  We investigate redshift evolution in the galaxy merger and accretion rates,
using a well-defined sample of 4184 galaxies with 0.12 < z < 0.55 and R_C <
21.5. We identify 88 galaxies in close (5 < r_p < 20 h^{-1} kpc) dynamical
(delta v < 500 km/s) pairs. These galaxies are used to compute global pair
statistics, after accounting for selection effects resulting from the flux
limit, k-corrections, luminosity evolution, and spectroscopic incompleteness.
We find that the number of companions per galaxy (for -21 < M_B^{k,e} < -18) is
Nc = 0.0321 +/- 0.0077 at z=0.3. The luminosity in companions, per galaxy, is
Lc = 0.0294 +/- 0.0084 x 10^10 h^2 L_sun. We assume that Nc is proportional to
the galaxy merger rate, while Lc is directly related to the mass accretion
rate. After increasing the maximum pair separation to 50 h^{-1} kpc, and
comparing with the low redshift SSRS2 pairs sample, we infer evolution in the
galaxy merger and accretion rates of (1+z)^{2.3 +/- 0.7} and (1+z)^{2.3 +/-
0.9} respectively. These are the first such estimates to be made using only
confirmed dynamical pairs. When combined with several additional assumptions,
this implies that approximately 15% of present epoch galaxies with -21 < M_B <
-18 have undergone a major merger since z=1.


  Budgets play a significant role in real-world sequential auction markets such
as those implemented by internet companies. To maximize the value provided to
auction participants, spending is smoothed across auctions so budgets are used
for the best opportunities. Motivated by a mechanism used in practice by
several companies, this paper considers a smoothing procedure that relies on
{\em pacing multipliers}: on behalf of each buyer, the auction market applies a
factor between 0 and 1 that uniformly scales the bids across all auctions.
Reinterpreting this process as a game between buyers, we introduce the notion
of {\em pacing equilibrium}, and prove that they are always guaranteed to
exist. We demonstrate through examples that a market can have multiple pacing
equilibria with large variations in several natural objectives. We show that
pacing equilibria refine another popular solution concept, competitive
equilibria, and show further connections between the two solution concepts.
Although we show that computing either a social-welfare-maximizing or a
revenue-maximizing pacing equilibrium is NP-hard, we present a mixed-integer
program (MIP) that can be used to find equilibria optimizing several relevant
objectives. We use the MIP to provide evidence that: (1) equilibrium
multiplicity occurs very rarely across several families of random instances,
(2) static MIP solutions can be used to improve the outcomes achieved by a
dynamic pacing algorithm with instances based on a real-world auction market,
and (3) for the instances we study, buyers do not have an incentive to
misreport bids or budgets provided there are enough participants in the
auction.


  This is a survey article with a limited list of references (as required by
the publisher) which appears in the Encyclopedia of Mathematical Physics, eds.
J.-P. Francoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, 2006. vol.4,
pp.94--104.


  By using the 1H(6Li,6Be)n charge-exchange reaction, continuum states in 6Be
were populated up to E_t=16 MeV, E_t being the 6Be energy above its three-body
decay threshold. In kinematically complete measurements performed by detecting
alpha+p+p coincidences, an E_t spectrum of high statistics was obtained,
containing approximately ~5x10^6 events. The spectrum provides detailed
correlation information about the well-known 0^+ ground state of 6Be at
E_t=1.37 MeV and its 2^+ state at E_t=3.05 MeV. Moreover, a broad structure
extending from 4 to 16 MeV was observed. It contains negative parity states
populated by Delta L=1 angular momentum transfer without other significant
contributions. This structure can be interpreted as a novel phenomenon, i.e.
the isovector soft dipole mode associated with the 6Li ground state. The
population of this mode in the charge-exchange reaction is a dominant
phenomenon for this reaction, being responsible for about 60% of the cross
section obtained in the measured energy range.


  Placing a minimum number of guards on a given watchman route in a polygonal
domain is called the {\em minimum vision points problem}. We prove that finding
the minimum number of vision points on a shortest watchman route in a simple
polygon is APX-Hard. We then extend the proof to the class of rectilinear
polygons having at most three dent orientations.


  We present Stable Video Diffusion - a latent video diffusion model for
high-resolution, state-of-the-art text-to-video and image-to-video generation.
Recently, latent diffusion models trained for 2D image synthesis have been
turned into generative video models by inserting temporal layers and finetuning
them on small, high-quality video datasets. However, training methods in the
literature vary widely, and the field has yet to agree on a unified strategy
for curating video data. In this paper, we identify and evaluate three
different stages for successful training of video LDMs: text-to-image
pretraining, video pretraining, and high-quality video finetuning. Furthermore,
we demonstrate the necessity of a well-curated pretraining dataset for
generating high-quality videos and present a systematic curation process to
train a strong base model, including captioning and filtering strategies. We
then explore the impact of finetuning our base model on high-quality data and
train a text-to-video model that is competitive with closed-source video
generation. We also show that our base model provides a powerful motion
representation for downstream tasks such as image-to-video generation and
adaptability to camera motion-specific LoRA modules. Finally, we demonstrate
that our model provides a strong multi-view 3D-prior and can serve as a base to
finetune a multi-view diffusion model that jointly generates multiple views of
objects in a feedforward fashion, outperforming image-based methods at a
fraction of their compute budget. We release code and model weights at
https://github.com/Stability-AI/generative-models .


  We discuss the wormholes associated with the four-dimensional Schwarzschild
(S4), Schwarzschild anti De Sitter (SaDS4), and Reissner-N\"ordstrom (RN4)
black holes, in Schwarzschild, isotropic and Kruskal-Szekeres cordinates. The
first two coordinate systems are valid outside the horizons, while the third
one is used for the interiors. In Schwarzschild coordinates, embedding for
SaDS4 exists only for a finite interval of the radial coordinate r, and similar
restrictions exist for RN4. The use of the K-S coordinates allows us to give an
explicit proof of the pinching-off of the bridges, making them non-traversable.
The case of the extreme Reissner-N\"ordstrom (ERN4) is also discussed.


  The coefficients occurring in summation formulae of the Lubbock type are
shown to be generalised Bernoulli polynomials which turn up in subdivision
questions such as quantum field theory around a conical singularity and on
spherical lunes. An image interpretation is made, generating functions are
brought in and some trigonometric summations encountered. A formal Lubbock
formula is introduced for a general delta operator.


  This paper studies a class of exponential family models whose canonical
parameters are specified as linear functionals of an unknown
infinite-dimensional slope function. The optimal minimax rates of convergence
for slope function estimation are established. The estimators that achieve the
optimal rates are constructed by constrained maximum likelihood estimation with
parameters whose dimension grows with sample size. A change-of-measure
argument, inspired by Le Cam's theory of asymptotic equivalence, is used to
eliminate the bias caused by the nonlinearity of exponential family models.


  3D Gaussian Splatting (3DGS) creates a radiance field consisting of 3D
Gaussians to represent a scene. With sparse training views, 3DGS easily suffers
from overfitting, negatively impacting rendering. This paper introduces a new
co-regularization perspective for improving sparse-view 3DGS. When training two
3D Gaussian radiance fields, we observe that the two radiance fields exhibit
point disagreement and rendering disagreement that can unsupervisedly predict
reconstruction quality, stemming from the randomness of densification
implementation. We further quantify the two disagreements and demonstrate the
negative correlation between them and accurate reconstruction, which allows us
to identify inaccurate reconstruction without accessing ground-truth
information. Based on the study, we propose CoR-GS, which identifies and
suppresses inaccurate reconstruction based on the two disagreements: (1)
Co-pruning considers Gaussians that exhibit high point disagreement in
inaccurate positions and prunes them. (2) Pseudo-view co-regularization
considers pixels that exhibit high rendering disagreement are inaccurate and
suppress the disagreement. Results on LLFF, Mip-NeRF360, DTU, and Blender
demonstrate that CoR-GS effectively regularizes the scene geometry,
reconstructs the compact representations, and achieves state-of-the-art novel
view synthesis quality under sparse training views.


  We prove tight upper and lower bounds on approximation ratios of all Boolean
Max-2CSP problems in the streaming model. Specifically, for every type of
Max-2CSP problem, we give an explicit constant $\alpha$, s.t. for any
$\epsilon>0$ (i) there is an $(\alpha-\epsilon)$-streaming approximation using
space $O(\log{n})$; and (ii) any $(\alpha+\epsilon)$-streaming approximation
requires space $\Omega(\sqrt{n})$. This generalizes the celebrated work of
[Kapralov, Khanna, Sudan SODA 2015; Kapralov, Krachun STOC 2019], who showed
that the optimal approximation ratio for Max-CUT was $1/2$.
  Prior to this work, the problem of determining this ratio was open for all
other Max-2CSPs. Our results are quite surprising for some specific Max-2CSPs.
For the Max-DCUT problem, there was a gap between an upper bound of $1/2$ and a
lower bound of $2/5$ [Guruswami, Velingker, Velusamy APPROX 2017]. We show that
neither of these bounds is tight, and the optimal ratio for Max-DCUT is $4/9$.
We also establish that the tight approximation for Max-2SAT is $\sqrt{2}/2$,
and for Exact Max-2SAT it is $3/4$. As a byproduct, our result gives a
separation between space-efficient approximations for Max-2SAT and Exact
Max-2SAT. This is in sharp contrast to the setting of polynomial-time
algorithms with polynomial space, where the two problems are known to be
equally hard to approximate. Finally, we prove that the tight streaming
approximation for \mksat{} is $\sqrt{2}/2$ for every $k\geq2$.


  Ramanujan's last letter to Hardy introduced the world to mock theta
functions, and the mock theta function identities found in Ramanujan's lost
notebook added to their intriguing nature. For example, we find the four
tenth-order mock theta functions and their six identities. The six identities
themselves are of a spectacular nature and were first proved by Choi. We also
find over eight sixth-order mock theta functions in the lost notebook, but
among their many identities there is only one relationship like those of the
tenth-orders. Recently, three new identities for the sixth-order mock theta
functions that are in the spirit of the six tenth-order identities were
discovered. Here we present several families of tenth-order like identities for
Appell functions, which are the building blocks of Ramanujan's mock theta
functions.


