  In this paper, we consider termination of probabilistic programs with
real-valued variables. The questions concerned are:
  1. qualitative ones that ask (i) whether the program terminates with
probability 1 (almost-sure termination) and (ii) whether the expected
termination time is finite (finite termination); 2. quantitative ones that ask
(i) to approximate the expected termination time (expectation problem) and (ii)
to compute a bound B such that the probability to terminate after B steps
decreases exponentially (concentration problem).
  To solve these questions, we utilize the notion of ranking supermartingales
which is a powerful approach for proving termination of probabilistic programs.
In detail, we focus on algorithmic synthesis of linear ranking-supermartingales
over affine probabilistic programs (APP's) with both angelic and demonic
non-determinism. An important subclass of APP's is LRAPP which is defined as
the class of all APP's over which a linear ranking-supermartingale exists.
  Our main contributions are as follows. Firstly, we show that the membership
problem of LRAPP (i) can be decided in polynomial time for APP's with at most
demonic non-determinism, and (ii) is NP-hard and in PSPACE for APP's with
angelic non-determinism; moreover, the NP-hardness result holds already for
APP's without probability and demonic non-determinism. Secondly, we show that
the concentration problem over LRAPP can be solved in the same complexity as
for the membership problem of LRAPP. Finally, we show that the expectation
problem over LRAPP can be solved in 2EXPTIME and is PSPACE-hard even for APP's
without probability and non-determinism (i.e., deterministic programs). Our
experimental results demonstrate the effectiveness of our approach to answer
the qualitative and quantitative questions over APP's with at most demonic
non-determinism.


  The $M$-dimensional unitary matrix $S(E)$, which describes scattering of
waves, is a strongly fluctuating function of the energy for complex systems
such as ballistic cavities, whose geometry induces chaotic ray dynamics. Its
statistical behaviour can be expressed by means of correlation functions of the
kind $\left \langle S_{ij}(E+\epsilon)S^\dag_{pq}(E-\epsilon)\right\rangle$,
which have been much studied within the random matrix approach. In this work,
we consider correlations involving an arbitrary number of matrix elements and
express them as infinite series in $1/M$, whose coefficients are rational
functions of $\epsilon$. From a mathematical point of view, this may be seen as
a generalization of the Weingarten functions of circular ensembles.


  We compute all irregular primes less than 2^31 = 2 147 483 648. We verify the
Kummer-Vandiver conjecture for each of these primes, and we check that the
p-part of the class group of Q(zeta_p) has the simplest possible structure
consistent with the index of irregularity of p. Our method for computing the
irregular indices saves a constant factor in time relative to previous methods,
by adapting Rader's algorithm for evaluating discrete Fourier transforms.


  We consider an internally heated fluid between parallel plates with fixed
thermal fluxes. For a large class of heat sources that vary in the direction of
gravity, we prove that $\langle\delta T \rangle_h \geq \sigma R^{-1/3} - \mu$,
where $\langle\delta T \rangle_h$ is the average temperature difference between
the bottom and top plates, $R$ is a `flux' Rayleigh number and the constants
$\sigma,\mu >0$ depend on the geometric properties of the internal heating.
This result implies that mean downward conduction (for which $\langle\delta T
\rangle_h< 0$) is impossible for a range of Rayleigh numbers smaller than a
critical value $R_0$. The bound demonstrates that $R_0$ depends on the heating
distribution and can be made arbitrarily large by concentrating the heating
near the bottom plate. However, for any given fixed heating profile of the
class we consider, the corresponding value of $R_0$ is always finite. This
points to a fundamental difference between internally heated convection and its
limiting case of Rayleigh-B\'enard convection with fixed flux boundary
conditions, for which $\langle\delta T \rangle_h$ is known to be positive for
all $R$.


  In this paper, we give a complete description of the deformation classes of
real structures on minimal ruled surfaces. In particular, we show that these
classes are determined by the topology of the real structure, which means that
real minimal ruled surfaces are quasi-simple. As an intermediate result, we
obtain the classification, up to conjugation, of real structures on
decomposable ruled surfaces.


  When rotating classical fluid drops merge together, angular momentum can be
advected from one to another due to the viscous shear flow at the drop
interface. It remains elusive what the corresponding mechanism is in inviscid
quantum fluids such as Bose-Einstein condensates (BECs). Here we report our
theoretical study of an initially static BEC merging with a rotating BEC in
three-dimensional space along the rotational axis. We show that a soliton sheet
resembling a "corkscrew" spontaneously emerges at the interface. Rapid angular
momentum transfer at a constant rate universally proportional to the initial
angular momentum density is observed. Strikingly, this transfer does not
necessarily involve fluid advection or drifting of the quantized vortices. We
reveal that the solitonic corkscrew can exert a torque that directly creates
angular momentum in the static BEC and annihilates angular momentum in the
rotating BEC. Uncovering this intriguing angular momentum transport mechanism
may benefit our understanding of various coherent matter-wave systems, spanning
from atomtronics on chips to dark matter BECs at cosmic scales.


  In the flurry of experiments looking for topological insulator materials, it
has been recently discovered that some bulk metals very close to topological
insulator electronic states, support the same topological surface states that
are the defining characteristic of the topological insulator. First observed in
spin-polarized ARPES in Sb (D. Hsieh et al. Science 323, 919 (2009)), the
helical surface states in the metallic systems appear to be robust to at least
mild disorder. We present here a theoretical investigation of the nature of
these "helical metals" - bulk metals with helical surface states. We explore
how the surface and bulk states can mix, in both clean and disordered systems.
Using the Fano model, we discover that in a clean system, the helical surface
states are \emph{not} simply absorbed by hybridization with a non-topological
parasitic metallic band. Instead, they are pushed away from overlapping in
momentum and energy with the bulk states, leaving behind a finite-lifetime
surface resonance in the bulk energy band. Furthermore, the hybridization may
lead in some cases to multiplied surface state bands, in all cases retaining
the helical characteristic. Weak disorder leads to very similar effects -
surface states are pushed away from the energy bandwidth of the bulk, leaving
behind a finite-lifetime surface resonance in place of the original surface
states.


  Using self consistent mean field and functional renormalization group
approaches we show that s-wave pairing symmetry is robust in the heavily
electron-doped iron chalcogenides $(\text{K, Cs}) \text{Fe}_{2-x}\text{Se}_2 $.
This is because in these materials the leading antiferromagnetic (AFM) exchange
coupling is between next-nearest-neighbor (NNN) sites while the nearest
neighbor (NN) magnetic exchange coupling is ferromagnetic (FM). This is
different from the iron pnictides, where the NN magnetic exchange coupling is
AFM and leads to strong competition between s-wave and d-wave pairing in the
electron overdoped region. Our finding of a robust s-wave pairing in $(\text{K,
Cs}) \text{Fe}_{2-x}\text{Se}_2$ differs from the d-wave pairing result
obtained by other theories where non-local bare interaction terms and the NNN
$J_2$ term are underestimated. Detecting the pairing symmetry in $(\text{K,
Cs}) \text{Fe}_{2-x}\text{Se}_2 $ may hence provide important insights
regarding the mechanism of superconducting pairing in iron based
superconductors.


  We consider semigroup actions on the interval generated by two attracting
maps. It is known that if the generators are sufficiently $C^2$-close to the
identity, then the minimal set coincides with the whole interval. In this
article, we give a counterexample to this result under the $C^1$-topology.


  We study a model for a massive test particle in a microscopic periodic
potential and interacting with a reservoir of light particles. In the regime
considered, the fluctuations in the test particle's momentum resulting from
collisions typically outweigh the shifts in momentum generated by the periodic
force, and so the force is effectively a perturbative contribution. The
mathematical starting point is an idealized reduced dynamics for the test
particle given by a linear Boltzmann equation. In the limit that the mass ratio
of a single reservoir particle to the test particle tends to zero, we show that
there is convergence to the Ornstein-Uhlenbeck process under the standard
normalizations for the test particle variables. Our analysis is primarily
directed towards bounding the perturbative effect of the periodic potential on
the particle's momentum.


  Various theoretical obstacles are associated with a homogeneous and isotropic
distribution of ``charge'' which is subject to a repulsive, long-range force.
We show how these can be overcome, for all practical purposes, by the simple
device of endowing the particle which carries the force with a small mass. The
resulting situation may be relevant to a phase of cosmological acceleration
which is triggered by the approach to masslessness of such a force carrier.


  Rank modulation is a way of encoding information to correct errors in flash
memory devices as well as impulse noise in transmission lines. Modeling rank
modulation involves construction of packings of the space of permutations
equipped with the Kendall tau distance.
  We present several general constructions of codes in permutations that cover
a broad range of code parameters. In particular, we show a number of ways in
which conventional error-correcting codes can be modified to correct errors in
the Kendall space. Codes that we construct afford simple encoding and decoding
algorithms of essentially the same complexity as required to correct errors in
the Hamming metric. For instance, from binary BCH codes we obtain codes
correcting $t$ Kendall errors in $n$ memory cells that support the order of
$n!/(\log_2n!)^t$ messages, for any constant $t= 1,2,...$ We also construct
families of codes that correct a number of errors that grows with $n$ at
varying rates, from $\Theta(n)$ to $\Theta(n^{2})$. One of our constructions
gives rise to a family of rank modulation codes for which the trade-off between
the number of messages and the number of correctable Kendall errors approaches
the optimal scaling rate. Finally, we list a number of possibilities for
constructing codes of finite length, and give examples of rank modulation codes
with specific parameters.


  In (Arnold, 1985), V.I. Arnold has obtained normal forms and has developed a
classifier for, in particular, all isolated hypersurface singularities over the
complex numbers up to modality 2. Building on a series of 105 theorems, this
classifier determines the type of the given singularity. However, for positive
modality, this does not fix the right equivalence class of the singularity,
since the values of the moduli parameters are not specified. In this paper, we
present a simple classification algorithm for isolated hypersurface
singularities of corank and modality up to two. For a singularity given by a
polynomial over the rationals, the algorithm determines its right equivalence
class by specifying a polynomial representative in Arnold's list of normal
forms.


