  Recent advancements in machine learning and natural language processing have
led to the rapid development of artificial intelligence (AI) as a valuable tool
in the healthcare industry. Using large language models (LLMs) as
conversational agents or chatbots has the potential to assist doctors in
diagnosing patients, detecting early symptoms of diseases, and providing health
advice to patients. This paper focuses on the role of chatbots in healthcare
and explores the use of avatars to make AI interactions more appealing to
patients. A framework of a general-purpose AI avatar application is
demonstrated by using a three-category prompt dictionary and prompt improvement
mechanism. A two-phase approach is suggested to fine-tune a general-purpose AI
language model and create different AI avatars to discuss medical issues with
users. Prompt engineering enhances the chatbot's conversational abilities and
personality traits, fostering a more human-like interaction with patients.
Ultimately, the injection of personality into the chatbot could potentially
increase patient engagement. Future directions for research include
investigating ways to improve chatbots' understanding of context and ensuring
the accuracy of their outputs through fine-tuning with specialized medical data
sets.


  We couple twisted non-compact N=(2,2) supersymmetric models to topological
gravity in two dimensions. We propose expressions for the genus zero
correlation functions based on a Kadomtsev-Petviashvili integrable hierarchy.
Moreover, we prove recursion relations satisfied by the topological gravity
amplitudes at all genera and compute characteristic critical exponents. We
discuss the extent to which moving beyond the N=2 central charge barrier opens
a window on two-dimensional gravity with central charge larger than one.


  Highlighted with improved long-term thermal and environmental stability,
all-inorganic metal halide perovskites exhibit tunable physical properties,
cost-effective synthesis, and satisfactory optoelectronic performance,
attracting increasing research interests worldwide. However, a less explored
feature of these materials is their strong spin-orbit coupling (SOC), which is
the hidden force influencing not only band structure but also properties
including magnetoresistance, spin lifetime and singlet-triplet splitting. This
review provides an overview of the fundamental aspects and the latest progress
of the SOC and debate regarding Rashba effects in all-inorganic metal halide
perovskites, providing critical insights into the physical phenomena and
potential applications. Meanwhile, crystal structures and photophysics of
all-inorganic perovskite are discussed in the context of SOC, along with the
related experimental and characterization techniques. Furthermore, a recent
understanding of the band topology in the all-inorganic halide perovskites is
introduced to push the boundary even further for the novel applications of
all-inorganic halide perovskites. Finally, an outlook is given on the potential
directions of breakthroughs via leveraging the SOC in halide perovskites.


  Search engines are the preferred tools for finding information on the Web.
They are advancing to be the common helpers to answer any of our search needs.
We use them to carry out simple look-up tasks and also to work on rather time
consuming and more complex search tasks. Yet, we do not know very much about
the user performance while carrying out those tasks -- especially not for
ordinary users. The aim of this study was to get more insight into whether Web
users manage to assess difficulty, time effort, query effort, and task outcome
of search tasks, and if their judging performance relates to task complexity.
Our study was conducted with a systematically selected sample of 56 people with
a wide demographic background. They carried out a set of 12 search tasks with
commercial Web search engines in a laboratory environment. The results confirm
that it is hard for normal Web users to judge the difficulty and effort to
carry out complex search tasks. The judgments are more reliable for simple
tasks than for complex ones. Task complexity is an indicator for judging
performance.


  Phenomenological thermodynamic theory describing the properties of metastable
states in disordered ferromagnets and ferroelectrics with frustrative random
interactions is developed and its ability to describe various nonergodic
phenomena in real crystals is demonstrated.


  Let~$E$ be a Hilbertian field of characteristic~$0$. R.W.K. Odoni conjectured
that for every positive integer~$n$ there exists a polynomial~$f\in E[X]$ of
degree~$n$ such that each iterate~$f^{\circ{k}}$ of~$f$ is irreducible and the
Galois group of the splitting field of~$f^{\circ k}$ is isomorphic to the
automorphism group of a regular,~$n$-branching tree of height~$k.$ We prove
this conjecture when~$E$ is a number field.


  It is known that one can define a consistent theory of extended, $N=2$
anti-de Sitter (AdS) Supergravity (SUGRA) in $D=4$. Besides the standard
gravitational part, this theory involves a single $U(1)$ gauge field and a pair
of Majorana vector-spinors that can be mixed into a pair of charged spin-$3/2$
gravitini. The action for $N=2$ $AdS_{4}$ SUGRA is invariant under
$SO(1,3)\times U(1)$ gauge transformations, and under local SUSY. We present a
geometric action that involves two "inhomogeneous" parts: an orthosymplectic
$OSp(4\vert 2)$ gauge-invariant action of the Yang-Mills type, and a
supplementary action invariant under purely bosonic $SO(2,3)\times U(1)\sim
Sp(4)\times SO(2)$ sector of $OSp(4\vert 2)$, that needs to be added for
consistency. This action reduces to $N=2$ $AdS_{4}$ SUGRA after gauge fixing,
for which we use a constrained auxiliary field in the manner of Stelle and
West. Canonical deformation is performed by using the Seiberg-Witten approach
to noncommutative (NC) gauge field theory with the Moyal product. The
NC-deformed action is expanded in powers of the deformation parameter
$\theta^{\mu\nu}$ up to the first order. We show that $N=2$ $AdS_{4}$ SUGRA has
non-vanishing linear NC correction in the physical gauge, originating from the
additional, purely bosonic action. For comparison, simple $N=1$ Poinacar\'{e}
SUGRA can be obtained in the same manner, directly from an $OSp(4\vert 1)$
gauge-invariant action. The first non-vanishing NC correction is quadratic in
$\theta^{\mu\nu}$ and therefore exceedingly difficult to calculate. Under
Wigner-In\"{o}n\"{u} (WI) contraction, $N=2$ AdS superalgebra reduces to $N=2$
Poincar\'{e} superalgebra, and it is not clear whether this relation holds
after canonical deformation. We present the linear NC correction to $N=2$
$AdS_{4}$ SUGRA explicitly, discuss its low-energy limit, and what remains of
it after WI contraction.


  In this article, we study hypersurfaces $\Sigma\subset \mathbb{R}^{n+1}$ with
constant weighted mean curvature. Recently, Wei-Peng proved a rigidity theorem
for CWMC hypersurfaces that generalizes Le-Sesum classification theorem for
self-shrinker. More specifically, they showed that a complete CWMC hypersurface
with polynomial volume growth, bounded norm of the second fundamental form and
that satisfies $|A|^2H(H-\lambda)\leq H^2/2$ must either be a hyperplane or a
generalized cylinder. We generalize this result by removing the bound condition
on the norm of the second fundamental form. Moreover, we prove that under some
conditions if the reverse inequality holds then the hypersurface must either be
a hyperplane or a generalized cylinder. As an application of one of the results
proved in this paper, we will obtain another version of the classification
theorem obtained by the authors of this article, that is, we show that under
some conditions, a complete CWMC hypersurface with $H\geq 0$ must either be a
hyperplane or a generalized cylinder.


  By means of a slight modification of the notion of GM-complexity, the present
paper performs a graph-theoretical approach to the computation of (Matveev's)
complexity for closed orientable 3-manifolds. In particular, the existing
crystallization catalogue C^{28}, due to Lins, is used to obtain upper bounds
for the complexity of closed orientable 3-manifolds triangulated by at most 28
tetrahedra. The experimental results actually coincide with the exact values of
complexity, for all but three elements. Moreover, in the case of at most 26
tetrahedra, the exact value of the complexity is shown to be always directly
computable via crystallization theory.


  In this paper, we propose a data-driven energy storage system (ESS)-based
method to enhance the online small-signal stability monitoring of power
networks with high penetration of intermittent wind power. To accurately
estimate inter-area modes that are closely related to the system's inherent
stability characteristics, a novel algorithm that leverages on recent advances
in wide-area measurement systems (WAMSs) and ESS technologies is developed. It
is shown that the proposed approach can smooth the wind power fluctuations in
near real-time using a small additional ESS capacity and thus significantly
enhance the monitoring of small-signal stability. Dynamic Monte Carlo
simulations on the IEEE 68-bus system are used to illustrate the effectiveness
of the proposed algorithm in smoothing wind power and estimating the inter-area
mode statistical properties.


  Recent work on recurrence in quantum walks has provided a representation of
Schur functions in terms of unitary operators. We propose a generalization of
Schur functions by extending this operator representation to arbitrary
operators on Banach spaces. Such generalized Schur functions meet the formal
structure of first return generating functions, thus we call them FR-functions.
We derive general properties of FR-functions, among them a generalization of
the renewal equation already known for random and quantum walks, as well as
splitting properties which extend useful factorizations of Schur functions.
  When specialized to self-adjoint operators, FR-functions become Nevanlinna
functions. This leads to new results on Nevanlinna functions: decomposition
rules which are the analogue of useful factorizations of Schur functions, a
simple Nevanlinna version of the Schur algorithm and new operator and integral
representations of Nevanlinna functions which, in contrast to standard ones,
are exact analogues of those already known for Schur functions, giving
similarly a one-to-one correspondence between Nevanlinna functions and measures
on the real line.
  The paper is completed with several applications of FR-functions to
orthogonal polynomials and random and quantum walks which illustrate their wide
interest: an analogue for orthogonal polynomials on the real line of the
Khrushchev formula for orthogonal polynomials on the unit circle, and the use
of FR-functions to study recurrence in random walks, quantum walks and open
quantum walks. These applications provide numerous explicit examples of
FR-functions and their splittings and show that these new tools, despite being
extensions of very classical ones, play an important role in the study of
physical problems of a highly topical nature.


  We study the phase diagram of a frustrated spin-1/2 ferromagnetic chain with
anisotropic exchange interactions in an external magnetic field, using the
density matrix renormalization group method. We show that an easy-axis
anisotropy enhances the tendency towards multimagnon bound states, while an
easy-plane anisotropy favors chirally ordered phases. In particular, a moderate
easy-plane anisotropy gives rise to a quantum phase transition at intermediate
magnetization. We argue that this transition is related to the finite-field
phase transition experimentally observed in the spin-1/2 compound LiCuVO_4.


