Approximate factorization constraint preconditioners for saddle-point matrices

We consider the application of the conjugate gradient method to the solution of large, symmetric indefinite linear systems. Special emphasis is put on the use of constraint preconditioners and a new factorization that can reduce the number of flops required by the preconditioning step. Results concerning the eigenvalues of the preconditioned matrix and its minimum polynomial are given. Numerical experiments validate these conclusions.

Life-history evolution under a production constraint

The recently formulated metabolic theory of ecology has profound implications for the evolution of life histories. Metabolic rate constrains the scaling of production with body mass, so that larger organisms have lower rates of production on a mass-specific basis than smaller ones. Here, we explore the implications of this constraint for life-history evolution. We show that for a range of very simple life histories, Darwinian fitness is equal to birth rate minus death rate. So, natural selection maximizes birth and production rates and minimizes death rates. This implies that decreased body size will generally be favored because it increases production, so long as mortality is unaffected. Alternatively, increased body size will be favored only if it decreases mortality or enhances reproductive success sufficiently to override the preexisting production constraint. Adaptations that may favor evolution of larger size include niche shifts that decrease mortality by escaping predation or that increase fecundity by exploiting new abundant food sources. These principles can be generalized to better understand the intimate relationship between the genetic currency of evolution and the metabolic currency of ecology.

Temperature and the development rates of thrips: evidence for a constraint on local adaptation?

Typically, the relationship between insect development and temperature is described by two characteristics: the minimum temperature needed for development to occur (T-min) and the number of day degrees required (DDR) for the completion of development. We investigated these characteristics in three English populations of Thrips major and T tabaci [Cawood, Yorkshire (N53degrees49', W1degrees7'); Boxworth, Cambridgeshire (N52degrees15', W0degrees1'); Silwood Park, Berkshire (N51degrees24', W0degrees38')], and two populations of Frankliniella occidentalis (Cawood; Silwood Park). While there were no significant differences among populations in either T-min (mean for T major = 7.0degreesC; T tabaci = 5.9degreesC; F. occidentalis = 6.7degreesC) or DDR (mean for T major = 229.9; T tabaci = 260.8; F occidentalis = 233.4), there were significant differences in the relationship between temperature and body size, suggesting the presence of geographic variation in this trait. Using published data, in addition to those newly collected, we found a negative relationship between T-min. and DDR for F occidentalis and T tabaci, supporting the hypothesis that a trade-off between T-min and DDR may constrain adaptation to local climatic conditions.

Sparse kernel density estimation technique based on zero-norm constraint

A sparse kernel density estimator is derived based on the zero-norm constraint, in which the zero-norm of the kernel weights is incorporated to enhance model sparsity. The classical Parzen window estimate is adopted as the desired response for density estimation, and an approximate function of the zero-norm is used for achieving mathemtical tractability and algorithmic efficiency. Under the mild condition of the positive definite design matrix, the kernel weights of the proposed density estimator based on the zero-norm approximation can be obtained using the multiplicative nonnegative quadratic programming algorithm. Using the -optimality based selection algorithm as the preprocessing to select a small significant subset design matrix, the proposed zero-norm based approach offers an effective means for constructing very sparse kernel density estimates with excellent generalisation performance.

Constraint release in entangled binary blends of linear polymers: a molecular dynamics study

We present extensive molecular dynamics simulations of the dynamics of diluted long probe chains entangled with a matrix of shorter chains. The chain lengths of both components are above the entanglement strand length, and the ratio of their lengths is varied over a wide range to cover the crossover from the chain reptation regime to tube Rouse motion regime of the long probe chains. Reducing the matrix chain length results in a faster decay of the dynamic structure factor of the probe chains, in good agreement with recent neutron spin echo experiments. The diffusion of the long chains, measured by the mean square displacements of the monomers and the centers of mass of the chains, demonstrates a systematic speed-up relative to the pure reptation behavior expected for monodisperse melts of sufficiently long polymers. On the other hand, the diffusion of the matrix chains is only weakly perturbed by the diluted long probe chains. The simulation results are qualitatively consistent with the theoretical predictions based on constraint release Rouse model, but a detailed comparison reveals the existence of a broad distribution of the disentanglement rates, which is partly confirmed by an analysis of the packing and diffusion of the matrix chains in the tube region of the probe chains. A coarse-grained simulation model based on the tube Rouse motion model with incorporation of the probability distribution of the tube segment jump rates is developed and shows results qualitatively consistent with the fine scale molecular dynamics simulations. However, we observe a breakdown in the tube Rouse model when the short chain length is decreased to around N-S = 80, which is roughly 3.5 times the entanglement spacing N-e(P) = 23. The location of this transition may be sensitive to the chain bending potential used in our simulations.

Using zero-norm constraint for sparse probability density function estimation

A new sparse kernel probability density function (pdf) estimator based on zero-norm constraint is constructed using the classical Parzen window (PW) estimate as the target function. The so-called zero-norm of the parameters is used in order to achieve enhanced model sparsity, and it is suggested to minimize an approximate function of the zero-norm. It is shown that under certain condition, the kernel weights of the proposed pdf estimator based on the zero-norm approximation can be updated using the multiplicative nonnegative quadratic programming algorithm. Numerical examples are employed to demonstrate the efficacy of the proposed approach.

Why was urban overcrowding much more severe in Scotland than in the rest of the British Isles? Evidence from the first (1904) official household expenditure survey

This article presents an analysis of British urban working-class housing conditions in 1904, using a rediscovered survey. We investigate overcrowding and find major regional differences. Scottish households in the survey were more overcrowded despite being less poor. Investigating the causes of this overcrowding, we find little support for supply-side theories or for the idea that the Scottish households in our survey experienced particularly great variations in income, causing them to commit to overly modest accommodation. We present evidence that is consistent with idea that particularly tough Scottish tenancy and local tax laws caused excess overcrowding. We also provide evidence that Scottish workers had a relatively high preference for food, rather than housing, expenditure, which can be at least partly attributed to their inheritance of more communal patterns of urban living.

Scope and constraint in the diagnosis of cluttering: combining two perspectives

A chapter outlining a theoretical position on the definition of the speech language disorder, cluttering.

Rental depreciation and capital expenditure in the UK commercial real estate market, 1993–2009

This paper identifies the long-term rental depreciation rates for UK commercial properties and rates of capital expenditure incurred to offset depreciation over the same period. It starts by reviewing the economic depreciation literature and the rationale for adopting a longitudinal method of measurement, before discussing the data used and results. Data from 1993 to 2009 were sourced from Investment Property Databank and CB Richard Ellis real estate consultants. This is used to compare the change in values of new buildings in different locations with the change in values of individual properties in those locations. The analysis is conducted using observations on 742 assets drawn from all major segments of the commercial real estate market. Overall rental depreciation and capital expenditure rates are similar to those in other recent UK studies. Depreciation rates are 0.8% pa for offices, 0.5% pa for industrial properties and 0.3% pa for standard retail properties. These results hide interesting variations at a segment level, notably in retail where location often dominates value rather than the building. The majority of properties had little (if any) money spent on them over the last 16 years, but those subject to higher rates of expenditure were found to have lower depreciation rates.