  Very recently, Monz, et al. [arXiv:1507.08852] have reported the
demonstration of factoring 15 using a scalable Shor algorithm with an ion-trap
quantum computer. In this note, we remark that the report is somewhat
misleading because there are three flaws in the proposed circuit diagram of
Shor algorithm. We also remark that the principles behind the demonstration
have not been explained properly, including its correctness and complexity.


  We study the bar-driven dynamics in the inner part of the Milky Way by using
invariant manifolds. This theory has been successfully applied to describe the
morphology and kinematics of rings and spirals in external galaxies, and now,
for the first time, we apply it to the Milky Way. We compute the orbits
confined by the invariant manifolds of the unstable periodic orbits located at
the ends of the bar. We discuss whether the COBE/DIRBE bar and the Long bar
compose a single bar or two independent bars and perform a number of
comparisons which, taken together, argue strongly in favour of the former. More
specifically, we favour the possibility that the so-called COBE/DIRBE bar is
the boxy/peanut bulge of a bar whose outer thin parts are the so-called Long
bar. This possibility is in good agreement both with observations of external
galaxies, with orbital structure theory and with simulations. We then analyse
in detail the morphology and kinematics given by five representative Galactic
potentials. Two have a Ferrers bar, two have a quadrupole bar and the last one
a composite bar. We first consider only the COBE/DIRBE bar and then extend it
to include the effect of the Long bar. We find that the large-scale structure
given by the manifolds describes an inner ring, whose size is similar to the
near and far 3-kpc arm, and an outer ring, whose properties resemble those of
the Galactic Molecular Ring. We also analyse the kinematics of these two
structures, under the different galactic potentials, and find they reproduce
the main over-densities found in the galactic longitude-velocity CO diagram.
Finally, we consider for what model parameters, the global morphology of the
manifolds may reproduce the two outer spiral arms. We conclude that this would
necessitate either more massive and more rapidly rotating bars, or including in
the potential an extra component describing the spiral arms.


  Atomic vacancy defects in single unit cell thick hexagonal boron nitride are
of significant interest because of their photophysical properties, including
single-photon emission, and promising applications in quantum communication and
computation. The spectroscopic assignment of emission energies to specific
atomic vacancies within the triangular lattice is confounded by the exponential
scaling of defect candidates with the number of removed atoms. Herein, we
collect more than 1000 spectra consisting of single, isolated zero-phonon lines
between 1.69 and 2.25 eV, observing 6 quantized zero-phonon lines arising from
hexagonal boron nitride vacancies. A newly developed computational framework
for isomer cataloguing significantly narrows the number of candidate vacancies.
Direct lattice imaging of hexagonal boron nitride, electronic structure
calculations, and subsequent boric acid etching are used to definitively assign
the 6 features. Systematic chemical etching supports the assignment by
demonstrating the sequence of growth of successively larger vacancy centres
from smaller ones, with the defects including a single B vacancy and a 16-atom
triangular defect. These features exhibit a range of emission lifetimes from 1
to 6 ns, and phonon sidebands offset by the dominant lattice phonon in
hexagonal boron nitride near 1370 cm-1. This assignment should significantly
advance the solid-state chemistry and photophysics of such vacancy emitters.


  Classification of relativistic wave equations is given on the ground of
interlocking representations of the Lorentz group. A system of interlocking
representations is associated with a system of eigenvector subspaces of the
energy operator. Such a correspondence allows one to define matter spectrum,
where the each level of this spectrum presents a some state of elementary
particle. An elementary particle is understood as a superposition of state
vectors in nonseparable Hilbert space. Classification of indecomposable systems
of relativistic wave equations is produced for bosonic and fermionic fields on
an equal footing (including Dirac and Maxwell equations). All these fields are
equivalent levels of matter spectrum, which differ from each other by the value
of mass and spin. It is shown that a spectrum of the energy operator,
corresponding to a given matter level, is non-degenerate for the fields of type
$(l,0)\oplus(0,l)$, where $l$ is a spin value, whereas for arbitrary spin
chains we have degenerate spectrum. Energy spectra of the stability levels
(electron and proton states) of the matter spectrum are studied in detail. It
is shown that these stability levels have a nature of threshold scales of the
fractal structure associated with the system of interlocking representations of
the Lorentz group.


  Lexical features are a major source of information in state-of-the-art
coreference resolvers. Lexical features implicitly model some of the linguistic
phenomena at a fine granularity level. They are especially useful for
representing the context of mentions. In this paper we investigate a drawback
of using many lexical features in state-of-the-art coreference resolvers. We
show that if coreference resolvers mainly rely on lexical features, they can
hardly generalize to unseen domains. Furthermore, we show that the current
coreference resolution evaluation is clearly flawed by only evaluating on a
specific split of a specific dataset in which there is a notable overlap
between the training, development and test sets.


  We investigate the dynamics of a particle moving randomly along a disordered
hetero-polymer subjected to rapid conformational changes which induce
superdiffusive motion in chemical coordinates. We study the antagonistic
interplay between the enhanced diffusion and the quenched disorder. The
dispersion speed exhibits universal behavior independent of the folding
statistics. On the other hand it is strongly affected by the structure of the
disordered potential. The results may serve as a reference point for a number
of translocation phenomena observed in biological cells, such as protein
dynamics on DNA strands.


  We demonstrate that gravitational particle production (GPP) of a massive,
Abelian, vector (Proca) field during inflation in the presence of nonminimal
coupling to gravity may suffer from an instability which leads to runaway
production of high-momentum modes. This is untenable unless there is some
mechanism to regulate the runaway. We discuss the parameter space of the
particle mass and nonminimal couplings where such a runaway occurs and possible
ways to tame the runaway. We find that there is no obvious way to resolve the
runaway in a UV completion or with kinetic mixing to the standard model.


  In a recent paper [14], we developed the generalized TAP approach for mixed
$p$-spin models with Ising spins at positive temperature. Here we extend these
results in two directions. We find a simplified representation for the energy
of the generalized TAP states in terms of the Parisi measure of the model and,
in particular, show that the energy of all states at a given distance from the
origin is the same. Furthermore, we prove the analogues of the positive
temperature results at zero temperature, which concern the ground-state energy
and the organization of ground-state configurations in space.


  Hindman's celebrated Finite Sums Theorem, and its high-dimensional version
due to Milliken and Taylor, are extended from covers of countable sets to
covers of arbitrary topological spaces with Menger's classic covering property.
The methods include, in addition to Hurewicz's game theoretic characterization
of Menger's property, extensions of the classic idempotent theory in the
Stone--Czech compactification of semigroups, and of the more recent theory of
selection principles. This provides strong versions of the mentioned celebrated
theorems, where the monochromatic substructures are large, beyond infinitude,
in an analytic sense. Reducing the main theorems to the purely combinatorial
setting, we obtain nontrivial consequences concerning uncountable cardinal
characteristics of the continuum.
  The main results, modulo technical refinements, are of the following type
(definitions provided in the main text): Let $X$ be a Menger space, and
$\mathcal{U}$ be an infinite open cover of $X$. Consider the complete graph,
whose vertices are the open sets in $X$. For each finite coloring of the
vertices and edges of this graph, there are disjoint finite subsets
$\mathcal{F}_1,\mathcal{F}_2,\dots$ of the cover $\mathcal{U}$ whose unions
$V_1 := \bigcup\mathcal{F}_1, V_2 := \bigcup\mathcal{F}_2,\dots$ have the
following properties:
  1. The sets $\bigcup_{n\in F}V_n$ and $\bigcup_{n\in H}V_n$ are distinct for
all nonempty finite sets $F<H$.
  2. All vertices $\bigcup_{n\in F}V_n$, for nonempty finite sets $F$, are of
the same color.
  3. All edges $\bigl\{\,\bigcup_{n\in F}V_n, \bigcup_{n\in H}V_n\,\bigr\}$,
for nonempty finite sets $F<H$, have the same color.
  4. The family $\{V_1,V_2,\dots\}$ is an open cover of $X$.
  A self-contained introduction to the necessary parts of the needed theories
is provided.


  Despite computation becomes much complex on data with an unprecedented scale,
we argue computers or smart devices should and will consistently provide
information and knowledge to human being in the order of a few tens
milliseconds. We coin a new term 10-millisecond computing to call attention to
this class of workloads. 10-millisecond computing raises many challenges for
both software and hardware stacks. In this paper, using a typical
workload-memcached on a 40-core server (a main-stream server in near future),
we quantitatively measure 10-ms computing's challenges to conventional
operating systems. For better communication, we propose a simple metric-outlier
proportion to measure quality of service: for N completed requests or jobs, if
M jobs or requests' latencies exceed the outlier threshold t, the outlier
proportion is M/N . For a 1K-scale system running Linux (version 2.6.32), LXC
(version 0.7.5) or XEN (version 4.0.0), respectively, we surprisingly find that
so as to reduce the service outlier proportion to 10% (10% users will feel QoS
degradation), the outlier proportion of a single server has to be reduced by
871X, 2372X, 2372X accordingly. Also, we discuss the possible design spaces of
10-ms computing systems from perspectives of datacenter architectures,
networking, OS and scheduling, and benchmarking.


  Scene text image super-resolution (STISR) aims at simultaneously increasing
the resolution and readability of low-resolution scene text images, thus
boosting the performance of the downstream recognition task. Two factors in
scene text images, visual structure and semantic information, affect the
recognition performance significantly. To mitigate the effects from these
factors, this paper proposes a Prior-Enhanced Attention Network (PEAN).
Specifically, an attention-based modulation module is leveraged to understand
scene text images by neatly perceiving the local and global dependence of
images, despite the shape of the text. Meanwhile, a diffusion-based module is
developed to enhance the text prior, hence offering better guidance for the SR
network to generate SR images with higher semantic accuracy. Additionally, a
multi-task learning paradigm is employed to optimize the network, enabling the
model to generate legible SR images. As a result, PEAN establishes new SOTA
results on the TextZoom benchmark. Experiments are also conducted to analyze
the importance of the enhanced text prior as a means of improving the
performance of the SR network. Code is available at
https://github.com/jdfxzzy/PEAN.


