911 research outputs found
Invariant Regions and Global Asymptotic Stability in an Isothermal Catalyst
A well-known model for the evolution of the (space-dependent) concentration and (lumped) temperature in a porous catalyst is considered. A sequence of invariant regions of the phase space is given, which converges to a globally asymptotically stable region . Quantitative sufficient conditions are obtained for (the region to consist of only one point and) the problem to have a (unique) globally asymptotically stable steady state
Sufficient stochastic maximum principle in a regime-switching diffusion model
We prove a sufficient stochastic maximum principle for the optimal control of
a regime-switching diffusion model. We show the connection to dynamic
programming and we apply the result to a quadratic loss minimization problem,
which can be used to solve a mean-variance portfolio selection problem
Random Time Forward Starting Options
We introduce a natural generalization of the forward-starting options, first
discussed by M. Rubinstein. The main feature of the contract presented here is
that the strike-determination time is not fixed ex-ante, but allowed to be
random, usually related to the occurrence of some event, either of financial
nature or not. We will call these options {\bf Random Time Forward Starting
(RTFS)}. We show that, under an appropriate "martingale preserving" hypothesis,
we can exhibit arbitrage free prices, which can be explicitly computed in many
classical market models, at least under independence between the random time
and the assets' prices. Practical implementations of the pricing methodologies
are also provided. Finally a credit value adjustment formula for these OTC
options is computed for the unilateral counterparty credit risk.Comment: 19 pages, 1 figur
Efficiently Clustering Very Large Attributed Graphs
Attributed graphs model real networks by enriching their nodes with
attributes accounting for properties. Several techniques have been proposed for
partitioning these graphs into clusters that are homogeneous with respect to
both semantic attributes and to the structure of the graph. However, time and
space complexities of state of the art algorithms limit their scalability to
medium-sized graphs. We propose SToC (for Semantic-Topological Clustering), a
fast and scalable algorithm for partitioning large attributed graphs. The
approach is robust, being compatible both with categorical and with
quantitative attributes, and it is tailorable, allowing the user to weight the
semantic and topological components. Further, the approach does not require the
user to guess in advance the number of clusters. SToC relies on well known
approximation techniques such as bottom-k sketches, traditional graph-theoretic
concepts, and a new perspective on the composition of heterogeneous distance
measures. Experimental results demonstrate its ability to efficiently compute
high-quality partitions of large scale attributed graphs.Comment: This work has been published in ASONAM 2017. This version includes an
appendix with validation of our attribute model and distance function,
omitted in the converence version for lack of space. Please refer to the
published versio
Eliashberg's proof of Cerf's theorem
Following a line of reasoning suggested by Eliashberg, we prove Cerf's
theorem that any diffeomorphism of the 3-sphere extends over the 4-ball. To
this end we develop a moduli-theoretic version of Eliashberg's
filling-with-holomorphic-discs method.Comment: 32 page
Jump-diffusion unravelling of a non Markovian generalized Lindblad master equation
The "correlated-projection technique" has been successfully applied to derive
a large class of highly non Markovian dynamics, the so called non Markovian
generalized Lindblad type equations or Lindblad rate equations. In this
article, general unravellings are presented for these equations, described in
terms of jump-diffusion stochastic differential equations for wave functions.
We show also that the proposed unravelling can be interpreted in terms of
measurements continuous in time, but with some conceptual restrictions. The
main point in the measurement interpretation is that the structure itself of
the underlying mathematical theory poses restrictions on what can be considered
as observable and what is not; such restrictions can be seen as the effect of
some kind of superselection rule. Finally, we develop a concrete example and we
discuss possible effects on the heterodyne spectrum of a two-level system due
to a structured thermal-like bath with memory.Comment: 23 page
A Model of Porous Catalyst Accounting for Incipiently Non-isothermal Effects*
An approximate model accounting for incipiently non-isothermal effects is derived from a well-known model of porous catalyst for appropriate, realistic limiting values of the parameters. In this limit, the original model is a singularly perturbed, m-D reaction–diffusion system, and the approximate model is given by the m-D heat equation with nonlinear boundary condition, coupled with infinitely many (ifm2) 1-D semilinear parabolic equations, one for each point of the boundary of the spatial domain. Some limiting cases are still considered in the approximate model that lead to further simplifications
Anomalous jumping in a double-well potential
Noise induced jumping between meta-stable states in a potential depends on
the structure of the noise. For an -stable noise, jumping triggered by
single extreme events contributes to the transition probability. This is also
called Levy flights and might be of importance in triggering sudden changes in
geophysical flow and perhaps even climatic changes. The steady state statistics
is also influenced by the noise structure leading to a non-Gibbs distribution
for an -stable noise.Comment: 11 pages, 7 figure
Symmetry reduction of Brownian motion and Quantum Calogero-Moser systems
Let be a Riemannian -manifold. This paper is concerned with the
symmetry reduction of Brownian motion in and ramifications thereof in a
Hamiltonian context. Specializing to the case of polar actions we discuss
various versions of the stochastic Hamilton-Jacobi equation associated to the
symmetry reduction of Brownian motion and observe some similarities to the
Schr\"odinger equation of the quantum free particle reduction as described by
Feher and Pusztai. As an application we use this reduction scheme to derive
examples of quantum Calogero-Moser systems from a stochastic setting.Comment: V2 contains some improvements thanks to referees' suggestions; to
appear in Stochastics and Dynamic
Global Stability of a Premixed Reaction Zone (Time-Dependent Liñan’s Problem)
Global stability properties of a premixed, three-dimensional reaction zone are considered. In the nonadiabatic case (i.e., when there is a heat exchange between the reaction zone and the burned gases) there is a unique, spatially one-dimensional steady state that is shown to be unstable (respectively, asymptotically stable) if the reaction zone is cooled (respectively, heated) by the burned mixture. In the adiabatic case, there is a unique (up to spatial translations) steady state that is shown to be stable. In addition, the large-time asymptotic behavior of the solution is analyzed to obtain sufficient conditions on the initial data for stabilization. Previous partial numerical results on linear stability of one-dimensional reaction zones are thereby confirmed and extended
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