  We develop an algebraic approach to the branching of representations of the
general linear Lie superalgebra $\mathfrak{gl}_{p|q}({\mathbb C})$, by
constructing certain super commutative algebras whose structure encodes the
branching rules. Using this approach, we derive the branching rules for
restricting any irreducible polynomial representation $V$ of
$\mathfrak{gl}_{p|q}({\mathbb C})$ to a regular subalgebra isomorphic to
$\mathfrak{gl}_{r|s}({\mathbb C})\oplus \mathfrak{gl}_{r'|s'}({\mathbb C})$,
$\mathfrak{gl}_{r|s}({\mathbb C})\oplus\mathfrak{gl}_1({\mathbb C})^{r'+s'}$ or
$\mathfrak{gl}_{r|s}({\mathbb C})$, with $r+r'=p$ and $s+s'=q$. In the case of
$\mathfrak{gl}_{r|s}({\mathbb C})\oplus\mathfrak{gl}_1({\mathbb C})^{r'+s'}$
with $s=0$ or $s=1$ but general $r$, we also construct a basis for the space of
$\mathfrak{gl}_{r|s}({\mathbb C})$ highest weight vectors in $V$; when $r=s=0$,
the branching rule leads to explicit expressions for the weight multiplicities
of $V$ in terms of Kostka numbers.


  The LHC is actively searching for narrow dijet resonances corresponding to
physics beyond the Standard Model. Among the many resonances that have been
postulated (e.g., colored vectors, scalars, and fermions) one that would have a
particularly large production rate at the LHC would be a scalar diquark
produced in the s-channel via fusion of two valence quarks. In previous work,
we introduced a color discriminant variable that distinguishes among various
dijet resonances, drawing on measurements of the dijet resonance mass, total
decay width and production cross-section. Here, we show that this
model-independent method applies well to color-triplet and color-sextet scalar
diquarks, distinguishing them clearly from other candidate resonances. We also
introduce a more transparent theoretical formulation of the color discriminant
variable that highlights its relationship to the branching ratios of the
resonance into incoming and outgoing partons and to the properties of those
partons. While the original description of the color discriminant variable
remains convenient for phenomenological use upon discovery of a new resonance,
the new formulation makes it easier to predict the value of the variable for a
given class of resonance.


  The preliminary results of an aging test performed at the CERN Gamma
Irradiation Facility on a single--gap RPC prototype developed for the LHCb Muon
System are presented. The results are based on an accumulated charge density of
0.42 C/cm^2, corresponding to about 4 years of LHCb running at the highest
background rate. We observe a rise in the dark current and noise measured with
source off. The current drawn with source on steadily decreased, possibly
indicating an increase of resistivity of the chamber plates. The performance of
the chamber, studied with a muon beam under several photon flux values, is
found to still fulfill the LHCb operation requirements.


  Currently, the only worldwide source of low-energy antiprotons is the
AD/ELENA facility located at CERN. To date, all precision measurements on
single antiprotons have been conducted at this facility and provide stringent
tests of the fundamental interactions and their symmetries. However, the
magnetic field fluctuations from the facility operation limit the precision of
upcoming measurements. To overcome this limitation, we have designed the
transportable antiproton trap system BASE-STEP to relocate antiprotons to
laboratories with a calm magnetic environment. We anticipate that the
transportable antiproton trap will facilitate enhanced tests of CPT invariance
with antiprotons, and provide new experimental possibilities of using
transported antiprotons and other accelerator-produced exotic ions. We present
here the technical design of the transportable trap system. This includes the
transportable superconducting magnet, the cryogenic inlay consisting of the
trap stack and the detection systems, and the differential pumping section to
suppress the residual gas flow into the cryogenic trap chamber.


  If $A$ is an associative algebra, then we can define the adjoint Lie algebra
$A^{(-)}$ and Jordan algebra $A^{(+)}$. It is easy to see that any associative
Rota--Baxter operator on $A$ induces a Lie and Jordan Rota--Baxter operator on
$A^{(-)}$ and $A^{(+)}$ respectively. Are there Lie (Jordan) Rota--Baxter
operators, which are not associative Rota--Baxter operators?
  In the present article we are studying these questions for the Sweedler
algebra $H_4$, that is a 4-dimension non-commutative Hopf algebra. More
precisely, we describe the Rota--Baxter operators on Lie algebra on the adjoint
Lie algebra $H_4^{(-)}$.


  Combination of electric fields and Joule self-heating is used to change the
oxygen stoichiometry and promote oxygen vacancy drift in a free-standing
$\mathrm{(La,Sr)MnO_3}$ thin film microbridge placed in controlled atmosphere.
By controlling the local oxygen vacancies concentration, we can reversibly
switch our LSMO-based microbridges from metallic to insulating behavior on
timescales lower than 1 s and with small applied voltages (<5 V). The strong
temperature gradients given by the microbridge geometry strongly confine the
motion of oxygen vacancies, limiting the modified region within the
free-standing area. Multiple resistive states can be set by selected current
pulses that determine different oxygen vacancies profiles within the device .
Qualitative analysis of device operation is also provided with the support of
Finite Element Analysis.


  The space of positive operator-valued measures on the Borel sets of a compact
(or even locally compact) Hausdorff space with values in the algebra of linear
operators acting on a d-dimensional Hilbert space is studied from the
perspectives of classical and non-classical convexity through a transform
$\Gamma$ that associates any positive operator-valued measure with a certain
completely positive linear map of the homogeneous C*-algebra $C(X)\otimes B(H)$
into $B(H)$. This association is achieved by using an operator-valued integral
in which non-classical random variables (that is, operator-valued functions)
are integrated with respect to positive operator-valued measures and which has
the feature that the integral of a random quantum effect is itself a quantum
effect. A left inverse $\Omega$ for $\Gamma$ yields an integral representation,
along the lines of the classical Riesz Representation Theorem for certain
linear functionals on $C(X)$, of certain (but not all) unital completely
positive linear maps $\phi:C(X)\otimes B(H) \rightarrow B(H)$. The extremal and
C*-extremal points of the space of POVMS are determined.


  The study investigates the gravitational scattering amplitude between two
Schwarzschild black holes in a two to two interaction, focusing on the Second
Post-Minkowskian correction (2 PM). Analyzing contributions from box and
cross-box diagrams, the research interprets Feynman integrals as pairings
between twisted co-cycles and cycles. The concept of twisted (co)-homology
groups is introduced, leading to a master integral decomposition formula. The
study successfully applies intersection theory to compute coefficients of the
master integral basis, marking the first application of intersection theory in
the quantum field theoretic description of gravity. The results align with
existing literature on the 2PM correction.


  We briefly review 3-dimensional untwisted Dijkgraaf-Witten theory over a
finite group $\Gamma$, and present a method of computing untwisted
Dijkgraaf-Witten invariants for arborescent links. Some explicit formulas are
given when $\Gamma=\mathbb{Z}/p\mathbb{Z}\rtimes\mathbb{Z}/(p-1)\mathbb{Z}$ for
an odd prime $p$.


  We solve the quantum discord completely as an optimization of certain one
variable function for arbitrary two qubit X state. Exact solutions of the
quantum discord are obtained for several nontrivial regions of the five
parametric space for the quantum state. Exceptional solutions are determined
via an iterative algorithm.


  Let S(n,k) be the Stirling number of the second kind. Wilf conjectured that
the alternating sum of S(n,k) for k from 0 to n is not zero for all n>2. In
this paper, we prove that Wilf conjecture is true except at most one number
with the properties of weighted Motzkin number.


  We have measured the resistance noise of a two-dimensional (2D)hole system in
a high mobility GaAs quantum well, around the 2D metal-insulator transition
(MIT) at zero magnetic field. The normalized noise power $S_R/R^2$ increases
strongly when the hole density p_s is decreased, increases slightly with
temperature (T) at the largest densities, and decreases strongly with T at low
p_s. The noise scales with the resistance, $S_R/R^2 \sim R^{2.4}$, as for a
second order phase transition such as a percolation transition. The p_s
dependence of the conductivity is consistent with a critical behavior for such
a transition, near a density p* which is lower than the observed MIT critical
density p_c.


  In this paper we consider the Klein-Gordon equation on spherically symmetric
background spacetimes with a constant area radius. The spacetimes under
consideration are Nariai and Pleba\'nski-Hacyan, and can be considered constant
radius limits of Reissner-Nordstr\"om-de Sitter spacetimes. We prove
boundedness in the case of a non-negative Klein Gordon mass and decay unless
the mass is zero. In the latter case we prove decay of solutions that are
supported on all harmonic modes with angular momentum l greater or equal to 1.
We show that the l=0 modes of solutions to the massless Klein-Gordon equation
do not decay. They are subject to conservation laws along degenerate Killing
horizons. We apply the estimates in Nariai to give decay of solutions to the
massive Klein-Gordon equation on an n-dimensional de Sitter background, using
only the vector field method and with no restrictions on the positive
Klein-Gordon mass.


  Blockchain has been forming the central piece of various types of
vehicle-to-everything (V2X) network for trusted data exchange. Recently,
permissioned blockchains garner particular attention thanks to their improved
scalability and diverse needs from different organizations. One representative
example of permissioned blockchain is Hyperledger Fabric ("Fabric"). Due to its
unique execute-order procedure, there is a critical need for a client to select
an optimal number of peers. The interesting problem that this paper targets to
address is the tradeoff in the number of peers: a too large number will degrade
scalability while a too small number will make the network vulnerable to faulty
nodes. This optimization issue gets especially challenging in V2X networks due
to mobility of nodes: a transaction must be executed and the associated block
must be committed before the vehicle leaves a network. To this end, this paper
proposes an optimal peers selection mechanism based on reinforcement learning
(RL) to keep a Fabric-empowered V2X network impervious to dynamicity due to
mobility. We model the RL as a contextual multi-armed bandit (MAB) problem. The
results demonstrate the outperformance of the proposed scheme.


  In the paper, G. Alessandrini and L. Rondi, ``Determining a sound-soft
polyhedral scatterer by a single far-field measurement'', Proc. Amer. Math.
Soc. 133 (2005), pp. 1685-1691, on the determination of a sound-soft polyhedral
scatterer by a single far-field measurement, the proof of Proposition 3.2 is
incomplete. In this corrigendum we provide a new proof of the same proposition
which fills the previous gap.