  In this work we look into adding a new language to a multilingual NMT system
in an unsupervised fashion. Under the utilization of pre-trained cross-lingual
word embeddings we seek to exploit a language independent multilingual sentence
representation to easily generalize to a new language. While using
cross-lingual embeddings for word lookup we decode from a yet entirely unseen
source language in a process we call blind decoding. Blindly decoding from
Portuguese using a basesystem containing several Romance languages we achieve
scores of 36.4 BLEU for Portuguese-English and 12.8 BLEU for Russian-English.
In an attempt to train the mapping from the encoder sentence representation to
a new target language we use our model as an autoencoder. Merely training to
translate from Portuguese to Portuguese while freezing the encoder we achieve
26 BLEU on English-Portuguese, and up to 28 BLEU when adding artificial noise
to the input. Lastly we explore a more practical adaptation approach through
non-iterative backtranslation, exploiting our model's ability to produce high
quality translations through blind decoding. This yields us up to 34.6 BLEU on
English-Portuguese, attaining near parity with a model adapted on real
bilingual data.


  Vertex deletion and edge deletion problems play a central role in
Parameterized Complexity. Examples include classical problems like Feedback
Vertex Set, Odd Cycle Transversal, and Chordal Deletion. Interestingly, the
study of edge contraction problems of this type from a parameterized
perspective has so far been left largely unexplored. We consider two basic edge
contraction problems, which we call Path-Contractibility and
Tree-Contractibility. Both problems take an undirected graph $G$ and an integer
$k$ as input, and the task is to determine whether we can obtain a path or an
acyclic graph, respectively, by contracting at most $k$ edges of $G$. Our main
contribution is an algorithm with running time $4^{k+O(\log^2 k)} + n^{O(1)}$
for Path-Contractibility and an algorithm with running time $4.88^k n^{O(1)}$
for Tree-Contractibility, based on a novel application of the color coding
technique of Alon, Yuster and Zwick. Furthermore, we show that
Path-Contractibility has a kernel with at most $5k+3$ vertices, while
Tree-Contractibility does not have a polynomial kernel unless coNP $\subseteq$
NP/poly. We find the latter result surprising, because of the strong connection
between Tree-Contractibility and Feedback Vertex Set, which is known to have a
vertex kernel with size $O(k^2)$.


  Lookup tables (finite maps) are a ubiquitous data structure. In pure
functional languages they are best represented using trees instead of hash
tables. In pure functional languages within constructive logic, without a
primitive integer type, they are well represented using binary tries instead of
search trees. In this work, we introduce canonical binary tries, an improved
binary-trie data structure that enjoys a natural extensionality property, quite
useful in proofs, and supports sparseness more efficiently. We provide full
proofs of correctness in Coq. We provide microbenchmark measurements of
canonical binary tries versus several other data structures for finite maps, in
a variety of application contexts; as well as measurement of canonical versus
original tries in two big, real systems. The application context of data
structures contained in theorem statements imposes unusual requirements for
which canonical tries are particularly well suited.


  Moving Sink (MS) in Wireless Sensor Networks (WSNs) has appeared as a
blessing because it collects data directly from the nodes where the concept of
relay nodes is becomes obsolete. There are, however, a few challenges to be
taken care of, like data delay tolerance and trajectory of MS which is NP-hard.
In our proposed scheme, we divide the square field in small squares. Middle
point of the partitioned area is the sojourn location of the sink, and nodes
around MS are in its transmission range, which send directly the sensed data in
a delay-tolerant fashion. Two sinks are moving simultaneously; one inside and
having four sojourn locations and other in outer trajectory having twelve
sojourn locations. Introduction of the joint mobility enhances network life and
ultimately throughput. As the MS comes under the NP-hard problem, we convert it
into a geometric problem and define it as, Geometric Sink Movement (GSM). A set
of linear programming equations has also been given in support of GSM which
prolongs network life time.


  The theory of representations of Clifford algebras is extended to employ the
division algebra of the octonions or Cayley numbers. In particular, questions
that arise from the non-associativity and non-commutativity of this division
algebra are answered. Octonionic representations for Clifford algebras lead to
a notion of octonionic spinors and are used to give octonionic representations
of the respective orthogonal groups. Finally, the triality automorphisms are
shown to exhibit a manifest $\perm_3 \times SO(8)$ structure in this framework.


  Information retrieval models have witnessed a paradigm shift from
unsupervised statistical approaches to feature-based supervised approaches to
completely data-driven ones that make use of the pre-training of large language
models. While the increasing complexity of the search models have been able to
demonstrate improvements in effectiveness (measured in terms of relevance of
top-retrieved results), a question worthy of a thorough inspection is - "how
explainable are these models?", which is what this paper aims to evaluate. In
particular, we propose a common evaluation platform to systematically evaluate
the explainability of any ranking model (the explanation algorithm being
identical for all the models that are to be evaluated). In our proposed
framework, each model, in addition to returning a ranked list of documents,
also requires to return a list of explanation units or rationales for each
document. This meta-information from each document is then used to measure how
locally consistent these rationales are as an intrinsic measure of
interpretability - one that does not require manual relevance assessments.
Additionally, as an extrinsic measure, we compute how relevant these rationales
are by leveraging sub-document level relevance assessments. Our findings show a
number of interesting observations, such as sentence-level rationales are more
consistent, an increase in complexity mostly leads to less consistent
explanations, and that interpretability measures offer a complementary
dimension of evaluation of IR systems because consistency is not
well-correlated with nDCG at top ranks.


  We present an in-depth analysis of the atomic and electronic structure of the
quasi one-dimensional (1D) surface reconstruction of Ga on Si(112) based on
Scanning Tunneling Microscopy and Spectroscopy (STM and STS), Rutherford
Backscattering Spectrometry (RBS) and Density Functional Theory (DFT)
calculations. A new structural model of the Si(112)6 x 1-Ga surface is
inferred. It consists of Ga zig-zag chains that are intersected by
quasi-periodic vacancy lines or misfit dislocations. The experimentally
observed meandering of the vacancy lines is caused by the co-existence of
competing 6 x 1 and 5 x 1 unit cells and by the orientational disorder of
symmetry breaking Si-Ga dimers inside the vacancy lines. The Ga atoms are fully
coordinated, and the surface is chemically passivated. STS data reveal a
semiconducting surface and show excellent agreement with calculated Local
Density of States (LDOS) and STS curves. The energy gain obtained by fully
passivating the surface calls the idea of step-edge decoration as a viable
growth method toward 1D metallic structures into question.


  Self-driving cars (SDC) commonly implement the perception pipeline to detect
the surrounding obstacles and track their moving trajectories, which lays the
ground for the subsequent driving decision making process. Although the
security of obstacle detection in SDC is intensively studied, not until very
recently the attackers start to exploit the vulnerability of the tracking
module. Compared with solely attacking the object detectors, this new attack
strategy influences the driving decision more effectively with less attack
budgets. However, little is known on whether the revealed vulnerability remains
effective in end-to-end self-driving systems and, if so, how to mitigate the
threat.
  In this paper, we present the first systematic research on the security of
object tracking in SDC. Through a comprehensive case study on the full
perception pipeline of a popular open-sourced self-driving system, Baidu's
Apollo, we prove the mainstream multi-object tracker (MOT) based on Kalman
Filter (KF) is unsafe even with an enabled multi-sensor fusion mechanism. Our
root cause analysis reveals, the vulnerability is innate to the design of
KF-based MOT, which shall error-handle the prediction results from the object
detectors yet the adopted KF algorithm is prone to trust the observation more
when its deviation from the prediction is larger. To address this design flaw,
we propose a simple yet effective security patch for KF-based MOT, the core of
which is an adaptive strategy to balance the focus of KF on observations and
predictions according to the anomaly index of the observation-prediction
deviation, and has certified effectiveness against a generalized hijacking
attack model. Extensive evaluation on $4$ KF-based existing MOT implementations
(including 2D and 3D, academic and Apollo ones) validate the defense
effectiveness and the trivial performance overhead of our approach.


  The nature of the pairing symmetry of the first heavy fermion superconductor
CeCu$_2$Si$_2$ has recently become the subject of controversy. While
CeCu$_2$Si$_2$ was generally believed to be a $d$-wave superconductor, recent
low temperature specific heat measurements showed evidence for fully gapped
superconductivity, contrary to the nodal behavior inferred from earlier
results. Here we report London penetration depth measurements, which also
reveal fully gapped behavior at very low temperatures. To explain these
seemingly conflicting results, we propose a fully gapped $d+d$ band-mixing
pairing state for CeCu$_2$Si$_2$, which yields very good fits to both the
superfluid density and specific heat, as well as accounting for a sign change
of the superconducting order parameter, as previously concluded from inelastic
neutron scattering results.


  We investigate the coherence properties of an atomic beam evaporatively
cooled in a magnetic guide, assuming thermal equilibrium in the quantum
degenerate regime. The gas experiences two-dimensional, transverse
Bose-Einstein condensation rather than a full three-dimensional condensation
because of the very elongated geometry of the magnetic guide. First order and
second order correlation functions of the atomic field are used to characterize
the coherence properties of the gas along the axis of the guide. The coherence
length of the gas is found to be much larger than the thermal de Broglie
wavelength in the strongly quantum degenerate regime. Large intensity
fluctuations present in the ideal Bose gas model are found to be strongly
reduced by repulsive atomic interactions; this conclusion is obtained with a
one-dimensional classical field approximation valid when the temperature of the
gas is much higher than its chemical potential, k_B T >> |mu|.


  We study the global convergence and global optimality of actor-critic, one of
the most popular families of reinforcement learning algorithms. While most
existing works on actor-critic employ bi-level or two-timescale updates, we
focus on the more practical single-timescale setting, where the actor and
critic are updated simultaneously. Specifically, in each iteration, the critic
update is obtained by applying the Bellman evaluation operator only once while
the actor is updated in the policy gradient direction computed using the
critic. Moreover, we consider two function approximation settings where both
the actor and critic are represented by linear or deep neural networks. For
both cases, we prove that the actor sequence converges to a globally optimal
policy at a sublinear $O(K^{-1/2})$ rate, where $K$ is the number of
iterations. To the best of our knowledge, we establish the rate of convergence
and global optimality of single-timescale actor-critic with linear function
approximation for the first time. Moreover, under the broader scope of policy
optimization with nonlinear function approximation, we prove that actor-critic
with deep neural network finds the globally optimal policy at a sublinear rate
for the first time.


