139 research outputs found
A Weighted Correlation Index for Rankings with Ties
Understanding the correlation between two different scores for the same set
of items is a common problem in information retrieval, and the most commonly
used statistics that quantifies this correlation is Kendall's . However,
the standard definition fails to capture that discordances between items with
high rank are more important than those between items with low rank. Recently,
a new measure of correlation based on average precision has been proposed to
solve this problem, but like many alternative proposals in the literature it
assumes that there are no ties in the scores. This is a major deficiency in a
number of contexts, and in particular while comparing centrality scores on
large graphs, as the obvious baseline, indegree, has a very large number of
ties in web and social graphs. We propose to extend Kendall's definition in a
natural way to take into account weights in the presence of ties. We prove a
number of interesting mathematical properties of our generalization and
describe an algorithm for its computation. We also validate the
usefulness of our weighted measure of correlation using experimental data
Excessive functions of continuous time Markov chains
AbstractWe consider transient continuous time Markov chains P(t) with PâČij(0)=qiÎ ij for iâ j and âqi for i=j. We assume 0<qi<â for all i. Then 1/qi is the mean time the process remains in state i, and Î is the transition matrix of the imbedded jump process. We let q be a diagonal matrix with diagonal entries qi.A non-negative function h is P(t)-excessive (invariant) if hâ„P(t)h, (h=P(t) h) for all t. It is Î -superregular (regular) if hâ„Î h (h=Î h). Our main results characterize the excessive functions of the minimal process in terms of q and Î . These results can also be used to characterize excessive functions of certain non-minimal processes
A Place Apart
The inaugural address pf Henry J. Copeland. 9th President of the College of Wooster. The program also includes an inaugural letter by John G. Kemeny, the President of Dartmouth Collegehttps://openworks.wooster.edu/presidents/1035/thumbnail.jp
Synchronous vs. asynchronous dynamics of diffusion-controlled reactions
An analytical method based on the classical ruin problem is developed to
compute the mean reaction time between two walkers undergoing a generalized
random walk on a 1d lattice. At each time step, either both walkers diffuse
simultaneously with probability (synchronous event) or one of them diffuses
while the other remains immobile with complementary probability (asynchronous
event). Reaction takes place through same site occupation or position exchange.
We study the influence of the degree of synchronicity of the walkers and
the lattice size on the global reaction's efficiency. For odd , the
purely synchronous case () is always the most effective one, while for
even , the encounter time is minimized by a combination of synchronous and
asynchronous events. This new parity effect is fully confirmed by Monte Carlo
simulations on 1d lattices as well as for 2d and 3d lattices. In contrast, the
1d continuum approximation valid for sufficiently large lattices predicts a
monotonic increase of the efficiency as a function of . The relevance of the
model for several research areas is briefly discussed.Comment: 21 pages (including 12 figures and 4 tables), uses revtex4.cls,
accepted for publication in Physica
Evolution Equation of Phenotype Distribution: General Formulation and Application to Error Catastrophe
An equation describing the evolution of phenotypic distribution is derived
using methods developed in statistical physics. The equation is solved by using
the singular perturbation method, and assuming that the number of bases in the
genetic sequence is large. Applying the equation to the mutation-selection
model by Eigen provides the critical mutation rate for the error catastrophe.
Phenotypic fluctuation of clones (individuals sharing the same gene) is
introduced into this evolution equation. With this formalism, it is found that
the critical mutation rate is sometimes increased by the phenotypic
fluctuations, i.e., noise can enhance robustness of a fitted state to mutation.
Our formalism is systematic and general, while approximations to derive more
tractable evolution equations are also discussed.Comment: 22 pages, 2 figure
Lumpability Abstractions of Rule-based Systems
The induction of a signaling pathway is characterized by transient complex
formation and mutual posttranslational modification of proteins. To faithfully
capture this combinatorial process in a mathematical model is an important
challenge in systems biology. Exploiting the limited context on which most
binding and modification events are conditioned, attempts have been made to
reduce the combinatorial complexity by quotienting the reachable set of
molecular species, into species aggregates while preserving the deterministic
semantics of the thermodynamic limit. Recently we proposed a quotienting that
also preserves the stochastic semantics and that is complete in the sense that
the semantics of individual species can be recovered from the aggregate
semantics. In this paper we prove that this quotienting yields a sufficient
condition for weak lumpability and that it gives rise to a backward Markov
bisimulation between the original and aggregated transition system. We
illustrate the framework on a case study of the EGF/insulin receptor crosstalk.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005
Randomised Phase I/II trial assessing the safety and efficacy of radiolabelled anti-carcinoembryonic antigen I131 KAb201 antibodies given intra-arterially or intravenously in patients with unresectable pancreatic adenocarcinoma
Understanding changing housing aspirations: A review of the evidence
This article reviews the literature on changing housing aspirations and expectations in contemporary housing systems. It argues that there is a conceptual and definitional gap in relation to the term âhousing aspirationsâ, as distinct from expectations, preferences, choices and needs. The article sets out working definitions of these terms, before discussing the evidence on changing housing (and related) systems. Emerging research has begun to consider whether trends such as declining homeownership, affordability concerns and precarious labour systems across a range of countries are fundamentally changing individualsâ aspirations for the forms of housing they aim to access at different stages of their lives. Whilst much of the research into housing aspirations has been considered in terms of tenure, and homeownership in particular, this article suggests that research needs to move beyond tenure and choice frameworks, to consider the range of dimensions that shape aspirations, from the political economy and the State to socialization and individualsâ dispositions for housing
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