  Spatial-temporal graph models are prevailing for abstracting and modelling
spatial and temporal dependencies. In this work, we ask the following question:
whether and to what extent can we localise spatial-temporal graph models? We
limit our scope to adaptive spatial-temporal graph neural networks (ASTGNNs),
the state-of-the-art model architecture. Our approach to localisation involves
sparsifying the spatial graph adjacency matrices. To this end, we propose
Adaptive Graph Sparsification (AGS), a graph sparsification algorithm which
successfully enables the localisation of ASTGNNs to an extreme extent (fully
localisation). We apply AGS to two distinct ASTGNN architectures and nine
spatial-temporal datasets. Intriguingly, we observe that spatial graphs in
ASTGNNs can be sparsified by over 99.5\% without any decline in test accuracy.
Furthermore, even when ASTGNNs are fully localised, becoming graph-less and
purely temporal, we record no drop in accuracy for the majority of tested
datasets, with only minor accuracy deterioration observed in the remaining
datasets. However, when the partially or fully localised ASTGNNs are
reinitialised and retrained on the same data, there is a considerable and
consistent drop in accuracy. Based on these observations, we reckon that
\textit{(i)} in the tested data, the information provided by the spatial
dependencies is primarily included in the information provided by the temporal
dependencies and, thus, can be essentially ignored for inference; and
\textit{(ii)} although the spatial dependencies provide redundant information,
it is vital for the effective training of ASTGNNs and thus cannot be ignored
during training. Furthermore, the localisation of ASTGNNs holds the potential
to reduce the heavy computation overhead required on large-scale
spatial-temporal data and further enable the distributed deployment of ASTGNNs.


  We study the effects of time and space correlations of an external additive
colored noise on the steady-state behavior of a Time-Dependent Ginzburg-Landau
model. Simulations show the existence of nonequilibrium phase transitions
controlled by both the correlation time and length of the noise. A
Fokker-Planck equation and the steady probability density of the process are
obtained by means of a theoretical approximation.


  We consider semilinear elliptic equations with double power nonlineaities.
The condition to assure the existence of positive solutions is well-known. In
the present paper, we remark that the additional condition to assure uniqueness
proposed by Ouyang and Shi is unnecessary.


  Many physical systems can be described in terms of matrix models that we
often cannot solve analytically. Fortunately, they can be studied numerically
in a straightforward way. Many commonly used algorithms follow the Monte Carlo
method, which is efficient for small matrix sizes but cannot guarantee
ergodicity when working with large ones. In this paper, we propose an
improvement of the algorithm that, for a large class of matrix models, allows
to tunnel between various vacua in a proficient way, where sign change of
eigenvalues is proposed externally. We test the method on two models: the pure
potential matrix model and the scalar field theory on the fuzzy sphere.


  Shape analyses of tephra grains result in understanding eruption mechanism of
volcanoes. However, we have to define and select parameter set such as
convexity for the precise discrimination of tephra grains. Selection of the
best parameter set for the recognition of tephra shapes is complicated.
Actually, many shape parameters have been suggested. Recently, neural network
has made a great success in the field of machine learning. Convolutional neural
network can recognize the shape of images without human bias and shape
parameters. We applied the simple convolutional neural network developed for
the handwritten digits to the recognition of tephra shapes. The network was
trained by Morphologi tephra images, and it can recognize the tephra shapes
with approximately 90% of accuracy.


  Moir\'e superlattices formed in two-dimensional semiconductor heterobilayers
provide a new realization of Hubbard model physics in which the number of
electrons per effective atom can be tuned at will. We report on an exact
diagonalization study of the electronic properties of half-filled narrow
moir\'e bands in which correlation strengths are varied by changing twist
angles or interaction strengths. We construct a phase diagram for the bilayer,
identifying where the metal-insulator phase transition occurs, estimating the
sizes of the charge gaps in the insulating phase, and commenting on the nature
of the transition and the importance of sub-dominant interaction parameters.


  After a sudden disruption, weakly interacting quantum systems first relax to
a prethermalized state that can be described by perturbation theory and a
generalized Gibbs ensemble. Using these properties of the prethermalized state
we perturbatively derive a kinetic equation which becomes a quantum Boltzmann
equation in the scaling limit of vanishing interaction. Applying this to
interaction quenches in the fermionic Hubbard model we find that the momentum
distribution relaxes to the thermal prediction of statistical mechanics. For
not too large interaction, this two-stage scenario provides a quantitative
understanding of the time evolution leading from the initial pure via a
metastable prethermal to the final thermal state.


  Following Babai's algorithm for the string isomorphism problem, we determine
that it is possible to write expressions of short length describing certain
permutation cosets, including all permutation subgroups; this is feasible both
in the original version of the algorithm and in its CFSG-free version,
partially done by Babai and completed by Pyber. The existence of such
descriptions gives a weak form of the Cameron-Mar\'oti classification even
without assuming CFSG. We also thoroughly explicate Babai's recursion process
(as given in Helfgott) and obtain explicit constants for the runtime of the
algorithm, both with and without the use of CFSG.


  An extremely compact object (ECO) is defined as a quantum object without
horizon, whose radius is just a small distance $s$ outside its Schwarzschild
radius. We show that any ECO of mass $M$ in $d+1$ dimensions with $s\ll
(M/m_p)^{2/(d-2)(d+1)}l_p$ must have (at leading order) the same thermodynamic
properties -- temperature, entropy and radiation rates -- as the corresponding
semiclassical black hole of mass $M$. An essential aspect of the argument
involves showing that the Tolman-Oppenheimer-Volkoff equation has no consistent
solution in the region just outside the ECO surface, unless this region is
filled with radiation at the (appropriately blueshifted) Hawking temperature.
In string theory it has been found that black hole microstates are fuzzballs --
objects with no horizon -- which are expected to have a radius that is only a
little larger than the horizon radius. Thus the arguments of this paper provide
a nice closure to the fuzzball paradigm: the absence of a horizon removes the
information paradox, and the thermodynamic properties of the semiclassical hole
are nonetheless recovered to an excellent approximation.


  The search for topologically non-trivial states of matter has become an
important goal for condensed matter physics. Recently, a new class of
topological insulators has been proposed. These topological insulators have an
insulating gap in the bulk, but have topologically protected edge states due to
the time reversal symmetry. In two dimensions the helical edge states give rise
to the quantum spin Hall (QSH) effect, in the absence of any external magnetic
field. Here we review a recent theory which predicts that the QSH state can be
realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of
the quantum well, the band structure changes from a normal to an "inverted"
type at a critical thickness $d_c$. We present an analytical solution of the
helical edge states and explicitly demonstrate their topological stability. We
also review the recent experimental observation of the QSH state in
HgTe/(Hg,Cd)Te quantum wells. We review both the fabrication of the sample and
the experimental setup. For thin quantum wells with well width $d_{QW}< 6.3$
nm, the insulating regime shows the conventional behavior of vanishingly small
conductance at low temperature. However, for thicker quantum wells ($d_{QW}>
6.3$ nm), the nominally insulating regime shows a plateau of residual
conductance close to $2e^2/h$. The residual conductance is independent of the
sample width, indicating that it is caused by edge states. Furthermore, the
residual conductance is destroyed by a small external magnetic field. The
quantum phase transition at the critical thickness, $d_c= 6.3$ nm, is also
independently determined from the occurrence of a magnetic field induced
insulator to metal transition.


  The pseudogap Kondo problem, describing quantum impurities coupled to
fermionic quasiparticles with a pseudogap density of states, rho(omega) ~
|omega|^r, shows a rich zero-temperature phase diagram, with different screened
and free moment phases and associated transitions. We analyze both the
particle-hole symmetric and asymmetric cases using renormalization group
techniques. In the vicinity of r=0, which plays the role of a lower-critical
dimension, an expansion in the Kondo coupling is appropriate. In contrast, r=1
is the upper-critical dimension in the absence of particle-hole symmetry, and
here insight can be gained using an expansion in the hybridization strength of
the Anderson model. As a by-product, we show that the particle-hole symmetric
strong-coupling fixed point for r<1 is described by a resonant level model, and
corresponds to an intermediate-coupling fixed point in the renormalization
group language. Interestingly, the value r=1/2 plays the role of a second
lower-critical dimension in the particle-hole symmetric case, and there we can
make progress by a novel expansion performed around a resonant level model. The
different expansions allow a complete description of all critical fixed points
of the models and can be used to compute a variety of properties near
criticality, describing universal local-moment fluctuations at these impurity
quantum phase transitions.


  Finding the most probable (MAP) model in SRL frameworks such as Markov logic
and Problog can, in principle, be solved by encoding the problem as a
`grounded-out' mixed integer program (MIP). However, useful first-order
structure disappears in this process motivating the development of first-order
MIP approaches. Here we present mfoilp, one such approach. Since the syntax and
semantics of mfoilp is essentially the same as existing approaches we focus
here mainly on implementation and algorithmic issues. We start with the
(conceptually) simple problem of using a logic program to generate a MIP
instance before considering more ambitious exploitation of first-order
representations.


  Kilonovae are optical flashes produced in the aftermath of neutron
star-neutron star mergers (NNMs) or neutron star-black hole mergers (NBMs). In
this work, we use the Millennium Simulation, combined with a semi-analytic
galaxy formation model--GABE (Galaxy Assembly with Binary Evolution) which
adopts binary stellar population synthesis models, to explore the cosmic event
rate of kilonovae, and the properties of their host galaxies in a cosmological
context. We find that model with supernova kick velocity of 0 km/s fits the
observation best, in agreement with the exception of some formation channels of
binary neutron star. This indicates that NNMs prefer to originate from binary
systems with low kick velocities. With V$_{\rm kick}$=0 km/s, the cosmic event
rate of NNMs and NBMs at z=0 are 283 Gpc$^{-3}$yr$^{-1}$ and 91
Gpc$^{-3}$yr$^{-1}$, respectively, marginally consistent with the constraint
from LVC GWTC-1. For Milky Way-mass galaxies, we predict the NNM rate is
$25.7^{+59.6}_{-7.1}$ Myr$^{-1}$, which is also in good agreement with the
observed properties of binary neutron stars in the Milky Way. Taking all the
NNMs into account in the history of Milky Way-mass galaxies, we find that the
averaged r-process elements yield with A>79 in a NNM and NBM event should be
0.01 M$_{\odot}$ to be consistent with observation. We conclude that NGC 4993,
the host galaxy of GW170817, is a typical host galaxy for NNMs. However,
generally NNMs and NBMs tend to reside in young, blue, star-forming, late-type
galaxies, with stellar mass and gaseous metallicity distribution peaking at
$10^{10.65}$ M$_{\odot}$ and 8.72-8.85, respectively. By studying kilonovae
host galaxies in the cosmological background, it is promising to constrain
model details better when we have more events in the forthcoming future.
(abridged)


  For fixed $k<g$ and a family of polarized abelian varieties of dimension $g$
over $\mathbb{R}$, we give a criterion for the density in the parameter space
of those abelian varieties over $\mathbb{R}$ containing a $k$-dimensional
abelian subvariety over $\mathbb{R}$. As application, we prove density of such
a set in the moduli space of polarized real abelian varieties of dimension $g$,
and density of real algebraic curves mapping non-trivially to real
$k$-dimensional abelian varieties in the moduli space of real algebraic curves
as well as in the space of real plane curves. This extends to the real setting
results by Colombo and Pirola as outlined in their paper "Some density results
for curves with non-simple jacobians", $\textit{Math. Ann.}$ (1990). We then
consider the real locus of an algebraic stack over $\mathbb{R}$, attaching a
topological space to it. For a real moduli stack, this defines a real moduli
space. We show that for $\mathcal{M}_g$ and $\mathcal{A}_g$, the real moduli
spaces that arise in this way coincide with the moduli spaces of Gross-Harris
("Real algebraic curves", $\textit{Ann. Sci. Ecole. Norm. Sup.}$ (1981)) and
Sepp\"al\"a-Silhol ("Moduli Spaces for Real Algebraic Curves and Real Abelian
Varieties", $\textit{Math. Z.}$ (1989)).


