of a
singularity in incompressible Euler equations obtained by Hou and Li (2006) and
Grafke et al. (2008). The comparison supports the conjecture of a singularity
developing exponentially in infinite time and described by a multiple-scale
self-similar asymptotic solution predicted by the RG theory.


  We report on the dark pulse emission of an all-normal dispersion erbium-doped
fiber laser with a polarizer in cavity. We found experimentally that apart from
the bright pulse emission, under appropriate conditions the fiber laser could
also emit single or multiple dark pulses. Based on numerical simulations we
interpret the dark pulse formation in the laser as a result of dark soliton
shaping.


  The equations for Widom lines for the supercritical van der Waals fluid were
considered in the paper J. Chem. Phys. 135, 084503 (2011). But the equations
for the speed of sound and its special Widom line were incorrect. The correct
equations are obtained.


  We investigate the ramifications of the Legendrian satellite construction on
the relation of Lagrangian cobordism between Legendrian knots. Under a simple
hypothesis, we construct a Lagrangian concordance between two Legendrian
satellites by stacking up a sequence of elementary cobordisms. This
construction narrows the search for "non-decomposable" Lagrangian cobordisms
and yields new families of decomposable Lagrangian slice knots. Finally, we
show that the maximum Thurston-Bennequin number of a smoothly slice knot
provides an obstruction to any Legendrian satellite of that knot being
Lagrangian slice.


  We study $k$-page upward book embeddings ($k$UBEs) of $st$-graphs, that is,
book embeddings of single-source single-sink directed acyclic graphs on $k$
pages with the additional requirement that the vertices of the graph appear in
a topological ordering along the spine of the book. We show that testing
whether a graph admits a $k$UBE is NP-complete for $k\geq 3$. A hardness result
for this problem was previously known only for $k = 6$ [Heath and Pemmaraju,
1999]. Motivated by this negative result, we focus our attention on $k=2$. On
the algorithmic side, we present polynomial-time algorithms for testing the
existence of $2$UBEs of planar $st$-graphs with branchwidth $\beta$ and of
plane $st$-graphs whose faces have a special structure. These algorithms run in
$O(f(\beta)\cdot n+n^3)$ time and $O(n)$ time, respectively, where $f$ is a
singly-exponential function on $\beta$. Moreover, on the combinatorial side, we
present two notable families of plane $st$-graphs that always admit an
embedding-preserving $2$UBE.


  We review the use of kinetically constrained models (KCMs) for the study of
dynamics in glassy systems. The characteristic feature of KCMs is that they
have trivial, often non-interacting, equilibrium behaviour but interesting slow
dynamics due to restrictions on the allowed transitions between configurations.
The basic question which KCMs ask is therefore how much glassy physics can be
understood without an underlying ``equilibrium glass transition''. After a
brief review of glassy phenomenology, we describe the main model classes, which
include spin-facilitated (Ising) models, constrained lattice gases, models
inspired by cellular structures such as soap froths, models obtained via
mappings from interacting systems without constraints, and finally related
models such as urn, oscillator, tiling and needle models. We then describe the
broad range of techniques that have been applied to KCMs, including exact
solutions, adiabatic approximations, projection and mode-coupling techniques,
diagrammatic approaches and mappings to quantum systems or effective models.
Finally, we give a survey of the known results for the dynamics of KCMs both in
and out of equilibrium, including topics such as relaxation time divergences
and dynamical transitions, nonlinear relaxation, aging and effective
temperatures, cooperativity and dynamical heterogeneities, and finally
non-equilibrium stationary states generated by external driving. We conclude
with a discussion of open questions and possibilities for future work.


  Let $S$ be an additively idempotent semiring and $\mathbf{M}_n(S)$ be the
semiring of all $n\times n$ matrices over $S$.
  We characterize the conditions of when the semiring $\mathbf{M}_n(S)$ is
congruence-simple provided that the semiring $S$ is either commutative or
finite.
  We also give a characterization of when the semiring $\mathbf{M}_n(S)$ is
subdirectly irreducible for $S$ beeing almost integral (i.e., $xy+yx+x=x$ for
all $x,y\in S$). In particular, we provide this characterization for the
semirings $S$ derived from the pseudo MV-algebras.


  We consider a class of L\'evy-driven stochastic differential equations (SDEs)
with McKean-Vlasov (MK-V) interaction in the drift coefficient. It is assumed
that the coefficient is bounded, affine in the state variable, and only
measurable in the law of the solution. We study the equivalent functional
fixed-point equation for the unknown time-dependent coefficients of the
associated Markovian SDE. By proving a contraction property for the functional
map in a suitable normed space, we infer existence and uniqueness results for
the MK-V SDE, and derive a discretized Picard iteration scheme that
approximates the law of the solution through its characteristic function.
Numerical illustrations show the effectiveness of our method, which appears to
be appropriate to handle the multi-dimensional setting.


