数学史上的一次艰难长征-- 费马最后定理的证明

1997年6月,普林斯顿大学的数学家安德鲁·J·怀尔斯在德国哥廷根大学领取了声名卓著的沃尔夫斯克尔奖金.这项奖金设立于1908年,获奖者将是任何一位能证明彼埃尔·德·费马著名的最后定理的数学家.对于怀尔斯来说,证明这个定理不但是给他的十年艰苦努力画了上了一个圆满的句号,也是圆了他的一个童年之梦.而对于数学界来说,怀尔斯的证明可望使数学的未来发生革命性的变化.     

Media and methods for isolation of aeromonads from fecal specimens. A multilaboratory study

An international multilaboratory study was conducted to establish the optimal combination of culture media, incubation time and temperature for recovery of aeromonads from stools using blood ampicillin (10 mg/l) agar (BAA), starch ampicillin (10 mg/l) agar (SAA), and cefsulodin irgasan novobiocin agar (CIN) with alkaline peptone water (APW) for enrichment. Optimal recovery of aeromonads (167/186) occurred using BAA (37 degrees C; 24 h) and CIN (25 degrees C; 48 h) with APW (25 degrees C; 24 h) subcultured to BAA (37 degrees C; 24 h) and CIN (25 degrees C; 48 h).     

A Bayesian reconstruction of the methodology of scientific research programmes

The paper is concerned with explaining some of the principal theoretical developments in elementary particle physics and discussing the associated methodological problems both in respect of heuristics and appraisal. Particular reference is made to relativistic quantum field theory, renormalization, Feynman diagram techniques, the analytic S-matrix and the Chew — Frautschi bootstrap.     

ISAF重构算法密度函数快速计算模型

球坐标系下的ISAF算法是一种新的20面体分子三维重构方法,该方法精度优于传统柱坐标系下的Fourier-Beseel算法,但其执行速度远低于Fourier-Bessel算法,严重制约了ISAF算法的实际应用.分析发现,在ISAF算法中密度函数计算是影响重构速度的主要瓶颈之一.针对上述问题,文中提出一种密度函数快速计算模型,该模型包括三个组成部分:球坐标系网格点密度函数快速计算方法、"球坐标系—直角坐标系"网格点密度函数转换方法、基于两阶段映射法的快速对称映射方法.该模型可以将密度函数计算阶段的时间复杂度由O[(LM)8]降低到O[(LM)7].采用Psv-F病毒数据进行实验,结果表明,在保证精度的前提下,该模型可以将密度函数的计算速度提高2个数量级,将三维重构整体速度提高30倍左右,并且随着数据规模的增大、重构精度的提高,该模型带来的加速比将进一步增大.     

A forecasting comparison of classical and Bayesian methods for modelling logistic diffusion

A Bayesian procedure for forecasting S‐shaped growth is introduced and compared to classical methods of estimation and prediction using three variants of the logistic functional form and annual times series of the diffusion of music compact discs in twelve countries. The Bayesian procedure was found not only to improve forecast accuracy, using the medians of the predictive densities as point forecasts, but also to produce intervals with a width and asymmetry more in accord with the outcomes than intervals from the classical alternative. While the analysis in this paper focuses on logistic growth, the problem is set up so that the methods are transportable to other characterizations of the growth process. Copyright © 2001 John Wiley & Sons, Ltd.     

Velocity sedimentation of tumor cells: A comparison of methods

Summary Tumor cells isolated from a murine fibrosarcoma were grown in primary culture for two days and then separated on a basis of size by velocity sedimentation. Centrifugal elutriation and STAPUT methods were compared for their ability to isolate biophysically unique tumor subpopulations. The isolated cell fractions were assayed for cell number, incorporation of triatiated thymidine and Coulter volume. Both methods were comparable with regard to ability to separate tumor cells on a basis of size. Elutriation had the advantage of speed but required sophisticated equipment. The STAPUT method was less expensive but required somewhat longer times for separation.Supported in part by NIH-NCI grants No. CA-06294 and CA-18628.     

