Search results for "Partition"

Probabilistic squares and hexagons of opposition under coherence

2017

Various semantics for studying the square of opposition and the hexagon of opposition have been proposed recently. We interpret sentences by imprecise (set-valued) probability assessments on a finite sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square and of the hexagon in terms of acceptability. Then, we show how to construct probabilistic versions of the square and of the hexagon of opposition by forming suitable tripartitions of the set of all coherent assessments on a finite sequence of conditional events. Finally, as an application, we present new versions of the square and of the…

Mapping of subsurface shell midden components through percussion coring: examples from the Dundas Islands

2009

Following earlier examples of mapping the subsurface of shell bearing sites using augering, we employ percussion coring to identify early Holocene shell midden components at two types of sites on the Northwest Coast of North America. We describe a method for mapping subsurface components at shell bearing sites including basal deposits, paleosols and transitions between distinct cultural components. Our research was undertaken for the purpose of identifying early Holocene shell middens above the modern shore, and as components below large shell midden villages. Our results augment the developmental trajectory of shell middens on the Northwest Coast by suggesting that pre-5000 BP forms of the…

Smooth Feshbach map and operator-theoretic renormalization group methods

2003

Abstract A new variant of the isospectral Feshbach map defined on operators in Hilbert space is presented. It is constructed with the help of a smooth partition of unity, instead of projections, and is therefore called smooth Feshbach map . It is an effective tool in spectral and singular perturbation theory. As an illustration of its power, a novel operator-theoretic renormalization group method is described and applied to analyze a general class of Hamiltonians on Fock space. The main advantage of the new renormalization group method over its predecessors is its technical simplicity, which it owes to the use of the smooth Feshbach map.

Equilibrium between Hydroxycycloalkanones and Oxabicycloalkanols

2009

Guido Kramer, Annette Oehlhof, and Herbert Meier Institute of Organic Chemistry, University of Mainz, Duesbergweg 10 – 14, 55099 Mainz, Germany Reprint requests to Prof. Dr. H. Meier. Fax: +49-(0)6131-3925396. E-mail: hmeier@mail.uni-mainz.de Z. Naturforsch. 2009, 64b, 847 – 850; received April 8, 2009 Hydroxycycloalkanones 1 of medium ring size (8 – 10) exist in a transannular tautomeric equilibrium with the corresponding oxabicycloalkan-1-ols 2, which represent hemiacetals. Normally, the bicyclic structures 2 predominate in solution although their portion decreases with increasing solvent polarity. A correlation of the Gibbs reaction enthalpies ∆G (1→2) with the solvent parameters ET (30)…

Role of Wood Macromolecules on Selective Sorption of Phenolic Compounds by Wood

2008

Wood is a complex structure of various macromolecules, mainly cellulose, hemicellulose, and lignin. Although the sorption process of some organic compounds by wood has been elucidated, the relative contribution of its different fractions in the sorption mechanism is not clearly determined. Certain works predict the amount of organic compounds sorbed on wood as a direct relationship to its lignin fraction. All wood macromolecules, however, seem to have the capacity to sorb organic compounds. Sorption of phenolic compounds on individual wood macromolecules has been studied and compared to that on wood. Wood-water partition coefficients ( K wood) for phenolic volatiles and their sorption rates…

A fast and recursive algorithm for clustering large datasets with k-medians

2012

Clustering with fast algorithms large samples of high dimensional data is an important challenge in computational statistics. Borrowing ideas from MacQueen (1967) who introduced a sequential version of the $k$-means algorithm, a new class of recursive stochastic gradient algorithms designed for the $k$-medians loss criterion is proposed. By their recursive nature, these algorithms are very fast and are well adapted to deal with large samples of data that are allowed to arrive sequentially. It is proved that the stochastic gradient algorithm converges almost surely to the set of stationary points of the underlying loss criterion. A particular attention is paid to the averaged versions, which…

Erratum: Partition function of the trigonometric SOS model with reflecting end

2010

Comparative Evaluation of Community Detection Algorithms: A Topological Approach

2012

International audience; Community detection is one of the most active fields in complex networks analysis, due to its potential value in practical applications. Many works inspired by different paradigms are devoted to the development of algorithmic solutions allowing to reveal the network structure in such cohesive subgroups. Comparative studies reported in the literature usually rely on a performance measure considering the community structure as a partition (Rand Index, Normalized Mutual information, etc.). However, this type of comparison neglects the topological properties of the communities. In this article, we present a comprehensive comparative study of a representative set of commu…

Statistically validated hierarchical clustering: Nested partitions in hierarchical trees

2022

We develop an algorithm that is fast and scalable in the detection of a nested partition extracted from a dendrogram that is obtained from hierarchical clustering of a multivariate series. Our algorithm provides a -value for each clade observed in the hierarchical tree. The -value is obtained by computing many bootstrap replicas of the dissimilarity matrix and by performing a statistical test on each difference between the dissimilarity associated with a given clade and the dissimilarity of the clade of its parent node. We prove the efficacy of our algorithm with a set of benchmarks generated by a hierarchically nested factor model. We compare results obtained by our algorithm with those of…

Partition function of the trigonometric SOS model with reflecting end

2010

We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of a sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms.