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Building Bricks with Bricks, with Mathematica [article]

Pietro Codara, Ottavio M. D'Antona, Daniele Filaretti
2013 arXiv   pre-print
In this work we solve a special case of the problem of building an n-dimensional parallelepiped using a given set of n-dimensional parallelepipeds. Consider the identity x^3 = x(x-1)(x-2)+3x(x-1+x). For sufficiently large x, we associate with x^3 a cube with edges of size x, with x(x-1)(x-2) a parallelepiped with edges x, x-1, x-2, with 3x(x-1+x) three parallelepipeds of edges x, x-1, 1, and with x a parallelepiped of edges x, 1, 1. The problem we takle is the actual construction of the cube
more » ... ng the given parallelepipeds. In [DDNP90] it was shown how to solve this specific problem and all similar instances in which a (monic) polynomial is expressed as a linear combination of a persistent basis. That is to say a sequence of polynomials q_0 = 1, and q_k(x) = q_k-1(x)(x-r_k) for k > 0. Here, after [Fil10], we deal with a multivariate version of the problem with respect to a basis of polynomials of the same degree (binomial basis). We show that it is possible to build the parallelepiped associated with a multivariate polynomial P(x_1, ..., x_n)=(x_1- s_1)...(x_n-s_n) with integer roots, using the parallelepipeds described by the elements of the basis. We provide an algorithm in Mathematica to solve the problem for each n. Moreover, for n = 2, 3, 4 (in the latter case, only when a projection is possible) we use Mathematica to display a step by step construction of the parallelepiped P(x1,...,x_n).
arXiv:1307.1343v1 fatcat:xw7hp7v22zgovm23k7xf4p6gwi

An Executable Formal Semantics of PHP [chapter]

Daniele Filaretti, Sergio Maffeis
2014 Lecture Notes in Computer Science  
Filaretti and Maffeis are supported by EPSRC grant EP/I004246/1.  ... 
doi:10.1007/978-3-662-44202-9_23 fatcat:ufvkf5725bfefoijfrete6oy5q

A trusted mechanised JavaSript specification

Martin Bodin, Arthur Chargueraud, Daniele Filaretti, Philippa Gardner, Sergio Maffeis, Daiva Naudziuniene, Alan Schmitt, Gareth Smith
2014 Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL '14  
Filaretti and Maffeis are supported by EPSRC grant EP/I004246/1. Gardner and Smith are partially supported by EP-SRC grant EP/K032089/1 and EPSRC programme grant EP/H008373.  ... 
doi:10.1145/2535838.2535876 dblp:conf/popl/BodinCFGMNSS14 fatcat:gjwvma6drzginetbxw2opqcuhi

A Digital App to Aid Detection, Monitoring, and Management of Dyslexia in Young Children (DIMMAND): Protocol for a Digital Health and Education Solution

Mariam R Sood, Annet Toornstra, Martin I Sereno, Mark Boland, Daniele Filaretti, Anuj Sood
2018 JMIR Research Protocols  
Dyslexia, a specific learning difficulty and a disability as defined in the Equality Act 2010, is a lifelong condition that affects a child from the start of education. Dyslexia is characterized by difficulties in language processing (reading, spelling, and writing) which do not correspond with the child's general intellectual abilities. Although dyslexia cannot be cured, there is a consensus that interventions are more effective and have greater impact the earlier they are administered.
more » ... ve interventions start with diagnosis. Currently, formal diagnosis requires an assessment by a dyslexia specialist or educational psychologist. These assessments are expensive and are not easy for a non-specialist teacher or parent to interpret. Consequently, formal assessments are normally performed at a much later age, when interventions are less likely to be effective. Combining the latest in scientific research, expertise of dyslexia practitioners and real-time interactivity facilitated by digital technologies, we aim to provide a cost-effective and convenient solution that focuses on early dyslexia detection and management. Objective: We discuss the rationale and protocol for the design and development of a digital health solution aimed at improving the early detection, monitoring and management of dyslexia (DIMMAND) in young children (4-8 years). The primary objective is to create a game-based digital solution aimed at children, parents, and teachers that firstly assesses, then monitors and manages progress in a convenient, cost-effective and private environment. Methods: The proposed solution will be designed and developed in phases. In the initial phase, the full functional specification of the games that constitute the app will be designed, together with the overall architecture of the solution. Prototype proof-of-concept implementation for few of these games, and commercialization strategies will also be developed. The follow-on phases will see the design implemented into a validated solution. Results: In the initial phase, we worked closely with dyslexia specialists, adult dyslexics, teachers of special-needs children, parents of dyslexic children, and senior dyslexia representatives for large organizations. These interactions provided insights into the range of language difficulties faced by dyslexics, which solutions are used by teachers and professionals, and an overall understanding of the market. We comprehensively defined the ethical, privacy, and data security issues. The detailed design spec of the games, the methodology to be followed to interpret the results, and flow diagrams illustrating how the game screens will be presented was completed. As proof of concept, a few reading, visual, and auditory games were developed and successfully tested by stakeholders on different digital devices. The stakeholders provided regular feedback and confirmed the viability of our game-based solution. Conclusions: DIMMAND has the potential to provide significant positive health care and economic impact. It is expected to reduce intervention costs, improve dyslexia detection at an early age and aid self-management.
doi:10.2196/resprot.9583 pmid:29773528 pmcid:PMC5981053 fatcat:cvrkpqmpozcy7ba7u2yobdulia