  The dissociation of excited electron-hole pairs is a microscopic process that
is fundamental to the performance of photovoltaic systems. For this process to
be successful, the oppositely charged electron and hole must overcome an
electrostatic binding energy before they undergo ground state recombination.
Here we use a simple model of charge dynamics to investigate the role of
molecular disorder in this process. This model reveals that moderate spatial
variations in electronic energy levels, such as those that arise in disordered
molecular systems, can actually increase charge dissociation yields. We
demonstrate that this is a nonequilibrium effect that is mediated by the
dissipation driven formation of partially dissociated intermediate states that
are long-lived because they cannot easily recombine. We present a kinetic model
that incorporates these states and show that it is capable of reproducing
similar behavior when it is parameterized with nonequilibrium rates.


  When data is unlabelled and the target task is not known a priori, divergent
search offers a strategy for learning a wide range of skills. Having such a
repertoire allows a system to adapt to new, unforeseen tasks. Unlabelled image
data is plentiful, but it is not always known which features will be required
for downstream tasks. We propose a method for divergent search in the few-shot
image classification setting and evaluate with Omniglot and Mini-ImageNet. This
high-dimensional behavior space includes all possible ways of partitioning the
data. To manage divergent search in this space, we rely on a meta-learning
framework to integrate useful features from diverse tasks into a single model.
The final layer of this model is used as an index into the `archive' of all
past behaviors. We search for regions in the behavior space that the current
archive cannot reach. As expected, divergent search is outperformed by models
with a strong bias toward the evaluation tasks. But it is able to match and
sometimes exceed the performance of models that have a weak bias toward the
target task or none at all. This demonstrates that divergent search is a viable
approach, even in high-dimensional behavior spaces.


  In-memory join is an essential operator in any database engine. It has been
extensively investigated in the database literature. In this paper, we study
whether exploiting the CDF-based learned models to boost the join performance
is practical or not. To the best of our knowledge, we are the first to fill
this gap. We investigate the usage of CDF-based partitioning and learned
indexes (e.g., Recursive Model Indexes (RMI) and RadixSpline) in the three join
categories; indexed nested loop join (INLJ), sort-based joins (SJ) and
hash-based joins (HJ). Our study shows that there is a room to improve the
performance of INLJ and SJ categories through our proposed optimized learned
variants. Our experimental analysis showed that these proposed learned variants
of INLJ and SJ consistently outperform the state-of-the-art techniques.


  Latest Generative Adversarial Networks (GANs) are gathering outstanding
results through a large-scale training, thus employing models composed of
millions of parameters requiring extensive computational capabilities. Building
such huge models undermines their replicability and increases the training
instability. Moreover, multi-channel data, such as images or audio, are usually
processed by realvalued convolutional networks that flatten and concatenate the
input, often losing intra-channel spatial relations. To address these issues
related to complexity and information loss, we propose a family of
quaternion-valued generative adversarial networks (QGANs). QGANs exploit the
properties of quaternion algebra, e.g., the Hamilton product, that allows to
process channels as a single entity and capture internal latent relations,
while reducing by a factor of 4 the overall number of parameters. We show how
to design QGANs and to extend the proposed approach even to advanced models.We
compare the proposed QGANs with real-valued counterparts on several image
generation benchmarks. Results show that QGANs are able to obtain better FID
scores than real-valued GANs and to generate visually pleasing images.
Furthermore, QGANs save up to 75% of the training parameters. We believe these
results may pave the way to novel, more accessible, GANs capable of improving
performance and saving computational resources.


  For a quiver $Q$, a $k$-algebra $A$, and a full subcategory $\mathcal X$ of
$A$-mod, the monomorphism category ${\rm Mon}(Q, \mathcal X)$ is introduced.
The main result says that if $T$ is an $A$-module such that there is an exact
sequence $0\rightarrow T_m\rightarrow...\rightarrow T_0\rightarrow
D(A_A)\rightarrow 0$ with each $T_i\in {\rm add} (T)$, then ${\rm Mon}(Q, \
^\perp T) = \ ^\perp (kQ\otimes_k T)$; and if $T$ is cotilting, then
$kQ\otimes_k T$ is a unique cotilting $\m$-module, up to multiplicities of
indecomposable direct summands, such that ${\rm Mon}(Q, \ ^\perp T)= \ ^\perp
(kQ \otimes_k T)$.
  As applications, the category of the Gorenstein-projective
$(kQ\otimes_kA)$-modules is characterized as ${\rm Mon}(Q, \mathcal{GP}(A))$ if
$A$ is Gorenstein; the contravariantly finiteness of ${\rm Mon}(Q, \mathcal X)$
can be described; and a sufficient and necessary condition for ${\rm Mon}(Q,
A)$ being of finite type is given.


  The calculation of the diffusion-controlled reaction rate for partially
absorbing, non-spherical boundaries presents a formidable problem of broad
relevance. In this paper we take the reference case of a spherical boundary and
work out a perturbative approach to get a simple analytical formula for the
first-order correction to the diffusive flux onto a non-spherical partially
absorbing surface of revolution. To assess the range of validity of this
formula, we derive exact and approximate expressions for the reaction rate in
the case of partially absorbing prolate and oblate spheroids. We also present
numerical solutions by a finite-element method that extend the validity
analysis beyond spheroidal shapes. Our perturbative solution provides a handy
way to quantify the effect of non-sphericity on the rate of capture in the
general case of partial surface reactivity.


  We have developed a microscopic theory on phonon energy dispersion in chiral
crystals within a harmonic approximation. One of the main issues is about the
splitting of sound velocity of acoustic phonons with opposite ``crystal''
angular momentum. We have shown that the splitting must be zero even in chiral
crystals and the difference starts from the order of at least $k^2$ or higher
in their energy dispersion. Splitting is evident for chiral optical phonons,
and we have derived a formula for their $k$-linear splitting. Another important
finding is about possible interactions of atomic displacements in microscopic
models. We have found that antisymmetric interactions of $\mathbf{D} _{ij}
\cdot (\mathbf{d} _i \times \mathbf{d} _j) $ type are not allowed in
microscopic Hamiltonians for chiral phonons in compatible with the stability
against the Nambu-Goldstone mode. We have identified that the splitting in both
acoustic and optical modes arises from the harmonic potentials with the
electric toroidal quadrupole of $G_{u}$-type symmetry. These constraint are
important for modeling real materials. Most of our microscopic calculations
have been performed for (quasi-)one-dimensional systems with a trigonal crystal
symmetry including Te, but these results generally hold also for other chiral
phonon systems.


  We introduce a $C^*$-algebra $\mathscr{A}_V$ of a variety $V$ over the number
field $K$ and a $C^*$-algebra $\mathscr{A}_G$ of a reductive group $G$ over the
ring of adeles of $K$. Using Pimsner's Theorem we construct an embedding
$\mathscr{A}_V\hookrightarrow \mathscr{A}_G$, where $V$ is a $G$-coherent
variety, e.g. the Shimura variety of $G$. The embedding is an analog of the
Langlands reciprocity for $C^*$-algebras. It follows from the $K$-theory of the
inclusion $\mathscr{A}_V\subset\mathscr{A}_G$ that the Hasse-Weil $L$-function
of $V$ is a product of the automorphic $L$-functions corresponding to
irreducible representations of the group $G$.


  We present a detailed theoretical study of nonfactorizable contributions of
the charm-quark loop to the amplitude of the $B_s\to \gamma\,\gamma$ decay.
This contribution involves the $B$-meson three-particle Bethe-Salpeter
amplitude, $\langle 0|\bar s(y)G_{\mu\nu}(x)b(0)|\bar B_s(p)\rangle$, for which
we take into account constraints from analyticity and continuity. The
charming-loop contribution of interest may be described as a correction to the
Wilson coefficient $C_{7\gamma}$, $C_{7\gamma}\to C_{7\gamma}(1+\delta
C_{7\gamma})$. We calculate an explicit dependence of $\delta C_{7\gamma}$ on
the parameter $\lambda_{B_s}$. Taking into account all theoretical
uncertainties, $\delta C_{7\gamma}$ may be predicted with better than 10\%
accuracy for any given value of $\lambda_{B_s}$. For our benchmark point
$\lambda_{B_s}=0.45$ GeV, we obtain $\delta C_{7\gamma}=0.045\pm 0.004$.
Presently, $\lambda_{B_s}$ is not known with high accuracy, but its value is
expected to lie in the range $0.3\le \lambda_{B_s}({\rm GeV})\le 0.6$. The
corresponding range of $\delta C_{7\gamma}$ is found to be $0.02\le \delta
C_{7\gamma}\le 0.1$. One therefore expects the correction given by charming
loops at the level of at least a few percent.


  In this paper necessary conditions and sufficient conditions are given for a
linear operator to be a positive operators of an Extended Lorentz cone.
Similarities and differences with the positive operators of Lorentz cones are
investigated.


  The charge/mass distribution f(q/m) of nanodrops and ions electrosprayed in
vacuum from mixtures of formamide (FM) and methylammonium formate (MAF) is
studied by time of flight mass spectrometry at MAF/FM volumetric concentrations
of 5%, 10%, 25% and 50%. Positive and negative polarities yield comparable
f(q/m) curves, though the negative mode yields ~30% larger currents. On
shifting from the highest to the lowest liquid flow rates, at which a cone-jet
is stable, the more conducting solutions evolve from mostly drop to primarily
ion emission. A purely ionic regime is not reached under any condition, but the
drops achieve unusually high q/m. As a result, these sprays have excellent
electrical propulsion characteristics, some being able to cover a 25-fold range
of average q/m with a propulsive efficiency typically in the range of 80%.
Results of formamide electrolytes with formates and nitrates of several other
amines are more briefly reported.


