NIFTy 3 – Numerical Information Field Theory: A Python Framework for Multicomponent Signal Inference on HPC Clusters

NIFTy , “Numerical Information Field Theory,” is a software framework designed to ease the development and implementation of field inference algorithms. Field equations are formulated independently of the underlying spatial geometry allowing the user to focus on the algorithmic design. Under the hood, NIFTy ensures that the discretization of the implemented equations is consistent. This enables the user to prototype an algorithm rapidly in 1D and then apply it to high‐dimensional real‐world problems. This paper introduces NIFTy  3, a major upgrade to the original NIFTy  framework. NIFTy  3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the field equations. It supports n‐dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts. Furthermore, NIFTy  3 is able to handle non‐scalar fields, such as vector or tensor fields. The functionality and performance of the software package is demonstrated with example code, which implements a mock inference inspired by a real‐world algorithm from the realm of information field theory. NIFTy  3 is open‐source software available under the GNU General Public License v3 (GPL‐3) at https://gitlab.mpcdf.mpg.de/ift/NIFTy/tree/NIFTy_3 .     

V-shaped nematogens with the "magic bent angle"

V-shaped nematogens 1a-c and 2a-b with benzodithiophene bending units have been synthesised. The derivatives 1a-c comprise a flat core with a bending angle of 109°, which is almost the tetrahedral angle proposed to be optimal in the realization of mesogens forming a biaxial nematic thermotropic mesophase.     

Adhesion of microcapsules

The adhesion of microcapsules to an attractive contact potential is studied theoretically. The axisymmetric shape equations are solved numerically. Beyond a universal threshold strength of the potential, the contact radius increases in proportion to the square root of the strength. Scaling functions for the corresponding amplitudes are derived as a function of the elastic parameters.     

Statistical evaluation of the influence of several sample pretreatment methods on the mercury content detectable by chemical analysis of contaminated soil samples under practical conditions