  The equation of state of asymmetric nuclear matter is still controversial, as
predictions at subsaturation as well as above normal density widely diverge. We
discuss several experimental results measured in heavy-ion collisions with the
INDRA array in the incident energy range 5-80 MeV/nucleon. In particular an
estimate of the density dependence of the symmetry energy is derived from
isospin diffusion results compared with a transport code: the potential part of
the symmetry energy linearly increases with the density. We demonstrate that
isospin equilibrium is reached in mid-central collisions for the two reactions
Ni+Au at 52 MeV/nucleon and Xe+Sn at 32 MeV/nucleon. New possible variables and
an improved modelization to investigate symmetry energy are discussed.


  Over the next five years, the Dark Energy Spectroscopic Instrument (DESI)
will use 10 spectrographs with 5000 fibers on the 4m Mayall Telescope at Kitt
Peak National Observatory to conduct the first Stage-IV dark energy galaxy
survey. At $z < 0.6$, the DESI Bright Galaxy Survey (BGS) will produce the most
detailed map of the Universe during the dark energy dominated epoch with
redshifts of >10 million galaxies over 14,000 deg$^2$. In this work, we present
and validate the final BGS target selection and survey design. From the Legacy
Surveys, BGS will target a $r < 19.5$ magnitude-limited sample (BGS Bright); a
fainter $19.5 < r < 20.175$ sample, color-selected to have high redshift
efficiency (BGS Faint); and a smaller low-z quasar sample. BGS will observe
these targets using exposure times, scaled to achieve uniform completeness, and
visit each point on the footprint three times. We use observations from the
Survey Validation programs conducted prior to the main survey along with
realistic simulations to show that BGS can complete its strategy and make
optimal use of `bright' time. We demonstrate that BGS targets have stellar
contamination <1% and that their densities do not depend strongly on imaging
properties. We also confirm that BGS Bright will achieve >80% fiber assignment
efficiency. Finally, we show that BGS Bright and Faint will achieve >95%
redshift success rates with no significant dependence on observing conditions.
BGS meets the requirements for an extensive range of scientific applications.
BGS will yield the most precise Baryon Acoustic Oscillations and Redshift-Space
Distortions measurements at $z < 0.4$. It also presents opportunities to
exploit new methods that require highly complete and dense galaxy samples (e.g.
N-point statistics, multi-tracers). BGS further provides a powerful tool to
study galaxy populations and the relations between galaxies and dark matter.


  The SUSY $SO(10)$ GUT is in severe tension with the experimental bounds on
proton partial lifetimes because proton decay mediated by colored Higgsinos
(dimension-five proton decay) is too rapid. In this paper, we pursue the
possibility that a texture of the Yukawa coupling matrices in a renormalizable
SUSY $SO(10)$ GUT model suppresses dimension-five proton decay. We focus on a
general renormalizable SUSY $SO(10)$ GUT model which contains ${\bf 10}+{\bf
126}+{\bf \overline{126}}+{\bf 120}$ representation fields and where the Yukawa
coupling matrices of the ${\bf 16}$ matter fields with the ${\bf 10}$, ${\bf
\overline{126}}$, ${\bf 120}$ fields, $Y_{10},Y_{126},Y_{120}$, provide the
quark and lepton Yukawa couplings and Majorana mass of the singlet neutrinos.
We find that if components in certain flavor bases, $(Y_{10})_{u_R d_R}$,
$(Y_{126})_{u_R d_R}$, $(Y_{10})_{u_R s_R}$, $(Y_{126})_{u_R s_R}$,
$(Y_{10})_{u_L d_L}$, $(Y_{126})_{u_L d_L}$, $(Y_{10})_{u_L s_L}$,
$(Y_{126})_{u_L s_L}$, $(Y_{10})_{u_L u_L}$, $(Y_{126})_{u_L u_L}$, are all on
the order of the up quark Yukawa coupling, dimension-five proton decay can be
suppressed while the Yukawa coupling matrices still reproduce the realistic
quark and lepton masses and flavor mixings. We numerically obtain specific
Yukawa coupling matrices satisfying the above conditions, calculate proton
partial lifetimes from them and evaluate how dimension-five proton decay is
suppressed when these conditions are met.


