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2010-12-19 | A counterexample to a Penrose inequality conjectured by Gibbons | We show that the Brill-Lindquist initial data provides a counterexample to a
Riemannian Penrose inequality with charge conjectured by G. Gibbons. The
observation illustrates a sub-additive characteristic of the area radii for the
individual connected components of an outermost horizon as a lower bound of the
ADM mass. | 1012.4190v2 |
2011-11-27 | A two-stage approach to relaxation in billiard systems of locally confined hard spheres | We consider the three-dimensional dynamics of systems of many interacting
hard spheres, each individually confined to a dispersive environment, and show
that the macroscopic limit of such systems is characterized by a coefficient of
heat conduction whose value reduces to a dimensional formula in the limit of
vanishingly small rate of interaction. It is argued that this limit arises from
an effective loss of memory. Similarities with the diffusion of a tagged
particle in binary mixtures are emphasized. | 1111.6272v1 |
2012-01-12 | Coil-helix transition in poly(L-glutamic acid) : Evidence for a 3-state non-cooperative process | A careful analysis of measurements of circular dichroism of poly(L-glutamic
acid) (PGA) shows that the data can be very accurately described by introducing
a third state for the PGA configuration, in addition to the helix and coil
ones, and considering a simple equilibrium between these three states, without
cooperativity. The third state is more conspicuous when high molecular weight
polyethyleneglycol (PEG) is added. Excluded volume effects shown by differences
in presence of short and long PEG chains indicate a direct interaction of PEG
and PGA rather than an osmotic effect. | 1201.2566v1 |
2012-03-20 | Vortex dynamics in the presence of excess energy for the Landau-Lifschitz-Gilbert equation | We study the Landau-Lifshitz-Gilbert equation for the dynamics of a magnetic
vortex system. We present a PDE-based method for proving vortex dynamics that
does not rely on strong well-preparedness of the initial data and allows for
instantaneous changes in the strength of the gyrovector force due to bubbling
events. The main tools are estimates of the Hodge decomposition of the
supercurrent and an analysis of the defect measure of weak convergence of the
stress energy tensor. Ginzburg-Landau equations with mixed dynamics in the
presence of excess energy are also discussed. | 1203.4426v1 |
2012-12-22 | Cumulative Distance Enumerators of Random Codes and their Thresholds | Cumulative weight enumerators of random linear codes are introduced, their
asymptotic properties are studied, and very sharp thresholds are exhibited; as
a consequence, it is shown that the asymptotic Gilbert-Varshamov bound is a
very sharp threshold point for the density of the linear codes whose relative
distance is greater than a given positive number. For arbitrary random codes,
similar settings and results are exhibited; in particular, the very sharp
threshold point for the density of the codes whose relative distance is greater
than a given positive number is located at half the asymptotic
Gilbert-Varshamov bound. | 1212.5679v1 |
2013-01-23 | The Importance of Continuous Value Based Project Management in the Context of Requirements Engineering | Despite several scientific achievements in the last years, there are still a
lot of IT projects that fail. Researchers found that one out of five
IT-projects run out of time, budget or value. Major reasons for this failure
are unexpected economic risk factors that emerge during the runtime of
projects. In order to be able to identify emerging risks early and to
counteract reasonably, financial methods for a continuous IT-project-steering
are necessary, which as of today to the best of our knowledge are missing
within scientific literature. | 1301.5438v1 |
2013-04-08 | On Automorphisms and Subtowers of an asymptotically optimal Tower of Function Fields | In this article we investigate the automorphism group of an asymptotically
optimal tower of function fields introduced by Garcia and Stichtenoth. In
particular we provide a detailed description of the decomposition group of some
rational places. This group acts on the algebraic-geometric standard codes
obtained by the Garcia-Stichtenoth tower exceeding the Gilbert-Varshamov bound.
The fields fixed by the decomposition groups form an asymptotically optimal
non-Galois subtower, which has been first found by Bezerra and Garcia and
yields an improvement for computing codes above the Gilbert-Varshamov bound. In
this article we also describe its proportionality to the Garcia-Stichtenoth
tower and obtain new precise results on its rational places and their
Weierstra{\ss} semigroups. | 1304.2145v1 |
2013-05-06 | The Moment Generating function for ray lengths in the Half Gilbert Model with Rectangular Cells | In the full rectangular version of Gilbert's tessellation lines extend either
horizontally (with east- and west--growing rays) or vertically (north- and
south--growing rays) from seed points which form a Poisson point process, each
ray stopping when another ray is met. In the half rectangular version, east and
south growing rays do not interact with west and north rays. Using techniques
developed in our previous paper, we derive an exact expression for the moment
generating function for the ray length distribution in the half rectangular
model. | 1305.1289v1 |
2013-07-15 | Degenerate transition pathways for screw dislocations: implications for migration | In body-centred-cubic (bcc) metals migrating 1/2<111> screw dislocations
experience a periodic energy landscape with a triangular symmetry. Atomistic
simulations, such as those performed using the nudged-elastic-band (NEB)
method, generally predict a transition-pathway energy-barrier with a
double-hump; contradicting Ab Initio findings. Examining the trajectories
predicted by NEB for a particle in a Peierls energy landscape representative of
that obtained for a screw dislocation, reveals an unphysical anomaly caused by
the occurrence of monkey saddles in the landscape. The implications for motion
of screws with and without stress are discussed. | 1307.3848v2 |
2013-08-17 | The Riemannian Penrose Inequality with Charge for Multiple Black Holes | We present a proof of the Riemannian Penrose inequality with charge $r\leq m
+ \sqrt{m^2-q^2}$, where $A=4\pi r^2$ is the area of the outermost apparent
horizon with possibly multiple connected components, $m$ is the total ADM mass,
and $q$ the total charge of a strongly asymptotically flat initial data set for
the Einstein-Maxwell equations, satisfying the charged dominant energy
condition, with no charged matter outside the horizon. | 1308.3771v3 |
2013-08-23 | Quotients and subgroups of Baumslag-Solitar groups | We determine all generalized Baumslag-Solitar groups (finitely generated
groups acting on a tree with all stabilizers infinite cyclic) which are
quotients of a given Baumslag-Solitar group BS(m,n), and (when BS(m,n) is not
Hopfian) which of them also admit BS(m,n) as a quotient. We determine for which
values of r,s one may embed BS(r,s) into a given BS(m,n), and we characterize
finitely generated groups which embed into some BS(n,n). | 1308.5122v2 |
2013-12-17 | Limit theory for the Gilbert graph | For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points
are connected by an edge if their distance is bounded by a prescribed distance
parameter. The behaviour of the resulting random graph, the Gilbert graph or
random geometric graph, is investigated as the intensity of the Poisson point
process is increased and the distance parameter goes to zero. The asymptotic
expectation and covariance structure of a class of length-power functionals are
computed. Distributional limit theorems are derived that have a Gaussian, a
stable or a compound Poisson limiting distribution. Finally, concentration
inequalities are provided using a concentration inequality for the convex
distance. | 1312.4861v2 |
2014-03-13 | Fibrations of ordered groupoids and the factorization of ordered functors | We investigate canonical factorizations of ordered functors of ordered
groupoids through star-surjective functors. Our main construction is a quotient
ordered groupoid, depending on an ordered version of the notion of normal
subgroupoid, that results is the factorization of an ordered functor as a
star-surjective functor followed by a star-injective functor. Any
star-injective functor possesses a universal factorization through a covering,
by Ehresmann's Maximum Enlargement Theorem. We also show that any ordered
functor has a canonical factorization through a functor with the ordered
homotopy lifting property. | 1403.3254v2 |
2014-06-10 | A thin-film limit in the Landau-Lifshitz-Gilbert equation relevant for the formation of Néel walls | We consider an asymptotic regime for two-dimensional ferromagnetic films that
is consistent with the formation of transition layers (N\'eel walls). We first
establish compactness of S2-valued magnetizations in the energetic regime of
N\'eel walls and characterize the set of accumulation points. We then prove
that N\'eel walls are asymptotically the unique energy minimizing
configurations. We finally study the corresponding dynamical issues, namely the
compactness properties of the magnetizations under the flow of the
Landau-Lifshitz-Gilbert equation. | 1406.2709v1 |
2014-08-02 | Machta-Zwanzig regime of anomalous diffusion in infinite-horizon billiards | We study diffusion on a periodic billiard table with infinite horizon in the
