  The stringy Euler number and stringy E-function are interesting invariants of
log terminal singularities, introduced by Batyrev. He used them to formulate a
topological mirror symmetry test for pairs of certain Calabi-Yau varieties, and
to show a version of the McKay correspondence. It is a natural question whether
one can extend these invariants beyond the log terminal case. Assuming the
Minimal Model Program, we introduce very general stringy invariants, associated
to 'almost all' singularities, more precisely to all singularities which are
not strictly log canonical. They specialize to the invariants of Batyrev when
the singularity is log terminal. For example the simplest form of our stringy
zeta function is in general a rational function in one variable, but it is just
a constant (Batyrev's stringy Euler number) in the log terminal case.


  Deep neural networks provide state-of-the-art accuracy for vision tasks but
they require significant resources for training. Thus, they are trained on
cloud servers far from the edge devices that acquire the data. This issue
increases communication cost, runtime and privacy concerns. In this study, a
novel hierarchical training method for deep neural networks is proposed that
uses early exits in a divided architecture between edge and cloud workers to
reduce the communication cost, training runtime and privacy concerns. The
method proposes a brand-new use case for early exits to separate the backward
pass of neural networks between the edge and the cloud during the training
phase. We address the issues of most available methods that due to the
sequential nature of the training phase, cannot train the levels of hierarchy
simultaneously or they do it with the cost of compromising privacy. In
contrast, our method can use both edge and cloud workers simultaneously, does
not share the raw input data with the cloud and does not require communication
during the backward pass. Several simulations and on-device experiments for
different neural network architectures demonstrate the effectiveness of this
method. It is shown that the proposed method reduces the training runtime for
VGG-16 and ResNet-18 architectures by 29% and 61% in CIFAR-10 classification
and by 25% and 81% in Tiny ImageNet classification when the communication with
the cloud is done over a low bit rate channel. This gain in the runtime is
achieved whilst the accuracy drop is negligible. This method is advantageous
for online learning of high-accuracy deep neural networks on sensor-holding
low-resource devices such as mobile phones or robots as a part of an edge-cloud
system, making them more flexible in facing new tasks and classes of data.


  Radio frequency driven plasma jets are frequently employed as efficient
plasma sources for surface modification and other processes at atmospheric
pressure. The radio-frequency driven micro atmospheric pressure plasma jet
($\mu$APPJ) is a particular variant of that concept whose geometry allows
direct optical access. In this work, the characteristics of the $\mu$APPJ
operated with a helium-oxygen mixture and its interaction with a helium
environment are studied by numerical simulation. The density and temperature of
the electrons, as well as the concentration of all reactive species are studied
both in the jet itself and in its effluent. It is found that the effluent is
essentially free of charge carriers but contains a substantial amount of
activated oxygen (O, O$_3$ and O$_2(^1\Delta)$). The simulation results are
verified by comparison with experimental data.


  We consider hereditary Artin algebras over arbitrary fields and prove that
there is a natural bijection between the Weyl groups and the sets of full
additive cofinite submodule closed subcategories of the module categories.
While Oppermann, Reiten and Thomas have shown this for algebraically closed
fields and finite fields, we give a different method of proof that holds
independently of the field. In particular, we show a relatively simple way to
construct all modules that contain a given preinjective module as a submodule.


  We discuss the leptonic flavor structure generated by a brane shifted extra
dimensional seesaw model with a single right handed neutrino in the bulk. In
contrast to previous works, no unitarity approximation for the $3 \times 3$
submatrix has been employed. This allows to study phenomenological signatures
such as lepton flavor violating decays. A strong prediction of the model,
assuming CP conservation, are the ratios of flavor violating charged lepton
decay and Z decay branching ratios which are correlated with the neutrino
mixing angles and the neutrino mass hierarchy. Furthermore, it is possible to
obtain branching ratios for $\mu \rightarrow e \gamma$ close to the
experimental bounds even with Yukawa couplings of order one.


  Exponential integrators have been introduced as an efficient alternative to
explicit and implicit methods for integrating large stiff systems of
differential equations. Over the past decades these methods have been studied
theoretically and their performance was evaluated using a range of test
problems. While the results of these investigations showed that exponential
integrators can provide significant computational savings, the research on
validating this hypothesis for large scale systems and understanding what
classes of problems can particularly benefit from the use of the new techniques
is in its initial stages. Resistive magnetohydrodynamic (MHD) modeling is
widely used in studying large scale behavior of laboratory and astrophysical
plasmas. In many problems numerical solution of MHD equations is a challenging
task due to the temporal stiffness of this system in the parameter regimes of
interest. In this paper we evaluate the performance of exponential integrators
on large MHD problems and compare them to a state-of-the-art implicit time
integrator. Both the variable and constant time step exponential methods of
EpiRK-type are used to simulate magnetic reconnection and the Kelvin--Helmholtz
instability in plasma. Performance of these methods, which are part of the EPIC
software package, is compared to the variable time step variable order BDF
scheme included in the CVODE (part of SUNDIALS) library. We study performance
of the methods on parallel architectures and with respect to magnitudes of
important parameters such as Reynolds, Lundquist, and Prandtl numbers. We find
that the exponential integrators provide superior or equal performance in most
circumstances and conclude that further development of exponential methods for
MHD problems is warranted and can lead to significant computational advantages
for large scale stiff systems of differential equations such as MHD.


  Recent advances in artificial intelligence and machine learning may soon
yield paradigm-shifting benefits for aerospace systems. However, complexity and
possible continued on-line learning makes neural network control systems (NNCS)
difficult or impossible to certify under the United States Military
Airworthiness Certification Criteria defined in MIL-HDBK-516C. Run time
assurance (RTA) is a control system architecture designed to maintain safety
properties regardless of whether a primary control system is fully verifiable.
This work examines how to satisfy compliance with MIL-HDBK-516C while using
active set invariance filtering (ASIF), an advanced form of RTA not envisaged
by the 516c committee. ASIF filters the commands from a primary controller,
passing on safe commands while optimally modifying unsafe commands to ensure
safety with minimal deviation from the desired control action. This work
examines leveraging the core theory behind ASIF as assurance argument
explaining novel satisfaction of 516C compliance criteria. The result
demonstrates how to support compliance of novel technologies with 516C as well
as elaborate how such standards might be updated for emerging technologies.


  Conformal quantum field theory is reviewed in the perspective of Axiomatic,
notably Algebraic QFT. This theory is particularly developped in two spacetime
dimensions, where many rigorous constructions are possible, as well as some
complete classifications. The structural insights, analytical methods and
constructive tools are expected to be useful also for four-dimensional QFT.


  Let $\mathcal{H}$ be a complex, separable Hilbert space and
$\mathcal{B}(\mathcal{H})$ denote the algebra of all bounded linear operators
acting on $\mathcal{H}$. Given a unitarily-invariant norm $\| \cdot \|_u$ on
$\mathcal{B}(\mathcal{H})$ and two linear operators $A$ and $B$ in
$\mathcal{B}(\mathcal{H})$, we shall say that $A$ and $B$ are
\emph{polynomially isometric relative to} $\| \cdot \|_u$ if $\| p(A) \|_u = \|
p(B) \|_u$ for all polynomials $p$. In this paper, we examine to what extent an
operator $A$ being polynomially isometric to a normal operator $N$ implies that
$A$ is itself normal. More explicitly, we first show that if $\| \cdot \|_u$ is
any unitarily-invariant norm on $\mathbb{M}_n(\mathbb{C})$, if $A, N \in
\mathbb{M}_n(\mathbb{C})$ are polynomially isometric and $N$ is normal, then
$A$ is normal. We then extend this result to the infinite-dimensional setting
by showing that if $A, N \in \mathcal{B}(\mathcal{H})$ are polynomially
isometric relative to the operator norm and $N$ is a normal operator whose
spectrum neither disconnects the plane nor has interior, then $A$ is normal,
while if the spectrum of $N$ is not of this form, then there always exists a
non-normal operator $B$ such that $B$ and $N$ are polynomially isometric.
Finally, we show that if $A$ and $N$ are compact operators with $N$ normal, and
if $A$ and $N$ are polynomially isometric with respect to the $(c,p)$-norm
studied by Chan, Li and Tu, then $A$ is again normal.


  We investigate dynamic hysteresis and Barkhausen noise in ferromagnetic
materials with a huge number of parallel and rigid Bloch domain walls.
Considering a disordered ferromagnetic system with strong in-plane uniaxial
anisotropy and in-plane magnetization driven by an external magnetic field, we
calculate the equations of motion for a set of coupled domain walls,
considering the effects of the long-range dipolar interactions and disorder. We
derive analytically an expression for the magnetic susceptivity, related to the
effective demagnetizing factor, and show that it has a logarithmic dependence
on the number of domains. Next, we simulate the equations of motion and study
the effect of the external field frequency and the disorder on the hysteresis
and noise properties. The dynamic hysteresis is very well explained by means of
the loss separation theory.


  We present a new model for the infrared emission of the high redshift
hyperluminous infrared galaxy IRAS F10214+4724 which takes into account recent
photometric data from Spitzer and Herschel that sample the peak of its spectral
energy distribution. We first demonstrate that the combination of the AGN
tapered disc and starburst models of Efstathiou and coworkers, while able to
give an excellent fit to the average spectrum of type 2 AGN measured by
Spitzer, fails to match the spectral energy distribution of IRAS F10214+4724.
This is mainly due to the fact that the nuSnu distribution of the galaxy falls
very steeply with increasing frequency (a characteristic of heavy absorption by
dust) but shows a silicate feature in emission. We propose a model that assumes
two components of emission: clouds that are associated with the narrow-line
region and a highly obscured starburst. The emission from the clouds must
suffer significantly stronger gravitational lensing compared to the emission
from the torus to explain the observed spectral energy distribution.


  We study phenomenological aspects of supersymmetric SU(5) grand unified
theories with non-universal gaugino masses. For large tan beta, we investigate
constraints from the requirement of successful electroweak symmetry breaking,
the positivity of stau mass squared and the b to s gamma decay rate. In the
allowed region, the nature of the lightest supersymmetric particle is
determined. Examples of mass spectra are given. We also calculate loop
corrections to the bottom mass due to superpartners.