  Integrating renewable energy production into the electricity grid is an
important policy goal to address climate change. However, such an integration
faces economic and technological challenges. As power generation by renewable
sources increases, power transmission patterns over the electric grid change.
Due to physical laws, these new transmission patterns lead to non-intuitive
grid congestion externalities. We derive the conditions under which negative
network externalities due to power trades occur. Calibration using a stylized
framework and data from Europe shows that each additional unit of power traded
between northern and western Europe reduces transmission capacity for the
southern and eastern regions by 27% per unit traded. Such externalities suggest
that new investments in the electric grid infrastructure cannot be made
piecemeal. In our example, power infrastructure investment in northern and
western Europe needs an accompanying investment in southern and eastern Europe
as well. An economic challenge is regions facing externalities do not always
have the financial ability to invest in infrastructure. Power transit fares can
help finance power infrastructure investment in regions facing network
congestion externalities. The resulting investment in the overall electricity
grid facilitates integration of renewable energy production.


  In Federated Learning (FL), a framework to train machine learning models
across distributed data, well-known algorithms like FedAvg tend to have slow
convergence rates, resulting in high communication costs during training. To
address this challenge, we introduce FedLion, an adaptive federated
optimization algorithm that seamlessly incorporates key elements from the
recently proposed centralized adaptive algorithm, Lion (Chen et al. 2o23), into
the FL framework. Through comprehensive evaluations on two widely adopted FL
benchmarks, we demonstrate that FedLion outperforms previous state-of-the-art
adaptive algorithms, including FAFED (Wu et al. 2023) and FedDA. Moreover,
thanks to the use of signed gradients in local training, FedLion substantially
reduces data transmission requirements during uplink communication when
compared to existing adaptive algorithms, further reducing communication costs.
Last but not least, this work also includes a novel theoretical analysis,
showcasing that FedLion attains faster convergence rate than established FL
algorithms like FedAvg.


  We study the condition of black hole formation in five-dimensional
space-time. We analytically solve the constraint equations of five-dimensional
Einstein equations for momentarily static and conformally flat initial data of
a spheroidal mass. We numerically search for an apparent horizon in various
initial hypersurfaces and find both necessary and sufficient conditions for the
horizon formation in terms of inequalities relating a geometric quantity and a
mass defined in an appropriate manner. In the case of infinitely thin spheroid,
our results suggest a possibility of naked singularity formation by the spindle
gravitational collapse in five-dimensional space-time.


  Deep neural networks, costly to train and rich in intellectual property
value, are increasingly threatened by model extraction attacks that compromise
their confidentiality. Previous attacks have succeeded in reverse-engineering
model parameters up to a precision of float64 for models trained on random data
with at most three hidden layers using cryptanalytical techniques. However, the
process was identified to be very time consuming and not feasible for larger
and deeper models trained on standard benchmarks. Our study evaluates the
feasibility of parameter extraction methods of Carlini et al. [1] further
enhanced by Canales-Mart\'inez et al. [2] for models trained on standard
benchmarks. We introduce a unified codebase that integrates previous methods
and reveal that computational tools can significantly influence performance. We
develop further optimisations to the end-to-end attack and improve the
efficiency of extracting weight signs by up to 14.8 times compared to former
methods through the identification of easier and harder to extract neurons.
Contrary to prior assumptions, we identify extraction of weights, not
extraction of weight signs, as the critical bottleneck. With our improvements,
a 16,721 parameter model with 2 hidden layers trained on MNIST is extracted
within only 98 minutes compared to at least 150 minutes previously. Finally,
addressing methodological deficiencies observed in previous studies, we propose
new ways of robust benchmarking for future model extraction attacks.


  Bitcoin is firmly becoming a mainstream asset in our global society. Its
highly volatile nature has traders and speculators flooding into the market to
take advantage of its significant price swings in the hope of making money.
This work brings an algorithmic trading approach to the Bitcoin market to
exploit the variability in its price on a day-to-day basis through the
classification of its direction. Building on previous work, in this paper, we
utilise both features internal to the Bitcoin network and external features to
inform the prediction of various machine learning models. As an empirical test
of our models, we evaluate them using a real-world trading strategy on
completely unseen data collected throughout the first quarter of 2021. Using
only a binary predictor, at the end of our three-month trading period, our
models showed an average profit of 86\%, matching the results of the more
traditional buy-and-hold strategy. However, after incorporating a risk
tolerance score into our trading strategy by utilising the model's prediction
confidence scores, our models were 12.5\% more profitable than the simple
buy-and-hold strategy. These results indicate the credible potential that
machine learning models have in extracting profit from the Bitcoin market and
act as a front-runner for further research into real-world Bitcoin trading.


  Effective potentials of the relativistic m\alpha^6 order correction for the
ground state of the Coulomb two-center problem are calculated. They can be used
to evaluate the relativistic contribution of that order to the energies of
hydrogen molecular ions or metastable states of the antiprotonic helium atom,
where precision spectroscopic data are available. In our studies we use the
variational expansion based on randomly chosen exponents that permits to
achieve high numerical accuracy.


  We study randomness properties of graphs and hypergraphs generated by simple
hash functions. Several hashing applications can be analyzed by studying the
structure of $d$-uniform random ($d$-partite) hypergraphs obtained from a set
$S$ of $n$ keys and $d$ randomly chosen hash functions $h_1,\dots,h_d$ by
associating each key $x\in S$ with a hyperedge $\{h_1(x),\dots, h_d(x)\}$.
Often it is assumed that $h_1,\dots,h_d$ exhibit a high degree of independence.
We present a simple construction of a hash class whose hash functions have
small constant evaluation time and can be stored in sublinear space. We devise
general techniques to analyze the randomness properties of the graphs and
hypergraphs generated by these hash functions, and we show that they can
replace other, less efficient constructions in cuckoo hashing (with and without
stash), the simulation of a uniform hash function, the construction of a
perfect hash function, generalized cuckoo hashing and different load balancing
scenarios.


  The nanoparticle packed bed (NPB) as a kind of promising thermal insulation
materials has drawn widely concern because of their quite low thermal
conductivities (k). In this paper, based on the concept that NPB morphology
enable low k, we further proposed a common method, a hybrid strategy, to
further reduce k and enhance mechanical strength, simultaneously. The lowest
effective thermal conductivity (k_e) of hybrid NPB can even as low as
0.018Wm-1K-1, which is much lower than the k of the free air and most common
thermal insulation materials, due to the quite low solid-phase thermal
conductivity (k_s), negligible thermal conductivity of the confined air (k_a)
and small radiative thermal conductivity (k_r). Neglecting the k_a, the minimum
k_e occurs at the porosity where domination role changes from k_s to k_r. In
addition, an excellent mechanical strength, nearly 40-50 % compared to bulk
silica, was also harvested in silica hybrid NPB. This study is expected to
supply some information for thermal insulation material design.


  Eye-GUIDE is an assistive communication tool designed for the paralyzed or
physically impaired people who were unable to move parts of their bodies
especially people whose communications are limited only to eye movements. The
prototype consists of a camera and a computer. Camera captures images then it
will be send to the computer, where the computer will be the one to interpret
the data. Thus, Eye-GUIDE focuses on camera-based gaze tracking. The proponent
designed the prototype to perform simple tasks and provides graphical user
interface in order the paralyzed or physically impaired person can easily use
it.


  Let $S$ be a closed surface of genus at least $2$, let $h$ be a smooth metric
of curvature $K<-1$ on $S$, and let $h_0$ be a hyperbolic metric on $S$. We
show that there exists a unique quasifuchsian AdS spacetime with left metric
isotopic to $h_0$, containing a past-convex Cauchy surface with induced metric
isotopic to $h$.


  We consider a class of minimal extensions of the Standard Model with an extra
massive neutral gauge boson Z'. They include both family-universal models,
where the extra U(1) is associated with (B-L), and non-universal models where
the Z' is coupled to a non-trivial linear combination of B and the lepton
flavours. After giving an estimate of the range of parameters compatible with a
Grand Unified Theory, we present the current experimental bounds, discussing
the interplay between electroweak precision tests and direct searches at the
Tevatron. Finally, we assess the discovery potential of the early LHC.


  We report the observation of a compensation point in the temperature
dependence of magnetization data of polycrystalline Sm2Al. Magnetization
measurements show that this compound magnetically orders at about 150 K. Below
this temperature, the magnetization data shows a compensation point, which
shifts with field. Hysteresis loops obtained below the compensation temperature
show that the compound possesses exchange anisotropy. Both the exchange
anisotropy field and the coercive field are found to be quite large and
comparable to those of the classical spin-orbit compensated ferromagnet
(Sm,Gd)Al2. The heat capacity data also suggest that there are similarities
between (Sm,Gd)Al2 and Sm2Al.


  Let $b \geq 3$ be a positive integer. A natural number is said to be a
base-$b$ Zuckerman number if it is divisible by the product of its base-$b$
digits. Let $\mathcal{Z}_b(x)$ be the set of base-$b$ Zuckerman numbers that do
not exceed $x$, and assume that $x \to +\infty$. First, we prove an upper bound
of the form $|\mathcal{Z}_b(x)| < x^{z_b^{+} + o(1)}$, where $z_b^{+} \in
(0,1)$ is an effectively computable constant. In particular, we have that
$z_{10}^+ = 0.665{\scriptstyle\ldots}$, which improves upon the previous upper
bound $|\mathcal{Z}_{10}(x)| < x^{0.717}$ due to Sanna. Moreover, we prove that
$|\mathcal{Z}_{10}(x)| > x^{0.204}$, which improves upon the previous lower
bound $|\mathcal{Z}_{10}(x)| > x^{0.122}$, due to De Koninck and Luca. Second,
we provide a heuristic suggesting that $|\mathcal{Z}_b(x)| = x^{z_b + o(1)}$,
where $z_b \in (0,1)$ is an effectively computable constant. In particular, we
have that $z_{10} = 0.419{\scriptstyle\ldots}$. Third, we provide algorithms to
count, respectively enumerate, the elements of $\mathcal{Z}_b(x)$, and we
determine their complexities. Implementing one of such counting algorithms, we
computed $|\mathcal{Z}_b(x)|$ for $b=3,\dots,12$ and large values of $x$
(depending on $b$), and we showed that the results are consistent with our
heuristic.


  What does it mean today to study a problem from a computational point of
view? We focus on parameterized complexity and on Column 16 "Graph Restrictions
and Their Effect" of D. S. Johnson's Ongoing guide, where several puzzles were
proposed in a summary table with 30 graph classes as rows and 11 problems as
columns. Several of the 330 entries remain unclassified into Polynomial or
NP-complete after 35 years. We provide a full dichotomy for the Steiner Tree
column by proving that the problem is NP-complete when restricted to Undirected
Path graphs. We revise Johnson's summary table according to the granularity
provided by the parameterized complexity for NP-complete problems.