  We describe a Bayesian rejection sampling algorithm designed to efficiently
compute posterior distributions of orbital elements for data covering short
fractions of long-period exoplanet orbits. Our implementation of this method,
Orbits for the Impatient (OFTI), converges up to several orders of magnitude
faster than two implementations of MCMC in this regime. We illustrate the
efficiency of our approach by showing that OFTI calculates accurate posteriors
for all existing astrometry of the exoplanet 51 Eri b up to 100 times faster
than a Metropolis-Hastings MCMC. We demonstrate the accuracy of OFTI by
comparing our results for several orbiting systems with those of various MCMC
implementations, finding the output posteriors to be identical within shot
noise. We also describe how our algorithm was used to successfully predict the
location of 51 Eri b six months in the future based on less than three months
of astrometry. Finally, we apply OFTI to ten long-period exoplanets and brown
dwarfs, all but one of which have been monitored over less than 3% of their
orbits, producing fits to their orbits from astrometric records in the
literature.


  Statically analyzing dynamically-typed code is a challenging endeavor, as
even seemingly trivial tasks such as determining the targets of procedure calls
are non-trivial without knowing the types of objects at compile time.
Addressing this challenge, gradual typing is increasingly added to
dynamically-typed languages, a prominent example being TypeScript that
introduces static typing to JavaScript. Gradual typing improves the developer's
ability to verify program behavior, contributing to robust, secure and
debuggable programs. In practice, however, users only sparsely annotate types
directly. At the same time, conventional type inference faces
performance-related challenges as program size grows. Statistical techniques
based on machine learning offer faster inference, but although recent
approaches demonstrate overall improved accuracy, they still perform
significantly worse on user-defined types than on the most common built-in
types. Limiting their real-world usefulness even more, they rarely integrate
with user-facing applications. We propose CodeTIDAL5, a Transformer-based model
trained to reliably predict type annotations. For effective result retrieval
and re-integration, we extract usage slices from a program's code property
graph. Comparing our approach against recent neural type inference systems, our
model outperforms the current state-of-the-art by 7.85% on the
ManyTypes4TypeScript benchmark, achieving 71.27% accuracy overall. Furthermore,
we present JoernTI, an integration of our approach into Joern, an open source
static analysis tool, and demonstrate that the analysis benefits from the
additional type information. As our model allows for fast inference times even
on commodity CPUs, making our system available through Joern leads to high
accessibility and facilitates security research.


  Power grid operations increasingly interact with environmental systems and
human systems such as transportation, agriculture, the economy, and financial
markets. Our objective is to discuss the modelling gaps and opportunities to
advance the science for multisector adaptation and tradeoffs. We focus on power
system operational models, which typically represent key physical and economic
aspects of grid operations over days to a year and assume a fixed power grid
infrastructure. Due to computational burden, models are typically customized to
reflect regional resource opportunities, data availability, and applications of
interest. While there are model intercomparison papers, there is however no
model-agnostic characterization and systematic overview of the state-of-the-art
process representations in operational power system models. To address our
objective, we conceptualize power system operational models with four core
processes: physical grid assets (generation, transmission, loads, and storage),
model objectives and purpose, institutions and decision agents, and performance
metrics. We taxonomize the representations of these core processes based on a
review of 23 existing open-source and commercial models. As we acknowledge the
computational burden of certain representations, we leverage this taxonomy to
describe tradeoffs in process fidelity and tractability that have been adopted
by the research community to address interactions between the power grid and
hydrometeorological uncertainties, global change, and/or technological
innovation. The core process taxonomy along with the existing computational
tradeoffs are used to identify technical gaps and recommend future model
development needs and research directions to better represent power grid
operations as part of integrated multisector dynamics modeling and
interdisciplinary research.


  We present an exact result for the non-adiabatic transition probability and
hence the defect density in the final state of a one-dimensional Kitaev model
following a slow quench of the parameter $J_-$, which estimates the anisotropy
between the interactions, as $J_-(t)\sim -|t/\tau|$. Here, time $t$ goes from
$-\infty$ to $+\infty$ and $\tau$ defines the rate of change of the
Hamiltonian. In other words, the spin chain initially prepared in its ground
state is driven by changing $J_-$ linearly in time up to the quantum critical
point, which in the model considered here occurs at at $t=0$, reversed and then
gradually decreased to its initial value at the same rate. We have thoroughly
compared the reverse quenching with its counterpart forward quenching $i.e.,$
$J_-\sim t/\tau$. Our exact calculation shows that the probability of
excitations is zero for the wave vector at which the instantaneous energy gap
is zero at the critical point $J_{-}=0$ as opposed to the maximum value of
unity in the forward quenching. It is also shown that the defect density in the
final state following a reverse quenching, we propose here, is nearly half of
the defects generated in the forward quenching. We argue that the defects
produced when the system reaches the quantum critical point gets redistributed
in the wave vector space at the final time in case of reverse quenching whereas
it keeps on increasing till the final time in the forward quenching. We study
the entropy density and also the time evolution of the diagonal entropy density
in the case of the reverse quenching and compare it with the forward case.


