scholarly journals Nearest $$\varOmega $$-stable matrix via Riemannian optimization

2021 ◽  
Author(s):  
Vanni Noferini ◽  
Federico Poloni
Keyword(s):  
Optimization Problem ◽  
Small Scale ◽  
Frobenius Norm ◽  
Unitary Matrices ◽  
Riemannian Optimization ◽  
Important Special Case ◽  
Closed Set ◽  
Standard Methods ◽  
Special Case ◽  
Stable Matrix

AbstractWe study the problem of finding the nearest $$\varOmega $$ Ω -stable matrix to a certain matrix A, i.e., the nearest matrix with all its eigenvalues in a prescribed closed set $$\varOmega $$ Ω . Distances are measured in the Frobenius norm. An important special case is finding the nearest Hurwitz or Schur stable matrix, which has applications in systems theory. We describe a reformulation of the task as an optimization problem on the Riemannian manifold of orthogonal (or unitary) matrices. The problem can then be solved using standard methods from the theory of Riemannian optimization. The resulting algorithm is remarkably fast on small-scale and medium-scale matrices, and returns directly a Schur factorization of the minimizer, sidestepping the numerical difficulties associated with eigenvalues with high multiplicity.

ON THE DENSITY OF HAUSDORFF DIMENSIONS OF BOUNDED TYPE CONTINUED FRACTION SETS: THE TEXAN CONJECTURE

2004 ◽  
Vol 04 (01) ◽  
pp. 63-76 ◽  
Author(s):  
OLIVER JENKINSON
Keyword(s):  
Hausdorff Dimension ◽  
Finite Subset ◽  
Continued Fraction ◽  
Cantor Set ◽  
Computational Method ◽  
Accurate Approximation ◽  
Natural Numbers ◽  
Important Special Case ◽  
The One ◽  
Special Case

Given a non-empty finite subset A of the natural numbers, let EA denote the set of irrationals x∈[0,1] whose continued fraction digits lie in A. In general, EA is a Cantor set whose Hausdorff dimension dim (EA) is between 0 and 1. It is shown that the set [Formula: see text] intersects [0,1/2] densely. We then describe a method for accurately computing dimensions dim (EA), and employ it to investigate numerically the way in which [Formula: see text] intersects [1/2,1]. These computations tend to support the conjecture, first formulated independently by Hensley, and by Mauldin & Urbański, that [Formula: see text] is dense in [0,1]. In the important special case A={1,2}, we use our computational method to give an accurate approximation of dim (E{1,2}), improving on the one given in [18].

Production and evaluation of jam produced from plum and African Star apple blends

Food Research ◽  
2021 ◽  
Vol 5 (4) ◽  
pp. 93-98
Author(s):  
A.O. Ogunlade ◽  
G.I. Oluwafemi
Keyword(s):  
Vitamin A ◽  
Vitamin C ◽  
Chemical Properties ◽  
Small Scale ◽  
Consumer Acceptability ◽  
Chemical Analyses ◽  
Standard Methods ◽  
Indigenous Fruits ◽  
African Star Apple ◽  
Lengthy Operation

The potential of some indigenous fruits such as yellow-plum (Spondias mombin) and African Star Apple (Chrysophyllum albidum) remained largely untapped. These fruits can be processed and preserved in small-scale operations using simple techniques that could replace both expensive fruits and the lengthy operation processes usually used for jam production. Blends were produced from African Star Apple and Plum in the following proportion: 100:0%; 90:10%; 80:20%; 70:30%; 60:40% and 50:50% respectively to produce six African Star Apple and plum blends. The chemical properties and consumer acceptability of jams made from these blends were investigated using standard methods. Chemical analyses of the jam showed that vitamin A ranged between 613.09 and 686.04 (IU), sample with the highest percentage of African Star Apple had the highest value of Vitamin A; vitamin C ranged between 30.51 and 46.12 (mg/100 g); pH ranged between 4.29 and 4.58; Brix ranged between 11.00 and 14.97°Bx. There were no significant (p>0.05) differences in the sensory attributes of the samples. It was observed that Jam produced from African Star Apple and plum blend at 50:50% proportion had the highest Vitamin A and those at 90:10% proportion had the highest Vitamin C contents and all the samples were of high nutritional and health benefits.