  We show that, in a resource allocation problem, the ex ante aggregate utility
of players with cumulative-prospect-theoretic preferences can be increased over
deterministic allocations by implementing lotteries. We formulate an
optimization problem, called the system problem, to find the optimal lottery
allocation. The system problem exhibits a two-layer structure comprised of a
permutation profile and optimal allocations given the permutation profile. For
any fixed permutation profile, we provide a market-based mechanism to find the
optimal allocations and prove the existence of equilibrium prices. We show that
the system problem has a duality gap, in general, and that the primal problem
is NP-hard. We then consider a relaxation of the system problem and derive some
qualitative features of the optimal lottery structure.


  In this paper, we are going to review the gravitating electromagnetic field
in the 1+3 formalism on a general hyperbolic space-time manifold. We also
discuss the recent results on the existence of the local field line solutions
of the Einstein-Maxwell equations that generalize the Ra\~{n}ada solutions from
the flat space-time. The global field line solutions do not always exist since
the space-time manifold could impose obstructions to the global extension of
various geometric objects necessary to build the fields. One example of a
gravitating field line solution is the Kopi\'{n}ski-Nat\'{a}rio field which is
discussed in some detail.


  This study proposes a novel method for developing discretization-consistent
closure schemes for implicitly filtered Large Eddy Simulation (LES). Here, the
induced filter kernel, and thus the closure terms, are determined by the
properties of the grid and the discretization operator, leading to additional
computational subgrid terms that are generally unknown in a priori analysis. In
this work, the task of adapting the coefficients of LES closure models is thus
framed as a Markov decision process and solved in an a posteriori manner with
Reinforcement Learning (RL). This optimization framework is applied to both
explicit and implicit closure models. The explicit model is based on an
element-local eddy viscosity model. The optimized model is found to adapt its
induced viscosity within discontinuous Galerkin (DG) methods to homogenize the
dissipation within an element by adding more viscosity near its center. For the
implicit modeling, RL is applied to identify an optimal blending strategy for a
hybrid DG and Finite Volume (FV) scheme. The resulting optimized discretization
yields more accurate results in LES than either the pure DG or FV method and
renders itself as a viable modeling ansatz that could initiate a novel class of
high-order schemes for compressible turbulence by combining turbulence modeling
with shock capturing in a single framework. All newly derived models achieve
accurate results that either match or outperform traditional models for
different discretizations and resolutions. Overall, the results demonstrate
that the proposed RL optimization can provide discretization-consistent
closures that could reduce the uncertainty in implicitly filtered LES.


  We present stellar and planetary properties for 1305 Kepler Objects of
Interest (KOIs) hosting 2025 planet candidates observed as part of the
California-Kepler Survey. We combine spectroscopic constraints, presented in
Paper I, with stellar interior modeling to estimate stellar masses, radii, and
ages. Stellar radii are typically constrained to 11%, compared to 40% when only
photometric constraints are used. Stellar masses are constrained to 4%, and
ages are constrained to 30%. We verify the integrity of the stellar parameters
through comparisons with asteroseismic studies and Gaia parallaxes. We also
recompute planetary radii for 2025 planet candidates. Because knowledge of
planetary radii is often limited by uncertainties in stellar size, we improve
the uncertainties in planet radii from typically 42% to 12%. We also leverage
improved knowledge of stellar effective temperature to recompute incident
stellar fluxes for the planets, now precise to 21%, compared to a factor of two
when derived from photometry.


  Clickbaits are surprising social posts or deceptive news headlines that
attempt to lure users for more clicks, which have posted at unprecedented rates
for more profit or commercial revenue. The spread of clickbait has significant
negative impacts on the users, which brings users misleading or even
click-jacking attacks. Different from fake news, the crucial problem in
clickbait detection is determining whether the headline matches the
corresponding content. Most existing methods compute the semantic similarity
between the headlines and contents for detecting clickbait. However, due to
significant differences in length and semantic features between headlines and
contents, directly calculating semantic similarity is often difficult to
summarize the relationship between them. To address this problem, we propose a
prompt-tuning method for clickbait detection via text summarization in this
paper, text summarization is introduced to summarize the contents, and
clickbait detection is performed based on the similarity between the generated
summary and the contents. Specifically, we first introduce a two-stage text
summarization model to produce high-quality news summaries based on pre-trained
language models, and then both the headlines and new generated summaries are
incorporated as the inputs for prompt-tuning. Additionally, a variety of
strategies are conducted to incorporate external knowledge for improving the
performance of clickbait detection. The extensive experiments on well-known
clickbait detection datasets demonstrate that our method achieved
state-of-the-art performance.


  A preceding paper demonstrated that explicit asymptotic methods generally
work much better for extremely stiff reaction networks than has previously been
shown in the literature. There we showed that for systems well removed from
equilibrium explicit asymptotic methods can rival standard implicit codes in
speed and accuracy for solving extremely stiff differential equations. In this
paper we continue the investigation of systems well removed from equilibrium by
examining quasi-steady-state (QSS) methods as an alternative to asymptotic
methods. We show that for systems well removed from equilibrium, QSS methods
also can compete with, or even exceed, standard implicit methods in speed, even
for extremely stiff networks, and in many cases give somewhat better
integration speed than for asymptotic methods. As for asymptotic methods, we
will find that QSS methods give correct results, but with non-competitive
integration speed as equilibrium is approached. Thus, we shall find that both
asymptotic and QSS methods must be supplemented with partial equilibrium
methods as equilibrium is approached to remain competitive with implicit
methods.


  We study global fixed points for actions of Coxeter groups on nonpositively
curved singular spaces. In particular, we consider property FA_n, an analogue
of Serre's property FA for actions on CAT(0) complexes. Property FA_n has
implications for irreducible representations and complex of groups
decompositions. In this paper, we give a specific condition on Coxeter
presentations that implies FA_n and show that this condition is in fact
equivalent to FA_n for n=1 and 2. As part of the proof, we compute the
Gersten-Stallings angles between special subgroups of Coxeter groups.


  Recent financial bubbles such as the emergence of cryptocurrencies and "meme
stocks" have gained increasing attention from both retail and institutional
investors. In this paper, we propose a game-theoretic model on optimal
liquidation in the presence of an asset bubble. Our setup allows the influx of
players to fuel the price of the asset. Moreover, traders will enter the market
at possibly different times and take advantage of the uptrend at the risk of an
inevitable crash. In particular, we consider two types of crashes: an
endogenous burst which results from excessive selling, and an exogenous burst
which cannot be anticipated and is independent from the actions of the traders.
  The popularity of asset bubbles suggests a large-population setting, which
naturally leads to a mean field game (MFG) formulation. We introduce a class of
MFGs with varying entry times. In particular, an equilibrium will depend on the
entry-weighted average of conditional optimal strategies. To incorporate the
exogenous burst time, we adopt the method of progressive enlargement of
filtrations. We prove existence of MFG equilibria using the weak formulation in
a generalized setup, and we show that the equilibrium strategy can be
decomposed into before-and-after-burst segments, each part containing only the
market information. We also perform numerical simulations of the solution,
which allow us to provide some intriguing results on the relationship between
the bubble burst and equilibrium strategies.


  In this article we construct a family of knot surgery $4$-manifolds admitting
arbitrarily many nonisomorphic Lefschetz fibration structures with the same
genus fiber. We obtain such families by performing knot surgery on an elliptic
surface $E(2)$ using connected sums of fibered knots obtained by Stallings
twist from a slice knot $3_1 \sharp 3^*_1$.
  By comparing their monodromy groups induced from the corresponding monodromy
factorizations, we show that they admit mutually nonisomorphic Lefschetz
fibration structures.


  In the field of natural language processing and human-computer interaction,
human attitudes and sentiments have attracted the researchers. However, in the
field of human-computer interaction, human abnormality detection has not been
investigated extensively and most works depend on image-based information. In
natural language processing, effective meaning can potentially convey by all
words. Each word may bring out difficult encounters because of their semantic
connection with ideas or categories. In this paper, an efficient and effective
human abnormality detection model is introduced, that only uses Bengali text.
This proposed model can recognize whether the person is in a normal or abnormal
state by analyzing their typed Bengali text. To the best of our knowledge, this
is the first attempt in developing a text based human abnormality detection
system. We have created our Bengali dataset (contains 2000 sentences) that is
generated by voluntary conversations. We have performed the comparative
analysis by using Naive Bayes and Support Vector Machine as classifiers. Two
different feature extraction techniques count vector, and TF-IDF is used to
experiment on our constructed dataset. We have achieved a maximum 89% accuracy
and 92% F1-score with our constructed dataset in our experiment.


  The aim of this research is twofold: Firstly, to model and solve a complex
nurse scheduling problem with an integer programming formulation and
evolutionary algorithms. Secondly, to detail a novel statistical method of
comparing and hence building better scheduling algorithms by identifying
successful algorithm modifications. The comparison method captures the results
of algorithms in a single figure that can then be compared using traditional
statistical techniques. Thus, the proposed method of comparing algorithms is an
objective procedure designed to assist in the process of improving an
algorithm. This is achieved even when some results are non-numeric or missing
due to infeasibility. The final algorithm outperforms all previous evolutionary
algorithms, which relied on human expertise for modification.


  Multi-scale spectrum sensing is proposed to overcome the cost of full network
state information on the spectrum occupancy of primary users (PUs) in dense
multi-cell cognitive networks. Secondary users (SUs) estimate the local
spectrum occupancies and aggregate them hierarchically to estimate spectrum
occupancy at multiple spatial scales. Thus, SUs obtain fine-grained estimates
of spectrum occupancies of nearby cells, more relevant to scheduling tasks, and
coarse-grained estimates of those of distant cells. An agglomerative clustering
algorithm is proposed to design a cost-effective aggregation tree, matched to
the structure of interference, robust to local estimation errors and delays.
Given these multi-scale estimates, the SU traffic is adapted in a decentralized
fashion in each cell, to optimize the trade-off among SU cell throughput,
interference caused to PUs, and mutual SU interference. Numerical evaluations
demonstrate a small degradation in SU cell throughput (up to 15% for a 0dB
interference-to-noise ratio experienced at PUs) compared to a scheme with full
network state information, using only one-third of the cost incurred in the
exchange of spectrum estimates. The proposed interference-matched design is
shown to significantly outperform a random tree design, by providing more
relevant information for network control, and a state-of-the-art
consensus-based algorithm, which does not leverage the spatio-temporal
structure of interference across the network.


