856 research outputs found
Linear Programming Decoding of Spatially Coupled Codes
For a given family of spatially coupled codes, we prove that the LP threshold
on the BSC of the graph cover ensemble is the same as the LP threshold on the
BSC of the derived spatially coupled ensemble. This result is in contrast with
the fact that the BP threshold of the derived spatially coupled ensemble is
believed to be larger than the BP threshold of the graph cover ensemble as
noted by the work of Kudekar et al. (2011, 2012). To prove this, we establish
some properties related to the dual witness for LP decoding which was
introduced by Feldman et al. (2007) and simplified by Daskalakis et al. (2008).
More precisely, we prove that the existence of a dual witness which was
previously known to be sufficient for LP decoding success is also necessary and
is equivalent to the existence of certain acyclic hyperflows. We also derive a
sublinear (in the block length) upper bound on the weight of any edge in such
hyperflows, both for regular LPDC codes and for spatially coupled codes and we
prove that the bound is asymptotically tight for regular LDPC codes. Moreover,
we show how to trade crossover probability for "LP excess" on all the variable
nodes, for any binary linear code.Comment: 37 pages; Added tightness construction, expanded abstrac
Local dynamics for fibered holomorphic transformations
Fibered holomorphic dynamics are skew-product transformations over an
irrational rotation, whose fibers are holomorphic functions. In this paper we
study such a dynamics on a neighborhood of an invariant curve. We obtain some
results analogous to the results in the non fibered case
Combining Relational Algebra, SQL, Constraint Modelling, and Local Search
The goal of this paper is to provide a strong integration between constraint
modelling and relational DBMSs. To this end we propose extensions of standard
query languages such as relational algebra and SQL, by adding constraint
modelling capabilities to them. In particular, we propose non-deterministic
extensions of both languages, which are specially suited for combinatorial
problems. Non-determinism is introduced by means of a guessing operator, which
declares a set of relations to have an arbitrary extension. This new operator
results in languages with higher expressive power, able to express all problems
in the complexity class NP. Some syntactical restrictions which make data
complexity polynomial are shown. The effectiveness of both extensions is
demonstrated by means of several examples. The current implementation, written
in Java using local search techniques, is described. To appear in Theory and
Practice of Logic Programming (TPLP)Comment: 30 pages, 5 figure
Counting Arithmetical Structures on Paths and Cycles
Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag (d) - A) r=0 , where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices (diag (d) - A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients ((2n-1)/(n-1)) , and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles
Counting Arithmetical Structures on Paths and Cycles
Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag (d) - A) r=0 , where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices (diag (d) - A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients ((2n-1)/(n-1)) , and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles
Data layout types : a type-based approach to automatic data layout transformations for improved SIMD vectorisation
The increasing complexity of modern hardware requires sophisticated programming
techniques for programs to run efficiently. At the same time, increased power of
modern hardware enables more advanced analyses to be included in compilers. This
thesis focuses on one particular optimisation technique that improves utilisation
of vector units. The foundation of this technique is the ability to chose memory
mappings for data structures of a given program.
Usually programming languages use a fixed layout for logical data structures
in physical memory. Such a static mapping often has a negative effect on usability
of vector units. In this thesis we consider a compiler for a programming language
that allows every data structure in a program to have its own data layout. We
make sure that data layouts across the program are sound, and most importantly
we solve a problem of automatic data layout reconstruction. To consistently do this,
we formulate this as a type inference problem, where type encodes a data layout
for a given structure as well as implied program transformations. We prove that
type-implied transformations preserve semantics of the original programs and we
demonstrate significant performance improvements when targeting SIMD-capable
architectures
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