  We define the cyclic matching sequencibility of a graph to be the largest
integer $d$ such that there exists a cyclic ordering of its edges so that every
$d$ consecutive edges in the cyclic ordering form a matching. We show that the
cyclic matching sequencibility of $K_{2m}$ and $K_{2m+1}$ equal $m-1$.


  In this article we extend a theorem of Andrews, Crippa, and Simon on the
asymptotic behavior of polynomials defined by a general class of recursive
equations. Here the polynomials are in the variable $q$, and the recursive
definition at step $n$ introduces a polynomial in $n$. Our extension replaces
the polynomial in $n$ with either an exponential or periodic function of $n$.


  Recently it was found that a broad class of existing inflationary models
based on supergravity can be significantly simplified if some of the standard,
unconstrained chiral superfields are replaced by nilpotent superfields,
associated with Volkov-Akulov supersymmetry. The same method allows to simplify
the existing models of uplifting of AdS vacua in string theory. In this paper
we will show that one can go well beyond simplifying the models that already
exist. We will propose a broad class of new models of chaotic inflation based
on supergravity with nilpotent superfields, which simultaneously incorporate
both inflation and uplifting. They provide a simple unified description of
inflation and the present acceleration of the universe in the supergravity
context.


  Based on time-dependent Hartree-Fock theory, a new inverse quasifission
mechanism is proposed to produce neutron-rich transfermium nuclei, in collision
of prolate deformed actinides. Calculations show that collision of the tip of
one nucleus with the side of the other results in a nucleon flux toward the
latter. The role of nucleon evaporation and impact parameter, as well as the
collision time are discussed.


  Some of the most interesting scenarios that can be studied in astrophysics,
contain fluids and plasma moving under the influence of strong gravitational
fields. To study these problems it is required to implement numerical
algorithms robust enough to deal with the equations describing such scenarios,
which usually involve hydrodynamical shocks. It is traditional that the first
problem a student willing to develop research in this area is to numerically
solve the one dimensional Riemann problem, both Newtonian and relativistic.
Even a more basic requirement is the construction of the exact solution to this
problem in order to verify that the numerical implementations are correct. We
describe in this paper the construction of the exact solution and a detailed
procedure of its implementation.


  We uplift 5-dimensional super-Yang-Mills theory to a 6-dimensional gauge
theory with the help of a space-like constant vector $\eta^M$, whose norm
determines the Yang-Mills coupling constant. After the localization of $\eta^M$
the 6D gauge theory acquires Lorentzian invariance as well as scale invariance.
We discuss KK states, instantons and the flux quantization. The 6D theory
admits extended solutions like 1/2 BPS `strings' and monopoles.


  Strong numerical evidence is presented for the existence of a continuous
family of time-periodic solutions with ``weak'' spatial localization of the
spherically symmetric non-linear Klein-Gordon equation in 3+1 dimensions. These
solutions are ``weakly'' localized in space in that they have slowly decaying
oscillatory tails and can be interpreted as localized standing waves
(quasi-breathers). By a detailed analysis of long-lived metastable states
(oscillons) formed during the time evolution it is demonstrated that the
oscillon states can be quantitatively described by the weakly localized
quasi-breathers.It is found that the quasi-breathers and their oscillon
counterparts exist for a whole continuum of frequencies.


  Linear algebra is usually defined over a field such as the reals or complex
numbers. It is possible to extend this to skew fields such as the quaternions.
However, to the authors' knowledge there is no commonly accepted notation of
linear algebra over skew fields. To this end, we discuss ways of notation that
account for the non-commutativity of the quaternion multiplication.


  The first aim of this paper is to give four types of examples of surface
bundles over surfaces with non-zero signature. The first example is with base
genus 2, a prescribed signature, a 0-section and the fiber genus greater than a
certain number which depends on the signature. This provides a new upper bound
on the minimal base genus for fixed signature and fiber genus. The second one
gives a new asymptotic upper bound for this number in the case that fiber genus
is odd. The third one has a small Euler characteristic. The last is a
non-holomorphic example.
  The second aim is to improve upper bounds for stable commutator lengths of
Dehn twists by giving factorizations of powers of Dehn twists as products of
commutators. One of the factorizations is used to construct the second examples
of surface bundles. As a corollary, we see that there is a gap between the
stable commutator length of the Dehn twist along a nonseparating curve in the
mapping class group and that in the hyperelliptic mapping class group if the
genus of the surface is greater than or equal to 8.


  Cosmic-rays with energies up to $3\times10^{20}$ eV have been observed, as
have as have astrophysical neutrinos with energies above 1 PeV. In this talk, I
will discuss some of the unique phenomena that occur when particles with TeV
energies and above interact with matter. The emphasis will be on lepton
interactions. The cross-sections for electron bremsstrahlung and photon pair
conversion are suppressed at high energies, by the Landau-Pomeranchuk-Migdal
(LPM) effect, lengthening electromagnetic showers. At still higher energies
(above $10^{20}$ eV), photonuclear and electronuclear interactions dominate,
and showers become predominantly hadronic. Muons interact much less strongly,
so can travel long distances through solids before losing energy. Tau leptons
behave similarly, although their short livetime limits how far they can travel.
The hadronic interaction cross-section is believed to continue to increase
slowly with rising energy; measurements of cosmic-ray air showers support this
prediction.


  We examine the Cardy-Verlinde formula for finite temperature N=4 Super
Yang-Mills theory on $R\times S^3$, and its AdS dual. We find that curvature
effects introduce non-trivial corrections to thermodynamic quantities computed
on both sides. We find a modified version of the Cardy-Verlinde formula for the
SYM theory, incorporating these. On the gravity side, these corrections imply
that the Cardy-Verlinde formula is exact.


  The presence of a topologically non-trivial discrete invariants implies the
existence of gapless modes in finite samples, but it does not necessarily imply
their localization. The disappearance of the indirect energy gap in the bulk
generically leads to the absence of localized edge states. We illustrate this
behavior in two fundamental lattice models on the single-particle level. By
tuning a hopping parameter the indirect gap is closed while maintaining the
topological properties. The inverse participation ratio is used to measure the
degree of localization.


  Domain adaptive object detection aims to leverage the knowledge learned from
a labeled source domain to improve the performance on an unlabeled target
domain. Prior works typically require the access to the source domain data for
adaptation, and the availability of sufficient data on the target domain.
However, these assumptions may not hold due to data privacy and rare data
collection. In this paper, we propose and investigate a more practical and
challenging domain adaptive object detection problem under both source-free and
few-shot conditions, named as SF-FSDA. To overcome this problem, we develop an
efficient labeled data factory based approach. Without accessing the source
domain, the data factory renders i) infinite amount of synthesized
target-domain like images, under the guidance of the few-shot image samples and
text description from the target domain; ii) corresponding bounding box and
category annotations, only demanding minimum human effort, i.e., a few manually
labeled examples. On the one hand, the synthesized images mitigate the
knowledge insufficiency brought by the few-shot condition. On the other hand,
compared to the popular pseudo-label technique, the generated annotations from
data factory not only get rid of the reliance on the source pretrained object
detection model, but also alleviate the unavoidably pseudo-label noise due to
domain shift and source-free condition. The generated dataset is further
utilized to adapt the source pretrained object detection model, realizing the
robust object detection under SF-FSDA. The experiments on different settings
showcase that our proposed approach outperforms other state-of-the-art methods
on SF-FSDA problem. Our codes and models will be made publicly available.


  Discovering the Higgs boson is one of the primary goals of both the Tevatron
and the Large Hadron Collider (LHC). The present status of the Higgs search is
reviewed and future prospects for discovery at the Tevatron and LHC are
considered. This talk focuses primarily on the Higgs boson of the Standard
Model and its minimal supersymmetric extension. Theoretical expectations for
the Higgs boson and its phenomenological consequences are reviewed.


  We report the low temperature current-voltage (I-V) characteristics studies
in quasi-one dimensional conducting polymer nanofibers. We find a threshold
voltage Vt below which little current flows at temperatures below 30-40 K. For
V > Vt current scales as (V/Vt - 1)^zeta, where zeta ~ 1.8-2.1 at high biases.
Differential conductance oscillations are found whose magnitude increases as
temperature decreases below 10 K. We attribute the observed low temperature I-V
behavior to Coulomb blockade effects with a crossover to Luttinger liquid-like
behavior at high temperature. We demonstrate that at low temperatures such a
doped conjugated polymer fiber can be considered as an array of small
conducting regions separated by nanoscale barriers, where the Coulomb blockade
tunneling is the dominant transport mechanism.


  In this paper we study the application of the Sobolev gradients technique to
the problem of minimizing several Schr\"odinger functionals related to timely
and difficult nonlinear problems in Quantum Mechanics and Nonlinear Optics. We
show that these gradients act as preconditioners over traditional choices of
descent directions in minimization methods and show a computationally
inexpensive way to obtain them using a discrete Fourier basis and a Fast
Fourier Transform. We show that the Sobolev preconditioning provides a great
convergence improvement over traditional techniques for finding solutions with
minimal energy as well as stationary states and suggest a generalization of the
method using arbitrary linear operators.


  We investigate the decomposition problem of balls into finitely many
congruent pieces in dimension $d=2k$. In addition, we prove that the $d$
dimensional unit ball $B_d$ can be divided into finitely many congruent pieces
if $d=4$ or $d\ge 6$. We show that the minimal number of required pieces is
less than $20d$ if $d \ge 10$.


  We prove that many features of Thurston's Dehn surgery theory for hyperbolic
3-manifolds generalize to Einstein metrics in any dimension. In particular,
this gives large, infinite families of new Einstein metrics on compact
manifolds.


  We examine certain nonassociative deformations of quantum mechanics and
gravity in three dimensions related to the dynamics of electrons in uniform
distributions of magnetic charge. We describe a quantitative framework for
nonassociative quantum mechanics in this setting, which exhibits new effects
compared to ordinary quantum mechanics with sourceless magnetic fields, and the
extent to which these theoretical consequences may be experimentally testable.
We relate this theory to noncommutative Jordanian quantum mechanics, and show
that its underlying algebra can be obtained as a contraction of the alternative
algebra of octonions. The uncontracted octonion algebra conjecturally describes
a nonassociative deformation of three-dimensional quantum gravity induced by
magnetic monopoles, which we propose is realised by a non-geometric
Kaluza-Klein monopole background in M-theory.


