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A Unifying Framework for Measuring Weighted Rich Clubs  [PDF]
Jeff Alstott,Pietro Panzarasa,Mikail Rubinov,Ed Bullmore,Petra Vertes
Computer Science , 2014, DOI: 10.1038/srep07258
Abstract: Network analysis can help uncover meaningful regularities in the organization of complex systems. Among these, rich clubs are a functionally important property of a variety of social, technological and biological networks. Rich clubs emerge when nodes that are somehow prominent or 'rich' (e.g., highly connected) interact preferentially with one another. The identification of rich clubs is non-trivial, especially in weighted networks, and to this end multiple distinct metrics have been proposed. Here we describe a unifying framework for detecting rich clubs which intuitively generalizes various metrics into a single integrated method. This generalization rests upon the explicit incorporation of randomized control networks into the measurement process. We apply this framework to real-life examples, and show that, depending on the selection of randomized controls, different kinds of rich-club structures can be detected, such as topological and weighted rich clubs.
A Unifying Framework for Local Throughput in Wireless Networks  [PDF]
Pedro C. Pinto,Moe Z. Win
Mathematics , 2010,
Abstract: With the increased competition for the electromagnetic spectrum, it is important to characterize the impact of interference in the performance of a wireless network, which is traditionally measured by its throughput. This paper presents a unifying framework for characterizing the local throughput in wireless networks. We first analyze the throughput of a probe link from a connectivity perspective, in which a packet is successfully received if it does not collide with other packets from nodes within its reach (called the audible interferers). We then characterize the throughput from a signal-to-interference-plus-noise ratio (SINR) perspective, in which a packet is successfully received if the SINR exceeds some threshold, considering the interference from all emitting nodes in the network. Our main contribution is to generalize and unify various results scattered throughout the literature. In particular, the proposed framework encompasses arbitrary wireless propagation effects (e.g, Nakagami-m fading, Rician fading, or log-normal shadowing), as well as arbitrary traffic patterns (e.g., slotted-synchronous, slotted-asynchronous, or exponential-interarrivals traffic), allowing us to draw more general conclusions about network performance than previously available in the literature.
A unifying framework for quantifying the nature of animal interactions  [PDF]
Jonathan R. Potts,Karl Mokross,Mark A. Lewis
Quantitative Biology , 2014, DOI: 10.1098/rsif.2014.0333
Abstract: Collective phenomena, whereby agent-agent interactions determine spatial patterns, are ubiquitous in the animal kingdom. On the other hand, movement and space use are also greatly influenced by interactions between animals and their environment. Despite both types of interaction fundamentally influencing animal behaviour, there has hitherto been no unifying framework for the various models so far proposed. Here, we construct systems of coupled step selection functions, providing a general method for inferring population-level spatial patterns from underlying individual movement and interaction processes, a key ingredient in building a statistical mechanics for ecological systems. We show that resource selection functions, as well as several examples of collective motion models, arise as special cases of our framework, thus bringing together resource selection analysis and collective animal behaviour into a single theory. In particular, we focus on combining the various mechanistic models of territorial interactions in the literature with step selection functions, by incorporate interactions into the step selection framework and demonstrating how to derive territorial patterns from the resulting models. We demonstrate the efficacy of our model by application to a population of insectivore birds in the Amazon rainforest.
Objects and their computational framework  [PDF]
Viacheslav Wolfengagen
Computer Science , 2001,
Abstract: Most of the object notions are embedded into a logical domain, especially when dealing with a database theory. Thus, their properties within a computational domain are not yet studied properly. The main topic of this paper is to analyze different concepts of the distinct computational primitive frames to extract the useful object properties and their possible advantages. Some important metaoperators are used to unify the approaches and to establish their possible correspondences.
Framework flexibility and rational design of new zeolites for catalysis
Asel Sartbaeva,Stephen A. Wells
Applied Petrochemical Research , 2012, DOI: 10.1007/s13203-012-0017-3
Abstract: Zeolite materials have proved very useful as chemical catalysts and the search for new zeolite structures with novel channel and pore shapes is ongoing. We discuss a geometric feature of zeolite frameworks, the flexibility window, which may provide a criterion to identify hypothetical structures which can be synthesised as zeolites. In recent research using data on zeolite frameworks under compression, we show strong links between this geometric feature and the physics of zeolite frameworks.