  We present a theory for the spin-Peierls transition in CuGeO_3. We map the
elementary excitations of the dimerized chain (solitons) on an effective Ising
model. Inter-chain coupling (or phonons) then introduce a linear binding
potential between a pair of soliton and anti-soliton, leading to a finite
transition temperature. We evaluate, as a function of temperature, the order
parameter, the singlet-triplet gap, the specific heat, and the susceptibility
and compare with experimental data on CuGeO_3. We find that CuGeO_3 is close to
a first-order phase transition. We point out, that the famous scaling law
\sim\delta^{2/3} of the triplet gap is a simple consequence of the linear
binding potential between pairs of solitons and anti-solitons in dimerized spin
chains.


  An efficient matrix formalism for finding power series solutions to boundary
value problems typical for technological plasticity is developed. Hyperbolic
system of two first order quasilinear PDEs that models two-dimensional plastic
flow of von Mises material is converted to the telegraph equation by the
hodograph transformation. Solutions to the boundary value problems are found in
terms of hypergeometric functions. Convergence issue is also addressed. The
method is illustrated by two test problems of metal forming.


  We give a formula to calculate a matrix element of a conserved current in the
effective quantum mechanics defined by the wave function equivalent potentials
proposed by HAL QCD collaboration. As a first step, a non-relativistic field
theory with two channel coupling is considered as the original theory, with
which a wave function equivalent HAL QCD potential is obtained in a closed
analytic form. The external field method is used to derive the formula by
demanding that the result should agree with the original theory. With this
formula, the matrix element is obtained by sandwiching the effective current
operator between the left and the right eigen functions of the effective
Hamiltonian associated with the HAL QCD potential. In addition to the naive
one-body current, the effective current operator contains an additional
two-body term emerging from the degrees of freedom which has been integrated
out.


  Extracting graph representation of visual scenes in image is a challenging
task in computer vision. Although there has been encouraging progress of scene
graph generation in the past decade, we surprisingly find that the performance
of existing approaches is largely limited by the strong biases, which mainly
stem from (1) unconsciously assuming relations with certain semantic properties
such as symmetric and (2) imbalanced annotations over different relations. To
alleviate the negative effects of these biases, we proposed a new and simple
architecture named Rich and Fair semantic extraction network (RiFa for short),
to not only capture rich semantic properties of the relations, but also fairly
predict relations with different scale of annotations. Using pseudo-siamese
networks, RiFa embeds the subject and object respectively to distinguish their
semantic differences and meanwhile preserve their underlying semantic
properties. Then, it further predicts subject-object relations based on both
the visual and semantic features of entities under certain contextual area, and
fairly ranks the relation predictions for those with a few annotations.
Experiments on the popular Visual Genome dataset show that RiFa achieves
state-of-the-art performance under several challenging settings of scene graph
task. Especially, it performs significantly better on capturing different
semantic properties of relations, and obtains the best overall per relation
performance.


  In this work we investigate the observability of Inert Doublet Model scalars
at the LHC operating at the center of mass energy of 14 TeV. The signal
production process is $pp \to AH^\pm \to ZHW^{\pm}H$ leading to two different
final states of $\ell^+\ell^-Hjj H$ and $\ell^+\ell^-H\ell^\pm\nu H$ based on
the hadronic and leptonic decay channels of the W boson. All the relevant
background processes are considered and an event selection is designed to
distinguish the signal from the large Standard Model background. We found that
signals of the selected search channels are well observable at the LHC with
integrated luminosity of 300 fb$^{-1}$.


  To obtain the highest confidence on the correction of numerical simulation
programs implementing the finite element method, one has to formalize the
mathematical notions and results that allow to establish the soundness of the
method. The Lax-Milgram theorem may be seen as one of those theoretical
cornerstones: under some completeness and coercivity assumptions, it states
existence and uniqueness of the solution to the weak formulation of some
boundary value problems. The purpose of this document is to provide the formal
proof community with a very detailed pen-and-paper proof of the Lax-Milgram
theorem.


