44,472 research outputs found
Spatial Aggregation: Theory and Applications
Visual thinking plays an important role in scientific reasoning. Based on the
research in automating diverse reasoning tasks about dynamical systems,
nonlinear controllers, kinematic mechanisms, and fluid motion, we have
identified a style of visual thinking, imagistic reasoning. Imagistic reasoning
organizes computations around image-like, analogue representations so that
perceptual and symbolic operations can be brought to bear to infer structure
and behavior. Programs incorporating imagistic reasoning have been shown to
perform at an expert level in domains that defy current analytic or numerical
methods. We have developed a computational paradigm, spatial aggregation, to
unify the description of a class of imagistic problem solvers. A program
written in this paradigm has the following properties. It takes a continuous
field and optional objective functions as input, and produces high-level
descriptions of structure, behavior, or control actions. It computes a
multi-layer of intermediate representations, called spatial aggregates, by
forming equivalence classes and adjacency relations. It employs a small set of
generic operators such as aggregation, classification, and localization to
perform bidirectional mapping between the information-rich field and
successively more abstract spatial aggregates. It uses a data structure, the
neighborhood graph, as a common interface to modularize computations. To
illustrate our theory, we describe the computational structure of three
implemented problem solvers -- KAM, MAPS, and HIPAIR --- in terms of the
spatial aggregation generic operators by mixing and matching a library of
commonly used routines.Comment: See http://www.jair.org/ for any accompanying file
A Multi-Game Framework for Harmonized LTE-U and WiFi Coexistence over Unlicensed Bands
The introduction of LTE over unlicensed bands (LTE-U) will enable LTE base
stations (BSs) to boost their capacity and offload their traffic by exploiting
the underused unlicensed bands. However, to reap the benefits of LTE-U, it is
necessary to address various new challenges associated with LTE-U and WiFi
coexistence. In particular, new resource management techniques must be
developed to optimize the usage of the network resources while handling the
interdependence between WiFi and LTE users and ensuring that WiFi users are not
jeopardized. To this end, in this paper, a new game theoretic tool, dubbed as
\emph{multi-game} framework is proposed as a promising approach for modeling
resource allocation problems in LTE-U. In such a framework, multiple,
co-existing and coupled games across heterogeneous channels can be formulated
to capture the specific characteristics of LTE-U. Such games can be of
different properties and types but their outcomes are largely interdependent.
After introducing the basics of the multi-game framework, two classes of
algorithms are outlined to achieve the new solution concepts of multi-games.
Simulation results are then conducted to show how such a multi-game can
effectively capture the specific properties of LTE-U and make of it a
"friendly" neighbor to WiFi.Comment: Accepted for publication at IEEE Wireless Communications Magazine,
Special Issue on LTE in Unlicensed Spectru
Construction of aggregation operators with noble reinforcement
This paper examines disjunctive aggregation operators used in various recommender systems. A specific requirement in these systems is the property of noble reinforcement: allowing a collection of high-valued arguments to reinforce each other while avoiding reinforcement of low-valued arguments. We present a new construction of Lipschitz-continuous aggregation operators with noble reinforcement property and its refinements. <br /
Ground-state Stabilization of Open Quantum Systems by Dissipation
Control by dissipation, or environment engineering, constitutes an important
methodology within quantum coherent control which was proposed to improve the
robustness and scalability of quantum control systems. The system-environment
coupling, often considered to be detrimental to quantum coherence, also
provides the means to steer the system to desired states. This paper aims to
develop the theory for engineering of the dissipation, based on a ground-state
Lyapunov stability analysis of open quantum systems via a Heisenberg-picture
approach. Algebraic conditions concerning the ground-state stability and
scalability of quantum systems are obtained. In particular, Lyapunov stability
conditions expressed as operator inequalities allow a purely algebraic
treatment of the environment engineering problem, which facilitates the
integration of quantum components into a large-scale quantum system and draws
an explicit connection to the classical theory of vector Lyapunov functions and
decomposition-aggregation methods for control of complex systems. The
implications of the results in relation to dissipative quantum computing and
state engineering are also discussed in this paper.Comment: 18 pages, to appear in Automatic
Small gain theorems for large scale systems and construction of ISS Lyapunov functions
We consider interconnections of n nonlinear subsystems in the input-to-state
stability (ISS) framework. For each subsystem an ISS Lyapunov function is given
that treats the other subsystems as independent inputs. A gain matrix is used
to encode the mutual dependencies of the systems in the network. Under a small
gain assumption on the monotone operator induced by the gain matrix, a locally
Lipschitz continuous ISS Lyapunov function is obtained constructively for the
entire network by appropriately scaling the individual Lyapunov functions for
the subsystems. The results are obtained in a general formulation of ISS, the
cases of summation, maximization and separation with respect to external gains
are obtained as corollaries.Comment: provisionally accepted by SIAM Journal on Control and Optimizatio
On Spectra of Linearized Operators for Keller-Segel Models of Chemotaxis
We consider the phenomenon of collapse in the critical Keller-Segel equation
(KS) which models chemotactic aggregation of micro-organisms underlying many
social activities, e.g. fruiting body development and biofilm formation. Also
KS describes the collapse of a gas of self-gravitating Brownian particles. We
find the fluctuation spectrum around the collapsing family of steady states for
these equations, which is instrumental in derivation of the critical collapse
law. To this end we develop a rigorous version of the method of matched
asymptotics for the spectral analysis of a class of second order differential
operators containing the linearized Keller-Segel operators (and as we argue
linearized operators appearing in nonlinear evolution problems). We explain how
the results we obtain are used to derive the critical collapse law, as well as
for proving its stability.Comment: 22 pages, 1 figur
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