  A systematic investigation has been performed to elucidate effects of
Rare-Earth (RE) type and local atomic configuration on magnetic properties of
icosahedral quasicrystal (iQC) and their cubic approximants (2/1 and 1/1 ACs)
in the ternary Cd-Mg-RE (RE = Gd, Tb, Dy, Ho, Er, and Tm) systems. At low
temperatures, iQC and 2/1 ACs exhibit spin-glass-like freezing for RE = Gd, Tb,
Dy, and Ho, while Er and Tm systems do not show freezing behaviour down to the
base temperature ~ 2 K. The 1/1 ACs exhibit either spin-glass-like freezing or
antiferromagnetic (AFM) ordering depending on their constituent Mg content. The
Tf values show increasing trend from iQC to 2/1 and 1/1 ACs. In contrast, the
absolute values of Weiss temperature for iQCs are larger than those in 2/1 and
1/1 ACs, indicating that the total AFM interactions between the neighboring
spins are larger in aperiodic, rather than periodic systems. Competing spin
interactions originating from the long-range Ruderman-Kittel-Kasuya-Yoshida
mechanism along with chemical disorder of Cd/Mg ions presumably account for the
observed spin-glass-like behavior in Cd-Mg-RE iQCs and ACs.


  We present a theoretical framework to understand a modified
fluctuation-dissipation theorem valid for systems close to non-equilibrium
steady-states and obeying markovian dynamics. We discuss the interpretation of
this result in terms of trajectory entropy excess. The framework is illustrated
on a simple pedagogical example of a molecular motor. We also derive in this
context generalized Green-Kubo relations similar to the ones derived recently
by Seifert., Phys. Rev. Lett., 104, 138101 (2010) for more general networks of
biomolecular states.


  We propose and demonstrate a compositional framework for training and
verifying reinforcement learning (RL) systems within a multifidelity
sim-to-real pipeline, in order to deploy reliable and adaptable RL policies on
physical hardware. By decomposing complex robotic tasks into component subtasks
and defining mathematical interfaces between them, the framework allows for the
independent training and testing of the corresponding subtask policies, while
simultaneously providing guarantees on the overall behavior that results from
their composition. By verifying the performance of these subtask policies using
a multifidelity simulation pipeline, the framework not only allows for
efficient RL training, but also for a refinement of the subtasks and their
interfaces in response to challenges arising from discrepancies between
simulation and reality. In an experimental case study we apply the framework to
train and deploy a compositional RL system that successfully pilots a Warthog
unmanned ground robot.


  Semiconducting nanowires in proximity to superconductors are promising
experimental systems for Majorana fermions which may ultimately be used as
building blocks for topological quantum computers. A serious challenge in the
experimental realization of the Majorana fermion in these
semiconductor-superconductor nanowire structures is tuning the semiconductor
chemical potential in close proximity to the metallic superconductor. We show
that, presently realizable structures in experiments with tunable chemical
potential lead to Majorana resonances, which are interesting in their own
right, but do not manifest non-Abelian statistics. This poses a central
challenge to the field. We show how to overcome this challenge, thus resolving
a crucial barrier to the solid state realization of a topological system
containing the Majorana fermion. We propose a new topological superconducting
array structure where introducing the superconducting proximity effect from
adjacent nanowires generates Majorana fermions with non-Abelian statistics.


  We obtain results on the geometry of D-semianalytic and subanalytic subsets
over a complete, non-trivially valued non-Archimedean field K, which is not
necessarily algebraically closed. Among the results are a parameterized smooth
stratification theorem and several results concerning the dimension of the
D-semianalytic and subanalytic sets. We also extend Bartenwerfer's definition
of piece number for analytic K-varieties to D-semianalytic sets and prove the
existence of a uniform bound for the piece number of the fibers of a
D-semianalytic set. We also establish a connection between the piece number and
complexity of D-semianalytic sets which are subsets of the line and thereby
give a simpler proof of the Complexity Theorem of Lipshitz and Robinson. We
finish by proving that for each D-semianalytic X, there is a semialgebraic Y
such that one dimensional fibers of X are among the one dimensional fibers of
Y. This is an analogue of a theorem by van den Dries, Haskell and Macpherson.


  Learning robust local image feature matching is a fundamental low-level
vision task, which has been widely explored in the past few years. Recently,
detector-free local feature matchers based on transformers have shown promising
results, which largely outperform pure Convolutional Neural Network (CNN) based
ones. But correlations produced by transformer-based methods are spatially
limited to the center of source views' coarse patches, because of the costly
attention learning. In this work, we rethink this issue and find that such
matching formulation degrades pose estimation, especially for low-resolution
images. So we propose a transformer-based cascade matching model -- Cascade
feature Matching TRansformer (CasMTR), to efficiently learn dense feature
correlations, which allows us to choose more reliable matching pairs for the
relative pose estimation. Instead of re-training a new detector, we use a
simple yet effective Non-Maximum Suppression (NMS) post-process to filter
keypoints through the confidence map, and largely improve the matching
precision. CasMTR achieves state-of-the-art performance in indoor and outdoor
pose estimation as well as visual localization. Moreover, thorough ablations
show the efficacy of the proposed components and techniques.


  In this paper, we propose a symbol-level precoding (SLP) design that aims to
minimize the weighted mean square error between the received signal and the
constellation point located in the constructive interference region (CIR).
Unlike most existing SLP schemes that rely on channel state information (CSI)
only, the proposed scheme exploits both CSI and the distribution information of
the noise to achieve improved performance. We firstly propose a simple generic
description of CIR that facilitates the subsequent SLP design. Such an
objective can further be formulated as a nonnegative least squares (NNLS)
problem, which can be solved efficiently by the active-set algorithm.
Furthermore, the weighted minimum mean square error (WMMSE) precoding and the
existing SLP can be easily verified as special cases of the proposed scheme.
Finally, simulation results show that the proposed precoding outperforms the
state-of-the-art SLP schemes in full signal-to-noise ratio ranges in both
uncoded and coded systems without additional complexity over conventional SLP.


  Robust feature selection is vital for creating reliable and interpretable
Machine Learning (ML) models. When designing statistical prediction models in
cases where domain knowledge is limited and underlying interactions are
unknown, choosing the optimal set of features is often difficult. To mitigate
this issue, we introduce a Multidata (M) causal feature selection approach that
simultaneously processes an ensemble of time series datasets and produces a
single set of causal drivers. This approach uses the causal discovery
algorithms PC1 or PCMCI that are implemented in the Tigramite Python package.
These algorithms utilize conditional independence tests to infer parts of the
causal graph. Our causal feature selection approach filters out
causally-spurious links before passing the remaining causal features as inputs
to ML models (Multiple linear regression, Random Forest) that predict the
targets. We apply our framework to the statistical intensity prediction of
Western Pacific Tropical Cyclones (TC), for which it is often difficult to
accurately choose drivers and their dimensionality reduction (time lags,
vertical levels, and area-averaging). Using more stringent significance
thresholds in the conditional independence tests helps eliminate spurious
causal relationships, thus helping the ML model generalize better to unseen TC
cases. M-PC1 with a reduced number of features outperforms M-PCMCI, non-causal
ML, and other feature selection methods (lagged correlation, random), even
slightly outperforming feature selection based on eXplainable Artificial
Intelligence. The optimal causal drivers obtained from our causal feature
selection help improve our understanding of underlying relationships and
suggest new potential drivers of TC intensification.


  Transformer models serve as the backbone of many state-ofthe-art language
models, and most use the scaled dot-product attention (SDPA) mechanism to
capture relationships between tokens. However, the straightforward
implementation of SDPA has quadratic compute and memory complexity with respect
to the sequence length. On processor architectures such as GPUs and TPUs, there
is a robust body of prior work. However, little work has been performed on
non-processor architectures.In this work, we show how the architecture and
execution model of Streaming Dataflow Accelerators can help tackle this
challenge. We first define abstract hardware that adopts a streaming execution
model, and we implement a cycle-accurate simulator of the abstract hardware
using the Dataflow Abstract Machine simulation framework. Second, we implement
the naive SDPA algorithm on this abstract hardware and show it requires linear
(O(N)) intermediate memory. Third, we then modify the naive algorithm, taking
inspiration from prior processor-oriented works, by reordering the
multiplication and division operations. Finally, we map the modified algorithm
to abstract hardware, and confirm that the implementation computes SDPA at full
throughput while only using a constant amount (O(1)) of intermediate memory.


  Quantum fluctuations (QFs) caused by zero-point phonon vibrations (ZPPVs) are
known to prevent the occurrence of polar phases in bulk incipient
ferroelectrics down to 0K1-3. On the other hand, little is known about the
effects of QFs on the recently discovered topological patterns in ferroelectric
nanostructures4-9. Here, by using an atomistic effective Hamiltonian within
classical Monte Carlo (CMC) and path integral quantum Monte Carlo
(PI-QMC)1,3,10,11, we unveil how QFs affect the topology of several dipolar
phases in ultrathin Pb(Zr0.4Ti0.6)O3 (PZT) films. In particular, our PI-QMC
simulations show that the ZPPVs do not suppress polar patterns but rather
stabilize the labyrinth4, bimeron5 and bubble phases12,13 within a wider range
of bias field magnitudes. Moreover, we reveal that quantum fluctuations induce
a quantum critical point (QCP) separating a hexagonal bubble lattice from a
liquid-like state characterized by spontaneous motion, creation and
annihilation of polar bubbles at cryogenic temperatures. Finally, we show that
the discovered quantum melting is associated with anomalous physical response,
as, e.g., demonstrated by a negative longitudinal piezoelectric coefficient.


  We establish the uniqueness of the positive solution for equations of the
form $-\Delta u=au-b(x)f(u)$ in $\Omega$, $u|\_{\partial\Omega}=\infty$. The
special feature is to consider nonlinearities $f$ whose variation at infinity
is \emph{not regular} (e.g., $\exp(u)-1$, $\sinh(u)$, $\cosh(u)-1$,
$\exp(u)\log(u+1)$, $u^\beta \exp(u^\gamma)$, $\beta\in {\mathbb R}$,
$\gamma>0$ or $\exp(\exp(u))-e$) and functions $b\geq 0$ in $\Omega$ vanishing
on $\partial\Omega$. The main innovation consists of using Karamata's theory
not only in the statement/proof of the main result but also to link the
non-regular variation of $f$ at infinity with the blow-up rate of the solution
near $\partial\Omega$.