  We study the effect of edge contractions on simplicial homology because these
contractions have turned to be useful in various applications involving
topology. It was observed previously that contracting edges that satisfy the so
called link condition preserves homeomorphism in low dimensional complexes, and
homotopy in general. But, checking the link condition involves computation in
all dimensions, and hence can be costly, especially in high dimensional
complexes. We define a weaker and more local condition called the p-link
condition for each dimension p, and study its effect on edge contractions. We
prove the following: (i) For homology groups, edges satisfying the p- and
(p-1)-link conditions can be contracted without disturbing the p-dimensional
homology group. (ii) For relative homology groups, the (p-1)-, and the
(p-2)-link conditions suffice to guarantee that the contraction does not
introduce any new class in any of the resulting relative homology groups,
though some of the existing classes can be destroyed. Unfortunately, the
surjection in relative homolgy groups does not guarantee that no new relative
torsion is created. (iii) For torsions, edges satisfying the p-link condition
alone can be contracted without creating any new relative torsion and the
p-link condition cannot be avoided. The results on relative homology and
relative torsion are motivated by recent results on computing optimal
homologous chains, which state that such problems can be solved by linear
programming if the complex has no relative torsion. Edge contractions that do
not introduce new relative torsions, can safely be availed in these contexts.


  We study temperature fluctuations in the initial stages of the relativistic
heavy ion collision using a multiphase transport model. We consider the plasma
in the initial stages after collision before it has a chance to equilibrate. We
have considered Au + Au collision with a center of mass energy of 200 GeV. We
use the non extensive Tsallis statistics to find the entropic index in the
partonic stages of the relativistic heavy ion collisions. We find that the
temperature and the entropic index have a linear relationship during the
partonic stages of the heavy ion collision. This has already been observed in
the hadronic phase. A detailed analysis of the dependence of the entropic index
on the system shows that for increasing space time rapidity, the entropic index
of the partonic system increases. The entropic index also depends on the beam
collision energy. The calculation of the entropic index from the experimental
data fitting of the transverse momenta deals with the hadronic phase. However,
our current study shows that the behaviour of the entropic index in the initial
non-equilibrium stage of the collision is very similar to the behaviour of the
entropic index in the hadronic stage.


  We present the first results of the Hubble Wide Field Camera 3 Test of
Surfaces in the Outer Solar System (H/WTSOSS). The purpose of this survey was
to measure the surface properties of a large number of Kuiper belt objects and
attempt to infer compositional and dynamical correlations. We find that the
Centaurs and the low-perihelion scattered disk and resonant objects exhibit
virtually identical bifurcated optical colour distributions and make up two
well defined groups of object. Both groups have highly correlated optical and
NIR colours which are well described by a pair of two component mixture models
that have different red components, but share a common neutral component. The
small, $H_{606}\gtrsim5.6$ high-perihelion excited objects are entirely
consistent with being drawn from the two branches of the mixing model
suggesting that the colour bifurcation of the Centaurs is apparent in all small
excited objects. On the other hand, objects larger than $H_{606}\sim5.6$ are
not consistent with the mixing model, suggesting some evolutionary process
avoided by the smaller objects. The existence of a bifurcation amongst all
excited populations argues that the two separate classes of object existed in
the primordial disk before the excited Kuiper belt was populated. The cold
classical objects exhibit a different type of surface which has colours that
are consistent with being drawn from the red branch of the mixing model, but
with much higher albedos.


  We present SciRIFF (Scientific Resource for Instruction-Following and
Finetuning), a dataset of 137K instruction-following demonstrations for 54
tasks covering five essential scientific literature understanding capabilities:
information extraction, summarization, question answering, claim verification,
and classification. SciRIFF demonstrations are notable for their long input
contexts, detailed task specifications, and complex structured outputs. While
instruction-following resources are available in specific domains such as
clinical medicine and chemistry, SciRIFF is the first dataset focused on
extracting and synthesizing information from research literature across a wide
range of scientific fields. To demonstrate the utility of SciRIFF, we develop a
sample-efficient strategy to adapt a general instruction-following model for
science by performing additional finetuning on a mix of general-domain and
SciRIFF demonstrations. In evaluations on nine held-out scientific tasks, our
model -- called SciTulu -- improves over a strong LLM baseline by 28.1% and
6.5% at the 7B and 70B scales respectively, while maintaining general
instruction-following performance within 2% of the baseline. We are optimistic
that SciRIFF will facilitate the development and evaluation of LLMs to help
researchers navigate the ever-growing body of scientific literature. We release
our dataset, model checkpoints, and data processing and evaluation code to
enable further research.


  We propose theoretical and empirical improvements for two-stage hashing
methods. We first provide a theoretical analysis on the quality of the binary
codes and show that, under mild assumptions, a residual learning scheme can
construct binary codes that fit any neighborhood structure with arbitrary
accuracy. Secondly, we show that with high-capacity hash functions such as
CNNs, binary code inference can be greatly simplified for many standard
neighborhood definitions, yielding smaller optimization problems and more
robust codes. Incorporating our findings, we propose a novel two-stage hashing
method that significantly outperforms previous hashing studies on widely used
image retrieval benchmarks.


  We discuss the phenomenology of an MeV-scale Dirac fermion coupled to the
Standard Model through a dark photon with kinetic mixing with the
electromagnetic field. We compute the dark matter relic density and explore the
interplay of direct detection and accelerator searches for dark photons. We
show that precise measurements of the temperature and polarization power
spectra of the Cosmic Microwave Background Radiation lead to stringent
constraints, leaving a small window for the thermal production of this MeV dark
matter candidate. The forthcoming MeV gamma-ray telescope e-ASTROGAM will offer
important and complementary opportunities to discover dark matter particles
with masses below 10 MeV. Lastly, we discuss how a late-time inflation episode
and freeze-in production could conspire to yield the correct relic density
while being consistent with existing and future constraints.


  In online advertising, search engines sell ad placements for keywords
continuously through auctions. This problem can be seen as an infinitely
repeated game since the auction is executed whenever a user performs a query
with the keyword. As advertisers may frequently change their bids, the game
will have a large set of equilibria with potentially complex strategies. In
this paper, we propose the use of natural strategies for reasoning in such
setting as they are processable by artificial agents with limited memory and/or
computational power as well as understandable by human users. To reach this
goal, we introduce a quantitative version of Strategy Logic with natural
strategies in the setting of imperfect information. In a first step, we show
how to model strategies for repeated keyword auctions and take advantage of the
model for proving properties evaluating this game. In a second step, we study
the logic in relation to the distinguishing power, expressivity, and
model-checking complexity for strategies with and without recall.


  We employ the stochastic path-integral formalism and action principle for
continuous quantum measurements - the Chantasri-Dressel-Jordan (CDJ) action
formalism [1, 2] - to understand the stages in which quantum Zeno effect helps
control the states of a simple quantum system. The detailed dynamics of a
driven two-level system subjected to repeated measurements unravels a myriad of
phases, so to say. When the detection frequency is smaller than the Rabi
frequency, the oscillations slow down, eventually coming to a halt at an
interesting resonance when measurements are spaced exactly by the time of
transition between the two states. On the other hand, in the limit of large
number of repeated measurements, the dynamics organizes itself in a rather
interesting way about two hyperbolic points in phase space whose stable and
unstable directions are reversed. Thus, the phase space flow occurs from one
hyperbolic point to another, in different ways organized around the
separatrices. We believe that the systematic treatment presented here paves the
way for a better and clearer understanding of quantum Zeno effect in the
context of quantum error correction.


  We show that the f_0(980) and a_0(980) states appearing in scattering and
production processes can be described quite well by the two-channel
Oller-Oset-Pel\'aez (OOP) version of unitarized chiral theories. It is
impossible, however, to deduce a conclusion on the nature of them from the
fitting to experimental data alone. Using explicit N_c dependence of parameters
in OOP amplitudes we demonstrate that light scalar resonances are not of q\bar
q states but dynamical rescattering effects generated under chiral symmetry,
unitarity and channel couplings.


  It is argued that an electronically charged dilaton black hole can support a
long range field of a Nielsen-Olesen string. Combining both numerical and
perturbative techniques we examine the properties of an Abelian-Higgs vortex in
the presence of the black hole under consideration. Allowing the black hole to
approach extremality we found that all fields of the vortex are expelled from
the extreme black hole. In the thin string limit we obtained the metric of a
conical electrically charged dilaton black hole. The effect of the vortex can
be measured from infinity justifying its characterization as black hole hair.


  These lecture notes cover the important developments in histories approach to
quantum mechanics with overall content and emphasis somewhat different from
other reviews and books on the subject.The idea of Houtappel, Van Dam and
Wigner of employing objects based on primitive concepts of physical theories is
discussed in some detail and the fact that histories are such objects is
emphasized. Application of histories formalism to the problem of understanding
the quasiclassical domain is treated in some detail. Other topics discussed
include generalized histories-based quantum mechanics and its application to
the quantum mechanics of space-time,generalization of the notion of time
sequences employing partial semigroups,quasitemporal structures, history
projection operator (HPO) formalism, the algebraic scheme of Isham and Linden,
an axiomatic scheme for quasitemporal histories-based theories and symmetries
and conservation laws in histories-based theories.


  Recent breakthroughs in Large-scale language models (LLMs) have demonstrated
impressive performance on various tasks. The immense sizes of LLMs have led to
very high resource demand and cost for running the models. Though the models
are largely served using uniform high-caliber GPUs nowadays, utilizing a
heterogeneous cluster with a mix of available high- and low-capacity GPUs can
potentially substantially reduce the serving cost. There is a lack of designs
to support efficient LLM serving using a heterogeneous cluster, while the
current solutions focus on model partition and uniform compression among
homogeneous devices. This paper proposes LLM-PQ, a system that advocates
adaptive model quantization and phase-aware partition to improve LLM serving
efficiency on heterogeneous GPU clusters. We carefully decide on
mixed-precision model quantization together with phase-aware model partition
and micro-batch sizing in distributed LLM serving with an efficient algorithm,
to greatly enhance inference throughput while fulfilling user-specified model
quality targets. Extensive experiments on production inference workloads in 11
different clusters demonstrate that LLM-PQ achieves up to 2.88x (2.26x on
average) throughput improvement in inference, showing great advantages over
state-of-the-art works.