limit of narrow corridors. An effective trapping mechanism emerges according to
which the process can be modeled by a L\'evy walk combining
exponentially-distributed trapping times with free propagation along paths
whose precise probabilities we compute. This description yields an
approximation of the mean squared displacement of infinite-horizon billiards in
terms of two transport coefficients which generalizes to this anomalous regime
the Machta-Zwanzig approximation of normal diffusion in finite-horizon
billiards [Phys. Rev. Lett. 50, 1959 (1983)]. | 1408.0349v1 |
2014-12-11 | Gamma factors of pairs and a local converse theorem in families | We prove a GL(n)xGL(n-1) local converse theorem for l-adic families of smooth
representations of GL(n,F) where F is a finite extension of Q_p and l is
different from p. To do so, we also extend the theory of Rankin-Selberg
integrals, first introduced by Jacquet, Piatetski-Shapiro, and Shalika, to the
setting of families, continuing previous work of the author. | 1412.3500v2 |
2015-05-28 | A Geometric Interpretation of the Boolean Gilbert-Johnson-Keerthi Algorithm | The Gilbert-Johnson-Keerthi (GJK) algorithm is an iterative improvement
technique for finding the minimum distance between two convex objects. It can
easily be extended to work with concave objects and return the pair of closest
points. [4] The key operation of GJK is testing whether a Voronoi region of a
simplex contains the origin or not. In this paper we show that, in the context
where one is interested only in the Boolean value of whether two convex objects
intersect, and not in the actual distance between them, the number of test
cases in GJK can be significantly reduced. This results in a simpler and more
efficient algorithm that can be used in many computational geometry
applications. | 1505.07873v1 |
2016-01-29 | Ordered groupoid quotients and congruences on inverse semigroups | We introduce a preorder on an inverse semigroup $S$ associated to any normal
inverse subsemigroup $N$, that lies between the natural partial order and
Green's ${\mathscr J}$-relation. The corresponding equivalence relation
$\simeq_N$ is not necessarily a congruence on $S$, but the quotient set does
inherit a natural ordered groupoid structure. We show that this construction
permits the factorisation of any inverse semigroup homomorphism into a
composition of a quotient map and a star-injective functor, and that this
decomposition implies a classification of congruences on $S$. We give an
application to the congruence and certain normal inverse subsemigroups
associate to an inverse monoid presentation. | 1601.08194v1 |
2016-10-11 | Converse theorems and the local Langlands correspondence in families | We prove a descent criterion for certain families of smooth representations
of GL_n(F) (F a p-adic field) in terms of the gamma factors of pairs
constructed in previous work of the second author. We then use this descent
criterion, together with a theory of gamma factors for families of
representations of the Weil group W_F (developed previously by both authors),
to prove a series of conjectures, due to the first author, that give a complete
description of the integral Bernstein center in terms of Galois theory and the
local Langlands correspondence. An immediate consequence is the conjectural
"local Langlands correspondence in families" of Emerton and Helm. | 1610.03277v1 |
2016-10-14 | An alternative view on dissipation in turbulent flows | An original experimental setup has been elaborated in order to get a better
view of turbulent flows in a von Karman geometry. The availability of a very
fast camera allowed to follow in time the evolution of the flows. A surprising
finding is that the development of smaller whorls ceases earlier than expected
and the aspect of the flows remains the same above Reynolds number of a few
thousand. This fact provides an explanation of the constancy of the reduced
dissipation in the same range without the need of singularity. Its cause could
be in relation with the same type of behavior observed in a rotating frame. | 1610.05356v2 |
2017-11-29 | On the local converse theorem and the descent theorem in families | We prove an analogue of Jacquet's conjecture on the local converse theorem
for \ell-adic families of co-Whittaker representations of GL_n(F), where F is a
finite extension of Q_p and \ell does not equal p. We also prove an analogue of
Jacquet's conjecture for a descent theorem, which asks for the smallest
collection of gamma factors determining the subring of definition of an
\ell-adic family. These two theorems are closely related to the local Langlands
correspondence in \ell-adic families. | 1711.11159v1 |
2018-06-23 | List Decodability of Symbol-Pair Codes | We investigate the list decodability of symbol-pair codes in the present
paper. Firstly, we show that list decodability of every symbol-pair code does
not exceed the Gilbert-Varshamov bound. On the other hand, we are able to prove
that with high probability, a random symbol-pair code can be list decoded up to
the Gilbert-Varshamov bound. Our second result of this paper is to derive the
Johnson-type bound, i.e., a lower bound on list decoding radius in terms of
minimum distance. Finally, we present a list decoding algorithm of Reed-Solomon
codes beyond the Johnson-type bound. | 1806.08992v1 |
2018-07-05 | Volumetric performance capture from minimal camera viewpoints | We present a convolutional autoencoder that enables high fidelity volumetric
reconstructions of human performance to be captured from multi-view video
comprising only a small set of camera views. Our method yields similar
end-to-end reconstruction error to that of a probabilistic visual hull computed
using significantly more (double or more) viewpoints. We use a deep prior
implicitly learned by the autoencoder trained over a dataset of view-ablated
multi-view video footage of a wide range of subjects and actions. This opens up
the possibility of high-end volumetric performance capture in on-set and
prosumer scenarios where time or cost prohibit a high witness camera count. | 1807.01950v2 |
2019-06-26 | Fairness criteria through the lens of directed acyclic graphical models | A substantial portion of the literature on fairness in algorithms proposes,
analyzes, and operationalizes simple formulaic criteria for assessing fairness.
Two of these criteria, Equalized Odds and Calibration by Group, have gained
significant attention for their simplicity and intuitive appeal, but also for
their incompatibility. This chapter provides a perspective on the meaning and
consequences of these and other fairness criteria using graphical models which
reveals Equalized Odds and related criteria to be ultimately misleading. An
assessment of various graphical models suggests that fairness criteria should
ultimately be case-specific and sensitive to the nature of the information the
algorithm processes. | 1906.11333v1 |
2017-04-12 | The homology of principally directed ordered groupoids | We present some homological properties of a relation $\beta$ on ordered
groupoids that generalises the minimum group congruence for inverse semigroups.
When $\beta$ is a transitive relation on an ordered groupoid $G$, the quotient
$G / \beta$ is again an ordered groupoid, and construct a pair of adjoint
functors between the module categories of $G$ and of $G / \beta$. As a
consequence, we show that the homology of $G$ is completely determined by that
of $G / \beta$, generalising a result of Loganathan for inverse semigroups. | 1704.03689v1 |
2018-10-26 | Immobilization of convex bodies in $R^n$ | We extend to arbitrary finite $n$ the notion of immobilization of a convex
body $O$ in $R^n$ by a finite set of points $P$ in the boundary of $O$. Because
of its importance for this problem, necessary and sufficient conditions are
found for the immobilization of an $n$-simplex. A fairly complete geometric
description of these conditions is given: as $n$ increases from $n = 2$, some
qualitative difference in the nature of the sets $P$ emerges. | 1810.11381v1 |
2019-01-14 | Groupoids and the algebra of rewriting in group presentations | Presentations of groups by rewriting systems (that is, by monoid
presentations), have been fruitfully studied by encoding the rewriting system
in a $2$--complex -- the Squier complex -- whose fundamental groupoid then
describes the derivation of consequences of the rewrite rules. We describe a
reduced form of the Squier complex, investigate the structure of its
fundamental groupoid, and show that key properties of the presentation are
still encoded in the reduced form. | 1901.04348v1 |
2016-08-16 | Closed inverse subsemigroups of graph inverse semigroups | As part of his study of representations of the polycylic monoids, M.V. Lawson
described all the closed inverse submonoids of a polycyclic monoid $P_n$ and
classified them up to conjugacy. We show that Lawson's description can be
extended to closed inverse subsemigroups of graph inverse semigroups. We then
apply B. Schein's theory of cosets in inverse semigroups to the closed inverse
subsemigroups of graph inverse semigroups: we give necessary and sufficient
conditions for a closed inverse subsemigroup of a graph inverse semigroup to
have finite index, and determine the value of the index when it is finite. | 1608.04538v1 |
2010-04-09 | Strict inequalities of critical probabilities on Gilbert's continuum percolation graph | Any infinite graph has site and bond percolation critical probabilities
satisfying $p_c^{site}\geq p_c^{bond}$. The strict version of this inequality
holds for many, but not all, infinite graphs.