  Information gathering while interacting with other agents under sensing and
motion uncertainty is critical in domains such as driving, service robots,
racing, or surveillance. The interests of agents may be at odds with others,
resulting in a stochastic non-cooperative dynamic game. Agents must predict
others' future actions without communication, incorporate their actions into
these predictions, account for uncertainty and noise in information gathering,
and consider what information their actions reveal. Our solution uses local
iterative dynamic programming in Gaussian belief space to solve a
game-theoretic continuous POMDP. Solving a quadratic game in the backward pass
of a game-theoretic belief-space variant of iLQG achieves a runtime polynomial
in the number of agents and linear in the planning horizon. Our algorithm
yields linear feedback policies for our robot, and predicted feedback policies
for other agents. We present three applications: active surveillance, guiding
eyes for a blind agent, and autonomous racing. Agents with game-theoretic
belief-space planning win 44% more races than without game theory and 34% more
than without belief-space planning.


  This paper is an experience report on migrating an American newspaper
company's business-critical IBM mainframe application to Linux servers by
automatically translating the application's source code from COBOL to Java and
converting the mainframe data store from VSAM KSDS files to an Oracle
relational database. The mainframe application had supported daily home
delivery of the newspaper since 1979. It was in need of modernization in order
to increase interoperability and enable future convergence with newer
enterprise systems as well as to reduce operating costs. Testing the modernized
application proved to be the most vexing area of work. This paper explains the
process that was employed to test functional equivalence between the legacy and
modernized applications, the main testing challenges, and lessons learned after
having operated and maintained the modernized application in production over
the last eight months. The goal of delivering a functionally equivalent system
was achieved, but problems remained to be solved related to new feature
development, business domain knowledge transfer, and recruiting new software
engineers to work on the modernized application.


  The widespread belief that the effective action is convex and has a flat
bottom under broken global symmetry is shown to be wrong. We show spontaneous
symmetry breaking necessarily accompanies non-convexity in the effective action
for quantum field theory, or in the free energy for statistical mechanics, and
clarify the magnitude of non-convexity. For quantum field theory, it is also
proved that translational invariance breaks spontaneously when the system is in
the non-convex region, and that different vacua of spontaneously broken
symmetry cannot be superposed.
  As applications of non-convexity, we study the first-order phase transition
which happens at the zero field limit of spontaneously broken symmetry, and we
propose a simple model of phase coexistence which obeys the Born rule.


  We prove that any divisible dynamical simplex is the set of invariant
measures of some Toeplitz subshift. We apply our construction to prove that
orbit equivalence of Toeplitz subshifts is Borel bireducible to the universal
equivalence relation induced by a Borel action of a nonarchimedean Polish
group.


  In the quest to align deep learning with the sciences to address calls for
rigor, safety, and interpretability in machine learning systems, this
contribution identifies key missing pieces: the stages of hypothesis
formulation and testing, as well as statistical and systematic uncertainty
estimation -- core tenets of the scientific method. This position paper
discusses the ways in which contemporary science is conducted in other domains
and identifies potentially useful practices. We present a case study from
physics and describe how this field has promoted rigor through specific
methodological practices, and provide recommendations on how machine learning
researchers can adopt these practices into the research ecosystem. We argue
that both domain-driven experiments and application-agnostic questions of the
inner workings of fundamental building blocks of machine learning models ought
to be examined with the tools of the scientific method, to ensure we not only
understand effect, but also begin to understand cause, which is the raison
d'\^{e}tre of science.


  We have re-analyzed the data used by Bessel, von Struve, and Henderson in the
1830s to measure the first parallax distances to stars. We can generally
reproduce their results, although we find that von Struve and Henderson have
underestimated some of their measurement errors, leading to optimistic parallax
uncertainties. We find that temperature corrections for Bessel's measured
positions are larger than anticipated, explaining some systematics apparent in
his data. It has long been a mystery as to why von Struve first announced a
parallax for Vega of 0.125 arcsec, only later with more data to revise it to
double that value. We resolve this mystery by finding that von Struve's early
result used two dimensions of position data, which independently give
significantly different parallaxes, but when combined only fortuitously give
the correct result. With later data, von Struve excluded the "problematic"
dimension, leading to the larger parallax value. Allowing for likely
temperature corrections, and using his data from both dimensions, reduces von
Struve's parallax for Vega to a value consistent with the correct value.


  This paper presents an eXplainable Fault Detection and Diagnosis System
(XFDDS) for incipient faults in PV panels. The XFDDS is a hybrid approach that
combines the model-based and data-driven framework. Model-based FDD for PV
panels lacks high fidelity models at low irradiance conditions for detecting
incipient faults. To overcome this, a novel irradiance based three diode model
(IB3DM) is proposed. It is a nine parameter model that provides higher accuracy
even at low irradiance conditions, an important aspect for detecting incipient
faults from noise. To exploit PV data, extreme gradient boosting (XGBoost) is
used due to its ability to detecting incipient faults. Lack of explainability,
feature variability for sample instances, and false alarms are challenges with
data-driven FDD methods. These shortcomings are overcome by hybridization of
XGBoost and IB3DM, and using eXplainable Artificial Intelligence (XAI)
techniques. To combine the XGBoost and IB3DM, a fault-signature metric is
proposed that helps reducing false alarms and also trigger an explanation on
detecting incipient faults. To provide explainability, an eXplainable
Artificial Intelligence (XAI) application is developed. It uses the local
interpretable model-agnostic explanations (LIME) framework and provides
explanations on classifier outputs for data instances. These explanations help
field engineers/technicians for performing troubleshooting and maintenance
operations. The proposed XFDDS is illustrated using experiments on different PV
technologies and our results demonstrate the perceived benefits.


  Understanding the fluctuations by which phenomenological evolution equations
with thermodynamic structure can be enhanced is the key to a general framework
of nonequilibrium statistical mechanics. These fluctuations provide an
idealized representation of microscopic details. We consider
fluctuation-enhanced equations associated with Markov processes and elaborate
the general recipes for evaluating dynamic material properties, which
characterize force-flux constitutive laws, by statistical mechanics. Markov
processes with continuous trajectories are conveniently characterized by
stochastic differential equations and lead to Green-Kubo-type formulas for
dynamic material properties. Markov processes with discontinuous jumps include
transitions over energy barriers with the rates calculated by Kramers. We
describe a unified approach to Markovian fluctuations and demonstrate how the
appropriate type of fluctuations (continuous versus discontinuous) is reflected
in the mathematical structure of the phenomenological equations.


  We report calculations of the effective electronic response of aligned
multishell carbon nanotubes. A local graphite-like dielectric tensor is
assigned to every point of the multishell tubules, and the effective transverse
dielectric function of the composite is computed by solving Maxwell's
equations. Calculations of both real and imaginary parts of the effective
dielectric function are presented, for various values of the filling fraction
and the ratio of the internal and external radii of hollow tubules. Our full
calculations indicate that the experimentally measured macroscopic dielectric
function of carbon nanotube materials is the result of a strong electromagnetic
coupling between the tubes, which cannot be accounted for with the use of
simplified effective medium theories. The presence of surface plasmons is
investigated, and both optical absorption cross sections and energy-loss
spectra of aligned tubules are calculated.


  Quantum cascade lasers are of high interest in the scientific community due
to unique applications utilizing the emission in mid-IR range. The possible
designs of QCL are quite limited and require careful engineering to overcome
some crucial disadvantages. One of them is an active region (ARn) overheat,
that significantly affects the laser characteristics in the pulsed operation
mode. In this work we consider the effects related to the non-equilibrium
temperature distribution, when thermal resistance formalism is irrelevant. We
employ the heat equation and discuss the possible limitations and structural
features stemming from the chemical composition of the AR. We show that the
presence of alloys in the ARn structure fundamentally limits the heat
dissipation in pulsed and CW regimes due to their low thermal conductivity.
Also the QCL post-growths affects the thermal properties of a device only in
(near)CW mode while it is absolutely invaluable in the pulsed mode


  Many properties of photonic structures rely on band topology characterized by
the integer invariants that can change during the topological transitions and
give rise to the disorder-robust topological edge, corner, or interface states.
Typically the periods of such structures are comparable to the wavelength.
However, in many cases, the unit cell becomes deeply subwavelength and hence
the entire metamaterial can be described in terms of the effective material
parameters. Here, focusing on subwavelength topological metamaterials, we
identify the behavior of permittivity and permeability accompanying the
topological transition on the example of the two structures possessing $D_6$
symmetry.


  In the superconducting state, the presence of a finite gap in the excitation
spectrum implies that the number of excitations (quasiparticles) is
exponentially small at temperatures well below the critical one. Conversely,
minute perturbations can significantly impact both the distribution in energy
and number of quasiparticles. Typically, the interaction with the
electromagnetic environment is the main perturbation source driving
quasiparticles out of thermal equilibrium, while a phonon bath is responsible
for restoration of equilibrium. Here we derive approximate analytical solutions
for the quasiparticle distribution function in superconducting resonators and
explore the impact of nonequilibrium on two measurable quantities: the
resonator's quality factor and its resonant frequency. Applying our results to
experimental data, we conclude that while at intermediate temperatures there is
clear evidence for the nonequilibrium effects due to heating of the
quasiparticles by photons, the low-temperature measurements are not explained
by this mechanism.


  Prime end boundaries $\partial_P\Omega$ of domains $\Omega$ are studied in
the setting of complete doubling metric measure spaces supporting a
$p$-Poincar\'e inequality. Notions of rectifiably (in)accessible- and
(in)finitely far away prime ends are introduced and employed in classification
of prime ends. We show that, for a given domain, the prime end capacity of the
collection of all rectifiably inaccessible prime ends together will all
non-singleton prime ends is zero. We show the resolutivity of continouous
functions on $\partial_P\Omega$ which are Lipschitz continuous with respect to
the Mazurkiewicz metric when restricted to the collection $\partial_{SP}\Omega$
of all accessible prime ends. Furthermore, bounded perturbations of such
functions in $\partial_P\Omega\setminus\partial_{SP}\Omega$ yield the same
Perron solution. In the final part of the paper, we demonstrate the
(resolutive) Kellogg property with respect to the prime end boundary of bounded
domains in the metric space. Notions given in this paper are illustrated by a
number of examples.


