scholarly journals Frank–Wolfe and friends: a journey into projection-free first-order optimization methods

4OR ◽  
2021 ◽  
Vol 19 (3) ◽  
pp. 313-345
Author(s):  
Immanuel M. Bomze ◽  
Francesco Rinaldi ◽  
Damiano Zeffiro
Keyword(s):  
Data Science ◽  
Recent Progress ◽  
Optimization Methods ◽  
Seminal Paper ◽  
First Order ◽  
Wide Range

AbstractInvented some 65 years ago in a seminal paper by Marguerite Straus-Frank and Philip Wolfe, the Frank–Wolfe method recently enjoys a remarkable revival, fuelled by the need of fast and reliable first-order optimization methods in Data Science and other relevant application areas. This review tries to explain the success of this approach by illustrating versatility and applicability in a wide range of contexts, combined with an account on recent progress in variants, improving on both the speed and efficiency of this surprisingly simple principle of first-order optimization.

The chemistry of 4-(dicyanomethylene)-3-methyl-l-phenyl-2-pyrazoline-5- ones as a privileged scaffold in synthesis of heterocycles

2020 ◽  
Vol 17 ◽  
Author(s):  
Mohsen A.-M. Gomaa ◽  
Huda A. Ali
Keyword(s):  
Building Block ◽  
Heterocyclic Compounds ◽  
Recent Progress ◽  
Reaction Conditions ◽  
Azacrown Ethers ◽  
Wide Range ◽  
Privileged Scaffold ◽  
Number Of Publications ◽  
Near Future

Background : The reactivity of 4-(dicyanomethylene)-3-methyl-l-phenyl-2-pyrazoline-5-one DCNP 1 and its derivatives makes it valuable as a building block for the synthesis of heterocyclic compounds like pyrazolo-imidazoles, - thiazoles, spiropyridines, spiropyrroles, spiropyrans and others. As a number of publications have reported on the reactivity of DCNP and its derivatives, we compiled some features of this interesting molecule. Objective: This article aims to review the preparation of DCNP, its reactivity and application in heterocyclic and dyes synthesis. Conclusion: In this review we have provided an overview of recent progress in the chemistry of DCNP and its significance in synthesis of various classes of heterocyclic compounds and dyes. The unique reactivity of DCNP offers unprecedentedly mild reaction conditions for the generation of versatile cynomethylene dyes from a wide range of precursors including amines, α-aminocarboxylic acids, their esters, phenols, malononitriles and azacrown ethers. We anticipate that more innovative transformations involving DCNP will continue to emerge in the near future.

scholarly journals Electrodeposited Hydroxyapatite-Based Biocoatings: Recent Progress and Future Challenges

Coatings ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 110
Author(s):  
Mir Saman Safavi ◽  
Frank C. Walsh ◽  
Maria A. Surmeneva ◽  
Roman A. Surmenev ◽  
Jafar Khalil-Allafi
Keyword(s):  
Recent Progress ◽  
Tribological Behavior ◽  
Metallic Materials ◽  
Industrial Processing ◽  
Component Size ◽  
Polymeric Particles ◽  
Operational Variables ◽  
Wide Range ◽  
Future Challenges ◽  
Coating Methods

Hydroxyapatite has become an important coating material for bioimplants, following the introduction of synthetic HAp in the 1950s. The HAp coatings require controlled surface roughness/porosity, adequate corrosion resistance and need to show favorable tribological behavior. The deposition rate must be sufficiently fast and the coating technique needs to be applied at different scales on substrates having a diverse structure, composition, size, and shape. A detailed overview of dry and wet coating methods is given. The benefits of electrodeposition include controlled thickness and morphology, ability to coat a wide range of component size/shape and ease of industrial processing. Pulsed current and potential techniques have provided denser and more uniform coatings on different metallic materials/implants. The mechanism of HAp electrodeposition is considered and the effect of operational variables on deposit properties is highlighted. The most recent progress in the field is critically reviewed. Developments in mineral substituted and included particle, composite HAp coatings, including those reinforced by metallic, ceramic and polymeric particles; carbon nanotubes, modified graphenes, chitosan, and heparin, are considered in detail. Technical challenges which deserve further research are identified and a forward look in the field of the electrodeposited HAp coatings is taken.

Critical examination of various approaches used for analysing helical cables

1994 ◽  
Vol 29 (1) ◽  
pp. 43-55 ◽  
Author(s):  
M Raoof ◽  
I Kraincanic
Keyword(s):  
Large Diameter ◽  
Numerical Results ◽  
Hertzian Contact ◽  
Critical Examination ◽  
First Order ◽  
Wide Range ◽  
End Conditions ◽  
Parametric Studies ◽  
The Individual ◽  
Fixed End