  Lagrangian relaxation and approximate optimization algorithms have received
much attention in the last two decades. Typically, the running time of these
methods to obtain a $\epsilon$ approximate solution is proportional to
$\frac{1}{\epsilon^2}$. Recently, Bienstock and Iyengar, following Nesterov,
gave an algorithm for fractional packing linear programs which runs in
$\frac{1}{\epsilon}$ iterations. The latter algorithm requires to solve a
convex quadratic program every iteration - an optimization subroutine which
dominates the theoretical running time.
  We give an algorithm for convex programs with strictly convex constraints
which runs in time proportional to $\frac{1}{\epsilon}$. The algorithm does NOT
require to solve any quadratic program, but uses gradient steps and elementary
operations only. Problems which have strictly convex constraints include
maximum entropy frequency estimation, portfolio optimization with loss risk
constraints, and various computational problems in signal processing.
  As a side product, we also obtain a simpler version of Bienstock and
Iyengar's result for general linear programming, with similar running time.
  We derive these algorithms using a new framework for deriving convex
optimization algorithms from online game playing algorithms, which may be of
independent interest.


  Silicon photomultipliers present saturation effects as they have a limited
number of pixels and work in Geiger mode. Their response to light pulses in the
nonlinear region is very complex for two reasons: pixel recharging after an
avalanche affects the trigger probability and charge multiplication of
subsequent avalanches, and non-trivial effects due to crosstalk and
afterpulsing.
  A parametrization of the nonlinear response of silicon photomultipliers was
developed where the above effects were readily accounted for. The model was
tested on a setup of gamma-ray spectrometry using different combinations of
scintillation crystals and detectors. The model parameters were interpreted in
terms of fundamental characteristics of the setup (e.g., lifetime of the
scintillation crystal and pixel recovery time). The proper conversion from
signal resolution to energy resolution was provided.


  We efficiently solve the optimal multi-dimensional mechanism design problem
for independent bidders with arbitrary demand constraints when either the
number of bidders is a constant or the number of items is a constant. In the
first setting, we need that each bidder's values for the items are sampled from
a possibly correlated, item-symmetric distribution, allowing different
distributions for each bidder. In the second setting, we allow the values of
each bidder for the items to be arbitrarily correlated, but assume that the
distribution of bidder types is bidder-symmetric.
  For all eps>0, we obtain an additive eps-approximation, when the value
distributions are bounded, or a multiplicative (1-eps)-approximation when the
value distributions are unbounded, but satisfy the Monotone Hazard Rate
condition, covering a widely studied class of distributions in Economics. Our
runtime is polynomial in max{#items,#bidders}, and not the size of the support
of the joint distribution of all bidders' values for all items, which is
typically exponential in both the number of items and the number of bidders.
Our mechanisms are randomized, explicitly price bundles, and can sometimes
accommodate budget constraints.
  Our results are enabled by establishing several new tools and structural
properties of Bayesian mechanisms. We provide a symmetrization technique
turning any truthful mechanism into one that has the same revenue and respects
all symmetries in the underlying value distributions. We also prove that
item-symmetric mechanisms satisfy a natural monotonicity property which, unlike
cyclic-monotonicity, can be harnessed algorithmically. Finally, we provide a
technique that turns any given eps-BIC mechanism (i.e. one where incentive
constraints are violated by eps) into a truly-BIC mechanism at the cost of
O(sqrt{eps}) revenue. We expect our tools to be used beyond the settings we
consider here.


  Although group convolutional networks are able to learn powerful
representations based on symmetry patterns, they lack explicit means to learn
meaningful relationships among them (e.g., relative positions and poses). In
this paper, we present attentive group equivariant convolutions, a
generalization of the group convolution, in which attention is applied during
the course of convolution to accentuate meaningful symmetry combinations and
suppress non-plausible, misleading ones. We indicate that prior work on visual
attention can be described as special cases of our proposed framework and show
empirically that our attentive group equivariant convolutional networks
consistently outperform conventional group convolutional networks on benchmark
image datasets. Simultaneously, we provide interpretability to the learned
concepts through the visualization of equivariant attention maps.


  Let $R$ be a standard graded Noetherian algebra over an infinite field $K$
and $M$ a finitely generated $\mathbb{Z}$-graded $R$-module. Then for any
graded ideal $I\subseteq R_+$ of $R$, we show that there exist integers
$e_1\geq e_2$ such that $r(I^nM)=\rho_I(M)n+e_1$ and $D(I^nM)=\rho_I(M)n+e_2$
for $n\gg0$. Here $r(M)$ and $D(M)$ denote the reduction number of $M$ and the
maximal degree of minimal generators of $M$ respectively, and $\rho_I(M)$ is an
integer determined by both $M$ and $I$. We introduce the notion of generalized
regularity function $\Gamma$ for a standard graded algebra over a Noetherian
ring and prove that $\Gamma(I^nM)$ is also a linear function in $n$ for $n\gg
0$.


  It is shown that smooth maps $f: S^3 \rightarrow S^3$ contain two countable
families of harmonic representatives in the homotopy classes of degree zero and
one.