  The bursting aggregation assembly in edge nodes is one of the key
technologies in OBS (Optical Burst Switching) network, which has a direct
impact on flow characteristics and packet loss rate. An optical burst assembly
technique supporting QoS is presented through this paper, which can
automatically adjust the threshold along with the increasing and decreasing
volume of business, reduce the operational burst, and generate corresponding
BDP (Burst Data Packet) and BCP (Burst Control Packet). In addition to the
burst aggregation technique a packet recovery technique by restoration method
is also described. The data packet loss due to the physical optical link
failure is not currently included in the QoS descriptions. This link failure is
also a severe problem which reduces the data throughput of the transmitter
node. A mechanism for data recovery from this link failure is vital for
guaranteeing the QoS demanded by each user. So this paper will also discusses a
specific protocol for reducing the packet loss by utilizing the features of
both optical circuit switching (OCS) and Optical Burst switching (OBS)
techniques.


  In the heavy quark limit, the heavy baryons \omega_{Q}^{(*)} (\omega could be
\Sigma, \Xi or \Omega and Q=b or c) are regarded as composed of a heavy quark
and an axial vector, light diquark with good spin and isospin quantum numbers.
Based on this diquark picture we establish the Bethe-Salpeter (B-S) equation
for \omega_{Q}^{(*)} in the limit where the heavy quark has infinite mass, m_Q
-> \infty. It is found that in this limit there are three components in the B-S
wave function for \omega_{Q}^{(*)}. Assuming the kernel to consist of a scalar
confinement term and a one-gluon-exchange term we derive three coupled integral
equations for the three B-S scalar functions in the covariant instantaneous
approximation. Numerical solutions for the three B-S scalar functions are
presented, including a discussion about their dependence on the various input
parameters. These solutions are applied to calculate the Isgur-Wise functions
\xi (\omega) and \zeta (\omega) for the weak transitions \Omega_{b}^{(*)} \to
\Omega_{c}^{(*)}. Using these we give predictions for the Cabibbo-allowed
nonleptonic decay widths and up-down asymmetries for \Omega_{b} \to
\Omega_{c}^{(*)} plus a pseudoscalar or vector meson.


  Processors with large numbers of cores are becoming commonplace. In order to
take advantage of the available resources in these systems, the programming
paradigm has to move towards increased parallelism. However, increasing the
level of concurrency in the program does not necessarily lead to better
performance. Parallel programming models have to provide flexible ways of
defining parallel tasks and at the same time, efficiently managing the created
tasks. OpenMP is a widely accepted programming model for shared-memory
architectures. In this paper we highlight some of the drawbacks in the OpenMP
tasking approach, and propose an alternative model based on the Glasgow
Parallel Reduction Machine (GPRM) programming framework. As the main focus of
this study, we deploy our model to solve a fundamental linear algebra problem,
LU factorisation of sparse matrices. We have used the SparseLU benchmark from
the BOTS benchmark suite, and compared the results obtained from our model to
those of the OpenMP tasking approach. The TILEPro64 system has been used to run
the experiments. The results are very promising, not only because of the
performance improvement for this particular problem, but also because they
verify the task management efficiency, stability, and flexibility of our model,
which can be applied to solve problems in future many-core systems.


  Hybrid neural network models combine the advantages of a neural network's
fitting functionality with differential equation models to reflect actual
physical processes and are widely used in analyzing time-series data. Most
related studies have focused on linear hybrid models, but only a few have
examined nonlinear problems. In this work, we use a hybrid nonlinear epidemic
neural network as the entry point to study its power in predicting the correct
infection function of an epidemic model. To achieve this goal, we combine the
bifurcation theory of the nonlinear differential model with the mean-squared
error loss and design a novel loss function to ensure model trainability.
Furthermore, we find the unique existence conditions supporting ordinary
differential equations to estimate the correct infection function. Using the
Runge Kutta method, we perform numerical experiments on our proposed model and
verify its soundness. We also apply it to real COVID-19 data to accurately
discover the change law of its infectivity.


  We introduce a category of 'rigid spaces with overconvergent structure sheaf'
which we call dagger spaces --- this is the correct category in which de Rham
cohomology in rigid analysis should be studied. We compare it with the (usual)
category of rigid spaces, give Serre and Poincar\'e duality theorems and
explain the relation with Berthelot's rigid cohomology.


  Understanding oscillations and waves in astrophysical fluid bodies helps to
elucidate their observed variability and the underlying physical mechanisms.
Indeed, global oscillations and bending modes of accretion discs or tori may be
relevant to quasi-periodicity and warped structures around compact objects.
While most studies rely on linear theory, observationally significant,
nonlinear dynamics is still poorly understood, especially in Keplerian discs
for which resonances typically demand a separate treatment. In this work we
introduce a novel analytical model which exactly solves the ideal, compressible
fluid equations for a non-self-gravitating elliptical cylinder within a local
shearing sheet. The aspect ratio of the ring is an adjustable parameter,
allowing a continuum of models ranging from a torus of circular cross-section
to a thin ring. We restrict attention to flow fields which are a linear
function of the coordinates, capturing the lowest order global motions and
reducing the dynamics to a set of coupled ordinary differential equations
(ODEs). This system acts as a framework for exploring a rich range of
hydrodynamic phenomena in both the large amplitude and Keplerian regimes. We
demonstrate the connection between tilting tori and warped discs within this
model, showing that the linear modes of the ring correspond to oppositely
precessing global bending modes. These are further confirmed within a numerical
grid based simulation. Crucially, the ODE system developed here allows for a
more tractable investigation of nonlinear dynamics. This will be demonstrated
in a subsequent paper which evidences mode coupling between warping and
vertical motions in thin tilted rings.


  BVRI and H-alpha imaging and long-slit optical spectroscopic data are
presented for four morphologically normal and relatively isolated Sa galaxies,
NGC3626, NGC3900, NGC4772 and NGC5854. VLA HI synthesis imaging is presented
for the first 3 objects. In all 4 galaxies, evidence of kinematic decoupling of
ionized gas components is found; the degree and circumstances of the distinct
kinematics vary from complete counterrotation of all of the gas from all of the
stars (NGC3626) to nuclear gas disks decoupled from the stars (NGC5854) to
anomalous velocity central gas components (NGC3900 and NGC4772). In the 3
objects mapped in HI, the neutral gas extends far beyond the optical radius,
R_HI/R_25 > 2. In general, the HI surface density is very low and the outer HI
is patchy and asymmetric or found in a distinct ring, exterior to the optical
edge. While the overall HI velocity fields are dominated by circular motions,
strong warps are suggested in the outer regions. Optical imaging is also
presented for NGC 4138 previously reported by Jore et al. (1996) to show
counterrotating stellar components. The multiwavelength evidence is interpreted
in terms of the kinematic "memory" of past minor mergers in objects that
otherwise exhibit no morphological signs of interaction.


  This work presents fluid dynamics videos obtained via numerical (CFD)
calculations using ComSol (finite elements method) software, showing the
evaporation of HFE7100 (3M company refrigerant) into a nitrogen gas flow along
the liquid interface. The overall temperature evolution and liquid motion,
which is caused by surface-tension (Marangoni) and buoyancy (Rayleigh)
instability mechanisms, are shown as well. Flow behavior in the liquid caused
by the aforementioned instability mechanisms can be nicely seen. Finally, these
observations are made for three liquid thicknesses in order to appreciate the
qualitative influence of confinement.


  We explore the hyperbolic band theory under a magnetic field for the first
time. Our theory is a general extension of the conventional band theory defined
on a Euclidean lattice into the band theory on a general hyperbolic
lattice/Riemann surface. Our methods and results can be confirmed
experimentally by circuit quantum electrodynamics (cQED), which enables us to
create novel materials in a hyperbolic space. To investigate the band
structures, we construct directly the hyperbolic magnetic Bloch states and find
that they form Dirac cones on a coordinate neighborhood, by which they can be
regarded as a global quantum gravity solution detectable in a laboratory.
Besides this is the first explicit example of a massless Dirac state on a
higher genus surface. Moreover we show that the energy spectrum exhibits an
unusual fractal structure refracting the negative curvature, when plotted as a
function of a magnetic flux.


  Multi-task learning has recently become a promising solution for a
comprehensive understanding of complex scenes. Not only being memory-efficient,
multi-task models with an appropriate design can favor exchange of
complementary signals across tasks. In this work, we jointly address 2D
semantic segmentation, and two geometry-related tasks, namely dense depth,
surface normal estimation as well as edge estimation showing their benefit on
indoor and outdoor datasets. We propose a novel multi-task learning
architecture that exploits pair-wise cross-task exchange through
correlation-guided attention and self-attention to enhance the average
representation learning for all tasks. We conduct extensive experiments
considering three multi-task setups, showing the benefit of our proposal in
comparison to competitive baselines in both synthetic and real benchmarks. We
also extend our method to the novel multi-task unsupervised domain adaptation
setting. Our code is available at https://github.com/cv-rits/DenseMTL.


  We discuss the nature of electron-lattice interaction in optimally doped
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ samples, using isotope effect (IE) in angle
resolved photoemission spectroscopy (ARPES) data. The IE in the ARPES line
width and the IE in the ARPES dispersion are both quite large, implying a
strong electron-lattice correlation. The strength of the electron-lattice
interaction is ``intermediate,'' i.e. stronger than the Migdal-Eliashberg
regime but weaker than the small polaron regime, requiring a more general
picture of the ARPES ``kink'' than the commonly used Migdal-Eliashberg picture.
The two IEs also imply a complex interaction, due to their strong momentum
dependence and their differing sign behaviors. In sum, we propose an
intermediate-strength coupling of electrons to localized lattice vibrations via
charge density fluctuations.


  The contribution that Jefferson Lab has made, with its 6 GeV electron beam,
and will make, with its 12 GeV upgrade, to our understanding of the way the
fundamental interactions work, particularly strong coupling QCD, is outlined.
The physics at the GeV scale is essential even in TeV collisions.


  We prove limit theorems for the homological winding of geodesic rays
distributed via a harmonic measure on a Gromov hyperbolic space. We obtain
applications to the inverse problem for the harmonic measure, and winding
statistics for Patterson-Sullivan measures.


