Functorial Semantics for Petri Nets under the Individual Token Philosophy

Although the algebraic semantics of place/transition Petri nets under the collective token philosophy has been fully explained in terms of (strictly) symmetric (strict) monoidal categories, the analogous construction under the individual token philosophy is not completely satisfactory because it lacks universality and also functoriality. We introduce the notion of pre-net to recover these aspects, obtaining a fully satisfactory categorical treatment centered on the notion of adjunction. This allows us to present a purely logical description of net behaviours under the individual token philosophy in terms of theories and theory morphisms in partial membership equational logic, yielding a complete match with the theory developed by the authors for the collective token view of net

Causes and consequences of natural hybridisation among coral reef butterflyfishes (Chaetodon: Chaetodontidae)

Natural hybridisation is the successful interbreeding of individuals from different populations, distinguishable through one or more heritable characters, and is a widespread phenomenon in the plant and animal kingdoms. The development of hybridisation theories has largely been based on studies in terrestrial and freshwater ecosystems. Hybridisation was traditionally considered rare and unimportant in marine systems and therefore received little attention. Recently however, there has been a surge of reported marine hybrids, particularly in corals and reef fishes. The ecological promoters and evolutionary and adaptive consequences of reef fish hybridisation are yet to be thoroughly evaluated. Butterflyfishes (f. Chaetodontidae) form a disproportionate number of hybrids and therefore represent an appropriate model group to investigate hybridisation in reef fishes. This thesis examines the causes and consequences of hybridisation in reef fishes and focuses on butterflyfishes (genus Chaetodon) at Christmas Island (Indian Ocean), a global hotspot for reef fish hybridisation. The aims of this thesis were to i) review the incidence and ecological/behavioural precursors of hybridisation in reef fishes, while providing a tentative framework for conducting studies within hybrid zones; ii) develop a microsatellite toolkit for species of the Chaetodon genus; iii) compare the ecology, behaviour and population genetics of hybridising sister species of butterflyfishes in order to, not only provide a snapshot of the evolutionary consequences of hybridisation in this group, but also determine which processes are likely to promote it; iv) use a comparative life history approach to determine the fitness of butterflyfish hybrids relative to their parental species. Chapter 1 reviews the current knowledge of hybridisation with a focus on marine fishes. Hybridisation was found to be highly prevalent in marine fish, despite previous assertions of rarity, and showed a taxonomic as well as latitudinal bias. Further, the current marine fish hybridisation literature was found to be largely lacking ecological and behavioural data, in contrast with freshwater counterparts, therefore highlighting the need for a framework to fill the data gap in order to better accompany the wealth of genetic data produced in the assessment of hybridisation. The development of a molecular toolkit, necessary for the rest of our investigations, is presented in Chapter 2. Twenty microsatellite loci were developed using 454 sequencing, to apply to the population genetic analysis of the Chaetodon guttatissimus × C. punctatofasciatus complex. This was done to facilitate direct comparison of the genetic underpinnings of hybridisation in this group to those of another previously studied group (C. trifasciatus and C. lunulatus), for which species-specific microsatellite loci had been designed and used. Chapter 3 uses the molecular toolkit and experimental framework outlined in the previous chapters to examine hybridisation between two butterflyfish sister species, Chaetodon guttatissimus and C. punctatofasciatus. The largely overlapping spatial and dietary ecologies of these species favour heterospecific encounters. Lack of assortative mating and local rarity of C. punctatofasciatus promote the formation of heterospecific breeding pairs. Analyses of mtDNA and microsatellite DNA were consistent with the hybrid status of the intermediately coloured hybrids. Maternal contribution to hybridisation in this complex was bidirectional, and introgression by C. punctatofasciatus mtDNA was detected in C. guttatissimus individuals within and beyond the hybrid zone (almost 1000 km to the west), potentially indicating a Pacific invasion of an Indian Ocean species genome. The comparisons drawn with previous work on hybrdising Chaetodon trifasciatus and C. lunulatus showed that, despite being driven by similar factors, hybridisation in reef fishes can have varying evolutionary consequences, possibly due to the magnitude of the genetic distance between hybridising species. Chapter 4 evaluates hybrid fitness in both Chaetodon hybridising groups presented in the previous study. Histology confirmed the reproductive viability of hybrids, and liver lipid analyses showed that hybrid condition was not different from parental species. Further, otolith data highlighted no difference in growth rate and maximum length between hybrids and parents. According to the fitness-related traits measured here, Chaetodon hybrids are as fit as their parents, and unlikely to promote the formation of a hybrid swarm. However, sufficient fitness and rapid transfer of genetic material between species allow persistence of hybrids within the suture zone, where they positively contribute to genetic diversity. The cases of hybridisation studied here appear to be initiated by similar ecological and behavioural settings, albeit showing different genetic consequences. Determining this was possible through the use of a comprehensive approach, which combined molecular analyses and extensive field observations. Further, the apparent lack of differences in fitness between hybrids and parental species points at the persistence of hybrid individuals within the Indo- Pacific suture zone, where they may continue to contribute positively to genetic diversity. The role of hybridisation in evolution and adaptability had been appreciated in terrestrial and freshwater systems, and this thesis shows that hybridisation can have a role in maintaining reef fish diversity. The studies presented here constitute a comprehensive overview of the relevance of hybridisation for reef fishes and may be a stepping stone toward ascertaining its role in the evolution and adaptation of new species in such a diverse group