In this paper, the class of graphs for which the strict inequality holds is
extended to a continuum percolation model. In Gilbert's graph with
supercritical density on the Euclidean plane, there is almost surely a unique
infinite connected component. We show that on this component $p_c^{site} >
p_c^{bond}$. This also holds in higher dimensions. | 1004.1596v2 |
2010-04-15 | Rank of mapping tori and companion matrices | Given $f$ in $GL(d,Z)$, it is decidable whether its mapping torus (the
semi-direct product of $Z^d$ with $Z$) may be generated by two elements or not;
if so, one can classify generating pairs up to Nielsen equivalence. If $f$ has
infinite order, the mapping torus of $f^n$ cannot be generated by two elements
for $n$ large enough; equivalently, $f^n$ is not conjugate to a companion
matrix in $GL(d,Z)$ if $n$ is large. | 1004.2649v1 |
2017-03-02 | Small Superposition Dimension and Active Set Construction for Multivariate Integration Under Modest Error Demand | Constructing active sets is a key part of the Multivariate Decomposition
Method. An algorithm for constructing optimal or quasi-optimal active sets is
proposed in the paper. By numerical experiments, it is shown that the new
method can provide sets that are significantly smaller than the sets
constructed by the already existing method. The experiments also show that the
superposition dimension could surprisingly be very small, at most 3, when the
error demand is not smaller than $10^{-3}$ and the weights decay sufficiently
fast. | 1703.00985v1 |
2017-03-03 | Heat conduction and the nonequilibrium stationary states of stochastic energy exchange processes | I revisit the exactly solvable Kipnis--Marchioro--Presutti model of heat
conduction [J. Stat. Phys. 27 65 (1982)] and describe, for one-dimensional
systems of arbitrary sizes whose ends are in contact with thermal baths at
different temperatures, a systematic characterization of their non-equilibrium
stationary states. These arguments avoid resorting to the analysis of a dual
process and yield a straightforward derivation of Fourier's law, as well as
higher-order static correlations, such as the covariant matrix. The
transposition of these results to families of gradient models generalizing the
KMP model is established and specific cases are examined. | 1703.01240v1 |
2017-03-04 | Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound | It was shown by Massey that linear complementary dual (LCD for short) codes
are asymptotically good. In 2004, Sendrier proved that LCD codes meet the
asymptotic Gilbert-Varshamov (GV for short) bound. Until now, the GV bound
still remains to be the best asymptotical lower bound for LCD codes. In this
paper, we show that an algebraic geometry code over a finite field of even
characteristic is equivalent to an LCD code and consequently there exists a
family of LCD codes that are equivalent to algebraic geometry codes and exceed
the asymptotical GV bound. | 1703.01441v1 |
2017-03-17 | A finite element approximation for the stochastic Landau--Lifshitz--Gilbert equation with multi-dimensional noise | We propose an unconditionally convergent linear finite element scheme for the
stochastic Landau--Lifshitz--Gilbert (LLG) equation with multi-dimensional
noise. By using the Doss-Sussmann technique, we first transform the stochastic
LLG equation into a partial differential equation that depends on the solution
of the auxiliary equation for the diffusion part. The resulting equation has
solutions absolutely continuous with respect to time. We then propose a
convergent $\theta$-linear scheme for the numerical solution of the
reformulated equation. As a consequence, we are able to show the existence of
weak martingale solutions to the stochastic LLG equation. | 1703.05901v1 |
2019-05-27 | Tuning Free Rank-Sparse Bayesian Matrix and Tensor Completion with Global-Local Priors | Matrix and tensor completion are frameworks for a wide range of problems,
including collaborative filtering, missing data, and image reconstruction.
Missing entries are estimated by leveraging an assumption that the matrix or
tensor is low-rank. Most existing Bayesian techniques encourage rank-sparsity
by modelling factorized matrices and tensors with Normal-Gamma priors. However,
the Horseshoe prior and other "global-local" formulations provide
tuning-parameter-free solutions which may better achieve simultaneous
rank-sparsity and missing-value recovery. We find these global-local priors
outperform commonly used alternatives in simulations and in a collaborative
filtering task predicting board game ratings. | 1905.11496v1 |
2020-01-14 | Neural Architecture Search for Deep Image Prior | We present a neural architecture search (NAS) technique to enhance the
performance of unsupervised image de-noising, in-painting and super-resolution
under the recently proposed Deep Image Prior (DIP). We show that evolutionary
search can automatically optimize the encoder-decoder (E-D) structure and
meta-parameters of the DIP network, which serves as a content-specific prior to
regularize these single image restoration tasks. Our binary representation
encodes the design space for an asymmetric E-D network that typically converges
to yield a content-specific DIP within 10-20 generations using a population
size of 500. The optimized architectures consistently improve upon the visual
quality of classical DIP for a diverse range of photographic and artistic
content. | 2001.04776v1 |
2020-07-18 | Finslerian convolution metrics and their special classes | Here, it is introduced a concept of convolution metric in Finslerian
Geometry. This convolution metric is a kind of function obtained by a given
mathematical operation between two Finslerian metrics. Some basic properties of
the Finslerian convolution metrics are studied. Then it is characterized
Finslerian convolution metrics which are of type Riemannian, Minkowskian as
well as Randers. Furthermore, some examples of the Finslerian convolutions are
given. | 2007.14803v3 |
2020-09-14 | What mathematical billiards teach us about statistical physics? | We survey applications of the theory of hyperbolic (and to a lesser extent
non hyperbolic) billiards to some fundamental problems of statistical physics
and their mathematically rigorous derivations in the framework of classical
Hamiltonian systems. | 2009.06284v2 |
2020-11-29 | Applications of the Backus-Gilbert method to linear and some non linear equations | We investigate the use of a functional analytical version of the
Backus-Gilbert Method as a reconstruction strategy to get specific information
about the solution of linear and slightly non-linear systems with Frech\'et
derivable operators. Some a priori error estimates are shown and tested for two
classes of problems: a nonlinear moment problem and a linear elliptic Cauchy
problem. For this second class of problems a special version of the
Green-formula is developed in order to analyze the involved adjoint equations. | 2011.14407v1 |
2021-11-30 | Global weak solutions for the Landau-Lifshitz-Gilbert-Vlasov-Maxwell system coupled via emergent electromagnetic fields | Motivated by recent models of current driven magnetization dynamics, we
examine the coupling of the Landau-Lifshitz-Gilbert equation and classical
electron transport governed by the Vlasov-Maxwell system. The interaction is
based on space-time gyro-coupling in the form of emergent electromagnetic
fields of quantized helicity that add up to the conventional Maxwell fields. We
construct global weak solutions of the coupled system in the framework of
frustrated magnets with competing first and second order gradient interactions
known to host topological solitons such as magnetic skyrmions and hopfions. | 2111.15482v1 |
2022-04-02 | Introduction to the Artificial Intelligence that can be applied to the Network Automation Journey | The computer network world is changing and the NetDevOps approach has brought
the dynamics of applications and systems into the field of communication
infrastructure. Businesses are changing and businesses are faced with
difficulties related to the diversity of hardware and software that make up
those infrastructures. The "Intent-Based Networking - Concepts and Definitions"
document describes the different parts of the ecosystem that could be involved
in NetDevOps. The recognize, generate intent, translate and refine features
need a new way to implement algorithms. This is where artificial intelligence
comes in. | 2204.00800v1 |
2022-05-24 | Theory of the Energy Variance in a Quantum Bit | We define a new quantum Hermitian operator (namely, the energy variance
operator) which is simply duplicated from the statistical definition of energy
variance in classical physics. Its expectation value yields the standard
deviation of the energy about the mean value of this latter. We show by use of
an exact Hamiltonian description that this standard deviation is due to the
high-frequeny energy oscillations which are usually discarded in the rotating
wave aproximation. We check the present theory by recovering the duration of an
abrupt quantum jump that has been described in a recent experiment. | 2205.12763v1 |
2022-07-11 | Quasilinear rough evolution equations | We investigate the abstract Cauchy problem for a quasilinear parabolic
