scholarly journals Uncertainty relations for mesoscopic coherent light

2021 ◽  
Vol 2021 (12) ◽  
pp. 123302
Author(s):  
Ariane Soret ◽  
Ohad Shpielberg ◽  
Eric Akkermans
Keyword(s):  
Cost Function ◽  
Entropy Production ◽  
Statistical Physics ◽  
Mesoscopic Physics ◽  
Uncertainty Relations ◽  
Zero Temperature ◽  
Thermal Systems ◽  
Coherent Effects ◽  
Critical Resource ◽  
The Cost

Abstract Thermodynamic uncertainty relations unveil useful connections between fluctuations in thermal systems and entropy production. This work extends these ideas to the disparate field of zero temperature quantum mesoscopic physics where fluctuations are due to coherent effects and entropy production is replaced by a cost function. The cost function arises naturally as a bound on fluctuations, induced by coherent effects—a critical resource in quantum mesoscopic physics. Identifying the cost function as an important quantity demonstrates the potential of importing powerful methods from non-equilibrium statistical physics to quantum mesoscopics.

scholarly journals An Adaptive Optimization Method Based on Learning Rate Schedule for Neural Networks

2021 ◽  
Vol 11 (2) ◽  
pp. 850
Author(s):  
Dokkyun Yi ◽  
Sangmin Ji ◽  
Jieun Park
Keyword(s):  
Artificial Intelligence ◽  
Cost Function ◽  
Numerical Experiments ◽  
Global Minimum ◽  
Optimization Method ◽  
Learning Method ◽  
Adaptive Optimization ◽  
The Cost ◽  
Proof Of Convergence ◽  
Learning Data

Artificial intelligence (AI) is achieved by optimizing the cost function constructed from learning data. Changing the parameters in the cost function is an AI learning process (or AI learning for convenience). If AI learning is well performed, then the value of the cost function is the global minimum. In order to obtain the well-learned AI learning, the parameter should be no change in the value of the cost function at the global minimum. One useful optimization method is the momentum method; however, the momentum method has difficulty stopping the parameter when the value of the cost function satisfies the global minimum (non-stop problem). The proposed method is based on the momentum method. In order to solve the non-stop problem of the momentum method, we use the value of the cost function to our method. Therefore, as the learning method processes, the mechanism in our method reduces the amount of change in the parameter by the effect of the value of the cost function. We verified the method through proof of convergence and numerical experiments with existing methods to ensure that the learning works well.

Sorting permutations by fragmentation-weighted operations

2020 ◽  
Vol 18 (02) ◽  
pp. 2050006 ◽  
Author(s):  
Alexsandro Oliveira Alexandrino ◽  
Carla Negri Lintzmayer ◽  
Zanoni Dias
Keyword(s):  
Approximation Algorithms ◽  
Computational Biology ◽  
Cost Function ◽  
Traditional Approach ◽  
Upper Bounds ◽  
Evolutionary Distance ◽  
Lower And Upper Bounds ◽  
Approximation Factor ◽  
New Type ◽  
The Cost

One of the main problems in Computational Biology is to find the evolutionary distance among species. In most approaches, such distance only involves rearrangements, which are mutations that alter large pieces of the species’ genome. When we represent genomes as permutations, the problem of transforming one genome into another is equivalent to the problem of Sorting Permutations by Rearrangement Operations. The traditional approach is to consider that any rearrangement has the same probability to happen, and so, the goal is to find a minimum sequence of operations which sorts the permutation. However, studies have shown that some rearrangements are more likely to happen than others, and so a weighted approach is more realistic. In a weighted approach, the goal is to find a sequence which sorts the permutations, such that the cost of that sequence is minimum. This work introduces a new type of cost function, which is related to the amount of fragmentation caused by a rearrangement. We present some results about the lower and upper bounds for the fragmentation-weighted problems and the relation between the unweighted and the fragmentation-weighted approach. Our main results are 2-approximation algorithms for five versions of this problem involving reversals and transpositions. We also give bounds for the diameters concerning these problems and provide an improved approximation factor for simple permutations considering transpositions.