  A complete flag in $\mathbb{R}^n$ is a sequence of nested subspaces $V_1
\subset \cdots \subset V_{n-1}$ such that each $V_k$ has dimension $k$. It is
called totally nonnegative if all its Pl\"ucker coordinates are nonnegative. We
may view each $V_k$ as a subspace of polynomials in $\mathbb{R}[x]$ of degree
at most $n-1$, by associating a vector $(a_1, \dots, a_n)$ in $\mathbb{R}^n$ to
the polynomial $a_1 + a_2x + \cdots + a_nx^{n-1}$. We show that a complete flag
is totally nonnegative if and only if each of its Wronskian polynomials
$\mathsf{Wr}(V_k)$ is nonzero on the interval $(0, \infty)$. In the language of
Chebyshev systems, this means that the flag forms a Markov system or
$ECT$-system on $(0, \infty)$. This gives a new characterization and membership
test for the totally nonnegative flag variety. Similarly, we show that a
complete flag is totally positive if and only if each $\mathsf{Wr}(V_k)$ is
nonzero on $[0, \infty]$. We use these results to show that a conjecture of
Eremenko (2015) in real Schubert calculus is equivalent to the following
conjecture: if $V$ is a finite-dimensional subspace of polynomials such that
all complex zeros of $\mathsf{Wr}(V)$ lie in the interval $(-\infty, 0)$, then
all Pl\"ucker coordinates of $V$ are real and positive. This conjecture is a
totally positive strengthening of a result of Mukhin, Tarasov, and Varchenko
(2009), and can be reformulated as saying that all complex solutions to a
certain family of Schubert problems in the Grassmannian are real and totally
positive. We also show that our conjecture is equivalent to a totally positive
version of the secant conjecture of Sottile (2003).


  We study the Anderson transition in the SU(2) model and the Ando model. We
report a new precise estimate of the critical exponent for the symplectic
universality class of the Anderson transition. We also report numerical
estimation of the $\beta$ function.


  The computation of the structured pseudospectral abscissa and radius (with
respect to the Frobenius norm) of a Toeplitz matrix is discussed and two
algorithms based on a low rank property to construct extremal perturbations are
presented. The algorithms are inspired by those considered in [SIAM J. Matrix
Anal. Appl., 32 (2011), pp. 1166-1192] for the unstructured case, but their
extension to structured pseudospectra and analysis presents several
difficulties. Natural generalizations of the algorithms, allowing to draw
significant sections of the structured pseudospectra in proximity of extremal
points are also discussed. Since no algorithms are available in the literature
to draw such structured pseudospectra, the approach we present seems promising
to extend existing software tools (Eigtool, Seigtool) to structured
pseudospectra representation for Toeplitz matrices. We discuss local
convergence properties of the algorithms and show some applications to a few
illustrative examples.


  The Leibniz bracket of an operator on a (graded) algebra is defined and some
of its properties are studied. A basic theorem relating the Leibniz bracket of
the commutator of two operators to the Leibniz bracket of them, is obtained.
Under some natural conditions, the Leibniz bracket gives rise to a (graded) Lie
algebra structure. In particular, those algebras generated by the Leibniz
bracket of the divergence and the Laplacian operators on the exterior algebra
are considered, and the expression of the Laplacian for the product of two
functions is generalized for arbitrary exterior forms.


  Machine learning (ML) models are increasingly used in various applications,
from recommendation systems in e-commerce to diagnosis prediction in
healthcare. In this paper, we present a novel dynamic framework for thinking
about the deployment of ML models in a performative, human-ML collaborative
system. In our framework, the introduction of ML recommendations changes the
data generating process of human decisions, which are only a proxy to the
ground truth and which are then used to train future versions of the model. We
show that this dynamic process in principle can converge to different stable
points, i.e. where the ML model and the Human+ML system have the same
performance. Some of these stable points are suboptimal with respect to the
actual ground truth. We conduct an empirical user study with 1,408 participants
to showcase this process. In the study, humans solve instances of the knapsack
problem with the help of machine learning predictions. This is an ideal setting
because we can see how ML models learn to imitate human decisions and how this
learning process converges to a stable point. We find that for many levels of
ML performance, humans can improve the ML predictions to dynamically reach an
equilibrium performance that is around 92% of the maximum knapsack value. We
also find that the equilibrium performance could be even higher if humans
rationally followed the ML recommendations. Finally, we test whether monetary
incentives can increase the quality of human decisions, but we fail to find any
positive effect. Our results have practical implications for the deployment of
ML models in contexts where human decisions may deviate from the indisputable
ground truth.


  Star formation and quenching are two of the most important processes in
galaxy formation and evolution. We explore in the local Universe the
interrelationships among key integrated galaxy properties, including stellar
mass $M_*$, star formation rate (SFR), specific SFR (sSFR), molecular gas mass
$M_{\rm H_2}$, star formation efficiency (SFE) of the molecular gas and
molecular gas to stellar mass ratio $\mu$. We aim to identify the most
fundamental scaling relations among these key galaxy properties and their
interrelationships. We show the integrated $M_{\rm H_2}$-SFR, SFR-$M_*$ and
$M_{\rm H_2}$-$M_*$ relation can be simply transformed from the $\mu$-sSFR,
SFE-$\mu$ and SFE-sSFR relation, respectively. The transformation, in
principle, can increase or decrease the scatter of each relation.
Interestingly, we find the latter three relations all have significantly
smaller scatter than the former three corresponding relations. We show the
probability to achieve the observed small scatter by accident is extremely
close to zero. This suggests that the smaller scatters of the latter three
relations are driven by a more fundamental physical connection among these
quantities. We then show the large scatters in the former relations are due to
their systematic dependence on other galaxy properties, and on star formation
and quenching process. We propose the sSFR-$\mu$-SFE relation as the
Fundamental Formation Relation (FFR), which governs the star formation and
quenching process, and provides a simple framework to study galaxy evolution.
Other scaling relations, including integrated Kennicutt-Schmidt law,
star-forming main sequence and molecular gas main sequence, can all be derived
from the FFR.


  In this paper, we display methods for the computation of convergence and
perturbation bounds for $M_t/M_t/1$ system with balking, catastrophes, server
failures and repairs. Based on the logarithmic norm of linear operators, the
bounds on the rate of convergence, perturbation bounds, and the main limiting
characteristics of the queue-length process are obtained. Finally, we consider
the application of all obtained estimates to a specific model.


  Radio emission from cosmic ray air showers has the potential to become an
additional, cost-effective observing technique for cosmic ray research, being
largely complementary to the well-established particle detector and air
fluorescence techniques. We present Monte Carlo simulatios of radio emission
from extensive air showers in the scheme of coherent geosynchrotron radiation
from electron-positron pairs gyrating in the earth's magnetic field.
Preliminary results of our simulations are the predicted frequency, primary
particle energy, shower zenith angle, shower azimuth angle and polarization
dependence of the radio emission. These properties can be directly related to
data measured by LOPES and other experiments.


  Recent Monte Carlo simulations of the critical point of the restricted
primitive model for ionic solutions are reported. Only the continuum version of
the model is considered. A finite size scaling analysis based in the
Bruce-Wilding procedure gives critical exponents in agreement with those of the
three-dimensional Ising universality class. An anomaly in the scaling of the
specific heat with system size is pointed out.


  Media with engineered magnetization are essential building blocks in
superconductivity, magnetism and magnon spintronics. However, the established
thin-film and lithographic techniques insufficiently suit the realization of
planar components with on-demand-tailored magnetization in the lateral
dimension. Here, we demonstrate the engineering of the magnetic properties of
CoFe-based nanodisks fabricated by the mask-less technique of focused electron
beam induced deposition (FEBID). The material composition in the nanodisks is
tuned \emph{in-situ} via the e-beam waiting time in the FEBID process and their
post-growth irradiation with Ga ions. The magnetization $M_s$ and exchange
stiffness $A$ of the disks are deduced from perpendicular ferromagnetic
resonance measurements. The achieved $M_s$ variation in the broad range from
$720$ emu/cm$^3$ to $1430$ emu/cm$^3$ continuously bridges the gap between the
$M_s$ values of such widely used magnonic materials as permalloy and CoFeB. The
presented approach paves a way towards nanoscale 2D and 3D systems with
controllable and space-varied magnetic properties.


  We carefully bootstrap the crossing kernels of Virasoro conformal blocks from
first principles. Our approach emphasizes the Hilbert space structure of the
space of Virasoro conformal blocks which makes the consistency of crossing
transformations obvious. We give a pedagogical explanation of the necessary
background about Virasoro conformal blocks and special functions. We also
explain several applications and prove new results about the crossing kernels.


  Network meta-analysis is an evidence synthesis method for comparative
effectiveness analyses of multiple available treatments. To justify evidence
synthesis, consistency is a relevant assumption; however, existing methods
founded on statistical testing possibly have substantial limitations of
statistical powers or several drawbacks in treating multi-arm studies. Besides,
inconsistency is theoretically explained as design-by-treatment interactions,
and the primary purpose of these analyses is prioritizing "designs" for further
investigations to explore sources of biases and irregular issues that might
influence the overall results. In this article, we propose an alternative
framework for inconsistency evaluations using influence diagnostic methods that
enable quantitative evaluations of the influences of individual designs to the
overall results. We provide four new methods to quantify the influences of
individual designs through a "leave-one-design-out" analysis framework. We also
propose a simple summary measure, the O-value, for prioritizing designs and
interpreting these influential analyses straightforwardly. Furthermore, we
propose another testing approach based on the leave-one-design-out analysis
framework. By applying the new methods to a network meta-analysis of
antihypertensive drugs, we demonstrate the new methods located potential
sources of inconsistency accurately. The proposed methods provide new insights
into alternatives to existing test-based methods, especially quantifications of
influences of individual designs on the overall network meta-analysis results.


  We generalize the Lagrangian of N = 1 supergravity (SUGRA) by using an
arbitrary parameter $\xi$, which corresponds to the inverse of Barbero's
parameter $\beta$. This generalized Lagrangian involves the chiral one as a
special case of the value $\xi = \pm i$. We show that the generalized
Lagrangian gives the canonical formulation of N = 1 SUGRA with the real
Ashtekar variable after the 3+1 decomposition of spacetime. This canonical
formulation is also derived from those of the usual N = 1 SUGRA by performing
Barbero's type canonical transformation with an arbitrary parameter $\beta
(=\xi^{-1})$. We give some comments on the canonical formulation of the theory.