equation in a Banach space of the form \( du_t -L_t(u_t)u_t dt = N_t(u_t)dt +
F(u_t)\cdot d\mathbf X_t \), where \( \mathbf X\) is a \( \gamma\)-H\"older
rough path for \( \gamma\in(1/3,1/2)\). We explore the mild formulation that
combines functional analysis techniques and controlled rough paths theory which
entail the local well-posedness of such equations. We apply our results to the
stochastic Landau-Lifshitz-Gilbert and Shigesada-Kawasaki-Teramoto equation. In
this framework we obtain a random dynamical system associated to the
Landau-Lifshitz-Gilbert equation. | 2207.04787v1 |
2022-08-01 | A Pansiot-type subword complexity theorem for automorphisms of free groups | Inspired by Pansiot's work on substitutions, we prove a similar theorem for
automorphisms of a free group F of finite rank: if a right-infinite word
represents an attracting fixed point of an automorphism of F, the subword
complexity of X is equivalent to n, n log log n, n log n, or n^2. The proof
uses combinatorial arguments analogue to Pansiot's as well as train tracks. We
also define the recurrence complexity of X, and we apply it to laminations. In
particular, we show that attracting laminations have complexity equivalent to
n, n log log n, n log n, or n^2 (to n if the automorphism is fully
irreducible). | 2208.00676v1 |
2022-08-13 | May the force be with you | Modern methods in dimensionality reduction are dominated by nonlinear
attraction-repulsion force-based methods (this includes t-SNE, UMAP,
ForceAtlas2, LargeVis, and many more). The purpose of this paper is to
demonstrate that all such methods, by design, come with an additional feature
that is being automatically computed along the way, namely the vector field
associated with these forces. We show how this vector field gives additional
high-quality information and propose a general refinement strategy based on
ideas from Morse theory. The efficiency of these ideas is illustrated
specifically using t-SNE on synthetic and real-life data sets. | 2208.06676v1 |
2022-10-26 | Linearized frequency domain Landau-Lifshitz-Gilbert equation formulation | We present a general finite element linearized Landau-Lifshitz-Gilbert
equation (LLGE) solver for magnetic systems under weak time-harmonic excitation
field. The linearized LLGE is obtained by assuming a small deviation around the
equilibrium state of the magnetic system. Inserting such expansion into LLGE
and keeping only first order terms gives the linearized LLGE, which gives a
frequency domain solution for the complex magnetization amplitudes under an
external time-harmonic applied field of a given frequency. We solve the linear
system with an iterative solver using generalized minimal residual method. We
construct a preconditioner matrix to effectively solve the linear system. The
validity, effectiveness, speed, and scalability of the linear solver are
demonstrated via numerical examples. | 2210.14525v1 |
2022-11-10 | Secure Aggregation Is Not All You Need: Mitigating Privacy Attacks with Noise Tolerance in Federated Learning | Federated learning is a collaborative method that aims to preserve data
privacy while creating AI models. Current approaches to federated learning tend
to rely heavily on secure aggregation protocols to preserve data privacy.
However, to some degree, such protocols assume that the entity orchestrating
the federated learning process (i.e., the server) is not fully malicious or
dishonest. We investigate vulnerabilities to secure aggregation that could
arise if the server is fully malicious and attempts to obtain access to
private, potentially sensitive data. Furthermore, we provide a method to
further defend against such a malicious server, and demonstrate effectiveness
against known attacks that reconstruct data in a federated learning setting. | 2211.06324v1 |
2022-12-22 | Theory and construction of Quasi-Monte Carlo rules for option pricing and density estimation | In this paper we propose and analyse a method for estimating three quantities
related to an Asian option: the fair price, the cumulative distribution
function, and the probability density. The method involves preintegration with
respect to one well chosen integration variable to obtain a smooth function of
the remaining variables, followed by the application of a tailored lattice
Quasi-Monte Carlo rule to integrate over the remaining variables. | 2212.11493v2 |
2022-12-22 | Novel Bottomonium Results | We present the latest results from the use of the Backus-Gilbert method for
reconstructing the spectra of NRQCD bottomonium mesons using anisotropic
FASTSUM ensembles at non-zero temperature. We focus in particular on results
from the $\eta_b$, $\Upsilon$, $\chi_{b1}$ and $h_b$ generated from
Tikhonov-regularized Backus-Gilbert coefficient sets. We extend previous work
on the Laplace shifting theorem as a means of resolution improvement and
present new results from its use. We conclude with a discussion of the
limitations of the improvement routine and elucidate a connection with
Parisi-Lepage statistical scaling. | 2212.12016v1 |
2022-12-30 | Asymptotic stability of 2-domain walls for the Landau-Lifshitz-Gilbert equation in a nanowire with Dzyaloshinskii-Moriya interaction | We consider a ferromagnetic nanowire, with an energy functional $E$ with
easy-axis in the direction $e_1$, and which takes into account the
Dzyaloshinskii-Moriya interaction. We consider configurations of the
magnetization which are perturbations of two well separated domain wall, and
study their evolution under the Landau-Lifshitz-Gilbert flow associated to E.
Our main result is that, if the two walls have opposite speed, these
configurations are asymptotically stable, up to gauges intrinsic to the
invariances of the energy $E$. Our analysis builds on the framework developed
in [4], taking advantage that it is amenable to space localisation. | 2212.14589v1 |
2023-01-12 | Time Domain Verification of Differential Transmission Line Modeling Methods | The advantages and limitations of time-domain pseudo-random binary sequence
(PRBS) excitation methods for system identification of individual modes within
a multi-conductor transmission system are discussed. We develop the
modifications necessary to standard frequency-domain transmission-line models
to match time-domain experimental data from several types of transmission
systems. We show a variety of experimental results showing very good to
excellent agreement with our model's predictions, up to approximately 10 GHz. | 2301.05281v1 |
2023-01-17 | Power Supply Compensation for Capacitive Loads | As ASIC supply voltages approach one volt, the source-impedance goals for
power distribution networks are driven ever lower as well. One approach to
achieving these goals is to add decoupling capacitors of various values until
the desired impedance profile is obtained. An unintended consequence of this
approach can be reduced power supply stability and even oscillation. In this
paper, we present a case study of a system design which encountered these
problems and we describe how these problems were resolved. Time-domain and
frequency-domain analysis techniques are discussed and measured data is
presented. | 2301.09580v1 |
2023-01-17 | Applications of Optimization Routines in Signal Integrity Analysis | Signal integrity analysis often involves the development of design guidelines
through manual manipulation of circuit parameters and judicious interpretation
of results. Such an approach can result in significant effort and sub-optimal
conclusions. Optimization routines have been well proven to aid analysis across
a variety of common tasks. In addition, there are several non-traditional
applications where optimization can be useful. This paper begins by describing
the basics of optimization followed by two specific case studies where
non-traditional optimization provides significant improvements in both analysis
efficiency and channel performance. | 2301.10157v1 |
2023-01-17 | High Speed Parallel Signal Crosstalk Cancellation Concept | High performance computing (HPC) systems make extensive use of high speed
electrical interconnects, in routing signals among processing elements, or
between processing elements and memory. Increasing bandwidth demands result in
high density, parallel I/O exposed to crosstalk due to tightly coupled
transmission lines. The crosstalk cancellation signaling concept discussed in
this paper utilizes the known, predictable theory of coupled transmission lines
to cancel crosstalk from neighboring traces with carefully chosen resistive
cross-terminations between them. Through simulation and analysis of practical
bus architectures, we explore the merits of crosstalk cancellation which could
be used in dense interconnect HPC (or other) applications. | 2301.10170v1 |
2023-04-05 | Elimination and Factorization | If a matrix $A$ has rank $r$, then its row echelon form (from elimination)
contains the identity matrix in its first $r$ independent columns. How do we
\emph{interpret the matrix} $F$ that appears in the remaining columns of that
echelon form\,? $F$ multiplies those first $r$ independent columns of $A$ to
give its $n-r$ dependent columns. Then $F$ reveals bases for the row space and