  Tiny face detection aims to find faces with high degrees of variability in
scale, resolution and occlusion in cluttered scenes. Due to the very little
information available on tiny faces, it is not sufficient to detect them merely
based on the information presented inside the tiny bounding boxes or their
context. In this paper, we propose to exploit the semantic similarity among all
predicted targets in each image to boost current face detectors. To this end,
we present a novel framework to model semantic similarity as pairwise
constraints within the metric learning scheme, and then refine our predictions
with the semantic similarity by utilizing the graph cut techniques. Experiments
conducted on three widely-used benchmark datasets have demonstrated the
improvement over the-state-of-the-arts gained by applying this idea.


  We report a high-resolution photocurrent (PC) spectroscopy of a single
self-assembled InAs/GaAs quantum dot (QD) embedded in an n-i-Schottky device
with an applied vector magnetic field. The PC spectra of positively charged
exciton (X$^+$) and neutral exciton (X$^0$) are obtained by two-color resonant
excitation. With an applied magnetic field in Voigt geometry, the double
$\Lambda$ energy level structure of X$^+$ and the dark states of X$^0$ are
observed in PC spectra clearly. In Faraday geometry, the PC amplitude of X$^+$
decreases and then quenches with the increasing of the magnetic field, which
provides a new way to determine the relative sign of the electron and the hole
g-factors. With an applied vector magnetic field, the electron and the hole
g-factor tensors of X$^+$ and X$^0$ are obtained. The anisotropy of the hole
g-factors of both X$^+$ and X$^0$ is larger than that of the electron.


  We present the first evidence for the production of Upsilon(1D) states in the
four-photon cascade, Upsilon(3S)-->gamma chib(2P), chib(2P)-->gamma
Upsilon(1D), Upsilon(1D)-->gamma chib(1P), chib(1P)-->gamma Upsilon(1S),
followed by the Upsilon(1S) annihilation into e+e- or mu+mu-. The signal has a
significance of 10.2 standard deviations. The measured product branching ratio
for these five decays, (2.5+-0.5+-0.5)x10^(-5), is consistent with the
theoretical estimates. The data are dominated by the production of one
Upsilon(1D) state consistent with the J=2 assignment. Its mass is determined to
be (10161.1+-0.6+-1.6) MeV, which is consistent with the predictions from
potential models and lattice QCD calculations.
  We also searched for Upsilon(3S)-->gammachib(2P),
chib(2P)-->gammaUpsilon(1D), followed by either Upsilon(1D)-->eta Upsilon(1S)
or Upsilon(1D)-->pi+pi- Upsilon(1S). We find no evidence for such decays and
set upper limits on the product branching ratios.


  The monolayer of $\textrm{CrI}_3$ has been reported to exhibit the
ferromagnetic order, with a Curie temperature of $45 K$ and off-plane easy
axis, which has attracted much attention in the community of condensed matter
physics. Using the Density Matrix Renormalization Group method, we investigate
the role of correlation effects and using classical Monte Carlo simulations
analyze the nature of phase transitions in the XXZ Hamiltonian on a honeycomb
lattice, which can effectively model $\textrm{CrI}_3$. We show, that the
magnetic ordering of the Hamiltonian's ground state can be well approximated by
classical models in a wide range of an anisotropy parameter space. Using
classical Monte Carlo simulations we estimate the Curie temperature of $49.7 K$
which is in good agreement with experimental result.


  We show there is a closed (in fact effectively closed, i.e., $\Pi^0_1$)
eventually different family (working in ZF or less).


  We study a colloidal suspension confined between two quasi-parallel walls as
a model system for glass transitions in confined geometries. The suspension is
a mixture of two particle sizes to prevent wall-induced crystallization. We use
confocal microscopy to directly observe the motion of colloidal particles. This
motion is slower in confinement, thus producing glassy behavior in a sample
which is a liquid in an unconfined geometry. For higher volume fraction samples
(closer to the glass transition), the onset of confinement effects occurs at
larger length scales.


  We present a detailed investigation of the electrical properties of epitaxial
La0.7Sr0.3MnO3/SrTi0.98Nb0.02O3 Schottky junctions. A fabrication process that
allows reduction of the junction dimensions to current electronic device size
has been employed. A heavily doped semiconductor has been used as a substrate
in order to suppress its series resistance. We show that, unlike standard
semiconductors, high-quality oxide-based Schottky junctions maintain a highly
rectifying behavior for doping concentration of the semiconductor larger than
10^20 cm^(-3). Moreover, the junctions show hysteretic current-voltage
characteristics.


  This application note describes how to model diffusion-limited crystal growth
from vapor using QuickField - a commercial finite-element analysis code. The
crystal growth problem is cast into the format of a steady-state heat diffusion
problem, which is one type of problem QuickField is designed to solve, and we
derive the relevant conversion factors and correspondences between variables.
We also describe three types of boundary conditions in the crystal growth
problem and their corresponding boundary conditions in the heat diffusion
problem. As an example, we examine the crystal growth of ice from water vapor
in a background gas using a variety of mixed boundary conditions.


  The Monin--Obukhov similarity theory-based wind speed and potential
temperature profiles are inherently coupled to each other. We have developed
hybrid approaches to disentangle them, and as a direct consequence, the
estimation of Obukhov length (and associated turbulent fluxes) from either
wind-speed or temperature measurements becomes an effortless task.
Additionally, our approaches give rise to two easily measurable indices of
atmospheric stability. We compare these approaches with the traditional
gradient and profile methods that require both wind-speed and temperature
profile data. Using Monte-Carlo-type numerical experiments we demonstrate that,
if the input profiles are free of any random errors, the performance of the
proposed hybrid approaches is almost equivalent to the profile method and
better than the gradient method. However, the proposed hybrid approaches are
less competitive in comparison to their traditional counterparts in the
presence of random errors.


  We study optical bistable behavior of a Rydberg electromagnetically-induced
transparency (EIT) atomic medium in a unidirectional optical ring-cavity. Due
to strong van del Waal (vdW) interactions between the atoms, both optical
nonlinear dispersion and nonlinear absorption coefficients are enhanced
substantially. Under the condition of two-photon on resonance, we show that
probe one-photon detuning can change the phase of the third order nonlinearity
coefficient, which tunes the character of the optical bistability within
different ratios of dispersive and absorptive types. This enables the
single-photon control over photonic devices for further manipulation of light
other than switches and transistors. More interestingly, we predict appearance
of a scaling phenomena for optical bistabilities with the factors of coupling
Rabi frequency and atomic density. Additionally, we also discuss the influence
of the cavity detuning and the mirror transmission coefficient on the optical
bistable behavior. The strong bistable feature provides a good ingredient for
realizing all-optical logic gate devices in optical computing.


  In this work we show how sublabel-accurate multilabeling approaches can be
derived by approximating a classical label-continuous convex relaxation of
nonconvex free-discontinuity problems. This insight allows to extend these
sublabel-accurate approaches from total variation to general convex and
nonconvex regularizations. Furthermore, it leads to a systematic approach to
the discretization of continuous convex relaxations. We study the relationship
to existing discretizations and to discrete-continuous MRFs. Finally, we apply
the proposed approach to obtain a sublabel-accurate and convex solution to the
vectorial Mumford-Shah functional and show in several experiments that it leads
to more precise solutions using fewer labels.


  The performance of integer-forcing equalization for communication over the
compound multiple-input multipleoutput channel is investigated. An upper bound
on the resulting outage probability as a function of the gap to capacity has
been derived previously, assuming a random precoding matrix drawn from the
circular unitary ensemble is applied prior to transmission. In the present work
a simple and explicit lower bound on the worst-case outage probability is
derived for the case of a system with two transmit antennas and two or more
receive antennas, leveraging the properties of the Jacobi ensemble. The derived
lower bound is also extended to random space-time precoding, and may serve as a
useful benchmark for assessing the relative merits of various algebraic
space-time precoding schemes. We further show that the lower bound may be
adapted to the case of a $1 \times N_t$ system. As an application of this, we
derive closed-form bounds for the symmetric-rate capacity of the Rayleigh
fading multiple-access channel where all terminals are equipped with a single
antenna. Lastly, we demonstrate that the integer-forcing equalization coupled
with distributed space-time coding is able to approach these bounds.


  In recent years, high-speed wireless communication is in vogue. In wireless
communication systems, multipath fading, delay and interference occurres by
reflection or diffraction. In a high-speed wireless communication, it becomes a
necessary to separate desired signal from delay or interference signal. Thus to
overcome these problems Smart antenna systems have been developed. Basically
there are two types of smart antenna systems, one is Switched beam system and
another Adaptive array system.This paper presents the optimum design of a 4x4
plannar Butler matrix array as a key component of a switched beam smart antenna
system, operating at 5.2 GHz for WLAN with a dielectric substrate, FR4 of er
=4.9 and h=1.6mm. Conception details, simulation results and measurements are
also given for the components (microstrip antenna, hybrid couplers,
cross-coupler, phase shifter) used to implement the matrix. In this
dissertation, mathematical calculations for all the components using MATLAB is
done and then every individual component is designed using the commercial
software SONNET. Then these entire components have been combined on a single
substrate and simulated using SONNET.


  In order to further expand the flight envelope of quadrotors under actuator
failures, we design a nonlinear sensor-based fault-tolerant controller to
stabilize a quadrotor with failure of two opposing rotors in the high-speed
flight condition (> 8m/s). The incremental nonlinear dynamic inversion (INDI)
approach which excels in handling model uncertainties is adopted to compensate
for the significant unknown aerodynamic effects. The internal dynamics of such
an underactuated system have been analyzed, and subsequently stabilized by
re-defining the control output. The proposed method can be generalized to
control a quadrotor under single-rotor-failure and nominal conditions. For
validation, flight tests have been carried out in a large-scale open jet wind
tunnel. The position of a damaged quadrotor can be controlled in the presence
of significant wind disturbances. A linear quadratic regulator (LQR) approach
from the literature has been compared to demonstrate the advantages of the
proposed nonlinear method in the windy and high-speed flight condition.


