7,709 research outputs found
Generalised Reichenbachian common cause systems
The principle of the common cause claims that if an improbable coincidence has occurred, there must exist a common cause. This is generally taken to mean that positive correlations between non-causally related events should disappear when conditioning on the action of some underlying common cause. The extended interpretation of the principle, by contrast, urges that common causes should be called for in order to explain positive deviations between the estimated correlation of two events and the expected value of their correlation. The aim of this paper is to provide the extended reading of the principle with a general probabilistic model, capturing the simultaneous action of a system of multiple common causes. To this end, two distinct models are elaborated, and the necessary and sufficient conditions for their existence are determined
Generalised Reichenbachian Common Cause Systems
The principle of the common cause claims that if an improbable coincidence
has occurred, there must exist a common cause. This is generally taken to mean
that positive correlations between non-causally related events should disappear
when conditioning on the action of some underlying common cause. The extended
interpretation of the principle, by contrast, urges that common causes should
be called for in order to explain positive deviations between the estimated
correlation of two events and the expected value of their correlation. The aim
of this paper is to provide the extended reading of the principle with a
general probabilistic model, capturing the simultaneous action of a system of
multiple common causes. To this end, two distinct models are elaborated, and
the necessary and sufficient conditions for their existence are determined
Sudden violation of the CHSH inequality in a two qubits system
I study the dynamics of the violation of the CHSH inequality for two qubits
interacting with a common zero-temperature non-Markovian environment. I
demonstrate sudden violation of the inequality for two qubits initially
prepared in a factorized state. Due to the strong coupling between the qubits
and the reservoir, the dynamics is characterized by numerous sharp revivals.
Furthermore I focus on a more realistic physical system in which the
spontaneous emission for the qubits is taken into account. When including
spontaneous emission even for small decay parameters, revivals in the violation
are heavily damped out. If the decay rates exceed a certain threshold, the
inequality turns out to be always satisfied.Comment: Accepted by Physica Scripta as part of the Proceedings of CEWQO0
Global Propagation of Singularities for Time Dependent Hamilton-Jacobi Equations
We investigate the properties of the set of singularities of semiconcave
solutions of Hamilton-Jacobi equations of the form \begin{equation*}
u_t(t,x)+H(\nabla u(t,x))=0, \qquad\text{a.e. }(t,x)\in
(0,+\infty)\times\Omega\subset\mathbb{R}^{n+1}\,. \end{equation*} It is well
known that the singularities of such solutions propagate locally along
generalized characteristics. Special generalized characteristics, satisfying an
energy condition, can be constructed, under some assumptions on the structure
of the Hamiltonian . In this paper, we provide estimates of the dissipative
behavior of the energy along such curves. As an application, we prove that the
singularities of any viscosity solution of the above equation cannot vanish in
a finite time
A Projection-Oriented Mathematical Model for Second-Species Counterpoint
Drawing inspiration from both the classical Guerino Mazzola's symmetry-based
model for first-species counterpoint (one note against one note) and Johann
Joseph Fux's "Gradus ad Parnassum", we propose an extension for second-species
(two notes against one note)
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