  We study star cluster formation in a low-metallicity environment using three
dimensional hydrodynamic simulations. Starting from a turbulent cloud core, we
follow the formation and growth of protostellar systems with different
metallicities ranging from $10^{-6}$ to $0.1~Z_{\odot}$. The cooling induced by
dust grains promotes fragmentation at small scales and the formation of
low-mass stars with $M_{*} \sim 0.01$--$0.1~M_{\odot}$ when $Z/Z_{\odot}
\gtrsim 10^{-5}$. While the number of low-mass stars increases with
metallicity, the stellar mass distribution is still top-heavy for $Z/Z_{\odot}
\lesssim 10^{-2}$ compared to the Chabrier initial mass function (IMF). In
these cases, star formation begins after the turbulent motion decays and a
single massive cloud core monolithically collapses to form a central massive
stellar system. The circumstellar disk preferentially feeds the mass to the
central massive stars, making the mass distribution top-heavy. When
$Z/Z_{\odot}=0.1$, collisions of the turbulent flows promote the onset of the
star formation and a highly filamentary structure develops owing to efficient
fine-structure line cooling. In this case, the mass supply to the massive stars
is limited by the local gas reservoir and the mass is shared among the stars,
leading to a Chabrier-like IMF. We conclude that cooling at the scales of the
turbulent motion promotes the development of the filamentary structure and
works as an important factor leading to the present-day IMF.


  This paper introduces a network coding-based protection scheme against single
and multiple link failures. The proposed strategy ensures that in a connection,
each node receives two copies of the same data unit: one copy on the working
circuit, and a second copy that can be extracted from linear combinations of
data units transmitted on a shared protection path. This guarantees
instantaneous recovery of data units upon the failure of a working circuit. The
strategy can be implemented at an overlay layer, which makes its deployment
simple and scalable. While the proposed strategy is similar in spirit to the
work of Kamal '07 & '10, there are significant differences. In particular, it
provides protection against multiple link failures. The new scheme is simpler,
less expensive, and does not require the synchronization required by the
original scheme. The sharing of the protection circuit by a number of
connections is the key to the reduction of the cost of protection. The paper
also conducts a comparison of the cost of the proposed scheme to the 1+1 and
shared backup path protection (SBPP) strategies, and establishes the benefits
of our strategy.


  Vehicular Edge Clouds (VECs) is a new distributed processing paradigm that
exploits the revolution in the processing capabilities of vehicles to offer
energy efficient services and improved QoS. In this paper we tackle the problem
of processing allocation in a cloud-fog-VEC architecture by developing a joint
optimization Mixed Integer Linear Programming (MILP) model to minimize power
consumption, propagation delay, and queuing delay. The results show that while
VEC processing can reduce the power consumption and propagation delay, VEC
processing can increase the queuing delay because of the low data rate
connectivity between the vehicles and the data source nodes.


  Let G be a cocompact lattice in a virtually connected Lie group or the
fundamental group of a 3-manifold. We prove the K-theoretic Farrell-Jones
Conjecture (up to dimension one) and the L-theoretic Farrell-Jones Conjecture
for G, where we allow coefficients in additive G-categories with (involution).


  Vibrations appearance, either unstability system, is the result of the
dynamic interaction of the cutting process with the elastic system of machine
tools in various working conditions. Our objective is to develop an
experimental three-dimensional dynamic model in milling. Our purpose is to
applied this model to optimize the cutting parameters and to monitor cutting
process, milling tool and machine-tool. To reach the detailed knowledge of the
dynamic phenomena we divide our study into two parts : the machine and the
cutting process. The dynamic analysis of the machine is compulsory before
modelling the vibratory phenomena during the cutting. A dynamic analysis method
is developed to characterize completely the various machine tools components.


  We introduce a dependent Bayesian nonparametric model for the probabilistic
modeling of membership of subgroups in a community based on partially
replicated data. The focus here is on species-by-site data, i.e. community data
where observations at different sites are classified in distinct species. Our
aim is to study the impact of additional covariates, for instance environmental
variables, on the data structure, and in particular on the community diversity.
To that purpose, we introduce dependence a priori across the covariates, and
show that it improves posterior inference. We use a dependent version of the
Griffiths-Engen-McCloskey distribution defined via the stick-breaking
construction. This distribution is obtained by transforming a Gaussian process
whose covariance function controls the desired dependence. The resulting
posterior distribution is sampled by Markov chain Monte Carlo. We illustrate
the application of our model to a soil microbial dataset acquired across a
hydrocarbon contamination gradient at the site of a fuel spill in Antarctica.
This method allows for inference on a number of quantities of interest in
ecotoxicology, such as diversity or effective concentrations, and is broadly
applicable to the general problem of communities response to environmental
variables.


  We report our results on non-periodic experimental time series of pressure in
a spark ignition engine. The experiments were performed for a low rotational
velocity of a crankshaft and a relatively large spark advance angle. We show
that the combustion process has many chaotic features. Surprisingly, the
reconstructed attractor has a characteristic butterfly shape similar to a
chaotic attractor of Lorentz type. The suitable recurrence plot shows that the
dynamics of the combustion is a nonlinear multidimensional process mediated by
stochastic noise.


  Accurate fovea localization is essential for analyzing retinal diseases to
prevent irreversible vision loss. While current deep learning-based methods
outperform traditional ones, they still face challenges such as the lack of
local anatomical landmarks around the fovea, the inability to robustly handle
diseased retinal images, and the variations in image conditions. In this paper,
we propose a novel transformer-based architecture called DualStreamFoveaNet
(DSFN) for multi-cue fusion. This architecture explicitly incorporates
long-range connections and global features using retina and vessel
distributions for robust fovea localization. We introduce a spatial attention
mechanism in the dual-stream encoder to extract and fuse self-learned
anatomical information, focusing more on features distributed along blood
vessels and significantly reducing computational costs by decreasing token
numbers. Our extensive experiments show that the proposed architecture achieves
state-of-the-art performance on two public datasets and one large-scale private
dataset. Furthermore, we demonstrate that the DSFN is more robust on both
normal and diseased retina images and has better generalization capacity in
cross-dataset experiments.


  We show under general conditions that the linearized force-based
quasicontinuum (QCF) operator has a positive spectrum, which is identical to
the spectrum of the quasinonlocal quasicontinuum (QNL) operator in the case of
second-neighbour interactions. Moreover, we establish a bound on the condition
number of a matrix of eigenvectors that is uniform in the number of atoms and
the size of the atomistic region. These results establish the validity of and
improve upon recent conjectures ([arXiv:0907.3861, Conjecture 2] and
[arXiv:0910.2013, Conjecture 8]) which were based on numerical experiments.
  As immediate consequences of our results we obtain rigorous estimates for
convergence rates of (preconditioned) GMRES algorithms, as well as a new
stability estimate for the QCF method.


  We investigate the dynamical properties of the classical antiferromagnetic
Heisenberg model on the kagome lattice using a combination of Monte Carlo and
molecular dynamics simulations. We find that frustration induces a distribution
of timescales in the cooperative paramagnetic regime (i.e. far above the onset
of coplanarity), as recently reported experimentally in deuterium jarosite. At
lower temperature, when the coplanar correlations are well established, we show
that the weath- ervane loop fluctuations control the system relaxation : the
time distribution observed at higher temperatures splits into two distinct
timescales associated with fluctuations in the plane and out of the plane of
coplanarity. The temperature and wave vector dependences of these two
components are qualitatively consistent with loops diffusing in the
entropically dominated free energy landscape. Numerical results are discussed
and compared with the $O(N)$ model and recent experiments for both classical
and quantum realizations of the kagome magnets.


  We introduce a U(1) lattice gauge theory which incorporates explicit
frustration in $d>2$. We show, by identifying an appropiate order parameter and
through computer simulations, the existence of a frustrated region in the phase
diagram of the model. We study this phase diagram and the nature of the
transition lines.


  We present the results of an analysis of the large angular scale distribution
of the arrival directions of cosmic rays with energy above 4 EeV detected at
the Pierre Auger Observatory including for the first time events with zenith
angle between $60^\circ$ and $80^\circ$. We perform two Rayleigh analyses, one
in the right ascension and one in the azimuth angle distributions, that are
sensitive to modulations in right ascension and declination, respectively. The
largest departure from isotropy appears in the $E > 8$ EeV energy bin, with an
amplitude for the first harmonic in right ascension $r_1^\alpha =(4.4 \pm
1.0){\times}10^{-2}$, that has a chance probability $P(\ge
r_1^\alpha)=6.4{\times}10^{-5}$, reinforcing the hint previously reported with
vertical events alone.


  Scattering of the cosmic microwave background (CMB) in clusters of galaxies
polarizes the radiation. We explore several polarization components which have
their origin in the kinematic quadrupole moments induced by the motion of the
scattering electrons, either directed or random. Polarization levels and
patterns are determined in a cluster simulated by the hydrodynamical Enzo code.
We find that polarization signals can be as high as $\sim 1 \mu$K, a level that
may be detectable by upcoming CMB experiments.


  Tries are among the most versatile and widely used data structures on words.
They are pertinent to the (internal) structure of (stored) words and several
splitting procedures used in diverse contexts ranging from document taxonomy to
IP addresses lookup, from data compression (i.e., Lempel-Ziv'77 scheme) to
dynamic hashing, from partial-match queries to speech recognition, from leader
election algorithms to distributed hashing tables and graph compression. While
the performance of tries under a realistic probabilistic model is of
significant importance, its analysis, even for simplest memoryless sources, has
proved difficult. Rigorous findings about inherently complex parameters were
rarely analyzed (with a few notable exceptions) under more realistic models of
string generations. In this paper we meet these challenges: By a novel use of
the contraction method combined with analytic techniques we prove a central
limit theorem for the external path length of a trie under a general Markov
source. In particular, our results apply to the Lempel-Ziv'77 code. We envision
that the methods described here will have further applications to other trie
parameters and data structures.


  Let $p_n$ be the $n$th prime, and consider the sequence $s_n = (2\cdot3\cdots
p_n)^{1/n} = (p_n\#)^{1/n}$, the geometric mean of the first $n$ primes. We
give a short proof that $p_n/s_n \to e$, a result conjectured by Vrba (2010)
and proved by Sandor and Verroken (2011). We show that $p_n/s_n = \exp(1+1/\log
p_n + O(1/\log^2 p_n))$ as $n\to\infty$, and give explicit lower and upper
bounds for the $O(1/\log^2 p_n)$ term.


