Inference and Learning in a Latent Variable Model for Beta Distributed Interval Data

Latent Variable Models (LVMs) are well established tools to accomplish a range of different data processing tasks. Applications exploit the ability of LVMs to identify latent data structure in order to improve data (e.g., through denoising) or to estimate the relation between latent causes and measurements in medical data. In the latter case, LVMs in the form of noisy-OR Bayes nets represent the standard approach to relate binary latents (which represent diseases) to binary observables (which represent symptoms). Bayes nets with binary representation for symptoms may be perceived as a coarse approximation, however. In practice, real disease symptoms can range from absent over mild and intermediate to very severe. Therefore, using diseases/symptoms relations as motivation, we here ask how standard noisy-OR Bayes nets can be generalized to incorporate continuous observables, e.g., variables that model symptom severity in an interval from healthy to pathological. This transition from binary to interval data poses a number of challenges including a transition from a Bernoulli to a Beta distribution to model symptom statistics. While noisy-OR-like approaches are constrained to model how causes determine the observables’ mean values, the use of Beta distributions additionally provides (and also requires) that the causes determine the observables’ variances. To meet the challenges emerging when generalizing from Bernoulli to Beta distributed observables, we investigate a novel LVM that uses a maximum non-linearity to model how the latents determine means and variances of the observables. Given the model and the goal of likelihood maximization, we then leverage recent theoretical results to derive an Expectation Maximization (EM) algorithm for the suggested LVM. We further show how variational EM can be used to efficiently scale the approach to large networks. Experimental results finally illustrate the efficacy of the proposed model using both synthetic and real data sets. Importantly, we show that the model produces reliable results in estimating causes using proofs of concepts and first tests based on real medical data and on images.     

Asymptotic Resonance, Interaction of Modes and Subharmonic Bifurcation

We study the existence of small amplitude oscillations near elliptic equilibria of autonomous systems, which mix different normal modes. The reference problem is the Fermi-Pasta-Ulam β-model: a chain of nonlinear oscillators with nearest-neighborhood interaction. We develop a new bifurcation approach that locates secondary bifurcations from the unimodal primary branches. Two sufficient conditions for bifurcation are given: one involves only the arithmetic properties of the eigenvalues of the linearized system (asymptotic resonance), while the other takes into account the nonlinear character of the interaction between normal modes (nonlinear coupling). Both conditions are checked for the Fermi-Pasta-Ulam problem.     

Synthesis of Nanocomposites from Pd0 and a Hyper‐Cross‐Linked Functional Resin Obtained from a Conventional Gel‐Type Precursor

Hyper‐cross‐linked resins stemming from a gel‐type poly‐chloromethylated poly(styrene‐co‐divinylbenzene) resin (GT) have been investigated by a multi‐methodological approach based on elemental analysis, scanning electron microscopy, X‐ray microanalysis, and solvent absorption. The hyper‐cross‐linking of the parent resin was accomplished by Friedel–Crafts alkylation of the phenyl rings of the resins with the chloromethyl groups. This produced a permanent pore system comprising both micropores (<2.0 nm in diameter) and mesopores (2.2 nm). The chloromethyl groups that did not react in the hyper‐cross‐linking step were transformed into methylmercaptan groups and the latter were then converted into sulfonic groups by oxidation with hydrogen peroxide. By this procedure the extensive permanent porosity of the parent unsulfonated hyper‐cross‐linked polymer (HGT) was retained by the sulfonated polymer (HGTS). The final exchange capacity of HGTS was determined to be 0.36 mmol g^?1. HGTS was easily metalated with Pd^II and the subsequent reduction of the metal centers with either aqueous sodium borohydride, formaldehyde, or dihydrogen produced three Pd⁰/HGTS nanocomposites. The metal nanoparticles had diameters in the 1–6 nm range for all the nanocomposites, as determined by TEM, but with somewhat different distributions. When formaldehyde was used, more than 90 % of the nanoparticles were less than 3 nm and their radial distribution throughout the polymer beads was quite homogeneous. These findings show that with this reducing agent the metal nanoparticles are generated within the pore system of the polymer matrix, hence their size is controlled by the dimensions of the pores of the polymeric support.     

Assessment of reproducibility and uncertainty of food microbiology methods: statistical approach of a multi-site laboratory

The validation of food microbiology methods and assessment of measurement uncertainty are required for laboratories operating EN ISO/IEC 17025 accreditation systems. This paper aims to describes the statistical approach adopted by a multi-site laboratory to satisfy these requirements and to routinely check the performance of the methods. A validation protocol was performed, reflecting a great variability of experimental conditions, represented by the period of time during which determinations were made, the different laboratories concerned, the large number of technicians involved, the differences in the level of contamination of the matrix analyzed and the operating conditions (equipment, reagents, culture media, environmental conditions, etc.). Despite the very high variability of the experimental conditions, the values of repeatability and reproducibility obtained for the methods were lower than those stated in the respective regulations. In addition, the top-down approach adopted in this study is to be considered effective overtime and allows to randomize all variable factors, including the effects of sensitivity and specificity, in order to simulate the conditions of real reproducibility. A specific Excel spreadsheet was also developed for the routine expression of analytical results. This spreadsheet represents a very useful tool for operators to calculate and routinely check the results, as well as to assess the uncertainty of measurement. This particular quality assessment system is enabling the multi-site laboratory to implement the accuracy, reliability and comparability of the analytical results and to ensure the analytical control of data output.     