Constraint optimization and landscapes

We describe an effective landscape introduced in [1] for the analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring. This geometric construction reexpresses these problems in the more familiar terms of optimization in rugged energy landscapes. In particular, it allows one to understand the puzzling fact that unsophisticated programs are successful well beyond what was considered to be the `hard' transition, and suggests an algorithm defining a new, higher, easy-hard frontier.Comment: Contribution to STATPHYS2

Replicated Bethe Free Energy: A Variational Principle behind Survey Propagation

A scheme to provide various mean-field-type approximation algorithms is presented by employing the Bethe free energy formalism to a family of replicated systems in conjunction with analytical continuation with respect to the number of replicas. In the scheme, survey propagation (SP), which is an efficient algorithm developed recently for analyzing the microscopic properties of glassy states for a fixed sample of disordered systems, can be reproduced by assuming the simplest replica symmetry on stationary points of the replicated Bethe free energy. Belief propagation and generalized SP can also be offered in the identical framework under assumptions of the highest and broken replica symmetries, respectively.Comment: appeared in Journal of the Physical Society of Japan 74, 2133-2136 (2005

Long-range frustration in T=0 first-step replica-symmetry-broken solutions of finite-connectivity spin glasses

In a finite-connectivity spin-glass at the zero-temperature limit, long-range correlations exist among the unfrozen vertices (whose spin values being non-fixed). Such long-range frustrations are partially removed through the first-step replica-symmetry-broken (1RSB) cavity theory, but residual long-range frustrations may still persist in this mean-field solution. By way of population dynamics, here we perform a perturbation-percolation analysis to calculate the magnitude of long-range frustrations in the 1RSB solution of a given spin-glass system. We study two well-studied model systems, the minimal vertex-cover problem and the maximal 2-satisfiability problem. This work points to a possible way of improving the zero-temperature 1RSB mean-field theory of spin-glasses.Comment: 5 pages, two figures. To be published in JSTA

Loop Calculus in Statistical Physics and Information Science

Considering a discrete and finite statistical model of a general position we introduce an exact expression for the partition function in terms of a finite series. The leading term in the series is the Bethe-Peierls (Belief Propagation)-BP contribution, the rest are expressed as loop-contributions on the factor graph and calculated directly using the BP solution. The series unveils a small parameter that often makes the BP approximation so successful. Applications of the loop calculus in statistical physics and information science are discussed.Comment: 4 pages, submitted to Phys.Rev.Lett. Changes: More general model, Simpler derivatio

Analytic determination of dynamical and mosaic length scales in a Kac glass model

We consider a disordered spin model with multi-spin interactions undergoing a glass transition. We introduce a dynamic and a static length scales and compute them in the Kac limit (long--but--finite range interactions). They diverge at the dynamic and static phase transition with exponents (respectively) -1/4 and -1. The two length scales are approximately equal well above the mode coupling transition. Their discrepancy increases rapidly as this transition is approached. We argue that this signals a crossover from mode coupling to activated dynamics.Comment: 4 pages, 4 eps figures. New version conform to the published on

Open History Map

OpenHistoryMap aspires to become the open source geographical system for archaeological information, both from an academic and an educational point of view. There are many fragmented online web-GIS experiences targeted at very specific projects, but no tool enables a broader overview of both research and studies. For these reasons, in order to create an Open Access platform, one of the most important aspects is the creation of tools that can facilitate both the sharing of archaeological spatial and temporal information as well as the easy reuse of the generated data. OpenHistoryMap is supposed to create a tool that is both a map of the archaeological world as well as a repository for the connected data within structured research papers. The project finds its roots first of all within the collective experience of ‘archaeology’ that refers to non-expert users, and in the second place within the academic scientific experience of research centres and universities. While the first approach gives an integrated and reliable picture of the cultural item, the second provides consistent and solid datasets with a perspective on the mixture of specific types of information

Error-correcting code on a cactus: a solvable model

An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica symmetric theory results and provides a very good approximation to finite systems of moderate size. The probability propagation decoding algorithm emerges naturally from the analysis. A phase transition between decoding success and failure phases is found to coincide with an information-theoretic upper bound. The method is employed to compare Gallager and MN codes.Comment: 7 pages, 3 figures, with minor correction

A Generalization of the Finite-Length Scaling Approach Beyond the BEC

We want to extend the approximation of the error probability via a scaling approach from the BEC to general binary-input memoryless output-symmetric (BMS) channels. In particular, we consider such scaling laws for regular LDPC ensembles and message-passing (MP) decoders with a finite number of messages. We first show how to re-derive the scaling law for transmission over the BEC using an “EXIT-like” curve instead of the density evolution curve of the peeling decoder. The advantage of the new derivation is that the new expression of the scaling parameter α only contains quantities that can be meaningfully interpreted also for general message-passing algorithms. In particular, this expression only depends on the curvature of the EXIT-like curve as well as the variance of the messages, both taken at the critical channel parameter. We discuss how to compute these quantities for general MP algorithms and we evaluate the expressions for the specific cases of the Gallager algorithm A as well as the Decoder with Erasures and compare the resulting predictions on the error probability with simulation results