  A quantum critical point (QCP) occurs upon chemical doping of the weak
itinerant ferromagnet Sc_{3.1}In. Remarkable for a system with no local
moments, the QCP is accompanied by non-Fermi liquid (NFL) behavior, manifested
in the logarithmic divergence of the specific heat both in the ferro- and the
paramagnetic states. Sc_{3.1}In displays critical scaling and NFL behavior in
the ferromagnetic state, akin to what had been observed only in f-electron,
local moment systems. With doping, critical scaling is observed close to the
QCP, as the critical exponents, and delta, gamma and beta have weak composition
dependence, with delta nearly twice, and beta almost half of their respective
mean-field values. The unusually large paramagnetic moment mu_PM~1.3 mu_B/F.U.
is nearly composition-independent. Evidence for strong spin fluctuations,
accompanying the QCP at x_c = 0.035 +- 0.005, may be ascribed to the reduced
dimensionality of Sc_{3.1}In, associated with the nearly one-dimensional Sc-In
chains.


  Several types of foreshock transients upstream of Earth's bow shock
possessing a tenuous, hot core have been observed and simulated. Because of the
low dynamic pressure in their cores, these phenomena can significantly disturb
the bow shock and the magnetosphere-ionosphere system. Recent observations have
also demonstrated that foreshock transients can accelerate particles which,
when transported earthward, can affect space weather. Understanding the
potential of foreshock transients to accelerate particles can help us
understand shock acceleration at Earth and at other planetary and astrophysical
systems. To further investigate foreshock transients' potential for
acceleration we conduct a statistical study of ion and electron energization in
the core of foreshock transients. We find that electron energies typically
increase there, evidently due to an internal acceleration process, whereas, as
expected, ion energies most often decrease to support transient formation and
expansion. Nevertheless, ion energy enhancements can be seen in some events
suggesting an internal ion acceleration process as well. Formation conditions
of foreshock transients are related to weak solar wind magnetic field strength
and fast solar wind speed. Ion and electron energization are also positively
correlated with solar wind speed.


  The Hamiltonian formulation of guiding-center Vlasov-Maxwell equations, which
contain dipole contributions to the guiding-center polarization and
magnetization, is presented in terms of a guiding-center Hamiltonian functional
that is derived from the exact guiding-center Vlasov-Maxwell energy
conservation law, and an antisymmetric functional bracket that satisfies the
Jacobi property. Exact energy-momentum and angular momentum conservation laws
are expressed in Hamiltonian form and the guiding-center Vlasov-Maxwell entropy
functional is shown to be a Casimir functional.


  The RXTE All Sky Monitor provides a public database that includes more than
one year of X-ray monitoring observations (2-12 keV) of X-ray binaries and a
few active galactic nuclei. The instrument operates with a 40% duty cycle, and
the exposures yield roughly 5 celestial scans per day. There have been 109
source detections, including 16 X-ray transients, the majority of which are
recurrent cases. The two sources of relativistic radio jets have exhibited
particularly complex light curves and new types of emission states. Progress
has been achieved in understanding the outburst mechanism via the reported
detection of an optical precursor to the April 1996 X-ray outburst in GRO
J1655-40. The ASM has also detected state changes in both Cyg X-1 and Cyg X-3,
leading to new constraints on the accretion disk geometry associated with the
``soft/high'' state. X-ray variations are seen in extragalactic nuclei, such as
NGC4151 and Mkn501, providing new opportunities for multifrequency timing or
spectral studies. The ASM archive empowers observers with the opportunity for
state-dependent observing programs with RXTE and other instruments. The ASM
also provides a long-term context for source behavior, and this knowledge may
be crucial in shaping the interpretation of brief observations with other
telescopes.


  3D hand-object pose estimation is an important issue to understand the
interaction between human and environment. Current hand-object pose estimation
methods require detailed 3D labels, which are expensive and labor-intensive. To
tackle the problem of data collection, we propose a semi-supervised 3D
hand-object pose estimation method with two key techniques: pose dictionary
learning and an object-oriented coordinate system. The proposed pose dictionary
learning module can distinguish infeasible poses by reconstruction error,
enabling unlabeled data to provide supervision signals. The proposed
object-oriented coordinate system can make 3D estimations equivariant to the
camera perspective. Experiments are conducted on FPHA and HO-3D datasets. Our
method reduces estimation error by 19.5% / 24.9% for hands/objects compared to
straightforward use of labeled data on FPHA and outperforms several baseline
methods. Extensive experiments also validate the robustness of the proposed
method.


  Malicious software is abundant in a world of innumerable computer users, who
are constantly faced with these threats from various sources like the internet,
local networks and portable drives. Malware is potentially low to high risk and
can cause systems to function incorrectly, steal data and even crash. Malware
may be executable or system library files in the form of viruses, worms,
Trojans, all aimed at breaching the security of the system and compromising
user privacy. Typically, anti-virus software is based on a signature definition
system which keeps updating from the internet and thus keeping track of known
viruses. While this may be sufficient for home-users, a security risk from a
new virus could threaten an entire enterprise network. This paper proposes a
new and more sophisticated antivirus engine that can not only scan files, but
also build knowledge and detect files as potential viruses. This is done by
extracting system API calls made by various normal and harmful executable, and
using machine learning algorithms to classify and hence, rank files on a scale
of security risk. While such a system is processor heavy, it is very effective
when used centrally to protect an enterprise network which maybe more prone to
such threats.


  We investigate the relic density n_\chi of non-relativistic long-lived or
stable particles \chi in non-standard cosmological scenarios. We calculate the
relic abundance starting from arbitrary initial temperatures of the
radiation-dominated epoch, and derive the lower bound on the initial
temperature T_0 \geq m_\chi/23, assuming that thermally produced \chi particles
account for the dark matter energy density in the universe; this bound holds
for all \chi annihilation cross sections. We also investigate cosmological
scenarios with modified expansion rate. Even in this case an approximate
formula similar to the standard one is capable of predicting the final relic
abundance correctly. Choosing the \chi annihilation cross section such that the
observed cold dark matter abundance is reproduced in standard cosmology, we
constrain possible modifications of the expansion rate at T \sim m_\chi/20,
well before Big Bang nucleosynthesis.


  This paper develops a high-accuracy algorithm for time fractional wave
problems, which employs a spectral method in the temporal discretization and a
finite element method in the spatial discretization. Moreover, stability and
convergence of this algorithm are derived, and numerical experiments are
performed, demonstrating the exponential decay in the temporal discretization
error provided the solution is sufficiently smooth.


  We show that 3D Lifshitz fermions arising as the critical theory at the Weyl
semimetal/insulator transition naturally develop an anomalous Hall viscosity at
finite temperature. We discuss how to couple the system to non-relativistic
background sources for stress-tensor and momentum currents via a form of
Newton-Cartan geometry with torsion and derive the Kubo formulas for the Hall
viscosities. While the Lifshitz system that arises most naturally has scaling
exponent $z=2$ we also generalize the theory for arbitrary Lifshitz scaling $z$
and show that, in the limit $z \to 0$, it may be given a Chern-Simons
interpretation by dimensionally reducing along the anisotropic direction. The
Hall viscosities are expressed in terms of zeta functions and their temperature
dependence is dictated by the scaling exponent.


  We study the thermodynamic properties associated with the black hole event
horizon and the cosmological horizon for black hole solutions in asymptotically
de Sitter spacetimes. We examine thermodynamics of these horizons on the basis
of the conserved charges according to Teitelboim's method. In particular, we
have succeeded in deriving the generalized Smarr formula among thermodynamical
quantities in a simple and natural way. We then show that cosmological constant
must decrease when one takes into account the quantum effect. These
observations have been obtained if and only if cosmological constant plays the
role of a thermodynamical state variable. We also touch upon the relation
between inflation of our universe and a phase transition of black holes.


  We explore connections between Krein's spectral shift function
$\xi(\lambda,H_0,H)$ associated with the pair of self-adjoint operators
$(H_0,H)$, $H=H_0+V$ in a Hilbert space $\calH$ and the recently introduced
concept of a spectral shift operator $\Xi(J+K^*(H_0-\lambda-i0)^{-1}K)$
associated with the operator-valued Herglotz function $J+K^*(H_0-z)^{-1}K$,
$\Im(z)>0$ in $\calH$, where $V=KJK^*$ and $J=\sgn(V)$. Our principal results
include a new representation for $\xi(\lambda,H_0,H)$ in terms of an averaged
index for the Fredholm pair of self-adjoint spectral projections
$(E_{J+A(\lambda)+tB(\lambda)}((-\infty,0)),E_J((-\infty,0)))$, $t\in\bbR$,
where $A(\lambda)=\Re(K^*(H_0-\lambda-i0)^{-1}K)$,
$B(\lambda)=\Im(K^*(H_0-\lambda-i0)^{-1}K)$ a.e. Moreover, introducing the new
concept of a trindex for a pair of operators $(A,P)$ in $\calH$, where $A$ is
bounded and $P$ is an orthogonal projection, we prove that $\xi(\lambda,H_0,H)$
coincides with the trindex associated with the pair
$(\Xi(J+K^*(H_0-\lambda-i0)^{-1}K),\Xi(J))$. In addition, we discuss a variant
of the Birman-Krein formula relating the trindex of a pair of $\Xi$-operators
and the Fredholm determinant of the abstract scattering matrix.
  We also provide a generalization of the classical Birman-Schwinger principle,
replacing the traditional eigenvalue counting functions by appropriate spectral
shift functions.


  In this series of three lectures, we discuss several aspects of high energy
scattering among hadrons in Quantum Chromodynamics. The first lecture is
devoted to a description of the parton model, Bjorken scaling and the scaling
violations due to the evolution of parton distributions with the transverse
resolution scale. The second lecture describes parton evolution at small
momentum fraction x, the phenomenon of gluon saturation and the Color Glass
Condensate (CGC). In the third lecture, we present the application of the CGC
to the study of high energy hadronic collisions, with emphasis on
nucleus-nucleus collisions. In particular, we provide the outline of a proof of
high energy factorization for inclusive gluon production.