  We use a recent numerical security proof approach to calculate tight secure
key rates in the presence of collective attacks for a continuous-variable (CV)
eight-state phase-shift keying (8PSK) protocol with heterodyne detection in the
asymptotic limit. The results are compared to achievable secure key rates of a
QPSK protocol obtained with the same security proof technique. Furthermore, we
investigate the influence of radial postselection on the secure key rate and
examine a recently suggested strategy to reduce the computational requirements
on the error-correction phase for four-state phase-shift-keying protocols.
Based on our investigations, we suggest different strategies to reduce the raw
key of 8PSK protocols significantly, only on the cost of a slightly lower
secure key rate. This can be used to lower the computational effort of the
error-correction phase, a known bottleneck in many practical implementations,
considerably.


  We present a new global optical potential (GOP) for nucleus-nucleus systems,
including neutron-rich and proton-rich isotopes, in the energy range of $50
\sim 400$ MeV/u. The GOP is derived from the microscopic folding model with the
complex $G$-matrix interaction CEG07 and the global density presented by S{\~
a}o Paulo group. The folding model well accounts for realistic complex optical
potentials of nucleus-nucleus systems and reproduces the existing elastic
scattering data for stable heavy-ion projectiles at incident energies above 50
MeV/u. We then calculate the folding-model potentials (FMPs) for projectiles of
even-even isotopes, $^{8-22}$C, $^{12-24}$O, $^{16-38}$Ne, $^{20-40}$Mg,
$^{22-48}$Si, $^{26-52}$S, $^{30-62}$Ar, and $^{34-70}$Ca, scattered by stable
target nuclei of $^{12}$C, $^{16}$O, $^{28}$Si, $^{40}$Ca $^{58}$Ni, $^{90}$Zr,
$^{120}$Sn, and $^{208}$Pb at the incident energy of 50, 60, 70, 80, 100, 120,
140, 160, 180, 200, 250, 300, 350, and 400 MeV/u. The calculated FMP is
represented, with a sufficient accuracy, by a linear combination of 10-range
Gaussian functions. The expansion coefficients depend on the incident energy,
the projectile and target mass numbers and the projectile atomic number, while
the range parameters are taken to depend only on the projectile and target mass
numbers. The adequate mass region of the present GOP by the global density is
inspected in comparison with FMP by realistic density. The full set of the
range parameters and the coefficients for all the projectile-target
combinations at each incident energy are provided on a permanent open-access
website together with a Fortran program for calculating the microscopic-basis
GOP (MGOP) for a desired projectile nucleus by the spline interpolation over
the incident energy and the target mass number.


  The main purpose of this paper is to establish a Schwarz lemma for the
solutions to the Dirichlet problems for the invariant Laplacians. The obtained
result of this paper is a generalization of the corresponding known results
[11, Theorem 1.1] and [15, Theorem 2.1].


  The unfolding of detector effects is a key aspect of comparing experimental
data with theoretical predictions. In recent years, different Machine-Learning
methods have been developed to provide novel features, e.g. high dimensionality
or a probabilistic single-event unfolding based on generative neural networks.
Traditionally, many analyses unfold detector effects using
transfer-matrix--based algorithms, which are well established in
low-dimensional unfolding. They yield an unfolded distribution of the total
spectrum, together with its covariance matrix. This paper proposes a method to
obtain probabilistic single-event unfolded distributions, together with their
uncertainties and correlations, for the transfer-matrix--based unfolding. The
algorithm is first validated on a toy model and then applied to pseudo-data for
the $pp\rightarrow Z\gamma \gamma$ process. In both examples the performance is
compared to the single-event unfolding of the Machine-Learning--based Iterative
cINN unfolding (IcINN).


  We introduce and study a new variant of shadowing namely mean ergodic
shadowing. We establish relationship of this variant with several other
variants of shadowing. We show that a minimal system with shadowing cannot have
mean ergodic shadowing. We give a necessary and sufficient condition for an
orbital limit function to have mean ergodic shadowing property.


  This paper considers Bayesian revenue maximization in the $k$-unit setting,
where a monopolist seller has $k$ copies of an indivisible item and faces $n$
unit-demand buyers (whose value distributions can be non-identical). Four basic
mechanisms among others have been widely employed in practice and widely
studied in the literature: {\sf Myerson Auction}, {\sf Sequential
Posted-Pricing}, {\sf $(k + 1)$-th Price Auction with Anonymous Reserve}, and
{\sf Anonymous Pricing}. Regarding a pair of mechanisms, we investigate the
largest possible ratio between the two revenues (a.k.a.\ the revenue gap), over
all possible value distributions of the buyers.
  Divide these four mechanisms into two groups: (i)~the discriminating
mechanism group, {\sf Myerson Auction} and {\sf Sequential Posted-Pricing}, and
(ii)~the anonymous mechanism group, {\sf Anonymous Reserve} and {\sf Anonymous
Pricing}. Within one group, the involved two mechanisms have an asymptotically
tight revenue gap of $1 + \Theta(1 / \sqrt{k})$. In contrast, any two
mechanisms from the different groups have an asymptotically tight revenue gap
of $\Theta(\log k)$.


  We demonstrate a technique for shaping current inputs for the direct
modulation of a semiconductor laser for digital communication. The introduction
of shaped current inputs allows for the suppression of relaxation oscillations
and the avoidance of dynamical memory in the physical laser device, i.e., the
output will not be influenced by previously communicated information. On the
example of time-optimized bits, the possible performance enhancement for high
data rate communications is shown numerically.


  There is a natural descending filtration on the singular cohomology of a
complex smooth projective variety called the coniveau filtration. The
generalized Hodge conjecture would imply, rather trivially, that the coniveau
filtration is compatible with pushforwards, pullbacks and products. The purpose
of this paper is to prove this statement unconditionally. This completes the
argument in math.AG/0102070.


  This paper puts forward the concept of Small Private Online Judge (SPOJ).
Compared with Massive Open Online Judge (MOOJ), SPOJ has advantages in
structured data acquisition of students' virtual behavior for its specific
function and tight coupling with the classroom. SPOJ-based empirical education
research can be conducted within "Acquisition-Analysis-Application" (3A)
Framework. The case study of a SPOJ program clarifies the standard pattern of
SPOJ-based 3A research and highlights the emergence of education-intelligence
concept. The challenges of SPOJ-based empirical education research and
implications of SPOJ are also discussed.


  Despite its elegance, the theory of General Relativity is subject to
experimental, observational, and theoretical scrutiny to arrive at tighter
constraints or an alternative, more preferred theory. In alternative gravity
theories, the macroscopic properties of neutron stars, such as mass, radius,
tidal deformability, etc. are modified. This creates a degeneracy between the
uncertainties in the equation of state (EoS) and gravity since assuming a
different EoS can be mimicked by changing to a different theory of gravity. We
formulate a hierarchical Bayesian framework to simultaneously infer the EoS and
gravity parameters by combining multiple astrophysical observations. We test
this framework for a particular 4D Horndeski scalar-tensor theory originating
from higher-dimensional Einstein-Gauss-Bonnet gravity and a set of 20 realistic
EoS and place improved constraints on the coupling constant of the theory with
current observations. Assuming a large number of observations with upgraded or
third-generation detectors, we find that the $A+$ upgrade could place
interesting bounds on the coupling constant of the theory, whereas with the
LIGO Voyager upgrade or the third-generation detectors (Einstein Telescope and
Cosmic Explorer), the degeneracy between EoS and gravity could be resolved with
high confidence, even for small deviations from GR.


  Using supersymmetric grand unified theories, we have recently invented a
framework which allows the prediction of three quark masses, two of the
parameters of the Kobayashi-Maskawa matrix and tan $\beta$, the ratio of the
two vevs. These predictions are used to calculate $\epsilon$ and $\epsilon'$ in
the kaon system, B meson mass mixing and the size of CP asymmetries in the
decays of neutral B mesons to explicit final states of given CP.


  We establish a renormalization group approach which is implemented on the
degrees of freedom defined by the overlap of two replicas to determine the
critical fixed point and to extract four critical exponents for the phase
transition of the three-dimensional Edwards-Anderson model. In addition, we
couple the overlap order parameter to a fictitious field and introduce it
within the two-replica Hamiltonian of the system to study its explicit
symmetry-breaking with the renormalization group. Overlap transformations do
not require a renormalization of the random couplings of a system to extract
the critical exponents associated with the relevant variables of the
renormalization group. We conclude by discussing the applicability of such
transformations in the study of any phase transition which is fully
characterized by an overlap order parameter.


  Recently, there has been a growing interest in rescue robots due to their
vital role in addressing emergency scenarios and providing crucial support in
challenging or hazardous situations where human intervention is difficult.
However, very few of these robots are capable of actively engaging with humans
and undertaking physical manipulation tasks. This limitation is largely
attributed to the absence of tools that can realistically simulate physical
interactions, especially the contact mechanisms between a robotic gripper and a
human body. In this letter, we aim to address key limitations in current
developments towards robotic casualty manipulation. Firstly, we present an
integrative simulation framework for casualty manipulation. We adapt a finite
element method (FEM) tool into the grasping and manipulation scenario, and the
developed framework can provide accurate biomechanical reactions resulting from
manipulation. Secondly, we conduct a detailed assessment of grasping stability
during casualty grasping and manipulation simulations. To validate the
necessity and superior performance of the proposed high-fidelity simulation
framework, we conducted a qualitative and quantitative comparison of grasping
stability analyses between the proposed framework and the state-of-the-art
multi-body physics simulations. Through these efforts, we have taken the first
step towards a feasible solution for robotic casualty manipulation.


  We have developed antenna-coupled transition-edge sensor (TES) bolometers for
a wide range of cosmic microwave background (CMB) polarimetry experiments,
including BICEP2, Keck Array, and the balloon borne SPIDER. These detectors
have reached maturity and this paper reports on their design principles,
overall performance, and key challenges associated with design and production.
Our detector arrays repeatedly produce spectral bands with 20%-30% bandwidth at
95, 150, or 220~GHz. The integrated antenna arrays synthesize symmetric
co-aligned beams with controlled side-lobe levels. Cross-polarized response on
boresight is typically ~0.5%, consistent with cross-talk in our multiplexed
readout system. End-to-end optical efficiencies in our cameras are routinely
35% or higher, with per detector sensitivities of NET~300 uKrts. Thanks to the
scalability of this design, we have deployed 2560 detectors as 1280 matched
pairs in Keck Array with a combined instantaneous sensitivity of ~9 uKrts, as
measured directly from CMB maps in the 2013 season. Similar arrays have
recently flown in the SPIDER instrument, and development of this technology is
ongoing.


