Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

A Unified Model for XVA, including Interest Rates and Rating

We start in Chapter 2 to investigate linear matrix-valued SDEs and the Itô-stochastic Magnus expansion. The Itô-stochastic Magnus expansion provides an efficient numerical scheme to solve matrix-valued SDEs. We show convergence of the expansion up to a stopping time τ and provide an asymptotic estimate of the cumulative distribution function of τ. Moreover, we show how to apply it to solve SPDEs with one and two spatial dimensions by combining it with the method of lines with high accuracy. We will see that the Magnus expansion allows us to use GPU techniques leading to major performance improvements compared to a standard Euler-Maruyama scheme. In Chapter 3, we study a short-rate model in a Cox-Ingersoll-Ross (CIR) framework for negative interest rates. We define the short rate as the difference of two independent CIR processes and add a deterministic shift to guarantee a perfect fit to the market term structure. We show how to use the Gram-Charlier expansion to efficiently calibrate the model to the market swaption surface and price Bermudan swaptions with good accuracy. We are taking two different perspectives for rating transition modelling. In Section 4.4, we study inhomogeneous continuous-time Markov chains (ICTMC) as a candidate for a rating model with deterministic rating transitions. We extend this model by taking a Lie group perspective in Section 4.5, to allow for stochastic rating transitions. In both cases, we will compare the most popular choices for a change of measure technique and show how to efficiently calibrate both models to the available historical rating data and market default probabilities. At the very end, we apply the techniques shown in this thesis to minimize the collateral-inclusive Credit/ Debit Valuation Adjustments under the constraint of small collateral postings by using a collateral account dependent on rating trigger.

Life Cycle Assessment of Peach Nectar: a comparative analysis between conventional and bioenergy-from-waste integrated food chains

Modern food systems are characterized by a high energy intensity as well as by the production of large amounts of waste, residuals and food losses. This inefficiency presents major consequences, in terms of GHG emissions, waste disposal, and natural resource depletion. The research hypothesis is that residual biomass material could contribute to the energetic needs of food systems, if recovered as an integrated renewable energy source (RES), leading to a sensitive reduction of the impacts of food systems, primarily in terms of fossil fuel consumption and GHG emissions. In order to assess these effects, a comparative life cycle assessment (LCA) has been conducted to compare two different food systems: a fossil fuel-based system and an integrated system with the use of residual as RES for self-consumption. The food product under analysis has been the peach nectar, from cultivation to end-of-life. The aim of this LCA is twofold. On one hand, it allows an evaluation of the energy inefficiencies related to agro-food waste. On the other hand, it illustrates how the integration of bioenergy into food systems could effectively contribute to reduce this inefficiency. Data about inputs and waste generated has been collected mainly through literature review and databases. Energy balance, GHG emissions (Global Warming Potential) and waste generation have been analyzed in order to identify the relative requirements and contribution of the different segments. An evaluation of the energy “loss” through the different categories of waste allowed to provide details about the consequences associated with its management and/or disposal. Results should provide an insight of the impacts associated with inefficiencies within food systems. The comparison provides a measure of the potential reuse of wasted biomass and the amount of energy recoverable, that could represent a first step for the formulation of specific policies on the integration of bioenergies for self-consumption.

Markov Constraints for Generating Texts with Style

This thesis addresses the issue of generating texts in the style of an existing author, that also satisfy structural constraints imposed by the genre of the text. Although Markov processes are known to be suitable for representing style, they are difficult to control in order to satisfy non-local properties, such as structural constraints, that require long distance modeling. The framework of Constrained Markov Processes allows to precisely generate texts that are consistent with a corpus, while being controllable in terms of rhymes and meter. Controlled Markov processes consist in reformulating Markov processes in the context of constraint satisfaction. The thesis describes how to represent stylistic and structural properties in terms of constraints in this framework and how this approach can be used for the generation of lyrics in the style of 60 differents authors An evaluation of the desctibed method is provided by comparing it to both pure Markov and pure constraint-based approaches. Finally the thesis describes the implementation of an augmented text editor, called Perec. Perec is intended to improve creativity, by helping the user to write lyrics and poetry, exploiting the techniques presented so far.

Life Cycle Thinking for sustainability assessment and decision-making in selected food supply chains in Costa Rica

The Agenda 2030 contains 17 integrated Sustainable Development Goals (SDGs). SDG 12 for Sustainable Consumption and Production (SCP) promotes the efficient use of resources through a systemic change that decouples economic growth from environmental degradation. The Food Systems (FS) pillar in SDG 12 entails paramount relevance due to its interconnection to many other SDGs, and even when being a crucial world food supplier, the Latin American and Caribbean (LAC) Region struggles with environmental and social externalities, low investment in agriculture, inequity, food insecurity, poverty, and migration. Life Cycle Thinking (LCT) was regarded as a pertinent approach to identify hotspots and trade-offs, and support decision-making process to aid LAC Region countries as Costa Rica to diagnose sustainability and overcome certain challenges. This thesis aimed to ‘evaluate the sustainability of selected products from food supply chains in Costa Rica, to provide inputs for further sustainable decision-making, through the application of Life Cycle Thinking’. To do this, Life Cycle Assessment (LCA), Life Cycle Costing (LCC), and Social Life Cycle Assessment (S-LCA) evaluated the sustainability of food-waste-to-energy alternatives, and the production of green coffee, raw milk and leafy vegetables, and identified environmental, social and cost hotspots. This approach also proved to be a useful component of decision-making and policy-making processes together with other methods. LCT scientific literature led by LAC or Costa Rican researchers is still scarce; therefore, this research contributed to improve capacities in the use of LCT in this context, while offering potential replicability of the developed frameworks in similar cases. Main limitations related to the representativeness and availability of primary data; however, future research and extension activities are foreseen to increase local data availability, capacity building, and the discussion of potential integration through Life Cycle Sustainability Assessment (LCSA).