  Fashion merchandising is one of the most complicated problems in forecasting,
given the transient nature of trends in colours, prints, cuts, patterns, and
materials in fashion, the economies of scale achievable only in bulk
production, as well as geographical variations in consumption. Retailers that
serve a large customer base spend a lot of money and resources to stay prepared
for meeting changing fashion demands, and incur huge losses in unsold inventory
and liquidation costs [2]. This problem has been addressed by analysts and
statisticians as well as ML researchers in a conventional fashion - of building
models that forecast for future demand given a particular item of fashion with
historical data on its sales. To our knowledge, none of these models have
generalized well to predict future demand at an abstracted level for a new
design/style of fashion article. To address this problem, we present a study of
large scale fashion sales data and directly infer which clothing/footwear
attributes and merchandising factors drove demand for those items. We then
build generalised models to forecast demand given new item attributes, and
demonstrate robust performance by experimenting with different neural
architectures, ML methods, and loss functions.


  In this paper, we first prove a theorem by a little modification on the
Lax-Milgram theorem. Then, using $K$-frames, we obtain lower and upper bounds
for the results obtained from this theorem. Also, we present some methods for
the characterization of scalable $K$-frames.
  Finally, we introduce piecewise scalable $K$-frames and give necessary and
sufficient conditions for a $K$-frame to be piecewise scalable.


  The recent discovery of magnetic van der Waals materials has triggered a
wealth of investigations in materials science, and now offers genuinely new
prospects for both fundamental and applied research. Although the catalogue of
van der Waals ferromagnets is rapidly expanding, most of them have a Curie
temperature below 300 K, a notable disadvantage for potential applications.
Combining element-selective x-ray magnetic imaging and magnetic force
microscopy, we resolve at room temperature the magnetic domains and domains
walls in micron-sized flakes of the CrTe$_2$ van der Waals ferromagnet.
Flux-closure magnetic patterns suggesting in-plane six-fold symmetry are
observed. Upon annealing the material above its Curie point (315 K), the
magnetic domains disappear. By cooling back down the sample, a different
magnetic domain distribution is obtained, indicating material stability and
lack of magnetic memory upon thermal cycling. The domain walls presumably have
N\'eel texture, are preferentially oriented along directions separated by 120
degrees, and have a width of several tens of nanometers. Besides microscopic
mapping of magnetic domains and domain walls, the coercivity of the material is
found to be of a few mT only, showing that the CrTe$_2$ compound is
magnetically soft. The coercivity is found to increase as the volume of the
material decreases.


  We present a theory for quantum nondemolition (QND) measurements of an atomic
ensemble in the presence of spontaneous emission. We derive the master equation
that governs the evolution of the ground state of the atoms and the quantum
state of light. Solving the master equation exactly without invoking the
Holstein-Primakoff approximation and projecting out the quantum state of light,
we derive a positive operator-valued measure that describes the QND
measurement. We show that at high spontaneous emission conditions, the QND
measurement has a unique dominant state to which the measurement collapses. We
additionally investigate the behavior of the QND measurement in the limiting
case of strong atom-light interactions, where we show that the positive
operator valued measure becomes a projection operator. We further analyze the
effect of spontaneous emission noise on atomic state preparation. We find that
it limits the width of the eigenvalue spectrum available to a quantum state in
a linear superposition. This effect leads to state collapse on the dominant
state. We generate various non-classical states of the atom by tuning the
atom-light interaction strength. We find that non-classical states such as the
Schr\"odinger-cat state, whose coherence spans the entire eigenvalue spectrum
of the total spin operator $J_z$ for a given spin eigenvalue $J$, lose their
coherence because spontaneous emission limits the accessibility of states
farther away from the dominant state.


  $\gamma$-ray observations of the Cygnus Cocoon, an extended source
surrounding the Cygnus X star-forming region, suggest the presence of a cosmic
ray accelerator reaching energies up to a few PeV. The very-high-energy (VHE;
0.1-100~TeV) $\gamma$-ray emission may be explained by the interaction of
cosmic-ray hadrons with matter inside the Cocoon, but an origin of inverse
Compton radiation by relativistic electrons cannot be ruled out. Inverse
Compton $\gamma$-rays at VHE are accompanied by synchrotron radiation peaked in
X-rays. Hence, X-ray observations may probe the electron population and
magnetic field of the source. We observed eleven fields in or near the Cygnus
Cocoon with the Neil Gehrels Swift Observatory's X-Ray Telescope (Swift-XRT)
totaling 110 ksec. We fit the fields to a Galactic and extra-galactic
background model and performed a log-likelihood ratio test for an additional
diffuse component. We found no significant additional emission and established
upper limits in each field. By assuming that the X-ray intensity traces the TeV
intensity and follows an $dN/dE\propto E^{-2.5}$ spectrum, we obtained a 90\%
upper limit of $F_X < 8.7\times 10^{-11}\rm~erg\,cm^{-2}\,s^{-1}$ or $<
5.2\times 10^{-11}\rm~erg\,cm^{-2}\,s^{-1}$ on the X-ray flux of the entire
Cygnus Cocoon between 2 and 10 keV depending on the choice of hydrogen column
density model. This suggests that no more than one quarter of the $\gamma$-ray
flux at 1 TeV is produced by inverse Compton scattering, when assuming an
equipartition magnetic field of $\sim 20\,\mu$G.


