Bilateral symmetry and modified Pascal triangles in Parsimonious games

We discuss the prominent role played by bilateral symmetry and modified Pascal triangles in self twin games, a subset of constant sum homogeneous weighted majority games. We show that bilateral symmetry of the free representations unequivocally identifies and characterizes this class of games and that modified Pascal triangles describe their cardinality for combinations of m and k, respectively linked through linear transforms to the key parameters n, number of players and h, number of types in the game. Besides, we derive the whole set of self twin games in the form of a genealogical tree obtained through a simple constructive procedure in which each game of a generation, corresponding to a given value of m, is able to give birth to one child or two children (depending on the parity of m), self twin games of the next generation. The breeding rules are, given the parity of m, invariant through generations and quite simple.Comment: pp. 2

Twin relationships in Parsimonious Games: some results

In a vintage paper concerning Parsimonious games, a subset of constant sum homogeneous weighted majority games, Isbell introduced a twin relationship based on transposition properties of the incidence matrices upon minimal winning coalitions of such games. A careful investigation of such properties allowed the discovery of some results on twin games presented in this paper. In detail we show that a) twin games have the same minimal winning quota and b) each Parsimonious game admits a unique balanced lottery on minimal winning coalitions, whose probabilities are given by the individual weights of its twin game

K-Fibonacci sequences and minimal winning quota in Parsimonious game

Parsimonious games are a subset of constant sum homogeneous weighted majority games unequivocally described by their free type representation vector. We show that the minimal winning quota of parsimonious games satisfies a second order, linear, homogeneous, finite difference equation with nonconstant coefficients except for uniform games. We provide the solution of such an equation which may be thought as the generalized version of the polynomial expansion of a proper k-Fibonacci sequence. In addition we show that the minimal winning quota is a symmetric function of the representation vector; exploiting this property it is straightforward to prove that twin Parsimonious games, i.e. a couple of games whose free type representations are each other symmetric, share the same minimal winning quota

Technological Strategies for the Sustainable Valorisation of Fruit and Vegetable Waste