  We present a brief synopsis of related work (gr-qc/0007039), describing a
study of black hole threshold phenomena for a self-gravitating, massive complex
scalar field in spherical symmetry. We construct Type I critical solutions
dynamically by tuning a one-parameter family of initial data consisting of a
boson star and a massless real scalar field, and numerically evolving this
data. The resulting critical solutions appear to correspond to boson stars on
the unstable branch, as we show via comparisons between our simulations and
perturbation theory. For low-mass critical solutions, we find small ``halos''
of matter in the tails of the solutions, and these distort the profiles which
otherwise agree with unstable boson stars. These halos seem to be artifacts of
the collisions between the original boson stars and the massless fields, and do
not appear to belong to the true critical solutions. From this study, it
appears that unstable boson stars are unstable to dispersal (``explosion'') in
addition to black hole formation. Given the similarities in macroscopic
stability between boson stars and neutron stars, we suggest that similar
phenomena could occur in models of neutron stars.


  The problem of target localization with noise is addressed. The target is a
sample from a continuous random variable with known distribution and the goal
is to locate it with minimum mean squared error distortion. The localization
scheme or policy proceeds by queries, or questions, weather or not the target
belongs to some subset as it is addressed in the 20-question framework. These
subsets are not constrained to be intervals and the answers to the queries are
noisy. While this situation is well studied for adaptive querying, this paper
is focused on the non adaptive querying policies based on dyadic questions. The
asymptotic minimum achievable distortion under such policies is derived.
Furthermore, a policy named the Aurelian1 is exhibited which achieves
asymptotically this distortion.


  With the aim to get an insight in the origin of differences in the earlier
reported calculation results for KNbO3 and to test the recently proposed
implementation of the FP-LMTO method by Methfessel and van Schilfgaarde, we
perform a comparative study of the ferroelectric instability in KNbO3 by
FP-LMTO and LAPW methods. It is shown that a high precision in the description
of the charge density variations over the interstitial region in perovskite
materials is essential; the technical limitations of the accuracy of
charge-density description apparently accounted for previously reported slight
disagreement with the LAPW results. With more accurate description of the
charge density by sufficiently fine real-space grid, the results obtained by
both methods became almost identical.
  In order to extract additional information (beyond the harmonic
approximation) from the total energy fit obtainable in total-energy
calculations, a scheme is proposed to solve the multidimensional vibrational
Schroedinger equation in the model of non-interacting anharmonic oscillators
via the expansion in hyperspherical harmonics.


  The size distribution and orbital architecture of dust, grains, boulders,
asteroids, and major planets during the giant branch phases of evolution
dictate the preponderance and observability of the eventual debris, which have
been found to surround white dwarfs and pollute their atmospheres with metals.
Here, we utilize the photogravitational planar restricted three-body problem in
one-planet giant branch systems in order to characterize the orbits of grains
as the parent star luminosity and mass undergo drastic changes. We perform a
detailed dynamical analysis of the character of grain orbits (collisional,
escape, or bounded) as a function of location and energy throughout giant
branch evolution. We find that for stars with main-sequence masses of
$2.0M_{\odot}$, giant branch evolution, combined with the presence of a planet,
ubiquitously triggers escape in grains smaller than about 1 mm, while leaving
grains larger than about 5 cm bound to the star. This result is applicable for
systems with either a terrestrial or giant planet, is largely independent of
the location of the planet, and helps establish a radiative size threshold for
escape of small particles in giant branch planetary systems.


  In our preceding paper, we have proposed an algorithm for obtaining
finite-norm solutions of higher-order linear ordinary differential equations of
the Fuchsian type [\sum_m p_m (x) (d/dx)^m] f(x) = 0 (where p_m is a polynomial
with rational-number-valued coefficients), by using only the four arithmetical
operations on integers, and we proved its validity. For any nonnegative integer
k, it is guaranteed mathematically that this method can produce all the
solutions satisfying \int |f(x)|^2 (x^2+1)^k dx < \infty, under some
conditions. We materialize this algorithm in practical procedures. An
interger-type quasi-orthogonalization used there can suppress the explosion of
calculations. Moreover, we give an upper limit of the errors. We also give some
results of numerical experiments and compare them with the corresponding exact
analytical solutions, which show that the proposed algorithm is successful in
yielding solutions with high accuracy (using only arithmetical operations on
integers).


  The solution of the wave equation in the envelope approximation with temporal
corrections for a laser pulse propagating in a medium where the Kerr effect,
field ionization, and associated absorption take place, is obtained through a
first-order perturbative approach. The closed-form expressions so obtained
clarify the influence of the various terms of the equation on the laser
amplitude and on the frequency generation as a function of the retarded time.
Furthermore, they allow extracting scaling parameters which size the nonlinear
effects. The results are illustrated quantitatively on the case of a
femtosecond pulse focused in the air with typical parameters.


  We describe the algorithms used in the Matlab continuation and bifurcation
package pde2path for Hopf bifurcation and continuation of branches of periodic
orbits in systems of PDEs in 1, 2, and 3 spatial dimensions, including the
computation of Floquet multipliers. We first test the methods on three reaction
diffusion examples, namely a complex Ginzburg-Landau equation as a toy problem,
a reaction diffusion system on a disk with rotational waves including stable
(anti) spirals bifurcating out of the trivial solution, and a Brusselator
system with interaction of Turing and Turing-Hopf bifurcations. Then we
consider a system from distributed optimal control, which is ill-posed as an
initial value problem and thus needs a particularly stable method for computing
Floquet multipliers, for which we use a periodic Schur decomposition. The
implementation details how to use pde2path on these problems are given in an
accompanying tutorial, which, together with all other downloads (function
libraries, demos and further documentation) can be found at
http://www.staff.uni-oldenburg.de/hannes.uecker/pde2path.


  We address the problem of optimal path planning for a simple nonholonomic
vehicle in the presence of obstacles. Most current approaches are either split
hierarchically into global path planning and local collision avoidance, or
neglect some of the ambient geometry by assuming the car is a point mass. We
present a Hamilton-Jacobi formulation of the problem that resolves time-optimal
paths and considers the geometry of the vehicle.


  We consider a two dimensional quantum Hamiltonian separable in Cartesian
coordinates and allowing a fifth-order integral of motion. We impose the
superintegrablity condition and find all doubly exotic superintegrable
potentials (i.e potentials V (x, y) = V_1(x)+V_2(y) where neither V_1(x) nor
V_2(y) satisfy a linear ODE) allowing the existence of such an integral. All of
these potentials are found to have the Painlev\'e property. Most of them are
expressed in terms of known Painlev\'e transcendents or elliptic functions but
some may represent new higher order Painlev\'e transcendents.


  Zero shot learning (ZSL) has seen a surge in interest over the decade for its
tight links with the mechanism making young children recognize novel objects.
Although different paradigms of visual semantic embedding models are designed
to align visual features and distributed word representations, it is unclear to
what extent current ZSL models encode semantic information from distributed
word representations. In this work, we introduce the split of tiered-ImageNet
to the ZSL task, in order to avoid the structural flaws in the standard
ImageNet benchmark. We build a unified framework for ZSL with contrastive
learning as pre-training, which guarantees no semantic information leakage and
encourages linearly separable visual features. Our work makes it fair for
evaluating visual semantic embedding models on a ZSL setting in which semantic
inference is decisive. With this framework, we show that current ZSL models
struggle with encoding semantic relationships from word analogy and word
hierarchy. Our analyses provide motivation for exploring the role of context
language representations in ZSL tasks.


  In order to apply Optical Character Recognition (OCR) to historical printings
of Latin script fully automatically, we report on our efforts to construct a
widely-applicable polyfont recognition model yielding text with a Character
Error Rate (CER) around 2% when applied out-of-the-box. Moreover, we show how
this model can be further finetuned to specific classes of printings with
little manual and computational effort. The mixed or polyfont model is trained
on a wide variety of materials, in terms of age (from the 15th to the 19th
century), typography (various types of Fraktur and Antiqua), and languages
(among others, German, Latin, and French). To optimize the results we combined
established techniques of OCR training like pretraining, data augmentation, and
voting. In addition, we used various preprocessing methods to enrich the
training data and obtain more robust models. We also implemented a two-stage
approach which first trains on all available, considerably unbalanced data and
then refines the output by training on a selected more balanced subset.
Evaluations on 29 previously unseen books resulted in a CER of 1.73%,
outperforming a widely used standard model with a CER of 2.84% by almost 40%.
Training a more specialized model for some unseen Early Modern Latin books
starting from our mixed model led to a CER of 1.47%, an improvement of up to
50% compared to training from scratch and up to 30% compared to training from
the aforementioned standard model. Our new mixed model is made openly available
to the community.


  We consider the description of the fractal media that uses the fractional
integrals. We derive the fractional generalizations of the equation that
defines the medium mass. We prove that the fractional integrals can be used to
describe the media with noninteger mass dimensions. The fractional equation of
continuity is considered.


  This paper presents a novel approach for deciding on the appropriateness or
not of an acquired fingerprint image into a given database. The process begins
with the assembly of a training base in an image space constructed by combining
Principal Component Analysis (PCA) and edge detection. Then, the parameter H, a
new feature that helps in the decision making about the relevance of a
fingerprint image in databases, is derived from a relationship between
Euclidean and Mahalanobian distances. This procedure ends with the lifting of
the curve of the Receiver Operating Characteristic (ROC), where the thresholds
defined on the parameter H are chosen according to the acceptable rates of
false positives and false negatives.


  This is a presentation of recent work on quantum permutation groups.
Contains: a short introduction to operator algebras and Hopf algebras; quantum
permutation groups, and their basic properties; diagrams, integration formulae,
asymptotic laws, matrix models; the hyperoctahedral quantum group, free wreath
products, quantum automorphism groups of finite graphs, graphs having no
quantum symmetry; complex Hadamard matrices, cocycle twists of the symmetric
group, quantum groups acting on 4 points; remarks and comments.