Maximum Likelihood Ensemble Filter: Theoretical Aspects

2005 ◽  
Vol 133 (6) ◽  
pp. 1710-1726 ◽  
Author(s):  
Milija Zupanski
Keyword(s):  
Maximum Likelihood ◽  
Data Assimilation ◽  
Cost Function ◽  
Ensemble Data Assimilation ◽  
Error Covariance ◽  
Ensemble Data ◽  
Analysis Error ◽  
Nonlinear Observation ◽  
The Cost ◽  
Maximum Likelihood Ensemble Filter

Abstract A new ensemble-based data assimilation method, named the maximum likelihood ensemble filter (MLEF), is presented. The analysis solution maximizes the likelihood of the posterior probability distribution, obtained by minimization of a cost function that depends on a general nonlinear observation operator. The MLEF belongs to the class of deterministic ensemble filters, since no perturbed observations are employed. As in variational and ensemble data assimilation methods, the cost function is derived using a Gaussian probability density function framework. Like other ensemble data assimilation algorithms, the MLEF produces an estimate of the analysis uncertainty (e.g., analysis error covariance). In addition to the common use of ensembles in calculation of the forecast error covariance, the ensembles in MLEF are exploited to efficiently calculate the Hessian preconditioning and the gradient of the cost function. A sufficient number of iterative minimization steps is 2–3, because of superior Hessian preconditioning. The MLEF method is well suited for use with highly nonlinear observation operators, for a small additional computational cost of minimization. The consistent treatment of nonlinear observation operators through optimization is an advantage of the MLEF over other ensemble data assimilation algorithms. The cost of MLEF is comparable to the cost of existing ensemble Kalman filter algorithms. The method is directly applicable to most complex forecast models and observation operators. In this paper, the MLEF method is applied to data assimilation with the one-dimensional Korteweg–de Vries–Burgers equation. The tested observation operator is quadratic, in order to make the assimilation problem more challenging. The results illustrate the stability of the MLEF performance, as well as the benefit of the cost function minimization. The improvement is noted in terms of the rms error, as well as the analysis error covariance. The statistics of innovation vectors (observation minus forecast) also indicate a stable performance of the MLEF algorithm. Additional experiments suggest the amplified benefit of targeted observations in ensemble data assimilation.

Using the cost function to generate Marshallian demand systems

2000 ◽  
Vol 25 (2) ◽  
pp. 209-227 ◽  
Author(s):  
Keith R. McLaren ◽  
Peter D. Rossitter ◽  
Alan A. Powell
Keyword(s):  
Cost Function ◽  
Demand Systems ◽  
The Cost

Optimal actuator placement in adaptive optics systems

2021 ◽  
pp. 107754632110324
Author(s):  
Berk Altıner ◽  
Bilal Erol ◽  
Akın Delibaşı
Keyword(s):  
Cost Function ◽  
Adaptive Optics ◽  
Disturbance Attenuation ◽  
Linear Quadratic ◽  
Placement Problem ◽  
Convex Optimization Problem ◽  
Wavefront Aberrations ◽  
The Cost ◽  
Actuator Placement ◽  
Quadratic Cost Function

Adaptive optics systems are powerful tools that are implemented to degrade the effects of wavefront aberrations. In this article, the optimal actuator placement problem is addressed for the improvement of disturbance attenuation capability of adaptive optics systems due to the fact that actuator placement is directly related to the enhancement of system performance. For this purpose, the linear-quadratic cost function is chosen, so that optimized actuator layouts can be specialized according to the type of wavefront aberrations. It is then considered as a convex optimization problem, and the cost function is formulated for the disturbance attenuation case. The success of the presented method is demonstrated by simulation results.

Sparse Incremental Delta-Bar-Delta for System Identification

2014 ◽  
Vol 665 ◽  
pp. 643-646
Author(s):  
Ying Liu ◽  
Yan Ye ◽  
Chun Guang Li
Keyword(s):  
System Identification ◽  
Cost Function ◽  
Learning Algorithm ◽  
Learning System ◽  
The Other ◽  
Sparse System ◽  
Speed Up ◽  
Sparse System Identification ◽  
The Cost ◽  
Zero Attractor

Metalearning algorithm learns the base learning algorithm, targeted for improving the performance of the learning system. The incremental delta-bar-delta (IDBD) algorithm is such a metalearning algorithm. On the other hand, sparse algorithms are gaining popularity due to their good performance and wide applications. In this paper, we propose a sparse IDBD algorithm by taking the sparsity of the systems into account. Thenorm penalty is contained in the cost function of the standard IDBD, which is equivalent to adding a zero attractor in the iterations, thus can speed up convergence if the system of interest is indeed sparse. Simulations demonstrate that the proposed algorithm is superior to the competing algorithms in sparse system identification.