the nullspace of the original matrix $A$. And $F$ is the key to the column-row
factorization $\boldsymbol{A}=\boldsymbol{CR}$. | 2304.02659v1 |
2023-04-25 | Jet: Multilevel Graph Partitioning on Graphics Processing Units | The multilevel heuristic is the dominant strategy for high-quality sequential
and parallel graph partitioning. Partition refinement is a key step of
multilevel graph partitioning. In this work, we present Jet, a new parallel
algorithm for partition refinement specifically designed for Graphics
Processing Units (GPUs). We combine Jet with GPU-aware coarsening to develop a
$k$-way graph partitioner, the Jet partitioner. The new partitioner achieves
superior quality compared to state-of-the-art shared memory partitioners on a
large collection of test graphs. | 2304.13194v2 |
2023-05-16 | QHDL: a Low-Level Circuit Description Language for Quantum Computing | This paper proposes a descriptive language called QHDL, akin to VHDL, to
program gate-based quantum computing systems. Unlike other popular quantum
programming languages, QHDL targets low-level quantum computing programming and
aims to provide a common framework for programming FPGAs and gate-based quantum
computing systems. The paper presents an initial implementation and design
principles of the QHDL framework, including a compiler and quantum computer
simulator. We discuss the challenges of low-level integration of streaming
models and quantum computing for programming FPGAs and gate-based quantum
computing systems. | 2305.09419v1 |
2023-05-21 | An Alternative Derivation of the Landau-Lifshitz-Gilbert Equation for Saturated Ferromagnets | The Landau-Lifshitz-Gilbert equation for rigid and saturated ferromagnets is
derived using a two-continuum model constructed by H.F. Tiersten for elastic
and saturated ferromagnets. The relevant basic laws of physics are applied
systematically to the two continua or their combination. The exchange
interaction is introduced into the model through surface distributed magnetic
couples. This leads to a continuum theory with magnetization gradients in the
stored energy density. The saturation condition of the magnetization functions
as constraints on the energy density and has implications in the constitutive
relations. | 2305.18232v1 |
2023-06-25 | Gilbert's conjecture and A new way to octonionic analytic functions from the clifford analysis | In this article we will give a affirmative answer to Gilbert's conjecture on
Hardy spaces of Clifford analytic functions in upper half-space of
$\mathbb{R}^8$. It depends on a explicit construction of Spinor space
$\mathcal{R}_8$ and Clifford algebra $Cl_8$ by octonion algbra. What's more ,
it gives us an associative way to octonionic analytic function theory. And the
similar question has been discussed in Octonionic Hardy space in upper-half
space, some classical results about octonionic analytic functions have been
reformulated, too. | 2306.14164v1 |
2023-06-28 | Stochastic Landau-Lifshitz-Gilbert equations for frustrated magnets under fluctuating currents | We examine a stochastic Landau-Lifshitz-Gilbert equation for a frustrated
ferromagnet with competing first and second order exchange interactions exposed
to deterministic and random spin transfer torques in form of transport noise.
We prove the existence and pathwise uniqueness of weak martingale solutions in
the energy space. The result ensures the persistence of topological patterns,
occurring in such magnetic systems, under the influence of a fluctuating spin
current. | 2306.15843v1 |
2023-07-28 | MDS, Hermitian Almost MDS, and Gilbert-Varshamov Quantum Codes from Generalized Monomial-Cartesian Codes | We construct new stabilizer quantum error-correcting codes from generalized
monomial-Cartesian codes. Our construction uses an explicitly defined twist
vector, and we present formulas for the minimum distance and dimension.
Generalized monomial-Cartesian codes arise from polynomials in $m$ variables.
When $m=1$ our codes are MDS, and when $m=2$ and our lower bound for the
minimum distance is $3$ the codes are at least Hermitian Almost MDS. For an
infinite family of parameters when $m=2$ we prove that our codes beat the
Gilbert-Varshamov bound. We also present many examples of our codes that are
better than any known code in the literature. | 2307.15488v1 |
2023-09-06 | Optimal Control of the 2D Landau-Lifshitz-Gilbert Equation with Control Energy in Effective Magnetic Field | The optimal control of magnetization dynamics in a ferromagnetic sample at a
microscopic scale is studied. The dynamics of this model is governed by the
Landau-Lifshitz-Gilbert equation on a two-dimensional bounded domain with the
external magnetic field (the control) applied through the effective field. We
prove the global existence and uniqueness of a regular solution in $\mathbb
S^2$ under a smallness condition on control and initial data. We establish the
existence of optimal control and derive a first-order necessary optimality
condition using the Fr\'echet derivative of the control-to-state operator and
adjoint problem approach. | 2309.02786v1 |
2023-09-22 | Relaxed optimal control for the stochastic Landau-Lifshitz-Gilbert equation | We consider the stochastic Landau-Lifshitz-Gilbert equation, perturbed by a
real-valued Wiener process. We add an external control to the effective field
as an attempt to drive the magnetization to a desired state and also to control
thermal fluctuations. We use the theory of Young measures to relax the given
control problem along with the associated cost. We consider a control operator
that can depend (possibly non-linearly) on both the control and the associated
solution. Moreover, we consider a fairly general associated cost functional
without any special convexity assumption. We use certain compactness arguments,
along with the Jakubowski version of the Skorohod Theorem to show that the
relaxed problem admits an optimal control. | 2309.12556v1 |
2023-11-29 | Bayesian interpretation of Backus-Gilbert methods | The extraction of spectral densities from Euclidean correlators evaluated on
the lattice is an important problem, as these quantities encode physical
information on scattering amplitudes, finite-volume spectra, inclusive decay
rates, and transport coefficients. In this contribution, we show that the
Bayesian approach to this "inverse" problem, based on Gaussian processes, can
be reformulated in a way that yields a solution equivalent, up to statistical
uncertainties, to the one obtained in a Backus-Gilbert approach. After
discussing this equivalence, we point out its implications for a reliable
determination of spectral densities from lattice simulations. | 2311.18125v1 |
2024-01-14 | Multilevel Metamodels: A Novel Approach to Enhance Efficiency and Generalizability in Monte Carlo Simulation Studies | Metamodels, or the regression analysis of Monte Carlo simulation (MCS)
results, provide a powerful tool to summarize MCS findings. However, an as of
yet unexplored approach is the use of multilevel metamodels (MLMM) that better
account for the dependent data structure of MCS results that arises from
fitting multiple models to the same simulated data set. In this study, we
articulate the theoretical rationale for the MLMM and illustrate how it can
dramatically improve efficiency over the traditional regression approach,
better account for complex MCS designs, and provide new insights into the
generalizability of MCS findings. | 2401.07294v2 |
2024-02-29 | Evaluating the Gilbert-Varshamov Bound for Constrained Systems | We revisit the well-known Gilbert-Varshamov (GV) bound for constrained
systems. In 1991, Kolesnik and Krachkovsky showed that GV bound can be
determined via the solution of some optimization problem. Later, Marcus and
Roth (1992) modified the optimization problem and improved the GV bound in many
instances. In this work, we provide explicit numerical procedures to solve
these two optimization problems and hence, compute the bounds. We then show the
procedures can be further simplified when we plot the respective curves. In the
case where the graph presentation comprise a single state, we provide explicit
formulas for both bounds. | 2402.18869v1 |
1992-06-18 | Wormholes and Supersymmetry | Revisions: reference added to: G. Gilbert, {\sl Nucl.Phys.} {\bf B328}, 159
(1989) | 9206072v2 |
1993-05-26 | Musings on Magnus | The object of this paper is to describe a simple method for proving that
certain groups are residually torsion-free nilpotent, to describe some new
parafree groups and to raise some new problems in honour of the memory of
Wilhelm Magnus. | 9305201v1 |
2001-10-17 | Expected number of distinct part sizes in a random integer composition | The asymptotics, as $n\to\infty$, for the expected number of distinct part
sizes in a random composition of an integer n is obtained. | 0110189v1 |
2003-12-29 | Non-hopfian relatively free groups | To solve problems of Gilbert Baumslag and Hanna Neumann, posed in the 1960's,
we construct a nontrivial variety of groups all of whose noncyclic free groups
are non-hopfian. | 0312491v1 |
2005-10-26 | Winning rate in the full-information best choice problem | Following a long-standing suggestion by Gilbert and Mosteller, we derive an
explicit formula for the asymptotic winning rate in the full-information