  We report on specific heat measurements on clean overdoped
$\mathrm{BaFe_{2}(As_{1-x}P_x)_2}$ single crystals performed with a high
resolution membrane-based nanocalorimeter. A nonzero residual electronic
specific heat coefficient at zero temperature $\gamma_\mathrm{r}={C/T}|_{T \to
0}$ is seen for all doping compositions, indicating a considerable fraction of
the Fermi surface ungapped or having very deep minima. The remaining
superconducting electronic specific heat is analyzed through a two-band s-wave
$\alpha$ model in order to investigate the gap structure. Close to optimal
doping we detect a single zero-temperature gap of $\Delta_0 \sim
5.3\,\mathrm{meV}$, corresponding to $\Delta_0 / k_\mathrm{B} T_\mathrm{c} \sim
2.2$. Increasing the phosphorus concentration $x$, the main gap reduces till a
value of $\Delta_0 \sim 1.9\,\mathrm{meV}$ for $x = 0.55$ and a second weaker
gap becomes evident. From the magnetic field effect on $\gamma_\mathrm{r}$, all
samples however show similar behavior [$\gamma_\mathrm{r}(H) -
\gamma_\mathrm{r}(H=0) \propto H^n$, with $n$ between 0.6 and 0.7]. This
indicates that, despite a considerable redistribution of the gap weights, the
total degree of gap anisotropy does not change drastically with doping.


  We trade matrix factorizations and Koszul complexes for Hochschild homology
of Soergel bimodules to modify the construction of triply-graded link homology
and relate it to Kazhdan-Lusztig theory.


  Aspect-based sentiment analysis produces a list of aspect terms and their
corresponding sentiments for a natural language sentence. This task is usually
done in a pipeline manner, with aspect term extraction performed first,
followed by sentiment predictions toward the extracted aspect terms. While
easier to develop, such an approach does not fully exploit joint information
from the two subtasks and does not use all available sources of training
information that might be helpful, such as document-level labeled sentiment
corpus. In this paper, we propose an interactive multi-task learning network
(IMN) which is able to jointly learn multiple related tasks simultaneously at
both the token level as well as the document level. Unlike conventional
multi-task learning methods that rely on learning common features for the
different tasks, IMN introduces a message passing architecture where
information is iteratively passed to different tasks through a shared set of
latent variables. Experimental results demonstrate superior performance of the
proposed method against multiple baselines on three benchmark datasets.


  Evaluating safety performance in a resource-efficient way is crucial for the
development of autonomous systems. Simulation of parameterized scenarios is a
popular testing strategy but parameter sweeps can be prohibitively expensive.
To address this, we propose HiddenGems: a sample-efficient method for
discovering the boundary between compliant and non-compliant behavior via
active learning. Given a parameterized scenario, one or more compliance
metrics, and a simulation oracle, HiddenGems maps the compliant and
non-compliant domains of the scenario. The methodology enables critical test
case identification, comparative analysis of different versions of the system
under test, as well as verification of design objectives. We evaluate
HiddenGems on a scenario with a jaywalker crossing in front of an autonomous
vehicle and obtain compliance boundary estimates for collision, lane keep, and
acceleration metrics individually and in combination, with 6 times fewer
simulations than a parameter sweep. We also show how HiddenGems can be used to
detect and rectify a failure mode for an unprotected turn with 86% fewer
simulations.


  While quantum computing provides an exponential advantage in solving system
of linear equations, there is little work to solve system of nonlinear
equations with quantum computing. We propose quantum Newton's method (QNM) for
solving $N$-dimensional system of nonlinear equations based on Newton's method.
In QNM, we solve the system of linear equations in each iteration of Newton's
method with quantum linear system solver. We use a specific quantum data
structure and $l_{\infty}$ tomography with sample error $\epsilon_s$ to
implement the classical-quantum data conversion process between the two
iterations of QNM, thereby constructing the whole process of QNM. The
complexity of QNM in each iteration is $O(\log^4N/\epsilon_s^2)$. Through
numerical simulation, we find that when $\epsilon_s>>1/\sqrt{N}$, QNM is still
effective, so the complexity of QNM is sublinear with $N$, which provides
quantum advantage compared with the optimal classical algorithm.


  An approximation of the density of states for the Ising and Potts models
based on the high- and low-temperature series are developed.


  We explore the consequences of gluonic hot spots inside the proton for the
initial eccentricities in a proton-nucleus collision, and the constraints on
the parameters describing these hot spots from coherent and incoherent
exclusive vector meson production cross sections in deep inelastic scattering.
We show that geometric fluctuations of hot spots inside the proton are the
dominant source of eccentricity whereas color charge fluctuations only give a
negligible correction. We find that the coherent cross section is sensitive to
both the size of the target and the structure of the probe. The incoherent
cross section is dominated by color fluctuations at small transverse momentum
transfer (t), by proton and hot spot sizes as well as the structure of the
probe at medium -t and again by color fluctuations at large -t.


  For dimension reduction in $l_1$, the method of {\em Cauchy random
projections} multiplies the original data matrix $\mathbf{A}
\in\mathbb{R}^{n\times D}$ with a random matrix $\mathbf{R} \in
\mathbb{R}^{D\times k}$ ($k\ll\min(n,D)$) whose entries are i.i.d. samples of
the standard Cauchy C(0,1). Because of the impossibility results, one can not
hope to recover the pairwise $l_1$ distances in $\mathbf{A}$ from $\mathbf{B} =
\mathbf{AR} \in \mathbb{R}^{n\times k}$, using linear estimators without
incurring large errors. However, nonlinear estimators are still useful for
certain applications in data stream computation, information retrieval,
learning, and data mining.
  We propose three types of nonlinear estimators: the bias-corrected sample
median estimator, the bias-corrected geometric mean estimator, and the
bias-corrected maximum likelihood estimator. The sample median estimator and
the geometric mean estimator are asymptotically (as $k\to \infty$) equivalent
but the latter is more accurate at small $k$. We derive explicit tail bounds
for the geometric mean estimator and establish an analog of the
Johnson-Lindenstrauss (JL) lemma for dimension reduction in $l_1$, which is
weaker than the classical JL lemma for dimension reduction in $l_2$.
  Asymptotically, both the sample median estimator and the geometric mean
estimators are about 80% efficient compared to the maximum likelihood estimator
(MLE). We analyze the moments of the MLE and propose approximating the
distribution of the MLE by an inverse Gaussian.


  As Large Language Models (LLMs) achieve remarkable progress in language
understanding and generation, their training efficiency has become a critical
concern. Traditionally, LLMs are trained to predict the next token in a
sequence. Despite the success of token-level training, it suffers from
considerable computational costs due to the need to process an extensive number
of tokens. To mitigate this issue, this paper introduces patch-level training
for LLMs, which reduces the sequence length by compressing multiple tokens into
a single patch. During patch-level training, we feed the language model shorter
sequences of patches and train it to predict the next patch, thereby processing
the majority of the training data at a significantly reduced computational
cost. Following this, the model continues token-level training on the remaining
training data to align with the inference mode. Experiments on a diverse range
of models (370M-2.7B parameters) demonstrate that patch-level training can
reduce overall computational costs to 0.5$\times$, without compromising the
model performance compared to token-level training. Source code:
\url{https://github.com/shaochenze/PatchTrain}.


  We study the analytical solution of the Monte Carlo dynamics in the spherical
Sherrington-Kirkpatrick model using the technique of the generating function.
Explicit solutions for one-time observables (like the energy) and two-time
observables (like the correlation and response function) are obtained. We show
that the crucial quantity which governs the dynamics is the acceptance rate. At
zero temperature, an adiabatic approximation reveals that the relaxational
behavior of the model corresponds to that of a single harmonic oscillator with
an effective renormalized mass.


  Mean field games with a major player were introduced in (Huang, 2010) within
a linear-quadratic (LQ) modeling framework. Due to the rich structure of
major-minor player models, the past ten years have seen significant research
efforts for different solution notions and analytical techniques. For LQ
models, we address the relation between three solution frameworks: the Nash
certainty equivalence (NCE) approach in (Huang, 2010), master equations, and
asymptotic solvability, which have been developed starting with different
ideas. We establish their equivalence relationships.


  There is a growing desire to create computer systems that can communicate
effectively to collaborate with humans on complex, open-ended activities.
Assessing these systems presents significant challenges. We describe a
framework for evaluating systems engaged in open-ended complex scenarios where
evaluators do not have the luxury of comparing performance to a single right
answer. This framework has been used to evaluate human-machine creative
collaborations across story and music generation, interactive block building,
and exploration of molecular mechanisms in cancer. These activities are
fundamentally different from the more constrained tasks performed by most
contemporary personal assistants as they are generally open-ended, with no
single correct solution, and often no obvious completion criteria.
  We identified the Key Properties that must be exhibited by successful
systems. From there we identified "Hallmarks" of success -- capabilities and
features that evaluators can observe that would be indicative of progress
toward achieving a Key Property. In addition to being a framework for
assessment, the Key Properties and Hallmarks are intended to serve as goals in
guiding research direction.


  Understanding and tailoring static and dynamic properties of magnetic
insulator thin films is important for spintronic device applications. Here, we
grow atomically flat epitaxial europium iron garnet (EuIG) thin films by pulsed
laser deposition on (111)-oriented garnet substrates with a range of lattice
parameters. By controlling the lattice mismatch between EuIG and the
substrates, we tune the strain in EuIG films from compressive to tensile
regime, which is characterized by X-ray diffraction. Using ferromagnetic
resonance, we find that in addition to the first-order perpendicular magnetic
anisotropy which depends linearly on the strain, there is a significant
second-order one that has a quadratic strain dependence. Inhomogeneous
linewidth of the ferromagnetic resonance increases notably with increasing
strain, while the Gilbert damping parameter remains nearly constant (~
2x10^-2). These results provide valuable insight into the spin dynamics in
ferrimagnetic insulators and useful guidance for material synthesis and
engineering of next-generation spintronics applications.


  We propose an alternative scenario to cosmic inflation for producing the
initial seeds of cosmic structures. The cosmological fluctuations are generated
by thermal fluctuation of the energy density of the ideal string gas in three
compact spatial dimensions. Statistical mechanics of the strings reveals that
scalar power spectrum of the cosmological fluctuations on cosmic scales is
scale-invariant for closed strings and inclines towards red for open strings in
three compact spatial dimensions. This generation of thermal fluctuations
happens during the Hagedorn era of string gas cosmology and without invoking an
inflationary epoch the perturbations enter the radiation-dominated era. The
amplitude of the fluctuations is proportional to the ratio of the two length
scales in the theory, i.e., the Planck length over the string length. Since
modes with the shorter wavelengths exit the Hubble radius at the end of the
Hagedorn phase at later times compare to the modes with long wavelengths, the
scalar fluctuations gain mild tilt towards red.