Using theoretical parametric studies covering a wide range of cable (and wire) diameters and lay angles, the range of validity of various approaches used for analysing helical cables are critically examined. Numerical results strongly suggest that for multi-layered steel strands with small wire/cable diameter ratios, the bending and torsional stiffnesses of the individual wires may safely be ignored when calculating the 2 × 2 matrix for strand axial/torsional stiffnesses. However, such bending and torsional wire stiffnesses are shown to be first order parameters in analysing the overall axial and torsional stiffnesses of, say, seven wire stands, especially under free-fixed end conditions with respect to torsional movements. Interwire contact deformations are shown to be of great importance in evaluating the axial and torsional stiffnesses of large diameter multi-layered steel strands. Their importance diminishes as the number of wires associated with smaller diameter cables decreases. Using a modified version of a previously reported theoretical model for analysing multilayered instrumentation cables, the importance of allowing for the influence of contact deformations in compliant layers on cable overall characteristics such as axial or torsional stiffnesses is demonstrated by theoretical numerical results. In particular, non-Hertzian contact formulations are used to obtain the interlayer compliances in instrumentation cables in preference to a previously reported model employing Hertzian theory with its associated limitations.

scholarly journals Product formalisms for measures on spaces with binary tree structures: representation, visualization, and multiscale noise

2020 ◽  
Vol 8 ◽  
Author(s):  
Devasis Bassu ◽  
Peter W. Jones ◽  
Linda Ness ◽  
David Shallcross
Keyword(s):  
Data Science ◽  
Theoretical Foundation ◽  
Continuous Functions ◽  
Noise Model ◽  
Data Types ◽  
Data Set ◽  
Tree Structures ◽  
Simple Concept ◽  
Wide Range ◽  
Computer Scientists

Abstract In this paper, we present a theoretical foundation for a representation of a data set as a measure in a very large hierarchically parametrized family of positive measures, whose parameters can be computed explicitly (rather than estimated by optimization), and illustrate its applicability to a wide range of data types. The preprocessing step then consists of representing data sets as simple measures. The theoretical foundation consists of a dyadic product formula representation lemma, and a visualization theorem. We also define an additive multiscale noise model that can be used to sample from dyadic measures and a more general multiplicative multiscale noise model that can be used to perturb continuous functions, Borel measures, and dyadic measures. The first two results are based on theorems in [15, 3, 1]. The representation uses the very simple concept of a dyadic tree and hence is widely applicable, easily understood, and easily computed. Since the data sample is represented as a measure, subsequent analysis can exploit statistical and measure theoretic concepts and theories. Because the representation uses the very simple concept of a dyadic tree defined on the universe of a data set, and the parameters are simply and explicitly computable and easily interpretable and visualizable, we hope that this approach will be broadly useful to mathematicians, statisticians, and computer scientists who are intrigued by or involved in data science, including its mathematical foundations.

Nonsmooth Optimization Method for Image Restoration

1995 ◽  
Author(s):  
Kazufumi Ito ◽  
Karl Kunisch
Keyword(s):  
Image Restoration ◽  
Nonsmooth Optimization ◽  
Numerical Optimization ◽  
Augmented Lagrangian ◽  
Energy Criterion ◽  
Optimization Methods ◽  
Optimization Method ◽  
Augmented Lagrangian Methods ◽  
Active Set ◽  
First Order

Abstract In this paper we discuss applications of the numerical optimization methods for nonsmooth optimization, developed in [IK1] for the variational formulation of image restoration problems involving bounded variation type energy criterion. The Uzawa’s algorithm, first order augmented Lagrangian methods and Newton-like update using the active set strategy are described.

scholarly journals Mito Hacker: a set of tools to enable high-throughput analysis of mitochondrial network morphology

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Ali Rohani ◽  
Jennifer A. Kashatus ◽  
Dane T. Sessions ◽  
Salma Sharmin ◽  
David F. Kashatus
Keyword(s):  
Single Cell ◽  
High Throughput ◽  
Data Science ◽  
Structural Information ◽  
Morphological Changes ◽  
Mitochondrial Morphology ◽  
Single Cell Level ◽  
Mitochondrial Network ◽  
Cell Level ◽  
Wide Range

Abstract Mitochondria are highly dynamic organelles that can exhibit a wide range of morphologies. Mitochondrial morphology can differ significantly across cell types, reflecting different physiological needs, but can also change rapidly in response to stress or the activation of signaling pathways. Understanding both the cause and consequences of these morphological changes is critical to fully understanding how mitochondrial function contributes to both normal and pathological physiology. However, while robust and quantitative analysis of mitochondrial morphology has become increasingly accessible, there is a need for new tools to generate and analyze large data sets of mitochondrial images in high throughput. The generation of such datasets is critical to fully benefit from rapidly evolving methods in data science, such as neural networks, that have shown tremendous value in extracting novel biological insights and generating new hypotheses. Here we describe a set of three computational tools, Cell Catcher, Mito Catcher and MiA, that we have developed to extract extensive mitochondrial network data on a single-cell level from multi-cell fluorescence images. Cell Catcher automatically separates and isolates individual cells from multi-cell images; Mito Catcher uses the statistical distribution of pixel intensities across the mitochondrial network to detect and remove background noise from the cell and segment the mitochondrial network; MiA uses the binarized mitochondrial network to perform more than 100 mitochondria-level and cell-level morphometric measurements. To validate the utility of this set of tools, we generated a database of morphological features for 630 individual cells that encode 0, 1 or 2 alleles of the mitochondrial fission GTPase Drp1 and demonstrate that these mitochondrial data could be used to predict Drp1 genotype with 87% accuracy. Together, this suite of tools enables the high-throughput and automated collection of detailed and quantitative mitochondrial structural information at a single-cell level. Furthermore, the data generated with these tools, when combined with advanced data science approaches, can be used to generate novel biological insights.