  The influence of atomic interactions on time-dependent tunneling processes of
Bose-Einstein condensates is investigated. In a variety of contexts the
relevant condensate dynamics can be described by a Landau-Zener equation
modified by the appearance of nonlinear contributions. Based on this equation
it is discussed how the interactions modify the tunneling probability. In
particular, it is shown that for certain parameter values, due to a nonlinear
hysteresis effect, complete adiabatic population transfer is impossible however
slowly the resonance is crossed. The results also indicate that the
interactions can cause significant increase as well as decrease of tunneling
probabilities which should be observable in currently feasible experiments.


  Context. In order to study the association of the origin of ultra high energy
cosmic rays (UHECR) with active galactic nuclei (AGN) at all levels of their
activity we require an unbiased sample of black holes. Aims. Here we describe
such a sample, of about 6 000 black holes, within the local Universe, inside
the GZK (Greisen Zatsepin Kuzmin) limit, around 100 Mpc. Methods. The starting
point is the 2 micron all sky survey, with the next steps as: test its com-
pleteness down to low flux densities, confine it to redshifts z < 0.025, limit
it to early Hubble type galaxies, test with B-V colors and with the FIR/Radio
ratio the possible separation in classes of sources for the ultra high energy
cosmic rays, use the spheroidal stellar component - black hole mass
relationship to derive black hole masses, and test them with known black hole
masses. Results. The statistics are consistent with the mass function of black
hole masses, with a rel- atively flat distribution to about 10^8 Msol, and
thereafter a very steep spectrum. Our sample cuts off just below 10^7 Msol,
indicating a gap for lower masses, below somewhere near 10^6 Msol. We construct
the sky distribution for all black holes above 10^7 Msol, 10^8 Msol, and 3 x
10^8 Msol, and also show the sky distribution for the five redshift ranges 0.0
- 0.005, 0.005 - 0.0010, 0.010 - 0.015, 0.015 - 0.020, and 0.020 to 0.025.


  Left Right Symmetric Model (LRSM) being an extension of the Standard model of
particle physics incorporates within itself Type-I and Type-II seesaw mass
terms naturally. Both the mass terms can have significant amount of
contribution to the resulting light neutrino mass within the model and hence on
the different phenomenology associated within. In this paper, we have
thoroughly analyzed and discussed the implications of specifying different
weightages to the type-I and type-II mass terms and also the study has been
carried out for different values of $M_{W_R}$ which is mass of the right-handed
gauge boson. This paper also gives a deeper insight into the new physics
contributions of Neutrinoless Double Beta Decay $(0\nu\beta\beta)$ and their
variations with the net baryon asymmetry arising out of the model. Therefore,
the main objective of the present paper rests on investigating the implications
of imposing different weightage to the type-I and type-II seesaw terms and
different values of $M_{W_R}$ on the new physics contributions of
$0\nu\beta\beta$ and net baryon asymmetry arising out as a result of resonant
leptogenesis. LRSM in this work has been realized using modular group of level
3, $\Gamma(3)$ which is isomorphic to non-abelian discrete symmetry group
$A_4$, the advantage being the non-requirement of flavons within the model and
hence maintaining the minimality of the model.


  We investigate the relation between the Laplacian-$b$ motion and stochastic
Komatu-Loewner evolution (SKLE) on multiply connected subdomains of the upper
half-plane, both of which are analogues to SLE. In particular, we show that, if
the driving function of an SKLE is given by a certain stochastic differential
equation, then this SKLE is the same as a time-changed Laplacian-$b$ motion. As
an application, we prove the finite time explosion of SKLE corresponding to
Laplacian-$0$ motion, or $\mathrm{SLE_6}$, in the sense that the solution to
the Komatu-Loewner equation for the slits blows up.


  We study the geometry of complexified moduli spaces of special Lagrangian
submanifolds in the complement of an anticanonical divisor in a compact Kahler
manifold. In particular, we explore the connections between T-duality and
mirror symmetry in concrete examples, and show how quantum corrections arise in
this context.


  This paper presents a novel approach to learn and detect distinctive regions
on 3D shapes. Unlike previous works, which require labeled data, our method is
unsupervised. We conduct the analysis on point sets sampled from 3D shapes,
then formulate and train a deep neural network for an unsupervised shape
clustering task to learn local and global features for distinguishing shapes
with respect to a given shape set. To drive the network to learn in an
unsupervised manner, we design a clustering-based nonparametric softmax
classifier with an iterative re-clustering of shapes, and an adapted
contrastive loss for enhancing the feature embedding quality and stabilizing
the learning process. By then, we encourage the network to learn the point
distinctiveness on the input shapes. We extensively evaluate various aspects of
our approach and present its applications for distinctiveness-guided shape
retrieval, sampling, and view selection in 3D scenes.


  We study relaxation dynamics of a three dimensional elastic manifold in
random potential from a uniform initial condition by numerically solving the
Langevin equation.We observe growth of roughness of the system up to larger
wavelengths with time.We analyze structure factor in detail and find a compact
scaling ansatz describing two distinct time regimes and crossover between them.
We find short time regime corresponding to length scale smaller than the Larkin
length $L_c$ is well described by the Larkin model which predicts a power law
growth of domain size $L(t)$. Longer time behavior exhibits the random manifold
regime with slower growth of $L(t)$.


  We deal with rigidity results for compact gradient Einstein-type manifolds
with nonempty boundaries. As a result, we obtain new characterizations for
hemispheres and geodesic balls in simply connected space forms. In dimensions
three and five, we obtain topological characterizations for the boundary and
upper bounds for its area.


  We prove algebraic analogues of the facts that a curve on a surface with
self-intersection number zero is homotopic to a cover of a simple curve, and
that two simple curves on a surface with intersection number zero can be
isotoped to be disjoint.


  Using equidistribution criteria, we establish divisibility by cyclotomic
polynomials of several partition polynomials of interest, including
$spt$-crank, overpartition pairs, and $t$-core partitions. As corollaries, we
obtain new proofs of various Ramanujan-type congruences for associated
partition functions. Moreover, using results of Erd\"os and Tur\'an, we
establish the equidistribution of roots of partition polynomials on the unit
circle including those for the rank, crank, $spt$, and unimodal sequences. Our
results complement earlier work on this topic by Stanley, Boyer-Goh, and
others. We explain how our methods may be used to establish similar results for
other partition polynomials of interest, and offer many related open questions
and examples.


  With the help of metadynamics it is possible to calculate efficiently the
free energy of systems displaying high energy barriers as a function of few
selected "collective variables". In doing this, the contribution of all the
other degrees of freedom ("microscopic" variables) is averaged out and, thus,
lost. In the following, it is shown that it is possible to calculate the
thermal average of these microscopic degrees of freedom during the
metadynamics, not loosing this piece of information.


  We analyze two alterations of the standard susceptible-infected-susceptible
(SIS) dynamics that preserve the central properties of spontaneous healing and
infection capacity of a vertex increasing unlimitedly with its degree. All
models have the same epidemic thresholds in mean-field theories but depending
on the network properties, simulations yield a dual scenario, in which the
epidemic thresholds of the modified SIS models can be either dramatically
altered or remain unchanged in comparison with the standard dynamics. For
uncorrelated synthetic networks having a power-law degree distribution with
exponent $\gamma<5/2$, the SIS dynamics are robust exhibiting essentially the
same outcomes for all investigated models. A threshold in better agreement with
the heterogeneous rather than quenched mean-field theory is observed in the
modified dynamics for exponent $\gamma>5/2$. Differences are more remarkable
for $\gamma>3$ where a finite threshold is found in the modified models in
contrast with the vanishing threshold of the original one. This duality is
elucidated in terms of epidemic lifespan on star graphs. We verify that the
activation of the modified SIS models is triggered in the innermost component
of the network given by a $k$-core decomposition for $\gamma<3$ while it
happens only for $\gamma<5/2$ in the standard model. For $\gamma>3$, the
activation in the modified dynamics is collective involving essentially the
whole network while it is triggered by hubs in the standard SIS. The duality
also appears in the finite-size scaling of the critical quantities where
mean-field behaviors are observed for the modified, but not for the original
dynamics. Our results feed the discussions about the most proper conceptions of
epidemic models to describe real systems and the choices of the most suitable
theoretical approaches to deal with these models.


  We approach the problem of counting the number of walks in a digraph from
three different perspectives: enumerative combinatorics, linear algebra, and
symbolic dynamics.


  Motivated by a host of recent applications requiring some amount of
redundancy, frames are becoming a standard tool in the signal processing
toolbox. In this paper, we study a specific class of frames, known as discrete
Fourier transform (DFT) codes, and introduce the notion of systematic frames
for this class. This is encouraged by application of systematic DFT codes in
distributed source coding using DFT codes, a new application for frames.
Studying their extreme eigenvalues, we show that, unlike DFT frames, systematic
DFT frames are not necessarily tight. Then, we come up with conditions for
which these frames can be tight. In either case, the best and worst systematic
frames are established from reconstruction error point of view. Eigenvalues of
DFT frames, and their subframes, play a pivotal role in this work.


  We study shape coexistence and low-energy excitation spectra in
neutron-deficient Pb isotopes using configuration mixing of angular-momentum
and particle-number projected self-consistent mean-field states. The same
Skyrme interaction SLy6 is used everywhere in connection with a
density-dependent zero-range pairing force.


  We begin by studying inventory accumulation at a LIFO (last-in-first-out)
retailer with two products. In the simplest version, the following occur with
equal probability at each time step: first product ordered, first product
produced, second product ordered, second product produced. The inventory thus
evolves as a simple random walk on Z^2. In more interesting versions, a p
fraction of customers orders the "freshest available" product regardless of
type. We show that the corresponding random walks scale to Brownian motions
with diffusion matrices depending on p.
  We then turn our attention to the critical Fortuin-Kastelyn random planar map
model, which gives, for each q>0, a probability measure on random (discretized)
two-dimensional surfaces decorated by loops, related to the q-state Potts
model. A longstanding open problem is to show that as the discretization gets
finer, the surfaces converge in law to a limiting (loop-decorated) random
surface. The limit is expected to be a Liouville quantum gravity surface
decorated by a conformal loop ensemble, with parameters depending on q. Thanks
to a bijection between decorated planar maps and inventory trajectories
(closely related to bijections of Bernardi and Mullin), our results about the
latter imply convergence of the former in a particular topology. A phase
transition occurs at p = 1/2, q=4.


