On the Stable Paths Problem and a Restricted Variant

Interdomain routing on the Internet is performed using route preference policies specified independently, and arbitrarily by each Autonomous System in the network. These policies are used in the border gateway protocol (BGP) by each AS when selecting next-hop choices for routes to each destination. Conflicts between policies used by different ASs can lead to routing instabilities that, potentially, cannot be resolved no matter how long BGP is run. The Stable Paths Problem (SPP) is an abstract graph theoretic model of the problem of selecting nexthop routes for a destination. A stable solution to the problem is a set of next-hop choices, one for each AS, that is compatible with the policies of each AS. In a stable solution each AS has selected its best next-hop given that the next-hop choices of all neighbors are fixed. BGP can be viewed as a distributed algorithm for solving SPP. In this report we consider the stable paths problem, as well as a family of restricted variants of the stable paths problem, which we call F stable paths problems. We show that two very simple variants of the stable paths problem are also NP-complete. In addition we show that for networks with a DAG topology, there is an efficient centralized algorithm to solve the stable paths problem, and that BGP always efficiently converges to a stable solution on such networks.

Orientational Harmonic Model for Rotation, Translation, and Scale Invariant Pattern Representation in Biological Vision

An extension to the orientational harmonic model is presented as a rotation, translation, and scale invariant representation of geometrical form in biological vision.

Orientational Harmonic Model for Rotation, Translation, and Scale Invariant Pattern Representation in Biological Vision

The proposed model, called the combinatorial and competitive spatio-temporal memory or CCSTM, provides an elegant solution to the general problem of having to store and recall spatio-temporal patterns in which states or sequences of states can recur in various contexts. For example, fig. 1 shows two state sequences that have a common subsequence, C and D. The CCSTM assumes that any state has a distributed representation as a collection of features. Each feature has an associated competitive module (CM) containing K cells. On any given occurrence of a particular feature, A, exactly one of the cells in CMA will be chosen to represent it. It is the particular set of cells active on the previous time step that determines which cells are chosen to represent instances of their associated features on the current time step. If we assume that typically S features are active in any state then any state has K^S different neural representations. This huge space of possible neural representations of any state is what underlies the model's ability to store and recall numerous context-sensitive state sequences. The purpose of this paper is simply to describe this mechanism.

Synthetic and stereochemical aspects of intramolecular reactions of α-diazoketones catalysed by rhodium(II) carboxylates

Chapter 1 of this thesis is a brief introduction to the preparation and reactions of α-diazocarbonyl compounds, with particular emphasis on the areas relating to the research undertaken: C-H insertion, addition to aromatics, and oxonium ylide generation and rearrangement. A short summary of catalyst development illustrates the importance of rhodium(II)carboxylates for α-diazocarbonyl decomposition. Chapter 2 describes intramolecular C-H insertion reactions of α-diazo-β-keto sulphones to form substituted cyclopentanones. Rhodium(II) carboxylates derived from homochiral carboxylic acids were used as catalysts in these reactions and enantioselection achieved through their use is discussed. Chapter 3 describes intramolecular Buchner cyclisation of aryl diazoketones with emphasis on the stereochemical aspects of the cyclisation and subsequent reaction of the bicyclo[5.3.0]decatrienones produced. The partial asymmetric synthesis achieved through use of chiral rhodium(II) carboxylates as catalysts is discussed. The application of the intramolecular Buchner reaction to the synthesis of hydroazulene lactones is illustrated. Chapter 4 demonstrates oxonium ylide formation and rearrangement in the decomposition of an α-diazoketone. The consequences of the use of chiral rhodium(II) carboxylates as catalysts are described. Particularly significant was the discovery that rhodium(II) (S)-mandelate acts as a very efficient catalyst for α-diazoketone decompositions, in general. Moderate asymmetric induction was possible in the decomposition of α-diazoketones with chiral rhodium(II) carboxylates, with rhodium(II) (S)-mandelate being one of the more enantioselective catalysts investigated. However, the asymmetric induction obtained was very dependent on the exact structure of the α-diazoketone, the catalyst, and the nature of the reaction. Chapter 5 contains the experimental details, and the spectral and analytical data for all new compounds reported.

Catalyst, additive and substrate effects in intramolecular aromatic additions of alpha-diazoketones

This thesis is focused on transition metal catalysed reaction of α-diazoketones leading to aromatic addition to form azulenones, with particular emphasis on enantiocontrol through use of chiral copper catalysts. The first chapter provides an overview of the influence of variation of the substituent at the diazo carbon on the outcome of subsequent reaction pathways, focusing in particular on C-H insertion, cyclopropanation, aromatic addition and ylide formation drawing together for the first time input from a range of primary reports. Chapter two describes the synthesis of a range of novel α-diazoketones. Rhodium and copper catalysed cyclisation of these to form a range of azulenones is described. Variation of the transition metal catalyst was undertaken using both copper and rhodium based systems and ligand variation, including the design and synthesis of a novel bisoxazoline ligand. The influence of additives, especially NaBARF, on the enantiocontrol was explored in detail and displayed an interesting impact which was sensitive to substituent effects. Further exploration demonstrated that it is the sodium cation which is critical in the additive effects. For the first time, enantiocontrol in the aromatic addition of terminal diazoketones was demonstrated indicating enantiofacial control in the aromatic addition is feasible in the absence of a bridgehead substituent. Determination of the enantiopurity in these compounds was particularly challenging due to the lability of the products. A substantial portion of the work was focused on determining the stereochemical outcome of the aromatic addition processes, both the absolute stereochemistry and extent of enantiopurity. Formation of PTAD adducts was beneficial in this regard. The third chapter contains the full experimental details and spectral characterisation of all novel compounds synthesised in this project, while details of chiral stationary phase HPLC and 1H NMR analysis are included in the appendix.

Vibration-rotation pattern in acetylene. II. Introduction of Coriolis coupling in the global model and analysis of emission spectra of hot acetylene around 3 microns

This paper was selected by the editors of the Journal of Chemical Physics as one of the few of the many notable JCP articles published in 2009 that present ground-breaking research

Vibration-rotation pattern in acetylene: Introduction of Coriolis coupling in the global model and analysis of emission spectra of hot acetylene around 3 µm

info:eu-repo/semantics/nonPublished

Soybean - Corn rotation : efect of the stubble mineralization on the nitrates production and corn yield

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Soybean - Corn rotation : efect of the stubble mineralization on the nitrates production and corn yield

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