  Entropy estimation, due in part to its connection with mutual information,
has seen considerable use in the study of time series data including causality
detection and information flow. In many cases, the entropy is estimated using
$k$-nearest neighbor (Kozachenko-Leonenko) based methods. However, analytic
results on this estimator are limited to independent data. In the article, we
show rigorous bounds on the rate of decay of the bias in the number of samples,
$N$, assuming they are drawn from a stationary process which satisfies a
suitable mixing condition. Numerical examples are presented which demonstrate
the efficiency of the estimator when applied to a Markov process with
stationary Gaussian density. These results support the asymptotic rates derived
in the theoretical work.


  It is well known that it is impossible to clone an arbitrary quantum state.
However, this inability does not lead directly to no-cloning of quantum
coherence. Here, we show that it is impossible to clone the coherence of an
arbitrary quantum state which is a stronger statement than the 'no-cloning of
quantum state'. In particular, with ancillary system as machine state, we show
that it is impossible to clone the coherence of states whose coherence is
greater than the coherence of the known states on which the transformations are
defined. Also, we characterize the class of states for which coherence cloning
will be possible for a given choice of machine. Furthermore, we find the
maximum range of states whose coherence can be cloned perfectly. The
impossibility proof also holds when we do not include machine states.


  We investigate electric current in a single-electron tunnelling device weakly
coupled to an ac-driven underdamped harmonic nanomechanical oscillator. In the
linear regime, the current can respond to the external frequency in a resonant
as well as in an anti-resonant fashion. The main resonance is accompanied by an
additional resonance at a half of the external frequency.


  The measurements of the linear polarisation of visible light from quasars
give strong evidence for large-scale coherent orientations of their
polarisation vectors in some regions of the sky. We show that these
observations can be explained by the mixing of the photons with very light
pseudoscalar (axion-like) particles in extragalactic magnetic fields during
their propagation. We present a new treatment in terms of wave packets and
discuss the circular polarisation.


  We introduce a duality construction for toric Landau-Ginzburg models,
applicable to complete intersections in toric varieties via the sigma model /
Landau-Ginzburg model correspondence. This construction is shown to reconstruct
those of Batyrev-Borisov, Berglund-H"ubsch, Givental, and Hori-Vafa. It can be
done in more general situations, and provides partial resolutions when the
above constructions give a singular mirror. An extended example is given: the
Landau-Ginzburg models dual to elliptic curves in (P^1)^2 .


  We study the asymptotic behavior of mixed functionals of the form
$I_T(t)=F_T(\xi_T(t))+\int_0^tg_T(\xi_T(s))\,d\xi_T(s)$, $t\ge0$, as
$T\to\infty$. Here $\xi_T(t)$ is a strong solution of the stochastic
differential equation $d\xi_T(t)=a_T(\xi_T(t))\,dt+dW_T(t)$, $T>0$ is a
parameter, $a_T=a_T(x)$ are measurable functions such that
$\left|a_T(x)\right|\leq C_T$ for all $x\in \mathbb {R}$, $W_T(t)$ are standard
Wiener processes, $F_T=F_T(x)$, $x\in \mathbb {R}$, are continuous functions,
$g_T=g_T(x)$, $x\in \mathbb {R}$, are locally bounded functions, and everything
is real-valued. The explicit form of the limiting processes for $I_T(t)$ is
established under very nonregular dependence of $g_T$ and $a_T$ on the
parameter $T$.


  A fully dynamic three-layer active constrained layer (ACL) beam is modeled
for cantilevered boundary conditions by using a thorough variational approach.
The Rao-Nakra thin compliant layer assumptions are adopted to model the
sandwich structure, and all magnetic effects for the piezoelectric layers are
retained. The piezoelectric layers are activated by two different voltage
sources. When there are no "mechanical" boundary forces acting in the
longitudinal direction, it is shown that the system with certain parameter
combinations is not uniformly strongly stabilizable by the $B^*-$type feedback
controller, which is the total current accumulated at the electrodes for the
piezoelectric layers. However, as the magnetic effects are ignored
(electrostatic assumption), the closed-loop system with all mechanical feedback
controllers is shown to be uniformly exponentially stable.


  Human intention is an internal, mental characterization for acquiring desired
information. From interactive interfaces containing either textual or graphical
information, intention to perceive desired information is subjective and
strongly connected with eye gaze. In this work, we determine such intention by
analyzing real-time eye gaze data with a low-cost regular webcam. We extracted
unique features (e.g., Fixation Count, Eye Movement Ratio) from the eye gaze
data of 31 participants to generate a dataset containing 124 samples of visual
intention for perceiving textual or graphical information, labeled as either
TEXT or IMAGE, having 48.39% and 51.61% distribution, respectively. Using this
dataset, we analyzed 5 classifiers, including Support Vector Machine (SVM)
(Accuracy: 92.19%). Using the trained SVM, we investigated the variation of
visual intention among 30 participants, distributed in 3 age groups, and found
out that young users were more leaned towards graphical contents whereas older
adults felt more interested in textual ones. This finding suggests that
real-time eye gaze data can be a potential source of identifying visual
intention, analyzing which intention aware interactive interfaces can be
designed and developed to facilitate human cognition.


  The agro-food industry is turning to robots to address the challenge of
labour shortage. However, agro-food environments pose difficulties for robots
due to high variation and occlusions. In the presence of these challenges,
accurate world models, with information about object location, shape, and
properties, are crucial for robots to perform tasks accurately. Building such
models is challenging due to the complex and unique nature of agro-food
environments, and errors in the model can lead to task execution issues. In
this paper, we propose MinkSORT, a novel method for generating tracking
features using a 3D sparse convolutional network in a deepSORT-like approach to
improve the accuracy of world models in agro-food environments. We evaluated
our feature extractor network using real-world data collected in a tomato
greenhouse, which significantly improved the performance of our baseline model
that tracks tomato positions in 3D using a Kalman filter and Mahalanobis
distance. Our deep learning feature extractor improved the HOTA from 42.8% to
44.77%, the association accuracy from 32.55% to 35.55%, and the MOTA from
57.63% to 58.81%. We also evaluated different contrastive loss functions for
training our deep learning feature extractor and demonstrated that our approach
leads to improved performance in terms of three separate precision and recall
detection outcomes. Our method improves world model accuracy, enabling robots
to perform tasks such as harvesting and plant maintenance with greater
efficiency and accuracy, which is essential for meeting the growing demand for
food in a sustainable manner.


  The output of gravitational-wave interferometers, such as LIGO and Virgo, can
be highly non-stationary. Broadband detector noise can affect the detector
sensitivity on the order of tens of seconds. Gravitational-wave transient
searches, such as those for colliding black holes, estimate this noise in order
to identify gravitational-wave events. During times of non-stationarity we see
a higher rate of false events being reported. To accurately separate signal
from noise, it is imperative to incorporate the changing detector state into
gravitational-wave searches. We develop a new statistic which estimates the
variation of the interferometric detector noise. We use this statistic to
re-rank candidate events identified during LIGO-Virgo's second observing run by
the PyCBC search pipeline. This results in a 5% improvement in the sensitivity
volume for low mass binaries, particularly binary neutron stars mergers.


  We present a new grid of model photospheres for the SDSS-III/APOGEE survey of
stellar populations of the Galaxy, calculated using the ATLAS9 and MARCS codes.
New opacity distribution functions were generated to calculate ATLAS9 model
photospheres. MARCS models were calculated based on opacity sampling
techniques. The metallicity ([M/H]) spans from -5 to 1.5 for ATLAS and -2.5 to
0.5 for MARCS models. There are three main differences with respect to previous
ATLAS9 model grids: a new corrected H2O linelist, a wide range of carbon
([C/M]) and alpha element [alpha/M] variations, and solar reference abundances
from Asplund et al. 2005. The added range of varying carbon and alpha element
abundances also extends the previously calculated MARCS model grids. Altogether
1980 chemical compositions were used for the ATLAS9 grid, and 175 for the MARCS
grid. Over 808 thousand ATLAS9 models were computed spanning temperatures from
3500K to 30000K and log g from 0 to 5, where larger temperatures only have high
gravities. The MARCS models span from 3500K to 5500K, and log g from 0 to 5.
All model atmospheres are publically available online.


  We investigate how the conductance G through a clean interacting quantum wire
is affected by the presence of contacts and noninteracting leads. The contacts
are defined by a vanishing two-particle interaction to the left and a finite
repulsive interaction to the right or vice versa. No additional single-particle
scattering terms (impurities) are added. We first use bosonization and the
local Luttinger liquid picture and show that within this approach G is
determined by the properties of the leads regardless of the details of the
spatial variation of the Luttinger liquid parameters. This generalizes earlier
results obtained for step-like variations. In particular, no single-particle
backscattering is generated at the contacts. We then study a microscopic model
applying the functional renormalization group and show that the spatial
variation of the interaction produces single-particle backscattering, which in
turn leads to a reduced conductance. We investigate how the smoothness of the
contacts affects G and show that for decreasing energy scale its deviation from
the unitary limit follows a power law with the same exponent as obtained for a
system with a weak single-particle impurity placed in the contact region of the
interacting wire and the leads.


  We should cease teaching frequentist statistics to undergraduates and switch
to Bayes. Doing so will reduce the amount of confusion and over-certainty rife
among users of statistics.


  In this paper, we have continued the work of Herrera \emph{et al.}
\cite{herrera2012dynamical} in $f(G)$ gravitational theory. For this purpose, a
spherically symmetric fluid exhibiting locally anisotropic pressure along with
the energy density, is taken under consideration. The perturbation scheme is
imposed on modified field equations and the dynamical equations. The collapse
equation is devised from these perturbed equations which stimulates to disclose
the instability zone under both Newtonian and post-Newtonian constraints. It is
wrapped up by concluding that dynamical instability is interpreted by the
adiabatic index $\Gamma$ which relies on the anisotropic pressure, energy
density and the dark source terms due to $f(G)$ gravity.


