LEIBNIZ\u2019S MIRROR THESIS. SOLIPSISM, PRIVATE PERSPECTIVES AND CONCEPTUAL HOLISM

One of the symbolic images to which Leibniz constantly entrusted the synthesis of his philosophy regards the idea of considering one and the same city from various visual perspectives. Such an image is diffused throughout all Leibniz\u2019s writings and clearly reflects the philosopher\u2019s interest for matters regarding perspective as well as optical phenomena. The point of view of its inhabitants can therefore be compared to a mirror that reflects some different portions of reality. But what do the city-viewers really see? Do they all see exactly the same thing? And assuming the plurality of points of view, how one can be sure that they share the same representative content? The paper presented here tries to offer a plausible interpretation of this topic also by linking different and somehow remote Leibnizian doctrines together

Scaling laws in microbial growth

openMicrobial growth and division are fundamental processes shaping organisms’ life cycle. Mathematical models of such biological processes have been developed, but several questions remain open, especially when focusing on single-cell lineages. The development of new microfluidic devices, combining single-molecule microscopy and automated image analysis, allows to track individual cells and their quantities of interest for many generations. Furthermore, recent discoveries of scaling laws hint at the existence of universal growth laws, not yet formulated. In this thesis work we hypothesize that cells operate in the vicinity of a critical point and we therefore aim at describing temporal and size scaling of lineages both from a theoretical and an empirical point of view. Our first step is indeed an analytical one, carried out with the purpose of putting the problem in the proper theoretical framework. Simulations are coded in order to explore the behavior of the system at different distances from the critical point. They are based on various models having different numbers of traits which range from 1 to 2, but belonging to the same universality class. Finally, we want to probe the proposed theoretical results by making use of available cell data from two different experiments and comparing them to the predictions of our model. Analysis’ results are presented both for the numerical approach and for the comparison with experimental data. We show how simulations confirm the hypothesized scalings and clarify exponents upon which different theoretical results can be found in literature. Furthermore, the moment scaling we find in experimental data is consistent with the criticality hypothesis. To corroborate this result we infer the control parameters of a particular model from the universality class with the aid of Bayesian Inference (BI) and find that they are indeed close to the critical point. Data quality shows to be an hurdle in probing the scaling of the autocorrelation length ξ with respect to . No clear behaviour arises indeed from the analysis.Microbial growth and division are fundamental processes shaping organisms’ life cycle. Mathematical models of such biological processes have been developed, but several questions remain open, especially when focusing on single-cell lineages. The development of new microfluidic devices, combining single-molecule microscopy and automated image analysis, allows to track individual cells and their quantities of interest for many generations. Furthermore, recent discoveries of scaling laws hint at the existence of universal growth laws, not yet formulated. In this thesis work we hypothesize that cells operate in the vicinity of a critical point and we therefore aim at describing temporal and size scaling of lineages both from a theoretical and an empirical point of view. Our first step is indeed an analytical one, carried out with the purpose of putting the problem in the proper theoretical framework. Simulations are coded in order to explore the behavior of the system at different distances from the critical point. They are based on various models having different numbers of traits which range from 1 to 2, but belonging to the same universality class. Finally, we want to probe the proposed theoretical results by making use of available cell data from two different experiments and comparing them to the predictions of our model. Analysis’ results are presented both for the numerical approach and for the comparison with experimental data. We show how simulations confirm the hypothesized scalings and clarify exponents upon which different theoretical results can be found in literature. Furthermore, the moment scaling we find in experimental data is consistent with the criticality hypothesis. To corroborate this result we infer the control parameters of a particular model from the universality class with the aid of Bayesian Inference (BI) and find that they are indeed close to the critical point. Data quality shows to be an hurdle in probing the scaling of the autocorrelation length ξ with respect to . No clear behaviour arises indeed from the analysis

Graded Monads and Graded Logics for the Linear Time - Branching Time Spectrum

State-based models of concurrent systems are traditionally considered under a variety of notions of process equivalence. In the case of labelled transition systems, these equivalences range from trace equivalence to (strong) bisimilarity, and are organized in what is known as the linear time - branching time spectrum. A combination of universal coalgebra and graded monads provides a generic framework in which the semantics of concurrency can be parametrized both over the branching type of the underlying transition systems and over the granularity of process equivalence. We show in the present paper that this framework of graded semantics does subsume the most important equivalences from the linear time - branching time spectrum. An important feature of graded semantics is that it allows for the principled extraction of characteristic modal logics. We have established invariance of these graded logics under the given graded semantics in earlier work; in the present paper, we extend the logical framework with an explicit propositional layer and provide a generic expressiveness criterion that generalizes the classical Hennessy-Milner theorem to coarser notions of process equivalence. We extract graded logics for a range of graded semantics on labelled transition systems and probabilistic systems, and give exemplary proofs of their expressiveness based on our generic criterion

Strategic polymorphism requires just two combinators!

In previous work, we introduced the notion of functional strategies: first-class generic functions that can traverse terms of any type while mixing uniform and type-specific behaviour. Functional strategies transpose the notion of term rewriting strategies (with coverage of traversal) to the functional programming paradigm. Meanwhile, a number of Haskell-based models and combinator suites were proposed to support generic programming with functional strategies. In the present paper, we provide a compact and matured reconstruction of functional strategies. We capture strategic polymorphism by just two primitive combinators. This is done without commitment to a specific functional language. We analyse the design space for implementational models of functional strategies. For completeness, we also provide an operational reference model for implementing functional strategies (in Haskell). We demonstrate the generality of our approach by reconstructing representative fragments of the Strafunski library for functional strategies.Comment: A preliminary version of this paper was presented at IFL 2002, and included in the informal preproceedings of the worksho