Rigidity results in diffusion Markov triples

We consider stable solutions of semilinear equations in a very general setting. The equation is set on a Polish topological space endowed with a measure and the linear operator is induced by a carré du champs (equivalently, the equation is set in a diffusion Markov triple).Under suitable curvature dimension conditions, we establish that stable solutions with integrable carré du champs are necessarily constant (weaker conditions characterize the structure of the carré du champs and carré du champ itéré).The proofs are based on a geometric Poincaré formula in this setting. From the general theorems established, several previous results are obtained as particular cases and new ones are provided as well.     

Supramolecular assemblies tailored by dipyridyl-1,2-4-thiadiazoles: influence of the building blocks in the predictability of the final network

ABSTRACT

Coordinatively unsaturated dithiophosphato complex [Cd((MeO)₂PS₂)₂] (1) was reacted with the bifunctional ligands 3,5-di-(4-pyridyl)-1,2,4-thiadiazole (L1) and 3,5-di-(3-pyridyl)-1,2,4-thiadiazole (L2) to give the helicoidal coordination polymer (1·L1)_∞ and the paddle-wheel dimer (1·L2)₂, both characterised by single-crystal X-ray diffraction. A comparison of the structures with the different supramolecular constructs obtained by reacting L1 and L2 with differently P-substituted dithiophosphoric Ni^II complexes allowed to evaluate the role of the metal ion for the predictable assembly of this class of coordination polymers.     

Dye-Doped Silica Nanoparticles for Enhanced ECL-Based Immunoassay Analytical Performance

The combination of highly sensitive techniques such as electrochemiluminescence (ECL) with nanotechnology sparked new analytical applications, in particular for immunoassay-based detection systems. In this context, nanomaterials, particularly dye-doped silica nanoparticles (DDSNPs) are of high interest, since they can offer several advantages in terms of sensitivity and performance. In this work we synthesized two sets of monodispersed and biotinylated [Ru(bpy)₃]²⁺-doped silica nanoparticles, named bio-Triton@RuNP and bio-Igepal@RuNP, obtained following the reverse microemulsion method using two different types of nonionic surfactants. Controlling the synthetic procedures, we were able to obtain nanoparticles (NPs) offering highly intense signal, using tri-n-propylamine (TPrA) as coreactant, with bio-Triton@RuNps being more efficient than bio-Igepal@RuNP.     

Evidence of Noncentrosymmetry of Human Tooth Hydroxyapatite Crystals

Herein, we investigate human single hydroxyapatite crystals (enamel and dentine) by convergent‐beam electron diffraction (CBED) and automated electron‐diffraction tomography (ADT). The CBED pattern shows the absence of the mirror plane perpendicular to the c axis leading to the P6₃ space group instead of the P6₃/m space group considered for larger‐scale crystals, this is confirmed by ADT. This experimental evidence is of prime importance for understanding the morphogenesis and the architectural organization of calcified tissues.     

Synthesis of Porphyrin‐Anthraquinone Conjugates as Photosensitizing Agents

A series of 5,10,15,20‐tetraarylporphyrins covalently linked to anthraquinones belonging to the class of emodin were synthesized following two different pathways. The first method exploits the functionalization of the methyl group in position 6 of O‐protected emodins, which can be converted either into a carboxylic acid or into a bromo‐methyl derivative. The modified emodins were then bound through amido or ether bonds to one of the tetraarylporphyrins meso phenyl rings bearing an amino or hydroxyl group, respectively. An alternative synthesis exploits the mixed condensation of triacetoxy‐emodinaldehyde (or trimethoxy‐emodinaldehyde) with pyrrole in the presence of variable amounts of benzaldehyde, thus affording two similar 5‐emodin‐10,15,20‐triphenylporphyrins differing from one another in the emodin hydroxyl group protection. These compounds are characterized by direct conjugation of the emodin moiety to the tetrapyrrolic ring. Preliminary experiments were performed in vitro on the human colon adenocarcinoma cell line HCT116 to evaluate the photocytotoxicity of the new compounds.     

The Effect of the Molecular Size and Shape on the Volume Behavior of Binary Liquid Mixtures. Branched and Cyclic Alkanes in Heptane at 298.15 K

Excess molar volumes V ^E for 40 mixtures of heptane with a liquid alkane and apparent molar volumes in heptane for eight solid alkanes have been obtained at 298.15 K. They include five linear, 30 branched-chain, and 13 cyclic alkanes. Almost all systems exhibit negative V ^E values. For mixtures with open chain alkanes, V ^E increases from C5 to C7 and then decreases. A similar trend is shown by mixtures with cycloalkanes. V ^E values are compared with known H ^E data for mixtures with heptane and tetrachloromethane. Signs and trends of V ^E and H ^E are correlated with the free volume and interactional terms of the Flory theory. The partial molar volumes at infinite dilution in heptane, V°, have also been obtained and discussed together with literature data on other hydrocarbons and polar compounds. The calculated contributions to V° by CH₃, CH₂, CH and C groups are compared with previously determined contributions of polar groups. The lower contributions of the latter groups are explained with the volume contraction caused by dipole-induced dipole interaction. The volume effects associated with branching and cyclization have been evaluated and compared with the corresponding effects on solvation enthalpy. The branching effect, in the order of magnitude of few cm³·mol^?1, and the larger negative values of cyclization volumes, down to ?24 cm³·mol^?1, are discussed in terms of packing and solute–solvent interactions, in analogy to polar organic solutes either in heptane and tetrachloromethane. A negative cyclization effect is also exhibited by the solvation enthalpies.