  We study the two-dimensional superconductor-insulator transition (SIT) in
thin films of tantalum nitride. At zero magnetic field, films can be
disorder-tuned across the SIT by adjusting thickness and film stoichiometry;
insulating films exhibit classical hopping transport. Superconducting films
exhibit a magnetic field-tuned SIT, whose insulating ground state at high field
appears to be a quantum-corrected metal. Scaling behavior at the field-tuned
SIT shows classical percolation critical exponents $z \nu \approx$ 1.3, with a
corresponding critical field $H_c \ll H_{c2}$. The Hall effect shows a crossing
point near $H_c$, but with a non-universal critical value $\rho_{xy}^c$
comparable to the normal state Hall resistivity. We propose that high-carrier
density metals will always exhibit this pattern of behavior at the boundary
between superconducting and (trivially) insulating ground states.


  Limits on dark matter spin dependent elastic scattering cross section on
protons derived from IceCube data are obtained for different dark matter
annihilation channels using micrOMEGAs. The uncertainty on the derived limits,
estimated by using different neutrino spectra, can reach a factor two. For all
dark matter annihilation channels except for quarks, the limits on the spin
dependent cross section are more stringent than those obtained in direct
detection experiments. The new functions that allow to derive those limits are
described.


  A new method to tag the barium daughter in the double beta decay of
$^{136}$Xe is reported. Using the technique of single molecule fluorescent
imaging (SMFI), individual barium dication (Ba$^{++}$) resolution at a
transparent scanning surface has been demonstrated. A single-step photo-bleach
confirms the single ion interpretation. Individual ions are localized with
super-resolution ($\sim$2~nm), and detected with a statistical significance of
12.9~$\sigma$ over backgrounds. This lays the foundation for a new and
potentially background-free neutrinoless double beta decay technology, based on
SMFI coupled to high pressure xenon gas time projection chambers.


  Measurements of ellipticities of background galaxies are sensitive to the
reduced shear, the cosmic shear divided by $(1-\kappa)$ where $\kappa$ is the
projected density field. We compute the difference between shear and reduced
shear both analytically and with simulations. The difference becomes more
important on smaller scales, and will impact cosmological parameter estimation
from upcoming experiments. A simple recipe is presented to carry out the
required correction.


  In this paper, a robust linear quadratic optimal control approach for
accurate active power tracking of wind turbines is presented. For control
synthesis, linear matrix inequalities are employed using an augmented wind
turbine state model with uncertain parameters. The resulting controller ensures
robust stability in different operating regions. In a case study, the novel
approach is compared to existing controllers from literature. Simulations
indicate that the controller improves power tracking accuracy while leading to
similar mechanical wear as existing approaches.


  Context. While Gaia enables to probe in great detail the extended local
neighbourhood, the thin disk structure at larger distances remains sparsely
explored.
  Aims. We aim here to build a non-parametric 3D model of the thin disc
structures handling both the extinction and the stellar density simultaneously.
  Methods. We developed a Bayesian deconvolution method in two dimensions:
extinction and distance. It uses a reference catalogue which completeness
information defines the selection function. It is designed so that any
complementary information from other catalogues can be added. It has also been
designed to be robust to outliers, frequent in crowded fields, and differential
extinction. The prior information is designed to be minimal: only a reference
H-R diagram. We derived for this an empirical H-R diagram of the thin disk
using Gaia DR2 data and synthetic isochrone-based H-R diagrams can also be
used.
  Results. We validated the method on simulations and real fields using 2MASS
and UKIDSS data complemented by Gaia DR2 photometry and parallaxes. We detail
the results of two test fields: a 2MASS field centred around the NGC 4815 open
cluster which shows an over-density of both extinction and stellar density at
the cluster distance, and a UKIDSS field at $l=10^{\circ}$ where we recover the
position of the Galactic bar.


  We present optical spectroscopy data that allowed a measurement of the
redshift for the X-ray selected BL Lacertae object 1517+656. With a redshift of
z = 0.702 this object has an absolute magnitude of B = -26.4 and is also an
extremely powerful radio and X-ray source. Although being a high frequency
peaked BL Lac, this object is one of the most luminous BL Lac objects known so
far. Being also a candidate for gravitational lensing, this object is of high
interest for the BL Lac research. Assuming several cosmological models and a
realistic redshift for the lensed object, we find that 1517+656 has a mass > 2
* 10^12 solar masses and a high velocity dispersion > 350 km/sec.


  Our aim is to bring the theory of analogous polytopes to bear on the study of
quasitoric manifolds, in the context of stably complex manifolds with
compatible torus action. By way of application, we give an explicit
construction of a quasitoric representative for every complex cobordism class
as the quotient of a free torus action on a real quadratic complete
intersection. We suggest a systematic description for omnioriented quasitoric
manifolds in terms of combinatorial data, and explain the relationship with
non-singular projective toric varieties (otherwise known as toric manifolds).
By expressing the first and third authors' approach to the representability of
cobordism classes in these terms, we simplify and correct two of their original
proofs concerning quotient polytopes; the first relates to framed embeddings in
the positive cone, and the second involves modifying the operation of connected
sum to take account of orientations. Analogous polytopes provide an informative
setting for several of the details.


  The coupled nonlinear dynamics of ultracold quantum matter and
electromagnetic field modes in an optical resonator exhibits a wealth of
intriguing collective phenomena. Here we study a $\Lambda$-type,
three-component Bose-Einstein condensate coupled to four dynamical running-wave
modes of a ring cavity, where only two of the modes are externally pumped.
However, the unpumped modes play a crucial role in the dynamics of the system
due to coherent back-scattering of photons. On a mean- field level we identify
three fundamentally different steady-state phases with distinct characteristics
in the density and spatial spin textures: a combined density and spin wave, a
continuous spin spiral with a homogeneous density, and a spin spiral with a
modulated density. The spin-spiral states, which are topological, are
intimately related to cavity-induced spin-orbit coupling emerging beyond a
critical pump power. The topologically trivial density-wave--spin-wave state
has the characteristics of a supersolid with two broken continuous symmetries.
The transitions between different phases are either simultaneously topological
and first order, or second order. The proposed setup allows the simulation of
intriguing many-body quantum phenomena by solely tuning the pump amplitudes and
frequencies, with the cavity output fields serving as a built-in nondestructive
observation tool.


  The functional relation between interquark potential and interquark distance
is explicitly derived by considering the Nambu--Goto action in the $AdS_5
\times S^5$ background. It is also shown that a similar relation holds in a
general background. The implications of this relation for confinement are
briefly discussed.


  Lawvere showed that generalised metric spaces are categories enriched over
$[0, \infty]$, the quantale of the positive extended reals. The statement of
enrichment is a quantitative analogue of being a preorder. Towards seeking a
logic for quantitative metric reasoning, we investigate three
$[0,\infty]$-valued propositional logics over the Lawvere quantale. The basic
logical connectives shared by all three logics are those that can be
interpreted in any quantale, viz finite conjunctions and disjunctions, tensor
(addition for the Lawvere quantale) and linear implication (here a truncated
subtraction); to these we add, in turn, the constant $1$ to express integer
values, and scalar multiplication by a non-negative real to express general
affine combinations. Quantitative equational logic can be interpreted in the
third logic if we allow inference systems instead of axiomatic systems. For
each of these logics we develop a natural deduction system which we prove to be
decidably complete w.r.t. the quantale-valued semantics. The heart of the
completeness proof makes use of the Motzkin transposition theorem. Consistency
is also decidable; the proof makes use of Fourier-Motzkin elimination of linear
inequalities. Strong completeness does not hold in general, even (as is known)
for theories over finitely-many propositional variables; indeed even an
approximate form of strong completeness in the sense of Pavelka or Ben Yaacov
-- provability up to arbitrary precision -- does not hold. However, we can show
it for theories axiomatized by a (not necessarily finite) set of judgements in
normal form over a finite set of propositional variables when we restrict to
models that do not map variables to $\infty$; the proof uses Hurwicz's general
form of the Farkas' Lemma.


  If, on one hand, the inverse seesaw is the paradigm of TeV scale seesaw
mechanism, on the other it is a challenge to find scenarios capable of
realizing it. In this work we propose a scenario, based on the framework of
R-parity violation, that realizes minimally the supersymmetric inverse seesaw
mechanism. In it the energy scale parameters involved in the mechanism are
recognized as the vacuum expectation values of the scalars that compose the
singlet superfields $\hat N^C$ and $\hat S$. We develop also the scalar sector
of the model and show that the Higgs mass receives a new tree-level
contribution that, when combined with the standard contribution plus loop
correction, is capable of attaining $125$GeV without resort to heavy stops.


  We propose an approach for calculating one-loop effective actions and vacuum
energies in quantum field theory. Spectral functions are functions defined by
the eigenvalues of an operator. One-loop effective actions and vacuum energies
in quantum field theory, as well as scattering phase shifts and scattering
amplitudes in quantum mechanics, are all spectral functions. If a
transformation between different spectral functions is identified, we can
obtain a spectral function from another through the transformation. In this
paper, we convert quantum mechanical methods for calculating scattering phase
shifts and scattering amplitudes into quantum field theory methods for
calculating one-loop effective actions and vacuum energies. As examples, the
Born approximation and the WKB approximation in quantum mechanics are converted
into quantum field theory methods. We also calculate the one-loop effective
action and vacuum energy of scalar fields in the Schwarzschild spacetime and
the Reissner-Nordstr\"{o}m spacetime as examples. Some integral representations
of the Bessel function are given in appendices.


