Exact simulation of the Wright-Fisher diffusion

The Wright-Fisher family of diffusion processes is a widely used class of evolutionary models. However, simulation is difficult because there is no known closed-form formula for its transition function. In this article we demonstrate that it is in fact possible to simulate exactly from a broad class of Wright-Fisher diffusion processes and their bridges. For those diffusions corresponding to reversible, neutral evolution, our key idea is to exploit an eigenfunction expansion of the transition function; this approach even applies to its infinite-dimensional analogue, the Fleming-Viot process. We then develop an exact rejection algorithm for processes with more general drift functions, including those modelling natural selection, using ideas from retrospective simulation. Our approach also yields methods for exact simulation of the moment dual of the Wright-Fisher diffusion, the ancestral process of an infinite-leaf Kingman coalescent tree. We believe our new perspective on diffusion simulation holds promise for other models admitting a transition eigenfunction expansion.Comment: 36 pages, 2 figure, 2 tables. This version corrects an error in the proof of Lemma 6.

Consistency of Bayesian nonparametric inference for discretely observed jump diffusions

We introduce verifiable criteria for weak posterior consistency of identifiable Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient and uniformly Lipschitz drift and jump coefficients in arbitrary dimension. The criteria are expressed in terms of coefficients of the SDEs describing the process, and do not depend on intractable quantities such as transition densities. We also show that products of discrete net and Dirichlet mixture model priors satisfy our conditions, again under an identifiability assumption. This generalises known results by incorporating jumps into previous work on unit diffusions with uniformly Lipschitz drift coefficients.Comment: 20 page

Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model

A new super-Backlund transformation for the N=1 supersymmetric sinh-Gordon equation is constructed. Based on this construction we propose a type-II integrable defect for the supersymmetric sinh-Gordon model consistent with this new transformation through the Lagrangian formalism. Explicit expressions for the modified conserved energy, momentum and supercharges are also computed. In addition, we show for the model that the type-II defect can also been regarded as a pair of fused defects of a previously introduced type. The explicit derivation of the associated defect matrices is also presented as a necessary condition for the integrability of the model.Comment: Latex 31 pages. Version accepted for publicatio

N=1 super sinh-Gordon model with defects revisited

The Lax pair formalism is considered to discuss the integrability of the N=1 supersymmetric sinh-Gordon model with a defect. We derive associated defect matrix for the model and construct the generating functions of the modified conserved quantities. The corresponding defect contributions for the modified energy and momentum of the model are explicitly computed.Comment: Latex 26 page

Legodroid: A Type-Driven Library for Android and LEGO Mindstorms Interoperability

LEGO Mindstorms robots are widely used as educational tools to acquire skills in programming complex systems involving the interaction of sensors and actuators, and they offer a flexible and modular workbench to design and evaluate user-machine interaction prototypes in the robotic area. However, there is still a lack of support to interoperability features and the need of high-level tools to program the interaction of a robot with other devices. In this paper, we introduce Legodroid, a new Java library enabling cross-programming LEGO Mindstorms robots through Android smartphones that exploits their combined computational and sensorial capabilities in a seamless way. The library provides a number of type-driven coding patterns for interacting with sensors and motors. In this way, the robustness of the software managing robot's sensors dramatically improves

Defects in the supersymmetric mKdV hierarchy via Backlund transformations

The integrability of the ${\cal N}=1$ supersymmetric modified Korteweg de-Vries (smKdV) hierarchy in the presence of defects is investigated through the construction of its super B\"acklund transformation. The construction of such transformation is performed by using essentially two methods: the B\"acklund-defect matrix approach and the superfield approach. Firstly, we employ the defect matrix associated to the hierarchy which turns out to be the same for the supersymmetric sinh-Gordon (sshG) model. The method is general for all flows and as an example we derive explicitly the B\"acklund equations in components for the first few flows of the hierarchy, namely $t_3$ and $t_5$. Secondly, the supersymmetric extension of the B\"acklund transformation in the superspace formalism is constructed for those flows. Finally, this super B\"acklund transformation is employed to introduce type I defects for the supersymmetric mKdV hierarchy. Further integrability aspects by considering modified conserved quantities are derived from the defect matrix.Comment: 40 pages. Some comments and references added. Version accepted for publication in JHE

L'ingegnerizzazione dei processi per il miglioramento delle performance delle aziende pubbliche

Nonostante gli approcci teorici più recenti, dal New Public Management al Public Value, sottolineino l’importanza della centralità dei bisogni del destinatario dei beni e dei servizi nella definizione dell’azione pubblica, il tema dell’ingegnerizzazione e della re-ingegnerizzazione dei processi organizzativi continua a rappresentare un aspetto poco affrontato nella Pubblica Amministrazione italiana. Nato come progetto fortemente interdisciplinare grazie al contributo di economisti aziendalisti, sociologi dell’organizzazione, psicologi del lavoro e ingegneri, questo lavoro si concentra sull’uso di alcuni strumenti capaci di migliorare la performance organizzativa, ma solitamente utilizzati in ambito privato, quali il Quality Funcion Deployment (QFD) e il Failure Modes and Effects Analysis (FMEA). Gli spazi organizzativi indagati, l’area di supporto alla ricerca scientifica dell’Ateneo di Cagliari e il servizio di asili nido del Comune di Cagliari, hanno consentito di approfondire la conoscenza dei processi produttivi in modo diffuso, agevolando la riscrittura di parte dell’architettura dei processi partendo dai bisogni dei destinatari degli output realizzati

A Wearable System for Jump Detection in Inline Figure Skating

This article presents the design and experimental evaluation of a non-invasive wearable sensor system that can be used to acquire crucial information about athletes’ performance during inline figure skating training. By combining distance and time-of-flight sensors and gyroscopes, the system is able to detect when jumps are performed and provides a live view of the data (e.g., the number and height of jumps) through a graphical user interface. The main novelty of our approach lies in the way in which the optical sensors are orientated. Typically, the sensors are orientated horizontally and positioned in pairs on the ground, where they measure the time interval between the moment the athlete leaves the ground and the moment they land. In our system, an optical sensor is placed under each foot and is vertically orientated so as to constantly measure the distance from the ground. In addition, a gyroscope sensor is placed on the athlete’s back, which provides information on the direction and angular momentum of the movement. By combining this data, the system provides the accurate detection of various jumps and technical elements without any constraints on the training ground. In this paper, the system is also compared to similar platforms in the literature, although there are no other specific systems that are available for inline figure skating. The results of the experimental evaluation, which was performed by high profile athletes, confirm its effectiveness in correctly detecting jumps, especially considering its compromise between precision and the overall cost of the equipment