Indagini in Deep Inference

La tesi è uno studio di alcuni aspetti della nuova metodologia “deep inference”, abbinato ad una rivisitazione dei concetti classici di proof theory, con l'aggiunta di alcuni risultati originali orientati ad una maggior comprensione dell'argomento, nonché alle applicazioni pratiche. Nel primo capitolo vengono introdotti, seguendo un approccio di stampo formalista (con alcuni spunti personali), i concetti base della teoria della dimostrazione strutturale – cioè quella che usa strumenti combinatoriali (o “finitistici”) per studiare le proprietà delle dimostrazioni. Il secondo capitolo focalizza l'attenzione sulla logica classica proposizionale, prima introducendo il calcolo dei sequenti e dimostrando il Gentzen Hauptsatz, per passare poi al calcolo delle strutture (sistema SKS), dimostrando anche per esso un teorema di eliminazione del taglio, appositamente adattato dall'autore. Infine si discute e dimostra la proprietà di località per il sistema SKS. Un percorso analogo viene tracciato dal terzo ed ultimo capitolo, per quanto riguarda la logica lineare. Viene definito e motivato il calcolo dei sequenti lineari, e si discute del suo corrispettivo nel calcolo delle strutture. L'attenzione qui è rivolta maggiormente al problema di definire operatori non-commutativi, che mettono i sistemi in forte relazione con le algebre di processo.

Inference on copula-based correlation structures

We propose an extension of the approach provided by Kluppelberg and Kuhn (2009) for inference on second-order structure moments. As in Kluppelberg and Kuhn (2009) we adopt a copula-based approach instead of assuming normal distribution for the variables, thus relaxing the equality in distribution assumption. A new copula-based estimator for structure moments is investigated. The methodology provided by Kluppelberg and Kuhn (2009) is also extended considering the copulas associated with the family of Eyraud-Farlie-Gumbel-Morgenstern distribution functions (Kotz, Balakrishnan, and Johnson, 2000, Equation 44.73). Finally, a comprehensive simulation study and an application to real financial data are performed in order to compare the different approaches.

Partial reconstruction of the trajectories of a discretely observed branching diffusion with immigration and an application to inference

In this treatise we consider finite systems of branching particles where the particles move independently of each other according to d-dimensional diffusions. Particles are killed at a position dependent rate, leaving at their death position a random number of descendants according to a position dependent reproduction law. In addition particles immigrate at constant rate (one immigrant per immigration time). A process with above properties is called a branching diffusion withimmigration (BDI). In the first part we present the model in detail and discuss the properties of the BDI under our basic assumptions. In the second part we consider the problem of reconstruction of the trajectory of a BDI from discrete observations. We observe positions of the particles at discrete times; in particular we assume that we have no information about the pedigree of the particles. A natural question arises if we want to apply statistical procedures on the discrete observations: How can we find couples of particle positions which belong to the same particle? We give an easy to implement 'reconstruction scheme' which allows us to redraw or 'reconstruct' parts of the trajectory of the BDI with high accuracy. Moreover asymptotically the whole path can be reconstructed. Further we present simulations which show that our partial reconstruction rule is tractable in practice. In the third part we study how the partial reconstruction rule fits into statistical applications. As an extensive example we present a nonparametric estimator for the diffusion coefficient of a BDI where the particles move according to one-dimensional diffusions. This estimator is based on the Nadaraya-Watson estimator for the diffusion coefficient of one-dimensional diffusions and it uses the partial reconstruction rule developed in the second part above. We are able to prove a rate of convergence of this estimator and finally we present simulations which show that the estimator works well even if we leave our set of assumptions.

Development of a multi-species method by GC-coupling with inductively coupled plasma isotope dilution mass spectrometry for the simultaneous determination of alkylated lead, mercury and tin compounds

An accurate and sensitive species-specific GC-ICP-IDMS (gas chromatography inductively coupled plasma isotope dilution mass spectrometry) method for the determination of trimethyllead and a multi-species-specific GC-ICP-IDMS method for the simultaneous determination of trimethyllead, methylmercury, and butyltins in biological and environmental samples were developed. They allow the determination of corresponding elemental species down to the low ng g-1 range. The developed synthesis scheme for the formation of isotopically labeled Me3206Pb+ can be used for future production of this spike. The novel extraction technique, stir bar sorptive extraction (SBSE), was applied for the first time in connection with species-specific isotope dilution GC-ICP-MS for the determination of trimethyllead, methylmercury and butyltins. The results were compared with liquid-liquid extraction. The developed methods were validated by the analysis of certified reference materials. The liquid-liquid extraction GC-ICP-IDMS method was applied to seafood samples purchased from a supermarket. The methylated lead fraction in these samples, correlated to total lead, varied in a broad range of 0.01-7.6 %. On the contrary, the fraction of methylmercury is much higher, normally in the range of 80-98 %. The highest methylmercury content of up to 12 µg g-1 has been determined in shark samples, an animal which is at the end of the marine food chain, whereas in other seafood samples a MeHg+ content of less than 0.2 µg g-1 was found. Butyltin species could only be determined in samples, where anthropogenic contaminations must be assumed. This explains the observed broad variation of the butylated tin fraction in the range of <0.3-49 % in different seafood samples. Because all isotope-labelled spike compounds, except trimethyllead, are commercially available, the developed multi-species-specific GC-ICP-IDMS method has a high potential in future for routine analysis.