  On 2008 October 7, small asteroid 2008 TC3 turned itself into the parent body
of the first meteor ever to be predicted before entering the Earth's
atmosphere. Over five years later, the 2014 AA event became the second instance
of such an occurrence. The uncertainties associated with the pre-impact orbit
of 2008 TC3 are relatively small because thousands of observations were made
during the hours preceding the actual meteor airburst. In sharp contrast, 2014
AA was only observed seven times before impact and consequently its trajectory
is somewhat uncertain. Here, we present a recalculation of the impact
parameters -location and timing- of this meteor based on infrasound recordings.
The new values and their uncertainties together with Monte Carlo and N-body
techniques, are applied to obtain an independent determination of the
pre-impact orbit of 2014 AA. Our orbital solution is used to investigate the
possible presence of known near-Earth objects (NEOs) moving in similar orbits.
Prior to impact, 2014 AA was subjected to a web of overlapping secular
resonances and it followed a path similar to those of 2011 GJ3, 2011 JV10, 2012
DJ54, and 2013 NJ4. NEOs in this transient group have their orbits controlled
by close encounters with the Earth-Moon system at perihelion and Mars at
aphelion, perhaps constituting a dynamical family. Extensive comparison with
other studies is also presented.


  Quantum mechanics under the Copenhagen interpretation is one of the most
experimentally well verified formalisms. However, it is known that the
interpretation makes explicit reference to external observation or
"measurement." One says that the Copenhagen interpretation suffers from the
measurement problem. This deficiency of the interpretation excludes it as a
viable fundamental formalism and prevents the use of standard quantum mechanics
in discussions of quantum cosmology. Numerous alternative interpretations have
been developed with the goals of reproducing its predictive success while
obviating the measurement problem. While several interpretations make distinct,
falsifiable, predictions, many claim to precisely reproduce the results of
standard quantum mechanics. The sheer number of interpretations raises several
issues. If the experimental predictions are identical, how are they to be
assessed? On what grounds can an interpretation be said to trump another?
Without recourse to experimental findings, one may continue to assess an
interpretation on its logical structure, self-consistency, and simplicity
(number and plausibility of its assumptions). We argue, and where possible,
demonstrate, that all common interpretations have unresolved deficiencies.
Among these deficiencies are failures to resolve the measurement problem,
fine-tuning problems, logical/mathematical inconsistencies, disagreement with
experiment, and others. Shortcomings as severe as these call into question the
viability of any of the common interpretations. When appropriate, we indicate
where future work may resolve some of these issues.


  In this paper we prove certain properties of cellular and acyclic classes of
chain complexes of modules over a commutative Noetherian ring. In particular we
show that if X is finite and belongs to some cellular class C then \Sigma^n H_X
also belongs to C, for every n.


  We analyze situations in which players build reputations for honesty rather
than for playing particular actions. A patient player facing a sequence of
short-run opponents makes an announcement about their intended action after
observing an idiosyncratic shock, and before players act. The patient player is
either an honest type whose action coincides with their announcement, or an
opportunistic type who can freely choose their actions. We show that the
patient player can secure a high payoff by building a reputation for being
honest when the short-run players face uncertainty about which of the patient
player's actions are currently feasible, but may receive a low payoff when
there is no such uncertainty.


  The factorisation method for Schr\"odinger operators with magnetic fields on
a two-dimensional surface $M^2$ with non-trivial metric is investigated. This
leads to the new integrable examples of such operators and brings a new look at
some classical problems such as Dirac magnetic monopole and Landau problem. The
global geometric aspects and related spectral properties of the operators from
the factorisation chains are discussed in details. We also consider the Laplace
transformations on a curved surface and extend the class of Schr\"odinger
operators with two integrable levels introduced in the flat case by S.P.Novikov
and one of the authors.


  Neutron scattering experiments have revealed a field-induced
antiferroquadrupolar order parameter in the Pr-based heavy-fermion
superconductor PrOs$_4$Sb$_{12}$. We observed the field-induced
antiferromagnetic dipole moment with the propagation vector
{\textit{\textbf{q}}} = (1 0 0) for the applied field direction both
{\textit{\textbf{H}}}${\parallel}$[1 1 0] and [0 0 1]. For
{\textit{\textbf{H}}}${\parallel}$[1 1 0] at 8 T, it should be noted that the
induced antiferromagnetic moment of 0.16(10) ${\mu}_{\rm B}$/Pr orients
parallel to the field within our experimental accuracy. This observation is
strong evidence that the $O_{xy}$ electric quadrupole to be the primary order
parameter for {\textit{\textbf{H}}}${\parallel}$[1 1 0]. A mean-field
calculation, based on ${\Gamma}_1$ singlet and ${\Gamma}_4^{(2)}$ excited
triplet with the $O_{xy}$ quadrupolar interaction, reproduces the induced
moment direction and its field response. These facts indicate the predominance
of $O_{xy}$-type antiferroquadrupolar interaction in PrOs$_4$Sb$_{12}$.


  The paper uses the technique of finite-dimensional approximation to show that
a constant scalr curvature Kahler metric (on a polarised algebraic variety
without holomorphic vector fields) minimises the Mabuchi functional.


  Data lakes hold a growing amount of cold data that is infrequently accessed,
yet require interactive response times. Serverless functions are seen as a way
to address this use case since they offer an appealing alternative to
maintaining (and paying for) a fixed infrastructure. Recent research has
analyzed the potential of serverless for data processing. In this paper, we
expand on such work by looking into the question of serverless resource
allocation to data processing tasks (number and size of the functions). We
formulate a general model to roughly estimate completion time and financial
cost, which we apply to augment an existing serverless data processing system
with an advisory tool that automatically identifies configurations striking a
good balance -- which we define as being close to the "knee" of their Pareto
frontier. The model takes into account key aspects of serverless: start-up,
computation, network transfers, and overhead as a function of the input sizes
and intermediate result exchanges. Using (micro)benchmarks and parts of TPC-H,
we show that this advisor is capable of pinpointing configurations desirable to
the user. Moreover, we identify and discuss several aspects of data processing
on serverless affecting efficiency. By using an automated tool to configure the
resources, the barrier to using serverless for data processing is lowered and
the narrow window where it is cost effective can be expanded by using a more
optimal allocation instead of having to over-provision the design.


  The conformal invariance properties of the QCD Pomeron in the transverse
plane allow us to give an explicit analytical expression for the solution of
the BFKL equations both in the transverse coordinate and momentum spaces. This
result is obtained from the solution of the conformal eigenvectors in the mixed
representation in terms of two conformal blocks, each block being the product
of an holomorphic times an antiholomorphic function. This property is used to
give an exact expression for the QCD dipole multiplicities and dipole-dipole
cross-sections in the whole parameter space, proving the equivalence between
the BFKL and dipole representations of the QCD Pomeron.


  In a previous paper, we introduced L^p UHF algebras for p in [1, \infty). We
concentrated on the spatial L^p UHF algebras, which are classified up to
isometric isomorphism by p and the scaled ordered K_0-group. In this paper, we
concentrate on a larger class, the L^p UHF algebras of tensor product type
constructed using diagonal similarities. Such an algebra is still simple and
has the same K-theory as the corresponding spatial L^p UHF algebra. For each
choice of p and the K-theory, we provide uncountably many nonisomorphic such
algebras. We further characterize the spatial algebras among them. In
particular, if A is one of these algebras, then A is isomorphic (not
necessarily isometrically) to a spatial L^p UHF algebra if and only if A is
amenable as a Banach algebra, also if and only if A has approximately inner
tensor flip. These conditions are also equivalent to a natural numerical
condition defined in terms of the ingredients used to construct the algebra.


  The central issue in quantum parameter estimation is to find out the optimal
measurement setup that leads to the ultimate lower bound of an estimation
error. We address here a question of whether a Gaussian measurement scheme can
achieve the ultimate bound for phase estimation in single-mode Gaussian
metrology that exploits single-mode Gaussian probe states in a Gaussian
environment. We identify three types of optimal Gaussian measurement setups
yielding the maximal Fisher information depending on displacement, squeezing,
and thermalization of the probe state. We show that the homodyne measurement
attains the ultimate bound for both displaced thermal probe states and squeezed
vacuum probe states, whereas for the other single-mode Gaussian probe states,
the optimized Gaussian measurement cannot be the optimal setup, although they
are sometimes nearly optimal. We then demonstrate that the measurement on the
basis of the product quadrature operators XP+PX, i.e., a non-Gaussian
measurement, is required to be fully optimal.


  The emerging microresonator-based frequency combs revolutionize a broad range
of applications from optical communications to astronomical calibration.
Despite of their significant merits, low energy efficiency and the lack of
all-optical dynamical control severely hinder the transfer of microcomb system
to real-world applications. Here, by introducing active lasing medium into the
soliton microcomb, for the first time, we experimentally achieve the chiral
soliton with agile on-off switch and tunable dual-comb generation in a packaged
microresonator. It is found that such a microresonator enables a soliton
slingshot effect, the rapid soliton formation arising from the extra energy
accumulation induced by inter-modal couplings. Moreover, tuning the erbium gain
can generate versatile multi-soliton states, and extend the soliton operation
window to a remarkable range over 18 GHz detuning. Finally, the gain-assisted
chirality of counterpropagating soliton is demonstrated, which enables an
unprecedented fast on-off switching of soliton microcombs. The non-trivial
chiral soliton formation with active controllability inspires new paradigms of
miniature optical frequency combs and brings the fast tunable soliton tools
within reach.


  Least squares (LS) fitting is one of the most fundamental techniques in
science and engineering. It is used to estimate parameters from multiple noisy
observations. In many problems the parameters are known a-priori to be bounded
integer valued, or they come from a finite set of values on an arbitrary finite
lattice. In this case finding the closest vector becomes NP-Hard problem. In
this paper we propose a novel algorithm, the Tomographic Least Squares Decoder
(TLSD), that not only solves the ILS problem, better than other sub-optimal
techniques, but also is capable of providing the a-posteriori probability
distribution for each element in the solution vector. The algorithm is based on
reconstruction of the vector from multiple two-dimensional projections. The
projections are carefully chosen to provide low computational complexity.
Unlike other iterative techniques, such as the belief propagation, the proposed
algorithm has ensured convergence. We also provide simulated experiments
comparing the algorithm to other sub-optimal algorithms.