Integration of by-products and waste from agri-food supply chains into the «water-energy-food» nexus (RECOW-ER): the role of fungi

The agricultural sector is undoubtedly one of the sectors that has the greatest impact on the use of water and energy to produce food. The circular economy allows to reduce waste, obtaining maximum value from products and materials, through the extraction of all possible by-products from resources. Circular economy principles for agriculture include recycling, processing, and reusing agricultural waste in order to produce bioenergy, nutrients, and biofertilizers. Since agro-industrial wastes are principally composed of lignin, cellulose, and hemicellulose they can represent a suitable substrate for mushroom growth and cultivation. Mushrooms are also considered healthy foods with several medicinal properties. The thesis is structured in seven chapters. In the first chapter an introduction on the water, energy, food nexus, on agro-industrial wastes and on how they can be used for mushroom cultivation is given. Chapter 2 details the aims of this dissertation thesis. In chapters three and four, corn digestate and hazelnut shells were successfully used for mushroom cultivation and their lignocellulosic degradation capacity were assessed by using ATR-FTIR spectroscopy. In chapter five, through the use of the Surface-enhanced Raman Scattering (SERS) spectroscopy was possible to set-up a new method for studying mushroom composition and for identifying different mushroom species based on their spectrum. In chapter six, the isolation of different strains of fungi from plastic residues collected in the fields and the ability of these strains to growth and colonizing the Low-density Polyethylene (LDPE) were explored. The structural modifications of the LDPE, by the most efficient fungal strain, Cladosporium cladosporioides Clc/1 strain were monitored by using the Scanning Electron Microscope (SEM) and ATR-FTIR spectroscopy. Finally, chapter seven outlines the conclusions and some hints for future works and applications are provided.

Risk assessment to improve food safety along different food chains

The great challenges of today pose great pressure on the food chain to provide safe and nutritious food that meets regulations and consumer health standards. In this context, Risk Analysis is used to produce an estimate of the risks to human health and to identify and implement effective risk-control measures. The aims of this work were 1) describe how QRA is used to evaluate the risk for consumers health, 2) address the methodology to obtain models to apply in QMRA; 3) evaluate solutions to mitigate the risk. The application of a QCRA to the Italian milk industry enabled the assessment of Aflatoxin M1 exposure, impact on different population categories, and comparison of risk-mitigation strategies. The results highlighted the most sensitive population categories, and how more stringent sampling plans reduced risk. The application of a QMRA to Spanish fresh cheeses evidenced how the contamination of this product with Listeria monocytogenes may generate a risk for the consumers. Two risk-mitigation actions were evaluated, i.e. reducing shelf life and domestic refrigerator temperature, both resulting effective in reducing the risk of listeriosis. A description of the most applied protocols for data generation for predictive model development, was provided to increase transparency and reproducibility and to provide the means to better QMRA. The development of a linear regression model describing the fate of Salmonella spp. in Italian salami during the production process and HPP was described. Alkaline electrolyzed water was evaluated for its potential use to reduce microbial loads on working surfaces, with results showing its effectiveness. This work showed the relevance of QRA, of predictive microbiology, and of new technologies to ensure food safety on a more integrated way. Filling of data gaps, the development of better models and the inclusion of new risk-mitigation strategies may lead to improvements in the presented QRAs.

Methods and tools to foster territorial approaches for the assessment of food supply chains

The challenges of the current global food systems are often framed around feeding the world's growing population while meeting sustainable development for future generations. Globalization has brought to a fragmentation of food spaces, leading to a flexible and mutable supply chain. This poses a major challenge to food and nutrition security, affecting also rural-urban dynamics in territories. Furthermore, the recent crises have highlighted the vulnerability to shocks and disruptions of the food systems and the eco-system due to the intensive management of natural, human and economic capital. Hence, a sustainable and resilient transition of the food systems is required through a multi-faceted approach that tackles the causes of unsustainability and promotes sustainable practices at all levels of the food system. In this respect, a territorial approach becomes a relevant entry point of analysis for the food system’s multifunctionality and can support the evaluation of sustainability by quantifying impacts associated with quantitative methods and understanding the territorial responsibility of different actors with qualitative ones. Against this background the present research aims to i) investigate the environmental, costing and social indicators suitable for a scoring system able to measure the integrated sustainability performance of food initiatives within the City/Region territorial context; ii) develop a territorial assessment framework to measure sustainability impacts of agricultural systems; and iii) define an integrated methodology to match production and consumption at a territorial level to foster a long-term vision of short food supply chains. From a methodological perspective, the research proposes a mixed quantitative and qualitative research method. The outcomes provide an in-depth view into the environmental and socio-economic impacts of food systems at the territorial level, investigating possible indicators, frameworks, and business strategies to foster their future sustainable development.