11,938 research outputs found
On the relation between plausibility logic and the maximum-entropy principle: a numerical study
What is the relationship between plausibility logic and the principle of
maximum entropy? When does the principle give unreasonable or wrong results?
When is it appropriate to use the rule `expectation = average'? Can
plausibility logic give the same answers as the principle, and better answers
if those of the principle are unreasonable? To try to answer these questions,
this study offers a numerical collection of plausibility distributions given by
the maximum-entropy principle and by plausibility logic for a set of fifteen
simple problems: throwing dice.Comment: 24 pages of main text and references, 8 pages of tables, 7 pages of
additional reference
The Laplace-Jaynes approach to induction
An approach to induction is presented, based on the idea of analysing the
context of a given problem into `circumstances'. This approach, fully Bayesian
in form and meaning, provides a complement or in some cases an alternative to
that based on de Finetti's representation theorem and on the notion of infinite
exchangeability. In particular, it gives an alternative interpretation of those
formulae that apparently involve `unknown probabilities' or `propensities'.
Various advantages and applications of the presented approach are discussed,
especially in comparison to that based on exchangeability. Generalisations are
also discussed.Comment: 38 pages, 1 figure. V2: altered discussion on some points, corrected
typos, added reference
Numerical Bayesian state assignment for a three-level quantum system. I. Absolute-frequency data; constant and Gaussian-like priors
This paper offers examples of concrete numerical applications of Bayesian
quantum-state-assignment methods to a three-level quantum system. The
statistical operator assigned on the evidence of various measurement data and
kinds of prior knowledge is computed partly analytically, partly through
numerical integration (in eight dimensions) on a computer. The measurement data
consist in absolute frequencies of the outcomes of N identical von Neumann
projective measurements performed on N identically prepared three-level
systems. Various small values of N as well as the large-N limit are considered.
Two kinds of prior knowledge are used: one represented by a plausibility
distribution constant in respect of the convex structure of the set of
statistical operators; the other represented by a Gaussian-like distribution
centred on a pure statistical operator, and thus reflecting a situation in
which one has useful prior knowledge about the likely preparation of the
system.
In a companion paper the case of measurement data consisting in average
values, and an additional prior studied by Slater, are considered.Comment: 23 pages, 14 figures. V2: Added an important note concerning
cylindrical algebraic decomposition and thanks to P B Slater, corrected some
typos, added reference
Numerical Bayesian quantum-state assignment for a three-level quantum system. II. Average-value data with a constant, a Gaussian-like, and a Slater prior
This paper offers examples of concrete numerical applications of Bayesian
quantum-state assignment methods to a three-level quantum system. The
statistical operator assigned on the evidence of various measurement data and
kinds of prior knowledge is computed partly analytically, partly through
numerical integration (in eight dimensions) on a computer. The measurement data
consist in the average of outcome values of N identical von Neumann projective
measurements performed on N identically prepared three-level systems. In
particular the large-N limit will be considered. Three kinds of prior knowledge
are used: one represented by a plausibility distribution constant in respect of
the convex structure of the set of statistical operators; another one
represented by a prior studied by Slater, which has been proposed as the
natural measure on the set of statistical operators; the last prior is
represented by a Gaussian-like distribution centred on a pure statistical
operator, and thus reflecting a situation in which one has useful prior
knowledge about the likely preparation of the system. The assigned statistical
operators obtained with the first two kinds of priors are compared with the one
obtained by Jaynes' maximum entropy method for the same measurement situation.
In the companion paper the case of measurement data consisting in absolute
frequencies is considered.Comment: 10 pages, 4 figures. V2: added "Post scriptum" under Conclusions,
slightly changed Acknowledgements, and corrected some spelling error
The forward kinematics of doubly-planar Gough-Stewart platforms and the position analysis of strips of tetrahedra
The final publication is available at link.springer.comA strip of tetrahedra is a tetrahedron-tetrahedron truss where any tetrahedron has two neighbors except those in the extremes which have only one. The problem of finding all the possible lengths for an edge in the strip compatible with a given distance imposed between the strip end-points has been revealed of relevance due to the large number of possible applications. In this paper, this is applied to solve the forward kinematics of 6-6 Gough-Stewart platforms with planar base and moving platform, a problem which is known to have up to 40 solutions (20 if we do not consider mirror configurations with respect to the base as different solutions).Peer ReviewedPostprint (author's final draft
Fasce di rispetto e alberate stradali: Normativa
E??? possibile conciliare la sicurezza dei conducenti e la presenza delle piante? Il presente Capitolo entra nel merito di una problematica che non è annoverata come vexata quaestio. Difficile reperire documentazione sul tema, pochissime le pubblicazioni tecniche o giuridiche. Il tema è divenuto di attualità a seguito di una Sentenza della Corte di Cassazione che si è espressa in merito ad un incidente stradale mortale causato dalla fuoriuscita del veicolo e successivo impatto contro un albero ???che si trovava a meno di sei metri dal confine stradale, e quindi in posizione non consentita???. Il punto è quindi il seguente: è consentita la presenza di alberi all???interno delle fasce di pertinenza e delle fasce di rispetto
Dimensional analysis in relativity and in differential geometry
This note provides a short guide to dimensional analysis in Lorentzian and
general relativity and in differential geometry. It tries to revive Dorgelo and
Schouten's notion of 'intrinsic' or 'absolute' dimension of a tensorial
quantity. The intrinsic dimension is independent of the dimensions of the
coordinates and expresses the physical and operational meaning of a tensor. The
dimensional analysis of several important tensors and tensor operations is
summarized. In particular it is shown that the components of a tensor need not
have all the same dimension, and that the Riemann (once contravariant and
thrice covariant), Ricci (twice covariant), and Einstein (twice covariant)
curvature tensors are dimensionless. The relation between dimension and
operational meaning for the metric and stress-energy-momentum tensors is
discussed; and the possible conventions for the dimensions of these two tensors
and of Einstein's constant , including the curious possibility without factors, are reviewed.Comment: 37 pages. V2: corrected typos and added references. V3: corrected and
extended discussions of the metric and stress-energy-momentum tensors, and of
Einstein's constant; added reference
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