537 research outputs found
Symmetric L-graphs
In this paper we characterize symmetric L-graphs, which are either Kronecker products of two cycles or Gaussian graphs.
Vertex symmetric networks have the property that the communication load is uniformly distributed on all the vertices so that
there is no point of congestion. A stronger notion of symmetry, edge symmetry, requires that every edge in the graph looks the
same. Such property ensures that the communication load is uniformly distributed over all the communication links, so that
there is no congestion at any link.Peer Reviewe
Energy Aware Transmission in Cellular Uplink with Clustered Base Station Cooperation
We provide an analytical formula to evaluate the performance of the uplink of planar cellular networks when joint processing is enabled among limited number of base stations in a generalised fading environment. Focusing on user transmission power allocation techniques to mitigate inter-cluster interference we investigate the system's spectral-energy efficiency trade-off. The paper addresses the gains in both cell throughput and transmissions energy efficiency due to the combined strategies of base station cooperation and user power management. We assess the effect of the propagation environment and of the key network design parameters of cooperation cluster size and inter-site distance on the overall performance providing numerical results for a real-world scenario
Learning the Irreducible Representations of Commutative Lie Groups
We present a new probabilistic model of compact commutative Lie groups that
produces invariant-equivariant and disentangled representations of data. To
define the notion of disentangling, we borrow a fundamental principle from
physics that is used to derive the elementary particles of a system from its
symmetries. Our model employs a newfound Bayesian conjugacy relation that
enables fully tractable probabilistic inference over compact commutative Lie
groups -- a class that includes the groups that describe the rotation and
cyclic translation of images. We train the model on pairs of transformed image
patches, and show that the learned invariant representation is highly effective
for classification
Classes of Symmetric Cayley Graphs over Finite Abelian Groups of Degrees 4 and 6
The present work is devoted to characterize the family of symmetric
undirected Cayley graphs over finite Abelian groups for degrees 4 and 6.Comment: 12 pages. A previous version of some of the results in this paper
where first announced at 2010 International Workshop on Optimal
Interconnection Networks (IWONT 2010). It is accessible at
http://upcommons.upc.edu/revistes/handle/2099/1037
Rigorous direct and inverse design of photonic-plasmonic nanostructures
Designing photonic-plasmonic nanostructures with desirable electromagnetic properties is a central problem in modern photonics engineering. As limited by available materials, engineering geometry of optical materials at both element and array levels becomes the key to solve this problem. In this thesis, I present my work on the development of novel methods and design strategies for photonic-plasmonic structures and metamaterials, including novel Green’s matrix-based spectral methods for predicting the optical properties of large-scale nanostructures of arbitrary geometry. From engineering elements to arrays, I begin my thesis addressing toroidal electrodynamics as an emerging approach to enhance light absorption in designed nanodisks by geometrically creating anapole configurations using high-index dielectric materials. This work demonstrates enhanced absorption rates driven by multipolar decomposition of current distributions involving toroidal multipole moments for the first time. I also present my work on designing helical nano-antennas using the rigorous Surface Integral Equations method. The helical nano-antennas feature unprecedented beam-forming and polarization tunability controlled by their geometrical parameters, and can be understood from the array perspective. In these projects, optimization of optical performances are translated into systematic study of identifiable geometric parameters. However, while array-geometry engineering presents multiple advantages, including physical intuition, versatility in design, and ease of fabrication, there is currently no rigorous and efficient solution for designing complex resonances in large-scale systems from an available set of geometrical parameters. In order to achieve this important goal, I developed an efficient numerical code based on the Green’s matrix method for modeling scattering by arbitrary arrays of coupled electric and magnetic dipoles, and show its relevance to the design of light localization and scattering resonances in deterministic aperiodic geometries. I will show how universal properties driven by the aperiodic geometries of the scattering arrays can be obtained by studying the spectral statistics of the corresponding Green’s matrices and how this approach leads to novel metamaterials for the visible and near-infrared spectral ranges. Within the thesis, I also present my collaborative works as examples of direct and inverse designs of nanostructures for photonics applications, including plasmonic sensing, optical antennas, and radiation shaping
Symmetric Interconnection Networks from Cubic Crystal Lattices
Torus networks of moderate degree have been widely used in the supercomputer
industry. Tori are superb when used for executing applications that require
near-neighbor communications. Nevertheless, they are not so good when dealing
with global communications. Hence, typical 3D implementations have evolved to
5D networks, among other reasons, to reduce network distances. Most of these
big systems are mixed-radix tori which are not the best option for minimizing
distances and efficiently using network resources. This paper is focused on
improving the topological properties of these networks.
By using integral matrices to deal with Cayley graphs over Abelian groups, we
have been able to propose and analyze a family of high-dimensional grid-based
interconnection networks. As they are built over -dimensional grids that
induce a regular tiling of the space, these topologies have been denoted
\textsl{lattice graphs}. We will focus on cubic crystal lattices for modeling
symmetric 3D networks. Other higher dimensional networks can be composed over
these graphs, as illustrated in this research. Easy network partitioning can
also take advantage of this network composition operation. Minimal routing
algorithms are also provided for these new topologies. Finally, some practical
issues such as implementability and preliminary performance evaluations have
been addressed
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