  We study the Lie and Noether point symmetries of a class of systems of
second-order differential equations with $n$ independent and $m$ dependent
variables ($n\times m$ systems). We solve the symmetry conditions in a
geometric way and determine the general form of the symmetry vector and of the
Noetherian conservation laws. We prove that the point symmetries are generated
by the collineations of two (pseudo)metrics, which are defined in the spaces of
independent and dependent variables. We demonstrate the general results in two
special cases (a) a system of $m$ coupled Laplace equations and (b) the
Klein-Gordon equation of a particle in the context of Generalized Uncertainty
Principle. In the second case we determine the complete invariant group of
point transformations, and we apply the Lie invariants in order to find
invariant solutions of the wave function for a spin-$0$ particle in the two
dimensional hyperbolic space.


  Recent developments in the evaluation of vector-meson spectral functions in
hot and dense matter are discussed with emphasis on connections to the chiral
phase transition in QCD. Model independent approaches including chiral
low-density expansions, lattice QCD, chiral and QCD sum rules are put into
context with model predictions for in-medium vector-spectral function utilizing
effective Lagrangians. Hadronic many-body calculations predict a strong
broadening (and little mass shift) of the $\rho$ spectral function which
rapidly increases close to the expected phase boundary of hadronic and
quark-gluon matter. Pertinent dilepton rates appear to degenerate with
perturbative quark-antiquark annihilation in the Quark-Gluon Plasma, suggestive
for chiral symmetry restoration. Applications to low-mass dilepton spectra in
heavy-ion collisions result in quantitative agreement with recent high-quality
data at the CERN-SPS. Thermal radiation from temperatures around $T_c$
consistently reproduces the experimental dilepton excess observed at masses
above 1 GeV as well. The interpretation of dilepton sources at high transverse
momentum appears to be more involved.


  We estimate the power spectra of CMB temperature anisotropy in localized
regions on the sky using the WMAP 7-year data. Here, we report that the north
hat and the south hat regions at the high Galactic latitude (|b| >= 30 deg)
show anomaly in the power spectrum amplitude around the third peak, which is
statistically significant up to 3 sigma. We try to figure out the cause of the
observed anomaly by analyzing the low Galactic latitude (|b|< 30 deg) regions
where the galaxy contamination is expected to be stronger, and regions that are
weakly or strongly dominated by the WMAP instrument noise. We also consider the
possible effect of unresolved radio point sources. We found another but less
statistically significant anomaly in the low Galactic latitude north and south
regions whose behavior is opposite to the one at the high latitude. Our
analysis shows that the observed north-south anomaly at high latitude becomes
weaker on the regions with high number of observations (weak instrument noise),
suggesting that the anomaly is significant at sky regions that are dominated by
the WMAP instrument noise. We have checked that the observed north-south
anomaly has weak dependences on the bin-width used in the power spectrum
estimation and the Galactic latitude cut. We have also discussed the
possibility that the detected anomaly may hinge on the particular choice of the
multipole bin around the third peak. We anticipate that the issue of whether
the anomaly is intrinsic one or due to the WMAP instrument noise will be
resolved by the forthcoming Planck data.


  The new wave of Large Language Models (LLM) has offered an efficient tool to
curate sizeable conversational datasets. So far studies have mainly focused on
task-oriented or generic open-domain dialogs, and have not fully explored the
ability of LLMs in following complicated prompts. In this work, we focus on
personalization, and employ LLMs to curate a dataset which is difficult and
costly to crowd-source: PersonalityChat is a synthetic conversational dataset
based upon the popular PersonaChat dataset, but conditioned on both personas
and (Big-5) personality traits. Evaluating models fine-tuned on this dataset,
we show that the personality trait labels can be used for trait-based
personalization of generative dialogue models. We also perform a head-to-head
comparison between PersonalityChat and PersonaChat, and show that training on
the distilled dataset results in more fluent and coherent dialog agents in the
small-model regime.


  Scanning nano-beam electron diffraction with a pixelated detector was
employed to investigate the orientation relationship of nanometer sized,
irradiation induced G-phase (M$_6$Ni$_{16}$Si$_{7}$) precipitates in an
austenite matrix. Using this detector, the faint diffraction spots originating
from the small G-phase particles could be resolved simultaneously as the
intense matrix reflections. The diffraction patterns were analyzed using a
two-stage template matching scheme, whereby the matrix is indexed first and the
precipitates are indexed second after subtraction of the matrix contribution to
the diffraction patterns. The results show that G-phase forms with orientation
relationships relative to austenite that are characteristic of face-centered
cubic (FCC) to body-centered cubic (BCC) transformations. This work
demonstrates that nano-beam electron diffraction with a pixelated detector is a
promising technique to investigate orientation relationships of nano-sized
precipitates with complex crystal structures in other material systems with
relative ease.


  We propose that the bimodal nature of the kick velocity distribution of radio
pulsars is connected with the dichotomy between hadronic stars ({\it i.e.}
neutron stars with no quark matter content) and quark stars. Bimodality can
appear due to different mechanisms of explosion which leads to the formation of
two types of compact stars or due to two different sets of parameters mastering
a particular kick mechanism. The low velocity maximum (at $\sim 100$ km
s$^{-1}$) is connected with hadronic star formation, whereas the second peak
corresponds to quark stars. In the model of delayed collapse of hadronic stars
to quark stars (Berezhiani et al. 2003\nocite{bbd2003}) quark deconfinement
leads to a second energy release, and to a second kick, in addition to the kick
imparted to the newly formed hadronic star during the supernova explosion. If
the electromagnetic rocket mechanism can give a significant contribution to
pulsar kicks, then the high velocity peak can be connected with the shorter
initial spin periods of quark stars with respect to hadronic stars. We discuss
{\it pro et contra} of these scenarios.


  Light field (LF) cameras record both intensity and directions of light rays,
and capture scenes from a number of viewpoints. Both information within each
perspective (i.e., spatial information) and among different perspectives (i.e.,
angular information) is beneficial to image super-resolution (SR). In this
paper, we propose a spatial-angular interactive network (namely, LF-InterNet)
for LF image SR. Specifically, spatial and angular features are first
separately extracted from input LFs, and then repetitively interacted to
progressively incorporate spatial and angular information. Finally, the
interacted features are fused to superresolve each sub-aperture image.
Experimental results demonstrate the superiority of LF-InterNet over the
state-of-the-art methods, i.e., our method can achieve high PSNR and SSIM
scores with low computational cost, and recover faithful details in the
reconstructed images.


  In this paper we are concerned with the analysis of heavy-tailed data when a
portion of the extreme values is unavailable. This research was motivated by an
analysis of the degree distributions in a large social network. The degree
distributions of such networks tend to have power law behavior in the tails. We
focus on the Hill estimator, which plays a starring role in heavy-tailed
modeling. The Hill estimator for this data exhibited a smooth and increasing
"sample path" as a function of the number of upper order statistics used in
constructing the estimator. This behavior became more apparent as we
artificially removed more of the upper order statistics. Building on this
observation we introduce a new version of the Hill estimator. It is a function
of the number of the upper order statistics used in the estimation, but also
depends on the number of unavailable extreme values. We establish functional
convergence of the normalized Hill estimator to a Gaussian process. An
estimation procedure is developed based on the limit theory to estimate the
number of missing extremes and extreme value parameters including the tail
index and the bias of Hill's estimator. We illustrate how this approach works
in both simulations and real data examples.


  Interactive segmentation allows users to extract target masks by making
positive/negative clicks. Although explored by many previous works, there is
still a gap between academic approaches and industrial needs: first, existing
models are not efficient enough to work on low power devices; second, they
perform poorly when used to refine preexisting masks as they could not avoid
destroying the correct part. FocalClick solves both issues at once by
predicting and updating the mask in localized areas. For higher efficiency, we
decompose the slow prediction on the entire image into two fast inferences on
small crops: a coarse segmentation on the Target Crop, and a local refinement
on the Focus Crop. To make the model work with preexisting masks, we formulate
a sub-task termed Interactive Mask Correction, and propose Progressive Merge as
the solution. Progressive Merge exploits morphological information to decide
where to preserve and where to update, enabling users to refine any preexisting
mask effectively. FocalClick achieves competitive results against SOTA methods
with significantly smaller FLOPs. It also shows significant superiority when
making corrections on preexisting masks. Code and data will be released at
github.com/XavierCHEN34/ClickSEG


  Sparse Gaussian Processes are a key component of high-throughput Bayesian
Optimisation (BO) loops; however, we show that existing methods for allocating
their inducing points severely hamper optimisation performance. By exploiting
the quality-diversity decomposition of Determinantal Point Processes, we
propose the first inducing point allocation strategy designed specifically for
use in BO. Unlike existing methods which seek only to reduce global uncertainty
in the objective function, our approach provides the local high-fidelity
modelling of promising regions required for precise optimisation. More
generally, we demonstrate that our proposed framework provides a flexible way
to allocate modelling capacity in sparse models and so is suitable broad range
of downstream sequential decision making tasks.


  Code LLMs are being rapidly deployed and there is evidence that they can make
professional programmers more productive. Current benchmarks for code
generation measure whether models generate correct programs given an expert
prompt. In this paper, we present a new benchmark containing multiple prompts
per problem, written by a specific population of non-expert prompters:
beginning programmers. StudentEval contains 1,749 prompts for 48 problems,
written by 80 students who have only completed one semester of Python
programming. Our students wrote these prompts while working interactively with
a Code LLM, and we observed very mixed success rates. We use StudentEval to
evaluate 5 Code LLMs and find that StudentEval is a better discriminator of
model performance than existing benchmarks. We analyze the prompts and find
significant variation in students' prompting techniques. We also find that
nondeterministic LLM sampling could mislead students into thinking that their
prompts are more (or less) effective than they actually are, which has
implications for how to teach with Code LLMs.


  Magnetic induction in magnetohydrodynamic fluids at magnetic Reynolds number
(Rm) less than~1 has long been known to cause magnetic drag. Here, we show that
when $\mathrm{Rm} \gg 1$ and the fluid is in a hydrodynamic-dominated regime in
which the magnetic energy is much smaller than the kinetic energy, induction
due to a mean shear flow leads to a magnetic eddy viscosity. The magnetic
viscosity is derived from simple physical arguments, where a coherent response
due to shear flow builds up in the magnetic field until decorrelated by
turbulent motion. The dynamic viscosity coefficient is approximately
$(B_p^2/2\mu_0) \tau_{\rm corr}$, the poloidal magnetic energy density
multiplied by the correlation time. We confirm the magnetic eddy viscosity
through numerical simulations of two-dimensional incompressible
magnetohydrodynamics. We also consider the three-dimensional case, and in
cylindrical or spherical geometry, theoretical considerations similarly point
to a nonzero viscosity whenever there is differential rotation. Hence, these
results serve as a dynamical generalization of Ferraro's law of isorotation.
The magnetic eddy viscosity leads to transport of angular momentum and may be
of importance to zonal flows in astrophysical domains such as the interior of
some gas giants.