  We demonstrate the use of computational phylogenetic techniques to solve a
central problem in inferential network monitoring. More precisely, we design a
novel algorithm for multicast-based delay inference, i.e. the problem of
reconstructing the topology and delay characteristics of a network from
end-to-end delay measurements on network paths. Our inference algorithm is
based on additive metric techniques widely used in phylogenetics. It runs in
polynomial time and requires a sample of size only $\poly(\log n)$.


  Graph Neural Networks (GNNs) rely on graph convolutions to exploit meaningful
patterns in networked data. Based on matrix multiplications, convolutions incur
in high computational costs leading to scalability limitations in practice. To
overcome these limitations, proposed methods rely on training GNNs in smaller
number of nodes, and then transferring the GNN to larger graphs. Even though
these methods are able to bound the difference between the output of the GNN
with different number of nodes, they do not provide guarantees against the
optimal GNN on the very large graph. In this paper, we propose to learn GNNs on
very large graphs by leveraging the limit object of a sequence of growing
graphs, the graphon. We propose to grow the size of the graph as we train, and
we show that our proposed methodology -- learning by transference -- converges
to a neighborhood of a first order stationary point on the graphon data. A
numerical experiment validates our proposed approach.


  The aim of this paper is to introduce a finite element formulation within
Arbitrary Lagrangian Eulerian framework with vanishing discrete {\it Space
Conservation Law} (SCL) for differential equations on time dependent domains.
The novelty of the formulation is the method for temporal integration which
results in preserving the SCL property and retaining the higher order accuracy
at the same time. Once the time derivative is discretized (based on integration
or differentiation formula), the common approach for terms in differential
equation which do not involve temporal derivative is classified to be a kind of
"time averaging" between time steps. In the spirit of classical approaches,
this involves evaluating these terms in several points in time between the
current and the previous time step ($[t_n,t_{n+1}]$), and then averaging them
in order to provide the satisfaction of discrete SCL. Here, we fully use the
polynomial in time form of mapping through which evolution of domain is
realized -- the so called ALE map -- in order to avoid the problematics arising
due to the moving grids. We give a general recipe on temporal schemes that have
to be employed once the discretization for the temporal derivative is chosen.
Numerical investigations on stability, accuracy and convergence are performed
and the simulated results are compared with benchmark problems set up by other
authors.


  We construct a D2-D8-$\bar{D8}$ configuration in string theory, it can be
described at low energy by two dimensional field theory. In the weak coupling
region, the low energy theory is a nonlocal generalization of Gross-Neveu(GN)
model which dynamically breaks the chiral flavor symmetry $U(N_f)_L \times
U(N_f)_R$ at large $N_c$ and finite $N_f$. However, in the strong coupling
region, we can use the SUGRA/Born-Infeld approximation to describe the low
energy dynamics of the system. Also, we analyze the low energy dynamics about
the configuration of wrapping the one direction of D2 brane on a circle with
anti-periodic boundary condition of fermions. The fermions and scalars on D2
branes get mass and decouple from the low energy theory. The IR dynamics is
described by the $QCD_2$ at weak coupling. In the opposite region, the dynamics
has a holographic dual description. And we have discussed the phase transition
of chiral symmetry breaking at finite temperature. Finally, after performing
T-duality, this configuration is related to some other brane configurations.


  The present paper has developed an integro-differential equation to propagate
cosmological gravitation waves in matter-dominated era in accounting for the
presence of free streaming neutrinos as a traceless transverse tensor part of
the anisotropic stress tensor. Its focus is on short and long wavelengths of
GWs that enter the horizon in matter-dominated era. Results show that the
anisotropic stress reduces the squared amplitude by $ 0.03\%$ for wavelengths,
entering the horizon during matter-dominated phase. This reduction is less for
those wavelengths that enter the horizon at $ \Lambda $ dominated era in flat
spacetime. All of the calculations have been done in closed spacetime and the
results have been compared with the radiation-dominated case for both flat and
closed spacetimes. Finally the paper investigates the effect of closed
background on the amplitude of the gravitational waves.


  The trace formula for the evolution operator associated with nonlinear
stochastic flows with weak additive noise is cast in the path integral
formalism. We integrate over the neighborhood of a given saddlepoint exactly by
means of a smooth conjugacy, a locally analytic nonlinear change of field
variables. The perturbative corrections are transfered to the corresponding
Jacobian, which we expand in terms of the conjugating function, rather than the
action used in defining the path integral. The new perturbative expansion which
follows by a recursive evaluation of derivatives appears more compact than the
standard Feynman diagram perturbation theory. The result is a stochastic analog
of the Gutzwiller trace formula with the ``hbar'' corrections computed an order
higher than what has so far been attainable in stochastic and
quantum-mechanical applications.


  The high penetration of transportation electrification and its associated
charging requirements magnify the interdependency of the transportation and
power distribution systems. The emergent interdependency requires that system
operators fully understand the status of both systems. To this end, a
visualization tool is presented to illustrate the interdependency of battery
bus transit and power distribution systems and the associated components. The
tool aims at monitoring components from both systems, such as the locations of
electric buses, the state of charge of batteries, the price of electricity,
voltage, current, and active/reactive power flow. The results showcase the
success of the visualization tool in monitoring the bus transit and power
distribution components to determine a reliable cost-effective scheme for
spatio-temporal charging of electric buses.


  We study a zero range process on scale-free networks in order to investigate
how network structure influences particle dynamics. The zero range process is
defined with the particle jumping rate function $p(n)=n^\delta$. We show
analytically that a complete condensation occurs when $\delta \leq \delta_c
\equiv 1/(\gamma-1)$ where $\gamma$ is the degree distribution exponent of the
underlying networks. In the complete condensation, those nodes whose degree is
higher than a threshold are occupied by macroscopic numbers of particles, while
the other nodes are occupied by negligible numbers of particles. We also show
numerically that the relaxation time follows a power-law scaling $\tau \sim
L^z$ with the network size $L$ and a dynamic exponent $z$ in the condensed
phase.


  Observations and theory suggest that core-collapse supernovae can span a
range of explosion energies, and when sub-energetic, the shockwave initiating
the explosion can decelerate to speeds comparable to the escape speed of the
progenitor. In these cases, gravity will complicate the explosion hydrodynamics
and conceivably cause the shock to stall at large radii within the progenitor
star. To understand these unique properties of weak explosions, we develop a
perturbative approach for modeling the propagation of an initially strong shock
into a time-steady, infalling medium in the gravitational field of a compact
object. This method writes the shock position and the post-shock velocity,
density, and pressure as series solutions in the (time-dependent) ratio of the
freefall speed to the shock speed, and predicts that the shock stalls within
the progenitor if the explosion energy is below a critical value. We show that
our model agrees very well with hydrodynamic simulations, and accurately
predicts (e.g.) the time-dependent shock position and velocity and the radius
at which the shock stalls. Our results have implications for black hole
formation and the newly detected class of fast X-ray transients (FXTs). In
particular, we propose that a ``phantom shock breakout'' -- where the outer
edge of the star falls through a stalled shock -- can yield a burst of X-rays
without a subsequent optical/UV signature, similar to FXTs. This model predicts
the rise time of the X-ray burst, $t_{\rm d}$, and the mean photon energy,
$kT$, are anti-correlated, approximately as $T \propto t_{\rm d}^{-5/8}$.


  This paper is devoted to study the effects of electromagnetic field on the
energy density inhomogeneity in the relativistic self-gravitating fluids for
spherically symmetric spacetime. Two important equations of the Weyl tensor are
formulated which help to analyze the energy density inhomogeneity in this
scenario. We investigate two types of fluids, i.e., non-dissipative and
dissipative. The non-dissipative fluid further includes dust, locally
isotropic, and locally anisotropic charged fluids. We explore the effects of
different factors on energy density inhomogeneity in all these cases, in
particular, the effect of charge.


  Allcock constructed a 13-dimensional complex ball quotient of which he
conjectured that it admits a natural covering with covering group isomorphic to
the Bimonster. This ball quotient contains the moduli space of cubic threefolds
as an open dense subset of a 10-dimensional complex subball quotient. We prove
that this subball quotient has a neighborhood in the Allcock ball quotient over
which the conjectured cover exists.


  In the high luminosity era of the Large Hadron Collider, the HL-LHC, the
instantaneous luminosity is expected to reach unprecedented values, resulting
in about 200 proton-proton interactions in a typical bunch crossing. To cope
with the resultant increase in occupancy, bandwidth and radiation damage, the
ATLAS Inner Detector will be replaced by an all-silicon system, the Inner
Tracker (ITk). The ITk consists of a silicon pixel and a strip detector and
exploits the concept of modularity. Prototyping and testing of various strip
detector components has been carried out. This paper presents the developments
and results obtained with reduced-size structures equivalent to those foreseen
to be used in the forward region of the silicon strip detector. Referred to as
petalets, these structures are built around a composite sandwich with embedded
cooling pipes and electrical tapes for routing the signals and power. Detector
modules built using electronic flex boards and silicon strip sensors are glued
on both the front and back side surfaces of the carbon structure. Details are
given on the assembly, testing and evaluation of several petalets. Measurement
results of both mechanical and electrical quantities are shown. Moreover, an
outlook is given for improved prototyping plans for large structures.


  Hadronic diffractive processes characterised by a hard scale (hard
diffraction) contain a nontrivial interplay of hard and soft, nonperturbative
interactions, which breaks down factorisation of short and long distances. On
the contrary to the expectations based on the factorization hypothesis,
assuming that hard diffraction is a higher twist, these processes should be
classified as a leading twist. We overview various implications of this
important observation for diffractive radiation of Abelian (Drell-Yan, gauge
bosons, Higgs boson) and non-Abelian (heavy flavors) particles, as well as
direct coalescence into the Higgs boson of the non-perturbative intrinsic heavy
flavour component of the hadronic wave function.


  Models of one-dimensional driven diffusive systems sometimes exhibit an
abrupt increase of the correlation length to an anomalously large but finite
value as the parameters of the model are varied. This behavior may be
misinterpreted as a genuine phase transition. A simple mechanism for this sharp
increase is presented. The mechanism is introduced within the framework of a
recently suggested correspondence between driven diffusive systems and
zero-range processes. It is shown that when the dynamics of the model is such
that small domains are suppressed in the steady-state distribution, anomalously
large correlation length may build up. The mechanism is examined in detail in
two models.