  DNA methylation is a well-studied genetic modification that regulates gene
transcription of Eukaryotes. Its alternations have been recognized as a
significant component of cancer development. In this study, we use the DNA
methylation 450k data from The Cancer Genome Atlas to evaluate the efficacy of
DNA methylation data on cancer classification for 30 cancer types. We propose a
new method for gene selection in high dimensional data(over 450 thousand).
Variance filtering is first introduced for dimension reduction and Recursive
feature elimination (RFE) is then used for feature selection. We address the
problem of selecting a small subsets of genes from large number of methylated
sites, and our parsimonious model is demonstrated to be efficient, achieving an
accuracy over 91%, outperforming other studies which use DNA micro-arrays and
RNA-seq Data . The performance of 20 models, which are based on 4 estimators
(Random Forest, Decision Tree, Extra Tree and Support Vector Machine) and 5
classifiers (k-Nearest Neighbours, Support Vector Machine, XGboost, Light GBM
and Multi-Layer Perceptron), is compared and robustness of the RFE algorithm is
examined. Results suggest that the combined model of extra tree plus catboost
classifier offers the best performance in cancer identification, with an
overall validation accuracy of 91% , 92.3%, 93.3% and 93.5% for 20, 30, 40 and
50 features respectively. The biological functions in cancer development of 50
selected genes is also explored through enrichment analysis and the results
show that 12 out of 16 of our top features have already been identified to be
specific with cancer and we also propose some more genes to be tested for
future studies. Therefore, our method may be utilzed as an auxiliary diagnostic
method to determine the actual clinicopathological status of a specific cancer.


  When trying to gain better visibility into a machine learning model in order
to understand and mitigate the associated risks, a potentially valuable source
of evidence is: which training examples most contribute to a given behavior?
Influence functions aim to answer a counterfactual: how would the model's
parameters (and hence its outputs) change if a given sequence were added to the
training set? While influence functions have produced insights for small
models, they are difficult to scale to large language models (LLMs) due to the
difficulty of computing an inverse-Hessian-vector product (IHVP). We use the
Eigenvalue-corrected Kronecker-Factored Approximate Curvature (EK-FAC)
approximation to scale influence functions up to LLMs with up to 52 billion
parameters. In our experiments, EK-FAC achieves similar accuracy to traditional
influence function estimators despite the IHVP computation being orders of
magnitude faster. We investigate two algorithmic techniques to reduce the cost
of computing gradients of candidate training sequences: TF-IDF filtering and
query batching. We use influence functions to investigate the generalization
patterns of LLMs, including the sparsity of the influence patterns, increasing
abstraction with scale, math and programming abilities, cross-lingual
generalization, and role-playing behavior. Despite many apparently
sophisticated forms of generalization, we identify a surprising limitation:
influences decay to near-zero when the order of key phrases is flipped.
Overall, influence functions give us a powerful new tool for studying the
generalization properties of LLMs.


  Alkaline water electrolysis is considered a commercially viable option for
large-scale hydrogen production. However, this process still faces challenges
due to the high voltage (>1.65 V at 10 mA cm$^{-2}$) and its limited stability
at higher current densities due to the inefficient electron transport kinetics.
Herein, a novel cobalt based metallic heterostructure
(Co$_3$Mo3N/Co$_4$N/Co/Co) is designed for application for water electrolysis.
Operando Raman experiments reveal that the formation of Co$_3$Mo3N/Co$_4$N/Co
heterointerface boosts the free water adsorption and dissociation, resulting in
a surplus of protons available for subsequent hydrogen production. Furthermore,
the altered electronic structure of Co$_3$Mo3N/Co$_4$N/Co heterointerface
optimizes the {\Delta}GH of nitrogen atoms at the interface. This synergistic
effect between interfacial nitrogen atoms and metal phase cobalt creates highly
efficient hydrogen evolution reaction (HER) active sites, thereby enhancing the
overall performance. Additionally, the heterostructure exhibits a rapid OH-
adsorption rate, coupled with a strong adsorption strength, leading to improved
oxygen evolution reaction (OER) performance. Crucially, the metallic
heterojunction facilitates fast electron transport, expediting the
aforementioned reaction steps and ultimately improving the overall efficiency
of water splitting. The water electrolyzer with Co$_3$Mo3N/Co$_4$N/Co/Co as a
catalyst exhibits outstanding performance, requiring an impressively low cell
voltage of 1.58 V at 10 mA cm$^{-2}$ and maintaining approximately 100%
retention over a remarkable 100 h duration at 200 mA cm$^{-2}$. This
performance significantly exceeds that of the commercial Pt/C || RuO2
electrolyzer.


  We construct a complex of free-modules over a Gorenstein ring R of dimension
five, for which the Euler characteristic and Dutta multiplicity are different.
This complex is the resolution of an R-module of finite length and finite
projective dimension. As a consequence, the ring R has a nonzero Todd class
tau_3(R) and a bounded free complex whose local Chern character does not vanish
on this class.
  In the course of our work, we construct a module N of finite length and
finite projective dimension over the hypersurface A=K[u,v,w,x,y,z]/(ux+vy+wz),
such that the Serre intersection multiplicity of the modules N and A/(u,v,w)A
is -2.


  Prior research shows that public opinion on climate politics sorts along
partisan lines. However, they leave open the question of whether climate
politics and other politically salient issues exhibit tendencies for issue
alignment, which the political polarization literature identifies as among the
most deleterious aspects of polarization. Using a network approach and social
media data from the Twitter platform, we study polarization of public opinion
toward climate politics and ten other politically salient topics during the
2019 Finnish elections as the emergence of opposing groups in a public forum.
We find that while climate politics is not particularly polarized compared to
the other topics, it is subject to partisan sorting and issue alignment within
the universalist-communitarian dimension of European politics that arose
following the growth of right-wing populism. Notably, climate politics is
consistently aligned with the immigration issue, and temporal trends indicate
that this phenomenon will likely persist.


  We prove, using elementary methods of complex analysis, the following
generalization of the isoperimetric inequality: if $p\in\re$,
$\Omega\subset\re^2$ then the inequality $$
  \left(\frac{|\Omega|}{\pi}\right)^{\frac{p+1}{2}}\leq\frac{1}{2\pi}\int_{\delomega}|x|^pd\sigma(x)
$$ holds true under appropriate assumptions on $\Omega$ and $p.$ This solves an
open problem arising in the context of isoperimetric problems with density and
poses some new ones (for instance generalizations to $\re^n$). We prove the
equivalence with a Hardy-Sobolev inequality, giving the best constant, and
generalize thereby the equivalence between the classical isoperimetric
inequality and the Sobolev inequality. Furthermore, the inequality paves the
way for solving another problem: the generalization of the harmonic
transplantation method of Flucher to the singular Moser-Trudinger embedding.


  The updating required by students in the marketing area is of utmost
importance, since they cannot wait until they are professionals to be updated,
especially in entrepreneurship and around digital marketing. The objective of
this work was to develop a digital marketing specialty module that allows
changing the academic-entrepreneurial-entrepreneurial paradigm of the graduate
of the Centro Universitario de los Altos (CUAltos) in economic-administrative
sciences at the undergraduate, graduate and specialty levels. The module aims
to instruct the student in the latest in digital marketing. As part of this,
two surveys were applied to the teachers of this center to know the viability
and willingness to participate in this module. Among the results, it was
discovered that marketing research specialists who work as teachers at CUAltos
are willing to train other teachers and students of the University of
Guadalajara's system, as well as to advise students in their ventures so that
they can apply different components of this field.


  Subscription privacy of a user has been a historical concern with all the
previous generation mobile networks, namely, GSM, UMTS,and LTE. While a little
improvement have been achieved in securing the privacy of the long-term
identity of a subscriber, the so called IMSI catchers are still in existence
even in the LTE and advanced LTE networks. Proposals have been published to
tackle this problem in 5G based on pseudonyms, and different public-key
technologies. This paper looks into the problem of concealing long-term
identity of a subscriber and presents a technique based on identity based
encryption (IBE) to tackle it. The proposed solution can be extended to a
mutual authentication and key agreement protocol between a serving network (SN)
and a user equipment (UE). This mutual authentication and key agreement
protocol does not need to connect with the home network (HN) on every run. A
qualitative comparison of the advantages and disadvantages of different
techniques show that our solution is competitive for securing the long-term
identity privacy of a user in the 5G network.


  Previous works have validated that text generation APIs can be stolen through
imitation attacks, causing IP violations. In order to protect the IP of text
generation APIs, a recent work has introduced a watermarking algorithm and
utilized the null-hypothesis test as a post-hoc ownership verification on the
imitation models. However, we find that it is possible to detect those
watermarks via sufficient statistics of the frequencies of candidate
watermarking words. To address this drawback, in this paper, we propose a novel
Conditional wATERmarking framework (CATER) for protecting the IP of text
generation APIs. An optimization method is proposed to decide the watermarking
rules that can minimize the distortion of overall word distributions while
maximizing the change of conditional word selections. Theoretically, we prove
that it is infeasible for even the savviest attacker (they know how CATER
works) to reveal the used watermarks from a large pool of potential word pairs
based on statistical inspection. Empirically, we observe that high-order
conditions lead to an exponential growth of suspicious (unused) watermarks,
making our crafted watermarks more stealthy. In addition, \cater can
effectively identify the IP infringement under architectural mismatch and
cross-domain imitation attacks, with negligible impairments on the generation
quality of victim APIs. We envision our work as a milestone for stealthily
protecting the IP of text generation APIs.


  Robust estimation of the essential matrix, which encodes the relative
position and orientation of two cameras, is a fundamental step in structure
from motion pipelines. Recent deep-based methods achieved accurate estimation
by using complex network architectures that involve graphs, attention layers,
and hard pruning steps. Here, we propose a simpler network architecture based
on Deep Sets. Given a collection of point matches extracted from two images,
our method identifies outlier point matches and models the displacement noise
in inlier matches. A weighted DLT module uses these predictions to regress the
essential matrix. Our network achieves accurate recovery that is superior to
existing networks with significantly more complex architectures.


