pinecone/core-2020-05-10-deduplication huggingface dataset:
On the roots of the node reliability polynomial

Given a graph $G$ whose edges are perfectly reliable and whose nodes each
operate independently with probability $p\in[0,1],$ the node reliability of $G$
is the probability that at least one node is operational and that the
operational nodes can all communicate in the subgraph that they induce; it is
the analogous node measure of robustness to the well studied
\textit{all-terminal reliability}, where the nodes are perfectly reliable but
the edges fail randomly. In sharp contrast to what is known about the roots of
the all-terminal reliability polynomial, we show that the node reliability
polynomial of any connected graph on at least three nodes has a nonreal
polynomial root, the collection of real roots of all node reliability
polynomials is unbounded, and the collection of complex roots of all node
reliability polynomials is dense in the entire complex plane.Comment: 3 figure
Designing Networks: A Mixed-Integer Linear Optimization Approach

Designing networks with specified collective properties is useful in a
variety of application areas, enabling the study of how given properties affect
the behavior of network models, the downscaling of empirical networks to
workable sizes, and the analysis of network evolution. Despite the importance
of the task, there currently exists a gap in our ability to systematically
generate networks that adhere to theoretical guarantees for the given property
specifications. In this paper, we propose the use of Mixed-Integer Linear
Optimization modeling and solution methodologies to address this Network
Generation Problem. We present a number of useful modeling techniques and apply
them to mathematically express and constrain network properties in the context
of an optimization formulation. We then develop complete formulations for the
generation of networks that attain specified levels of connectivity, spread,
assortativity and robustness, and we illustrate these via a number of
computational case studies
A parameterized approximation algorithm for the mixed and windy
  Capacitated Arc Routing Problem: theory and experiments

We prove that any polynomial-time $\alpha(n)$-approximation algorithm for the
$n$-vertex metric asymmetric Traveling Salesperson Problem yields a
polynomial-time $O(\alpha(C))$-approximation algorithm for the mixed and windy
Capacitated Arc Routing Problem, where $C$ is the number of weakly connected
components in the subgraph induced by the positive-demand arcs---a small number
in many applications. In conjunction with known results, we obtain
constant-factor approximations for $C\in O(\log n)$ and $O(\log C/\log\log
C)$-approximations in general. Experiments show that our algorithm, together
with several heuristic enhancements, outperforms many previous polynomial-time
heuristics. Finally, since the solution quality achievable in polynomial time
appears to mainly depend on $C$ and since $C=1$ in almost all benchmark
instances, we propose the Ob benchmark set, simulating cities that are divided
into several components by a river.Comment: A preliminary version of this article appeared in the Proceedings of
  the 15th Workshop on Algorithmic Approaches for Transportation Modeling,
  Optimization, and Systems (ATMOS'15). This version describes several
  algorithmic enhancements, contains an experimental evaluation of our
  algorithm, and provides a new benchmark data se
Dedicated protection of multicast sessions in mixed-graph sparse-splitting optical networks

This work addresses the problem of dedicated protection of multicast sessions in mixed-graph optical networks, where only a fraction of the nodes have optical splitting capabilities. 
A novel multicast routing algorithm for sparse splitting optical networks (the Modified Steiner Tree Heuristic (MSTH)) is initially presented  and is subsequently utilized (together with two existing heuristics (MUS and MSH)) by an effective scheme for the calculation of a pair of disjoint trees. 
The key idea of this New Arc-Disjoint Trees (NADT) protection technique is to gradually construct the primary tree, verifying that after the addition of each one of the destinations of the multicast session, a secondary (arc-disjoint) tree can still be obtained. 
Performance results demonstrate that the proposed NADT protection technique clearly outperforms the conventional Arc-Disjoint Trees (ADT) approach in terms of blocking ratio, while incurring only a negligible increase of the average cost of the derived pair of arc-disjoint trees. 
Furthermore, it is shown that the newly proposed algorithm, MSTH-NADT, is the one having the best performance in terms of cost and blocking, with MSH-NADT having similar, albeit slightly worse, performance. However, as MSH-NADT requires much less CPU time compared to MSTH-NADT, MSH-NADT can be considered the best compromise technique
Network Coding Algorithms for Multi-Layered Video Broadcast

In this paper we give network coding algorithms for multi-layered video
streaming. The problem is motivated by video broadcasting in a communication
network to users with varying demands. We give a polynomial time algorithm for
deciding feasibility for the case of two layers, and show that the problem
becomes NP-hard if the task is to maximize the number of satisfied demands. For
the case of three layers we also show NP-hardness of the problem. Finally, we
propose a heuristic for three layers and give experimental comparison with
previous approaches.Comment: A preliminary version entitled "A Network Coding Algorithm for
  Multi-Layered Video Streaming" presented at International Symposium on
  Network Coding (NetCod), 201
Safe sets, network majority on weighted trees