  Inference of Large Language Models (LLMs) across computer clusters has become
a focal point of research in recent times, with many acceleration techniques
taking inspiration from CPU speculative execution. These techniques reduce
bottlenecks associated with memory bandwidth, but also increase end-to-end
latency per inference run, requiring high speculation acceptance rates to
improve performance. Combined with a variable rate of acceptance across tasks,
speculative inference techniques can result in reduced performance.
Additionally, pipeline-parallel designs require many user requests to maintain
maximum utilization. As a remedy, we propose PipeInfer, a pipelined speculative
acceleration technique to reduce inter-token latency and improve system
utilization for single-request scenarios while also improving tolerance to low
speculation acceptance rates and low-bandwidth interconnects. PipeInfer
exhibits up to a 2.15$\times$ improvement in generation speed over standard
speculative inference. PipeInfer achieves its improvement through Continuous
Asynchronous Speculation and Early Inference Cancellation, the former improving
latency and generation speed by running single-token inference simultaneously
with several speculative runs, while the latter improves speed and latency by
skipping the computation of invalidated runs, even in the middle of inference.


  The detection of binary neutron star mergers represents one of the most
important astrophysical discoveries of the recent years. Due to the extreme
matter and gravity conditions and the rich dynamics developed, it becomes a
tremendous challenge to accurately simulate numerically all the scales present
during the collision. Here we present how to study such systems by using large
eddy simulations with a self-consistent subgrid-scale gradient model, that we
generalized to the special relativistic case in a previous work and now extend
to the general relativistic case. Adapted from nonrelativistic scenarios, the
so-called gradient model allows to capture part of the effects of the hidden
dynamics on the resolved scales, by means of a physically-agnostic,
mathematically-based Taylor expansion of the nonlinear terms in the
conservative evolution equations' fluxes. We assess the validity of this
approach in bounding-box simulations of the magnetic Kelvin-Helmholtz
instability. Several resolutions and a broad range of scenarios are considered
in order to carefully test the performance of the model under three crucial
aspects: (i) highly curved backgrounds, (ii) jumps on the fluid density
profiles and (iii) strong shocks. The results suggest our extension of the
gradient subgrid-scale model to general relativistic magnetohydrodynamics is a
promising approach for studying binary neutron stars mergers, and potentially
to other relevant astrophysical scenarios.


  We describe an attempt to model numerically Bose-Einstein correlations (BEC)
from "within", i.e., by using them as the most fundamental ingredient of some
Monte Carlo event generator (MC) rather than considering them as a kind of
(more or less important, depending on the actual situation) "afterburner",
which inevitably changes original physical content of the MC code used to model
multiparticle production process.


  We study the off-equilibrium critical phenomena across a hysteretic
first-order transition in disordered athermal systems. The study focuses on the
zero temperature random field Ising model (ZTRFIM) above the critical disorder
for spatial dimensions $d=2,3,$ and $4$. We use Monte Carlo simulations to show
that disorder suppresses critical slowing down in phase ordering time for
finite-dimensional systems. The dynamic hysteresis scaling, the measure of
explicit finite-time scaling, is used to subsequently quantify the critical
slowing down. The scaling exponents in all dimensions increase with disorder
strength and finally reach a stable value where the transformation is no longer
critical. The associated critical behavior in the mean-field limit is very
different, where the exponent values for various disorders in all dimensions
are similar. The non-mean-field exponents asymptotically approach the
mean-field value ($\Upsilon \approx 2/3$) with increase in dimensions. The
results suggest that the critical features in the hysteretic metastable phase
are controlled by inherent mean-field spinodal instability that gets blurred by
disorder in low-dimension athermal systems.


  We prove that non-commutative martingale transforms are of weak type $(1,1)$.
More precisely, there is an absolute constant $C$ such that if $\M$ is a
semi-finite von Neumann algebra and $(\M_n)_{n=1}^\infty$ is an increasing
filtration of von Neumann subalgebras of $\M$ then for any non-commutative
martingale $x=(x_n)_{n=1}^\infty$ in $L^1(\M)$, adapted to
$(\M_n)_{n=1}^\infty$, and any sequence of signs $(\epsilon_n)_{n=1}^\infty$,
$$\left\Vert \epsilon_1 x_1 + \sum_{n=2}^N \epsilon_n(x_n -x_{n-1})
\right\Vert_{1,\infty} \leq C \left\Vert x_N \right\Vert_1 $$ for $N\geq 2$.
This generalizes a result of Burkholder from classical martingale theory to
non-commutative setting and answers positively a question of Pisier and Xu. As
applications, we get the optimal order of the UMD-constants of the Schatten
class $S^p$ when $p \to \infty$. Similarly, we prove that the UMD-constant of
the finite dimensional Schatten class $S_n^{1}$ is of order $\log(n+1)$. We
also discuss the Pisier-Xu non-commutative Burkholder-Gundy inequalities.


  Strong blocking sets, introduced first in 2011 in connection with saturating
sets, have recently gained a lot of attention due to their correspondence with
minimal codes. In this paper, we dig into the geometry of the concatenation
method, introducing the concept of outer strong blocking sets and their coding
theoretical counterpart. We investigate their structure and provide bounds on
their size. As a byproduct, we improve the best-known upper bound on the
minimum size of a strong blocking set. Finally, we present a geometric
construction of small strong blocking sets, whose computational cost is
significantly smaller than the previously known ones.


  Given a two-variable invertible polynomial, we show that its category of
maximally-graded matrix factorisations is quasi-equivalent to the Fukaya-Seidel
category of its Berglund-H\"ubsch transpose. This was previously shown for
Brieskorn-Pham and $D$-type singularities by Futaki-Ueda. The proof involves
explicit construction of a tilting object on the B-side, and comparison with a
specific basis of Lefschetz thimbles on the A-side.


  We consider a game played between a hider, who hides a static object in one
of several possible positions in a bounded planar region, and a searcher, who
wishes to reach the object by querying sensors placed in the plane. The
searcher is a mobile agent, and whenever it physically visits a sensor, the
sensor returns a random direction, corresponding to a half-plane in which the
hidden object is located. We first present a novel search heuristic and
characterize bounds on the expected distance covered before reaching the
object. Next, we model this game as a large-dimensional zero-sum dynamic game
and we apply a recently introduced randomized sampling technique that provides
a probabilistic level of security to the hider. We observe that, when the
randomized sampling approach is only allowed to select a very small number of
samples, the cost of the heuristic is comparable to the security level provided
by the randomized procedure. However, as we allow the number of samples to
increase, the randomized procedure provides a higher probabilistic security
level.


  Observational programmes currently underway with both Chandra and XMM-Newton
are set to revolutionize our view of our own Galaxy. This is fortunate since
the X-ray band can provide crucial diagnostics in the quest to understand the
composition and structure of the Galaxy and the high energy processes which
influence its evolution. Here we review several areas in which rapid progress
is being made. These include investigations into the nature of the Galactic
X-ray source population at faint fluxes, the distribution and origin of the
X-ray emission emanating from the Galactic Centre Region and the spectral
characteristics of the Galactic Soft X-ray Background.


  Hochster established the existence of a commutative noetherian ring $\tilde
C$ and a universal resolution $U$ of the form $0\to \tilde C^{e}\to \tilde
C^{f}\to \tilde C^{g}\to 0$ such that for any commutative noetherian ring $S$
and any resolution $V$ equal to $0\to S^{e}\to S^{f}\to S^{g}\to 0$, there
exists a unique ring homomorphism $\tilde C\to S$ with $V=U\otimes_{\tilde C}
S$. In the present paper we assume that $f=e+g$ and we find the minimal
resolution of ${\bf K}\otimes \tilde C$ by free $B$-modules, where $\bf K$ is a
field of characteristic zero and $B$ is a polynomial ring over $\bf K$. Our
techniques are geometric. We use the Bott algorithm and the Representation
Theory of the General Linear Group. As a by-product of our work, we resolve a
family of maximal Cohen-Macaulay modules defined over a determinantal ring.


  Sharing medical data between institutions is difficult in practice due to
data protection laws and official procedures within institutions. Therefore,
most existing algorithms are trained on relatively small electroencephalogram
(EEG) data sets which is likely to be detrimental to prediction accuracy. In
this work, we simulate a case when the data can not be shared by splitting the
publicly available data set into disjoint sets representing data in individual
institutions. We propose to train a (local) detector in each institution and
aggregate their individual predictions into one final prediction. Four
aggregation schemes are compared, namely, the majority vote, the mean, the
weighted mean and the Dawid-Skene method. The method was validated on an
independent data set using only a subset of EEG channels. The ensemble reaches
accuracy comparable to a single detector trained on all the data when
sufficient amount of data is available in each institution. The weighted mean
aggregation scheme showed best performance, it was only marginally outperformed
by the Dawid--Skene method when local detectors approach performance of a
single detector trained on all available data.


  We investigate a class of sharp Fourier extension inequalities on the planar
curves $s=|y|^p$, $p>1$. We identify the mechanism responsible for the possible
loss of compactness of nonnegative extremizing sequences, and prove that
extremizers exist if $1<p<p_0$, for some $p_0>4$. In particular, this resolves
the dichotomy of Jiang, Pausader & Shao concerning the existence of extremizers
for the Strichartz inequality for the fourth order Schr\"odinger equation in
one spatial dimension. One of our tools is a geometric comparison principle for
$n$-fold convolutions of certain singular measures in $\mathbb{R}^d$, developed
in a companion paper. We further show that any extremizer exhibits fast
$L^2$-decay in physical space, and so its Fourier transform can be extended to
an entire function on the whole complex plane. Finally, we investigate the
extent to which our methods apply to the case of the planar curves
$s=y|y|^{p-1}$, $p>1$.


  In this paper we consider the prescribed mean curvature flow of a non-compact
space-like Cauchy hypersurface of bounded geometry in a generalized
Robertson-Walker space-time. We prove that the flow preserves the
space-likeness condition and exists for infinite time. We also prove
convergence in the setting of manifolds with boundary. Our discussion
generalizes previous work by Ecker, Huisken, Gerhardt and others with respect
to a crucial aspects: we consider any non-compact Cauchy hypersurface under the
assumption of bounded geometry. Moreover, we specialize the aforementioned
works by considering globally hyperbolic Lorentzian space-times equipped with a
specific class of warped product metrics.