An Elementary Proof of Suslin Reciprocity

2005 ◽  
Vol 48 (2) ◽  
pp. 221-236 ◽  
Author(s):  
Matt Kerr
Keyword(s):  
Elementary Proof ◽  
Function Fields ◽  
Algebraic Cycles ◽  
Important Special Case ◽  
Special Case

AbstractWe state and prove an important special case of Suslin reciprocity that has found significant use in the study of algebraic cycles. An introductory account is provided of the regulator and norm maps on Milnor K2-groups (for function fields) employed in the proof.

scholarly journals Cloud Brokering with Bundles: Multi-objective Optimization of Services Selection

2019 ◽  
Vol 44 (4) ◽  
pp. 407-426
Author(s):  
Jedrzej Musial ◽  
Emmanuel Kieffer ◽  
Mateusz Guzek ◽  
Gregoire Danoy ◽  
Shyam S. Wagle ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Real Data ◽  
Cloud Service ◽  
Optimal Choice ◽  
Cloud Services ◽  
Multi Objective Optimization ◽  
Problem Instances ◽  
The Cost ◽  
Special Case ◽  
Single Objective

Abstract Cloud computing has become one of the major computing paradigms. Not only the number of offered cloud services has grown exponentially but also many different providers compete and propose very similar services. This situation should eventually be beneficial for the customers, but considering that these services slightly differ functionally and non-functionally -wise (e.g., performance, reliability, security), consumers may be confused and unable to make an optimal choice. The emergence of cloud service brokers addresses these issues. A broker gathers information about services from providers and about the needs and requirements of the customers, with the final goal of finding the best match. In this paper, we formalize and study a novel problem that arises in the area of cloud brokering. In its simplest form, brokering is a trivial assignment problem, but in more complex and realistic cases this does not longer hold. The novelty of the presented problem lies in considering services which can be sold in bundles. Bundling is a common business practice, in which a set of services is sold together for the lower price than the sum of services’ prices that are included in it. This work introduces a multi-criteria optimization problem which could help customers to determine the best IT solutions according to several criteria. The Cloud Brokering with Bundles (CBB) models the different IT packages (or bundles) found on the market while minimizing (maximizing) different criteria. A proof of complexity is given for the single-objective case and experiments have been conducted with a special case of two criteria: the first one being the cost and the second is artificially generated. We also designed and developed a benchmark generator, which is based on real data gathered from 19 cloud providers. The problem is solved using an exact optimizer relying on a dichotomic search method. The results show that the dichotomic search can be successfully applied for small instances corresponding to typical cloud-brokering use cases and returns results in terms of seconds. For larger problem instances, solving times are not prohibitive, and solutions could be obtained for large, corporate clients in terms of minutes.

Space Contraction and Partition Algorithm for Combinatorial Optimization

2011 ◽  
Vol 421 ◽  
pp. 559-563
Author(s):  
Yong Chao Gao ◽  
Li Mei Liu ◽  
Heng Qian ◽  
Ding Wang
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Solution Space ◽  
Search Space ◽  
Small Scale ◽  
Optimal Solutions ◽  
Solution Quality ◽  
Intelligent Algorithms ◽  
Combinatorial Optimization Problems

The scale and complexity of search space are important factors deciding the solving difficulty of an optimization problem. The information of solution space may lead searching to optimal solutions. Based on this, an algorithm for combinatorial optimization is proposed. This algorithm makes use of the good solutions found by intelligent algorithms, contracts the search space and partitions it into one or several optimal regions by backbones of combinatorial optimization solutions. And optimization of small-scale problems is carried out in optimal regions. Statistical analysis is not necessary before or through the solving process in this algorithm, and solution information is used to estimate the landscape of search space, which enhances the speed of solving and solution quality. The algorithm breaks a new path for solving combinatorial optimization problems, and the results of experiments also testify its efficiency.

Introduction

2020 ◽  
pp. 1-6
Author(s):  
Peter Scholze ◽  
Jared Weinstein
Keyword(s):  
Moduli Spaces ◽  
Function Fields ◽  
Number Fields ◽  
Important Special Case ◽  
Langlands Correspondence ◽  
Key Innovation ◽  
Perfectoid Spaces ◽  
Definition Of ◽  
Special Case

This introductory chapter provides an overview of Drinfeld's work on the global Langlands correspondence over function fields. Whereas the global Langlands correspondence is largely open in the case of number fields K, it is a theorem for function fields, due to Drinfeld and L. Lafforgue. The key innovation in this case is Drinfeld's notion of an X-shtuka (or simply shtuka). The Langlands correspondence for X is obtained by studying moduli spaces of shtukas. A large part of this course is about the definition of perfectoid spaces and diamonds. There is an important special case where the moduli spaces of shtukas are classical rigid-analytic spaces. This is the case of local Shimura varieties. Some examples of these are the Rapoport-Zink spaces.

