Certified lattice reduction

Quadratic form reduction and lattice reduction are fundamental tools in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra-Lenstra-Lov\'asz reduction algorithm (so-called LLL) has been improved in many ways through the past decades and remains one of the central methods used for reducing integral lattice basis. In particular, its floating-point variants-where the rational arithmetic required by Gram-Schmidt orthogonalization is replaced by floating-point arithmetic-are now the fastest known. However, the systematic study of the reduction theory of real quadratic forms or, more generally, of real lattices is not widely represented in the literature. When the problem arises, the lattice is usually replaced by an integral approximation of (a multiple of) the original lattice, which is then reduced. While practically useful and proven in some special cases, this method doesn't offer any guarantee of success in general. In this work, we present an adaptive-precision version of a generalized LLL algorithm that covers this case in all generality. In particular, we replace floating-point arithmetic by Interval Arithmetic to certify the behavior of the algorithm. We conclude by giving a typical application of the result in algebraic number theory for the reduction of ideal lattices in number fields.Comment: 23 page

A Probabilistic Analysis of the Power of Arithmetic Filters

The assumption of real-number arithmetic, which is at the basis of conventional geometric algorithms, has been seriously challenged in recent years, since digital computers do not exhibit such capability. A geometric predicate usually consists of evaluating the sign of some algebraic expression. In most cases, rounded computations yield a reliable result, but sometimes rounded arithmetic introduces errors which may invalidate the algorithms. The rounded arithmetic may produce an incorrect result only if the exact absolute value of the algebraic expression is smaller than some (small) varepsilon, which represents the largest error that may arise in the evaluation of the expression. The threshold varepsilon depends on the structure of the expression and on the adopted computer arithmetic, assuming that the input operands are error-free. A pair (arithmetic engine,threshold) is an "arithmetic filter". In this paper we develop a general technique for assessing the efficacy of an arithmetic filter. The analysis consists of evaluating both the threshold and the probability of failure of the filter. To exemplify the approach, under the assumption that the input points be chosen randomly in a unit ball or unit cube with uniform density, we analyze the two important predicates "which-side" and "insphere". We show that the probability that the absolute values of the corresponding determinants be no larger than some positive value V, with emphasis on small V, is Theta(V) for the which-side predicate, while for the insphere predicate it is Theta(V^(2/3)) in dimension 1, O(sqrt(V)) in dimension 2, and O(sqrt(V) ln(1/V)) in higher dimensions. Constants are small, and are given in the paper.Comment: 22 pages 7 figures Results for in sphere test inproved in cs.CG/990702

A review of data-driven building performance analysis and design on big on-site building performance data

Building performance design (BPD) is a crucial pathway to achieve high-performance buildings. Previous simulation-based BPD is being questioned due to the performance gaps between simulated and measured values. In recent years, accumulated on-site building performance data (OBPD) make it possible to analyze and design buildings with data-driven methods. This article makes a review of previous studies that conducted data-driven building performance analysis and design on a large amount of OBPD. The covered studies are summarized by the applied techniques, i.e., statistics, regression, classification, and clustering. The data used by these studies are compared and discussed emphasizing the data size and public availability. A comprehensive discussion is given about the achievements of existing studies, and challenges for boosting data-driven BPD from three aspects, i.e., developing data-driven models, the availability of building performance data, and stimulation of industrial practices. The review results indicate that data-driven methods were commonly applied to estimate energy consumptions, and explore energy trends, determinant features, and reference buildings. Identifying determinant features is one of the most successful applications. This study highlights the future research gaps for boosting data-driven building performance design

SPLIT DECISIONS: PRACTICAL MACHINE LEARNING FOR EMPIRICAL LEGAL SCHOLARSHIP

Multivariable regression may be the most prevalent and useful task in social science. Empirical legal studies rely heavily on the ordinary least squares method. Conventional regression methods have attained credibility in court, but by no means do they dictate legal outcomes. Using the iconic Boston housing study as a source of price data, this Article introduces machine-learning regression methods. Although decision trees and forest ensembles lack the overt interpretability of linear regression, these methods reduce the opacity of black-box techniques by scoring the relative importance of dataset features. This Article will also address the theoretical tradeoff between bias and variance, as well as the importance of training, cross-validation, and reserving a holdout dataset for testing

Certification of a reference material of Campylobacter coli and jejuni (CNET068 and CNET112) agarose plugs for PFGE: IRMM-313

This report describes the production of IRMM-313, a Campylobacter coli and jenuni gDNA material certified for the size of the DNA fragments obtained by enzymatic restriction and Pulsed Field Gel Electrophoresis (PFGE). The material was produced following ISO Guide 34:2009. The CRM was produced from cultures of Campylobacter coli CNET068 and jejuni CNET112 which were pooled and processed into agarose plugs suited for PFGE. The bacterial cells were lysed as to release the gDNA within the plug. Between unit-homogeneity and stability during dispatch and storage were assessed in accordance with ISO Guide 35:2006. The material was characterised by an intercomparison among laboratories of demonstrated competence and complying to ISO/IEC 17025. Technically invalid results were removed but no outlier was eliminated on statistical grounds only. The certified values were obtained by PFGE. Uncertainties of the certified values were calculated in compliance with the Guide to the Expression of Uncertainty in Measurement (GUM). The material is intended for quality control and assessment of method performance. As any reference material, it can also be used for control charts or validation studies. The CRM is available in plastic screw cap vials containing 1 plug suspended in Tris EDTA buffer solution. The minimum amount of sample recommended to be used is ½ plug.JRC.D.2-Standards for Innovation and sustainable Developmen