A comparison of adaptive structural forecasting methods for electricity sales

This paper presents the results of a study to determine whether new forecasting technologies might be of use to electric utilities for sales forecasting up to 3 years into the future. The methods considered included ordinary least squares on dynamic structural models, autocorrelated error models, adaptive variance and adaptive parameter models. Overall, the more adaptive models performed best, but most of the methods proved vastly superior to simple least squares models which do not take dynamics into account.     

A comparison of methods for bootstrapping in the local level model

Bootstrap in time series models is not straightforward to implement, as in this case the observations are not independent. One of the alternatives is to bootstrap the residuals in order to obtain the bootstrap series and thus use these series for inference purposes. This work deals with the problem of assessing the accuracy of hyperparameters in structural models. We study the simplest case, the local level model, where the hyperparameters are given by the variances of the disturbance terms. As their distribution is not known, we employ the bootstrap to approximate the true distribution, using parametric and non‐parametric approaches. Bootstrap standard deviations are computed and their performances compared to the asymptotic and empirical standard errors, calculated using a Monte Carlo simulation. We also build confidence intervals to the hyperparameters, using four bootstrap methods and the results are compared by means of the length, shape and coverage probabilities of the intervals. Copyright © 2002 John Wiley & Sons, Ltd.     

图像视频信号的压缩采样与稀疏重建

要视觉传感器通常不知道它们“看到”的现象之下的物理过程,以远远超出图像视频信号有效维度的Shannon／Nyquist采样率获取图像视频数据,从而导致了对图像视频信号的存储、传输等数字处理的巨大压力．压缩感知（compressivesensing,CS）理论表明：在某个线性变换域下稀疏的信号,可以利用少量的观测数据精确地重建,或在噪声情况下鲁棒地重建．压缩感知是实现图像视频信号有效维度采样的理论基础,为图像视频信号的采样、处理和识别等领域带来了前所未有的突破．本文对图像视频信号领域压缩感知面临的基本问题：压缩采样、稀疏重建模型及其优化求解算法的研究进展进行了综述．在采样方面,分析了图像视频信号随机观测矩阵和有结构观测矩阵的性能;在稀疏重建模型方面,从图像视频信号的稀疏先验性出发、介绍了分析型的重建模型和合成型重建模型的构建方法;在优化求解方面,针对重建模型,介绍了约束优化问题和无约束优化问题两类求解算法．以此为基础,分析了在图像视频领域压缩感知的理论与应用的进一步发展所面临的问题和挑战,展望了未来的发展方向．     

A comparison of methods for the inactivation of third component of guinea-pig complement

Riassunto Sono stati esaminati comparativamente tre reagenti per la titolazione di C₃, rispettivamente allestiti con siero di cavia inattivato con zymosan, formalina e «Liquoid». Le differenze esistenti tra essi sono state analizzate e discusse in base alle attuali conoscenze sulla natura del terzo componente complementare.

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Supported in part by Contract DA-49-007-MD-696 with the Office of the Surgeon General, Department of the Army.     

A comparison of methods for the extraction of amino acids from fungal mycelium

Résumé En comparant plusieurs techniques pour extraire l'amino-acide libre de la mycose fongique on a observé de grandes différences entre elles. L'eau bouillante et la méthyléthylcétone HCl se sont montrés les solvents les plus efficaces et donnant chromatogrammes les plus clairs.     

