2,189 research outputs found
Detecting an Intermittent Change of Unknown Duration
Oftentimes in practice, the observed process changes statistical properties
at an unknown point in time and the duration of a change is substantially
finite, in which case one says that the change is intermittent or transient. We
provide an overview of existing approaches for intermittent change detection
and advocate in favor of a particular setting driven by the intermittent nature
of the change. We propose a novel optimization criterion that is more
appropriate for many applied areas such as the detection of threats in
physical-computer systems, near-Earth space informatics, epidemiology,
pharmacokinetics, etc. We argue that controlling the local conditional
probability of a false alarm, rather than the familiar average run length to a
false alarm, and maximizing the local conditional probability of detection is a
more reasonable approach versus a traditional quickest change detection
approach that requires minimizing the expected delay to detection. We adopt the
maximum likelihood (ML) approach with respect to the change duration and show
that several commonly used detection rules (CUSUM, window-limited CUSUM, and
FMA) are equivalent to the ML-based stopping times. We discuss how to choose
design parameters for these rules and provide a comprehensive simulation study
to corroborate intuitive expectations.Comment: 34 pages, 7 figures, 6 table
An introduction to quantum gravity
After an overview of the physical motivations for studying quantum gravity,
we reprint THE FORMAL STRUCTURE OF QUANTUM GRAVITY, i.e. the 1978 Cargese
Lectures by Professor B.S. DeWitt, with kind permission of Springer. The reader
is therefore introduced, in a pedagogical way, to the functional integral
quantization of gravitation and Yang-Mills theory. It is hoped that such a
paper will remain useful for all lecturers or Ph.D. students who face the task
of introducing (resp. learning) some basic concepts in quantum gravity in a
relatively short time. In the second part, we outline selected topics such as
the braneworld picture with the same covariant formalism of the first part, and
spectral asymptotics of Euclidean quantum gravity with diffeomorphism-invariant
boundary conditions. The latter might have implications for singularity
avoidance in quantum cosmology.Comment: 68 pages, Latex file. Sections from 2 to 17 are published thanks to
kind permission of Springe
Hamiltonian Frenet-Serret dynamics
The Hamiltonian formulation of the dynamics of a relativistic particle
described by a higher-derivative action that depends both on the first and the
second Frenet-Serret curvatures is considered from a geometrical perspective.
We demonstrate how reparametrization covariant dynamical variables and their
projections onto the Frenet-Serret frame can be exploited to provide not only a
significant simplification of but also novel insights into the canonical
analysis. The constraint algebra and the Hamiltonian equations of motion are
written down and a geometrical interpretation is provided for the canonical
variables.Comment: Latex file, 14 pages, no figures. Revised version to appear in Class.
Quant. Gra
Local and nonlocal solvable structures in ODEs reduction
Solvable structures, likewise solvable algebras of local symmetries, can be
used to integrate scalar ODEs by quadratures. Solvable structures, however, are
particularly suitable for the integration of ODEs with a lack of local
symmetries. In fact, under regularity assumptions, any given ODE always admits
solvable structures even though finding them in general could be a very
difficult task. In practice a noteworthy simplification may come by computing
solvable structures which are adapted to some admitted symmetry algebra. In
this paper we consider solvable structures adapted to local and nonlocal
symmetry algebras of any order (i.e., classical and higher). In particular we
introduce the notion of nonlocal solvable structure
A theory of \pi/2 superconducting Josephson junctions
We consider theoretically a Josephson junction with a superconducting
critical current density which has a random sign along the junction's surface.