Let G = (V, E) be a graph and let w : V → ℝ>0 be a positive weight function on the vertices of G. For every subset X of V, let w(X) ≔ ∑v∈Gw(v). A non-empty subset ∑ is a weighted safe set if, for every component C of the subgraph induced by S and every component D of G/S, we have w(C) ≥ w(D) whenever there is an edge between C and D. If the subgraph G(S) induced by a weighted safe set S is connected, then the set S is called a weighted connected safe set. In this article, we show that the problem of computing the minimum weight of a safe set is NP-hard for trees, even if the underlying tree is restricted to be a star, but it is polynomially solvable for paths. We also give an O(n log n) time 2-approximation algorithm for finding a weighted connected safe set with minimum weight in a weighted tree. Then, as a generalization of the concept of a minimum safe set, we define the concept of a parameterized infinite family of proper central subgraphs on weighted trees, whose polar ends are the vertex set of the tree and the centroid points. We show that each of these central subgraphs includes a centroid point. © 2017 Wiley Periodicals, Inc
Probabilistic $N$-$k$ Failure-Identification for Power Systems

This paper considers a probabilistic generalization of the $N$-$k$
failure-identification problem in power transmission networks, where the
probability of failure of each component in the network is known a priori and
the goal of the problem is to find a set of $k$ components that maximizes
disruption to the system loads weighted by the probability of simultaneous
failure of the $k$ components. The resulting problem is formulated as a bilevel
mixed-integer nonlinear program. Convex relaxations, linear approximations, and
heuristics are developed to obtain feasible solutions that are close to the
optimum. A general cutting-plane algorithm is proposed to solve the convex
relaxation and linear approximations of the $N$-$k$ problem. Extensive
numerical results corroborate the effectiveness of the proposed algorithms on
small-, medium-, and large-scale test instances, the test instances include the
IEEE 14-bus system, the IEEE single-area and three-area RTS96 systems, the IEEE
118-bus system, the WECC 240-bus test system, the 1354-bus PEGASE system, and
the 2383-bus Polish winter-peak test system.Comment: 17 pages, Networks, 201
Faster Parametric Shortest Path and Minimum Balance Algorithms

The parametric shortest path problem is to find the shortest paths in graph
where the edge costs are of the form w_ij+lambda where each w_ij is constant
and lambda is a parameter that varies. The problem is to find shortest path
trees for every possible value of lambda.
  The minimum-balance problem is to find a ``weighting'' of the vertices so
that adjusting the edge costs by the vertex weights yields a graph in which,
for every cut, the minimum weight of any edge crossing the cut in one direction
equals the minimum weight of any edge crossing the cut in the other direction.
  The paper presents fast algorithms for both problems. The algorithms run in
O(nm+n^2 log n) time. The paper also describes empirical studies of the
algorithms on random graphs, suggesting that the expected time for finding a
minimum-mean cycle (an important special case of both problems) is O(n log(n) +
m)
Behavioral genetic approaches to visual system development and function in zebrafish.

The zebrafish is a recent vertebrate model system that shows great potential for a genetic analysis of behavior. Early development is extraordinarily rapid, so that larvae already display a range of behaviors 5 days after fertilization. In particular the visual system develops precociously, supporting a number of visually mediated behaviors in the larva. This provides the opportunity to use these visually mediated behaviors to screen chemically mutagenized strains for defects in vision. Larval optokinetic and optomotor responses have already been successfully employed to screen for mutant strains with defects in the visual system. In the adult zebrafish a visually mediated escape response has proved useful for screening for dominant mutations of the visual system. Here, I summarize visually mediated behaviors of both larval and adult zebrafish and their applicability for genetic screens, and present, the approaches and results of visual behavior carried out to date
Some Inverse Eigenproblems for Jacobi and Arrow Matrices

The first and third authors were supported by direct grant from the Naval Postgraduate School.  The third author also acknowledges support from the Interdisciplinary Project Center for Supercomputing at the ETH, Zurich.The article of record as published may be found at DOI: 10.1002/nla.1680020302We consider the problem of reconstruction Jacobi matrices and real symmetric arrow matrices from two eigenpairs.  Algorithms for solving these inverse problems are presented.  We show that there are reasonable conditions under which this reconstruction is always possible.  Moreover, it is seen that in certain cases reconstruction can proceed with little or no cancellation.  The algorithm is particularly elegant for the tridiagonal matrix associated with a bidiagonal singular value decomposition
A Subspace Shift Technique for Nonsymmetric Algebraic Riccati Equations