  Mean field games were introduced independently by J-M. Lasry and P-L. Lions,
and by M. Huang, R.P. Malham\'e and P. E. Caines, in order to bring a new
approach to optimization problems with a large number of interacting agents.
The description of such models split in two parts, one describing the evolution
of the density of players in some parameter space, the other the value of a
cost functional each player tries to minimize for himself, anticipating on the
rational behavior of the others.
  Quadratic Mean Field Games form a particular class among these systems, in
which the dynamics of each player is governed by a controlled Langevin equation
with an associated cost functional quadratic in the control parameter. In such
cases, there exists a deep relationship with the non-linear Schr\"odinger
equation in imaginary time, connexion which lead to effective approximation
schemes as well as a better understanding of the behavior of Mean Field Games.
  The aim of this paper is to serve as an introduction to Quadratic Mean Field
Games and their connexion with the non-linear Schr\"odinger equation, providing
to physicists a good entry point into this new and exciting field.


  As crowd-sourced curation of news and information become the norm, it is
important to understand not only how individuals consume information through
social news Web sites, but also how they contribute to their ranking systems.
In the present work, we introduce and make available a new dataset containing
the activity logs that recorded all activity for 309 Reddit users for one year.
Using this newly collected data, we present findings that highlight the
browsing and voting behavior of the study's participants. We find that most
users do not read the article that they vote on, and that, in total, 73% of
posts were rated (ie, upvoted or downvoted) without first viewing the content.
We also show evidence of cognitive fatigue in the browsing sessions of users
that are most likely to vote.


  We report on the study of the mass-radius (M-R) relation and the radial
oscillations of proto strange stars. For the quark matter we have employed the
well known density dependent quark mass model and its very recent modification,
the temperature and density dependent quark mass model. We find that the
maximum mass the star can support increases significantly with the temperature
of the star in this model which implies that transition to a black hole at the
early stage of formation of the star is inhibited. As for the neutrinos, we
find, contrary to the expectation that the M-R and oscillation frequencies are
almost independent of the neutrino chemical potentials.


  In this paper, we prove that if $G$ is a finite group in which elements of
the same order outside the center are conjugate, then $G$ is abelian or is
isomorphic to $S_3$, the symmetry group of degree 3.


  We investigate directed motion in non-adiabatically rocked ratchet systems
sustaining few bands below the barrier. Upon restricting the dynamics to the
lowest M bands, the total system-plus-bath Hamiltonian is mapped onto a
discrete tight-binding model containing all the information both on the intra-
and inter-well tunneling motion. A closed form for the current in the
incoherent tunneling regime is obtained. In effective single-band ratchets, no
current rectification occurs. We apply our theory to describe rectification
effects in vortex quantum ratchets devices. Current reversals upon variation of
the ac-field amplitude or frequency are predicted.


  Discovery of the first interstellar asteroid (ISA) - 1I/2017 'Oumuamua -
raised a number of questions regarding its origin. Many of them relate to its
lack of cometary activity, suggesting refractory composition of 'Oumuamua. Here
we explore the possibility that 'Oumuamua-like ISAs are produced in tidal
disruption events (TDEs) of refractory planetoids (asteroids, dwarf planets,
etc.) by the white dwarfs (WDs). This idea is supported by existing
spectroscopic observations of metal-polluted WDs, hinting at predominantly
volatile-poor composition of accreted material. We show that such TDEs sourced
by realistic planetary systems (including a population of >1000 km planetoids
and massive perturbers - Neptune-to-Saturn mass planets) can eject to
interstellar space up to 30% of planetary mass involved in them. Collisional
fragmentation, caused by convergent vertical motion of the disrupted
planetoid's debris inside the Roche sphere of the WD, channels most of the
original mass into 0.1-1 km fragments, similar to 'Oumuamua. Such size spectrum
of ISAs (very different from the top-heavy distributions expected in other
scenarios) implies that planetary TDEs can account for a significant fraction
(up to ~30% under optimistic assumptions) of the ISAs. This figure is based on
existing observations of WD metal pollution and accounts for observational
biases by using realistic models of circum-WD planetary systems. ISAs should
exhibit kinematic characteristics similar to old, dynamically hot Galactic
populations; we interpret 'Oumuamua's slow Galactic motion as a statistical
fluctuation. ISA ejection in individual planetary TDEs is highly anisotropic,
resulting in large fluctuations of their space density. We also show that other
ISA production mechanisms involving stellar remnants - direct ejection by
massive planets around WDs and SN explosions - have difficulty explaining
'Oumuamua-like ISAs.