  Labeled oriented trees, LOT's, encode spines of ribbon discs in the 4-ball
and ribbon 2-knots in the 4-sphere. The unresolved asphericity question for
these spines is a major test case for Whitehead's asphericity conjecture. In
this paper we give a complete description of the link of a reduced injective
LOT complex. An important case is the following: If $\Gamma$ is a reduced
injective LOT that does not contain boundary reduced sub-LOTs, then
$lk(K(\Gamma))$ is a bi-forest. As a consequence $K(\Gamma)$ is aspherical, in
fact DR, and its fundamental group is locally indicable. We also show that a
general injective LOT complex is aspherical. Some of our results have already
appeared in print over the last two decades and are collected here.


  Detecting biases in artificial intelligence has become difficult because of
the impenetrable nature of deep learning. The central difficulty is in relating
unobservable phenomena deep inside models with observable, outside quantities
that we can measure from inputs and outputs. For example, can we detect
gendered perceptions of occupations (e.g., female librarian, male electrician)
using questions to and answers from a word embedding-based system? Current
techniques for detecting biases are often customized for a task, dataset, or
method, affecting their generalization. In this work, we draw from
Psychophysics in Experimental Psychology---meant to relate quantities from the
real world (i.e., "Physics") into subjective measures in the mind (i.e.,
"Psyche")---to propose an intellectually coherent and generalizable framework
to detect biases in AI. Specifically, we adapt the two-alternative forced
choice task (2AFC) to estimate potential biases and the strength of those
biases in black-box models. We successfully reproduce previously-known biased
perceptions in word embeddings and sentiment analysis predictions. We discuss
how concepts in experimental psychology can be naturally applied to
understanding artificial mental phenomena, and how psychophysics can form a
useful methodological foundation to study fairness in AI.


  We present a diagrammatic approach to construct self-energy approximations
within many-body perturbation theory with positive spectral properties. The
method cures the problem of negative spectral functions which arises from a
straightforward inclusion of vertex diagrams beyond the GW approximation. Our
approach consists of a two-steps procedure: we first express the approximate
many-body self-energy as a product of half-diagrams and then identify the
minimal number of half-diagrams to add in order to form a perfect square. The
resulting self-energy is an unconventional sum of self-energy diagrams in which
the internal lines of half a diagram are time-ordered Green's functions whereas
those of the other half are anti-time-ordered Green's functions, and the lines
joining the two halves are either lesser or greater Green's functions. The
theory is developed using noninteracting Green's functions and subsequently
extended to self-consistent Green's functions. Issues related to the conserving
properties of diagrammatic approximations with positive spectral functions are
also addressed. As a major application of the formalism we derive the minimal
set of additional diagrams to make positive the spectral function of the GW
approximation with lowest-order vertex corrections and screened interactions.
The method is then applied to vertex corrections in the three-dimensional
homogeneous electron gas by using a combination of analytical frequency
integrations and numerical Monte-Carlo momentum integrations to evaluate the
diagrams.


  In 2010, G.-N. Han obtained the generating function for the number of size
$t$ hooks among integer partitions. Here we obtain these generating functions
for self-conjugate partitions, which are particularly elegant for even $t$. If
$n_t(\lambda)$ is the number of size $t$ hooks in a partition $\lambda,$ then
for even $t$ we have $$\sum_{\lambda\in \mathcal{SC}} x^{n_t(\lambda)}
q^{\vert\lambda\vert} = (-q;q^2)_{\infty} \cdot
((1-x^2)q^{2t};q^{2t})_{\infty}^{\frac{t}2}. $$ As a consequence, if $a_t^*(n)$
is the number of such hooks among the self-conjugate partitions of $n,$ then
for even $t$ we obtain the simple formula $$ a_t^*(n)=t\sum_{j\geq 1}
q^*(n-2tj), $$ where $q^*(m)$ is the number of partitions of $m$ into distinct
odd parts. As a corollary, we find that $t\mid a_t^*(n),$ which confirms a
conjecture of Ballantine, Burson, Craig, Folsom, and Wen.


  We construct a space classifying divisor classes of a fixed degree on all
tropical curves of a fixed combinatorial type and show that the function taking
a divisor class to its rank is upper semicontinuous. We extend the definition
of the Brill-Noether rank of a metric graph to tropical curves and use the
upper semicontinuity of the rank function on divisors to show that the
Brill-Noether rank varies upper semicontinuously in families of tropical
curves. Furthermore, we present a specialization lemma relating the
Brill-Noether rank of a tropical curve with the dimension of the Brill-Noether
locus of an algerbaic curve.


  We present a method of subtracting the foreground contamination for the
measurement of CMB polarization. We calculate the resultant errors on CMB
polarization and temperature-polarization cross correlation power spectra for
the high frequency instrument (HFI) aboard Planck Surveyor, and estimate the
corresponding errors on cosmological parameters.


  Satellite Laser Ranging (SLR) is an established technology used for geodesy,
fundamental science and precise orbit determination. This paper reports on the
first successful SLR measurement from the German Aerospace Center research
observatory in Stuttgart. While many SLR stations are in operation, the
experiment described here is unique in several ways: The modular system has
been assembled completely from commercial off-the-shelf components, which
increases flexibility and significantly reduces hardware costs. To our
knowledge it has been the first time that an SLR measurement has been conducted
using an optical fibre rather than a coud\'e path to direct the light from the
laser source onto the telescope. The transmitter operates at an output power of
about 75 mW and a repetition rate of 3 kHz, and at a wavelength of 1064 nm. Due
to its rather small diameter of only 80 {\mu}{\mu}m, the receiver detector
features a low noise rate of less than 2 kHz and can be operated without gating
in many cases. With this set-up, clear return signals have been received from
several orbital objects equipped with retroreflectors. In its current
configuration, the system does not yet achieve the same performance as other
SLR systems in terms of precision, maximum distance and the capability of
daylight ranging; however, plans to overcome these limitations are outlined.


  We discuss a class of proofs of Bell-type inequalities that are based on
tables of potential outcomes. These proofs state in essence: if one can only
imagine (or write down in a table) the potential outcome of a hidden parameter
model for EPR experiments then a contradiction to experiment and quantum
mechanics follows. We show that these proofs do not contain hidden variables
that relate to time or, if they do, lead to logical contradictions that render
them invalid.


  Predicate intuitionistic logic is a well established fragment of dependent
types. According to the Curry-Howard isomorphism proof construction in the
logic corresponds well to synthesis of a program the type of which is a given
formula. We present a model of automata that can handle proof construction in
full intuitionistic first-order logic. The automata are constructed in such a
way that any successful run corresponds directly to a normal proof in the
logic. This makes it possible to discuss formal languages of proofs or
programs, the closure properties of the automata and their connections with the
traditional logical connectives.


  We present a conjecture in Diophantine geometry concerning the construction
of line bundles over smooth projective varieties over $\bar{\mathbb Q}}$. This
conjecture, closely related to the Grothendieck Period Conjecture for cycles of
codimension 1, is also motivated by classical algebraization results in
analytic and formal geometry and in transcendence theory. Its formulation
involves the consideration of $D$-group schemes attached to abelian schemes
over algebraic curves over $\bar{\mathbb Q}}$. We also derive the Grothendieck
Period Conjecture for cycles of codimension 1 in abelian varieties over
$\bar{\mathbb Q}}$ from a classical transcendence theorem \`a la
Schneider-Lang.


  We study synchronization in delay-coupled neural networks of heterogeneous
nodes. It is well known that heterogeneities in the nodes hinder
synchronization when becoming too large. We show that an adaptive tuning of the
overall coupling strength can be used to counteract the effect of the
heterogeneity. Our adaptive controller is demonstrated on ring networks of
FitzHugh-Nagumo systems which are paradigmatic for excitable dynamics but can
also -- depending on the system parameters -- exhibit self-sustained periodic
firing. We show that the adaptively tuned time-delayed coupling enables
synchronization even if parameter heterogeneities are so large that excitable
nodes coexist with oscillatory ones.


  The time complexity of making observations and loop closures in a graph-based
visual SLAM system is a function of the number of views stored. Clever
algorithms, such as approximate nearest neighbor search, can make this function
sub-linear. Despite this, over time the number of views can still grow to a
point at which the speed and/or accuracy of the system becomes unacceptable,
especially in computation- and memory-constrained SLAM systems. However, not
all views are created equal. Some views are rarely observed, because they have
been created in an unusual lighting condition, or from low quality images, or
in a location whose appearance has changed. These views can be removed to
improve the overall performance of a SLAM system. In this paper, we propose a
method for pruning views in a visual SLAM system to maintain its speed and
accuracy for long term use.


  We calculate reduced $B(E2)$ electromagnetic transition strengths for light
nuclei of mass numbers $B=8,12,16,20,24$ and $32$ within the Skyrme model. We
find that the predicted transition strengths are of the correct order of
magnitude and the computed intrinsic quadrupole moments match the
experimentally observed effective nuclear shapes. For the Hoyle state we
predict a large $B(E2)\!\uparrow$ value of $0.0521\, \rm{e}^2\rm{b}^2$. For
Oxygen-16, we can obtain a quantitative understanding of the ground state
rotational band and the rotational excitations of the second spin-0 state,
$0_2^+$.


  On-chip optical interconnect has been widely accepted as a promising
technology to realize future large-scale multiprocessors. Mode-division
multiplexing (MDM) provides a new degree of freedom for optical interconnects
to dramatically increase the link capacity. Present on-chip multimode devices
are based on traditional wave-optics. Although large amount of computation and
optimization are adopted to support more modes, mode-independent manipulation
is still hard to be achieved due to severe mode dispersion. Here, we propose a
universal solution to standardize the design of fundamental multimode building
blocks, by introducing a geometrical-optics-like concept adopting waveguide
width larger than the working wavelength. The proposed solution can tackle a
group of modes at the same time with very simple processes, avoiding
demultiplexing procedure and ensuring compact footprint. Compare to
conventional schemes, it is scalable to larger mode channels without increasing
the complexity and whole footprint. As a proof of concept, we demonstrate a set
of multimode building blocks including crossing, bend, coupler and switches.
Low losses of multimode waveguide crossing and bend are achieved, as well as
ultra-low power consumption of the multimode switch is realized since it
enables reconfigurable routing for a group of modes simultaneously. Our work
promotes the multimode photonics research and makes the MDM technique more
practical.