An executable formal semantics of PHP with applications to program analysis

Daniele Filaretti, Sergio Maffeis, Engineering And Physical Sciences Research Council
Nowadays, many important activities in our lives involve the web. However, the software and protocols on which web applications are based were not designed with the appropriate level of security in mind. Many web applications have reached a level of complexity for which testing, code reviews and human inspection are no longer sufficient quality-assurance guarantees. Tools that employ static analysis techniques are needed in order to explore all possible execution paths through an application
more » ... guarantee the absence of undesirable behaviours. To make sure that an analysis captures the properties of interest, and to navigate the trade-offs between efficiency and precision, it is necessary to base the design and the development of static analysis tools on a firm understanding of the language to be analysed. When this underlying knowledge is missing or erroneous, tools can't be trusted no matter what advanced techniques they use to perform their task. In this Thesis, we introduce KPHP, the first executable formal semantics of PHP, one of the most popular languages for server-side web programming. Then, we demonstrate its practical relevance by developing two verification tools, of increasing complexity, on top of it - a simple verifier based on symbolic execution and LTL model checking and a general purpose, fully configurable and extensible static analyser based on Abstract Interpretation. Our LTL-based tool leverages the existing symbolic execution and model checking support offered by K, our semantics framework of choice, and constitutes a first proof-of-concept of the usefulness of our semantics. Our abstract interpreter, on the other hand, represents a more significant and novel contribution to the field of static analysis of dynamic scripting languages (PHP in particular). Although our tool is still a prototype and therefore not well suited for handling large real-world codebases, we demonstrate how our semantics-based, principled approach to the development of verification tools has lead to the design of sta [...]
doi:10.25560/40922 fatcat:6j7bs5eydzcgjh276yxpqe3dia

Report from Dagstuhl Seminar Scripting Languages and Frameworks: Analysis and Verification 1 Executive Summary

Fritz Henglein, Ranjit Jhala, Shriram Krishnamurthi, Peter Thiemann, Fritz Ranjit, Jhala Shriram, Krishnamurthi Peter, Thiemann License
Seminar   unpublished
Filaretti (Imperial College London, GB)Creative Commons BY 3.0 Unported license © Daniele Filaretti Joint work of Filaretti, Daniele; Maffeis, Sergio Main reference D.  ...  Filaretti, P. Gardner, S. Maffeis, D. Naudziuniene, A. Schmitt, G.  ... 

A Trusted Mechanised Specification of JavaScript: One Year On [chapter]

Philippa Gardner, Gareth Smith, Conrad Watt, Thomas Wood
2015 Lecture Notes in Computer Science  
We would like to thank the other coauthors for continuing invaluable discussions about this project: Martin Bodin, Arthur Charguéraud and Alan Schmitt from Inria; and Daniel Filaretti, Sergio Maffeis and  ... 
doi:10.1007/978-3-319-21690-4_1 fatcat:h7auclaybzhkvmbj3mizdunshm