4,877 research outputs found
An algebraic framework for urgency
A sub-class of timed automata known as timed automata with deadlines was presented. Parallel composition and other operators were defined according to 'orthogonality' principal, for timed process algebras and hybrid automata. The compositional description methods that are based on 'flexible' composition rules that relax urgency constraints to preserve time reactivity was also studied
From the arrow of time in Badiali's quantum approach to the dynamic meaning of Riemann's hypothesis
The novelty of the Jean Pierre Badiali last scientific works stems to a
quantum approach based on both (i) a return to the notion of trajectories
(Feynman paths) and (ii) an irreversibility of the quantum transitions. These
iconoclastic choices find again the Hilbertian and the von Neumann algebraic
point of view by dealing statistics over loops. This approach confers an
external thermodynamic origin to the notion of a quantum unit of time (Rovelli
Connes' thermal time). This notion, basis for quantization, appears herein as a
mere criterion of parting between the quantum regime and the thermodynamic
regime. The purpose of this note is to unfold the content of the last five
years of scientific exchanges aiming to link in a coherent scheme the Jean
Pierre's choices and works, and the works of the authors of this note based on
hyperbolic geodesics and the associated role of Riemann zeta functions. While
these options do not unveil any contradictions, nevertheless they give birth to
an intrinsic arrow of time different from the thermal time. The question of the
physical meaning of Riemann hypothesis as the basis of quantum mechanics, which
was at the heart of our last exchanges, is the backbone of this note.Comment: 13 pages, 2 figure
Mapping RT-LOTOS specifications into Time Petri Nets
RT-LOTOS is a timed process algebra which enables compact
and abstract specification of real-time systems. This paper proposes and illustrates a structural translation of RT-LOTOS terms into behaviorally equivalent (timed bisimilar) finite Time Petri nets. It is therefore possible to apply Time Petri nets verification techniques to the profit of RT-LOTOS. Our approach has been implemented in RTL2TPN, a prototype tool which takes as input an RT-LOTOS specification and outputs a TPN. The latter is verified using TINA, a TPN analyzer developed by LAAS-CNRS. The toolkit made of RTL2TPN and TINA has been positively benchmarked against previously developed RT-LOTOS verification tool
Anomalous Scale Dimensions from Timelike Braiding
Using the previously gained insight about the particle/field relation in
conformal quantum field theories which required interactions to be related to
the existence of particle-like states associated with fields of anomalous
scaling dimensions, we set out to construct a classification theory for the
spectra of anomalous dimensions. Starting from the old observations on
conformal superselection sectors related to the anomalous dimensions via the
phases which appear in the spectral decomposition of the center of the
conformal covering group we explore the possibility
of a timelike braiding structure consistent with the timelike ordering which
refines and explains the central decomposition. We regard this as a preparatory
step in a new construction attempt of interacting conformal quantum field
theories in D=4 spacetime dimensions. Other ideas of constructions based on the
- or the perturbative SYM approach in their relation to the
present idea are briefly mentioned.Comment: completely revised, updated and shortened replacement, 24 pages
tcilatex, 3 latexcad figure
Spacetime Encodings IV - The Relationship between Weyl Curvature and Killing Tensors in Stationary Axisymmetric Vacuum Spacetimes
The problem of obtaining an explicit representation for the fourth invariant
of geodesic motion (generalized Carter constant) of an arbitrary stationary
axisymmetric vacuum spacetime generated from an Ernst Potential is considered.
The coupling between the non-local curvature content of the spacetime as
encoded in the Weyl tensor, and the existence of a Killing tensor is explored
and a constructive, algebraic test for a fourth order Killing tensor suggested.
The approach used exploits the variables defined for the B\"{a}ckland
transformations to clarify the relationship between Weyl curvature, constants
of geodesic motion, expressed as Killing tensors, and the solution generation
techniques. A new symmetric non-covariant formulation of the Killing equations
is given. This formulation transforms the problem of looking for fourth-order
Killing tensors in 4D into one of looking for four interlocking two-manifolds
admitting fourth-order Killing tensors in 2D.Comment: 15 page
Spectral Geometry and Causality
For a physical interpretation of a theory of quantum gravity, it is necessary
to recover classical spacetime, at least approximately. However, quantum
gravity may eventually provide classical spacetimes by giving spectral data
similar to those appearing in noncommutative geometry, rather than by giving
directly a spacetime manifold. It is shown that a globally hyperbolic
Lorentzian manifold can be given by spectral data. A new phenomenon in the
context of spectral geometry is observed: causal relationships. The employment
of the causal relationships of spectral data is shown to lead to a highly
efficient description of Lorentzian manifolds, indicating the possible
usefulness of this approach. Connections to free quantum field theory are
discussed for both motivation and physical interpretation. It is conjectured
that the necessary spectral data can be generically obtained from an effective
field theory having the fundamental structures of generalized quantum
mechanics: a decoherence functional and a choice of histories.Comment: AMS-Latex, 14 pages, 3 figures, using epsf macr
Cauchy, infinitesimals and ghosts of departed quantifiers
Procedures relying on infinitesimals in Leibniz, Euler and Cauchy have been
interpreted in both a Weierstrassian and Robinson's frameworks. The latter
provides closer proxies for the procedures of the classical masters. Thus,
Leibniz's distinction between assignable and inassignable numbers finds a proxy
in the distinction between standard and nonstandard numbers in Robinson's
framework, while Leibniz's law of homogeneity with the implied notion of
equality up to negligible terms finds a mathematical formalisation in terms of
standard part. It is hard to provide parallel formalisations in a
Weierstrassian framework but scholars since Ishiguro have engaged in a quest
for ghosts of departed quantifiers to provide a Weierstrassian account for
Leibniz's infinitesimals. Euler similarly had notions of equality up to
negligible terms, of which he distinguished two types: geometric and
arithmetic. Euler routinely used product decompositions into a specific
infinite number of factors, and used the binomial formula with an infinite
exponent. Such procedures have immediate hyperfinite analogues in Robinson's
framework, while in a Weierstrassian framework they can only be reinterpreted
by means of paraphrases departing significantly from Euler's own presentation.
Cauchy gives lucid definitions of continuity in terms of infinitesimals that
find ready formalisations in Robinson's framework but scholars working in a
Weierstrassian framework bend over backwards either to claim that Cauchy was
vague or to engage in a quest for ghosts of departed quantifiers in his work.
Cauchy's procedures in the context of his 1853 sum theorem (for series of
continuous functions) are more readily understood from the viewpoint of
Robinson's framework, where one can exploit tools such as the pointwise
definition of the concept of uniform convergence.
Keywords: historiography; infinitesimal; Latin model; butterfly modelComment: 45 pages, published in Mat. Stu
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