  We discuss how two birds---the little hierarchy problem of low-scale type-I
seesaw models and the search for a viable dark matter candidate---are
(proverbially) killed by one stone: a new inert scalar state


  Let $X$ be the exterior of connected sum of knots and $X_i$ the exteriors of
the individual knots. In \cite{morimoto1} Morimoto conjectured (originally for
$n=2$) that $g(X) < \sigma_{i=1}^n g(X_i)$ if and only if there exists a
so-called \em primitive meridian \em in the exterior of the connected sum of a
proper subset of the knots. For m-small knots we prove this conjecture and
bound the possible degeneration of the Heegaard genus (this bound was
previously achieved by Morimoto under a weak assumption \cite{morimoto2}):
  $$\sigma_{i=1}^n g(X_i) - (n-1) \leq g(X) \leq \sigma_{i=1}^n g(X_i).$$


  How can we construct an automated debate judge to evaluate an extensive,
vibrant, multi-turn debate? This task is challenging, as judging a debate
involves grappling with lengthy texts, intricate argument relationships, and
multi-dimensional assessments. At the same time, current research mainly
focuses on short dialogues, rarely touching upon the evaluation of an entire
debate. In this paper, by leveraging Large Language Models (LLMs), we propose
Debatrix, which makes the analysis and assessment of multi-turn debates more
aligned with majority preferences. Specifically, Debatrix features a vertical,
iterative chronological analysis and a horizontal, multi-dimensional evaluation
collaboration. To align with real-world debate scenarios, we introduced the
PanelBench benchmark, comparing our system's performance to actual debate
outcomes. The findings indicate a notable enhancement over directly using LLMs
for debate evaluation. Source code and benchmark data are available online at
https://github.com/ljcleo/debatrix .


  We consider the Hamiltonian $H$ of a 3D spinless non-relativistic quantum
particle subject to parallel constant magnetic and non-constant electric field.
The operator $H$ has infinitely many eigenvalues of infinite multiplicity
embedded in its continuous spectrum. We perturb $H$ by appropriate scalar
potentials $V$ and investigate the transformation of these embedded eigenvalues
into resonances. First, we assume that the electric potentials are
dilation-analytic with respect to the variable along the magnetic field, and
obtain an asymptotic expansion of the resonances as the coupling constant
$\varkappa$ of the perturbation tends to zero. Further, under the assumption
that the Fermi Golden Rule holds true, we deduce estimates for the time
evolution of the resonance states with and without analyticity assumptions; in
the second case we obtain these results as a corollary of suitable Mourre
estimates and a recent article of Cattaneo, Graf and Hunziker \cite{cgh}. Next,
we describe sets of perturbations $V$ for which the Fermi Golden Rule is valid
at each embedded eigenvalue of $H$; these sets turn out to be dense in various
suitable topologies. Finally, we assume that $V$ decays fast enough at infinity
and is of definite sign, introduce the Krein spectral shift function for the
operator pair $(H+V, H)$, and study its singularities at the energies which
coincide with eigenvalues of infinite multiplicity of the unperturbed operator
$H$.


  Quantum many-body scarring (QMBS) has emerged as an intriguing paradigm of
weak ergodicity breaking in nonintegrable quantum many-body models,
particularly lattice gauge theories (LGTs) in $1+1$ spacetime dimensions.
However, an open question is whether QMBS exists in higher-dimensional LGTs
with dynamical matter. Given that nonergodic dynamics in $d{=}1$ spatial
dimension tend to vanish in $d{>}1$, it is important to probe this question.
Using matrix product state techniques for both finite and infinite systems, we
show that QMBS occurs in the $2{+}1$D $\mathrm{U}(1)$ quantum link model (QLM),
as evidenced in persistent coherent oscillations in local observables, a marked
slowdown in the growth of the bipartite entanglement entropy, and revivals in
the fidelity. Interestingly, we see that QMBS is more robust when the matter
degrees of freedom are bosonic rather than fermionic. Our results further shed
light on the intimate connection between gauge invariance and QMBS, and
highlight the persistence of scarring in higher spatial dimensions. Our
findings can be tested in near-term analog and digital quantum simulators, and
we demonstrate their accessibility on a recently proposed cold-atom analog
quantum simulator.


  Experimental findings of CMS on properties of jets and underlying events at
high multiplicities in proton-proton interactions at 7 TeV are interpreted as
an indication of increasing role of central collisions with small impact
parameters. We find an indication that the rates of different hard processes
observed by CMS and ALICE universally depend on underlying event
charged-particles multiplicity until it becomes four times more than average.
It is shown that the increase of the overlap area of colliding protons is not
sufficient for explanation of the rate of jet production in events with
charged-particle multiplicity three times higher than average and some new
mechanisms are necessary like interaction of protons in rare configurations of
higher than average gluon density. Such mechanisms are not included in the
present Monte Carlo event generators. Further studies are proposed


  We describe the quasi-static collapse of a radiating, spherical shell of
matter in de Sitter space-time using a thermodynamical formalism. It is found
that the specific heat at constant area and other thermodynamical quantities
exhibit singularities related to phase transitions during the collapse.


  We theoretically study the THz-induced high-order harmonic generation (HHG)
and nonlinear electric transport in graphene based on the quantum master
equation with the relaxation time approximation. To obtain microscopic insight
into the phenomena, we compare the results of the fully dynamical calculations
with those under a quasi-static approximation, where the electronic system is
approximated as a nonequilibrium steady state. As a result, we find that the
THz-induced electron dynamics in graphene can be accurately modeled with the
nonequilibrium steady-state at each instance. The population distribution
analysis further clarifies that the THz-induced HHG in graphene originates from
the reduction of effective conductivity due to a large displacement of
electrons in the Brillouin zone. By comparing the present nonequilibrium
picture with a thermodynamic picture, we explore the role of the nonequilibrium
nature of electron dynamics on the extremely nonlinear optical and transport
phenomena in graphene.


  In this paper we study the typical speed of a generic earthquake trajectory
leaving compact sets in the moduli space of the once-punctured torus.
Mirzakhani showed that the earthquake flow is measurably equivalent to the
horocyclic flow, which has been studied extensively. Our main result shows that
the earthquake flow and the horocyclic flow behave very differently in cusp
excursions. In particular, we prove a relation between the systole function and
continued fractions and discuss the cusp excursions of earthquake trajectories.


  The classical concept of bounded completeness and its relation to sufficiency
and ancillarity play a fundamental role in unbiased estimation, unbiased
testing, and the validity of inference in the presence of nuisance parameters.
In this short note, we provide a direct proof of a little-known result by
\cite{Far62} on a characterization of bounded completeness based on an $L^1$
denseness property of the linear span of likelihood ratios. As an application,
we show that an experiment with infinite-dimensional observation space is
boundedly complete iff suitably chosen restricted subexperiments with
finite-dimensional observation spaces are.


  We report on the serendipitous X-ray detection, using the Chandra X-ray
Observatory, of the radio pulsar J1718-3718. This pulsar has one of the highest
inferred surface dipole magnetic fields in the radio pulsar population (B =
7.4e13 G), higher than that inferred for one well-known Anomalous X-ray Pulsar
(AXP). The X-ray emission for J1718-3718 appears point-like and has a purely
thermal spectrum, with kT = 0.145 keV and absorbed 0.5-2 keV flux of
(6.3-6.9)e-15 erg/s/cm^2. We show that the pulsar's 2-10 keV luminosity is
several orders of magnitude smaller than those of the non-transient AXPs, and
consistent with the predictions of standard models for initial cooling. The
number of high-magnetic-field radio pulsars observed at X-ray energies now
stands at five. All are X-ray faint, suggesting that either there is a
significant physical distinction between high-magnetic-field radio pulsars and
AXPs, or that high-magnetic-field radio pulsars are, in fact, quiescent AXPs.


  The discrepancy between the observed value of the cosmological constant (CC)
and its expected value from quantum field theoretical considerations motivates
the search for a theory in which the CC is decoupled from the vacuum energy. In
this article, we consider theories in which the CC is regarded as an
integration constant. These theories include trace-free Einstein gravity,
theories constructed from the Codazzi equation (which includes Cotton gravity
and a gauge-gravity inspired theory), and conformal Killing gravity. We remark
on a recent debate regarding the viability of Cotton gravity and find that
while the Codazzi equation is indeed underdetermined, the solutions of the
Codazzi equation trivialize to $\lambda g_{ab}$ on generic backgrounds, and
that in principle, one can close the system with the divergence-free condition
and an appropriate choice of initial data. We also propose a full variational
principle (full in the sense that variations in all variables are considered)
for each of the aforementioned theories that can incorporate the matter sector;
in this manner, we can obtain the trace-free Einstein equations without a
unimodular constraint.


  Large, multi-frequency imaging surveys, such as the Large Synaptic Survey
Telescope (LSST), need to do near-real time analysis of very large datasets.
This raises a host of statistical and computational problems where standard
methods do not work. In this paper, we study a proposed method for combining
stacks of images into a single summary image, sometimes referred to as a
template. This task is commonly referred to as image coaddition. In part, we
focus on a method proposed in previous work, which outlines a procedure for
combining stacks of images in an online fashion in the Fourier domain. We
evaluate this method by comparing it to two straightforward methods through the
use of various criteria and simulations. Note that the goal is not to propose
these comparison methods for use in their own right, but to ensure that
additional complexity also provides substantially improved performance.


