38,530 research outputs found

### An Analysis Tool for Push-Sum Based Distributed Optimization

The push-sum algorithm is probably the most important distributed averaging
approach over directed graphs, which has been applied to various problems
including distributed optimization. This paper establishes the explicit
absolute probability sequence for the push-sum algorithm, and based on which,
constructs quadratic Lyapunov functions for push-sum based distributed
optimization algorithms. As illustrative examples, the proposed novel analysis
tool can improve the convergence rates of the subgradient-push and stochastic
gradient-push, two important algorithms for distributed convex optimization
over unbalanced directed graphs. Specifically, the paper proves that the
subgradient-push algorithm converges at a rate of $O(1/\sqrt{t})$ for general
convex functions and stochastic gradient-push algorithm converges at a rate of
$O(1/t)$ for strongly convex functions, over time-varying unbalanced directed
graphs. Both rates are respectively the same as the state-of-the-art rates of
their single-agent counterparts and thus optimal, which closes the theoretical
gap between the centralized and push-sum based (sub)gradient methods. The paper
further proposes a heterogeneous push-sum based subgradient algorithm in which
each agent can arbitrarily switch between subgradient-push and
push-subgradient. The heterogeneous algorithm thus subsumes both
subgradient-push and push-subgradient as special cases, and still converges to
an optimal point at an optimal rate. The proposed tool can also be extended to
analyze distributed weighted averaging.Comment: arXiv admin note: substantial text overlap with arXiv:2203.16623,
arXiv:2303.1706

### MAS: A versatile Landau-fluid eigenvalue code for plasma stability analysis in general geometry

We have developed a new global eigenvalue code, Multiscale Analysis for
plasma Stabilities (MAS), for studying plasma problems with wave toroidal mode
number n and frequency omega in a broad range of interest in general tokamak
geometry, based on a five-field Landau-fluid description of thermal plasmas.
Beyond keeping the necessary plasma fluid response, we further retain the
important kinetic effects including diamagnetic drift, ion finite Larmor
radius, finite parallel electric field, ion and electron Landau resonances in a
self-consistent and non-perturbative manner without sacrificing the attractive
efficiency in computation. The physical capabilities of the code are evaluated
and examined in the aspects of both theory and simulation. In theory, the
comprehensive Landau-fluid model implemented in MAS can be reduced to the
well-known ideal MHD model, electrostatic ion-fluid model, and drift-kinetic
model in various limits, which clearly delineates the physics validity regime.
In simulation, MAS has been well benchmarked with theory and other gyrokinetic
and kinetic-MHD hybrid codes in a manner of adopting the unified physical and
numerical framework, which covers the kinetic Alfven wave, ion sound wave,
low-n kink, high-n ion temperature gradient mode and kinetic ballooning mode.
Moreover, MAS is successfully applied to model the Alfven eigenmode (AE)
activities in DIII-D discharge #159243, which faithfully captures the frequency
sweeping of RSAE, the tunneling damping of TAE, as well as the polarization
characteristics of KBAE and BAAE being consistent with former gyrokinetic
theory and simulation. With respect to the key progress contributed to the
community, MAS has the advantage of combining rich physics ingredients,
realistic global geometry and high computation efficiency together for plasma
stability analysis in linear regime.Comment: 40 pages, 21 figure

### An incremental input-to-state stability condition for a generic class of recurrent neural networks

This paper proposes a novel sufficient condition for the incremental
input-to-state stability of a generic class of recurrent neural networks
(RNNs). The established condition is compared with others available in the
literature, showing to be less conservative. Moreover, it can be applied for
the design of incremental input-to-state stable RNN-based control systems,
resulting in a linear matrix inequality constraint for some specific RNN
architectures. The formulation of nonlinear observers for the considered system
class, as well as the design of control schemes with explicit integral action,
are also investigated. The theoretical results are validated through simulation
on a referenced nonlinear system