  In this paper we analyze possible actions of an automorphism of order six on
a $2$-$(70, 24, 8)$ design, and give a complete classification for the action
of the cyclic automorphism group of order six $G= \langle \rho \rangle \cong
Z_6 \cong Z_2 \times Z_3$ where $\rho^3$ fixes exactly $14$ points (blocks) and
$\rho^2$ fixes $4$ points (blocks). Up to isomorphism, there are $3718$ such
designs. This result significantly increases the number of known
$2$-$(70,24,8)$ designs.


  The mean kinetic energy of protons in water is determined by Deep Inelastic
Neutron Scattering experiments, performed above and below the temperature of
maximum density and in the supercooled phase. The temperature dependence of
this energy shows an anomalous behavior, as it occurs for many water
properties. In particular two regions of maximum kinetic energy are identified:
the first one, in the supercooled phase in the range 269 K - 272 K, and a
second one above 273 K. In both these regions the measured proton kinetic
energy exceedes the theoretical prediction based on a semi-classical model.
Noteworthy, the proton mean kinetic energy has a maximum at 277 K, the
temperature of the maximum density of water. In the supercooled metastable
phase the measured mean kinetic energy and the proton momentum distribution
clearly indicate proton delocalization between two H-bonded oxygens.


  The MicroBooNE experiment at Fermilab uses liquid argon time projection
chamber (LArTPC) technology to study neutrino interactions in argon. A
fundamental requirement for LArTPCs is to achieve and maintain a low level of
electronegative contaminants in the liquid to minimize the capture of drifting
ionization electrons. The attenuation time for the drifting electrons should be
long compared to the maximum drift time, so that the signals from particle
tracks that generate ionization electrons with long drift paths can be detected
efficiently. In this talk we present MicroBooNE measurement of electron
attenuation using cosmic ray muons. The result yields a minimum electron 1/e
lifetime of 18 ms under typical operating conditions, which is long compared to
the maximum drift time of 2.3 ms.


  Online tracking has become of increasing concern in recent years, however our
understanding of its extent to date has been limited to snapshots from web
crawls. Previous at-tempts to measure the tracking ecosystem, have been done
using instrumented measurement platforms, which are not able to accurately
capture how people interact with the web. In this work we present a method for
the measurement of tracking in the web through a browser extension, as well as
a method for the aggregation and collection of this information which protects
the privacy of participants. We deployed this extension to more than 5 million
users, enabling measurement across multiple countries, ISPs and browser
configurations, to give an accurate picture of real-world tracking. The result
is the largest and longest measurement of online tracking to date based on real
users, covering 1.5 billion page loads gathered over 12 months. The data,
detailing tracking behaviour over a year, is made publicly available to help
drive transparency around online tracking practices.


  Motivated by recent experimental claims for the existence of a 17 keV
neutrino and by the solar neutrino problem, we construct a class of models
which contain in their low-energy spectrum a single light sterile neutrino and
one or more Nambu-Goldstone bosons. In these models the required pattern of
breaking of lepton-number symmetry takes place near the electroweak scale and
all mass heirarchies are technically natural. The models are compatible with
all cosmological and astrophysical constraints, and can solve the solar
neutrino problem via either the MSW effect or vacuum oscillations. The deficit
in atmospheric muon neutrinos seen in the Kamiokande and IMB detectors can also
be explained in these models.


  For a second-order phase transition the critical energy range of interest is
larger than the energy range covered by a canonical Monte Carlo simulation at
the critical temperature. Such an extended energy range can be covered by
performing a Wang-Landau recursion for the spectral density followed by a
multicanonical simulation with fixed weights. But in the conventional approach
one loses the advantage due to cluster algorithms. A cluster version of the
Wang-Landau recursion together with a subsequent multibondic simulation
improves for 2D and 3D Ising models the efficiency of the conventional
Wang-Landau/multicanonical approach by power laws in the lattice size. In our
simulations real gains in CPU time reach two orders of magnitude.


  Beyond the success story of pre-trained language models (PrLMs) in recent
natural language processing, they are susceptible to over-fitting due to
unusual large model size. To this end, dropout serves as a therapy. However,
existing methods like random-based, knowledge-based and search-based dropout
are more general but less effective onto self-attention based models, which are
broadly chosen as the fundamental architecture of PrLMs. In this paper, we
propose a novel dropout method named AttendOut to let self-attention empowered
PrLMs capable of more robust task-specific tuning. We demonstrate that
state-of-the-art models with elaborate training design may achieve much
stronger results. We verify the universality of our approach on extensive
natural language processing tasks.


  Predicting patient features from single-cell data can help identify cellular
states implicated in health and disease. Linear models and average cell type
expressions are typically favored for this task for their efficiency and
robustness, but they overlook the rich cell heterogeneity inherent in
single-cell data. To address this gap, we introduce MixMIL, a framework
integrating Generalized Linear Mixed Models (GLMM) and Multiple Instance
Learning (MIL), upholding the advantages of linear models while modeling cell
state heterogeneity. By leveraging predefined cell embeddings, MixMIL enhances
computational efficiency and aligns with recent advancements in single-cell
representation learning. Our empirical results reveal that MixMIL outperforms
existing MIL models in single-cell datasets, uncovering new associations and
elucidating biological mechanisms across different domains.


  The kamiokite, Fe$_2$Mo$_3$O$_8$, is regarded as a promising material
exhibiting giant magnetoelectric (ME) effect at the relatively high temperature
$T$. Here, we explore this phenomenon on the basis of first-principles
electronic structure calculations. For this purpose we construct a realistic
model describing the behavior of magnetic Fe $3d$ electrons and further map it
onto the isotropic spin model. Our analysis suggests two possible scenaria for
Fe$_2$Mo$_3$O$_8$. The first one is based on the homogeneous charge
distribution of the Fe$^{2+}$ ions amongst tetrahedral ($t$) and octahedral
($o$) sites, which tends to low the crystallographic P6$_3$mc symmetry through
the formation of an orbitally ordered state. Nevertheless, the effect of the
orbital ordering on interatomic exchange interactions does not seem to be
strong, so that the magnetic properties can be described reasonably well by
averaged interactions obeying the P6$_3$mc symmetry. The second scenario, which
is supported by obtained parameters of on-site Coulomb repulsion and respects
the P6$_3$mc symmetry, implies the charge disproportionation involving somewhat
exotic $1+$ ionization state of the $t$-Fe sites (and $3+$ state of the $o$-Fe
sites). Somewhat surprisingly, these scenarios are practically
indistinguishable from the viewpoint of exchange interactions, which are
practically identical in these two cases. However, the spin-dependent
properties of the electric polarization are expected to be different due to the
strong difference in the polarity of the Fe$^{2+}$-Fe$^{2+}$ and
Fe$^{1+}$-Fe$^{3+}$ bonds. Our analysis uncovers the basic aspects of the ME
effect in Fe$_2$Mo$_3$O$_8$. Nevertheless, the quantitative description should
involve other ingredients, apparently related to the lattice and orbitals
degrees of freedom.


  We analyse the UV divergences for the scattering amplitude in the Wess-Zumino
SUSY model with the quartic superpotential. Within the superfield formalism, we
calculate the corresponding Feynman diagrams and evaluate their leading
divergences up to 4 loop order of PT. Then we construct recurrence relations
that connect the leading UV divergences in subsequent orders of perturbation
theory. These recurrence relations allow us to calculate the leading
divergences in a pure algebraic way starting from the one loop contribution. We
check that the obtained relations correctly reproduce the lower order diagrams
evaluated explicitly. At last, we convert the recurrence relations into the RG
equations that have integro-differential form. Solving these equations for a
particular sequence of diagrams, we find out the high energy behaviour of the
amplitude. We then argue that the full amplitude has a similar behaviour with
the key feature of the existence of a pole in the s-channel corresponding to a
state with a mass ~1/g, where g is the original dimensionfull coupling of the
theory. We find out the this state is actually a ghost one similar to the
Landau pole in scalar theory.


  We non-perturbatively analyze the effect of electron-electron interactions on
weak localization (WL) in relatively short metallic conductors with a tunnel
barrier. We demonstrate that the main effect of interactions is electron
dephasing which persists down to T=0 and yields suppression of WL correction to
conductance below its non-interacting value. Our results may account for recent
observations of low temperature saturation of the electron decoherence time in
quantum dots.


  In these notes, we present some methods and applications of large deviations
to finance and insurance. We begin with the classical ruin problem related to
the Cramer's theorem and give en extension to an insurance model with
investment in stock market. We then describe how large deviation approximation
and importance sampling are used in rare event simulation for option pricing.
We finally focus on large deviations methods in risk management for the
estimation of large portfolio losses in credit risk and portfolio performance
in market investment.


  Syllables play an important role in speech synthesis, speech recognition, and
spoken document retrieval. A novel, low cost, and language agnostic approach to
dividing words into their corresponding syllables is presented. A hybrid
genetic algorithm constructs a categorization of phones optimized for
syllabification. This categorization is used on top of a hidden Markov model
sequence classifier to find syllable boundaries. The technique shows promising
preliminary results when trained and tested on English words.


  Primordial molecules were formed during the Dark Ages, i.e. the time between
recombination and reionization in the early Universe. The purpose of this
article is to analyze the formation of primordial molecules based on heavy
elements during the Dark Ages, with elemental abundances taken from different
nucleosynthesis models. We present calculations of the full non-linear equation
set governing the primordial chemistry. We consider the evolution of 45
chemical species and use an implicit multistep method of variable order of
precision with an adaptive stepsize control. We find that the most abundant
Dark Ages molecules based on heavy elements are CH and OH. Non-standard
nucleosynthesis can lead to higher heavy element abundances while still
satisfying the observed primordial light abundances. In that case, we show that
the abundances of molecular species based on C, N, O and F can be enhanced by
two orders of magnitude compared to the standard case, leading to a CH relative
abundance higher than that of HD+ or H2D+.


  In this paper we are concerned with a long-standing conjecture of Huneke and
Wiegand. We introduce a new class of ideals and prove thateach ideal from such
class satisfies the conclusion of the conjecture in question. We also study the
relation between the class of Burch ideals and that of the ideals we define,
and construct several examples that corroborate our results.