  Stochastic gradient descent procedures have gained popularity for parameter
estimation from large data sets. However, their statistical properties are not
well understood, in theory. And in practice, avoiding numerical instability
requires careful tuning of key parameters. Here, we introduce implicit
stochastic gradient descent procedures, which involve parameter updates that
are implicitly defined. Intuitively, implicit updates shrink standard
stochastic gradient descent updates. The amount of shrinkage depends on the
observed Fisher information matrix, which does not need to be explicitly
computed; thus, implicit procedures increase stability without increasing the
computational burden. Our theoretical analysis provides the first full
characterization of the asymptotic behavior of both standard and implicit
stochastic gradient descent-based estimators, including finite-sample error
bounds. Importantly, analytical expressions for the variances of these
stochastic gradient-based estimators reveal their exact loss of efficiency. We
also develop new algorithms to compute implicit stochastic gradient
descent-based estimators for generalized linear models, Cox proportional
hazards, M-estimators, in practice, and perform extensive experiments. Our
results suggest that implicit stochastic gradient descent procedures are poised
to become a workhorse for approximate inference from large data sets


  The increasing prevalence of neurodivergence has led society to give greater
recognition to the importance of neurodiversity. Yet societal perceptions of
neurodivergence continue to be predominantly negative. Drawing on Critical
Disability Studies, accessibility researchers have demonstrated how
neuronormative assumptions dominate HCI. Despite their guidance, neurodivergent
and disabled individuals are still marginalized in technology research. In
particular, intersectional identities remain largely absent from HCI
neurodivergence research. In this paper, I share my perspective as an outsider
of the academic research community: I use critical autoethnography to analyze
my experiences of coming to understand, accept, and value my neurodivergence
within systems of power, privilege, and oppression. Using Data Feminism as an
accessible and practical guide to intersectionality, I derive three tenets for
reconceptualizing neurodivergence to be more inclusive of intersectional
experiences: (1) neurodivergence is a functional difference, not a deficit; (2)
neurodivergent disability is a moment of friction, not a static label; and (3)
neurodivergence accessibility is a collaborative practice, not a one-sided
solution. Then, I discuss the tenets in the context of existing HCI research,
applying the same intersectional lens. Finally, I offer three suggestions for
how accessibility research can apply these tenets in future work, to bridge the
gap between accessibility theory and practice in HCI neurodivergence research


  A diagonal version of the strong reflection principle is introduced, along
with fragments of this principle associated to arbitrary forcing classes. The
relationships between the resulting principles and related principles, such as
the corresponding forcing axioms and the corresponding fragments of the strong
reflection principle are analyzed, and consequences are presented. Some of
these consequences are ``exact'' versions of diagonal stationary reflection
principles of sets of ordinals. We also separate some of these diagonal strong
reflection principles from related axioms.


  We present the light curve of an unusual variable object, DUO 2, detected
during the search for microlensing events by the DUO project. The star remained
stable for more than 150 days before it brightened by more than two magnitudes
in 6 days in the B and R bands. The light curves are achromatic during the
variability. We consider possible explanations of the photometric behavior,
with particular emphasis on the binary lens interpretation of the event. The
masses of the lenses are quite small, with the companion possibly in the range
of a brown dwarf or even a few times of Jupiter. We report evidence of blending
of the source by a companion through the first detection of shift in the light
centroid among all the microlensing experiments. This shift sets a lower limit
of $0.3^{\prime\prime}$ on the separation between the stars. The best lens
model obtained requires moderate blending, which was what motivated us to check
the centroid shift that was subsequently found. The best lens model predicts a
separation of $1^{\prime\prime}$ between the two blended stars. This prediction
was recently tested using two CCD images taken under good seeing conditions.
Both images show two components. Their separation and position angle are in
good agreement with our model.


  Cosmic rays (CRs) are a dynamically important component of the interstellar
medium (ISM) of galaxies. The $\sim$GeV CRs that carry most CR energy and
pressure are likely confined by self-generated turbulence, leading them to
stream along magnetic field lines at the ion Alfv\'en speed. However, the
consequences of self-confinement for CR propagation on galaxy scales remain
highly uncertain. In this paper, we use a large ensemble of
magnetohydrodynamical turbulence simulations to quantify how the basic
parameters describing ISM turbulence -- the sonic Mach number, $\mathcal{M}$
(plasma compressibility), Alfv\'en Mach number, $\mathcal{M}_{A0}$ (strength of
the large-scale field with respect to the turbulence), and ionisation fraction
by mass, $\chi$ -- affect the transport of streaming CRs. We show that the
large-scale transport of CRs whose small-scale motion consists of streaming
along field lines is well described as a combination of streaming along the
mean field and superdiffusion both along (parallel to) and across
(perpendicular to) it; $\mathcal{M}_{A0}$ drives the level of anisotropy
between parallel and perpendicular diffusion and $\chi$ modulates the magnitude
of the diffusion coefficients, while in our choice of units, $\mathcal{M}$ is
unimportant except in the sub-Alfv\'enic ($\mathcal{M}_{A0} \lesssim 0.5$)
regime. Our finding that superdiffusion is ubiquitous potentially explains the
apparent discrepancy between CR diffusion coefficients inferred from
measurements close to individual sources compared to those measured on larger,
Galactic scales. Finally, we present empirical fits for the diffusion
coefficients as a function of plasma parameters that may be used as sub-grid
recipes for global interstellar medium, galaxy or cosmological simulations.


  We introduce a minimal model description for the dynamics of transcriptional
regulatory networks. It is studied within a mean-field approximation, i.e., by
deterministic ode's representing the reaction kinetics, and by stochastic
simulations employing the Gillespie algorithm. We elucidate the different
results both approaches can deliver, depending on the network under study, and
in particular depending on the level of detail retained in the respective
description. Two examples are addressed in detail: the repressilator, a
transcriptional clock based on a three-gene network realized experimentally in
E. coli, and a bistable two-gene circuit under external driving, a
transcriptional network motif recently proposed to play a role in cellular
development.


  We prove that two Springer maps over a nilpotent orbit closure with the same
degree are connected by stratified Mukai flops and the latter is obtained by
extremal contractions of a natural resolution of the nilpotent orbit closure.


  In an attempt to understand the Penrose inequality for black holes with
angular momentum, an axisymmetric, vacuum, asymptotically Euclidean initial
data set subject to certain quasi stationary conditions is considered for a
case study. A new geometric definition of angular velocity of a rotating black
hole is defined in terms of the momentum constraint, without any reference to a
stationary Killing vector field. The momentum constraint is then shown to be
equivalent to a Beltrami equation for compressible fluid flow. In terms of
spinors, a generalised first law for rotating black holes (possibly with
multi-connected horizon located along the symmetry axis) is then proven and may
be regarded as a Penrose type inequality for black holes with angular momentum.


  We study a large class of BPS surface defects in 4d N=2 gauge theories. They
are defined by coupling a 2d N=(2,2) gauged linear sigma model to the 4d bulk
degrees of freedom. Our main result is an efficient computation of the
effective twisted superpotential for all these models in terms of a basic
object closely related to the resolvent of the 4d gauge theory, which encodes
the curve describing the 4d low energy dynamics. We reproduce and extend the
results of brane constructions and compute the effective twisted superpotential
for general monodromy surface defects. We encounter novel, puzzling field
theory phenomena in the low energy dynamics of the simplest surface defects and
we propose some local models to explain them. We also study in some detail the
behavior of surface defects near monopole points of the bulk theory's Coulomb
branch. Finally, we explore the effect on the defect of breaking the bulk
supersymmetry from N=2 to N=1 and show that certain quantities are independent
of this breaking.


  Controlling the magnetic state of two-dimensional (2D) materials is crucial
for spintronic applications. By employing data-mining and autonomous density
functional theory calculations, we demonstrate the switching of magnetic
properties of 2D non-van der Waals materials upon hydrogen passivation. The
magnetic configurations are tuned to states with flipped and enhanced moments.
For 2D CdTiO$_3$ - a nonmagnetic compound in the pristine case - we observe an
onset of ferromagnetism upon hydrogenation. Further investigation of the
magnetization density of the pristine and passivated systems provides a
detailed analysis of modified local spin symmetries and the emergence of
ferromagnetism. Our results indicate that selective surface passivation is a
powerful tool for tailoring magnetic properties of nanomaterials such as
non-vdW 2D compounds.


  (abridged) We continue the study of $\Lambda$SFDM cosmologies, which differ
from $\Lambda$CDM in that CDM is replaced by scalar field dark matter (SFDM) by
calculating the evolution of the background Universe, as well as linear
perturbations, focusing on scalar modes. We consider models with complex scalar
field with a repulsive, quartic self-interaction (SI), and models without SI,
referred to as fuzzy dark matter (FDM). To this end, we modify the Boltzmann
code CLASS, to incorporate the physics of complex SFDM which has as one of its
characteristics that its equation of state is maximally stiff in the very early
Universe, dominating then over all the other cosmic components, even over
radiation. We calculate CMB and matter power spectra as well as unconditional
Press-Schechter halo mass functions for various models, expanding previous
literature that were limited either to the background, or to a semi-analytical
approach to SFDM density perturbations neglecting the early stiff phase.
Comparing our results of each, SFDM and FDM, with real-field ultralight axion
models (ULAs) without SI, we characterize the differences between the
respective background evolution and linear structure growth. Our calculations
confirm previous results of recent literature, implying that SFDM models with
$\gtrsim$ kpc-size halo cores are disfavored, questioning their ability to
explain the small-scale problems on dwarf-galactic scales. Also we find that
the kinetic energy due to the phase of the complex field leads to marked
differences between SFDM/FDM versus ULAs. The mild falloff in the SFDM power
spectrum toward high k is similar to that of CDM but based on different
effects, namely the rapidly shrinking Jeans mass for SFDM as opposed to the
Meszaros effect for CDM. In addition, we find that the sharp cutoff in the ULA
power spectrum is also followed by a mild falloff, albeit at very small power.


  A review of recent electroweak results from hadron colliders is given.
Properties of the W and Z gauge bosons using final states containing electrons
and muons based on large integrated luminosities are presented. The emphasis is
placed on the measurement of the mass of the W boson and the measurement of
trilinear gauge boson couplings.


  We report on the single-step fabrication of homogeneous and highly ordered
Laser Induced Periodic Surface Structures (LIPSS) over large areas on Au
nanolayers, that can be used for plasmonic sensing. A comprehensive study on
LIPSS formation on 32 nm Au film upon double, 170 fs pulse irradiation,
unveiled the key importance of interpulse delay as the determining factor
behind the homogeneity of laser induced structures and confirmed that highly
ordered, functional LIPSS occur solely upon double pulse irradiation. In
particular, the impact of pulse overlap, fluence and interpulse delay reveals
that homogeneous LIPSS formation is optimized within a specific interpulse
delay range. At the same time, examination of nanoscale features of the
structures points out a significant differentiation of the LIPSS formation
characteristics between single and double pulse irradiation. Theoretical
investigation complements experimental results providing insights on the
structure formation mechanism. Ellipsometric measurements validate that such
structures exhibit characteristic plasmon resonances that can be exploited for
sensing applications. The presented data demonstrate a novel functionality of
LIPSS, while providing strong evidence of the capabilities of femtosecond
double pulse irradiation as a valuable and low-cost tool for the precise
fabrication of highly ordered structures.