Fruit and vegetable processing generates huge amounts of waste, which represents a wastage of valuable biomass and is characterised by high management cost and environmental impact. For these reasons, great attention has been dedicated in the last years to fruit and vegetable waste (FVW) valorisation, by its exploitation to produce value-added derivatives. Although it is generally assumed that FVW valorisation would deliver economic and environmental advantages, really few data on cost and energetic requirements of valorisation processes as well as on consumer response towards valorisation products are currently available. Based on these considerations, the aim of the Ph.D. research project \u201cTechnological Strategies for the Sustainable Valorisation of Fruit and Vegetable Waste\u201d was to develop a rational approach to FVW valorisation, useful to guarantee the production of value-added derivatives, but also to assess their technical feasibility, consumer acceptance, economic and environmental impact. The developed rational approach to FVW valorisation consists in four steps: waste characterisation, output definition, process design and feasibility study. This approach was validated on waste deriving from the production of fresh-cut lettuce (external leaves and cores), peach juice (pomace) and soy milk (okara). In particular, the characterisation step highlighted that waste generated during the processing of these vegetables ranges from 10 to 40%. Although the high water content (>76%), these wastes are particularly rich in fibre (>26% on dry weight basis) and polyphenolic compounds (>2.0 GAE/g of dry weight). Based on waste characteristics, different possible outputs were defined and specific processes exploiting the application of either traditional or novel sustainable technologies were designed: (i) convenient functional smoothies were produced from lettuce waste and okara using high pressure homogenization; (ii) antioxidant extracts were produced from lettuce waste and peach pomace using ultrasounds and microwaves; (iii) functional flour was obtained by air-drying and grinding of lettuce waste; (iv) supercritical-CO2-drying of lettuce waste allowed obtaining a porous material with high solvent loading capacity. The obtained valorisation outputs were then evaluated for their sensory acceptability and consumer response, in order to estimate their market potential. To this aim, the lettuce waste study-case, was analysed by the application of consumer-based methodologies. Obtained results highlighted the possibility to exploit nutritional and environmental claims to promote consumption of waste-derived food. Finally, a multi-objective method was applied to estimate the economic and environmental impact of the proposed valorisation strategies on an industrial scale. The developed approach could be considered a flexible decision support tool to guide stakeholders\u2019 aware choice and investment in the most sustainable valorisation strategies.Il processo produttivo di derivati di frutta e verdura genera enormi quantit\ue0 di scarto, che comporta la perdita di prodotti ad alto valore, elevati costi di gestione ed un notevole impatto ambientale. Per queste ragioni, negli ultimi anni, molta attenzione \ue8 stata dedicata alla valorizzazione degli scarti vegetali attraverso la loro trasformazione in derivati ad alto valore aggiunto. Sebbene la valorizzazione sia comunemente ritenuta vantaggiosa da un punto di vista economico ed ambientale, in realt\ue0 i dati disponibili su costi e richieste energetiche dei processi di valorizzazione, e sulla reazione dei consumatori nei confronti dei prodotti di valorizzazione sono molto limitati. Sulla base di queste considerazioni, lo scopo del progetto di Dottorato \u201cStrategie Tecnologiche per la Valorizzazione Sostenibile di Scarti Vegetali\u201d \ue8 stato quello di sviluppare un approccio razionale alla valorizzazione degli scarti vegetali, in grado di garantire l\u2019ottenimento di prodotti ad alto valore aggiunto, nonch\ue9 la loro fattibilit\ue0 tecnica, senza tralasciare la stima del livello di accettazione da parte dei consumatori e dell\u2019impatto economico ed ambientale. L\u2019approccio sviluppato nel corso del progetto consiste di 4 passaggi: caratterizzazione dello scarto, definizione dei prodotti di valorizzazione, design del processo produttivo e studio di fattibilit\ue0. Questo approccio \ue8 stato validato sugli scarti derivanti dalla produzione di insalata di IV gamma (foglie esterne e torsoli), succo di pesca (bucce e polpa residua) e latte di soia (okara). In particolare, la fase di caratterizzazione ha evidenziato che lo scarto generato durante la trasformazione di questi prodotti varia dal 10 al 40%. Nonostante l\u2019elevato contenuto di acqua (>76%), questi scarti presentano rilevanti quantit\ue0 di fibre (>26% su base secca) e composti fenolici (>2.0 GAE/g su base secca). Sulla base di queste caratteristiche sono stati identificati diversi possibili prodotti di valorizzazione e i corrispondenti processi produttivi, basati sull\u2019utilizzo di tecnologie sia tradizionali che innovative e sostenibili: (i) dagli scarti di insalata e dall\u2019okara, sfruttando l\u2019omogeneizzazione ad alta pressione, sono stati prodotti smoothies pronti all\u2019uso; (ii) dagli scarti di insalata e di pesca, utilizzando ultrasuoni e microonde, sono stati ottenuti estratti antiossidanti; (iii) dagli scarti di insalata, disidratati e macinati, \ue8 stata ricavata una farina funzionale; (iv) l\u2019applicazione dell\u2019essiccamento supercritico ha infine consentito di convertire gli scarti di insalata in un materiale poroso con elevata capacit\ue0 assorbente. I prodotti di valorizzazione cos\uec ottenuti sono stati analizzati in termini di accettabilit\ue0 sensoriale e attitudine dei consumatori, al fine di evidenziarne le potenzialit\ue0 di mercato. A questo scopo, \ue8 stato preso in considerazione il caso studio degli scarti di insalata, applicando metodi consumer-based. I risultati ottenuti hanno dimostrato la possibilit\ue0 di sfruttare claims nutrizionali e ambientali per promuovere il consumo di alimenti derivati da scarti vegetali. Infine, \ue8 stato applicato un metodo multi-objective per stimare l\u2019impatto economico ed ambientale delle strategie di valorizzazione proposte, se applicate su scala industriale. L\u2019approccio sviluppato in questo progetto pu\uf2 essere considerato un flessibile strumento di supporto alle decisioni, in grado di guidare gli stakeholders verso una scelta consapevole circa gli investimenti nelle strategie di valorizzazione pi\uf9 sostenibili

Effects of memory on the shapes of simple outbreak trees

Genomic tools, including phylogenetic trees derived from sequence data, are increasingly used to understand outbreaks of infectious diseases. One challenge is to link phylogenetic trees to patterns of transmission. Particularly in bacteria that cause chronic infections, this inference is affected by variable infectious periods and infectivity over time. It is known that non-exponential infectious periods can have substantial effects on pathogens’ transmission dynamics. Here we ask how this non-Markovian nature of an outbreak process affects the branching trees describing that process, with particular focus on tree shapes. We simulate Crump-Mode-Jagers branching processes and compare different patterns of infectivity over time. We find that memory (non-Markovian-ness) in the process can have a pronounced effect on the shapes of the outbreak’s branching pattern. However, memory also has a pronounced effect on the sizes of the trees, even when the duration of the simulation is fixed. When the sizes of the trees are constrained to a constant value, memory in our processes has little direct effect on tree shapes, but can bias inference of the birth rate from trees. We compare simulated branching trees to phylogenetic trees from an outbreak of tuberculosis in Canada, and discuss the relevance of memory to this dataset

