Dirac operators and spectral triples for some fractal sets built on curves

We construct spectral triples and, in particular, Dirac operators, for the algebra of continuous functions on certain compact metric spaces. The triples are countable sums of triples where each summand is based on a curve in the space. Several fractals, like a finitely summable infinite tree and the Sierpinski gasket, fit naturally within our framework. In these cases, we show that our spectral triples do describe the geodesic distance and the Minkowski dimension as well as, more generally, the complex fractal dimensions of the space. Furthermore, in the case of the Sierpinski gasket, the associated Dixmier-type trace coincides with the normalized Hausdorff measure of dimension $\log 3/ \log 2$.Comment: 48 pages, 4 figures. Elementary proofs omitted. To appear in Adv. Mat

Self-repelling diffusions via an infinite dimensional approach

In the present work we study self-interacting diffusions following an infinite dimensional approach. First we prove existence and uniqueness of a solution with Markov property. Then we study the corresponding transition semigroup and, more precisely, we prove that it has Feller property and we give an explicit form of an invariant probability of the system.Comment: Version 2: Typos are corrected. Section 6 is reorganised in order to make it more transparent; the results are unchanged. The presentation of the proof of Proposition 3 is improved. Statement of Lemma 5 is rephrased. Version 3: Acknowledgement of financial support is added. Accepted for publication in "Stochastic Partial Differential Equations: Analysis and Computations

Sequential Detection with Mutual Information Stopping Cost

This paper formulates and solves a sequential detection problem that involves the mutual information (stochastic observability) of a Gaussian process observed in noise with missing measurements. The main result is that the optimal decision is characterized by a monotone policy on the partially ordered set of positive definite covariance matrices. This monotone structure implies that numerically efficient algorithms can be designed to estimate and implement monotone parametrized decision policies.The sequential detection problem is motivated by applications in radar scheduling where the aim is to maintain the mutual information of all targets within a specified bound. We illustrate the problem formulation and performance of monotone parametrized policies via numerical examples in fly-by and persistent-surveillance applications involving a GMTI (Ground Moving Target Indicator) radar

Measuring Intergenerational Mobility and Equality of Opportunity

This paper explores the link between the measurement of intergenerational mobility and the notion of equality of opportunity. We show how recently proposed theories of equality of opportunity can be meaningfully adapted to the intergenerational context. This throws a new light on the interpretation of existing mobility measures: these may be interesting to measure mobility as movement, but they are inadequate to capture the notion of equality of opportunity. We propose some new mobility measures, which start from the idea that the intergenerational transition matrix gives useful information about the opportunity sets of the children of different social classes. These measures are used in an empirical illustration to evaluate the degree of inequality of opportunity in the US, Great Britain and Italy.

Measuring intergenerational mobility and equality of opportunity.

This paper explores the link between the measurement of intergenerational mobility and the notion of equality of opportunity. We show how recently proposed theories of equality of opportunity can be meaningfully adapted to the intergenerational context. This throws a new light on the interpretation of existing mobility measures: these may be interesting to measure mobility as movement, but they are inadequate to capture the notion of equality of opportunity. We propose some new mobility measures, which start from the idea that the intergenerational transition matrix gives useful information about the opportunity sets of the children of different social classes. These measures are used in an empirical illustration to evaluate the degree of inequality of opportunity in the US, Great Britain and Italy.

Measuring Intergenerational Mobility and Equality of Opportunity

This paper explores the link between the measurement of intergenerational mobility and the notion of equality of opportunity. We show how recently proposed theories of equality of opportunity can be meaningfully adapted to the intergenerational context. This throws a new light on the interpretation of existing mobility measures: these may be interesting to measure mobility as movement, but they are inadequate to capture the notion of equality of opportunity. We propose some new mobility measures, which start from the idea that the intergenerational transition matrix gives useful information about the opportunity sets of the children of different social classes. These measures are used in an empirical illustration to evaluate the degree of inequality of opportunity in the US, Great Britain and Italy.

iLIF: illumination by Laser-Induced Fluorescence for single flash imaging on a nanoseconds timescale \ud

The challenge in visualizing fast microscale fluid motion phenomena is to record high-quality images free of motion-blur. Here, we present an illumination technique based on laser-induced fluorescence which delivers high-intensity light pulses of 7 ns. The light source consists of a Q-switched Nd:YAG laser and a laser dye solution incorporated into a total internal reflection lens, resulting in a uni-directional light beam with a millimeter-sized circular aperture and 3° divergence. The laser coherence, considered undesirable for imaging purposes, is reduced while maintaining a nanoseconds pulse duration. The properties of the illumination by laser-induced fluorescence (iLIF) are quantified, and a comparison is made with other high-intensity pulsed and continuous light source

A Novel Business Model for Aggregating the Values of Electricity Storage

Electricity storage is considered a valuable source of flexibility whose applications cover the whole electricity value chain. However, most of the existing evaluation methods for electricity storage are conceived for only one specific use of the storage, which often leads to the conclusion that the investment on storage does not pay off. We think that the value of storage cannot be properly estimated without taking into account the possibility of aggregating the services that storage can offer to different actors. In this paper, we propose a new business model that allows aggregating multiple revenue streams of electricity storage in a systematic way. The main idea of the business model is to coordinate a series of auctions in which the right to utilize the storage unit is auctioned in different time horizons. The model consists of an optimization module and a coordination mechanism. The former simulates the optimal strategy of a certain actor using the available storage capacities in a certain auction, while the latter ensures non-conflicting uses of storage by actors in different auctions. The functioning of the model is demonstrated by a case study. The results show that a storage unit can achieve a higher return on investment in the manner proposed in the business model.electricity storage; business model; optimization

Collisional Formation and Modeling of Asteroid Families

In the last decade, thanks to the development of sophisticated numerical codes, major breakthroughs have been achieved in our understanding of the formation of asteroid families by catastrophic disruption of large parent bodies. In this review, we describe numerical simulations of asteroid collisions that reproduced the main properties of families, accounting for both the fragmentation of an asteroid at the time of impact and the subsequent gravitational interactions of the generated fragments. The simulations demonstrate that the catastrophic disruption of bodies larger than a few hundred meters in diameter leads to the formation of large aggregates due to gravitational reaccumulation of smaller fragments, which helps explain the presence of large members within asteroid families. Thus, for the first time, numerical simulations successfully reproduced the sizes and ejection velocities of members of representative families. Moreover, the simulations provide constraints on the family dynamical histories and on the possible internal structure of family members and their parent bodies.Comment: Chapter to appear in the (University of Arizona Press) Space Science Series Book: Asteroids I