  In this paper, we derive the capacity of a special class of mesh networks. A
mesh network is defined as a heterogeneous wireless network in which the
transmission among power limited nodes is assisted by powerful relays, which
use the same wireless medium. We find the capacity of the mesh network when
there is one source, one destination, and multiple relays. We call this channel
the single source multiple relay single destination (SSMRSD) mesh network. Our
approach is as follows. We first look at an upper bound on the information
theoretic capacity of these networks in the Gaussian setting. We then show that
the bound is achievable asymptotically using the compress-forward strategy for
the multiple relay channel. Theoretically, the results indicate the value of
cooperation and the utility of carefully deployed relays in wireless ad-hoc and
sensor networks. The capacity characterization quantifies how the relays can be
used to either conserve node energy or to increase transmission rate.


  The size and density of dust grains determine their response to gas drag in
protoplanetary discs. Aerodynamical (size x density) sorting is one of the
proposed mechanisms to explain the grain properties and chemical fractionation
of chondrites. However, the efficiency of aerodynamical sorting and the
location in the disc in which it could occur are still unknown. Although the
effects of grain sizes and growth in discs have been widely studied, a
simultaneous analysis including dust composition is missing. In this work we
present the dynamical evolution and growth of multicomponent dust in a
protoplanetary disc using a 3D, two-fluid (gas+dust) Smoothed Particle
Hydrodynamics (SPH) code. We find that the dust vertical settling is
characterised by two phases: a density-driven phase which leads to a vertical
chemical sorting of dust and a size-driven phase which enhances the amount of
lighter material in the midplane. We also see an efficient radial chemical
sorting of the dust at large scales. We find that dust particles are
aerodynamically sorted in the inner disc. The disc becomes sub-solar in its
Fe/Si ratio on the surface since the early stage of evolution but sub-solar
Fe/Si can be also found in the outer disc-midplane at late stages. Aggregates
in the disc mimic the physical and chemical properties of chondrites,
suggesting that aerodynamical sorting played an important role in determining
their final structure.


  We consider, and make precise, a certain extension of the Radon-Nikodym
derivative operator, to functions which are additive, but not necessarily
sigma-additive, on a subset of a given sigma-algebra. We give applications to
probability theory; in particular, to the study of $\mu$-Brownian motion, to
stochastic calculus via generalized It\^o-integrals, and their adjoints (in the
form of generalized stochastic derivatives), to systems of transition
probability operators indexed by families of measures $\mu$, and to adjoints of
composition operators.


  Anomalous couplings of the $Z$ boson to top quarks are only marginally
constrained by direct searches and are still sensitive to new particle dynamics
at the TeV scale. Employing an effective field theory approach we consider the
dimension-six operators which generate deviations from the standard-model
vector and axial-vector interactions. We show that rare $B$ and $K$ meson
decays together with electroweak precision observables provide strong
constraints on these couplings. We also consider constraints from t-channel
single-top production.


  We improve the entropic uncertainty relations for position and momentum
coarse-grained measurements. We derive the continuous, coarse-grained
counterparts of the discrete uncertainty relations based on the concept of
majorization. The obtained entropic inequalities involve two R\'enyi entropies
of the same order, and thus go beyond the standard scenario with conjugated
parameters. In a special case describing the sum of two Shannon entropies the
majorization-based bounds significantly outperform the currently known results
in the regime of larger coarse graining, and might thus be useful for
entanglement detection in continuous variables.


  The classical problem of the flow over a circular cylinder at Reynolds number
40 is considered using an accurate pseudo-spectral code. A new set of boundary
conditions is proposed to improve the representation of the infinite flow
domain, especially in the far wake area. It is shown that the resulting
accuracy of the computed flow allows its use as a reference solution for code
validation. This reference solution is reachable at any location up to 50
cylinder diameters far from the cylinder centre through spectral interpolation
with a user-friendly script provided in appendix. It is shown how this solution
offers the opportunity to perform a convergence study and to investigate the
spatial distribution of numerical errors. The main goal of this study is to
propose this reference solution as an helpful tool for numerical validation and
development, especially for the improvement of immersed boundary methods toward
high-order accuracy.


  Human activity recognition (HAR) using ambient sensors in smart homes has
numerous applications for human healthcare and wellness. However, building
general-purpose HAR models that can be deployed to new smart home environments
requires a significant amount of annotated sensor data and training overhead.
Most smart homes vary significantly in their layouts, i.e., floor plans and the
specifics of sensors embedded, resulting in low generalizability of HAR models
trained for specific homes. We address this limitation by introducing a novel,
layout-agnostic modeling approach for HAR systems in smart homes that utilizes
the transferrable representational capacity of natural language descriptions of
raw sensor data. To this end, we generate Textual Descriptions Of Sensor
Triggers (TDOST) that encapsulate the surrounding trigger conditions and
provide cues for underlying activities to the activity recognition models.
Leveraging textual embeddings, rather than raw sensor data, we create activity
recognition systems that predict standard activities across homes without
either (re-)training or adaptation on target homes. Through an extensive
evaluation, we demonstrate the effectiveness of TDOST-based models in unseen
smart homes through experiments on benchmarked CASAS datasets. Furthermore, we
conduct a detailed analysis of how the individual components of our approach
affect downstream activity recognition performance.


  The first direct detection of gravitational waves from binary neutron stars
on the 17th of August, 2017, (GW170817) heralded the arrival of a new messenger
for probing neutron star astrophysics and provided the first constraints on
neutron star equation of state from gravitational wave observations.
Significant computational effort was expended to obtain these first results and
therefore, as observations of binary neutron star coalescence become more
routine in the coming observing runs, there is a need to improve the analysis
speed and flexibility. Here, we present a rapid approach for inferring the
neutron star equation of state based on Normalising Flows. As a demonstration,
using the same input data, our approach, ASTREOS, produces results consistent
with those presented by the LIGO-Virgo collaboration but requires < 1 sec to
generate neutron star equation of state confidence intervals. Furthermore,
ASTREOS allows for non-parametric equation of state inference. This rapid
analysis will not only facilitate neutron star equation of state studies but
can potentially enhance future alerts for electromagnetic follow-up
observations of binary neutron star mergers.


  The realizations of the basic representation of $\widehat\mathfrak{gl}_r$ are
known to be parametrized by partitions of r and have an explicit description in
terms of vertex operators on the bosonic/fermionic Fock space. In this paper,
we give a geometric interpretation of these realizations in terms of geometric
operators acting on the equivariant cohomology of certain Nakajima quiver
varieties.


  Red clump stars (RCs) are useful tracers of distances, extinction, chemical
abundances, and Galactic structures and kinematics. Accurate estimation of the
RC parameters -- absolute magnitude and intrinsic color -- is the basis for
obtaining high-precision RC distances. By combining astrometric data from Gaia,
spectroscopic data from APOGEE and LAMOST, and multi-band photometric data from
Gaia, APASS, Pan-STARRS1, 2MASS, and WISE surveys, we use the Gaussian process
regression to train machine learners to derive the multi-band absolute
magnitudes $M_\lambda$ and intrinsic colors $(\lambda_1-\lambda_2)_0$ for each
spectral RC. The dependence of $M_\lambda$ on metallicity decreases from
optical to infrared bands, while the dependence of $M_\lambda$ on age is
relatively similar in each band. $(\lambda_1-\lambda_2)_0$ are more affected by
metallicity than age. The RC parameters are not suitable to be represented by
simple constants but are related to the Galactic stellar population structure.
By analyzing the variation of $M_\lambda$ and $(\lambda_1-\lambda_2)_0$ in the
spatial distribution, we construct $(R, z)$ dependent maps of mean absolute
magnitudes and mean intrinsic colors of the Galactic RCs. Through external and
internal validation, we find that using three-dimensional (3D) parameter maps
to determine RC parameters avoids systematic bias and reduces dispersion by
about 20% compared to using constant parameters. Based on Gaia's EDR3 parallax,
our 3D parameter maps, and extinction-distance profile selection, we obtain a
photometric RC sample containing 11 million stars with distance and extinction
measurements.


  We investigate the synchronization properties of the two-dimensional periodic
flow over a circular cylinder using the principles of phase-reduction theory.
The influence of harmonic external forcings on the wake dynamics, and the
possible synchronization of the vortex shedding behind the cylinder to these
forcings, is determined by evaluating the phase response of the system to weak
impulse perturbations. These horizontal and vertical perturbations are added at
different phase values over a period, in order to develop a linear
one-dimensional model with respect to the limit cycle that describes the
high-dimensional and nonlinear dynamics of the fluid flow via only a single
scalar phase variable. This model is then utilized to acquire the theoretical
conditions for the synchronization between the cylinder wake and the harmonic
forcings added in the global near-wake region. Valuable insights are gained by
comparing the findings of the present research against those rendered by the
dynamic mode decomposition and adjoint analysis of the wake dynamics in earlier
works. The present analysis reveals regions in the flow which enable phase
synchronization or desynchronization to periodic excitations for applications
such as active flow control and fluid-structure interactions.


  For many wiretap channel models asymptotically optimal coding schemes are
known, but less effort has been put into actual realizations of wiretap codes
for practical parameters. Bounds on the mutual information and error
probability when using coset coding on a Rayleigh fading channel were recently
established by Oggier and Belfiore, and the results in this paper build on
their work. However, instead of using their ultimate inverse norm sum
approximation, a more precise expression for the eavesdropper's probability of
correct decision is used in order to determine a general class of good coset
codes. The code constructions are based on well-rounded lattices arising from
simple geometric criteria. In addition to new coset codes and simulation
results, novel number-theoretic results on well-rounded ideal lattices are
presented.


