1,811 research outputs found
A Presentation For The Automorphisms Of The 3-Sphere That Preserve A Genus Two Heegaard Splitting
Scharlemann constructed a connected simplicial 2-complex with an
action by the group of isotopy classes of orientation
preserving homeomorphisms of that preserve the isotopy class of an
unknotted genus 2 handlebody . In this paper we prove that the 2-complex
is contractible. Therefore we get a finite presentation of .Comment: Completely rewritten. 21 pages with 22 figure
Cabling sequences of tunnels of torus knots
This is the second of three papers that refine and extend portions of our
earlier preprint, "The depth of a knot tunnel." Together, they rework the
entire preprint.
The theory of tunnel number 1 knots that we introduced in "The tree of knot
tunnels" yields a parameterization in which each tunnel is described uniquely
by a finite sequence of rational parameters and a finite sequence of 0's and
1's, that together encode a procedure for constructing the knot and tunnel. In
this paper we calculate these invariants for all tunnels of torus knots.Comment: 17 pages, 12 figures, to appear in Algebraic and Geometric Topolog
Charge transfer electrostatic model of compositional order in perovskite alloys
We introduce an electrostatic model including charge transfer, which is shown
to account for the observed B-site ordering in Pb-based perovskite alloys. The
model allows charge transfer between A-sites and is a generalization of
Bellaiche and Vanderbilt's purely electrostatic model. The large covalency of
Pb^{2+} compared to Ba^{2+} is modeled by an environment dependent effective
A-site charge. Monte Carlo simulations of this model successfully reproduce the
long range compositional order of both Pb-based and Ba-based complex
A(BB^{'}B^{''})O_3 perovskite alloys. The models are also extended to study
systems with A-site and B-site doping, such as
(Na_{1/2}La_{1/2})(Mg_{1/3}Nb_{2/3})O_3,
(Ba_{1-x}La_{x})(Mg_{(1+x)/3}Nb_{(2-x)/3})O_3 and
(Pb_{1-x}La_{x})(Mg_{(1+x)/3}Ta_{(2-x)/3})O_3. General trends are reproduced by
purely electrostatic interactions, and charge transfer effects indicate that
local structural relaxations can tip the balance between different B-site
orderings in Pb based materials.Comment: 15 pages, 6 figure
Cosine Similarity Measure According to a Convex Cost Function
In this paper, we describe a new vector similarity measure associated with a
convex cost function. Given two vectors, we determine the surface normals of
the convex function at the vectors. The angle between the two surface normals
is the similarity measure. Convex cost function can be the negative entropy
function, total variation (TV) function and filtered variation function. The
convex cost function need not be differentiable everywhere. In general, we need
to compute the gradient of the cost function to compute the surface normals. If
the gradient does not exist at a given vector, it is possible to use the
subgradients and the normal producing the smallest angle between the two
vectors is used to compute the similarity measure
Routing, Localization And Positioning Protocols For Wireless Sensor And Actor Networks
Wireless sensor and actor networks (WSANs) are distributed systems of sensor nodes and actors that are interconnected over the wireless medium. Sensor nodes collect information about the physical world and transmit the data to actors by using one-hop or multi-hop communications. Actors collect information from the sensor nodes, process the information, take decisions and react to the events. This dissertation presents contributions to the methods of routing, localization and positioning in WSANs for practical applications. We first propose a routing protocol with service differentiation for WSANs with stationary nodes. In this setting, we also adapt a sports ranking algorithm to dynamically prioritize the events in the environment depending on the collected data. We extend this routing protocol for an application, in which sensor nodes float in a river to gather observations and actors are deployed at accessible points on the coastline. We develop a method with locally acting adaptive overlay network formation to organize the network with actor areas and to collect data by using locality-preserving communication. We also present a multi-hop localization approach for enriching the information collected from the river with the estimated locations of mobile sensor nodes without using positioning adapters. As an extension to this application, we model the movements of sensor nodes by a subsurface meandering current mobility model with random surface motion. Then we adapt the introduced routing and network organization methods to model a complete primate monitoring system. A novel spatial cut-off preferential attachment model and iii center of mass concept are developed according to the characteristics of the primate groups. We also present a role determination algorithm for primates, which uses the collection of spatial-temporal relationships. We apply a similar approach to human social networks to tackle the problem of automatic generation and organization of social networks by analyzing and assessing interaction data. The introduced routing and localization protocols in this dissertation are also extended with a novel three dimensional actor positioning strategy inspired by the molecular geometry. Extensive simulations are conducted in OPNET simulation tool for the performance evaluation of the proposed protocol
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