On the Hyperplane Sections Through two Given Points of an Algebraic Variety

1970 ◽  
Vol 22 (1) ◽  
pp. 128-133 ◽  
Author(s):  
Wei-Eihn Kuan
Keyword(s):  
Simple Proof ◽  
Hyperplane Section ◽  
Rational Points ◽  
Infinite Field ◽  
Important Special Case ◽  
Irreducible Curve ◽  
Irreducible Variety ◽  
Dimension 2 ◽  
Hyperplane Sections ◽  
Special Case

1. Let k be an infinite field and let V/k be an irreducible variety of dimension ≧ 2 in a projective n-space Pn over k. Let P and Q be two k-rational points on V In this paper, we describe ideal-theoretically the generic hyperplane section of V through P and Q (Theorem 1) and prove that the section is almost always an absolutely irreducible variety over k1/pe if V/k is absolutely irreducible (Theorem 3). As an application (Theorem 4), we give a new simple proof of an important special case of the existence of a curve connecting two rational points of an absolutely irreducible variety [4], namely any two k-rational points on V/k can be connected by an irreducible curve.I wish to thank Professor A. Seidenberg for his continued advice and encouragement on my thesis research.

scholarly journals Deception through Half-Truths

2020 ◽  
Vol 34 (06) ◽  
pp. 10110-10117
Author(s):  
Andrew Estornell ◽  
Sanmay Das ◽  
Yevgeniy Vorobeychik
Keyword(s):  
Polynomial Time ◽  
Transition Function ◽  
Np Hard ◽  
Fundamental Issue ◽  
Fake News ◽  
False Information ◽  
Important Special Case ◽  
Bayes Network ◽  
Special Case

Deception is a fundamental issue across a diverse array of settings, from cybersecurity, where decoys (e.g., honeypots) are an important tool, to politics that can feature politically motivated “leaks” and fake news about candidates. Typical considerations of deception view it as providing false information. However, just as important but less frequently studied is a more tacit form where information is strategically hidden or leaked. We consider the problem of how much an adversary can affect a principal's decision by “half-truths”, that is, by masking or hiding bits of information, when the principal is oblivious to the presence of the adversary. The principal's problem can be modeled as one of predicting future states of variables in a dynamic Bayes network, and we show that, while theoretically the principal's decisions can be made arbitrarily bad, the optimal attack is NP-hard to approximate, even under strong assumptions favoring the attacker. However, we also describe an important special case where the dependency of future states on past states is additive, in which we can efficiently compute an approximately optimal attack. Moreover, in networks with a linear transition function we can solve the problem optimally in polynomial time.

Reverberation Intensity Decaying in Range-Dependent Waveguide

2019 ◽  
Vol 27 (03) ◽  
pp. 1950007
Author(s):  
J. R. Wu ◽  
T. F. Gao ◽  
E. C. Shang
Keyword(s):  
Large Scale ◽  
Back Propagation ◽  
Normal Modes ◽  
Small Scale ◽  
Signal Pulse ◽  
First Order ◽  
Orthogonal Property ◽  
Short Signal ◽  
Scale Roughness ◽  
Special Case

In this paper, an analytic range-independent reverberation model based on the first-order perturbation theory is extended to range-dependent waveguide. This model considers the effect of bottom composite roughness: small-scale bottom rough surface provides dominating energy for reverberation, whereas large-scale roughness has the effect of forward and back propagation. For slowly varying bottom and short signal pulse, analytic small-scale roughness backscattering theory is adapted in range-dependent waveguides. A parabolic equation is used to calculate Green functions in range-dependent waveguides, and the orthogonal property of local normal modes is employed to estimate the modal spectrum of PE field. Synthetic tests demonstrate that the proposed reverberation model works well, and it can also predict the reverberation of range-independent waveguide as a special case.

The New qd Algorithms

Acta Numerica ◽  
1995 ◽  
Vol 4 ◽  
pp. 459-491 ◽  
Author(s):  
Beresford N. Parlett
Keyword(s):  
Singular Values ◽  
Eigenvalues And Eigenvectors ◽  
Triangular Factorization ◽  
Matrix Computation ◽  
Important Special Case ◽  
Singular Vectors ◽  
Tridiagonal Matrices ◽  
Recent Origin ◽  
Special Case

Let us think about ways to find both eigenvalues and eigenvectors of tridiagonal matrices. An important special case is the computation of singular values and singular vectors of bidiagonal matrices. The discussion is addressed both to specialists in matrix computation and to other scientists whose main interests lie elsewhere. The reason for hoping to communicate with two such diverse sets of readers at the same time is that the content of the survey, though of recent origin, is quite elementary and does not demand familiarity with much beyond triangular factorization and the Gram-Schmidt process for orthogonalizing a set of vectors. For some readers the survey will cover familiar territory but from a novel perspective. The justification for presenting these ideas is that they lead to new variations of current methods that run a lot faster while achieving greater accuracy.

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