  The gradient flow renormalized coupling offers a simple and relatively
inexpensive way to calculate the step scaling function and the lattice scale,
but both applications can be hindered by large lattice artifacts. Recently we
introduced an empirical non-perturbative improvement that can reduce, even
remove $\mathcal{O}(a^2)$ lattice artifacts. The method is easy to implement
and can be applied to any lattice gauge theory of interest both in step scaling
studies and for scale setting. In this talk I will briefly review this
improvement method and discuss its application for determining the discrete
$\beta$ function of the 8 and 12 flavor SU(3) systems and for improved scale
setting in 2+1+1 flavor QCD


  Efficient navigation through uneven terrain remains a challenging endeavor
for autonomous robots. We propose a new geometric-based uneven terrain mapless
navigation framework combining a Sparse Gaussian Process (SGP) local map with a
Rapidly-Exploring Random Tree* (RRT*) planner. Our approach begins with the
generation of a high-resolution SGP local map, providing an interpolated
representation of the robot's immediate environment. This map captures crucial
environmental variations, including height, uncertainties, and slope
characteristics. Subsequently, we construct a traversability map based on the
SGP representation to guide our planning process. The RRT* planner efficiently
generates real-time navigation paths, avoiding untraversable terrain in pursuit
of the goal. This combination of SGP-based terrain interpretation and RRT*
planning enables ground robots to safely navigate environments with varying
elevations and steep obstacles. We evaluate the performance of our proposed
approach through robust simulation testing, highlighting its effectiveness in
achieving safe and efficient navigation compared to existing methods.


  Earth-based observations are complicated by the opacity of Earth's ionosphere
at very low frequencies and strong man-made radio frequency interference. This
explains long standing interest in building a low frequency radio telescope on
the farside of the Moon. Experience from ground-based observations near the
ionospheric cutoff in dealing with the interference, ionosphere, and wide-field
imaging/dynamic range problems provides crucial information for future
radioastronomic experiments on the Moon. In this purpose we observed
non-intensive solar bursts on the example of solar drift pairs (DP) at
decameter-meter wavelengths with large and small arrays as well as by a single
crossed active dipole. We used the large Ukrainian radio telescope UTR-2, the
URAN-2 array, a subarray of the Giant Ukrainian radio telescope (GURT) and a
single crossed active dipole to get the spectral properties of radio bursts at
the frequency range of 8-80 MHz during solar observations on July 12, 2017.
Statistical analysis of upper and lower frequencies, at which DPs are recorded,
shows that the occurrence of forward DPs is more preferable at lower
frequencies of the decameter range of observations in comparison with reverse
DPs generated more likely at meter wavelengths. We conclude that DPs can be
detected not only by antenna arrays, but even by a single crossed active
dipole. Thus the latter antenna has a good potential for future low-frequency
radio telescopes on the Moon.


  We study classic streaming and sparse recovery problems using deterministic
linear sketches, including l1/l1 and linf/l1 sparse recovery problems (the
latter also being known as l1-heavy hitters), norm estimation, and approximate
inner product. We focus on devising a fixed matrix A in R^{m x n} and a
deterministic recovery/estimation procedure which work for all possible input
vectors simultaneously. Our results improve upon existing work, the following
being our main contributions:
  * A proof that linf/l1 sparse recovery and inner product estimation are
equivalent, and that incoherent matrices can be used to solve both problems.
Our upper bound for the number of measurements is m=O(eps^{-2}*min{log n, (log
n / log(1/eps))^2}). We can also obtain fast sketching and recovery algorithms
by making use of the Fast Johnson-Lindenstrauss transform. Both our running
times and number of measurements improve upon previous work. We can also obtain
better error guarantees than previous work in terms of a smaller tail of the
input vector.
  * A new lower bound for the number of linear measurements required to solve
l1/l1 sparse recovery. We show Omega(k/eps^2 + klog(n/k)/eps) measurements are
required to recover an x' with |x - x'|_1 <= (1+eps)|x_{tail(k)}|_1, where
x_{tail(k)} is x projected onto all but its largest k coordinates in magnitude.
  * A tight bound of m = Theta(eps^{-2}log(eps^2 n)) on the number of
measurements required to solve deterministic norm estimation, i.e., to recover
|x|_2 +/- eps|x|_1.
  For all the problems we study, tight bounds are already known for the
randomized complexity from previous work, except in the case of l1/l1 sparse
recovery, where a nearly tight bound is known. Our work thus aims to study the
deterministic complexities of these problems.


  We discuss associated production of a Higgs boson with a pair of $t {\bar t}$
quarks at a future high energy $e^+e^-$ collider. The process $e^+e^-\to t
{\bar t}h$ is particularly sensitive to the presence of new physics and we
consider the MSSM and models with extra dimensions at the $TeV$ scale as
examples.


  We develop the concept of an infinite-energy statistical solution to the
Navier-Stokes and Euler equations in the whole plane. We use a velocity
formulation with enough generality to encompass initial velocities having
bounded vorticity, which includes the important special case of vortex patch
initial data. Our approach is to use well-studied properties of statistical
solutions in a ball of radius R to construct, in the limit as R goes to
infinity, an infinite-energy solution to the Navier-Stokes equations. We then
construct an infinite-energy statistical solution to the Euler equations by
making a vanishing viscosity argument.


  We employ a bispinor gap equation to study superfluidity at nonzero chemical
potential: mu .neq. 0, in two- and three-colour QCD. The two-colour theory,
QC2D, is an excellent exemplar: the order of truncation of the quark-quark
scattering kernel: K, has no qualitative impact, which allows a straightforward
elucidation of the effects of mu when the coupling is strong. In rainbow-ladder
truncation, diquark bound states appear in the spectrum of the three-colour
theory, a defect that is eliminated by an improvement of K. The corrected gap
equation describes a superfluid phase that is semi-quantitatively similar to
that obtained using the rainbow truncation. A model study suggests that the
width of the superfluid gap and the transition point in QC2D provide reliable
quantitative estimates of those quantities in QCD.


  We develop a Continuous Hugoniot Method for the efficient simulation of shock
wave fronts with molecular dynamics. This approach achieves a significantly
improved efficiency in the generation of a dense sampling of steady-state shock
front states, and allows for the study of shocks as a function of a continuous
shock strength parameter, $v_p$. This is, to our knowledge, the first attempt
to map out the Hugoniot in a continuous fashion.
  We first apply this method to shocks in single-crystal Lennard-Jonesium along
the <100> direction. Excellent agreement is found with both the published
Lennard-Jones Hugoniot and results of conventional simulation methods.
  We next present a continuous numerical Hugoniot for shocks in tin which
agrees to within 6% with experimental data. We study the strong shock to
elastic-plastic shock transition in tin and find that it is a continuous
transition consistent with a transcritical bifurcation.


  It is well-accepted that the ability to go from one place to another, or
mobility, contributes significantly to one's wellbeing. The need for mobility
is universal, but the demand for mobility shows a great variation on a country
basis. This particular study looks at what are some of the most important
factors on a global level that can help in predicting the
passengerkilometers-travelled or passenger-miles-travelled (PKT/PMT) on a
country by country basis. This particular work tries to quantify the impact of
some of the key variables like Gross Domestic Product (GDP), population growth,
employment rate, number of households, age demographics within the population
and macroeconomic variables on the total vehicle-based travel within each
country. A panel-based regression model is developed to identify the effect of
some of the key macroeconomic variables on the countries' PKT growth.


  The cross section for exclusive production of $\pi^+ \pi^-$ and $\pi^0 \pi^0$
meson pairs in ultrarelativistic heavy ion collisions is calculated for LHC
energy $\sqrt{s_{NN}} =$ 3.5 TeV taking into account photon-photon mechanism.
We concentrate on the production of large two-pion invariant masses where the
mechanism of the elementary $\gamma \gamma \to \pi \pi$ process is not fully
understood. In order to include a size of nuclei we perform calculation in the
impact-parameter equivalent photon approximation (EPA). Realistic charge
densities are used to calculate charged form factor of $^{208}$Pb nucleus and
to generate photon fluxes associated with ultrarelativistic heavy ions.
Sizeable cross sections are obtained that can be measured at LHC. The cross
section for elementary $\gamma \gamma \to \pi \pi$ is calculated in the
framework of pQCD Brodsky-Lepage (BL) mechanism with the distribution amplitude
used to descibe recent data of the BABAR collaboration on pion transition form
factor, using hand-bag mechanism advocated to describe recent Belle data as
well as $t$ and $u$-channel meson/reggeon exchanges. We present distributions
in two-pion invariant mass as well as the pion pair rapidity for the nuclear
process.


  We present a study of the average properties of luminous infrared galaxies
detected directly at 24 $\mu$m in the COSMOS field using a median stacking
analysis at 70$\mu$m and 160 $\mu$m. Over 35000 sources spanning 0<z<3 and 0.06
mJy<S_{24}<3.0 mJy are stacked, divided into bins of both photometric redshift
and 24 $\mu$m flux. We find no correlation of $S_{70}/S_{24}$ flux density
ratio with $S_{24}$, but find that galaxies with higher $S_{24}$ have a lower
$S_{160}/S_{24}$ flux density ratio. These observed ratios suggest that 24
$\mu$m selected galaxies have warmer SEDs at higher mid-IR fluxes, and
therefore have a possible higher fraction of AGN. Comparisons of the average
$S_{70}/S_{24}$ and $S_{160}/S_{24}$ colors with various empirical templates
and theoretical models show that the galaxies detected at 24 $\mu$m are
consistent with "normal" star-forming galaxies and warm mid-IR galaxies such as
Mrk 231, but inconsistent with heavily obscured galaxies such as Arp 220. We
perform a $\chi^{2}$ analysis to determine best fit galactic model SEDs and
total IR luminosities for each of our bins. We compare our results to previous
methods of estimating $L_{\rm{IR}}$ and find that previous methods show
considerable agreement over the full redshift range, except for the brightest
$S_{24}$ sources, where previous methods overpredict the bolometric IR
luminosity at high redshift, most likely due to their warmer dust SED. We
present a table that can be used as a more accurate and robust method for
estimating bolometric infrared luminosity from 24 $\mu$m flux densities.


  I discuss origin and possible experimental manifestations of charge-spin
separation in 1D Luttinger and Luther-Emery liquids, the latter describing 1D
Mott and Peierls insulators and superconductors. Emphasis is on photoemission
where the spectral function generically shows two dispersing peaks associated
with the collective charge and spin excitations, and on transport. I analyse
the temperature dependences of the charge and spin conductivities of two
organic conductors and conclude that most likely, charge-spin separation is not
realized there and that they can be described as fluctuating Peierls
insulators.


  Conditions for the detectability of topology variations in dynamical networks
are developed in a recent article in the IEEE Transactions on Control of
Network Systems [1]. Here, an example is presented which illustrates an error
in the network-theoretic conditions for detectability developed in [1].