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Boolean Autoencoders and Hypercube Clustering Complexity
 DESIGNS, CODES AND CRYPTOGRAPHY
"... We introduce and study the properties of Boolean autoencoder circuits. In particular, we show that the Boolean autoencoder circuit problem is equivalent to a clustering problem on the hypercube. We show that clustering m binary vectors on the ndimensional hypercube into k clusters is NPhard, as ..."
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We introduce and study the properties of Boolean autoencoder circuits. In particular, we show that the Boolean autoencoder circuit problem is equivalent to a clustering problem on the hypercube. We show that clustering m binary vectors on the ndimensional hypercube into k clusters is NP
Unique Games on the Hypercube
, 2014
"... In this paper, we investigate the validity of the Unique Games Conjecture when the constraint graph is the boolean hypercube. We construct an almost optimal integrality gap instance on the Hypercube for the GoemansWilliamson semidefinite program (SDP) for Max2LIN(Z2). We conjecture that adding tr ..."
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In this paper, we investigate the validity of the Unique Games Conjecture when the constraint graph is the boolean hypercube. We construct an almost optimal integrality gap instance on the Hypercube for the GoemansWilliamson semidefinite program (SDP) for Max2LIN(Z2). We conjecture that adding
Orca: A language for parallel programming of distributed systems
 IEEE Transactions on Software Engineering
, 1992
"... Orca is a language for implementing parallel applications on loosely coupled distributed systems. Unlike most languages for distributed programming, it allows processes on different machines to share data. Such data are encapsulated in dataobjects, which are instances of userdefined abstract data ..."
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Cited by 333 (46 self)
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Orca is a language for implementing parallel applications on loosely coupled distributed systems. Unlike most languages for distributed programming, it allows processes on different machines to share data. Such data are encapsulated in dataobjects, which are instances of userdefined abstract data types. The implementation of Orca takes care of the physical distribution of objects among the local memories of the processors. In particular, an implementation may replicate and/or migrate objects in order to decrease access times to objects and increase parallelism. This paper gives a detailed description of the Orca language design and motivates the design choices. Orca is intended for applications programmers rather than systems programmers. This is reflected in its design goals to provide a simple, easy to use language that is typesecure and provides clean semantics. The paper discusses three example parallel applications in Orca, one of which is described in detail. It also describes one of the existing implementations, which is based on reliable broadcasting. Performance measurements of this system are given for three parallel applications. The measurements show that significant speedups can be obtained for all three applications. Finally, the paper compares Orca with several related languages and systems. 1.
On the Hypercube Structure of the Genetic Code
, 2002
"... Abstract: A representation of the genetic code as a six–dimensional Boolean hypercube is proposed. It is assumed here that this structure is the result of the hierarchical order of the interaction energies of the bases in codon–anticodon recognition. The proposed structure demonstrates that in the g ..."
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Abstract: A representation of the genetic code as a six–dimensional Boolean hypercube is proposed. It is assumed here that this structure is the result of the hierarchical order of the interaction energies of the bases in codon–anticodon recognition. The proposed structure demonstrates
SPECIAL ISSUE: ANALYSIS OF BOOLEAN FUNCTIONS DimensionFree L2 Maximal Inequality for Spherical Means in the Hypercube
, 2013
"... Abstract: We establish the maximal inequality claimed in the title. In combinatorial terms this has the implication that for sufficiently small ε> 0, for all n, any marking of an ε fraction of the vertices of the ndimensional hypercube necessarily leaves a vertex x such that marked vertices are ..."
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are a minority of every sphere centered at x. ACM Classification: G.3 AMS Classification: 42B25 Key words and phrases: maximal inequality, Fourier analysis, boolean hypercube 1
Fortran D Language Specification
, 1990
"... This paper presents Fortran D, a version of Fortran enhanced with data decomposition specifications. It is designed to support two fundamental stages of writing a dataparallel program: problem mapping using sophisticated array alignments, and machine mapping through a rich set of data distribution ..."
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Cited by 303 (50 self)
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This paper presents Fortran D, a version of Fortran enhanced with data decomposition specifications. It is designed to support two fundamental stages of writing a dataparallel program: problem mapping using sophisticated array alignments, and machine mapping through a rich set of data distribution functions. We believe that Fortran D provides a simple machineindependent programming model for most numerical computations. We intend to evaluate its usefulness for both programmers and advanced compilers on a variety of parallel architectures.
No Free Lunch Theorems for Search
, 1995
"... We show that all algorithms that search for an extremum of a cost function perform exactly the same, when averaged over all possible cost functions. In particular, if algorithm A outperforms algorithm B on some cost functions, then loosely speaking there must exist exactly as many other functions wh ..."
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Cited by 292 (2 self)
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We show that all algorithms that search for an extremum of a cost function perform exactly the same, when averaged over all possible cost functions. In particular, if algorithm A outperforms algorithm B on some cost functions, then loosely speaking there must exist exactly as many other functions where B outperforms A. Starting from this we analyze a number of the other a priori characteristics of the search problem, like its geometry and its informationtheoretic aspects. This analysis allows us to derive mathematical benchmarks for assessing a particular search algorithm 's performance. We also investigate minimax aspects of the search problem, the validity of using characteristics of a partial search over a cost function to predict future behavior of the search algorithm on that cost function, and timevarying cost functions. We conclude with some discussion of the justifiability of biologicallyinspired search methods.
From Boolean to Probabilistic Boolean Networks as Models of Genetic Regulatory Networks
 Proc. IEEE
, 2002
"... Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles governing biological systems in an integrarive and holistic manner. It also paves the way toward the development of systematic approaches for effective therapeutic intervention in di ..."
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Cited by 122 (23 self)
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in disease. The central theme in this paper is the Boolean formalism as a building block for modeling complex, largescale, and dynamical networks of genetic interactions. We discuss the goals of modeling genetic networks as well as the data requirements. The Boolean formalism is justified from several
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