problem of the best choice. | 0510568v3 |
2007-12-20 | The dark matter as a light gravitino (II) | We address the question of gravitino dark matter in the context of gauge
mediated supersymmetry breaking models. | 0712.3465v1 |
2014-02-25 | Du-Hwang Characteristic Area: Catch-22 | The paper is devoted to description of two interconnected mistakes generated
by the gap in the Du and Hwang approach to Gilbert-Pollack Steiner ratio
conjecture. | 1402.6079v1 |
2018-10-28 | Asymptotic Gilbert-Varshamov bound on Frequency Hopping Sequences | Given a $q$-ary frequency hopping sequence set of length $n$ and size $M$
with Hamming correlation $H$, one can obtain a $q$-ary (nonlinear) cyclic code
of length $n$ and size $nM$ with Hamming distance $n-H$. Thus, every upper
bound on the size of a code from coding theory gives an upper bound on the size
of a frequency hopping sequence set. Indeed, all upper bounds from coding
theory have been converted to upper bounds on frequency hopping sequence sets
(\cite{Ding09}). On the other hand, a lower bound from coding theory does not
automatically produce a lower bound for frequency hopping sequence sets. In
particular, the most important lower bound--the Gilbert-Varshamov bound in
coding theory has not been transformed to frequency hopping sequence sets. The
purpose of this paper is to convert the Gilbert-Varshamov bound in coding
theory to frequency hopping sequence sets by establishing a connection between
a special family of cyclic codes (which are called hopping cyclic codes in this
paper) and frequency hopping sequence sets. We provide two proofs of the
Gilbert-Varshamov bound. One is based on probabilistic method that requires
advanced tool--martingale. This proof covers the whole rate region. The other
proof is purely elementary but only covers part of the rate region. | 1810.11757v2 |
2021-05-26 | Lee Weight for Nonbinary Quantum Error Correction | We propose the quantum Lee weight for quantum errors, provide a
Gilbert-Varshamov type bound, and a code construction for the proposed weight. | 2105.12354v1 |
2020-05-26 | Reidemeister Moves in Gauss Diagrams | We provide a simple algorithm for recognizing and performing Reidemeister
moves in a Gauss diagram. | 2005.12957v1 |
2021-09-19 | Compactness of isospectral conformal Finslerian metrics set on a 3-manifold | Let F be a Finslerian metric on an n-dimensional closed manifold M. In this
work, we study problems about compactness of isospectral sets of conformal
Finslerian metrics when n=3. | 2110.06338v2 |
2001-05-31 | Lower bound for the quantum capacity of a discrete memoryless quantum channel | We generalize the random coding argument of stabilizer codes and derive a
lower bound on the quantum capacity of an arbitrary discrete memoryless quantum
channel. For the depolarizing channel, our lower bound coincides with that
obtained by Bennett et al. We also slightly improve the quantum
Gilbert-Varshamov bound for general stabilizer codes, and establish an analogue
of the quantum Gilbert-Varshamov bound for linear stabilizer codes. Our proof
is restricted to the binary quantum channels, but its extension of to l-adic
channels is straightforward. | 0105151v4 |
2007-09-26 | Finite Element Formalism for Micromagnetism | The aim of this work is to present the details of the finite element approach
we developed for solving the Landau-Lifschitz-Gilbert equations in order to be
able to treat problems involving complex geometries. There are several
possibilities to solve the complex Landau-Lifschitz-Gilbert equations
numerically. Our method is based on a Galerkin-type finite element approach. We
start with the dynamic Landau-Lifschitz-Gilbert equations, the associated
boundary condition and the constraint on the magnetization norm. We derive the
weak form required by the finite element method. This weak form is afterwards
integrated on the domain of calculus. We compared the results obtained with our
finite element approach with the ones obtained by a finite difference method.
The results being in very good agreement, we can state that our approach is
well adapted for 2D micromagnetic systems. | 0709.4153v1 |
2009-05-07 | Heat transport in stochastic energy exchange models of locally confined hard spheres | We study heat transport in a class of stochastic energy exchange systems that
characterize the interactions of networks of locally trapped hard spheres under
the assumption that neighbouring particles undergo rare binary collisions. Our
results provide an extension to three-dimensional dynamics of previous ones
applying to the dynamics of confined two-dimensional hard disks [Gaspard P &
Gilbert T On the derivation of Fourier's law in stochastic energy exchange
systems J Stat Mech (2008) P11021]. It is remarkable that the heat conductivity
is here again given by the frequency of energy exchanges. Moreover the
expression of the stochastic kernel which specifies the energy exchange
dynamics is simpler in this case and therefore allows for faster and more
extensive numerical computations. | 0905.1051v1 |
2011-08-15 | Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation | We consider a kinetic model of self-propelled particles with alignment
interaction and with precession about the alignment direction. We derive a
hydrodynamic system for the local density and velocity orientation of the
particles. The system consists of the conservative equation for the local
density and a non-conservative equation for the orientation. First, we assume
that the alignment interaction is purely local and derive a first order system.
However, we show that this system may lose its hyperbolicity. Under the
assumption of weakly non-local interaction, we derive diffusive corrections to
the first order system which lead to the combination of a heat flow of the
harmonic map and Landau-Lifschitz-Gilbert dynamics. In the particular case of
zero self-propelling speed, the resulting model reduces to the phenomenological
Landau-Lifschitz-Gilbert equations. Therefore the present theory provides a
kinetic formulation of classical micromagnetization models and spin dynamics. | 1108.2951v1 |
2011-09-30 | Magnetization Dynamics, Gyromagnetic Relation, and Inertial Effects | The gyromagnetic relation - i.e. the proportionality between the angular
momentum $\vec L$ (defined by an inertial tensor) and the magnetization $\vec
M$ - is evidence of the intimate connections between the magnetic properties
and the inertial properties of ferromagnetic bodies. However, inertia is absent
from the dynamics of a magnetic dipole (the Landau-Lifshitz equation, the
Gilbert equation and the Bloch equation contain only the first derivative of
the magnetization with respect to time). In order to investigate this
paradoxical situation, the lagrangian approach (proposed originally by T. H.
Gilbert) is revisited keeping an arbitrary nonzero inertial tensor. A dynamic
equation generalized to the inertial regime is obtained. It is shown how both
the usual gyromagnetic relation and the well-known Landau-Lifshitz-Gilbert
equation are recovered at the kinetic limit, i.e. for time scales above the
relaxation time $\tau$ of the angular momentum. | 1109.6782v1 |
2012-08-28 | Decomposition of modified Landau-Lifshitz-Gilbert equation and corresponding analytic solutions | The Suzuki-Trotter decomposition in general allows one to divide the equation
of motion of a dynamical system into smaller parts whose integration are easier
than the original equation. In this study, we first rewrite by employing
feasible approximations the modified Landau-Lifshitz-Gilbert equation for
localized spins in a suitable form for simulations using the Suzuki-Trotter
decomposition. Next we decompose the equation into parts and demonstrate that
the parts are classified into three groups, each of which can be solved
exactly. Since the modified Landau-Lifshitz-Gilbert equation from which we
start is in rather a general form, simulations of spin dynamics in various
systems accompanying only small numerical errors are possible. | 1208.5545v1 |
2016-11-21 | On the List-Decodability of Random Self-Orthogonal Codes | In 2011, Guruswami-H{\aa}stad-Kopparty \cite{Gru} showed that the
list-decodability of random linear codes is as good as that of general random
codes. In the present paper, we further strengthen the result by showing that
the list-decodability of random {\it Euclidean self-orthogonal} codes is as
good as that of general random codes as well, i.e., achieves the classical
Gilbert-Varshamov bound. Specifically, we show that, for any fixed finite field
$\F_q$, error fraction $\delta\in (0,1-1/q)$ satisfying $1-H_q(\delta)\le
\frac12$ and small $\epsilon>0$, with high probability a random Euclidean
self-orthogonal code over $\F_q$ of rate $1-H_q(\delta)-\epsilon$ is $(\delta,
O(1/\epsilon))$-list-decodable. This generalizes the result of linear codes to
Euclidean self-orthogonal codes. In addition, we extend the result to list
decoding {\it symplectic dual-containing} codes by showing that the
list-decodability of random symplectic dual-containing codes achieves the
quantum Gilbert-Varshamov bound as well. This implies that list-decodability of
quantum stabilizer codes can achieve the quantum Gilbert-Varshamov bound.
