20,925 research outputs found
A reversible allelic partition process and Pitman sampling formula
We introduce a continuous-time Markov chain describing dynamic allelic
partitions which extends the branching process construction of the Pitman
sampling formula in Pitman (2006) and the birth-and-death process with
immigration studied in Karlin and McGregor (1967), in turn related to the
celebrated Ewens sampling formula. A biological basis for the scheme is
provided in terms of a population of individuals grouped into families, that
evolves according to a sequence of births, deaths and immigrations. We
investigate the asymptotic behaviour of the chain and show that, as opposed to
the birth-and-death process with immigration, this construction maintains in
the temporal limit the mutual dependence among the multiplicities. When the
death rate exceeds the birth rate, the system is shown to have reversible
distribution identified as a mixture of Pitman sampling formulae, with negative
binomial mixing distribution on the population size. The population therefore
converges to a stationary random configuration, characterised by a finite
number of families and individuals.Comment: 17 pages, to appear in ALEA , Latin American Journal of Probability
and Mathematical Statistic
A naturalistic justification of the generic multiverse with a core
In this paper, I argue that a naturalist approach in philosophy of mathematics justifies a pluralist conception of set theory. For the pluralist, there is not a Single Universe, but there is rather a Multiverse, composed by a plurality of universes generated by various set theories. In order to justify a pluralistic approach to sets, I apply the two naturalistic principles developed by Penelope Maddy (cfr. Maddy (1997)), UNIFY and MAXIMIZE, and analyze through them the potential of the set theoretic multiverse to be the best framework for mathematical practice. According to UNIFY, an adequate set theory should be foundational, in the sense that it should allow one to represent all the currently accepted mathematical theories. As for MAXIMIZE, this states that any adequate set theory should be as powerful as possible, allowing one to prove as many results and isomorphisms as possible. In a recent paper, Maddy (2017) has argued that this two principle justify ZFC as the best framework for mathematical practice. I argue that, pace Maddy, these two principles justify a multiverse conception of set theory, more precisely, the generic multiverse with a core (GMH)
On the interplay between fluctuations and efficiency in a model economy with heterogeneous adaptive consumers
We discuss the stationary states of a model economy in which
heterogeneous adaptive consumers purchase commodity bundles repeatedly from
sellers. The system undergoes a transition from an inefficient to an efficient
state as the number of consumers increases. In the latter phase, however, price
fluctuations may be much larger than in the inefficient regime. Results from
dynamical mean-field theory obtained for compare fairly well with
computer simulations.Comment: prepared for the proceedings of Fluctuations and Noise 200
Replica symmetry breaking in the minority game
We extend and complete recent work concerning the analytic solution of the
minority game. Nash equilibria (NE) of the game have been found to be related
to the ground states of a disordered hamiltonian with replica symmetry breaking
(RSB), signalling the presence of a large number of them. Here we study the
number of NE both analytically and numerically. We then analyze the stability
of the recently-obtained replica-symmetric (RS) solution and, in the region
where it becomes unstable, derive the solution within one-step RSB
approximation. We are finally able to draw a detailed phase diagram of the
model.Comment: Replaced with a revised versio
A fast and robust hand-driven 3D mouse
The development of new interaction paradigms requires a natural interaction. This means that people should be able to interact with technology with the same models used to interact with everyday real life, that is through gestures, expressions, voice. Following this idea, in this paper we propose a non intrusive vision based tracking system able to capture hand motion and simple hand gestures. The proposed device allows to use the hand as a "natural" 3D mouse, where the forefinger tip or the palm centre are used to identify a 3D marker and the hand gesture can be used to simulate the mouse buttons. The approach is based on a monoscopic tracking algorithm which is computationally fast and robust against noise and cluttered backgrounds. Two image streams are processed in parallel exploiting multi-core architectures, and their results are combined to obtain a constrained stereoscopic problem. The system has been implemented and thoroughly tested in an experimental environment where the 3D hand mouse has been used to interact with objects in a virtual reality application. We also provide results about the performances of the tracker, which demonstrate precision and robustness of the proposed syste
An incremental approach to the solution of global trajectory optimization problems
This paper presents an incremental approach to the solution of multiple gravity assist trajectories (MGA) with deep space maneuvers. The whole problem is decomposed in sub-problems that are solved incrementally. The solution of each sub-problem leads to a progressive reduction of the search space. Unlike other similar methods, the search for solutions of each sub-problem is performed through a stochastic approach. The resulting set of disconnected boxes is transformed into a connected collection of boxes through an affine transformation. For MGA problems, the incremental approach increases both the efficiency and reliability of the optimization process. Two relevant examples will illustrate the effectiveness of the proposed method
Quantum limits to estimation of photon deformation
We address potential deviations of radiation field from the bosonic behaviour
and employ local quantum estimation theory to evaluate the ultimate bounds to
precision in the estimation of these deviations using quantum-limited
measurements on optical signals. We consider different classes of boson
deformation and found that intensity measurement on coherent or thermal states
would be suitable for their detection making, at least in principle, tests of
boson deformation feasible with current quantum optical technology. On the
other hand, we found that the quantum signal-to-noise ratio (QSNR) is vanishing
with the deformation itself for all the considered classes of deformations and
probe signals, thus making any estimation procedure of photon deformation
inherently inefficient. A partial way out is provided by the polynomial
dependence of the QSNR on the average number of photon, which suggests that, in
principle, it would be possible to detect deformation by intensity measurements
on high-energy thermal states.Comment: 9 page
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