A metric on phylogenetic tree shapes

The shapes of evolutionary trees are influenced by the nature of the evolutionary process but comparisons of trees from different processes are hindered by the challenge of completely describing tree shape. We present a full characterization of the shapes of rooted branching trees in a form that lends itself to natural tree comparisons. We use this characterization to define a metric, in the sense of a true distance function, on tree shapes. The metric distinguishes trees from random models known to produce different tree shapes. It separates trees derived from tropical versus USA influenza A sequences, which reflect the differing epidemiology of tropical and seasonal flu. We describe several metrics based on the same core characterization, and illustrate how to extend the metric to incorporate trees’ branch lengths or other features such as overall imbalance. Our approach allows us to construct addition and multiplication on trees, and to create a convex metric on tree shapes which formally allows computation of average tree shapes

Effect of ultrasounds and high pressure homogenization on the extraction of antioxidant polyphenols from lettuce waste

The possibility to exploit ultrasound (US) and high pressure homogenization (HPH) to obtain ethanolic antioxidant extracts from lettuce waste was studied. The application of US (400\u202fW, 24\u202fkHz) for 120\u202fs led to polyphenol extraction yield (81\u202f\u3bcg/mL) and antioxidant activity (101\u202f\u3bcg\u202fTE/mL) significantly higher than those obtained by traditional solid-liquid extraction at 50\u202f\ub0C for 15\u202fmin. Despite the intense cell rupture effect, the application of HPH pre-treatments resulted in 25% lower phenolic yields as compared to US solely, possibly due to the 40% activation of polyphenoloxidase (PPO) upon HPH treatment. Industrial relevance The waste generated by fresh-cut processing of lettuce poses environmental and economic issues to companies, leading to the need for alternative strategies for its management. US can be successfully exploited as time-saving extraction procedure for obtaining antioxidant extracts from lettuce waste

High-pressure homogenisation combined with blanching to turn lettuce waste into a physically stable juice

Lettuce waste was blanched, ground, pre-homogenised at 40\u202fMPa and subjected to high pressure homogenisation (HPH) at 80 (1 pass) and 150\u202fMPa (1, 10 passes) to obtain an ingredient intended for blended juice formulation. When lettuce was subjected to HPH without previous blanching, physically unstable juices were obtained. By contrast, the combination of HPH with a blanching pre-treatment allowed obtaining juices showing no physical separation and characterised by a bright green colour. This high stability was attributed to the modification of lettuce fibrous structure and to a 90% and 60% inactivation of polyphenoloxidase and pectin methylesterase, respectively. Juices presented a phenolic content of 3.5\u202f\ub1\u202f1.3\u202fmg GAE/100\u202fg and a microbial count at least 1 Log lower than that of corresponding not-blanched samples and below limits usually indicated for juice quality (4.7 Log CFU/g). During storage (4\u202f\ub0C), no phase separation was observed but microbial counts rapidly increased, suggesting the need for a further stabilization step. Industrial application Solid waste generated by fresh-cut processing of lettuce could be valorised by the application of blanching and HPH, leading to an innovative ingredient potentially exploitable in the formulation of healthy blended juices, smoothies and comminuted food. This effort is worth making considering that HPH is being increasingly introduced as processing operation in various industrial contexts, showing good feasibility and cost effectiveness, and could allow valorisation of different leaf discards

Magnitude and sources of bias in the detection of mixed strain M. tuberculosis infection.

AbstractHigh resolution tests for genetic variation reveal that individuals may simultaneously host more than one distinct strain of Mycobacterium tuberculosis. Previous studies find that this phenomenon, which we will refer to as “mixed infection”, may affect the outcomes of treatment for infected individuals and may influence the impact of population-level interventions against tuberculosis. In areas where the incidence of TB is high, mixed infections have been found in nearly 20% of patients; these studies may underestimate the actual prevalence of mixed infection given that tests may not be sufficiently sensitive for detecting minority strains. Specific reasons for failing to detect mixed infections would include low initial numbers of minority strain cells in sputum, stochastic growth in culture and the physical division of initial samples into parts (typically only one of which is genotyped). In this paper, we develop a mathematical framework that models the study designs aimed to detect mixed infections. Using both a deterministic and a stochastic approach, we obtain posterior estimates of the prevalence of mixed infection. We find that the posterior estimate of the prevalence of mixed infection may be substantially higher than the fraction of cases in which it is detected. We characterize this bias in terms of the sensitivity of the genotyping method and the relative growth rates and initial population sizes of the different strains collected in sputum