Model selection by sequentially normalized least squares

Model selection by means of the predictive least squares (PLS) principle has been thoroughly studied in the context of regression model selection and autoregressive (AR) model order estimation. We introduce a new criterion based on sequentially minimized squared deviations, which are smaller than both the usual least squares and the squared prediction errors used in PLS. We also prove that our criterion has a probabilistic interpretation as a model which is asymptotically optimal within the given class of distributions by reaching the lower bound on the logarithmic prediction errors, given by the so called stochastic complexity, and approximated by BIC. This holds when the regressor (design) matrix is non-random or determined by the observed data as in AR models. The advantages of the criterion include the fact that it can be evaluated efficiently and exactly, without asymptotic approximations, and importantly, there are no adjustable hyper-parameters, which makes it applicable to both small and large amounts of data.     

Cholesterol supports headgroup superlattice domain formation in fluid phospholipid/cholesterol bilayers

Fluorescence and Fourier transform infrared (FTIR) spectroscopic techniques were used to explore the effect of added cholesterol on the composition-dependent formation of putative phospholipid headgroup superlattices in fluid 1-palmitoyl-2-oleoyl-phosphatidylethanolamine/1-palmitoyl-2-oleoyl-phosphatidylcholine/cholesterol (POPE/POPC/CHOL) bilayers. Steady-state fluorescence anisotropy measurements of diphenylhexatriene (DPH) chain-labeled phosphatidylcholine (DPH-PC) revealed significant dips at several POPE-to-phospholipid mole fractions (X(PE)'s) when the cholesterol-to-lipid mole fraction (X(CHOL)) was fixed at 0.00, 0.35, 0.40, and 0.50. Most of the observed dips occur at or close to critical X(PE)'s predicted by the Headgroup Superlattice (SL) model, suggesting that phospholipid headgroups of different structures tend to adopt regular distributions even in the presence of cholesterol. Time-resolved fluorescence anisotropy measurements revealed that DPH-PC senses a disordered and highly mobile microenvironment in the POPE/POPC/CHOL bilayers at those critical X(PE)'s, indicating that this probe may partition to defect regions in the bilayers. The presence of coexisting packing defect regions and regularly distributed SL domains is a key feature predicted by the Headgroup SL model. Importantly, probe-free FTIR measurements of acyl chain C-H, interfacial carbonyl, and headgroup phosphate stretching peak frequencies revealed the presence of abrupt changes at X(PE)'s close to those observed in the fluorescence data. When X(PE) was varied from 0.60 to 0.72 and X(CHOL) from 0.34 to 0.46, a clear dip at the lipid composition coordinates (X(PE), X(CHOL)) approximately (0.68, 0.40) was observed in the three-dimensional surface plots of DPH-PC anisotropy as well as the carbonyl and phosphate stretching frequencies. The critical X(CHOL) at 0.40 agrees with the Cholesterol SL model, which assumes that cholesterol and phospholipid form SL domains at the lipid acyl chain level. In conclusion, this study provides evidence that cholesterol supports formation of phospholipid headgroup SLs in fluid state ternary lipid bilayers. The feasibility of the parallel existence of SLs at the lipid headgroup and acyl chain levels supports the relevance of the lipid SL model for the membranes of eukaryotic cells that typically contain significant amounts of cholesterol. We speculate that lipid SL formation may play a central role in the regulation of membrane lipid compositions, maintenance of organelle boundaries, and other crucial phenomena in those cells.     

Convergence theorems for HL integrable vector-valued functions with applications

In this paper we prove dominated and monotone convergence theorems for HL integrable Banach-valued functions. These results and a fixed point theorem in ordered spaces are then applied to prove existence and comparison results for integral equations of Fredholm type in ordered Banach spaces involving Kurzweil integrals or improper integrals. Results are used also to solve concrete second-order functional boundary value problems involving discontinuities and singularities.     

Solution of linear equations with Hankel and Toeplitz matrices

Summary An algorithm is described for solving a linear equationA x=c, whereA is ann×n Hankel or Toeplitz matrix, inO (n ²) arithmetic operations. As contrasted with earlier such algorithms the present one does not require the principal minors ofA to be non-zero except detA.