Phage therapy: A software system for phage quantification and kinetic model inference.

One of the most serious problems of the modern medicine is the growing emergence of antibiotic resistance among pathogenic bacteria. In this circumstance, different and innovative approaches for treating infections caused by multidrug-resistant bacteria are imperatively required. Bacteriophage Therapy is one among the fascinating approaches to be taken into account. This consists of the use of bacteriophages, viruses that infect bacteria, in order to defeat specific bacterial pathogens. Phage therapy is not an innovative idea, indeed, it was widely used around the world in the 1930s and 1940s, in order to treat various infection diseases, and it is still used in Eastern Europe and the former Soviet Union. Nevertheless, Western scientists mostly lost interest in further use and study of phage therapy and abandoned it after the discovery and the spread of antibiotics. The advancement of scientific knowledge of the last years, together with the encouraging results from recent animal studies using phages to treat bacterial infections, and above all the urgent need for novel and effective antimicrobials, have given a prompt for additional rigorous researches in this field. In particular, in the laboratory of synthetic biology of the department of Life Sciences at the University of Warwick, a novel approach was adopted, starting from the original concept of phage therapy, in order to study a concrete alternative to antibiotics. The innovative idea of the project consists in the development of experimental methodologies, which allow to engineer a programmable synthetic phage system using a combination of directed evolution, automation and microfluidics. The main aim is to make “the therapeutics of tomorrow individualized, specific, and self-regulated” (Jaramillo, 2015). In this context, one of the most important key points is the Bacteriophage Quantification. Therefore, in this research work, a mathematical model describing complex dynamics occurring in biological systems involving continuous growth of bacteriophages, modulated by the performance of the host organisms, was implemented as algorithms into a working software using MATLAB. The developed program is able to predict different unknown concentrations of phages much faster than the classical overnight Plaque Assay. What is more, it gives a meaning and an explanation to the obtained data, making inference about the parameter set of the model, that are representative of the bacteriophage-host interaction.

Inference of Raja miraletus population structure using mitochondrial and nuclear DNA: comparing the resolution power of molecular markers in exploring species and population boundaries

This study focused on the role of oceanographic discontinuities and the presence of transitional areas in shaping the population structure and the phylogeography of the Raja miraletus species complex, coupled with the test of the effective occurrence of past speciation events. The comparisons between the Atlantic African and the North-Eastern Atlantic-Mediterranean geographic populations were unravelled using both Cytochrome Oxidase I and eight microsatellite loci. This approach guaranteed a robust dataset for the identification of a speciation event between the Atlantic African clade, corresponding to the ex Raja ocellifera nominal species, and the NE Atlantic-Mediterranean R. miraletus clade. As a matter of fact, the origin of the Atlantic Africa and the NE Atlantic-Mediterranean deep split dated about 11.74MYA and was likely due to the synergic influence currents and two upwelling areas crossing the Western African Waters. Within the Mediterranean Sea, particular attention was also paid to the transitional area represented by Adventura and Maltese Bank, that might have contributed in sustaining the connectivity of the Western and the Eastern Mediterranean geographical populations. Furthermore, the geology of the easternmost part of Sicily and the geo-morphological depression of the Calabrian Arc could have driven the differentiation of the Eastern Mediterranean Sea. Although bathymetric and oceanographic discontinuity could represent barriers to dispersal and migration between Eastern and Western Mediterranean samples, a clear and complete genetic separation among them was not detected. Results produced by this work identified a speciation event defining Raja ocellifera and R. miraletus as two different species, and describing the R. miraletus species complex as the most ancient cryptic speciation event in the family Rajidae, representing another example of how strictly connected the environment, the behavioural habits and the evolutionary and ecologic drivers are.

Simultaneous bilateral hip replacement reveals superior outcome and fewer complications than two-stage procedures: a prospective study including 1819 patients and 5801 follow-ups from a total joint replacement registry

Background Total joint replacements represent a considerable part of day-to-day orthopaedic routine and a substantial proportion of patients undergoing unilateral total hip arthroplasty require a contralateral treatment after the first operation. This report compares complications and functional outcome of simultaneous versus early and delayed two-stage bilateral THA over a five-year follow-up period. Methods The study is a post hoc analysis of prospectively collected data in the framework of the European IDES hip registry. The database query resulted in 1819 patients with 5801 follow-ups treated with bilateral THA between 1965 and 2002. According to the timing of the two operations the sample was divided into three groups: I) 247 patients with simultaneous bilateral THA, II) 737 patients with two-stage bilateral THA within six months, III) 835 patients with two-stage bilateral THA between six months and five years. Results Whereas postoperative hip pain and flexion did not differ between the groups, the best walking capacity was observed in group I and the worst in group III. The rate of intraoperative complications in the first group was comparable to that of the second. The frequency of postoperative local and systemic complication in group I was the lowest of the three groups. The highest rate of complications was observed in group III. Conclusions From the point of view of possible intra- and postoperative complications, one-stage bilateral THA is equally safe or safer than two-stage interventions. Additionally, from an outcome perspective the one-stage procedure can be considered to be advantageous.