### A family of total Lagrangian Petrov-Galerkin Cosserat rod finite element formulations

The standard in rod finite element formulations is the Bubnov-Galerkin
projection method, where the test functions arise from a consistent variation
of the ansatz functions. This approach becomes increasingly complex when highly
nonlinear ansatz functions are chosen to approximate the rod's centerline and
cross-section orientations. Using a Petrov-Galerkin projection method, we
propose a whole family of rod finite element formulations where the nodal
generalized virtual displacements and generalized velocities are interpolated
instead of using the consistent variations and time derivatives of the ansatz
functions. This approach leads to a significant simplification of the
expressions in the discrete virtual work functionals. In addition, independent
strategies can be chosen for interpolating the nodal centerline points and
cross-section orientations. We discuss three objective interpolation strategies
and give an in-depth analysis concerning locking and convergence behavior for
the whole family of rod finite element formulations.Comment: arXiv admin note: text overlap with arXiv:2301.0559

### Partial mass concentration for fast-diffusions with non-local aggregation terms

We study well-posedness and long-time behaviour of aggregation-diffusion
equations of the form $\frac{\partial \rho}{\partial t} = \Delta \rho^m +
\nabla \cdot( \rho (\nabla V + \nabla W \ast \rho))$ in the fast-diffusion
range, $0<m<1$, and $V$ and $W$ regular enough. We develop a well-posedness
theory, first in the ball and then in $\mathbb R^d$, and characterise the
long-time asymptotics in the space $W^{-1,1}$ for radial initial data. In the
radial setting and for the mass equation, viscosity solutions are used to prove
partial mass concentration asymptotically as $t \to \infty$, i.e. the limit as
$t \to \infty$ is of the form $\alpha \delta_0 + \widehat \rho \, dx$ with
$\alpha \geq 0$ and $\widehat \rho \in L^1$. Finally, we give instances of $W
\ne 0$ showing that partial mass concentration does happen in infinite time,
i.e. $\alpha > 0$

### Quantum resonances and analysis of the survival amplitude in the nonlinear Winter's model

In this paper we show that the typical effects of quantum resonances, namely,
the exponential-type decay of the survival amplitude, continue to exist even
when a nonlinear perturbative term is added to the time-dependent Schroedinger
equation. The difficulty in giving a rigorous and appropriate definition of
quantum resonances by means of the notions already used for linear equations is
also highlighted.Comment: 31 pages, 8 figure

### Jack Derangements

For each integer partition $\lambda \vdash n$ we give a simple combinatorial
expression for the sum of the Jack character $\theta^\lambda_\alpha$ over the
integer partitions of $n$ with no singleton parts. For $\alpha = 1,2$ this
gives closed forms for the eigenvalues of the permutation and perfect matching
derangement graphs, resolving an open question in algebraic graph theory. A
byproduct of the latter is a simple combinatorial formula for the immanants of
the matrix $J-I$ where $J$ is the all-ones matrix, which might be of
independent interest. Our proofs center around a Jack analogue of a hook
product related to Cayley's $\Omega$--process in classical invariant theory,
which we call the principal lower hook product

### Likelihood Asymptotics in Nonregular Settings: A Review with Emphasis on the Likelihood Ratio

This paper reviews the most common situations where one or more regularity
conditions which underlie classical likelihood-based parametric inference fail.
We identify three main classes of problems: boundary problems, indeterminate
parameter problems -- which include non-identifiable parameters and singular
information matrices -- and change-point problems. The review focuses on the
large-sample properties of the likelihood ratio statistic. We emphasize
analytical solutions and acknowledge software implementations where available.
We furthermore give summary insight about the possible tools to derivate the
key results. Other approaches to hypothesis testing and connections to
estimation are listed in the annotated bibliography of the Supplementary
Material

### A decoherence-based approach to the classical limit in Bohm's theory

The paper explains why the de Broglie-Bohm theory reduces to Newtonian mechanics in the macroscopic classical limit. The quantum-to-classical transition is based on three steps: (i) interaction with the environment produces effectively factorized states, leading to the formation of effective wave functions and hence decoherence; (ii) the effective wave functions selected by the environment–the pointer states of decoherence theory–will be well-localized wave packets, typically Gaussian states; (iii) the quantum potential of a Gaussian state becomes negligible under standard classicality conditions; therefore, the effective wave function will move according to Newtonian mechanics in the correct classical limit. As a result, a Bohmian system in interaction with the environment will be described by an effective Gaussian state and–when the system is macroscopic–it will move according to Newtonian mechanics

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