Forecasting Australia's real house price index: A comparison of time series and machine learning methods

We employ 47 different algorithms to forecast Australian log real house prices and growth rates, and compare their ability to produce accurate out-of-sample predictions. The algorithms, which are specified in both single- and multi-equation frameworks, consist of traditional time series models, machine learning (ML) procedures, and deep learning neural networks. A method is adopted to compute iterated multistep forecasts from nonlinear ML specifications. While the rankings of forecast accuracy depend on the length of the forecast horizon, as well as on the choice of the dependent variable (log price or growth rate), a few generalizations can be made. For one- and two-quarter-ahead forecasts we find a large number of algorithms that outperform the random walk with drift benchmark. We also report several such outperformances at longer horizons of four and eight quarters, although these are not statistically significant at any conventional level. Six of the eight top forecasts (4 horizons × 2 dependent variables) are generated by the same algorithm, namely a linear support vector regressor (SVR). The other two highest ranked forecasts are produced as simple mean forecast combinations. Linear autoregressive moving average and vector autoregression models produce accurate olne-quarter-ahead predictions, while forecasts generated by deep learning nets rank well across medium and long forecast horizons.     

Incorporating textual and management factors into financial distress prediction: A comparative study of machine learning methods

Financial distress prediction (FDP) has been widely considered as a promising approach to reducing financial losses. While financial information comprises the traditional factors involved in FDP, nonfinancial factors have also been examined in recent studies. In light of this, the purpose of this study is to explore the integrated factors and multiple models that can improve the predictive performance of FDP models. This study proposes an FDP framework to reveal the financial distress features of listed Chinese companies, incorporating financial, management, and textual factors, and evaluating the prediction performance of multiple models in different time spans. To develop this framework, this study employs the wrapper-based feature selection method to extract valuable features, and then constructs multiple single classifiers, ensemble classifiers, and deep learning models in order to predict financial distress. The experiment results indicate that management and textual factors can supplement traditional financial factors in FDP, especially textual ones. This study also discovers that integrated factors collected 4 years prior to the predicted benchmark year enable a more accurate prediction, and the ensemble classifiers and deep learning models developed can achieve satisfactory FDP performance. This study makes a novel contribution as it expands the predictive factors of financial distress and provides new findings that can have important implications for providing early warning signals of financial risk.     

Serial reconstruction with the electron microscope of carotid body tissue. The type I cell nerve supply

Zusammenfassung Rekonstruktionen aus elektronenmikroskopischen Serienschnitten ergeben, dass einige Zellen von Typ I im Glomus caroticum durch eine effecrente Nervenfaser zu einem Komplex zusammengefasst werden. Underschiede in den Synapsen an der Oberfläche der Typ I-Zellen wurden nicht gefunden.     

A beautiful sea: P. A. M. Dirac's epistemology and ontology of the vacuum

This paper charts P.A.M. Dirac's development of his theory of the electron, and its radical picture of empty space as an almost-full plenum. Dirac's Quantum Electrodynamics famously accomplished more than the unification of special relativity and quantum mechanics. It also accounted for the ‘duplexity phenomena’ of spectral line splitting that we now attribute to electron spin. But the extra mathematical terms that allowed for spin were not alone, and this paper charts Dirac's struggle to ignore or account for them as a sea of strange, negative-energy, particles with positive ‘holes’. This work was not done in solitude, but rather in exchanges with Dirac's correspondence network. This social context for Dirac’s work contests his image as a lone genius, and documents a community wrestling with the ontological consequences of their work. Unification, consistency, causality, and community are common factors in explanations in the history of physics. This paper argues on the basis of materials in Dirac's archive that --- in addition --- mathematical beauty was an epistemological factor in the development of the electron and hole theory. In fact, if we believe that Dirac's beautiful mathematics captures something of the world, then there is both an epistemology and an ontology of mathematical beauty.     

A comparison of approximate Bayesian forecasting methods for non‐Gaussian time series

We present the results on the comparison of efficiency of approximate Bayesian methods for the analysis and forecasting of non‐Gaussian dynamic processes. A numerical algorithm based on MCMC methods has been developed to carry out the Bayesian analysis of non‐linear time series. Although the MCMC‐based approach is not fast, it allows us to study the efficiency, in predicting future observations, of approximate propagation procedures that, being algebraic, have the practical advantage of being very quick. Copyright © 2000 John Wiley & Sons, Ltd.