The canonical subgroup: a "subgroup-free" approach

Beyond the crucial role they play in the foundations of the theory of overconvergent modular forms, canonical subgroups have found new applications to analytic continuation of overconvergent modular forms. For such applications, it is essential to understand various ``numerical'' aspects of the canonical subgroup, and in particular, the precise extent of its overconvergence. We develop a theory of canonical subgroups for a general class of curves (including the unitary and quaternionic Shimura curves), using formal and rigid geometry. In our approach, we use the common geometric features of these curves rather than their (possible) specific moduli-theoretic description.Comment: 16 pages, 1 figur

Culture-based artefacts to inform ICT design: foundations and practice

Cultural aspects frame our perception of the world and direct the many different ways people interact with things in it. For this reason, these aspects should be considered when designing technology with the purpose to positively impact people in a community. In this paper, we revisit the foundations of culture aiming to bring this concept in dialogue with design. To inform design with cultural aspects, we model reality in three levels of formality: informal, formal, and technical, and subscribe to a systemic vision that considers the technical solution as part of a more complex social system in which people live and interact. In this paper, we instantiate this theoretical and methodological view by presenting two case studies of technology design in which culture-based artefacts were employed to inform the design process. We claim that as important as including issues related to culture in the ICT design agenda—from the conception to the development, evaluation, and adoption of a technology—is the need to support the design process with adequate artefacts that help identifying cultural aspects within communities and translating them into sociotechnical requirements. We argue that a culturally informed perspective on design can go beyond an informative analysis, and can be integrated with the theoretical and methodological framework used to support design, throughout the entire design process

Domain Generalization by Marginal Transfer Learning

In the problem of domain generalization (DG), there are labeled training data sets from several related prediction problems, and the goal is to make accurate predictions on future unlabeled data sets that are not known to the learner. This problem arises in several applications where data distributions fluctuate because of environmental, technical, or other sources of variation. We introduce a formal framework for DG, and argue that it can be viewed as a kind of supervised learning problem by augmenting the original feature space with the marginal distribution of feature vectors. While our framework has several connections to conventional analysis of supervised learning algorithms, several unique aspects of DG require new methods of analysis. This work lays the learning theoretic foundations of domain generalization, building on our earlier conference paper where the problem of DG was introduced Blanchard et al., 2011. We present two formal models of data generation, corresponding notions of risk, and distribution-free generalization error analysis. By focusing our attention on kernel methods, we also provide more quantitative results and a universally consistent algorithm. An efficient implementation is provided for this algorithm, which is experimentally compared to a pooling strategy on one synthetic and three real-world data sets

Generalized Chiral Perturbation Theory

The Generalized Chiral Perturbation Theory enlarges the framework of the standard $\chi$PT, relaxing certain assumptions which do not necessarily follow from QCD or from experiment, and which are crucial for the usual formulation of the low energy expansion. In this way, experimental tests of the foundations of the standard $\chi$PT become possible. Emphasis is put on physical aspects rather than on formal developements of G$\chi$PT.Comment: 19 pages, Late

Model interoperability via model driven development

It is widely recognised that software development is a complex process. Among the factors that contribute to its inherent complexity is the gap between the design and the formal analysis domains. Software design is often considered a human oriented task while the analysis phase draws on formal representation and mathematical foundations. An example of this dichotomy is the use of UML for the software design phase and Petri Nets for the analysis; a separation of concerns that leads to the creation of heterogeneous models. Although UML is widely accepted as a language that can be used to model the structural and behavioural aspects of a system, its lack of mathematical foundations is seen as a serious impediment to rigorous analysis. Petri Nets on the other hand have a strong mathematical basis that is well suited for formal analysis; they lack however the appeal and the easeof-use of UML. A pressing concern for software developers is how to bridge the gap between these domains and allow for model interoperability and the integration of different toolsets across them, and thus reduce the complexity of the software development process. The aim of this paper is to present a Model Driven Development (MDD) model transformation which supports a seamless transition between UML and Petri Nets. This is achieved by model interoperability between UML Sequenc

On the foundations of thermodynamics

On the basis of new, concise foundations, this paper establishes the four laws of thermodynamics, the Maxwell relations, and the stability requirements for response functions, in a form applicable to global (homogeneous), local (hydrodynamic) and microlocal (kinetic) equilibrium. The present, self-contained treatment needs very little formal machinery and stays very close to the formulas as they are applied by the practicing physicist, chemist, or engineer. From a few basic assumptions, the full structure of phenomenological thermodynamics and of classical and quantum statistical mechanics is recovered. Care has been taken to keep the foundations free of subjective aspects (which traditionally creep in through information or probability). One might describe the paper as a uniform treatment of the nondynamical part of classical and quantum statistical mechanics ``without statistics'' (i.e., suitable for the definite descriptions of single objects) and ``without mechanics'' (i.e., independent of microscopic assumptions). When enriched by the traditional examples and applications, this paper may serve as the basis for a course on thermal physics.Comment: 78 page

On a Formal and User-friendly Linguistic Approach to Access Control of Electronic Health Data

The importance of the exchange of Electronic Health Records (EHRs) between hospitals has been recognized by governments and institutions. Due to the sensitivity of data exchanged, only mature standards and implementations can be chosen to operate. This exchange process is of course under the control of the patient, who decides who has the rights to access her personal healthcare data and who has not, by giving her personal privacy consent. Patients’ privacy consent is regulated by local legislations, which can vary frequently from region to region. The technology implementing such privacy aspects must be highly adaptable, often resulting in complex security scenarios that cannot be easily managed by patients and software designers. To overcome such security problems, we advocate the use of a linguistic approach that relies on languages for expressing policies with solid mathematical foundations. Our approach bases on FACPL, a policy language we have intentionally designed by taking inspiration from OASIS XACML, the de-facto standard used in all projects covering secure EHRs transmission protected by patients’ privacy consent. FACPL can express policies similar to those expressible by XACML but, differently from XACML, it has an intuitive syntax, a formal semantics and easy to use software tools supporting policy development and enforcement. In this paper, we present the potentialities of our approach and outline ongoing work