A new technique for simultaneous validation of two manual nonmercury auscultatory sphygmomanometers (A;D UM-101 and Accoson Greenlight 300) based on the International protocol

Auscultatory nonmercury manual devices seem good alternatives for the mercury sphygmomanometers in the clinic and for research settings, but individual internal validation of each device is time-consuming. The aim of this study was to validate a new technique capable of testing two devices simultaneously, based on the International protocol of the European Society of Hypertension.

Active regulation of cerebral venous tone: simultaneous arterial and venous transcranial Doppler sonography during a Valsalva manoeuvre

The aim of this study was to analyse the cerebral venous outflow in relation to the arterial inflow during a Valsalva manoeuvre (VM). In 19 healthy volunteers (mean age 24.1 +/- 2.6 years), the middle cerebral artery (MCA) and the straight sinus (SRS) were insonated by transcranial Doppler sonography. Simultaneously the arterial blood pressure was recorded using a photoplethysmographic method. Two VM of 10 s length were performed per participant. Tracings of the variables were then transformed to equidistantly re-sampled data. Phases of the VM were analysed regarding the increase of the flow velocities and the latency to the peak. The typical four phases of the VM were also found in the SRS signal. The relative flow velocity (FV) increase was significantly higher in the SRS than in the MCA for all phases, particularly that of phase IV (p < 0.01). Comparison of the time latency of the VM phases of the MCA and SRS only showed a significant difference for phase I (p < 0.01). In particular, there was no significant difference for phase IV (15.8 +/- 0.29 vs. 16.0 +/- 0.28 s). Alterations in venous outflow in phase I are best explained by a cross-sectional change of the lumen of the SRS, while phases II and III are compatible with a Starling resistor. However, the significantly lager venous than the arterial overshoot in phase IV may be explained by the active regulation of the venous tone.

ABCtoolbox: a versatile toolkit for approximate Bayesian computations

Background The estimation of demographic parameters from genetic data often requires the computation of likelihoods. However, the likelihood function is computationally intractable for many realistic evolutionary models, and the use of Bayesian inference has therefore been limited to very simple models. The situation changed recently with the advent of Approximate Bayesian Computation (ABC) algorithms allowing one to obtain parameter posterior distributions based on simulations not requiring likelihood computations. Results Here we present ABCtoolbox, a series of open source programs to perform Approximate Bayesian Computations (ABC). It implements various ABC algorithms including rejection sampling, MCMC without likelihood, a Particle-based sampler and ABC-GLM. ABCtoolbox is bundled with, but not limited to, a program that allows parameter inference in a population genetics context and the simultaneous use of different types of markers with different ploidy levels. In addition, ABCtoolbox can also interact with most simulation and summary statistics computation programs. The usability of the ABCtoolbox is demonstrated by inferring the evolutionary history of two evolutionary lineages of Microtus arvalis. Using nuclear microsatellites and mitochondrial sequence data in the same estimation procedure enabled us to infer sex-specific population sizes and migration rates and to find that males show smaller population sizes but much higher levels of migration than females. Conclusion ABCtoolbox allows a user to perform all the necessary steps of a full ABC analysis, from parameter sampling from prior distributions, data simulations, computation of summary statistics, estimation of posterior distributions, model choice, validation of the estimation procedure, and visualization of the results.

Development and validation of a liquid chromatography-tandem mass spectrometry method for the simultaneous determination of nine corticosteroid residues in bovine liver samples

A liquid chromatography tandem mass spectrometry (LC-MS/MS) confirmatory method for the simultaneous determination of nine corticosteroids in liver, including the four MRL compounds listed in Council Regulation 37/2010, was developed. After an enzymatic deconjugation and a solvent extraction of the liver tissue, the resulting solution was cleaned up through an SPE Oasis HLB cartridge. The analytes were then detected by liquid chromatography-negative-ion electrospray tandem mass spectrometry, using deuterium-labelled internal standards. The procedure was validated as a quantitative confirmatory method according to the Commission Decision 2002/657/EC criteria. The results showed that the method was suitable for statutory residue testing regarding the following performance characteristics: instrumental linearity, specificity, precision (repeatability and intra-laboratory reproducibility), recovery, decision limit (CCα), detection capability (CCβ) and ruggedness. All the corticosteroids can be detected at a concentration around 1 μg kg(-1); the recoveries were above 62% for all the analytes. Repeatability and reproducibility (within-laboratory reproducibility) for all the analytes were below 7.65% and 15.5%, respectively.