1,542 research outputs found
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Confidence: Its role in dependability cases for risk assessment
Society is increasingly requiring quantitative assessment of risk and associated dependability cases. Informally, a dependability case comprises some reasoning, based on assumptions and evidence, that supports a dependability claim at a particular level of confidence. In this paper we argue that a quantitative assessment of claim confidence is necessary for proper assessment of risk. We discuss the way in which confidence depends upon uncertainty about the underpinnings of the dependability case (truth of assumptions, correctness of reasoning, strength of evidence), and propose that probability is the appropriate measure of uncertainty. We discuss some of the obstacles to quantitative assessment of confidence (issues of composability of subsystem claims; of the multi-dimensional, multi-attribute nature of dependability claims; of the difficult role played by dependence between different kinds of evidence, assumptions, etc). We show that, even in simple cases, the confidence in a claim arising from a dependability case can be surprisingly low
Hopf algebras and characters of classical groups
Schur functions provide an integral basis of the ring of symmetric functions.
It is shown that this ring has a natural Hopf algebra structure by identifying
the appropriate product, coproduct, unit, counit and antipode, and their
properties. Characters of covariant tensor irreducible representations of the
classical groups GL(n), O(n) and Sp(n) are then expressed in terms of Schur
functions, and the Hopf algebra is exploited in the determination of
group-subgroup branching rules and the decomposition of tensor products. The
analysis is carried out in terms of n-independent universal characters. The
corresponding rings, CharGL, CharO and CharSp, of universal characters each
have their own natural Hopf algebra structure. The appropriate product,
coproduct, unit, counit and antipode are identified in each case.Comment: 9 pages. Uses jpconf.cls and jpconf11.clo. Presented by RCK at
SSPCM'07, Myczkowce, Poland, Sept 200
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Toward a Formalism for Conservative Claims about the Dependability of Software-Based Systems
In recent work, we have argued for a formal treatment of confidence about the claims made in dependability cases for software-based systems. The key idea underlying this work is "the inevitability of uncertainty": It is rarely possible to assert that a claim about safety or reliability is true with certainty. Much of this uncertainty is epistemic in nature, so it seems inevitable that expert judgment will continue to play an important role in dependability cases. Here, we consider a simple case where an expert makes a claim about the probability of failure on demand (pfd) of a subsystem of a wider system and is able to express his confidence about that claim probabilistically. An important, but difficult, problem then is how such subsystem (claim, confidence) pairs can be propagated through a dependability case for a wider system, of which the subsystems are components. An informal way forward is to justify, at high confidence, a strong claim, and then, conservatively, only claim something much weaker: "I'm 99 percent confident that the pfd is less than 10-5, so it's reasonable to be 100 percent confident that it is less than 10-3." These conservative pfds of subsystems can then be propagated simply through the dependability case of the wider system. In this paper, we provide formal support for such reasoning
Hermitian Young Operators
Starting from conventional Young operators we construct Hermitian operators
which project orthogonally onto irreducible representations of the (special)
unitary group.Comment: 15 page
Parafermions, parabosons and representations of so(\infty) and osp(1|\infty)
The goal of this paper is to give an explicit construction of the Fock spaces
of the parafermion and the paraboson algebra, for an infinite set of
generators. This is equivalent to constructing certain unitary irreducible
lowest weight representations of the (infinite rank) Lie algebra so(\infty) and
of the Lie superalgebra osp(1|\infty). A complete solution to the problem is
presented, in which the Fock spaces have basis vectors labelled by certain
infinite but stable Gelfand-Zetlin patterns, and the transformation of the
basis is given explicitly. We also present expressions for the character of the
Fock space representations
SU(3) Quantum Interferometry with single-photon input pulses
We develop a framework for solving the action of a three-channel passive
optical interferometer on single-photon pulse inputs to each channel using
SU(3) group-theoretic methods, which can be readily generalized to higher-order
photon-coincidence experiments. We show that features of the coincidence plots
vs relative time delays of photons yield information about permanents,
immanants, and determinants of the interferometer SU(3) matrix
Mixed Symmetry Solutions of Generalized Three-Particle Bargmann-Wigner Equations in the Strong-Coupling Limit
Starting from a nonlinear isospinor-spinor field equation, generalized
three-particle Bargmann-Wigner equations are derived. In the strong-coupling
limit, a special class of spin 1/2 bound-states are calculated. These solutions
which are antisymmetric with respect to all indices, have mixed symmetries in
isospin-superspin space and in spin orbit space. As a consequence of this mixed
symmetry, we get three solution manifolds. In appendix \ref{b}, table 2, these
solution manifolds are interpreted as the three generations of leptons and
quarks. This interpretation will be justified in a forthcoming paper.Comment: 17 page
Dipolar superfluidity in electron-hole bilayer systems
Bilayer electron-hole systems, where the electrons and holes are created via
doping and confined to separate layers, undergo excitonic condensation when the
distance between the layers is smaller than typical distance between particles
within a layer. We argue that the excitonic condensate is a novel dipolar
superfluid in which the phase of the condensate couples to the {\it gradient}
of the vector potential. We predict the existence of dipolar supercurrent which
can be tuned by an in-plane magnetic field and detected by independent contacts
to the layers. Thus the dipolar superfluid offers an example of excitonic
condensate in which the {\it composite} nature of its constituent excitons is
manifest in the macroscopic superfluid state. We also discuss various
properties of this superfluid including the role of vortices.Comment: 5 pages, 1 figure, minor changes and added few references; final
published versio
Energy evolution in time-dependent harmonic oscillator
The theory of adiabatic invariants has a long history, and very important
implications and applications in many different branches of physics,
classically and quantally, but is rarely founded on rigorous results. Here we
treat the general time-dependent one-dimensional harmonic oscillator, whose
Newton equation cannot be solved in general. We
follow the time-evolution of an initial ensemble of phase points with sharply
defined energy at time and calculate rigorously the distribution of
energy after time , which is fully (all moments, including the
variance ) determined by the first moment . For example,
, and all
higher even moments are powers of , whilst the odd ones vanish
identically. This distribution function does not depend on any further details
of the function and is in this sense universal. In ideal
adiabaticity , and the variance is
zero, whilst for finite we calculate , and for the
general case using exact WKB-theory to all orders. We prove that if is of class (all derivatives up to and including the order
are continuous) , whilst for class it is known to be exponential .Comment: 26 pages, 5 figure
Integrity bases for local invariants of composite quantum systems
Unitary group branchings appropriate to the calculation of local invariants
of density matrices of composite quantum systems are formulated using the
method of -function plethysms. From this, the generating function for the
number of invariants at each degree in the density matrix can be computed. For
the case of two two-level systems the generating function is . Factorisation of such series leads
in principle to the identification of an integrity basis of algebraically
independent invariants. This note replaces Appendix B of our paper\cite{us} J
Phys {\bf A33} (2000) 1895-1914 (\texttt{quant-ph/0001076}) which is incorrect.Comment: Latex, 4 pages, correcting Appendix B of quant-ph/0001076 Error in
corrected and conclusions modified accordingl
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