  A new law of physics is proposed, defined on the cosmological scale but with
significant implications for the microscale. Motivated by nonlinear dynamical
systems theory and black-hole thermodynamics, the Invariant Set Postulate
proposes that cosmological states of physical reality belong to a
non-computable fractal state-space geometry I, invariant under the action of
some subordinate deterministic causal dynamics. An exploratory analysis is made
of a possible causal realistic framework for quantum physics, based on key
properties of I. For example, sparseness is used to relate generic
counterfactual states to points not lying on I, thus providing a geometric
basis for the essential contextuality of quantum physics and the role of the
abstract Hilbert Space in quantum theory. Also, self-similarity, described in a
symbolic setting, provides a possible "realistic" perspective on the essential
role of complex numbers and quaternions in quantum theory. A new interpretation
is given to the standard "mysteries" of quantum theory: superposition,
measurement, nonlocality, emergence of classicality and so on. It is proposed
that heterogeneities in the fractal geometry of I are manifestations of the
phenomenon of gravity. Since quantum theory is inherently blind to the
existence of such state-space geometries, the analysis here suggests that
attempts to formulate unified theories of physics within a conventional
quantum-theoretic framework are misguided, and that a successful quantum theory
of gravity should unify the causal non-Euclidean geometry of space time with
the atemporal fractal geometry of state space.


  Despite recent progress in computer vision, fine-grained interpretation of
satellite images remains challenging because of a lack of labeled training
data. To overcome this limitation, we propose using Wikipedia as a previously
untapped source of rich, georeferenced textual information with global
coverage. We construct a novel large-scale, multi-modal dataset by pairing
geo-referenced Wikipedia articles with satellite imagery of their corresponding
locations. To prove the efficacy of this dataset, we focus on the African
continent and train a deep network to classify images based on labels extracted
from articles. We then fine-tune the model on a human annotated dataset and
demonstrate that this weak form of supervision can drastically reduce the
quantity of human annotated labels and time required for downstream tasks.


  Automatic Target Recognition (ATR) in Synthetic aperture radar (SAR) images
becomes a very challenging problem owing to containing high level noise. In
this study, a machine learning-based method is proposed to detect different
moving and stationary targets using SAR images. First Order Statistical (FOS)
features were obtained from Fast Fourier Transform (FFT), Discrete Cosine
Transform (DCT) and Discrete Wavelet Transform (DWT) on gray level SAR images.
Gray Level Co-occurrence Matrix (GLCM), Gray Level Run Length Matrix (GLRLM)
and Gray Level Size Zone Matrix (GLSZM) algorithms are also used. These
features are provided as input for the training and testing stage Support
Vector Machine (SVM) model with Gaussian kernels. 4-fold cross-validations were
implemented in performance evaluation. Obtained results showed that GLCM + SVM
algorithm is the best model with 95.26% accuracy. This proposed method shows
that moving and stationary targets in MSTAR database could be recognized with
high performance.


  We investigate here the degenerate bi-harmonic equation: $$\Delta_{m}^2
u=f(x,u)\; \;\;\mbox{in} \O,\quad u = \Delta u = 0\quad \mbox{on }\;
\p\Omega,$$ with $m\ge 2,$ and also the degenerate tri-harmonic equation: $$
-\Delta_{m}^3 u=f(x,u)\;\;\; \mbox{in} \O,\quad u = \frac{\p u}{\p \nu} =
\frac{\p^{2} u}{\p\nu^{2}} = 0\quad \mbox{on }\; \p\Omega,$$ where
$\Omega\subset \mathbb{R}^{N}$ is a bounded domain with smooth boundary $N>4$
or $N>6$ resp, and $f \in \mathrm{C}^{1}(\Omega\times \mathbb{R})$ satisfying
suitable m-superlinear and subcritical growth conditions. Our main purpose is
to establish $L^{p}$ and $L^{\infty}$ explicit bounds for weak solutions via
the Morse index. Our results extend previous explicit estimate obtained in
\cite{c, HHF, hyf, lec}.


  We present the orbital solution for the donor star of the candidate
transitional millisecond pulsar 3FGL J1544.6-1125, currently observed as an
accreting low-mass X-ray binary. The orbital period is $0.2415361(36)$ days,
entirely consistent with the spectral classification of the donor star as a mid
to late K dwarf. The semi-amplitude of the radial velocity curve is
exceptionally low at $K_2=39.3\pm1.5$ km s$^{-1}$, implying a remarkably
face-on inclination in the range 5--8$^{\circ}$, depending on the neutron star
and donor masses. After determining the veiling of the secondary, we derive a
distance to the binary of $3.8\pm0.7$ kpc, yielding a 0.3--10 keV X-ray
luminosity of $6.1\pm1.9\times10^{33}\,{\rm erg\,s^{-1}}$, similar to confirmed
transitional millisecond pulsars. As face-on binaries rarely occur by chance,
we discuss the possibility that Fermi-selected samples of transitional
milli-second pulsars in the sub-luminous disk state are affected by beaming. By
phasing emission line strength on the spectroscopic ephemeris, we find coherent
variations, and argue that these variations are most consistent with emission
from an asymmetric shock originating near the inner disk.


  In this note we present a construction which improves the best known bound on
the minimal dispersion of large volume boxes in the unit cube. Let $d>1$. The
dispersion of $T \subset [0,1]^d$ is defined as the supremum of the volume
taken over all axis parallel boxes in the cube which do not intersect $T$. The
minimal dispersion of $n$ points in the cube is defined as the infimum of the
dispersion taken over all $T$ such that $|T| = n$. Define the "large volume"
regime as the class of all volumes $\frac{1}{4} < r \leq \frac{1}{2}$. The
inverse of the minimal dispersion is denoted as $N(r,d)$. When the volume is
large, the best known upper bound on $N(r,d)$ is of the order $ {(r -
\frac{1}{4})}^{-1}.$ The construction presented in this note yields an upper
bound given by $$N(r,d) \leq \left \lfloor \frac{\pi}{\sqrt{r - \frac{1}{4}}}
\right \rfloor - 3 .$$ Some of our intermediate estimates are sharp given the
condition that $d \geq C_{r}$, where $C_r$ is a positive constant which depends
only on the volume $r$.


  We propose a random matrix approach to describe vibrational excitations in
disordered systems. The dynamical matrix M is taken in the form M=AA^T where A
is some real (not generally symmetric) random matrix. It guaranties that M is a
positive definite matrix which is necessary for mechanical stability of the
system. We built matrix A on a simple cubic lattice with translational
invariance and interaction between nearest neighbors. We found that for certain
type of disorder phonons cannot propagate through the lattice and the density
of states g(w) is a constant at small w. The reason is a breakdown of affine
assumptions and inapplicability of the elasticity theory. Young modulus goes to
zero in the thermodynamic limit. It strongly reminds of the properties of a
granular matter at the jamming transition point. Most of the vibrations are
delocalized and similar to diffusons introduced by Allen, Feldman et al., Phil.
Mag. B v.79, 1715 (1999).


  We calculate thermal fluctuation properties: volume-averaged order parameter,
Helmholtz free and internal energies, and their variances of a supersaturated
disordered phase in the Gibbs canonical ensemble for an asymmetric (third-order
interactions), athermal (independence of the supersaturation and thermal noise)
effective Hamiltonian. These properties are different from those of the
symmetric thermal one with the most important differences being the phase
coexistence and "thermal expansion." The fluctuation properties of the system
were calculated theoretically, using the perturbation method, and numerically,
using the "brute force" simulations method. Overall, the numerical calculations
match the theory within the accuracy of the numerical method. However, a
discrepancy of the dependence of the internal energy and its variance on the
supersaturation exists. Results of the present study can be used for
calculations of the fluctuation properties of the systems and modeling of
nucleation and other rare events in the framework of the Ginzburg-Landau
method.


  Autoencoder recommenders have recently shown state-of-the-art performance in
the recommendation task due to their ability to model non-linear item
relationships effectively. However, existing autoencoder recommenders use
fully-connected neural network layers and do not employ structure learning.
This can lead to inefficient training, especially when the data is sparse as
commonly found in collaborative filtering. The aforementioned results in lower
generalization ability and reduced performance. In this paper, we introduce
structure learning for autoencoder recommenders by taking advantage of the
inherent item groups present in the collaborative filtering domain. Due to the
nature of items in general, we know that certain items are more related to each
other than to other items. Based on this, we propose a method that first learns
groups of related items and then uses this information to determine the
connectivity structure of an auto-encoding neural network. This results in a
network that is sparsely connected. This sparse structure can be viewed as a
prior that guides the network training. Empirically we demonstrate that the
proposed structure learning enables the autoencoder to converge to a local
optimum with a much smaller spectral norm and generalization error bound than
the fully-connected network. The resultant sparse network considerably
outperforms the state-of-the-art methods like \textsc{Mult-vae/Mult-dae} on
multiple benchmarked datasets even when the same number of parameters and flops
are used. It also has a better cold-start performance.


  The unidentified X-ray source RX J0720.4-3125 is a candidate isolated neutron
star showing evidence for pulsed emission with an 8.39 s period and a spectrum
consistent with a blackbody at kT=80 eV (Haberl et al. 1996, 1997). We show
that this source is most likely an old isolated neutron star accreting from
surrounding media. We then argue that unless it was born with a long spin
period (P_i >~ 0.5 seconds) and weak field (B_i <~ 10^10 G), the magnetic field
on this star must have decayed. With B_i ~ 10^12 G, we find decay timescales >~
10^7 yrs for power law decay or >~ 10^8 yrs for exponential decay. A measured
period derivative Pdot <~ 10^{-16} s s^{-1} would be consistent with an old
accreting isolated neutron star. Both power law and exponential decay models
can give a Pdot ~ 10^{-16} s s^{-1}, though a Pdot substantially less than this
would be indicative of exponential field decay.


  We consider gravity duals to d+1 dimensional quantum critical points with
anisotropic scaling. The primary motivation comes from strongly correlated
electron systems in condensed matter theory but the main focus of the present
paper is on the gravity models in their own right. Physics at finite
temperature and fixed charge density is described in terms of charged black
branes. Some exact solutions are known and can be used to obtain a maximally
extended spacetime geometry, which has a null curvature singularity inside a
single non-degenerate horizon, but generic black brane solutions in the model
can only be obtained numerically. Charged matter gives rise to black branes
with hair that are dual to the superconducting phase of a holographic
superconductor. Our numerical results indicate that holographic superconductors
with anisotropic scaling have vanishing zero temperature entropy when the back
reaction of the hair on the brane geometry is taken into account.


  We extend and survey results in the theory of analysis on fractal sets from
the standard Laplacian on the Sierpi\'nski gasket to the energy Laplacian,
which is defined weakly by using the Kusuoka energy measure. We also extend
results from the Sierpi\'nski gasket to level-$k$ Sierpi\'nski gaskets, for all
$k\geq 2$. We observe that the pointwise formula for the energy Laplacian is
valid for all level-$k$ Sierpi\'nski gaskets, $SG_k$, and we provide a proof of
a known formula for the renormalization constants of the Dirichlet form for
post-critically finite self-similar sets along with a probabilistic
interpretation of the Laplacian pointwise formula. We also provide a vector
self-similar formula and a variable weight self-similar formula for the Kusuoka
measure on $SG_k$, as well as a formula for the scaling of the energy
Laplacian.