The estimation of the environmental risk of contaminated sites caused by hazardous components may be obtained, for instance, by means of a soil survey. There unavoidable errors by sampling, sample preparation and chemical analysis occur. Furthermore, in case of mercury contaminations, the mercury content detectable by chemical analysis can be falsified, if between sampling, on the one hand, and sample preparation and sample decomposition for chemical analysis, on the other hand, volatile components or elementary metallic mercury escape from the sample. Thus, in these cases, handling of samples such as air drying, storing in plastic bags or thermal evaporation, generally termed sample pretreatment, is a further source of error in evaluating a material. However, the measuring results are influenced not only by sampling, sample pretreatment, sample preparation by homogenization and splitting, and chemical analysis; they must also reflect the intrinsic properties of the soil sample subject to both global fluctuations and local heterogeneities. The present work shows by example of a non-uniformly contaminated site to what extent the analytically detectable mercury content is changed by the method of handling of soil samples in the period between sampling and chemical analysis. A hierarchical experimental design was realized in order to separately quantify the different sources of variation of the measured mercury contents, which are caused by global variations, local heterogeneities, sample preparation, sample pretreatment as well as chemical analysis. As turned out by variance analysis, the variance portion contributed to the total variance by sample pretreatment is highly significant and lies in the same order of magnitude as the variance caused by local heterogeneities of the soil. That means that the type of sample pretreatment influences the analytical results essentially. In order to quantify the effect of a definite pretreatment method in comparison with the mercury content of the unchanged original soil sample, the probable systematic error of a method was introduced. Investigations were only carried out at two sampling locations of the contaminated site because of the relatively high labour; the mean values and variances obtained cannot be immediately transferred to other sites. However, the general knowledge can be used as methodical basis for further investigations. Particularly, the consequence arises that the regulations existing for the treatment of mercury-contaminated samples between sampling and chemical analysis must be revised to obtain comparable criteria of evaluation.Symbols used level of error in statistical tests, - _i random effect of the i-th sampling location with respect to the mercury content, effect of global fluctuations - _ij random effect of the j-th primary sample (composite sample) at the i-th sampling location, effect of local heterogeneity, sampling error - _ijk random effect of the k-th subsample within the respective j-th primary sample (composite sample) at the i-th sampling location, sample preparation error - _ijkl random effect of the l-th pretreated sample belonging to the respective k-th subsample of the j-th primary or composite sample at the i-th sampling location, sample pretreatment effect - _1– probable relative systematic error of a pretreatment methods as compared with the original material at the coverage probability 1– - overall expected mercury content of the sampling results - _i expected mercury content of the i-th pretreated composite sample at a fixed location - û_{1.1 –} lower limit of a confidence interval for the unknown expected mercury content of unchanged original material at the confidence probability 1– - _i intraclass correlation coefficient - ² , ² , ² , ² , _Z ² variance components caused by global variability, local heterogeneity, sample preparation, sample pretreatment and analytical error, respectively - _total ² total variance of mercury content - D² operator of the variance of a random variable - E operator of the mathematical expectation of a random variable - F_i mean squared sum quotient of the Fisher's F-distribution - F_1–/2(fg_i, fg_j) critical value of the F-distribution at fg_i and fg_j degrees of freedom, respectively - fg_i degree of freedom of a (mean) sum of squared deviations - H_i hypothesis regarding a statistical law - I_1– confidence interval for the unknown expected value difference of two methods compared at the probability 1–, probable systematic error of a pretreatment method as compared with the unchanged original material at the coverage probability 1– - MQ_i, mq_i mean squared deviations as explained in the context - n_i number of sampling locations, primary samples per location, subsamples per primary sample, pretreatment methods and measuring values per pretreated sample, respectively - S _i ² , s _i ² variance estimation obtained by chemical analysis - SQ_i, sq_i sum of squared deviations - S(|Y₁–Y_i|) mean error of the absolute mean value difference |Y₁–Y_i|) - t_1–/2;m critical value of the Student's t-distribution at m degrees of freedom and the probability 1–/2 - Y_ijklm mercury content obtained on the m-th final sample of the l-th pretreated sample belonging to the k-th subsample of the j-th primary sample at the i-th sampling location - Y_i, y_i,... mean values obtained by sampling and chemical analysis - Z_ijklm random error of the ijklm-th measuring value (final sample value) Y_ijklm.     

Geometric Variational Inference

Efficiently accessing the information contained in non-linear and high dimensional probability distributions remains a core challenge in modern statistics. Traditionally, estimators that go beyond point estimates are either categorized as Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) techniques. While MCMC methods that utilize the geometric properties of continuous probability distributions to increase their efficiency have been proposed, VI methods rarely use the geometry. This work aims to fill this gap and proposes geometric Variational Inference (geoVI), a method based on Riemannian geometry and the Fisher information metric. It is used to construct a coordinate transformation that relates the Riemannian manifold associated with the metric to Euclidean space. The distribution, expressed in the coordinate system induced by the transformation, takes a particularly simple form that allows for an accurate variational approximation by a normal distribution. Furthermore, the algorithmic structure allows for an efficient implementation of geoVI which is demonstrated on multiple examples, ranging from low-dimensional illustrative ones to non-linear, hierarchical Bayesian inverse problems in thousands of dimensions.     

Über basische Aluminiumsalze und ihre Lösungen. (XIII). Kristalline basische Aluminiumchloride als Produkte der Rehydratisierung und Hydrochlorierung von Übergangstonerden

Basic Aluminum Salts and their Solutions. XIII. Crystalline Basic Aluminum Chlorides Formed as Products of Rehydration and Hydrochlorination of Transition Aluminas By reaction of transition aluminas with hydrochloric acid in sealed tubes at temperatures above 100°C crystalline basic aluminum chlorides were prepared. From the aluminum oxides used (χ-Al₂O₃, χ-Al₂O₃, and χ-Al₂O₃) χ-Al₂O₃ was most suitable for preparation. The homogeneous basic salts are characterized by a certain variability in composition as phases. After a treatment with water vapor there is a remarkable change in the X-ray diagrams of the compounds. It is shown, that at this alteration the lattice was only changed unessentially. Therefore the existence of intercalation compounds with a 3D host lattice is assumed; the water molecules are located at defined positions in the voids.     