  Epistemic logics are a primary formalism for multi-agent systems but major
reasoning tasks in such epistemic logics are intractable, which impedes
applications of multi-agent epistemic logics in automatic planning. Knowledge
compilation provides a promising way of resolving the intractability by
identifying expressive fragments of epistemic logics that are tractable for
important reasoning tasks such as satisfiability and forgetting. The property
of logical separability allows to decompose a formula into some of its
subformulas and thus modular algorithms for various reasoning tasks can be
developed. In this paper, by employing logical separability, we propose an
approach to knowledge compilation for the logic Kn by defining a normal form
SDNF. Among several novel results, we show that every epistemic formula can be
equivalently compiled into a formula in SDNF, major reasoning tasks in SDNF are
tractable, and formulas in SDNF enjoy the logical separability. Our results
shed some lights on modular approaches to knowledge compilation. Furthermore,
we apply our results in the multi-agent epistemic planning. Finally, we extend
the above result to the logic K45n that is Kn extended by introspection axioms
4 and 5.


  Educational research highlights that improved careers education is needed to
increase participation in science, technology, engineering, and mathematics
(STEM). Current UK careers resources concerning the space sector, however, are
found to perhaps not best reflect the diversity of roles present and may in
fact perpetuate misconceptions about the usefulness of science. We, therefore,
compile a more diverse set of space-related jobs, which will be used in the
development of a new space careers resource.


  In this paper we revisited the theory of selective reflection from a dilute
vapor cell. A self-consistent theory was developed for reflection spectrum for
Fabry-Perot interferometer. Formulas for single and multiple reflections were
obtained. We also obtained the effective refractive index for a single
selective reflection. The results of the paper are in a good agreement with
existing experimental results.


  Forming a hetero-interface is a materials-design strategy that can access an
astronomically large phase space. However, the immense phase space necessitates
a high-throughput approach for optimal interface design. Here we introduce a
high-throughput computational framework, InterMatch, for efficiently predicting
charge transfer, strain, and superlattice structure of an interface by
leveraging the databases of individual bulk materials. Specifically, the
algorithm reads in the lattice vectors, density of states, and the stiffness
tensors for each material in their isolated form from the Materials Project.
From these bulk properties, InterMatch estimates the interfacial properties. We
benchmark InterMatch predictions for the charge transfer against experimental
measurements and supercell density-functional theory calculations. We then use
InterMatch to predict promising interface candidates for doping transition
metal dichalcogenide MoSe$_2$. Finally, we explain experimental observation of
factor of 10 variation in the supercell periodicity within a few microns in
graphene/$\alpha$-RuCl$_3$ by exploring low energy superlattice structures as a
function of twist angle using InterMatch. We anticipate our open-source
InterMatch algorithm accelerating and guiding ever-growing interfacial design
efforts. Moreover, the interface database resulting from the InterMatch
searches presented in this paper can be readily accessed through
https://contribs.materialsproject.org/projects/intermatch/ .


  Using the uniform most powerful unbiased test, we observed the sales
distribution of consumer electronics in Japan on a daily basis and report that
it follows both a lognormal distribution and a power-law distribution and
depends on the state of the market. We show that these switches occur quite
often. The underlying sales dynamics found between both periods nicely matched
a multiplicative process. However, even though the multiplicative term in the
process displays a size-dependent relationship when a steady lognormal
distribution holds, it shows a size-independent relationship when the power-law
distribution holds. This difference in the underlying dynamics is responsible
for the difference in the two observed distributions.


  For Ch\^atelet surfaces defined over number fields, we study two arithmetic
properties, the Hasse principle and weak approximation, when passing to an
extension of the base field. Generalizing a construction of Y. Liang, we show
that for an arbitrary extension of number fields $L/K,$ there is a Ch\^atelet
surface over $K$ which does not satisfy weak approximation over any
intermediate field of $L/K,$ and a Ch\^atelet surface over $K$ which satisfies
the Hasse principle over an intermediate field $L'$ if and only if $[L' : K]$
is even.


  We provide a complete classification of well-rounded ideal lattices arising
from real quadratic fields. We show that the ideals that give rise to such
lattices are precisely the ones that correspond to divisors $a$ of the
discriminant $d$ that satisfy $\sqrt{\frac{d}{3}}<a<\sqrt{3d}.$


  For infectious diseases, characterizing symptom duration is of clinical and
public health importance. Symptom duration may be assessed by surveying
infected individuals and querying symptom status at the time of survey
response. For example, in a SARS-CoV-2 testing program at the University of
Washington, participants were surveyed at least 28 days after testing positive
and asked to report current symptom status. This study design yielded current
status data: Outcome measurements for each respondent consisted only of the
time of survey response and a binary indicator of whether symptoms had resolved
by that time. Such study design benefits from limited risk of recall bias, but
analyzing the resulting data necessitates specialized statistical tools. Here,
we review methods for current status data and describe a novel application of
modern nonparametric techniques to this setting. The proposed approach is valid
under weaker assumptions compared to existing methods, allows use of flexible
machine learning tools, and handles potential survey nonresponse. From the
university study, we estimate that 19% of participants experienced ongoing
symptoms 30 days after testing positive, decreasing to 7% at 90 days. Female
sex, history of seasonal allergies, fatigue during acute infection, and higher
viral load were associated with slower symptom resolution.


  We study the link between WZW model and the spin-1/2 XYZ chain. This is
achieved by comparing the second-order differential equations from them. In the
former case, the equation is the Ward-Takahashi identity satisfied by one-point
toric conformal blocks. In the latter case, it arises from Baxter's TQ
relation. We find that the dimension of the representation space w.r.t. the
V-valued primary field in these conformal blocks gets mapped to the total
number of chain sites. By doing so, Stroganov's "The Importance of being Odd"
(cond-mat/0012035) can be consistently understood in terms of WZW model
language. We first confirm this correspondence by taking a trigonometric limit
of the XYZ chain. That eigenstates of the resultant two-body Sutherland model
from Baxter's TQ relation can be obtained by deforming toric conformal blocks
supports our proposal.


  This paper gives a description of a new on-line database
http://lpsc.in2p3.fr/crdb and associated on-line tools (data selection, data
export, plots, etc.) for charged cosmic-ray measurements. The experimental
setups (type, flight dates, techniques) from which the data originate are
included in the database, along with the references to all relevant
publications. The database relies on the MySQL5 engine. The web pages and
queries are based on PHP, AJAX and the jquery, jquery.cluetip, jquery-ui, and
table-sorter third-party libraries. In this first release, we restrict
ourselves to Galactic cosmic rays with Z<=30 and a kinetic energy per nucleon
up to a few tens of TeV/n. This corresponds to more than 200 different
sub-experiments (i.e., different experiments, or data from the same experiment
flying at different times) in as many publications. We set up a cosmic-ray
database and provide tools to sort and visualise the data. New data can be
submitted, providing the community with a collaborative tool to archive past
and future cosmic-ray measurements. Any help/ideas to further expand and/or
complement the database is welcome (please contact crdatabase@lpsc.in2p3.fr).


  Realizing solution processed quantum dot (QD) lasers is one of the
holy-grails of nanoscience. The reason that QD lasers are not yet
commercialized is that the lasing threshold is too high: one needs > 1 exciton
per QD, which is hard to achieve due to fast non-radiative Auger recombination.
The optical gain threshold can be reduced by electronic doping of the QDs,
which lowers the absorption near the band-edge, such that the stimulated
emission (SE) can easily outcompete absorption. Here, we show that by
electrochemically doping films of CdSe/CdS/ZnS QDs we achieve quantitative
control over the gain threshold. We obtain stable and reversible doping with up
to two electrons per QD. We quantify the gain threshold and the charge carrier
dynamics using ultrafast spectroelectrochemistry and achieve quantitative
agreement between experiments and theory. Over a range of wavelengths with
appreciable gain coefficients, the gain thresholds reach record-low values of
~10^-5 excitons per QD. These results demonstrate an unprecedented level of
control over the gain threshold in doped QD solids, paving the way for the
creation of cheap, solution-processable low-threshold QD-lasers.


  We discuss the current knowledge of the Solar system, focusing on bodies in
the outer regions, on the information they provide concerning Solar system
formation, and on the possible relationships that may exist between our system
and the debris disks of other stars. Beyond the domains of the Terrestrial and
giant planets, the comets in the Kuiper belt and the Oort cloud preserve some
of our most pristine materials. The Kuiper belt, in particular, is a
collisional dust source and a scientific bridge to the dusty "debris disks"
observed around many nearby main-sequence stars. Study of the Solar system
provides a level of detail that we cannot discern in the distant disks while
observations of the disks may help to set the Solar system in proper context.


  A monolayer of graphene irradiated with circularly polarized light suggests a
unique platform for surface electromagnetic wave (plasmon-polariton)
manipulation. In fact, the time periodicity of the Hamiltonian leads to a
geometric Aharonov-Anandan phase and results in a photovoltaic Hall effect in
graphene, creating off-diagonal components of the conductivity tensor. The
latter drastically changes the dispersion relation of surface
plasmon-polaritons, leading to hybrid wave generation. In this paper we present
a systematic and self-contained analysis of the hybrid surface waves obtained
from Maxwell equations based on a microscopic formula for the conductivity. We
consider a practical example of graphene sandwiched between two dielectric
media and show that in the one-photon approximation there is formation of
propagating hybrid surface waves. From this analysis emerges the possibility of
a reliable experimental realization to study Zitterbewegung of charge carriers
of graphene.


  Striped superconductivity with lattice distortions is investigated based on
the three-band Hubbard model for high-Tc cuprates. A stable inhomogeneous
striped state is determined in the low-temperature tetragonal (LTT) phase with
lattice distortions using a quantum variational Monte Carlo method. The ground
state has vertical or horizontal hole-rich arrays coexisting with
incommensurate magnetism and superconductivity induced by several percent
lattice distortions. The superconductivity order parameter oscillates according
to the inhomogeneity in the antiferromagnetic background with its maxima in the
hole-rich regions, and the superconductivity condensation energy is reduced as
the doping rate decreases.


