Preconditioning and globalizing conjugate gradients in dual space for quadratically penalized nonlinear-least squares problems

When solving nonlinear least-squares problems, it is often useful to regularize the problem using a quadratic term, a practice which is especially common in applications arising in inverse calculations. A solution method derived from a trust-region Gauss-Newton algorithm is analyzed for such applications, where, contrary to the standard algorithm, the least-squares subproblem solved at each iteration of the method is rewritten as a quadratic minimization subject to linear equality constraints. This allows the exploitation of duality properties of the associated linearized problems. This paper considers a recent conjugate-gradient-like method which performs the quadratic minimization in the dual space and produces, in exact arithmetic, the same iterates as those produced by a standard conjugate-gradients method in the primal space. This dual algorithm is computationally interesting whenever the dimension of the dual space is significantly smaller than that of the primal space, yielding gains in terms of both memory usage and computational cost. The relation between this dual space solver and PSAS (Physical-space Statistical Analysis System), another well-known dual space technique used in data assimilation problems, is explained. The use of an effective preconditioning technique is proposed and refined convergence bounds derived, which results in a practical solution method. Finally, stopping rules adequate for a trust-region solver are proposed in the dual space, providing iterates that are equivalent to those obtained with a Steihaug-Toint truncated conjugate-gradient method in the primal space.     

Local stability analysis of a stochastic evolutionary financial market model with a risk-free asset

This paper introduces and analyzes an evolutionary model of a financial market with a risk-free asset. Focus is on the study of local stability of the wealth dynamics through the application of recent results on the linearization and stability of random dynamical systems (Evstigneev et al. Proc Am Math Soc 139:1061–1072, 2011). Conditions are derived for the linearization of the model at an equilibrium state which ensure local convergence of sample paths to this equilibrium. The paper also shows that the concept of local stability is closely related to the notion of evolutionary stability. A locally evolutionarily stable investment strategy in the evolutionary model with a risk-free asset is derived, extending previous research. The method illustrated here is applicable for the analysis of manifold economic and financial dynamic models involving randomness.     

Certification of reference materials for ochratoxin A analysis in coffee and wine

Mycotoxins are important non-anthropogenic food and feed contaminants, which can be present on almost every agricultural commodity. Effective consumer protection therefore essentially depends on food surveillance by reliable quantitative analysis enabled by appropriate quality control. Certified (matrix) reference materials (CRMs) are versatile tools to support quality assurance. However, in the case of ochratoxin A (OTA), a hepato- and nephrotoxic mycotoxin, which is regulated in various foods, there is a lack of suitable CRMs. This lack has now been overcome by the development of two European Reference Materials (ERM^?) for the determination of OTA in roasted coffee (ERM^?-BD475) and red wine (ERM^?-BD476). This article discusses the material preparation process as well as the results of homogeneity and stability testing. Furthermore, the results of the in-house certification studies carried out at BAM Federal Institute for Materials Research and Testing are presented and discussed. Interlaboratory comparison studies involving selected expert laboratories with documented expertise in the field of mycotoxin analysis were conducted to confirm the certified values determined by BAM. The certified ochratoxin A values and their corresponding expanded uncertainties (k?=?2) were assigned in full compliance with the requirements of ISO Guide 35 and are as follows: (6.0?±?0.6)???g?kg^?1 for roasted coffee, ERM^?-BD475, and (0.52?±?0.11)???g?L^?1 for red wine, ERM^?-BD476.     

M?ssbauer analysis of high-energy mechanical-milled sand fraction of a magnetic soil developing on basalt

A sample of the coarse sand fraction from the soil material of the A-horizon (0?C0.2 m from the soil surface) of a dusky red magnetic Oxisol was submitted to high-energy mechanical milling for different times. This assay aimed mainly at (a) monitoring the individualization of strongly aggregated mineral particles, and (b) measuring the effect of the milling pressure on the mineralogy changes of the material. These data are also intended to experimentally subside any physical model describing the mechanical behavior of the superficial soil layer that is subjected to intensive machine management, in agriculture fields. Powder X-ray data reveal that some mineralogical phases, notably gibbsite, disappear soon after the first few hours milling. The 298 K-transmission Mössbauer spectrum for the non-milled sand sample shows a qualitatively typical pattern for the sand fraction of basalt derived soils, with magnetically ordered sextets, assignable mainly to hematite and maghemite, and an intense central (super)paramagnetic Fe^3?+? doublet. For the milled samples, spectra revealed progressive spectral reduction of the magnetic hyperfine structure, with concomitant increase of relative subspectral areas due to (super)paramagnetic phases, as the milling time increased. This result is consistent with the reduction of measured saturation magnetization, from 4.96(8) J T^???1 kg^???1, for the non-milled sample, to 3.26(7) J T^???1 kg^???1, for the sample milled for 8 hours.     

The Clifford-Fourier Transform {\mathcal {F}_o} and Monogenic Extensions

In the last decade several versions of the Fourier transform have been formulated in the framework of Clifford algebra. We present a (Clifford-Fourier) transform, constructed using the geometric properties of Clifford algebra. We show the corresponding results of operational calculus, and a connection between the Fourier transform and this new transform. We obtain a technique to construct monogenic extensions of a certain type of continuous functions, and versions of the Paley-Wiener theorems are formulated.     

Maximum number of colors: C-coloring and related problems

We discuss problems and results on the maximum number of colors in combinatorial structures under the assumption that no totally multicolored sets of a specified type occur.     

Electronic structure and reactivity of 3-acetyl-2-methylbenzo[b]thiophene: a quantum chemical study

The electronic structures of 3-acetyl-2-methylbenzothiophene, the cations resulting from its C-protonation at positions 4?C7 and O-protonation, and the dications formed upon protonation at positions 4?C7 of the O-protonation product were studied by the MNDO, HF/3-21G, and B3LYP/3-21G methods. Analysis of the relative energies of these cations and dications is in line with the earlier authors?? data on the predominant reactivity of positions 4 and 6 of the 3-acetyl-2-methylbenzothiophene molecule toward acylation.     

Formal Verification of Numerical Programs: From C Annotated Programs to Mechanical Proofs

Numerical programs may require a high level of guarantee. This can be achieved by applying formal methods, such as machine-checked proofs. But these tools handle mathematical theorems while we are interested in C code, in which numerical computations are performed using floating-point arithmetic, whereas proof tools typically handle exact real arithmetic. To achieve this high level of confidence on C programs, we use a chain of tools: Frama-C, its Jessie plugin, Why and provers among Coq, Gappa, Alt-Ergo, CVC3 and Z3. This approach requires the C program to be annotated: each function must be precisely specified, and we prove the correctness of the program by proving both that it meets its specifications and that no runtime error may occur. The purpose of this paper is to illustrate, on various examples, the features of this approach.