  The problem of nuclear decays occurring due to the neutron-antineutron
oscillation is analyzed in the optical potentil model and within the
field-theoretic S-matrix approach. The result of the optical potential model is
rederived within the field theoretic S-matrix approach. The neutron-
antineutron oscillation in nuclei is suppressed drastically. We discuss an
example for the spin precession of an atom in which analogous suppression takes
place due to transparent physical reasons.


  We explore the implications of the discovery of hard, power-law X-ray sources
in the spectra of nearby elliptical galaxies for the origin of the X-ray
background. The spectra of these sources are consistent with models of thermal
bremsstrahlung emission from low radiative efficiency accretion flows around
central supermassive black holes and are unique in that they approximately
match that of the hard XRB. If such sources, with luminosities consistent with
those observed in nearby ellipticals, are present in most early-type galaxies,
then their integrated emission may contribute significantly to the XRB. These
sources may also contribute to the hard source counts detected in deep X-ray
surveys.


  In 1977 Kervaire and Murthy presented three conjectures regarding $K_0
\mathbb{Z} C_{p^n}$, where $C_{p^n}$ is the cyclic group of order $p^n$ and $p$
is a semi-regular prime. The Mayer-Vietoris exact sequence provides the
following short exact sequence $$0\to V_n\to \pic (\mathbb{Z} C_{p^n})\to \cl
\mathbb{Q} (\zeta_{n-1})\times \pic (\mathbb{Z} C_{p^{n-1}})\to 0$$ where
$\zeta_{n-1}$ is a primitive $p^n$-th root of unity. The group $V_n$ that
injects into $\pic \mathbb{Z} C_{p^n}\cong\tilde{K}_0\mathbb{Z} C_{p^n}$, is a
canonical quotient of an in some sense simpler group $\mathcal{V}_n$. Both
groups split in a ``positive'' and ``negative'' part. While $V_n^-$ is well
understood there is still no complete information on $V_n^+$. Kervaire and
Murthy showed that $K_0 \Z C_{p^n}$ and $V_n$ are tightly connected to class
groups of cyclotomic fields. They conjectured that $V_n^+\cong (\mathbb{Z}/p^n
\mathbb{Z})^{r(p)}$, where $r(p)$ is the index of regularity of the prime $p$
and that $\mathcal{V}_n^+\cong V_n^+$, and moreover, $\char\mathcal{V}_n^+\cong
\cl^{(p)} \mathbb{Q} (\zeta_{n-1})$, the $p$-part of the class group. In the
present paper we calculate $\mathcal{V}_n^+$ and prove that $\char
\mathcal{V}_n^+\cong \cl^{(p)} \mathbb{Q}(\zeta_{n-1})$ for all semi-regular
primes which also gives us the structure of $\cl^{(p)} \mathbb{Q}(\z_{n-1})$ as
an abelian group. Moreover we conclude that all three Kervaire and Murthy
conjectures hold is equivalent to that the Iwasawa invariant $\lambda$ equals
$r(p)$ and that this also implies that the Iwasawa invariant $\nu$ equals
$r(p)$.


  We prove that a finitely generated, right-angled, hyperbolic Coxeter group
can be quasiisometrically embedded into the product of n binary trees, where n
is the chromatic number of the group. As application we obtain certain strongly
aperiodic tilings of the Davis complex of these groups.


  We investigate the low-energy scattering properties of two identical
particles interacting via the polarized quadrupolar interaction. It is shown
that a series of $s$- and $p$-wave resonances appear for identical bosons and
fermions, respectively, as the strength of the quadrupolar interaction
increases. Interestingly, scattering resonances also appear on the generalized
scattering length corresponding to the coupling between the $s$ and $d$ waves.
This observation inspires us to propose a new pseudopotential for the
quadupolar interaction. We also explore the bound-state properties of two
particles in both free space and harmonic traps.


  Motivated by tug-of-war games and asymptotic analysis of certain variational
problems, we consider a gradient constraint problem involving the infinity
Laplace operator. We prove that this problem always has a solution that is
unique if a certain regularity condition on the constraint is satisfied. If
this regularity condition fails, then solutions obtained from game theory and
$L^p$-approximation need not coincide.


  In this paper, with the aid of direct numerical simulations (DNS) of forced
turbulence in a periodic domain, we mathematically reformulate the
Kolmogorov-Richardson energy cascade in terms of vortex stretching. By using
the description, we prove that if the Navier-Stokes flow satisfies a new
regularity criterion in terms of the enstrophy production rate, then the flow
does not blow up. Our DNS results seem to support this regularity criterion.
Next, we mathematically construct the hierarchy of tubular vortices, which is
statistically self-similar in the inertial range. Under the assumptions of the
scale-locally of the vortex stretching/compressing (i.e. energy cascade)
process and the statistical independence between vortices that are not directly
stretched or compressed, we can derive the $-5/3$ power law of the energy
spectrum of statistically stationary turbulence without directly using the
Kolmogorov hypotheses.


  We statistically study the physical properties of a sample of narrow
absorption line (NAL) systems looking for empirical evidences to distinguish
between intrinsic and intervening NALs without taking into account any a priori
definition or velocity cut-off. We analyze the spectra of 100 quasars with 3.5
< z$\rm_{em}$ < 4.5, observed with X-shooter/VLT in the context of the XQ-100
Legacy Survey. We detect a $\sim$ 8 $\sigma$ excess in the number density of
absorbers within 10,000 km/s of the quasar emission redshift with respect to
the random occurrence of NALs. This excess does not show a dependence on the
quasar bolometric luminosity and it is not due to the redshift evolution of
NALs. It extends far beyond the standard 5000 km/s cut-off traditionally
defined for associated absorption lines. We propose to modify this definition,
extending the threshold to 10,000 km/s when also weak absorbers (equivalent
width < 0.2 \AA) are considered. We infer NV is the ion that better traces the
effects of the quasar ionization field, offering the best statistical tool to
identify intrinsic systems. Following this criterion we estimate that the
fraction of quasars in our sample hosting an intrinsic NAL system is 33
percent. Lastly, we compare the properties of the material along the quasar
line of sight, derived from our sample, with results based on close quasar
pairs investigating the transverse direction. We find a deficiency of cool gas
(traced by CII) along the line of sight associated with the quasar host galaxy,
in contrast with what is observed in the transverse direction.


  We discuss several phenomenological implications of Very Special Relativity
(VSR). It is assumed that there is a small violation of Lorentz invariance and
the true symmetry group of nature is a subgroup called SIM(2). This symmetry
group postulates the existence of a fundamental or preferred direction in
space-time. We study its implications by using an effective action which
violates Lorentz invariance but respects VSR. We find that the problem of
finding the masses of fundamental fermions is in general intractable in the
presence of VSR term. The problem can be solved only in special cases which we
pursue in this paper. We next determine the signal of VSR in torsion pendulum
experiment as well as clock comparison experiment. We find that VSR predicts a
signal which is different from other Lorentz violating theories and hence a
dedicated data analysis is needed in order to impose reliable limits. Assuming
that signal is absent in data we determine the limits that can be imposed on
the VSR parameters. We also study the implications of VSR in particle decay
experiments taking the charged pion and kaon decay as an example. The effective
interaction between the charged pion and the final state leptons is related to
the fundamental VSR mass terms through a loop calculation. We also predict a
shift in the angular dependence of the decay products due to VSR. In particular
we find that these no longer display azimuthal symmetry with respect to the
momentum of the pion. Furthermore the azimuthal and polar angle distributions
show time dependence with a period of a sidereal day. This time dependence
provides us with a novel method to test VSR in future experiments.


  We report initial performance results emerging from 600 hours of observations
with the Automated Planet Finder (APF) telescope and Levy Spectrometer located
at UCO/Lick Observatory. We have obtained multiple spectra of 80 G, K and
M-type stars, which comprise 4,954 individual Doppler radial velocity (RV)
measurements with a median internal uncertainty of 1.35 ms$^{-1}$. We find a
strong, expected correlation between the number of photons accumulated in the
5000-6200$\AA$ iodine region of the spectrum, and the resulting internal
uncertainty estimates. Additionally, we find an offset between the population
of G and K stars and the M stars within the data set when comparing these
parameters. As a consequence of their increased spectral line densities, M-type
stars permit the same level of internal uncertainty with 2x fewer photons than
G-type and K-type stars. When observing M stars, we show that the APF/Levy has
essentially the same speed-on-sky as Keck/HIRES for precision RVs. In the
interest of using the APF for long-duration RV surveys, we have designed and
implemented a dynamic scheduling algorithm. We discuss the operation of the
scheduler, which monitors ambient conditions and combines on-sky information
with a database of survey targets to make intelligent, real-time targeting
decisions.


  Let $G\cong\mathbb{R}^{d} \ltimes \mathbb{R}$ be a finite-dimensional
two-step nilpotent group with the group multiplication
$(x,u)\cdot(y,v)\rightarrow(x+y,u+v+x^{T}Jy)$ where $J$ is a skew-symmetric
matrix satisfying a degeneracy condition with $2\leq {\rm rank}\, J <d$.
Consider the maximal function defined by $$ {\frak M}f(x,
u)=\sup_{t>0}\big|\int_{\Sigma} f(x-ty, u- t x^{T}Jy) d\mu(y)\big|, $$ where
$\Sigma$ is a smooth convex hypersurface and $d\mu$ is a compactly supported
smooth density on $\Sigma$ such that the Gaussian curvature of $\Sigma$ is
nonvanishing on supp $d\mu$. In this paper we prove that when $d\geq 4$, the
maximal operator ${\frak M}$ is bounded on $L^{p}(G)$ for the range
$(d-1)/(d-2)<p\leq\infty$.