  The POPLMARK Challenge comprises a set of problems intended to measure the
strength of reasoning systems in the realm of mechanizing programming language
meta-theory at the time the challenge was enunciated. Included in the
collection is the exercise of demonstrating transitivity of subtyping for a
specific algorithmic formulation of subtyping for an extension of System F. The
challenge represented by this problem derives from the fact that, for the given
formulation, subtyping must be proved simultaneously with another property
called narrowing. In a paper published as a proof pearl, Brigitte Pientka
claimed to have presented a solution to the problem in which "the full power of
parametric and higher-order judgments" is exploited to "get the narrowing lemma
for free." We show this claim to be inaccurate. In particular, we show that the
simplification is in substantial part the result of changing the formulation of
the subtyping relation in a way that modifies the challenge rather than the
outcome of the manner in which the argument is mechanized.


  Perhaps the best known kernelization result is the kernel of size 335k for
the Planar Dominating Set problem by Alber et al. [JACM 2004], later improved
to 67k by Chen et al. [SICOMP 2007]. This result means roughly, that the
problem of finding the smallest dominating set in a planar graph is easy when
the optimal solution is small. On the other hand, it is known that Planar
Dominating Set parameterized by k'=|V|-k (also known as Planar Nonblocker) has
a kernel of size 2k'. This means that Planar Dominating Set is easy when the
optimal solution is very large. We improve the kernel for Planar Nonblocker to
7/4k'. This also implies that Planar Dominating Set has no kernel of size at
most (7/3-epsilon)k, for any epsilon>0, unless P=NP. This improves the previous
lower bound of (2-epsilon)k of Chen et al. Both of these results immediately
generalize to H-minor free graphs (without changing the constants). In our
proof of the bound on the kernel size we use a variant of the discharging
method (used e.g. in the proof of the four color theorem). We give some
arguments that this method is natural in the context of kernelization and we
hope it will be applied to get improved kernel size bounds for other problems
as well. As a by-product we show a result which might be of independent
interest: every n-vertex graph with no isolated vertices and such that every
pair of degree 1 vertices is at distance at least 5 and every pair of degree 2
vertices is at distance at least 2 has a dominating set of size at most 3/7n.


  In this paper, we study the random field \begin{equation*} X(h) \circeq
\sum_{p \leq T} \frac{\text{Re}(U_p \, p^{-i h})}{p^{1/2}}, \quad h\in [0,1],
\end{equation*} where $(U_p, \, p ~\text{primes})$ is an i.i.d. sequence of
uniform random variables on the unit circle in $\mathbb{C}$. Harper (2013)
showed that $(X(h), \, h\in (0,1))$ is a good model for the large values of
$(\log |\zeta(\frac{1}{2} + i (T + h))|, \, h\in [0,1])$ when $T$ is large, if
we assume the Riemann hypothesis. The asymptotics of the maximum were found in
Arguin, Belius & Harper (2017) up to the second order, but the tightness of the
recentered maximum is still an open problem. As a first step, we provide large
deviation estimates and continuity estimates for the field's derivative
$X'(h)$. The main result shows that, with probability arbitrarily close to $1$,
\begin{equation*} \max_{h\in [0,1]} X(h) - \max_{h\in \mathcal{S}} X(h) = O(1),
\end{equation*} where $\mathcal{S}$ a discrete set containing $O(\log T
\sqrt{\log \log T})$ points.


  Medical image segmentation is an important task for computer aided diagnosis.
Pixelwise manual annotations of large datasets require high expertise and is
time consuming. Conventional data augmentations have limited benefit by not
fully representing the underlying distribution of the training set, thus
affecting model robustness when tested on images captured from different
sources. Prior work leverages synthetic images for data augmentation ignoring
the interleaved geometric relationship between different anatomical labels. We
propose improvements over previous GAN-based medical image synthesis methods by
jointly encoding the intrinsic relationship of geometry and shape. Latent space
variable sampling results in diverse generated images from a base image and
improves robustness. Given those augmented images generated by our method, we
train the segmentation network to enhance the segmentation performance of
retinal optical coherence tomography (OCT) images. The proposed method
outperforms state-of-the-art segmentation methods on the public RETOUCH dataset
having images captured from different acquisition procedures. Ablation studies
and visual analysis also demonstrate benefits of integrating geometry and
diversity.


  This paper investigates the performance of Large Language Models (LLMs) and
Tool-augmented LLMs in tackling complex mathematical reasoning tasks. We
introduce IMP-TIP: Improving Math Reasoning with Tool-augmented Interleaf
Prompting, a framework that combines the strengths of both LLMs and
Tool-augmented LLMs. IMP-TIP follows the ``From Good to Great" concept,
collecting multiple potential solutions from both LLMs and their Tool-Augmented
counterparts for the same math problem, and then selecting or re-generating the
most accurate answer after cross-checking these solutions via tool-augmented
interleaf prompting. The framework incorporates two key aspects: self-prompt
and tool-augmented interleaf prompting (TIP). The former allows LLMs to
autonomously refine and improve an initial prompt related to tool usage, while
the latter enables LLMs to derive the final answer by dynamically analyzing the
problem, cross-checking potential solutions, and revising previous reasoning
hints in an interleaved manner. Experimental analysis shows that IMP-TIP
achieves enhanced mathematical capabilities and outperforms traditional LLMs
and tool-augmented LLMs in accuracy and reasoning diversity on math reasoning
tasks. For instance, IMP-TIP can improve Tool-augmented ChatGPT on GSM8K-Hard
from 56.0% to 65.2%.


  The iterated conditional sequential Monte Carlo (i-CSMC) algorithm from
Andrieu, Doucet and Holenstein (2010) is an MCMC approach for efficiently
sampling from the joint posterior distribution of the $T$ latent states in
challenging time-series models, e.g. in non-linear or non-Gaussian state-space
models. It is also the main ingredient in particle Gibbs samplers which infer
unknown model parameters alongside the latent states. In this work, we first
prove that the i-CSMC algorithm suffers from a curse of dimension in the
dimension of the states, $D$: it breaks down unless the number of samples
("particles"), $N$, proposed by the algorithm grows exponentially with $D$.
Then, we present a novel "local" version of the algorithm which proposes
particles using Gaussian random-walk moves that are suitably scaled with $D$.
We prove that this iterated random-walk conditional sequential Monte Carlo
(i-RW-CSMC) algorithm avoids the curse of dimension: for arbitrary $N$, its
acceptance rates and expected squared jumping distance converge to non-trivial
limits as $D \to \infty$. If $T = N = 1$, our proposed algorithm reduces to a
Metropolis--Hastings or Barker's algorithm with Gaussian random-walk moves and
we recover the well known scaling limits for such algorithms.


  Sound event detection (SED) is essential for recognizing specific sounds and
their temporal locations within acoustic signals. This becomes challenging
particularly for on-device applications, where computational resources are
limited. To address this issue, we introduce a novel framework referred to as
dual knowledge distillation for developing efficient SED systems in this work.
Our proposed dual knowledge distillation commences with temporal-averaging
knowledge distillation (TAKD), utilizing a mean student model derived from the
temporal averaging of the student model's parameters. This allows the student
model to indirectly learn from a pre-trained teacher model, ensuring a stable
knowledge distillation. Subsequently, we introduce embedding-enhanced feature
distillation (EEFD), which involves incorporating an embedding distillation
layer within the student model to bolster contextual learning. On DCASE 2023
Task 4A public evaluation dataset, our proposed SED system with dual knowledge
distillation having merely one-third of the baseline model's parameters,
demonstrates superior performance in terms of PSDS1 and PSDS2. This highlights
the importance of proposed dual knowledge distillation for compact SED systems,
which can be ideal for edge devices.


  We deal with the problem of determining the shape of an inclusion embedded in
a homogenous background medium. The multifre-quency electrical impedance
tomography is used to image the inclusion. For different frequencies, a current
is injected at the boundary and the resulting potential is measured. It turns
out that the potential solves an elliptic equation in divergence form with
discontinuous leading coefficient. For this inverse problem we aim to establish
a logarithmic type stability estimate. The key point in our analysis consists
in reducing the original problem to that of determining an unknown part of the
inner boundary from a single boundary measurment. The stability estimate is
then used to prove uniqueness results. We also provide an expansion of the
solution of the BVP under consideration in the eigenfunction basis of the
Neumann-Poincar{\'e} operator associated to the Neumann-Green function.


  The research presented in this work is motivated by some recent papers
regarding hedging and valuation of financial securities subject to funding
costs, collateralization and counterparty credit risk. Our goal is to provide a
sound theoretical underpinning for some results presented in these papers by
developing a unified martingale framework for the non-linear approach to
hedging and pricing of OTC financial contracts. The impact that various funding
bases and margin covenants exert on the values and hedging strategies for OTC
contracts is examined.


  A basic finite dimensional algebra over an algebraically closed field $k$ is
isomorphic to a quotient of a tensor algebra by an admissible ideal. The
category of left modules over the algebra is isomorphic to the category of
representations of a finite quiver with relations. In this article we will
remove the assumption that $k$ is algebraically closed to look at both perfect
and non-perfect fields. We will introduce the notion of species with relations
to describe the category of left modules over such algebras. If the field is
not perfect, then the algebra is isomorphic to a quotient of a tensor algebra
by an ideal that is no longer admissible in general. This gives hereditary
algebras isomorphic to a quotient of a tensor algebra by a non-zero ideal. We
will show that these non-zero ideals correspond to cyclic subgraphs of the
graph associated to the species of the algebra. This will lead to the ideal
being zero in the case when the underlying graph of the algebra is a tree.


  The solution of dark energy problem in the models without scalars is
presented. It is shown that late-time accelerating cosmology may be generated
by the ideal fluid with some implicit equation of state. The universe evolution
within modified Gauss-Bonnet gravity is considered. It is demonstrated that
such gravitational approach may predict the (quintessential, cosmological
constant or transient phantom) acceleration of the late-time universe with
natural transiton from deceleration to acceleration (or from non-phantom to
phantom era in the last case).


  We study the elastic response of bilayer membranes with fixed projected area
to both stretching and shape deformations. A surface tension is associated to
each of these deformations. By using model amphiphilic membranes and computer
simulations, we are able to observe both the types of deformation, and thus,
both the surface tensions, related to each type of deformation, are measured
for the same system. These surface tensions are found to assume different
values in the same bilayer membrane: in particular they vanish for different
values of the projected area. We introduce a simple theory which relates the
two quantities and successfully apply it to the data obtained with computer
simulations.