A Unifying Framework for Structural Properties of CSPs: Definitions, Complexity, Tractability  [PDF]
Lucas Bordeaux,Marco Cadoli,Toni Mancini
Computer Science , 2014, DOI: 10.1613/jair.2538
Abstract: Literature on Constraint Satisfaction exhibits the definition of several structural properties that can be possessed by CSPs, like (in)consistency, substitutability or interchangeability. Current tools for constraint solving typically detect such properties efficiently by means of incomplete yet effective algorithms, and use them to reduce the search space and boost search. In this paper, we provide a unifying framework encompassing most of the properties known so far, both in CSP and other fields literature, and shed light on the semantical relationships among them. This gives a unified and comprehensive view of the topic, allows new, unknown, properties to emerge, and clarifies the computational complexity of the various detection problems. In particular, among the others, two new concepts, fixability and removability emerge, that come out to be the ideal characterisations of values that may be safely assigned or removed from a variables domain, while preserving problem satisfiability. These two notions subsume a large number of known properties, including inconsistency, substitutability and others. Because of the computational intractability of all the property-detection problems, by following the CSP approach we then determine a number of relaxations which provide sufficient conditions for their tractability. In particular, we exploit forms of language restrictions and local reasoning.
A unifying framework for $k$-statistics, polykays and their multivariate generalizations  [PDF]
Elvira Di Nardo,Giuseppe Guarino,Domenico Senato
Mathematics , 2006, DOI: 10.3150/07-BEJ6163
Abstract: Through the classical umbral calculus, we provide a unifying syntax for single and multivariate $k$-statistics, polykays and multivariate polykays. From a combinatorial point of view, we revisit the theory as exposed by Stuart and Ord, taking into account the Doubilet approach to symmetric functions. Moreover, by using exponential polynomials rather than set partitions, we provide a new formula for $k$-statistics that results in a very fast algorithm to generate such estimators.
A Unifying Framework to Characterize the Power of a Language to Express Relations  [PDF]
Paola Bonizzoni,Peter J. Cameron,Gianluca Della Vedova,Alberto Leporati,Giancarlo Mauri
Computer Science , 2012,
Abstract: In this extended abstract we provide a unifying framework that can be used to characterize and compare the expressive power of query languages for different data base models. The framework is based upon the new idea of valid partition, that is a partition of the elements of a given data base, where each class of the partition is composed by elements that cannot be separated (distinguished) according to some level of information contained in the data base. We describe two applications of this new framework, first by deriving a new syntactic characterization of the expressive power of relational algebra which is equivalent to the one given by Paredaens, and subsequently by studying the expressive power of a simple graph-based data model.
A computational framework for bioimaging simulation  [PDF]
Masaki Watabe,Satya N. V. Arjunan,Seiya Fukushima,Kazunari Iwamoto,Jun Kozuka,Satomi Matsuoka,Yuki Shindo,Masahiro Ueda,Koichi Takahashi
Quantitative Biology , 2014, DOI: 10.1371/journal.pone.0130089
Abstract: Using bioimaging technology, biologists have attempted to identify and document analytical interpretations that underlie biological phenomena in biological cells. Theoretical biology aims at distilling those interpretations into knowledge in the mathematical form of biochemical reaction networks and understanding how higher level functions emerge from the combined action of biomolecules. However, there still remain formidable challenges in bridging the gap between bioimaging and mathematical modeling. Generally, measurements using fluorescence microscopy systems are influenced by systematic effects that arise from stochastic nature of biological cells, the imaging apparatus, and optical physics. Such systematic effects are always present in all bioimaging systems and hinder quantitative comparison between the cell model and bioimages. Computational tools for such a comparison are still unavailable. Thus, in this work, we present a computational framework for handling the parameters of the cell models and the optical physics governing bioimaging systems. Simulation using this framework can generate digital images of cell simulation results after accounting for the systematic effects. We then demonstrate that such a framework enables comparison at the level of photon-counting units.
A constructive and unifying framework for zero-bit watermarking  [PDF]
Teddy Furon
Computer Science , 2006,
Abstract: In the watermark detection scenario, also known as zero-bit watermarking, a watermark, carrying no hidden message, is inserted in content. The watermark detector checks for the presence of this particular weak signal in content. The article looks at this problem from a classical detection theory point of view, but with side information enabled at the embedding side. This means that the watermark signal is a function of the host content. Our study is twofold. The first step is to design the best embedding function for a given detection function, and the best detection function for a given embedding function. This yields two conditions, which are mixed into one `fundamental' partial differential equation. It appears that many famous watermarking schemes are indeed solution to this `fundamental' equation. This study thus gives birth to a constructive framework unifying solutions, so far perceived as very different.
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