  Evaluating causal effects in the presence of interference is challenging in
network-based studies of hard-to-reach populations. Like many such populations,
people who inject drugs (PWID) are embedded in social networks and often exert
influence on others in their network. In our setting, the study design is
observational with a non-randomized network-based HIV prevention intervention.
Information is available on each participant and their connections that confer
possible HIV risk through injection and sexual behaviors. We considered two
inverse probability weighted (IPW) estimators to quantify the population-level
effects of non-randomized interventions on subsequent health outcomes. We
demonstrated that these two IPW estimators are consistent, asymptotically
normal, and derived a closed-form estimator for the asymptotic variance, while
allowing for overlapping interference sets (groups of individuals in which the
interference is assumed possible). A simulation study was conducted to evaluate
the finite-sample performance of the estimators. We analyzed data from the
Transmission Reduction Intervention Project, which ascertained a network of
PWID and their contacts in Athens, Greece, from 2013 to 2015. We evaluated the
effects of community alerts on HIV risk behavior in this observed network,
where the links between participants were defined by using substances or having
unprotected sex together. In the study, community alerts were distributed to
inform people of recent HIV infections among individuals in close proximity in
the observed network. The estimates of the risk differences for spillover using
either IPW estimator demonstrated a protective effect. The results suggest that
HIV risk behavior can be mitigated by exposure to a community alert when an
increased risk of HIV is detected in the network.


  The possibility of non-helical large scale dynamo action is investigated
using three-dimensional simulations of global accretion discs as well as
idealized local simulations without rotation and only shear. Particular
emphasis is placed on a certain correlation between vorticity and azimuthal
velocity gradient which has been predicted to drive large scale dynamo action,
independent of the presence or absence of kinetic helicity. In the global disc
simulations two types of behaviours are found: those which do show this type of
velocity correlation and those which do not. The former ones are typically also
the cases where the resistivity is larger. The latter ones show signs typical
of dynamo action based on the usual helicity effect. In the idealized
simulations without rotation and just shear the above correlation is found to
be particularly strong. In both cases there is, as expected, a systematic flux
of magnetic helicity through the midplane. However, very little helicity flux
leaves the domain through the top and bottom boundaries. The idealized
simulations reveal that much of this systematic flux comes from the rotational
component of the helicity flux and does not contribute to its divergence.


  Germs of locally homogeneous CR manifolds M can be characterized in terms of
certain algebraic data, e.g., by CR-algebras. We give an explicit formula which
relates the Levi form of such an M and its higher order analogues to the Lie
brackets in certain finite dimensional Lie algebras. As an application we give
a simple characterization of geometric properties of M such as minimality,
k-nondegeneracy, holomorphic degeneracy etc. in purely algebraic terms. We
present an example of a homogeneous 3-nondegenerate CR-manifold. We also
determine a universal upper bound for the order k of k-nondegenerate orbits of
real forms in flag manifolds.


  In this paper, we study the linear stability of the elliptic rhombus
solutions, which are the Keplerian homographic solution with the rhombus
central configurations in the classical planar four-body problems. Using
$\omega$-Maslov index theory and trace formula, we prove the linear instability
of elliptic rhombus solutions if the shape parameter $u$ and the eccentricity
of the elliptic orbit $e$ satisfy $(u,e) \in (1/\sqrt{3}, u_2)\times [0,
\hat{f}(\frac{27}{4})^{-1/2})\cup (u_2, 1/u_2) \times [0,1)\cup ( 1/u_2,
\sqrt{3})\times [0, \hat{f}(\frac{27}{4})^{-1/2})$ where $u_2\approx 0.6633$
and $\hat{f}(\frac{27}{4})^{-1/2} \approx 0.4454$. Motivated on numerical
results of the linear stability to the elliptic Lagrangian solutions in [R.
Mart\'{\i}nez, A. Sam\`{a}, and C. Sim\'{o}, J. Diff. Equa., 226(2006):
619--651.], we further analytically prove the linear instability of elliptic
rhombus solutions for $(u,e)\in (1/\sqrt{3}, \sqrt{3}) \times [0,1)$.


  We consider the ekpyrotic paradigm in the context of loop quantum cosmology.
In loop quantum cosmology the classical big-bang singularity is resolved due to
quantum gravity effects, and so the contracting ekpyrotic branch of the
universe and its later expanding phase are connected by a smooth bounce. Thus,
it is possible to explicitly determine the evolution of scalar perturbations,
from the contracting ekpyrotic phase through the bounce and to the post-bounce
expanding epoch. The possibilities of having either one or two scalar fields
have been suggested for the ekpyrotic universe, and both cases will be
considered here. In the case of a single scalar field, the constant mode of the
curvature perturbations after the bounce is found to have a blue spectrum. On
the other hand, for the two scalar field ekpyrotic model where scale-invariant
entropy perturbations source additional terms in the curvature perturbations,
the power spectrum in the post-bounce expanding cosmology is shown to be nearly
scale-invariant and so agrees with observations.


  We present Reward-Switching Policy Optimization (RSPO), a paradigm to
discover diverse strategies in complex RL environments by iteratively finding
novel policies that are both locally optimal and sufficiently different from
existing ones. To encourage the learning policy to consistently converge
towards a previously undiscovered local optimum, RSPO switches between
extrinsic and intrinsic rewards via a trajectory-based novelty measurement
during the optimization process. When a sampled trajectory is sufficiently
distinct, RSPO performs standard policy optimization with extrinsic rewards.
For trajectories with high likelihood under existing policies, RSPO utilizes an
intrinsic diversity reward to promote exploration. Experiments show that RSPO
is able to discover a wide spectrum of strategies in a variety of domains,
ranging from single-agent particle-world tasks and MuJoCo continuous control to
multi-agent stag-hunt games and StarCraftII challenges.


  We argue that Gaspard and coworkers [Nature 394, 865 (1998)] do not give
evidence for microscopic chaos in the sense in which they use the term. The
effectively infinite number of molecules in a fluid can generate the same
macroscopic disorder without any intrinsic instability. But we argue also that
the notion of chaos in infinitely extended systems needs clarification: In a
wider sense, even some systems without local instabilities can be considered
chaotic.


  The aim of this thesis is to study under which conditions $K3$ surfaces
allowing a triple-point-free model satisfy the monodromy property. This
property is a quantitative relation between the geometry of the degeneration of
a Calabi-Yau variety $X$ and the monodromy action on the cohomology of $X$: a
Calabi-Yau variety $X$ satisfies the monodromy property if poles of the motivic
zeta function $Z_{X,\omega}(T)$ induce monodromy eigenvalues on the cohomology
of $X$.
  In this thesis, we focus on $K3$ surfaces allowing a triple-point-free model,
i.e., $K3$ surfaces allowing a strict normal crossings model such that three
irreducible components of the special fiber never meet simultaneously. Crauder
and Morrison classified these models into two main classes: so-called flowerpot
degenerations and chain degenerations. This classification is very precise,
which allows to use a combination of geometrical and combinatorial techniques
to check the monodromy property in practice.
  The first main result is an explicit computation of the poles of
$Z_{X,\omega}(T)$ for a $K3$ surface $X$ allowing a triple-point-free model and
a volume form $\omega$ on $X$. We show that the motivic zeta function can have
more than one pole. This is in contrast with previous results: so far, all
Calabi-Yau varieties known to satisfy the monodromy property have a unique
pole. We prove that $K3$ surfaces allowing a flowerpot degeneration satisfy the
monodromy property. We also show that the monodromy property holds for $K3$
surfaces with a certain chain degeneration. We don't know whether all $K3$
surfaces with a chain degeneration satisfy the monodromy property, and we
investigate what characteristics a $K3$ surface $X$ not satisfying the
monodromy property should have.


  In this paper, we consider the nonlinear dynamical behaviors of some tabu
leaning neuron models. We first consider a tabu learning single neuron model.
By choosing the memory decay rate as a bifurcation parameter, we prove that
Hopf bifurcation occurs in the neuron. The stability of the bifurcating
periodic solutions and the direction of the Hopf bifurcation are determined by
applying the normal form theory. We give a numerical example to verify the
theoretical analysis. Then, we demonstrate the chaotic behavior in such a
neuron with sinusoidal external input, via computer simulations. Finally, we
study the chaotic behaviors in tabu learning two-neuron models, with linear and
quadratic proximity functions respectively.


  This note extends Radford's formula for the fourth power of the antipode of a
finite dimensional Hopf algebra to co-Frobenius Hopf algebras and studies
equivalent conditions to a Hopf algebra being involutory for finite dimensional
and co-Frobenius Hopf algebras.


  We investigate the electronic, ferroelectric and magnetic properties of
KTaO3/PbTiO3 interfaces by using conventional density functional theory (DFT)
and advanced DFT such as hybrid functional HSE06. We show that doped holes in
valence bands or electrons in conduction bands give rise to ferromagnetism at
the interfaces. The ferromagnetic states are ground states for both hole-doped
(p-type) and electron-doped (n-type) interfaces by comparison with their
corresponding nonmagnetic and antiferromagnetic states. Carriers (holes or
electrons) concentrate near the interface to screen the polarization charge and
thus the concentration of carrier varies with the ferroelectric polarization.
Furthermore, the interface magnetization, which is nearly proportional to the
concentration of carrier, can be tuned by ferroelectric polarization reversal,
leading to strong intrinsic magnetoelectric effects at the interface of
originally nonmagnetic KTaO3 and PbTiO3. Interestingly, a
ferromagnetic-nonmagnetic transition tuned by an applied electric field can be
realized at the p-type interface. This suggests an illuminating approach to
multiferroic materials beyond conventional single-phase multiferroics and
multi-phase multiferroics such as ferroelectric/ferromagnet heterostructures.
The KTaO3/PbTiO3 interfaces may be promising in future multiferroic devices
applications.


  Feature-fusion networks with duplex encoders have proven to be an effective
technique to solve the freespace detection problem. However, despite the
compelling results achieved by previous research efforts, the exploration of
adequate and discriminative heterogeneous feature fusion, as well as the
development of fallibility-aware loss functions remains relatively scarce. This
paper makes several significant contributions to address these limitations: (1)
It presents a novel heterogeneous feature fusion block, comprising a holistic
attention module, a heterogeneous feature contrast descriptor, and an
affinity-weighted feature recalibrator, enabling a more in-depth exploitation
of the inherent characteristics of the extracted features, (2) it incorporates
both inter-scale and intra-scale skip connections into the decoder architecture
while eliminating redundant ones, leading to both improved accuracy and
computational efficiency, and (3) it introduces two fallibility-aware loss
functions that separately focus on semantic-transition and depth-inconsistent
regions, collectively contributing to greater supervision during model
training. Our proposed heterogeneous feature fusion network (SNE-RoadSegV2),
which incorporates all these innovative components, demonstrates superior
performance in comparison to all other freespace detection algorithms across
multiple public datasets. Notably, it ranks the 1st on the official KITTI Road
benchmark.