The counting argument on self-orthogonal codes is an important ingredient to
prove our result. | 1611.06673v1 |
2017-11-29 | Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-Gilbert equation | Combining ideas from [Alouges et al. (Numer. Math., 128, 2014)] and
[Praetorius et al. (Comput. Math. Appl., 2017)], we propose a numerical
algorithm for the integration of the nonlinear and time-dependent
Landau-Lifshitz-Gilbert (LLG) equation which is unconditionally convergent,
formally (almost) second-order in time, and requires only the solution of one
linear system per time-step. Only the exchange contribution is integrated
implicitly in time, while the lower-order contributions like the
computationally expensive stray field are treated explicitly in time. Then, we
extend the scheme to the coupled system of the Landau-Lifshitz-Gilbert equation
with the eddy current approximation of Maxwell equations (ELLG). Unlike
existing schemes for this system, the new integrator is unconditionally
convergent, (almost) second-order in time, and requires only the solution of
two linear systems per time-step. | 1711.10715v1 |
2017-12-28 | Subquadratic time encodable codes beating the Gilbert-Varshamov bound | We construct explicit algebraic geometry codes built from the
Garcia-Stichtenoth function field tower beating the Gilbert-Varshamov bound for
alphabet sizes at least 192. Messages are identied with functions in certain
Riemann-Roch spaces associated with divisors supported on multiple places.
Encoding amounts to evaluating these functions at degree one places. By
exploiting algebraic structures particular to the Garcia-Stichtenoth tower, we
devise an intricate deterministic \omega/2 < 1.19 runtime exponent encoding and
1+\omega/2 < 2.19 expected runtime exponent randomized (unique and list)
decoding algorithms. Here \omega < 2.373 is the matrix multiplication exponent.
If \omega = 2, as widely believed, the encoding and decoding runtimes are
respectively nearly linear and nearly quadratic. Prior to this work, encoding
(resp. decoding) time of code families beating the Gilbert-Varshamov bound were
quadratic (resp. cubic) or worse. | 1712.10052v2 |
2018-11-15 | Hilbert-Schmidt distance and entanglement witnessing | Gilbert proposed an algorithm for bounding the distance between a given point
and a convex set. In this article we apply the Gilbert's algorithm to get an
upper bound on the Hilbert-Schmidt distance between a given state and the set
of separable states. While Hilbert Schmidt Distance does not form a proper
entanglement measure, it can nevertheless be useful for witnessing
entanglement. We provide here a few methods based on the Gilbert's algorithm
that can reliably qualify a given state as strongly entangled or practically
separable, while being computationally efficient. The method also outputs
successively improved approximations to the Closest Separable State for the
given state. We demonstrate the efficacy of the method with examples. | 1811.06599v3 |
2020-02-13 | Age of Information with Gilbert-Elliot Servers and Samplers | We study age of information in a status updating system that consists of a
single sampler, i.e., source node, that sends time-sensitive status updates to
a single monitor node through a server node. We first consider a Gilbert-Elliot
service profile at the server node. In this model, service times at the server
node follow a finite state Markov chain with two states: ${bad}$ state $b$ and
${good}$ state $g$ where the server is faster in state $g$. We determine the
time average age experienced by the monitor node and characterize the
age-optimal state transition matrix $P$ with and without an average cost
constraint on the service operation. Next, we consider a Gilbert-Elliot
sampling profile at the source. In this model, the interarrival times follow a
finite state Markov chain with two states: ${bad}$ state $b$ and ${good}$ state
$g$ where samples are more frequent in state $g$. We find the time average age
experienced by the monitor node and characterize the age-optimal state
transition matrix $P$. | 2002.05711v1 |
2005-08-26 | Damping of MHD turbulence in Solar Flares | (Abridged) We describe the cascade of plasma waves or turbulence injected,
presumably by reconnection, at scales comparable to the size of a solar flare
loop to scales comparable to particle gyroradii, and evaluate their damping by
various mechanisms. We show that the classical viscous damping is unimportant
for magnetically dominated or low beta plasmas and the primary damping
mechanism is the collisionless damping by the background particles. We show
that the damping rate is proportional to the total random momentum density of
the particles. For solar flare conditions this means that in most flares,
except the very large ones, the damping is dominated by thermal background
electrons. For large flares one requires acceleration of essentially all
background electrons into a nonthermal distribution so that the accelerated
electrons can be important in the damping of the waves. In general, damping by
thermal or nonthermal protons is negligible compared to that of electrons
except for quasi-perpendicular propagating waves or for rare proton dominated
flares with strong nuclear gamma-ray line emission. Using the rate for damping
we determine the critical scale below which the damping becomes important and
the spectrum of the turbulence steepens. This critical scale, however, has
strong dependence on the angle of propagation with respect to the magnetic
field direction. The waves can cascade down to very small scales, such as the
gyroradii of the particles at small angles (quasi-parallel propagation) and
possibly near 90 degree (quasi-perpendicular propagation) giving rise to a
highly anisotropic spectral distribution. | 0508567v1 |
2011-07-27 | Constraint damping for the Z4c formulation of general relativity | One possibility for avoiding constraint violation in numerical relativity
simulations adopting free-evolution schemes is to modify the continuum
evolution equations so that constraint violations are damped away. Gundlach et.
al. demonstrated that such a scheme damps low amplitude, high frequency
constraint violating modes exponentially for the Z4 formulation of General
Relativity. Here we analyze the effect of the damping scheme in numerical
applications on a conformal decomposition of Z4. After reproducing the
theoretically predicted damping rates of constraint violations in the linear
regime, we explore numerical solutions not covered by the theoretical analysis.
