24,179 research outputs found
Generalized Interference Alignment --- Part I: Theoretical Framework
Interference alignment (IA) has attracted enormous research interest as it
achieves optimal capacity scaling with respect to signal to noise ratio on
interference networks. IA has also recently emerged as an effective tool in
engineering interference for secrecy protection on wireless wiretap networks.
However, despite the numerous works dedicated to IA, two of its fundamental
issues, i.e., feasibility conditions and transceiver design, are not completely
addressed in the literature. In this two part paper, a generalised interference
alignment (GIA) technique is proposed to enhance the IA's capability in secrecy
protection. A theoretical framework is established to analyze the two
fundamental issues of GIA in Part I and then the performance of GIA in
large-scale stochastic networks is characterized to illustrate how GIA benefits
secrecy protection in Part II. The theoretical framework for GIA adopts
methodologies from algebraic geometry, determines the necessary and sufficient
feasibility conditions of GIA, and generates a set of algorithms that can solve
the GIA problem. This framework sets up a foundation for the development and
implementation of GIA.Comment: Minor Revision at IEEE Transactions on Signal Processin
Interference alignment for the MIMO interference channel
We study vector space interference alignment for the MIMO interference
channel with no time or frequency diversity, and no symbol extensions. We prove
both necessary and sufficient conditions for alignment. In particular, we
characterize the feasibility of alignment for the symmetric three-user channel
where all users transmit along d dimensions, all transmitters have M antennas
and all receivers have N antennas, as well as feasibility of alignment for the
fully symmetric (M=N) channel with an arbitrary number of users.
An implication of our results is that the total degrees of freedom available
in a K-user interference channel, using only spatial diversity from the
multiple antennas, is at most 2. This is in sharp contrast to the K/2 degrees
of freedom shown to be possible by Cadambe and Jafar with arbitrarily large
time or frequency diversity.
Moving beyond the question of feasibility, we additionally discuss
computation of the number of solutions using Schubert calculus in cases where
there are a finite number of solutions.Comment: 16 pages, 7 figures, final submitted versio
Category Theory and Model-Driven Engineering: From Formal Semantics to Design Patterns and Beyond
There is a hidden intrigue in the title. CT is one of the most abstract
mathematical disciplines, sometimes nicknamed "abstract nonsense". MDE is a
recent trend in software development, industrially supported by standards,
tools, and the status of a new "silver bullet". Surprisingly, categorical
patterns turn out to be directly applicable to mathematical modeling of
structures appearing in everyday MDE practice. Model merging, transformation,
synchronization, and other important model management scenarios can be seen as
executions of categorical specifications.
Moreover, the paper aims to elucidate a claim that relationships between CT
and MDE are more complex and richer than is normally assumed for "applied
mathematics". CT provides a toolbox of design patterns and structural
principles of real practical value for MDE. We will present examples of how an
elementary categorical arrangement of a model management scenario reveals
deficiencies in the architecture of modern tools automating the scenario.Comment: In Proceedings ACCAT 2012, arXiv:1208.430
Out of Many, One: Toward Rigorous Common Core Standards From the Ground Up
Analyzes high school standards for English in twelve states and math in sixteen states designed for college- and career-readiness. Examines their alignment with the American Diploma Project's benchmarks for common core standards. Discusses implications
Chebyshev polynomial filtered subspace iteration in the Discontinuous Galerkin method for large-scale electronic structure calculations
The Discontinuous Galerkin (DG) electronic structure method employs an
adaptive local basis (ALB) set to solve the Kohn-Sham equations of density
functional theory (DFT) in a discontinuous Galerkin framework. The adaptive
local basis is generated on-the-fly to capture the local material physics, and
can systematically attain chemical accuracy with only a few tens of degrees of
freedom per atom. A central issue for large-scale calculations, however, is the
computation of the electron density (and subsequently, ground state properties)
from the discretized Hamiltonian in an efficient and scalable manner. We show
in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can
be used to address this issue and push the envelope in large-scale materials
simulations in a discontinuous Galerkin framework. We describe how the subspace
filtering steps can be performed in an efficient and scalable manner using a
two-dimensional parallelization scheme, thanks to the orthogonality of the DG
basis set and block-sparse structure of the DG Hamiltonian matrix. The
on-the-fly nature of the ALBs requires additional care in carrying out the
subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI
approach in calculations of large-scale two-dimensional graphene sheets and
bulk three-dimensional lithium-ion electrolyte systems. Employing 55,296
computational cores, the time per self-consistent field iteration for a sample
of the bulk 3D electrolyte containing 8,586 atoms is 90 seconds, and the time
for a graphene sheet containing 11,520 atoms is 75 seconds.Comment: Submitted to The Journal of Chemical Physic
(0,2) string compactifications
Using the simple current method we study a class of SCFTs which we
conjecture to be equivalent to (0,2) sigma models constructed in the framework
of gauged linear sigma models.Comment: Talk at the International Symposium on the Theory of Elementary
Particles Buckow, August 27-31, 1996; LaTeX, fleqn.sty, espcrc2.sty; 6 page
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