  The novel technique of frequency-offset separated oscillatory fields (FOSOF)
has been originally proposed as a modification to Ramsey's method of separated
oscillatory fields. It has recently been employed in precision measurements
with atomic beams since it allows for an alternative approach to determine
absolute resonance frequencies. We present results from a systematic
investigation of the FOSOF technique adapted to a beam of cold neutrons.


  We develop a new set of models for intermediate-metallicity single stellar
populations in the blue/optical region and use those models to determine the
spectroscopic age of 47 Tuc. The models are based on a moderately
high-resolution (1.8 A FWHM) empirical spectral library, state-of-the-art
theoretical isochrones from M. Salaris and the most recent set from the Padova
group, and new semi-empirical calibrations between fundamental stellar
parameters and observables. We highlight the importance of correctly modeling
the luminosity function (LF) of the cluster at the level of the giant branch,
in order to achieve a good reproduction of the integrated spectrum; agreement
between the spectroscopic age and the age based on the cluster's
color-magnitude diagram (CMD) is achieved only if the observed LF is used
rather than the theoretical ones, which either do not include AGB stars
(Salaris) or underpredict the total number counts of bright giants in the
cluster by a factor of two(Padova). After all corrections are made, the CMD and
the spectroscopic ages (from Hgamma and Hbeta) are in close agreement: 11--12
Gyrs for Salaris isochrones and about 13 Gyrs for Padova. The difference
between the model ages is due to the inclusion of atomic diffusion in the
Salaris models. Previously older spectroscopic ages were due to the
underestimate of the number of red giants and/or the use of isochrones that
neglected the effects of He-diffusion and alpha-enhancement. A similar
underestimate in the bright giant LF, if it exists in current super-solar
metallicity models, would cause spectroscopic ages of elliptical galaxies
inferred from such models to be too high by approximately 30%.


  We present non-Abelian gaugings of supermembrane for general isometries for
compactifications from eleven-dimensions, starting with Abelian case as a
guide. We introduce a super Killing vector in eleven-dimensional superspace for
a non-Abelian group G associated with the compact space B for a general
compactification, and couple it to a non-Abelian gauge field on the
world-volume. As a technical tool, we use teleparallel superspace with no
manifest local Lorentz covariance. Interestingly, the coupling constant is
quantized for the non-Abelian group G, due to its generally non-trivial mapping
\pi_3(G).


  This paper presents a low-communication-overhead parallel method for solving
the 3D incompressible Navier-Stokes equations. A fully-explicit projection
method with second-order space-time accuracy is adopted. Combined with fast
Fourier transforms, the parallel diagonal dominant (PDD) algorithm for the
tridiagonal system is employed to solve the pressure Poisson equation,
differing from its recent applications to compact scheme derivatives
computation (Abide et al. 2017) and alternating-direction-implicit method (Moon
et al. 2020). The number of all-to-all communications is decreased to only two,
in a 2D pencil-like domain decomposition. The resulting MPI/OpenMP hybrid
parallel code shows excellent strong scalability up to $10^4$ cores and small
wall-clock time per timestep. Numerical simulations of turbulent channel flow
at different friction Reynolds numbers ($Re_{\tau}$ = 550, 1000, 2000) have
been conducted and the statistics are in good agreement with the reference
data. The proposed method allows massively simulation of wall turbulence at
high Reynolds numbers as well as many other incompressible flows.


  Performance tools for emerging heterogeneous exascale platforms must address
two principal challenges when analyzing execution measurements. First,
measurement of large-scale executions may record mountains of performance data.
Second, performance measurements for parallel programs are sparse in two ways:
the set of metrics present for any context and the set of contexts present in
different threads. For GPU-accelerated applications, an important source of
sparsity is that none of the myriad of GPU metrics apply to any of the many CPU
contexts. To address these challenges, we developed a novel streaming
aggregation approach to postmortem analysis that employs both shared and
distributed memory parallelism to aggregate sparse performance measurements
from every rank, thread, and GPU stream of an application, and attributes
heterogeneous call path profiles and traces to source code. Using the same
amount of resources, our approach analyzes large-scale performance measurements
of GPU-accelerated applications over an order of magnitude faster than
HPCToolkit and its sparse analysis results are as much as three orders of
magnitude smaller than HPCToolkit's dense representation of metrics.


  We propose a variant of the antiferromagnetic XY model on the triangular
lattice to study the interplay between the chiral and nematic orders in
addition to the magnetic order. The model has a significant bi-quadratic
interaction of the planar spins. When the bi-quadratic exchange energy
dominates, a large temperature window is shown to exist over which the nematic
and the chiral orders co-exist without the magnetic order, thus defining a
chiral-nematic state. The phase diagram of the model and some of its critical
properties are derived by means of the Monte Carlo simulation.


  Just as physicists strive to develop a TOE (theory of everything), which
explains and unifies the physical laws of the universe, the life-scientist
wishes to uncover the TOE as it relates to cellular systems. This can only be
achieved with a quantitative platform that can comprehensively deduce and
relate protein structure, functional, and evolution of genomes and proteomes in
a comparative fashion. Were this perfected, proper analyses would start to
uncover the underlying physical laws governing the emergent behavior of
biological systems and the evolutionary pressures responsible for functional
innovation. In the near term, such methodology would allow the vast quantities
of uncharacterized (e.g. metagenomic samples) primary amino acid sequences to
be rapidly decoded. Analogous to natural products found in the Amazon, genomes
of living organisms contain large numbers of proteins that would prove useful
as new therapeutics for human health, energy sources, and/or waste management
solutions if they could be identified and characterized. We previously
theorized that phylogenetic profiles could provide a quantitative platform for
obtaining unified measures of structure, function, and evolution (SF&E)(1). In
the present manuscript, we present data that support this theory and
demonstrates how refinements of our analysis algorithms improve the performance
of phylogenetic profiles for deriving structural/functional relationships.


  The James Webb Space Telescope (JWST) offers unprecedented sensitivity,
stability, and wavelength coverage for transiting exoplanet studies, opening up
new avenues for measuring atmospheric abundances, structure, and temperature
profiles. Taking full advantage of JWST spectroscopy of planets from 0.6um to
28um, however, will require many observations with a combination of the NIRISS,
NIRCam, NIRSpec, and MIRI instruments. In this white paper, we discuss a new
NIRCam mode (not yet approved or implemented) that can reduce the number of
necessary observations to cover the 1.0um to 5.0um wavelength range. Even
though NIRCam was designed primarily as an imager, it also includes several
grisms for phasing and aligning JWST's 18 hexagonal mirror segments. NIRCam's
long-wavelength channel includes grisms that cover 2.4um to 5.0um with a
resolving power of R = 1200 - 1550 using two separate configurations. The
long-wavelength grisms have already been approved for science operations,
including wide field and single object (time series) slitless spectroscopy. We
propose a new mode that will simultaneously measure spectra for science targets
in the 1.0um to 2.0um range using NIRCam's short-wavelength channel. This mode,
if approved, would take advantage of NIRCam's Dispersed Hartmann Sensor (DHS),
which produces 10 spatially separated spectra per source at R ~ 300. We discuss
the added benefit of the DHS in constraining abundances in exoplanet
atmospheres as well as its ability to observe the brightest systems. The DHS
essentially comes for free (at no time cost) with any NIRCam long-wavelength
grism observation, but the detector integration parameters have to be selected
to ensure that the long-wavelength grism observations do not saturate and that
JWST data volume downlink constraints are not violated.


  Task-oriented dialogue systems have become overwhelmingly popular in recent
researches. Dialogue understanding is widely used to comprehend users' intent,
emotion and dialogue state in task-oriented dialogue systems. Most previous
works on such discriminative tasks only models current query or historical
conversations. Even if in some work the entire dialogue flow was modeled, it is
not suitable for the real-world task-oriented conversations as the future
contexts are not visible in such cases. In this paper, we propose to jointly
model historical and future information through the posterior regularization
method. More specifically, by modeling the current utterance and past contexts
as prior, and the entire dialogue flow as posterior, we optimize the KL
distance between these distributions to regularize our model during training.
And only historical information is used for inference. Extensive experiments on
two dialogue datasets validate the effectiveness of our proposed method,
achieving superior results compared with all baseline models.


  We consider the Brenier-Schr{\"o}dinger problem on compact manifolds with
boundary. In the spirit of a work by Arnaudon, Cruzeiro, L{\'e}onard and
Zambrini, we study the kinetic property of regular solutions and obtain a link
to the Navier-Stokes equations with an impermeability condition. We also
enhance the class of models for which the problem admits a unique solution.
This involves a method of taking quotients by reflection groups for which we
give several examples.


  Label-free detection techniques for single particles and molecules play an
important role in basic science, disease diagnostics, and nanomaterial
investigations. While traditional fluorescence-based methods offer powerful
tools for single molecule detection and imaging, they are limited by a narrow
range of molecular probes and issues such as photoblinking and photobleaching.
Photothermal microscopy has emerged as a label-free imaging technique capable
of detecting individual nanoabsorbers with high sensitivity. Whispering gallery
mode microresonators can confine light in a small volume for enhanced
light-matter interaction and thus are a promising ultra-sensitive photothermal
microscopy platform. Previously microtoroid optical resonators were combined
with photothermal microscopy to detect 250 nm long gold nanorods. Here, we
combine whispering gallery mode microtoroid optical resonators with
photothermal microscopy to spatially detect 5 nm diameter quantum dots (QDs)
with a signal-to-noise ratio (SNR) exceeding $10^4$. To achieve this, we
integrated our microtoroid based photothermal microscopy setup with a low
amplitude modulated pump laser and utilized the
proportional-integral-derivative (PID) controller output as the photothermal
signal source to reduce noise and enhance signal stability. The measured heat
dissipation of these 5 nm QDs is below the detectable level from single dye
molecules, showcasing the high sensitivity and discrimination capabilities of
this platform. We anticipate that our work will have application in a wide
variety of fields, including the biological sciences, nanotechnology, materials
science, chemistry, and medicine.


  We investigate the numerical artifact known as a carbuncle, in the solution
of the shallow water equations. We propose a new Riemann solver that is based
on a local measure of the entropy residual and aims to avoid carbuncles while
maintaining high accuracy. We propose a new challenging test problem for
shallow water codes, consisting of a steady circular hydraulic jump that can be
physically unstable. We show that numerical methods are prone to either
suppress the instability completely or form carbuncles. We test existing cures
for the carbuncle. In our experiments, only the proposed method is able to
avoid unphysical carbuncles without suppressing the physical instability.