In particular we examine the effect of the damping scheme on low-frequency and
on high-amplitude perturbations of flat spacetime as well and on the long-term
dynamics of puncture and compact star initial data in the context of spherical
symmetry. We find that the damping scheme is effective provided that the
constraint violation is resolved on the numerical grid. On grid noise the
combination of artificial dissipation and damping helps to suppress constraint
violations. We find that care must be taken in choosing the damping parameter
in simulations of puncture black holes. Otherwise the damping scheme can cause
undesirable growth of the constraints, and even qualitatively incorrect
evolutions. In the numerical evolution of a compact static star we find that
the choice of the damping parameter is even more delicate, but may lead to a
small decrease of constraint violation. For a large range of values it results
in unphysical behavior. | 1107.5539v2 |
1994-01-10 | Radio Emitting Dust in the Free-Electron Layer of Spiral Galaxies: Testing the Disk/Halo Interface | We present a study of the radio emission from rotating, charged dust grains
immersed in the ionized gas constituting the thick, H$\alpha$-emitting disk of
many spiral galaxies. Using up-to-date optical constants, the charge on the
grains exposed to the diffuse galactic UV flux has been calculated. An
analytical approximation for the grain charge has been derived, which is then
used to obtain the grain rotation frequency. Grains are found to have
substantial radio emission peaked at a cutoff frequency in the range
10-100~GHz, depending on the grain size distribution and on the efficiency of
the radiative damping of the grain rotation. The dust radio emission is
compared to the free-free emission from the ionized gas component; some
constraints on the magnetic field strength in the observed dusty filaments are
also discussed. The model can be used to test the disk-halo interface
environment in spiral galaxies, to determine the amount and size distribution
of dust in their ionized component, and to investigate the rotation mechanisms
for the dust. Numerical estimates are given for experimental purposes. | 9401010v1 |
1994-11-01 | Toward Understanding CMB Anisotropies and Their Implications | Working toward a model independent understanding of cosmic microwave
background (CMB) anisotropies and their significance, we undertake a
comprehensive and self-contained study of scalar perturbation theory. Initial
conditions, evolution, thermal history, matter content, background dynamics,
and geometry all play a role in determining the anisotropy. By employing {\it
analytic} techniques to illuminate the numerical results, we are able to
separate and identify each contribution. We thus bring out the nature of the
{\it total} Sachs-Wolfe effect, acoustic oscillations, diffusion damping,
Doppler shifts, and reionization, as well as their particular manifestation in
a critical, curvature, or cosmological constant dominated universe. By studying
the full angular {\it and} spatial content of the resultant anisotropies, we
isolate the signature of these effects from the dependence on initial
conditions. Whereas structure in the Sachs-Wolfe anisotropy depends strongly on
the underlying power spectra, the acoustic oscillations provide features which
are nearly model independent. This may allow for future determination of the
matter content of the universe as well as the adiabatic and/or isocurvature
nature of the initial fluctuations. | 9411008v1 |
1995-02-20 | Constraints on Self-Interacting Dark Matter | We consider the growth of density perturbations in the presence of
self--interacting dark matter, SIDM, proposed by Carlson, Machacek and Hall
(1992). We determine the range of values for the coupling constant $\lambda$
and the particle mass $m^\prime$, for which the power spectrum lies in the
``allowed" range based on constraints from the IRAS galaxy survey and damped
Lyman--$\alpha $ systems. Our results show that no combination of parameters
can meet both limits. We consider constraints on the $\2-2$ scatterings which
keep the SIDM particles in pressure equilibrium, and we show that if such
interactions maintain pressure equilibrium down to the present, they will be
strong enough to disrupt galaxy mergers and may lead to stripping of galaxy
halos as galaxies move through the dark matter background of these particles.
Hence, we also investigate the evolution of large-scale structure in the SIDM
model when the particles drop out of pressure equilibrium at some higher
redshift. The resulting free-streaming leads to an additional suppression of
small-scale perturbations, but it does not significantly affect our results. | 9502087v1 |
1996-12-16 | Favored Variants of Cold Dark Matter Cosmologies | We discuss variants of Cold Dark Matter (CDM) dominated cosmological models
that give good agreement with a range of observations. We consider models with
hot dark matter, tilt, $\Omega < 1$, or a cosmological constant. We also
discuss the sensitivity of the results to other parameters, such as the Hubble
parameter and the baryon fraction. We obtain constraints by combining the COBE
data, cluster abundances, abundance of damped Lyman-$\alpha$ systems at
$z\sim3$, the small-angle Cosmic Microwave Background anisotropy, and the
small-scale non-linear power spectrum. We present non-linear power spectra from
a new suite of N-body simulations for the ``best-bet'' models from each
category. | 9612156v1 |
1997-08-07 | Gravitational Magnification of the Cosmic Microwave Background | Some aspects of gravitational lensing by large scale structure (LSS) are
investigated. We show that lensing causes the damping tail of the cosmic
microwave background (CMB) power spectrum to fall less rapidly with decreasing
angular scale than previously expected. This is due to a transfer of power from
larger to smaller angular scales which produces a fractional change in power
spectrum that increases rapidly beyond $\ell \sim 2000$. We also find that
lensing produces a nonzero mean magnification of structures on surfaces of
constant redshift if weighted by area on the sky. This is a result of the fact
that light-rays that are evenly distributed on the sky oversample overdense
regions. However this mean magnification has a negligible affect on the CMB
power spectrum. A new expression for the lensed power spectrum is derived and
it is found that future precision observations the high-$\ell$ tail of the
power spectrum will need to take into account lensing when determining
cosmological parameters. | 9708059v1 |
1997-09-09 | Thermochemical Instabilities in Optically Thin Reacting Plasmas | The linear stability analysis of an optically thin plasma where a general
reaction proceeds, including chemical relaxation time effects, is carried out .
A fifth order dispersion equation (instead of the fourth order one resulting
when such effects are neglected) is obtained. The new mode with the
corresponding instability criterion as well as the modifications of the
previous four modes and the corresponding instability criteria, are analyzed.
Generally, a further stabilizing effect on the unstable modes and an increasing
of the damping of stable modes appear because of the second viscosity generated
by the chemical reaction. The results are applied to: (1) a collisionally
ionized pure hydrogen plasma heated at a constant rate per unit mass and cooled
by free-free transitions, ionization, and e-H collisional excitations; (2) a
diffused gas with metallicity Z, photoionized and heated by a radiation field,
and cooled by excitation of hydrogen and heavy metal lines. | 9709079v1 |
1998-11-10 | Temperature Anisotropies and Distortions Induced by Hot Intracluster Gas on the Cosmic Microwave Background | The power spectrum of temperature anisotropies induced by hot intracluster
gas on the cosmic background radiation is calculated. For low multipoles it
remains constant while at multipoles above $l>2000$ it is exponentially damped.
The shape of the radiation power spectrum is almost independent of the average
intracluster gas density profile, gas evolution history or clusters virial
radii; but the amplitude depends strongly on those parameters and could be as
large as 20% that of intrinsic contribution. The exact value depends on the
global properties of the cluster population and the evolution of the
intracluster gas. The distortion on the Cosmic Microwave Background black body
spectra varies in a similar manner. The ratio of the temperature anisotropy to
the mean Comptonization parameters is shown to be almost independent of the
cluster model and, in first approximation, depends only on the number density
of clusters. | 9811158v1 |
2001-12-13 | Do the Fundamental Constants Vary in the Course of the Cosmological Evolution? | We estimate the cosmological variation of the proton-to-electron mass ratio
\mu=m_p/m_e by measuring the wavelengths of molecular hydrogen transitions in
the early universe. The analysis is performed using high spectral resolution
observations (FWHM ~ 7 km/s) of two damped Lyman-\alpha systems at
z_{abs}=2.3377 and 3.0249 observed along the lines of sight to the quasars Q
1232+082 and Q 0347-382 respectively. The most conservative result of the
analysis is a possible variation of \mu over the last ~ 10 Gyrs, with an
amplitude \Delta\mu/\mu = (5.7+-3.8)x10^{-5}. The result is significant at the
1.5\sigma level only and should be confirmed by further observations. This is
the most stringent estimate of a possible cosmological variation of \mu
obtained up to now. | 0112323v2 |
2002-10-20 | Non-Axisymmetric g-Mode and p-Mode Instability in a Hydrodynamic Thin Accretion Disk | It has been suggested that quasi-periodic oscillations of accreting X-ray
sources may relate to the modes named in the title. We consider
non-axisymmetric linear perturbations to an isentropic, isothermal,
unmagnetized thin accretion disk. The radial wave equation, in which the number
of vertical nodes (n) appears as a separation constant, admits a wave-action
current that is conserved except, in some cases, at corotation. Waves without
vertical nodes amplify when reflected by a barrier near corotation. Their
action is conserved. As was previously known, this amplification allows the n=0
modes to be unstable under appropriate boundary conditions. In contrast, we
find that waves with n >0 are strongly absorbed at corotation rather than
amplified; their action is not conserved. Therefore, non-axisymmetric p-modes
and g-modes with n>0 are damped and stable even in an inviscid disk. This
eliminates a promising explanation for quasi-periodic oscillations in
neutron-star and black-hole X-ray binaries. | 0210455v3 |
2003-10-23 | Atomic and Molecular Absorption at High Redshift | Strong constraints on possible variations in fundamental constants can be
derived from HI 21-cm and molecular rotational absorption lines observed
towards quasars. With the aim of forming a statistical sample of constraints we
have begun a program of systematic searches for such absorption systems. Here
we describe molecular rotational searches in 25 damped Lyman-alpha systems
where, in many cases, we set optical depth limits an order of magnitude better
than that required to detect the 4 known redshifted millimeter-wave absorbers.
We also discuss the contributory factors in the detectability of HI 21-cm
absorption, focusing on possible biases (e.g.low covering factors) in the
currently known sample of absorbers and non-detections. | 0310672v2 |
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