The worst situation in computing the minimal nonnegative solution of a
nonsymmetric algebraic Riccati equation associated with an M-matrix occurs when
the corresponding linearizing matrix has two very small eigenvalues, one with
positive and one with negative real part. When both these eigenvalues are
exactly zero, the problem is called critical or null recurrent. While in this
case the problem is ill-conditioned and the convergence of the algorithms based
on matrix iterations is slow, there exist some techniques to remove the
singularity and transform the problem to a well-behaved one. Ill-conditioning
and slow convergence appear also in close-to-critical problems, but when none
of the eigenvalues is exactly zero the techniques used for the critical case
cannot be applied.
  In this paper, we introduce a new method to accelerate the convergence
properties of the iterations also in close-to-critical cases, by working on the
invariant subspace associated with the problematic eigenvalues as a whole. We
present a theoretical analysis and several numerical experiments which confirm
the efficiency of the new method
Combination preconditioning of saddle point systems for positive definiteness

Amongst recent contributions to preconditioning methods for saddle point systems, standard iterative methods in nonstandard inner products have been usefully employed. Krzyzanowski ( ˙ Numer. Linear Algebra Appl. 2011; 18:123–140) identified a two-parameter family of preconditioners in this context and Stoll and Wathen (SIAM J. Matrix Anal. Appl. 2008; 30:582–608) introduced combination preconditioning, where two preconditioners, self-adjoint with respect to different inner products, can lead to further preconditioners and associated bilinear forms or inner products. Preconditioners that render the preconditioned saddle point matrix nonsymmetric but self-adjoint with respect to a nonstandard inner product always allow a MINREStype method (W-PMINRES) to be applied in the relevant inner product. If the preconditioned matrix is also positive definite with respect to the inner product a more efficient CG-like method (W-PCG) can be reliably used. We establish eigenvalue expressions for Krzyzanowski preconditioners and show that for a specific ˙ choice of parameters, although the Krzyzanowski preconditioned saddle point matrix is self-adjoint with ˙ respect to an inner product, it is never positive definite. We provide explicit expressions for the combination of certain preconditioners and prove the rather counterintuitive result that the combination of two specific preconditioners for which only W-PMINRES can be reliably used leads to a preconditioner for which, for certain parameter choices, W-PCG is reliably applicable. That is, combining two indefinite preconditioners can lead to a positive definite preconditioner. This combination preconditioner outperforms either of the two preconditioners from which it is formed for a number of test problems
Improved Seed Methods for Symmetric Positive Definite Linear Equations
  with Multiple Right-hand Sides

We consider symmetric positive definite systems of linear equations with
multiple right-hand sides. The seed conjugate gradient method solves one
right-hand side with the conjugate gradient method and simultaneously projects
over the Krylov subspace thus developed for the other right-hand sides. Then
the next system is solved and used to seed the remaining ones. Rounding error
in the conjugate gradient method limits how much the seeding can improve
convergence. We propose three changes to the seed conjugate gradient method:
only the first right-hand side is used for seeding, this system is solved past
convergence, and the roundoff error is controlled with some
reorthogonalization. We will show that results are actually better with only
one seeding, even in the case of related right-hand sides. Controlling rounding
error gives the potential for rapid convergence for the second and subsequent
right-hand sides.Comment: 11 pages, 7 figure
Computing a logarithm of a unitary matrix with general spectrum

We analyze an algorithm for computing a skew-Hermitian logarithm of a unitary
matrix. This algorithm is very easy to implement using standard software and it
works well even for unitary matrices with no spectral conditions assumed.
Certain examples, with many eigenvalues near -1, lead to very non-Hermitian
output for other basic methods of calculating matrix logarithms. Altering the
output of these algorithms to force an Hermitian output creates accuracy issues
which are avoided in the considered algorithm.
  A modification is introduced to deal properly with the $J$-skew symmetric
unitary matrices. Applications to numerical studies of topological insulators
in two symmetry classes are discussed.Comment: Added discussion of Floquet Hamiltonian
Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration

Convergence results are provided for inexact two-sided inverse and Rayleigh quotient iteration, which extend the previously established results to the generalized non-Hermitian eigenproblem and inexact solves with a decreasing solve tolerance. Moreover, the simultaneous solution of the forward and adjoint problem arising in two-sided methods is considered, and the successful tuning strategy for preconditioners is extended to two-sided methods, creating a novel way of preconditioning two-sided algorithms. Furthermore, it is shown that inexact two-sided Rayleigh quotient iteration and the inexact two-sided Jacobi-Davidson method (without subspace expansion) applied to the generalized preconditioned eigenvalue problem are equivalent when a certain number of steps of a Petrov-Galerkin-Krylov method is used and when this specific tuning strategy is applied
Multigrid-in-time for sensitivity analysis of chaotic dynamical systems