  We report on a direct mapping of acoustic slender waveguides to the one
dimensional trimer Su- Schrieffer-Heeger model, with neither chiral nor mirror
symmetry. Importantly, we can choose to perform this mapping for either the
acoustic velocity or pressure. We demonstrate that, for finite systems, this
choice is necessarily linked to the boundary conditions. It allows for the
unveiling of the edge states of the acoustic system through an edge state phase
diagram. An experimental realization of our setup in the audible regime
corroborates our theoretical predictions.


  Nanotechnology has revolutionized the fabrication of hybrid species with
tailored functionalities. A milestone in this field is the DNA conjugation of
nanoparticles, introduced almost 30 years ago, which typically exploits the
affinity between thiol groups and metallic surfaces. Over the last decades,
developments in colloidal research have enabled the synthesis of an assortment
of non-metallic structures, such as high-index dielectric nanoparticles, with
unique properties not previously accessible with traditional metallic
nanoparticles. However, to stabilize, integrate and provide further
functionality to non-metallic nanoparticles, reliable techniques for their
functionalization with DNA will be crucial. Here, we combine well-established
dibenzylcyclooctyne-azide click-chemistry with a simple freeze-thaw method to
achieve the functionalization of silica and silicon nanoparticles, which form
exceptionally stable colloids with a high DNA surface density of 0.2
molecules/nm2. Furthermore, we demonstrate that these functionalized colloids
can be self-assembled into high-index dielectric optical antennas with a yield
of up to 78% via the use of DNA origami. Finally, we extend this method to
functionalize other important nanomaterials, including oxides, polymers,
core-shell and metal nanostructures. Our results indicate that the method
presented herein serves as a crucial complement to conventional thiol
functionalization chemistry and thus greatly expands the toolbox of
DNA-functionalized nanoparticles currently available.


  Experimental observations recently reported in Nature are in accord with the
concept that spin orientation is a permanent feature of the spin carrier. It
follows that magnetization is realized by rearrangement of the crystal
structure. The rearrangement occurs by the general contact
nucleation-and-growth mechanism.


  The (yet-to-be confirmed) discovery of a Neptune-sized moon around the ~3.2
Jupiter-mass planet in Kepler 1625 puts interesting constraints on the
formation of the system. In particular, the relatively wide orbit of the moon
around the planet, at ~40 planetary radii, is hard to reconcile with planet
formation theories. We demonstrate that the observed characteristics of the
system can be explained from the tidal capture of a secondary planet in the
young system. After a quick phase of tidal circularization, the lunar orbit,
initially much tighter than 40 planetary radii, subsequently gradually widened
due to tidal synchronization of the spin of the planet with the orbit,
resulting in a synchronous planet-moon system. Interestingly, in our scenario
the captured object was originally a Neptune-like planet, turned into a moon by
its capture.


  A realistic equation of state (EOS) leads to realistic strange stars (ReSS)
which are compact in the mass radius plot, close to the Schwarzchild limiting
line (Dey et al 1998). Many of the observed stars fit in with this kind of
compactness, irrespective of whether they are X-ray pulsars, bursters or soft
$\gamma$ repeaters or even radio pulsars. We point out that a change in the
radius of a star can be small or large, when its mass is increasing and this
depends on the position of a particular star on the mass radius curve. We carry
out a stability analysis against radial oscillations and compare with the EOS
of other strange star (SS) models. We find that the ReSS is stable and an M-R
region can be identified to that effect.


  The reconfiguration graph $R_k(G)$ for the $k$-colorings of a graph $G$ has
as vertex set the set of all possible $k$-colorings of $G$ and two colorings
are adjacent if they differ in the color of exactly one vertex of $G$. Let $d,
k \geq 1$ be integers such that $k \geq d+1$. We prove that for every $\epsilon
> 0$ and every graph $G$ with $n$ vertices and maximum average degree $d -
\epsilon$, $R_k(G)$ has diameter $O(n(\log n)^{d - 1})$. This significantly
strengthens several existing results.