We show that the ground state of the junction corresponds to the phase
difference equal to \pi/2. Such a situation can take place in superconductor-
ferromagnet junction
Conceptually driven and visually rich tasks in texts and teaching practice: the case of infinite series
The study we report here examines parts of what Chevallard calls the institutional dimension of the students’ learning experience of a relatively under-researched, yet crucial, concept in Analysis, the concept of infinite series. In particular, we examine how the concept is introduced to students in texts and in teaching practice. To this purpose, we employ Duval's Theory of Registers of Semiotic Representation towards the analysis of 22 texts used in Canada and UK post-compulsory courses. We also draw on interviews with in-service teachers and university lecturers in order to discuss briefly teaching practice and some of their teaching suggestions. Our analysis of the texts highlights that the presentation of the concept is largely a-historical, with few graphical representations, few opportunities to work across different registers (algebraic, graphical, verbal), few applications or intra-mathematical references to the concept's significance and few conceptually driven tasks that go beyond practising with the application of convergence tests and prepare students for the complex topics in which the concept of series is implicated. Our preliminary analysis of the teacher interviews suggests that pedagogical practice often reflects the tendencies in the texts. Furthermore, the interviews with the university lecturers point at the pedagogical potential of: illustrative examples and evocative visual representations in teaching; and, student engagement with systematic guesswork and writing explanatory accounts of their choices and applications of convergence tests
Defects and boundary layers in non-Euclidean plates
We investigate the behavior of non-Euclidean plates with constant negative
Gaussian curvature using the F\"oppl-von K\'arm\'an reduced theory of
elasticity. Motivated by recent experimental results, we focus on annuli with a
periodic profile. We prove rigorous upper and lower bounds for the elastic
energy that scales like the thickness squared. In particular we show that are
only two types of global minimizers -- deformations that remain flat and saddle
shaped deformations with isolated regions of stretching near the edge of the
annulus. We also show that there exist local minimizers with a periodic profile
that have additional boundary layers near their lines of inflection. These
additional boundary layers are a new phenomenon in thin elastic sheets and are
necessary to regularize jump discontinuities in the azimuthal curvature across
lines of inflection. We rigorously derive scaling laws for the width of these
boundary layers as a function of the thickness of the sheet
Theory of quantum metal to superconductor transitions in highly conducting systems
We derive the theory of the quantum (zero temperature) superconductor to
metal transition in disordered materials when the resistance of the normal
metal near criticality is small compared to the quantum of resistivity. This
can occur most readily in situations in which ``Anderson's theorem'' does not
apply. We explicitly study the transition in superconductor-metal composites,
in an s-wave superconducting film in the presence of a magnetic field, and in a
low temperature disordered d-wave superconductor. Near the point of the
transition, the distribution of the superconducting order parameter is highly
inhomogeneous. To describe this situation we employ a procedure which is
similar to that introduced by Mott for description of the temperature
dependence of the variable range hopping conduction. As the system approaches
the point of the transition from the metal to the superconductor, the
conductivity of the system diverges, and the Wiedemann-Franz law is violated.
In the case of d-wave (or other exotic) superconductors we predict the
existence of (at least) two sequential transitions as a function of increasing
disorder: a d-wave to s-wave, and then an s-wave to metal transition
Geometrically induced singular behavior of entanglement
We show that the geometry of the set of quantum states plays a crucial role
in the behavior of entanglement in different physical systems. More
specifically it is shown that singular points at the border of the set of
unentangled states appear as singularities in the dynamics of entanglement of
smoothly varying quantum states. We illustrate this result by implementing a
photonic parametric down conversion experiment. Moreover, this effect is
connected to recently discovered singularities in condensed matter models.Comment: v2: 4 pags, 4 figs. A discussion before the proof of Proposition 1
and tomographic results were included, Propostion 2 was removed and the
references were fixe
Contact lines for fluid surface adhesion
When a fluid surface adheres to a substrate, the location of the contact line
adjusts in order to minimize the overall energy. This adhesion balance implies
boundary conditions which depend on the characteristic surface deformation
energies. We develop a general geometrical framework within which these
conditions can be systematically derived. We treat both adhesion to a rigid
substrate as well as adhesion between two fluid surfaces, and illustrate our
general results for several important Hamiltonians involving both curvature and
curvature gradients. Some of these have previously been studied using very
different techniques, others are to our knowledge new. What becomes clear in
our approach is that, except for capillary phenomena, these boundary conditions
are not the manifestation of a local force balance, even if the concept of
surface stress is properly generalized. Hamiltonians containing higher order
surface derivatives are not just sensitive to boundary translations but also
notice changes in slope or even curvature. Both the necessity and the
functional form of the corresponding additional contributions follow readily
from our treatment.Comment: 8 pages, 2 figures, LaTeX, RevTeX styl
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