  Several versions of the Fourier transform have been formulated in the
framework of Clifford algebra. We present a (Clifford-Fourier) transform,
constructed using the geometric properties of Clifford algebra. We show the
corresponding results of operational calculus. We obtain a technique to
construct monogenic extensions of a certain type of continuous functions, and
versions of the Paley-Wiener theorems are formulated.


  We demonstrate the possibility of engineering a single donor transistor
directly from a phosphorous doped quantum dot by making use of the intrinsic
glassy behaviour of the structure as well as the complex electron dynamics
during cooldown. Characterisation of the device at low temperatures and in
magnetic field shows single donors can be electrostatically isolated near one
of the tunnel barrier with either a single or a doubly occupancy. Such a model
is well supported by capacitance-based simulations. Ability of using the D0 of
such isolated donor as a charge detector is demonstrated by observing the
charge stability diagram of a nearby and capacitively coupled semi-connected
double quantum dot.


  We present the first microscopic images of the prewetting transition of a
liquid film on a solid surface. Pictures of the local coverage map of a helium
film on a cesium metal surface are taken while the temperature is raised
through the transition. The film edge is found to advance at constant
temperature by successive avalanches in a creep motion with a macroscopic
correlation length. The creep velocity varies strongly in a narrow temperature
range. The retreat motion is obtained only at much lower temperature,
conforming to the strong hysteresis observed for prewetting transition on a
disordered surface. Prewetting transition on such disordered surfaces appears
to give rise to dynamical phenomena similar to what is observed for domain wall
motions in 2D magnets.


  The BRST treatment of triaxial nuclei rotating at high spins, which had been
previously developed, is extended to relate states with neighboring values of
the angular momentum $I$. As a consequence, the irreducible multipole
transition operators can be unambiguously separated into their physical and
spurious components. As a by product, we give explicit expressions for the
operators associated with the Goldstone-Nambu modes in terms of the final
orthonormal set of physical and spurious modes.


  Let $\mathbb{N}$ denote the set of all nonnegative integers and $A$ be a
subset of $\mathbb{N}$. Let $h\geq2$ and let $r_h(A,n)=\sharp \{
(a_1,\ldots,a_h)\in A^{h}: a_1+\cdots+a_h=n\}.$ The set $A$ is called an
asymptotic basis of order $h$ if $r_h(A,n)\geq 1$ for all sufficiently large
integers $n$. An asymptotic basis $A$ of order $h$ is minimal if no proper
subset of $A$ is an asymptotic basis of order $h$. Recently, Chen and Tang
resoved a problem of Nathanson on minimal asymptotic bases of order $h$. In
this paper, we generalized this result to $g$-adic representations.


  Brunetti, Fredenhagen and Verch (BFV) have shown how the notion of local
covariance for quantum field theories can be formulated in terms of category
theory: a theory being described as a functor from a category of spacetimes to
a category of $(C)^*$-algebras. We discuss whether this condition is sufficient
to guarantee that a theory represents `the same physics' in all spacetimes,
giving examples to show that it does not. A new criterion, dynamical locality,
is formulated, which requires that descriptions of local physics based on
kinematical and dynamical considerations should coincide. Various applications
are given, including a proof that dynamical locality for quantum fields is
incompatible with the possibility of covariantly choosing a preferred state in
each spacetime. As part of this discussion we state a precise condition that
should hold on any class of theories each representing the same physics in all
spacetimes. This condition holds for the dynamically local theories but is
violated by the full class of locally covariant theories in the BFV sense. The
majority of results described form part of forthcoming papers with Rainer
Verch.


  We model and study the game mechanisms and human behavior of the anarchy mode
in Twitch Plays Pokemon with a pure-jump continuous-time Markov process. We
computed the winning probability and expected game time for $1$ player and $N$
players and identified when collaboration helps. A numerical plug-in example is
also provided.


  We prove that the class of linear context-free tree languages is not closed
under inverse linear tree homomorphisms. The proof is by contradiction: we
encode Dyck words into a context-free tree language and prove that its preimage
under a certain linear tree homomorphism cannot be generated by any
context-free tree grammar. A positive result can still be obtained: the linear
monadic context-free tree languages are closed under inverse linear tree
homomorphisms.


  The ratio of the cross sections for the transversely and longitudinally
virtual photon polarizations, $\sigma^{\gamma^{*}p}_{L/T}$, at high
photon-hadron energy scattering is studied. I investigate the relationship
between the gluon distribution obtained using the color dipole model and
standard gluons obtained from the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi
(DGLAP) evolution and the Altarelli-Martinelli equations. It is shown that the
color dipole bounds are dependent on the gluon distribution behavior. This
behavior is considered by the expansion and Laplace transform methods.
Numerical calculations and comparison with the color dipole model (CDM) bounds
can indicate the range of validity of this method at small dipole sizes, $r\sim
1/Q{\ll}1/Q_{s}$.


  Given a linear map on the vector space of symmetric matrices, every fiber
intersected with the set of positive semidefinite matrices is a spectrahedron.
Using the notion of the fiber body we can build the average over all such
fibers and thereby construct a compact, convex set, the fiber body. We show how
to determine the dimensions of faces and normal cones to study the boundary
structure of the fiber body given that we know about the boundary of the
fibers. We use this to study the fiber body of Gram spectrahedra in the case of
binary sextics and ternary quartics and find a large amount of structure on the
fiber body. We prove that the fiber body in the case of binary sextics has
exactly one face with a full-dimensional normal cone, whereas the Gram
spectrahedron of a generic positive binary sextic has four such points. The
fiber body in the case of ternary quartics changes drastically.


  We show that stochastic programming (SP) provides a framework to design
hierarchical model predictive control (MPC) schemes for periodic systems. This
is based on the observation that, if the state policy of an infinite-horizon
problem is periodic, the problem can be cast as a stochastic program (SP). This
reveals that it is possible to update periodic state targets by solving a
retroactive optimization problem that progressively accumulates historical
data. Moreover, we show that the retroactive problem is a statistical
approximation of the SP and thus delivers optimal targets in the long run.
Notably, this optimality property can be achieved without the need for data
forecasts and cannot be achieved by any known proactive receding horizon
scheme. The SP setting also reveals that the retroactive problem can be seen as
a high-level hierarchical layer that provides targets to guide a low-level MPC
controller that operates over a short period at high resolution. We derive a
retroactive scheme tailored to linear systems by using cutting plane techniques
and suggest strategies to handle nonlinear systems.


  Wireless short-packet communications pose challenges to the security and
reliability of the transmission. Besides, the proactive warder compounds these
challenges, who detects and interferes with the potential transmission. An
extra jamming channel is introduced by the proactive warder compared with the
passive one, resulting in the inapplicability of analytical methods and results
in exsiting works. Thus, effective system design schemes are required for
short-packet communications against the proactive warder. To address this
issue, we consider the analysis and design of covert and reliable transmissions
for above systems. Specifically, to investigate the reliable and covert
performance of the system, detection error probability at the warder and
decoding error probability at the receiver are derived, which is affected by
both the transmit power and the jamming power. Furthermore, to maximize the
effective throughput, an optimization framework is proposed under reliability
and covertness constraints. Numerical results verify the accuracy of analytical
results and the feasibility of the optimization framework. It is shown that the
tradeoff between transmission reliability and covertness is changed by the
proactive warder compared with the passive one. Besides, it is shown that
longer blocklength is always beneficial to improve the throughput for systems
with optimized transmission rates. But when transmission rates are fixed, the
blocklength should be carefully designed since the maximum one is not optimal
in this case.


  Given a fixed product of non-isogenous abelian varieties at least one of
which is general, we show how to construct complete families of indecomposable
abelian varieties whose very general fiber is isogenous to the given product
and whose connected monodromy group is a product of symplectic groups or is a
unitary group. As a consequence, we show how to realize any product of
symplectic groups of total rank $g$ as the connected monodromy group of a
complete family of $g'$-dimensional abelian varieties for any $g'\ge g$. These
methods also yield a construction of a new Kodaira fibration with fiber genus
$4$.


  Rademacher theorem states that every Lipschitz function on the Euclidean
space is differentiable almost everywhere, where "almost everywhere" refers to
the Lebesgue measure. In this paper we prove a differentiability result of
similar type, where the Lebesgue measure is replaced by an arbitrary measure
$\mu$. In particular we show that the differentiability properties of Lipschitz
functions at $\mu$-almost every point are related to the decompositions of
$\mu$ in terms of rectifiable one-dimensional measures. As a consequence we
obtain a differentiability result for Lipschitz functions with respect to
(measures associated to) $k$-dimensional normal currents, which we use to
extend certain formulas involving normal currents and maps of class $C^1$ to
Lipschitz maps.


  A description of strange quark matter at finite temperature is given, with
emphasis on the inclusion of finite size effects. For massless quarks all
thermodynamic quantities can be evaluated analytically, while the case of
massive quarks must be treated numerically. The resulting model is applied to
the phase equilibrium between strange hadronic matter and strangelets, and some
preliminary results are given.


  Weak Lensing (WL) surveys are reaching unprecedented depths, enabling the
investigation of very small angular scales. At these scales, nonlinear
gravitational effects lead to higher-order correlations making the matter
distribution highly non-Gaussian. Extracting this information using traditional
statistics has proven difficult, and Machine Learning based summary statistics
have emerged as a powerful alternative. We explore the capabilities of a
discriminative, Convolutional Neural Networks (CNN) based approach, focusing on
parameter constraints in the ($\Omega_m$, $\sigma_8$) cosmological parameter
space. Leveraging novel training loss functions and network representations on
WL mock datasets without baryons, we show that our models achieve $\sim 5$
times stronger constraints than the power spectrum, $\sim 3$ stronger
constraints than peak counts, and $\sim 2$ stronger constraints than previous
CNN-learned summary statistics and scattering transforms, for noise levels
relevant to Rubin or Euclid. For WL convergence maps with baryonic physics, our
models achieve $\sim 2.3$ times stronger constraining power than the power
spectrum at these noise levels, also outperforming previous summary statistics.
To further explore the possibilities of CNNs for this task, we also discuss
transfer learning where we adapt pre-trained models, trained on different tasks
or datasets, for cosmological inference, finding that these do not improve the
performance.