  Total inclusive cross sections for neutral and charged pion production in
proton-nucleus and nucleus-nucleus reactions have been calculated and compared
to experiment. Nucleon-nucleon theoretical cross sections have been scaled up
to nuclear collisions using a scaling factor similar to $(A_PA_T)^{2/3}$, where
$A_P$ and $A_T$ are the nucleon numbers of the projectile and target nuclei.
Variations in the power of this scaling factor have been studied and a good fit
to experiment is obtained with a small modification of the power. Theoretical
cross sections are written in a form that is very suitable for immediate input
into transport codes.


  The gluonic field created by a static quark anti-quark pair is described via
the AdS/CFT correspondence by a string connecting the pair which is located on
the boundary of AdS. Thus the gluonic field in a strongly coupled large N CFT
has a stringy spectrum of excitations. We trace the stability of these
excitations to a combination of large N suppressions and energy conservation.
Comparison of the physics of the N=infinity flux tube in the {\cal N}=4 SYM
theory at weak and strong coupling shows that the excitations are present only
above a certain critical coupling. The density of states of a highly excited
string with a fold reaching towards the horizon of AdS is in exact agreement at
strong coupling with that of the near-threshold states found in a ladder
diagram model of the weak-strong coupling transition. We also study large
distance correlations of local operators with a Wilson loop, and show that the
fall off at weak coupling and N=infinity (i.e. strictly planar diagrams)
matches the strong coupling predictions given by the AdS/CFT correspondence,
rather than those of a weakly coupled U(1) gauge theory.


  Evaluating retrieval-augmented generation (RAG) presents challenges,
particularly for retrieval models within these systems. Traditional end-to-end
evaluation methods are computationally expensive. Furthermore, evaluation of
the retrieval model's performance based on query-document relevance labels
shows a small correlation with the RAG system's downstream performance. We
propose a novel evaluation approach, eRAG, where each document in the retrieval
list is individually utilized by the large language model within the RAG
system. The output generated for each document is then evaluated based on the
downstream task ground truth labels. In this manner, the downstream performance
for each document serves as its relevance label. We employ various downstream
task metrics to obtain document-level annotations and aggregate them using
set-based or ranking metrics. Extensive experiments on a wide range of datasets
demonstrate that eRAG achieves a higher correlation with downstream RAG
performance compared to baseline methods, with improvements in Kendall's $\tau$
correlation ranging from 0.168 to 0.494. Additionally, eRAG offers significant
computational advantages, improving runtime and consuming up to 50 times less
GPU memory than end-to-end evaluation.


  General large language models (LLMs) such as ChatGPT have shown remarkable
success, but it has also raised concerns among people about the misuse of
AI-generated texts. Therefore, an important question is how to detect whether
the texts are generated by ChatGPT or by humans. Existing detectors are built
on the assumption that there is a distribution gap between human-generated and
AI-generated texts. These gaps are typically identified using statistical
information or classifiers. In contrast to prior research methods, we find that
large language models such as ChatGPT exhibit strong self-consistency in text
generation and continuation. Self-consistency capitalizes on the intuition that
AI-generated texts can still be reasoned with by large language models using
the same logical reasoning when portions of the texts are masked, which differs
from human-generated texts. Using this observation, we subsequently proposed a
new method for AI-generated texts detection based on self-consistency with
masked predictions to determine whether a text is generated by LLMs. This
method, which we call DetectGPT-SC. We conducted a series of experiments to
evaluate the performance of DetectGPT-SC. In these experiments, we employed
various mask scheme, zero-shot, and simple prompt for completing masked texts
and self-consistency predictions. The results indicate that DetectGPT-SC
outperforms the current state-of-the-art across different tasks.


  The potential of ChatGPT to transform the education landscape is drawing
increasing attention. With its translation-related capabilities being tested
and examined, ChatGPT presents both opportunities and challenges for
translation training. The effective integration of ChatGPT into translation
training necessitates an understanding of students' reactions to and acceptance
of ChatGPT-assisted translation. Against this backdrop, this study draws on the
Unified Theory of Acceptance and Use of Technology (UTAUT) to examine the
potential determinants of students' adoption of ChatGPT for translation and
investigates the moderating effects of use experience and translation training
on those relationships. An online survey targeting university students in Hong
Kong collected 308 valid responses, including 148 from translation students and
160 from non-translation students. Respondents were divided into two groups
based on their ChatGPT use experience. Data were analyzed using structural
equation modeling. A multigroup analysis revealed different structural
relationships between the influencing factors of students' intention to use
ChatGPT across groups. Notably, less-experienced users' behavioral intention to
use ChatGPT for translation was more strongly correlated with social influence
compared with experienced users. Non-translation students' use intention was
more strongly driven by facilitating conditions compared to translation majors.
These results are discussed with the different primary purposes of translation
and non-translation students' translation practices. The findings of this study
contribute to the growing body of research on AI-powered translation training
and provide insights for the ongoing adaptation of translation training
programs.


  A particle-swarm is a set of indivisible processing elements that traverse a
network in order to perform a distributed function. This paper will describe a
particular implementation of a particle-swarm that can simulate the behavior of
the popular PageRank algorithm in both its {\it global-rank} and {\it
relative-rank} incarnations. PageRank is compared against the particle-swarm
method on artificially generated scale-free networks of 1,000 nodes constructed
using a common gamma value, $\gamma = 2.5$. The running time of the
particle-swarm algorithm is $O(|P|+|P|t)$ where $|P|$ is the size of the
particle population and $t$ is the number of particle propagation iterations.
The particle-swarm method is shown to be useful due to its ease of extension
and running time.


  Elemental chromium orders antiferromagnetically near room temperature, but
the ordering temperature can be driven to zero by applying large pressures. We
combine diamond anvil cell and synchrotron x-ray diffraction techniques to
measure directly the spin and charge order in the pure metal at the approach to
its quantum critical point. Both spin and charge order are suppressed
exponentially with pressure, well beyond the region where disorder cuts off
such a simple evolution, and they maintain a harmonic scaling relationship over
decades in scattering intensity. By comparing the development of the order
parameter with that of the magnetic wavevector, it is possible to ascribe the
destruction of antiferromagnetism to the growth in electron kinetic energy
relative to the underlying magnetic exchange interaction.


  Quantum computers provide an opportunity to efficiently sample from
probability distributions that include non-trivial interference effects between
amplitudes. Using a simple process wherein all possible state histories can be
specified by a binary tree, we construct an explicit quantum algorithm that
runs in polynomial time to sample from the process once. The corresponding
naive Markov Chain algorithm does not produce the correct probability
distribution and an explicit classical calculation of the full distribution
requires exponentially many operations. However, the problem can be reduced to
a system of two qubits with repeated measurements, shedding light on a
quantum-inspired efficient classical algorithm.


  Job recommendation aims to provide potential talents with suitable job
descriptions (JDs) consistent with their career trajectory, which plays an
essential role in proactive talent recruitment. In real-world management
scenarios, the available JD-user records always consist of JDs, user profiles,
and click data, in which the user profiles are typically summarized as the
user's skill distribution for privacy reasons. Although existing sophisticated
recommendation methods can be directly employed, effective recommendation still
has challenges considering the information deficit of JD itself and the natural
heterogeneous gap between JD and user profile. To address these challenges, we
proposed a novel skill-aware recommendation model based on the designed
semantic-enhanced transformer to parse JDs and complete personalized job
recommendation. Specifically, we first model the relative items of each JD and
then adopt an encoder with the local-global attention mechanism to better mine
the intra-job and inter-job dependencies from JD tuples. Moreover, we adopt a
two-stage learning strategy for skill-aware recommendation, in which we utilize
the skill distribution to guide JD representation learning in the recall stage,
and then combine the user profiles for final prediction in the ranking stage.
Consequently, we can embed rich contextual semantic representations for
learning JDs, while skill-aware recommendation provides effective JD-user joint
representation for click-through rate (CTR) prediction. To validate the
superior performance of our method for job recommendation, we present a
thorough empirical analysis of large-scale real-world and public datasets to
demonstrate its effectiveness and interpretability.


  We comment on J. Phys. Soc. Jpn. 91, 024001 (2022) by Masaki-Kato et al. and
show that their results are in very good agreement with the semi-classical
spin-wave approximation of Bose-Hubbard model in the hardcore limit. This
allows for recovering the analytical formulae for both the s-wave scattering
length and the Lee-Huang-Yang correction.


  These notes give an elementary introduction to Lie groups, Lie algebras, and
their representations. Designed to be accessible to graduate students in
mathematics or physics, they have a minimum of prerequisites. Topics include
definitions and examples of Lie groups and Lie algebras, the relationship
between Lie groups and Lie algebras via the exponential mapping, the basics of
representations theory, the Baker-Campbell-Hausdorff formula, a detailed study
of the representations of SU(3), and a brief survey of the representation
theory of general semisimple groups.


  This article is the exploration of the viewpoint within which propelled
particles in a steady-state are regarded as a system with quenched disorder.
The analogy is exact when the rate of the drift orientation vanishes and the
linear potential, representing the drift, becomes part of an external
potential, resulting in the effective potential $u_{eff}$. The stationary
distribution is then calculated as a disorder-averaged quantity by considering
all contributing drift orientations. To extend this viewpoint to the case when
a drift orientation evolves in time, we reformulate the relevant Fokker-Planck
equation as a self-consistent relation. One interesting aspect of this
formulation is that it is represented in terms of the Boltzmann factor
$e^{-\beta u_{eff}}$. In the case of a run-and-tumble model, the formulation
reveals an effective interaction between particles.


  Empirical risk minimization (ERM) is known in practice to be non-robust to
distributional shift where the training and the test distributions are
different. A suite of approaches, such as importance weighting, and variants of
distributionally robust optimization (DRO), have been proposed to solve this
problem. But a line of recent work has empirically shown that these approaches
do not significantly improve over ERM in real applications with distribution
shift. The goal of this work is to obtain a comprehensive theoretical
understanding of this intriguing phenomenon. We first posit the class of
Generalized Reweighting (GRW) algorithms, as a broad category of approaches
that iteratively update model parameters based on iterative reweighting of the
training samples. We show that when overparameterized models are trained under
GRW, the resulting models are close to that obtained by ERM. We also show that
adding small regularization which does not greatly affect the empirical
training accuracy does not help. Together, our results show that a broad
category of what we term GRW approaches are not able to achieve
distributionally robust generalization. Our work thus has the following
sobering takeaway: to make progress towards distributionally robust
generalization, we either have to develop non-GRW approaches, or perhaps devise
novel classification/regression loss functions that are adapted to the class of
GRW approaches.