Radiant Panel Columns Magnetostrictive Transducers of Forced Vibration

2012 ◽  
Vol 588-589 ◽  
pp. 359-363
Author(s):  
Jian Ping Sun ◽  
Jian Xin Wang
Keyword(s):  
Forced Vibration ◽  
Radiation Effect ◽  
Optimization Methods ◽  
Motion Model ◽  
Spring Rate ◽  
Order Analysis ◽  
First Order ◽  
Radiant Panel ◽  
Magnetostrictive Transducer

the columns of magnetostrictive transducer for the object, the establishment of a Radiant Panel in magnetostrictive rods through the spring of motion model, gives a method for solving first-order analysis and solutions, discusses the spring rate on radiation effect of amplitude. On reasonable determination of Radiant Panel structure, the size of the transducer, and optimization methods.

First-order autoregressive gamma sequences and point processes

1980 ◽  
Vol 12 (3) ◽  
pp. 727-745 ◽  
Author(s):  
D. P. Gaver ◽  
P. A. W. Lewis
Keyword(s):  
Parameter Estimation ◽  
Point Processes ◽  
Random Variables ◽  
Innovation Process ◽  
Sums Of Random Variables ◽  
First Order ◽  
Wide Range ◽  
Serial Correlations ◽  
Generating Sequences ◽  
Stieltjes Transforms

It is shown that there is an innovation process {∊n} such that the sequence of random variables {Xn} generated by the linear, additive first-order autoregressive scheme Xn = pXn-1 + ∊n are marginally distributed as gamma (λ, k) variables if 0 ≦p ≦ 1. This first-order autoregressive gamma sequence is useful for modelling a wide range of observed phenomena. Properties of sums of random variables from this process are studied, as well as Laplace-Stieltjes transforms of adjacent variables and joint moments of variables with different separations. The process is not time-reversible and has a zero-defect which makes parameter estimation straightforward. Other positive-valued variables generated by the first-order autoregressive scheme are studied, as well as extensions of the scheme for generating sequences with given marginal distributions and negative serial correlations.

First-order autoregressive gamma sequences and point processes

1980 ◽  
Vol 12 (03) ◽  
pp. 727-745 ◽  
Author(s):  
D. P. Gaver ◽  
P. A. W. Lewis
Keyword(s):  
Parameter Estimation ◽  
Point Processes ◽  
Random Variables ◽  
Innovation Process ◽  
Sums Of Random Variables ◽  
First Order ◽  
Wide Range ◽  
Serial Correlations ◽  
Generating Sequences ◽  
Stieltjes Transforms

It is shown that there is an innovation process {∊ n } such that the sequence of random variables {X n } generated by the linear, additive first-order autoregressive scheme X n = pXn-1 + ∊ n are marginally distributed as gamma (λ, k) variables if 0 ≦p ≦ 1. This first-order autoregressive gamma sequence is useful for modelling a wide range of observed phenomena. Properties of sums of random variables from this process are studied, as well as Laplace-Stieltjes transforms of adjacent variables and joint moments of variables with different separations. The process is not time-reversible and has a zero-defect which makes parameter estimation straightforward. Other positive-valued variables generated by the first-order autoregressive scheme are studied, as well as extensions of the scheme for generating sequences with given marginal distributions and negative serial correlations.

scholarly journals Particles, conformal invariance and criticality in pure and disordered systems

2021 ◽  
Vol 94 (3) ◽  
Author(s):  
Gesualdo Delfino
Keyword(s):  
Conformal Invariance ◽  
Disordered Systems ◽  
Short Range ◽  
Recent Progress ◽  
Quenched Disorder ◽  
Exact Methods ◽  
Special Position ◽  
Infinite Dimensional ◽  
First Order ◽  
The Continuum

AbstractThe two-dimensional case occupies a special position in the theory of critical phenomena due to the exact results provided by lattice solutions and, directly in the continuum, by the infinite-dimensional character of the conformal algebra. However, some sectors of the theory, and most notably criticality in systems with quenched disorder and short-range interactions, have appeared out of reach of exact methods and lacked the insight coming from analytical solutions. In this article, we review recent progress achieved implementing conformal invariance within the particle description of field theory. The formalism yields exact unitarity equations whose solutions classify critical points with a given symmetry. It provides new insight in the case of pure systems, as well as the first exact access to criticality in presence of short range quenched disorder. Analytical mechanisms emerge that in the random case allow the superuniversality of some critical exponents and make explicit the softening of first-order transitions by disorder.Graphic abstract

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