Migration velocity analysis from locally coherent events in 2‐D laterally heterogeneous media, Part I: Theoretical aspects

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1202-1212 ◽  
Author(s):  
Hervé Chauris ◽  
Mark S. Noble ◽  
Gilles Lambaré ◽  
Pascal Podvin
Keyword(s):  
Cost Function ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Seismic Reflection Data ◽  
Velocity Models ◽  
Migration Velocity Analysis ◽  
Paraxial Ray ◽  
The Cost

We present a new method based on migration velocity analysis (MVA) to estimate 2‐D velocity models from seismic reflection data with no assumption on reflector geometry or the background velocity field. Classical approaches using picking on common image gathers (CIGs) must consider continuous events over the whole panel. This interpretive step may be difficult—particularly for applications on real data sets. We propose to overcome the limiting factor by considering locally coherent events. A locally coherent event can be defined whenever the imaged reflectivity locally shows lateral coherency at some location in the image cube. In the prestack depth‐migrated volume obtained for an a priori velocity model, locally coherent events are picked automatically, without interpretation, and are characterized by their positions and slopes (tangent to the event). Even a single locally coherent event has information on the unknown velocity model, carried by the value of the slope measured in the CIG. The velocity is estimated by minimizing these slopes. We first introduce the cost function and explain its physical meaning. The theoretical developments lead to two equivalent expressions of the cost function: one formulated in the depth‐migrated domain on locally coherent events in CIGs and the other in the time domain. We thus establish direct links between different methods devoted to velocity estimation: migration velocity analysis using locally coherent events and slope tomography. We finally explain how to compute the gradient of the cost function using paraxial ray tracing to update the velocity model. Our method provides smooth, inverted velocity models consistent with Kirchhoff‐type migration schemes and requires neither the introduction of interfaces nor the interpretation of continuous events. As for most automatic velocity analysis methods, careful preprocessing must be applied to remove coherent noise such as multiples.

scholarly journals HapSolo: an optimization approach for removing secondary haplotigs during diploid genome assembly and scaffolding

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Edwin A. Solares ◽  
Yuan Tao ◽  
Anthony D. Long ◽  
Brandon S. Gaut
Keyword(s):  
Cost Function ◽  
Anopheles Funestus ◽  
Hill Climbing ◽  
Optimization Approach ◽  
Sequencing Technology ◽  
Genome Data ◽  
A Genome ◽  
Long Read ◽  
Downstream Analysis ◽  
The Cost

Abstract Background Despite marked recent improvements in long-read sequencing technology, the assembly of diploid genomes remains a difficult task. A major obstacle is distinguishing between alternative contigs that represent highly heterozygous regions. If primary and secondary contigs are not properly identified, the primary assembly will overrepresent both the size and complexity of the genome, which complicates downstream analysis such as scaffolding. Results Here we illustrate a new method, which we call HapSolo, that identifies secondary contigs and defines a primary assembly based on multiple pairwise contig alignment metrics. HapSolo evaluates candidate primary assemblies using BUSCO scores and then distinguishes among candidate assemblies using a cost function. The cost function can be defined by the user but by default considers the number of missing, duplicated and single BUSCO genes within the assembly. HapSolo performs hill climbing to minimize cost over thousands of candidate assemblies. We illustrate the performance of HapSolo on genome data from three species: the Chardonnay grape (Vitis vinifera), with a genome of 490 Mb, a mosquito (Anopheles funestus; 200 Mb) and the Thorny Skate (Amblyraja radiata; 2650 Mb). Conclusions HapSolo rapidly identified candidate assemblies that yield improvements in assembly metrics, including decreased genome size and improved N50 scores. Contig N50 scores improved by 35%, 9% and 9% for Chardonnay, mosquito and the thorny skate, respectively, relative to unreduced primary assemblies. The benefits of HapSolo were amplified by down-stream analyses, which we illustrated by scaffolding with Hi-C data. We found, for example, that prior to the application of HapSolo, only 52% of the Chardonnay genome was captured in the largest 19 scaffolds, corresponding to the number of chromosomes. After the application of HapSolo, this value increased to ~ 84%. The improvements for the mosquito’s largest three scaffolds, representing the number of chromosomes, were from 61 to 86%, and the improvement was even more pronounced for thorny skate. We compared the scaffolding results to assemblies that were based on PurgeDups for identifying secondary contigs, with generally superior results for HapSolo.

scholarly journals A Re-Examination of Multistage Economies in Hog Farming

2017 ◽  
Vol 15 (2) ◽  
Author(s):  
Joshua D. Parcel ◽  
John R. Schroeter ◽  
Azzeddine M Azzam
Keyword(s):  
Resource Management ◽  
Cost Function ◽  
Cost Efficiency ◽  
Production Data ◽  
Hog Production ◽  
Current Trends ◽  
Production Practices ◽  
The Cost ◽  
The U.S ◽  
Agricultural Resource Management Survey

AbstractCurrent trends in the structure of hog production in the U.S. are toward facilities that are not only larger, but also more likely to be specialized, carrying out only some of the vertically linked phases of production in the same facility. This paper investigates the cost efficiency incentives for these changes by estimating a multistage cost function for hog production. Data are from the Hog Production Practices and Costs portion of the USDA’s 2004 Agricultural Resource Management Survey.

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