  We study the problem on how to get good lower estimates for the integral $$
\int_T^{T+H} |\zeta(\sigma+it)| dt, $$ when $H \ll 1$ is small and $\sigma$ is
close to $1$, as well as related integrals for other Dirichlet series, by using
ideas related to the Balasubramanian-Ramachandra method. We use
kernel-functions constructed by the Paley-Wiener theorem as well as the kernel
function of Ramachandra. We also notice that the Fourier transform of
Ramachandra's Kernel-function is in fact a $K$-Bessel function. This simplifies
some aspects of Balasubramanian-Ramachandra method since it allows use of the
theory of Bessel-functions.


  We consider singular limits of the three-dimensional Ginzburg-Landau
functional for a superconductor with thin-film geometry, in a constant external
magnetic field. The superconducting domain has characteristic thickness on the
scale $\eps>0$, and we consider the simultaneous limit as the thickness
$\eps\rightarrow 0$ and the Ginzburg-Landau parameter
$\kappa\rightarrow\infty$. We assume that the applied field is strong (on the
order of $\eps^{-1}$ in magnitude) in its components tangential to the film
domain, and of order $\log\kappa$ in its dependence on $\kappa$. We prove that
the Ginzburg-Landau energy $\Gamma$-converges to an energy associated with a
two-obstacle problem, posed on the planar domain which supports the thin film.
The same limit is obtained regardless of the relationship between $\eps$ and
$\kappa$ in the limit. Two illustrative examples are presented, each of which
demonstrating how the curvature of the film can induce the presence of both
(positively oriented) vortices and (negatively oriented) antivortices
coexisting in a global minimizer of the energy.


  Radial velocity (RV) searches for exoplanets have surveyed many of the
nearest and brightest stars for long-term velocity variations indicative of a
companion body. Such surveys often detect high-amplitude velocity signatures of
objects that lie outside the planetary mass regime, most commonly those of a
low-mass star. Such stellar companions are frequently discarded as false-alarms
to the main science goals of the survey, but high-resolution imaging techniques
can be employed to either directly detect or place significant constraints on
the nature of the companion object. Here, we present the discovery of a compact
companion to the nearby star HD~118475. Our Anglo-Australian Telescope (AAT) RV
data allow the extraction of the full Keplerian orbit of the companion, found
to have a minimum mass of 0.445~$M_\odot$. Follow-up speckle imaging
observations at the predicted time of maximum angular separation rule out a
main sequence star as the source of the RV signature at the 3.3$\sigma$
significance level, implying that the companion must be a low-luminosity
compact object, most likely a white dwarf. We provide an isochrone analysis
combined with our data that constrain the possible inclinations of the binary
orbit. We discuss the eccentric orbit of the companion in the context of tidal
circularization timescales and show that non-circular orbit was likely
inherited from the progenitor. Finally, we emphasize the need for utilizing
such an observation method to further understand the demographics of white
dwarf companions around nearby stars.


  We study an urn model introduced in the paper of Chen and Wei, where at each
discrete time step $m$ balls are drawn at random from the urn containing colors
white and black. Balls are added to the urn according to the inspected colors,
generalizing the well known P\'olya-Eggenberger urn model, case m=1. We provide
exact expressions for the expectation and the variance of the number of white
balls after n draws, and determine the structure of higher moments. Moreover,
we discuss extensions to more than two colors. Furthermore, we introduce and
discuss a new urn model where the sampling of the m balls is carried out in a
step-by-step fashion, and also introduce a generalized Friedman's urn model.


  With the rapid advancement of the Energy Internet strategy, the number of
sensors within the Power Distribution Internet of Things (PD-IoT) has increased
dramatically. In this paper, an edge intelligence-based PD-IoT multi-source
data processing and fusion method is proposed to solve the problems of
confusing storage and insufficient fusion computing performance of multi-source
heterogeneous distribution data. First, a PD-IoT multi-source data processing
and fusion architecture based on edge smart terminals is designed. Second, to
realize the uniform conversion of various sensor data sources in the
distribution network in terms of magnitude and order of magnitude. By
introducing the Box-Cox transform to improve the data offset problem in the
Zscore normalization process, a multi-source heterogeneous data processing
method for distribution networks based on the Box-Cox transform Zscore is
proposed. Then, the conflicting phenomena of DS inference methods in data
source fusion are optimally handled based on the PCA algorithm. A multi-source
data fusion model based on DS inference with conflict optimization is
constructed to ensure the effective fusion of distribution data sources from
different domains. Finally, the effectiveness of the proposed method is
verified by an experimental analysis of an IEEE39 node system in a regional
distribution network in China.


  An endomorphism $f:\mathbb{P}^k\to\mathbb{P}^k$ of degree $d\geq2$ is said to
be postcritically finite (or PCF) if its critical set $\mathrm{Crit}(f)$ is
preperiodic, i.e. if there are integers $m>n\geq0$ such that
$f^m(\mathrm{Crit}(f))\subseteq f^n(\mathrm{Crit}(f))$. When $k\geq2$, it was
conjectured by Ingram, Ramadas and Silverman that, in the space
$\mathrm{End}_d^k$ of all endomorphisms of degree $d$ of $\mathbb{P}^k$, such
endomorphisms are not Zariski dense. We prove this conjecture. Further, in the
space $\mathrm{Poly}_d^2$ of all regular polynomial endomorphisms of degree
$d\geq2$ of the affine plane $\mathbb{A}^2$, we construct a dense and Zariski
open subset where we have a uniform bound on the number of preperiodic points
lying in the critical set.
  The proofs are a combination of the theory of heights in arithmetic dynamics
and methods from real dynamics to produce open subsets with maximal
bifurcation.


  If the Standard Model is valid up to scales near the Planck mass, and if the
cosmological constant and Higgs mass parameters scan on a landscape of vacua,
it is well known that the observed orders of magnitude of these quantities can
be understood from environmental selection for large-scale structure and atoms.
If in addition the Higgs quartic coupling scans, with a probability
distribution peaked at low values, environmental selection for a phase having a
scale of electroweak symmetry breaking much less than the Planck scale leads to
a most probable Higgs mass of 106 GeV. While fluctuations below this are
negligible, the upward fluctuation is 25/p GeV, where p measures the strength
of the peaking of the a priori distribution of the quartic coupling. If the top
Yukawa coupling also scans, the most probable top quark mass is predicted to
lie in the range (174--178) GeV, providing the standard model is valid to at
least 10^{17} GeV. The downward fluctuation is 35 GeV/ \sqrt{p}, suggesting
that p is sufficiently large to give a very precise Higgs mass prediction.
While a high reheat temperature after inflation could raise the most probable
value of the Higgs mass to 118 GeV, maintaining the successful top prediction
suggests that reheating is limited to about 10^8 GeV, and that the most
probable value of the Higgs mass remains at 106 GeV. If all Yukawa couplings
scan, then the e,u,d and t masses are understood to be outliers having extreme
values induced by the pressures of strong environmental selection, while the s,
\mu, c, b, \tau Yukawa couplings span only two orders of magnitude, reflecting
an a priori distribution peaked around 10^{-3}. Extensions of these ideas allow
order of magnitude predictions for neutrino masses, the baryon asymmetry and
important parameters of cosmological inflation.


  A flexible wave localization is investigated using a spatial-temporal
modulation of point defects along the periodic array of electromechanical local
resonators of a piezoelectric bimorph beam. By changing the electrical
resonance of subsequent unit cells through a smooth and synchronized strategy,
a point defect is moved along the metastructure, which properly transfers the
vibration energy between the unit cells as well as perfectly induces wave
localization according to the final defect position. This wave manipulation by
programmable defects is also applied to a two-dimensional triangular lattice
composed by piezoelectric metamaterial beams, which illustrates the potential
and versatility of the proposed strategy in more complex systems. Therefore,
this work opens new possibilities for programmable wave localization and
manipulation using smart electromechanical metamaterials with applications that
may involve guiding, sensing, monitoring and harvesting.


  The phase of matter waves depends on proper time and is therefore susceptible
to special-relativistic (kinematic) and gravitational (redshift) time dilation.
Hence, it is conceivable that atom interferometers measure general-relativistic
time-dilation effects. In contrast to this intuition, we show: (i.) Closed
light-pulse interferometers without clock transitions during the pulse sequence
are not sensitive to gravitational time dilation in a linear potential. (ii.)
They can constitute a quantum version of the special-relativistic twin paradox.
(iii.) Our proposed experimental geometry for a quantum-clock interferometer
isolates this effect.


  In recent years there has been growing interest in solutions for the delivery
of clinical care for the elderly, due to the large increase in aging
population. Monitoring a patient in his home environment is necessary to ensure
continuity of care in home settings, but, to be useful, this activity must not
be too invasive for patients and a burden for caregivers. We prototyped a
system called SINDI (Secure and INDependent lIving), focused on i) collecting a
limited amount of data about the person and the environment through Wireless
Sensor Networks (WSN), and ii) inferring from these data enough information to
support caregivers in understanding patients' well being and in predicting
possible evolutions of their health. Our hierarchical logic-based model of
health combines data from different sources, sensor data, tests results,
common-sense knowledge and patient's clinical profile at the lower level, and
correlation rules between health conditions across upper levels. The logical
formalization and the reasoning process are based on Answer Set Programming.
The expressive power of this logic programming paradigm makes it possible to
reason about health evolution even when the available information is incomplete
and potentially incoherent, while declarativity simplifies rules specification
by caregivers and allows automatic encoding of knowledge. This paper describes
how these issues have been targeted in the application scenario of the SINDI
system.


  Despite the recent success in probabilistic modeling and their applications,
generative models trained using traditional inference techniques struggle to
adapt to new distributions, even when the target distribution may be closely
related to the ones seen during training. In this work, we present a
doubly-amortized variational inference procedure as a way to address this
challenge. By sharing computation across not only a set of query inputs, but
also a set of different, related probabilistic models, we learn transferable
latent representations that generalize across several related distributions. In
particular, given a set of distributions over images, we find the learned
representations to transfer to different data transformations. We empirically
demonstrate the effectiveness of our method by introducing the MetaVAE, and
show that it significantly outperforms baselines on downstream image
classification tasks on MNIST (10-50%) and NORB (10-35%).