  We prove new large sieve inequalities for the Fourier coefficients
$\rho_{j\mathfrak{a}}(n)$ of exceptional Maass forms of a given level, weighted
by sequences $(a_n)$ with sparse Fourier transforms - including two key types
of sequences that arise in the dispersion method. These give the first savings
in the exceptional spectrum for the critical case of sequences as long as the
level, and lead to improved bounds for various multilinear forms of Kloosterman
sums.
  We give three applications and suggest other likely consequences. We show
that both primes and smooth numbers are equidistributed in arithmetic
progressions to moduli up to $x^{5/8 - o(1)}$, using triply-well-factorable
weights for the primes; this completely eliminates the dependency on Selberg's
eigenvalue conjecture in previous results of Lichtman and the author.
Separately, we show that the greatest prime factor of $n^2+1$ is infinitely
often greater than $n^{1.3}$, improving Merikoski's $n^{1.279}$.


  The paper [1] presented the first results on generic identifiability of
dynamic networks with partial excitation and partial measurements, i.e.
networks where not all nodes are excited or not all nodes are measured. One key
contribution of that paper was to establish a set of necessary conditions on
the excitation and measurement pattern (EMP) that guarantee generic
identifiability. In a nutshell, these conditions established that all sources
must be excited and all sinks measured, and that all other nodes must be either
excited or measured. In the present paper, we show that two other types of
nodes, which are defined by the local topology of the network, play an
essential r\^ole in the search for a valid EMP, i.e. one that guarantees
generic identifiability. We have called these nodes dources and dinks. We show
that a network is generically identifiable only if, in addition to the above
mentioned conditions, all dources are excited and all dinks are measured. We
also show that sources and dources are the only nodes in a network that always
need to be excited, and that sinks and dinks are the only nodes that need to be
measured for an EMP to be valid.


  In critical as well as in non-critical string theory the partition function
reduces to an integral over moduli space after integration over matter fields.
For non-critical string theory this moduli integrand is known for genus one
surfaces. The formalism of dynamical triangulations provides us with a
regularization of non-critical string theory. We show how to assign in a simple
and geometrical way a moduli parameter to each triangulation. After integrating
over possible matter fields we can thus construct the moduli integrand. We show
numerically for $c=0$ and $c=-2$ non-critical strings that the moduli integrand
converges to the known continuum expression when the number of triangles goes
to infinity.


  The celebrated hook-length formula gives a product formula for the number of
standard Young tableaux of a straight shape. In 2014, Naruse announced a more
general formula for the number of standard Young tableaux of skew shapes as a
positive sum over excited diagrams of products of hook-lengths. We give an
algebraic and a combinatorial proof of Naruse's formula, by using factorial
Schur functions and a generalization of the Hillman--Grassl correspondence,
respectively.
  The main new results are two different $q$-analogues of Naruse's formula: for
the skew Schur functions, and for counting reverse plane partitions of skew
shapes. We establish explicit bijections between these objects and families of
integer arrays with certain nonzero entries, which also proves the second
formula.


  Video semantic segmentation aims to generate accurate semantic maps for each
video frame. To this end, many works dedicate to integrate diverse information
from consecutive frames to enhance the features for prediction, where a feature
alignment procedure via estimated optical flow is usually required. However,
the optical flow would inevitably suffer from inaccuracy, and then introduce
noises in feature fusion and further result in unsatisfactory segmentation
results. In this paper, to tackle the misalignment issue, we propose a
spatial-temporal fusion (STF) module to model dense pairwise relationships
among multi-frame features. Different from previous methods, STF uniformly and
adaptively fuses features at different spatial and temporal positions, and
avoids error-prone optical flow estimation. Besides, we further exploit feature
refinement within a single frame and propose a novel memory-augmented
refinement (MAR) module to tackle difficult predictions among semantic
boundaries. Specifically, MAR can store the boundary features and prototypes
extracted from the training samples, which together form the task-specific
memory, and then use them to refine the features during inference. Essentially,
MAR can move the hard features closer to the most likely category and thus make
them more discriminative. We conduct extensive experiments on Cityscapes and
CamVid, and the results show that our proposed methods significantly outperform
previous methods and achieves the state-of-the-art performance. Code and
pretrained models are available at https://github.com/jfzhuang/ST_Memory.


  We investigate the potential of exploiting Lya Emitters (LAEs) to constrain
the volume-weighted mean neutral hydrogen fraction of the IGM, x_H, at high
redshifts (specifically z~9). We use "semi-numerical'' simulations to
efficiently generate density, velocity, and halo fields at z=9 in a 250 Mpc
box, resolving halos with masses M>2.2e8 solar masses. We construct ionization
fields corresponding to various values of x_H. With these, we generate LAE
luminosity functions and "counts-in-cell'' statistics. As in previous studies,
we find that LAEs begin to disappear rapidly when x_H > 0.5. Constraining
x_H(z=9) with luminosity functions is difficult due to the many uncertainties
inherent in the host halo mass <--> Lya luminosity mapping. However, using a
very conservative mapping, we show that the number densities derived using the
six z~9 LAEs recently discovered by Stark et al. (2007) imply x_H < 0.7. On a
more fundamental level, these LAE number densities, if genuine, require
substantial star formation in halos with M < 10^9 solar masses, making them
unique among the current sample of observed high-z objects. Furthermore,
reionization increases the apparent clustering of the observed LAEs. We show
that a ``counts-in-cell'' statistic is a powerful probe of this effect,
especially in the early stages of reionization. Specifically, we show that a
field of view (typical of upcoming IR instruments) containing LAEs has >10%
higher probability of containing more than one LAE in a x_H>0.5 universe than a
x_H=0 universe with the same overall number density. With this statistic, a
fully ionized universe can be robustly distinguished from one with x_H > 0.5
using a survey containing only ~ 20--100 galaxies.


  Superconducting compounds of the family Hg-Ba-Ca-Cu-O have been the subject
of intense study since the current record-holder for the highest critical
temperature of a superconductor belongs to this class of materials. Thin films
of the compound with two adjacent copper-oxide layers and a critical
temperature of about 120 K were prepared by a two-step process that consists of
the pulsed-laser deposition of precursor films and the subsequent annealing in
mercury-vapor atmosphere. Like some other high-temperature superconductors,
Hg-Ba-Ca-Cu-O exhibits a specific anomaly of the Hall effect, a double-sign
change of the Hall coefficient close to the superconducting transition. We have
investigated this phenomenon by measurements of the Hall effect at different
angles between the magnetic field direction and the crystallographic c-axis.
The results concerning the upper part of the transition, where the first sign
change occurs, are discussed in terms of the renormalized fluctuation model for
the Hall conductivity, adapted through the field rescaling procedure in order
to take into account the arbitrary orientation of the magnetic field.


  Some systems of parabolic equations with nonlocal initial conditions are
studied. The systems arise when considering steady-state solutions to diffusive
age-structured cooperative or competing species. Local and global bifurcation
techniques are employed to derive a detailed description of the structure of
positive coexistence solutions.


  We compare two different formalisms for modeling the energy deposition of
macroscopically sized/massive quark nuggets (a.k.a. macros) in the Earth's
atmosphere. We show that for a reference mass of 1 g, there is a discrepancy in
the macro luminosity of about 14 orders of magnitude between the predictions of
the two formalisms. Armed with our finding we estimate the sensitivity for
macro detection at space-based (Mini-EUSO and POEMMA) and suborbital
(EUSO-SPB2) experiments.


  Neural fields have rapidly been adopted for representing 3D signals, but
their application to more classical 2D image-processing has been relatively
limited. In this paper, we consider one of the most important operations in
image processing: upsampling. In deep learning, learnable upsampling layers
have extensively been used for single image super-resolution. We propose to
parameterize upsampling kernels as neural fields. This parameterization leads
to a compact architecture that obtains a 40-fold reduction in the number of
parameters when compared with competing arbitrary-scale super-resolution
architectures. When upsampling images of size 256x256 we show that our
architecture is 2x-10x more efficient than competing arbitrary-scale
super-resolution architectures, and more efficient than sub-pixel convolutions
when instantiated to a single-scale model. In the general setting, these gains
grow polynomially with the square of the target scale. We validate our method
on standard benchmarks showing such efficiency gains can be achieved without
sacrifices in super-resolution performance.


  Inspired by Jacobson's thermodynamic approach[gr-qc/9504004], Cai et al
[hep-th/0501055,hep-th/0609128] have shown the emergence of Friedmann equations
from the first law of thermodynamics. We extend Akbar--Cai derivation
[hep-th/0609128] of Friedmann equations to accommodate a general entropy-area
law. Studying the resulted Friedmann equations using a specific entropy-area
law, which is motivated by the generalized uncertainty principle (GUP), reveals
the existence of a maximum energy density closed to Planck density. Allowing
for a general continuous pressure $p(\rho,a)$ leads to bounded curvature
invariants and a general nonsingular evolution. In this case, the maximum
energy density is reached in a finite time and there is no cosmological
evolution beyond this point which leaves the big bang singularity inaccessible
from a spacetime prospective. The existence of maximum energy density and a
general nonsingular evolution is independent of the equation of state and the
spacial curvature $k$. As an example we study the evolution of the equation of
state $p=\omega \rho$ through its phase-space diagram to show the existence of
a maximum energy which is reachable in a finite time.


  Let $S$ be the numerical semigroup generated by three consecutive numbers
$a,a+1,a+2$, where $a\in\mathbb{N}$, $a\geq 3$. We describe the elements of $S$
whose factorizations have all the same length, as well as the set of
factorizations of each of these elements. We give natural partitions of this
subset of $S$ in terms of the length and the denumerant. By using Ap\'ery sets
and Betti elements we are able to extend some results, first obtained by
elementary means.


  Causal discovery algorithms aim at untangling complex causal relationships
from data. Here, we study causal discovery and inference methods based on
staged tree models, which can represent complex and asymmetric causal
relationships between categorical variables. We provide a first graphical
representation of the equivalence class of a staged tree, by looking only at a
specific subset of its underlying independences. We further define a new
pre-metric, inspired by the widely used structural intervention distance, to
quantify the closeness between two staged trees in terms of their corresponding
causal inference statements. A simulation study highlights the efficacy of
staged trees in uncovering complexes, asymmetric causal relationships from
data, and real-world data applications illustrate their use in practical causal
analysis.