Messung derL-Auger-, Fluoreszenz- und Coster-Kronig-Ausbeuten von Gold

An apparatus is described, with which, for the first time, the spectra of Augere-lectrons and of X-rays, produced by the impact of electrons, were measured simultaneously. The electron spectrometer was a magnetic 180°-spectrometer with a half-width of 0·5%. The X-ray spectrometer was a NaJ-crystal with a photomultiplier. The electron- and the X-rays were produced in metallic foils of a thickness of 50 Å by the impact of 55-keV-electrons. The knownK-fluorescence-yields of copper and selenium were used to determine the various yields for theL-shells of gold. TheL-fluorescence-yields areω _L1 =0·08±0·01;ω _L2 =0·26±0·03;ω _L3 =0·24±0·02.     

Über die Zersetzlichkeit komplexer Metallcyanide bei der Cyanidbestimmung in Abwasser

Serial studies on the behaviour of simple and complex cyanides against the attack of dilute sulphuric acid within the determination of “total cyanide” in waste water resulted in the cyanide complexes of zinc, cadmium, copper, nickel, iron(II) and iron(III) being decomposed quite rapidly by dilute sulphuric acid in the concentration range of ≦ 100 mg CN-/l. Consequently, in such cases the total amount of cyanide can be determined in the first 25 ml of the distillate.     

Lipopolysaccharides from Serratia marcescens possess one or two 4-amino-4-deoxy-L-arabinopyranose 1-phosphate residues in the lipid A and D-glycero-D-talo-oct-2-ulopyranosonic acid in the inner core region

The carbohydrate backbones of the core-lipid A region were characterized from the lipopolysaccharides (LPSs) of Serratia marcescens strains 111R (a rough mutant strain of serotype O29) and IFO 3735 (a smooth strain not serologically characterized but possessing the O-chain structure of serotype O19). The LPSs were degraded either by mild hydrazinolysis (de-O-acylation) and hot 4 M KOH (de-N-acylation), or by hydrolysis in 2 % aqueous acetic acid, or by deamination. Oligosaccharide phosphates were isolated by high-performance anion-exchange chromatography. Through the use of compositional analysis, electrospray ionization Fourier transform mass spectrometry, and 1H and 13C NMR spectroscopy applying various one- and two-dimensional experiments, we identified the structures of the carbohydrate backbones that contained D-glycero-D-talo-oct-2-ulopyranosonic acid and 4-amino-4-deoxy-L-arabinose 1-phosphate residues. We also identified some truncated structures for both strains. All sugars were D-configured pyranoses and alpha-linked, except where stated otherwise.     

Zur Anwendung der magnetischen Titration

Zusammenfassung Eine einfache Meßanordnung für die magnetische Titration wird vorgestellt. Anhand der Umsetzung von [Ni(NH₃)₆]²⁺ mit CN^– und von J^– mit Cr₂O₇ ^2– wird gezeigt, daß sich dieses Meßverfahren unter bestimmten Voraussetzungen in der quantitativen Analyse einsetzen läßt. Zur Auswertung der Titrationskurven wird eine Auftragung der Kraft im Magnetfeld gegen das reziproke Gesamtvolumen vorgeschlagen.

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An application of magnetic titration

Summary A simple measuring equipment for magnetic titration is described. On the basis of the reaction of [Ni(NH₃)₆]²⁺ with CN^– and J^– with Cr₂O₇ ^2– it is shown that under certain conditions this method is useful in quantitative analysis. For evaluation of the titration curves, a plot of the force in the magnetic field against the reciprocal of the total volume is proposed.