  Large language models (LLMs) suffer from catastrophic forgetting during
continual learning. Conventional rehearsal-based methods rely on previous
training data to retain the model's ability, which may not be feasible in
real-world applications. When conducting continual learning based on a
publicly-released LLM checkpoint, the availability of the original training
data may be non-existent. To address this challenge, we propose a framework
called Self-Synthesized Rehearsal (SSR) that uses the LLM to generate synthetic
instances for rehearsal. Concretely, we first employ the base LLM for
in-context learning to generate synthetic instances. Subsequently, we utilize
the latest LLM to refine the instance outputs based on the synthetic inputs,
preserving its acquired ability. Finally, we select diverse high-quality
synthetic instances for rehearsal in future stages. Experimental results
demonstrate that SSR achieves superior or comparable performance compared to
conventional rehearsal-based approaches while being more data-efficient.
Besides, SSR effectively preserves the generalization capabilities of LLMs in
general domains.


  We study the effect of disorder induced by doping on the transition
temperature in high $T_c$ cuprates. Since the impurity lies between the CuO$_2$
planes, the momentum transfer is restricted by small angle with a range of
order of $1/(d k_F)$, where $k_F$ is the Fermi momentum and $d$ is the distance
between the plane and the impurity. We find that the leading correction on the
transition temperature in this case is in cubic order of $1/(d k_F)$, while the
single particle scattering rate is linearly proportional to $1/(d k_F)$.
Therefore, we conclude that the disorder induced by doping has rather small
effect on $T_c$, while it could give large single particle scattering rate. We
find that the reduction of $T_c$ is about $3-10 %$, using the single particle
scattering rate ($150-450 K$) observed in the recent angle-resolved-
photoemission-spectroscopy data on optimally doped Bi2212. The consequences of
the small angle scattering in other physical quantities such as transport are
also discussed.


  We study the coupling arising via perturbative QCD of zero 4-momentum Higgs
bosons to light quarks inside the nucleon. Qualitative comparison with the
results obtained from one-loop-order low energy theorems for the Higgs-nucleon
interaction suggests the existence of a dynamical light-quark mass which falls
off with momentum. Quantitative comparison leads to an estimate of $\alpha_s$
at very low $q^2$ quite near unity.


  We present the first attempt at calibrating the effective-one-body (EOB)
model to accurate numerical-relativity simulations of spinning, non-precessing
black-hole binaries. Aligning the EOB and numerical waveforms at low frequency
over a time interval of 1000M, we first estimate the phase and amplitude errors
in the numerical waveforms and then minimize the difference between numerical
and EOB waveforms by calibrating a handful of EOB-adjustable parameters. In the
equal-mass, spin aligned case, we find that phase and fractional amplitude
differences between the numerical and EOB (2,2) mode can be reduced to 0.01
radians and 1%, respectively, over the entire inspiral waveforms. In the
equal-mass, spin anti-aligned case, these differences can be reduced to 0.13
radians and 1% during inspiral and plunge, and to 0.4 radians and 10% during
merger and ringdown. The waveform agreement is within numerical errors in the
spin aligned case while slightly over numerical errors in the spin anti-aligned
case. Using Enhanced LIGO and Advanced LIGO noise curves, we find that the
overlap between the EOB and the numerical (2,2) mode, maximized over the
initial phase and time of arrival, is larger than 0.999 for binaries with total
mass 30-200Ms. In addition to the leading (2,2) mode, we compare four
subleading modes. We find good amplitude and frequency agreements between the
EOB and numerical modes for both spin configurations considered, except for the
(3,2) mode in the spin anti-aligned case. We believe that the larger difference
in the (3,2) mode is due to the lack of knowledge of post-Newtonian spin
effects in the higher modes.


  We examine the past and current work on the star formation (SF) histories of
dwarf galaxies in cosmological hydrodynamic simulations. The results obtained
from different numerical methods are still somewhat mixed, but the differences
are understandable if we consider the numerical and resolution effects. It
remains a challenge to simulate the episodic nature of SF history in dwarf
galaxies at late times within the cosmological context of a cold dark matter
model. More work is needed to solve the mysteries of SF history of dwarf
galaxies employing large-scale hydrodynamic simulations on the next generation
of supercomputers.


  An intrinsic mass generation mechanism for exotic ELKO dark matter fields is
scrutinized, in the context of the very special relativity (VSR). Our results
are reported on unraveling inequivalent spin structures that educe an
additional term on the associated Dirac operator. Contrary to the spinor fields
of mass dimension 3/2, this term is precluded to be absorbed as a shift of some
gauge vector potential, regarding the equations for the dark spinor fields. It
leads to some dynamical constraints that can be intrinsically converted into a
dark spinor mass generation mechanism, with the encoded symmetries maintained
by the VSR. The dynamical mass is embedded in the VSR framework through a
natural coupling to the kink solution of a \lambda \phi^{4} theory for a scalar
field \phi. Our results evince the possibility of novel effective scenarios,
derived from exotic couplings among dark spinor fields and scalar field
topological solutions.


  4U 1538-52, an absorbed high mass X-ray binary with an orbital period of 3.73
days, shows moderate orbital intensity modulations with a low level of counts
during the eclipse. Several models have been proposed to explain the accretion
at different orbital phases by a spherically symmetric stellar wind from the
companion. The aim of this work is to study both the light curve and orbital
phase spectroscopy of this source in the long term. Particularly, the folded
light curve and the changes of the spectral parameters with orbital phase to
analyse the stellar wind of QV Nor, the mass donor of this binary system. We
used all the observations made from the Gas Slit Camera on board MAXI of 4U
1538-52 covering many orbits continuously. We obtained the good interval times
for every orbital phase range which were the input to extract our data. We
estimated the orbital period of the system and then folded the light curves and
we fitted the X-ray spectra with the same model for every orbital phase
spectrum. We also extracted the averaged spectrum of all the MAXI data
available. The MAXI spectra in the 2-20 keV energy range were fitted with an
absorbed Comptonization of cool photons on hot electrons. We found a strong
orbital dependence of the absorption column density but neither the
fluorescence iron emission line nor low energy excess were needed to fit the
MAXI spectra. The variation of the spectral parameters over the binary orbit
were used to examine the mode of accretion onto the neutron star in 4U 1538-52.
We deduce a best value of $\dot{M}/v_\infty=0.65\times 10^{-9}$ $M_{\odot} \,
yr^{-1}/(km \, s^{-1})$ for QV Nor.


  A constant-rate creation of dark particles in the late-time FLRW spacetime
provides a cosmological model in accordance with precise observational tests.
The matter creation backreaction implies in this context a vacuum energy
density scaling linearly with the Hubble parameter, which is consistent with
the vacuum expectation value of the QCD condensate in a low-energy expanding
spacetime. Both the cosmological constant and coincidence problems are
alleviated in this scenario. We discuss the cosmological model that arises in
this context and present a joint analysis of observations of the first acoustic
peak in the cosmic microwave background (CMB) anisotropy spectrum, the Hubble
diagram for supernovas of type Ia (SNIa), the distance scale of baryonic
acoustic oscillations (BAO) and the distribution of large scale structures
(LSS). We show that a good concordance is obtained, albeit with a higher value
of the present matter abundance than in the standard model.


  Bitcoin is based on a P2P network that is used to propagate transactions and
blocks. While the P2P network design intends to hide the topology of the P2P
network, information about the topology is required to understand the network
from a scientific point of view. Thus, there is a natural tension between the
'desire' for unobservability on the one hand, and for observability on the
other hand. On a middle ground, one would at least be interested on some
statistical features of the Bitcoin network like the number of peers that
participate in the propagation of transactions and blocks. This number is
composed of the number of reachable peers that accept incoming connections and
unreachable peers that do not accept incoming connections. While the number of
reachable peers can be measured, it is inherently difficult to determine the
number of unreachable peers. Thus, the number of unreachable peers can only be
estimated based on some indicators. In this paper, we first define our
understanding of unreachable peers and then propose the PAL (Passive
Announcement Listening) method which gives an estimate of the number of
unreachable peers by observing ADDR messages that announce active IP addresses
in the network. The PAL method allows for detecting unreachable peers that
indicate that they provide services useful to the P2P network. In conjunction
with previous methods, the PAL method can help to get a better estimate of the
number of unreachable peers. We use the PAL method to analyze data from a
long-term measurement of the Bitcoin P2P network that gives insights into the
development of the number of unreachable peers over five years from 2015 to
2020. Results show that about 31,000 unreachable peers providing useful
services were active per day at the end of the year 2020. An empirical
validation indicates that the approach finds about 50 % of unreachable peers
that provide useful services.


  The interplay of topology and non-Hermiticity has led to diverse, exciting
manifestations in a plethora of systems. In this work, we systematically
investigate the role of non-Hermiticity in the Chern insulating Haldane model
on a dice lattice. Due to the presence of a non-dispersive flat band, the
dice-Haldane model hosts a topologically rich phase diagram with the
non-trivial phases accommodating Chern numbers $\pm 2$. We introduce
non-Hermiticity into this model in two ways -- through balanced non-Hermitian
gain and loss, and by non-reciprocal hopping in one direction. Both these types
of non-Hermiticity induce higher-order exceptional points of order three. We
substantiate the presence and the order of these higher-order exceptional
points using the phase rigidity and its scaling. Further, we construct a phase
diagram to identify and locate the occurrence of these exceptional points in
the parameter space. Non-Hermiticity has yet more interesting consequences on a
finite-sized lattice. Unlike for balanced gain and loss, in the case of
non-reciprocal hopping, the nearest-neighbour dice lattice system under
periodic boundary conditions accommodates a finite, non-zero spectral area in
the complex plane. This manifests as the non-Hermitian skin effect when open
boundary conditions are invoked. In the more general case of the dice-Haldane
lattice model, the non-Hermitian skin effect can be caused by both gain and
loss or non-reciprocity. Fascinatingly, the direction of localization of the
eigenstates depends on the nature and strength of the non-Hermiticity. We
establish the occurrence of the skin effect using the local density of states,
inverse participation ratio and the edge probability, and demonstrate its
robustness to disorder. Our results place the dice-Haldane model as an exciting
platform to explore non-Hermitian physics.