The following paper discusses the application of a multigrid-in-time scheme to Least Squares Shadowing (LSS), a novel sensitivity analysis method for chaotic dynamical systems. While traditional sensitivity analysis methods break down for chaotic dynamical systems, LSS is able to compute accurate gradients. Multigrid is used because LSS requires solving a very large Karush–Kuhn–Tucker system constructed from the solution of the dynamical system over the entire time interval of interest. Several different multigrid-in-time schemes are examined, and a number of factors were found to heavily influence the convergence rate of multigrid-in-time for LSS. These include the iterative method used for the smoother, how the coarse grid system is formed and how the least squares objective function at the center of LSS is weighted.United States. National Aeronautics and Space Administration (Award NNH11ZEA001N)American Society for Engineering Education. National Defense Science and Engineering Graduate Fellowshi
Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs

Symmetric collocation methods with RBFs allow approximation of the solution of a partial differential equation, even if the right-hand side is only known at scattered data points, without needing to generate a grid. However, the benefit of a guaranteed symmetric positive definite block system comes at a high computational cost. This cost can be alleviated somewhat by considering compactly supported RBFs and a multiscale technique. But the condition number and sparsity will still deteriorate with the number of data points. Therefore, we study certain block diagonal and triangular preconditioners. We investigate ideal preconditioners and determine the spectra of the preconditioned matrices before proposing more practical preconditioners based on a restricted additive Schwarz method with coarse grid correction. Numerical results verify the effectiveness of the preconditioners
BDDC for Mixed-Hybrid Formulation of Flow in Porous Media with Combined
  Mesh Dimensions

We extend the Balancing Domain Decomposition by Constraints (BDDC) method to
flows in porous media discretised by mixed-hybrid finite elements with combined
mesh dimensions. Such discretisations appear when major geological fractures
are modelled by 1D or 2D elements inside three-dimensional domains. In this
set-up, the global problem as well as the substructure problems have a
symmetric saddle-point structure, containing a `penalty' block due to the
combination of meshes. We show that the problem can be reduced by means of
iterative substructuring to an interface problem, which is symmetric and
positive definite. The interface problem can thus be solved by conjugate
gradients with the BDDC method as a preconditioner. A parallel implementation
of this algorithm is incorporated into an existing software package for
subsurface flow simulations. We study the performance of the iterative solver
on several academic and real-world problems. Numerical experiments illustrate
its efficiency and scalability.Comment: 27 pages, 13 figures, 7 table
Fast low-rank approximations of multidimensional integrals in ion-atomic
  collisions modelling

An efficient technique based on low-rank separated approximations is proposed
for computation of three-dimensional integrals arising in the energy deposition
model that describes ion-atomic collisions. Direct tensor-product quadrature
requires grids of size $4000^3$ which is unacceptable. Moreover, several of
such integrals have to be computed simultaneously for different values of
parameters. To reduce the complexity, we use the structure of the integrand and
apply numerical linear algebra techniques for the construction of low-rank
approximation. The resulting algorithm is $10^3$ faster than spectral
quadratures in spherical coordinates used in the original DEPOSIT code. The
approach can be generalized to other multidimensional problems in physics.Comment: arXiv admin note: text overlap with arXiv:1403.406
Iterative representing set selection for nested cross approximation

A new fast algebraic method for obtaining an $\mathcal{H}^2$-approximation of
a matrix from its entries is presented. The main idea behind the method is
based on the nested representation and the maximum-volume principle to select
submatrices in low-rank matrices. A special iterative approach for the
computation of so-called representing sets is established. The main advantage
of the method is that it uses only the hierarchical partitioning of the matrix
and does not require special "proxy surfaces" to be selected in advance.
  The numerical experiments for the electrostatic problem and for the boundary
integral operator confirm the effectiveness and robustness of the approach. The
complexity is linear in the matrix size and polynomial in the ranks. The
algorithm is implemented as an open-source Python package that is available
online.Comment: Numer. Linear Algebra Appl. 201
Reducing complexity of algebraic multigrid by aggregation

A typical approach to decrease computational costs and memory requirements of classical algebraic multigrid methods is to replace a conservative coarsening algorithm and short-distance interpolation on a fixed number of fine levels by an aggressive coarsening with a long-distance interpolation. Although the quality of the resulting algebraic multigrid grid preconditioner often deteriorates in terms of convergence rates and iteration counts of the preconditioned iterative solver, the overall performance can improve substantially. We investigate here, as an alternative, a possibility to replace the classical aggressive coarsening by aggregation, which is motivated by the fact that the convergence of aggregation methods can be independent of the problem size provided that the number of levels is fixed. The relative simplicity of aggregation can lead to improved solution and setup costs. The numerical experiments show the relevance of the proposed combination on both academic and benchmark problems in reservoir simulation from oil industry