Convex equipartitions: the spicy chicken theorem

We show that, for any prime power $n$ and any convex body $K$ (i.e., a compact convex set with interior) in $\mathbb{R }^d$ , there exists a partition of $K$ into $n$ convex sets with equal volumes and equal surface areas. Similar results regarding equipartitions with respect to continuous functionals and absolutely continuous measures on convex bodies are also proven. These include a generalization of the ham-sandwich theorem to arbitrary number of convex pieces confirming a conjecture of Kaneko and Kano, a similar generalization of perfect partitions of a cake and its icing, and a generalization of the Gromov–Borsuk–Ulam theorem for convex sets in the model spaces of constant curvature.     

On D-posets of fuzzy sets

D-posets of fuzzy sets constitute a natural simple mathematical structure in which relevant notions of generalized probability theory can be formalized. We present a classification of D-posets leading to a hierarchy of distinguished subcategories of D-posets related to probability and study their relationships. This contributes to a better understanding of the transition from classical probability theory to fuzzy probability theory. In particular, we describe the transition from the Boolean cogenerator {0, 1} to the fuzzy cogenerator [0, 1] and prove that the generated ?ukasiewicz tribes form an epireflective subcategory of the bold algebras.     

Weber and Beltrami integrals of squared spherical Bessel functions: finite series evaluation and high‐index asymptotics

Weber integrals and Beltrami integrals are studied, which arise in the multipole expansions of spherical random fields. These integrals define spectral averages of squared spherical Bessel functions with Gaussian or exponentially cut power‐law densities. Finite series representations of the integrals are derived for integer power‐law index μ, which admit high‐precision evaluation at low and moderate Bessel index n. At high n, numerically tractable uniform asymptotic approximations are obtained on the basis of the Debye expansion of modified spherical Bessel functions in the case of Weber integrals. The high‐n approximation of Beltrami integrals can be reduced to Legendre asymptotics. The Airy approximation of Weber and Beltrami integrals is derived as well, and numerical tests are performed over a wide range of Bessel indices by comparing the exact finite series expansions of the integrals with their high‐index asymptotics. Copyright © 2013 John Wiley & Sons, Ltd.     

Simulation and multicriteria optimization modeling approach for regional water restoration management

This paper presents a modeling framework that intends to select the optimal robust wastewater reclamation program of measures (PoM) to achieve the European Water Framework Directive (WFD) objectives in the inner Catalonia watersheds. The integrative methodological tool developed incorporates a water quality model to simulate the effects of the PoM used to reduce pollution pressures on the hydrologic network. A Multi-Objective Evolutionary Algorithm (MOEA) helps to identify efficient trade-offs between PoM cost and water quality. Interactive Decisions Map (IDM)—a multi-criteria visualization—based decision support tool is used to provide a clear idea of the trade-off between water status and the cost to achieve such situation. Lastly, a stochastic simulation model to analyze the sensitivity under varied environmental uncertainties is run. Moreover, the tool is oriented to guide water managers in their decision-making processes. Additionally, this paper analyzes the results of the application of the management tool in the inner Catalan watershed in order to perform the European WFD. This tool has had a key role in the design of part of the PoM which shall be implemented to achieve objectives of the WFD in 2015 in all the Catalan catchments.     

Fixed points of a mapping and Hyers–Ulam stability

We show that many general results on Hyers–Ulam stability of some functional equations in a single variable follow immediately from a simple fixed point theorem. The theorem is formulated for self-maps of some subsets of the space of functions from a nonempty set into the set of reals. We also give some applications of that theorem, e.g., in investigations of solutions of some difference equations and functional inequalities.     

Estimates for the Derivatives of the Poisson Kernel on Nilpotent Meta-Abelian Groups

Let S be a semi direct product \(S=N\rtimes A\) where N is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and A is isomorphic with ? ^k , k?>?1. We consider a class of second order left-invariant differential operators on S of the form \(\mathcal{L}_\alpha=L^a+\Delta_\alpha,\) where α?∈?? ^k , and for each a?∈?? ^k , L ^a is left-invariant second order differential operator on N and \(\Delta_\alpha=\Delta-\langle\alpha,\nabla\rangle,\) where Δ is the usual Laplacian on ? ^k . Using some probabilistic techniques (skew-product formulas for diffusions on S and N respectively, the concept of the derivative of a measure, etc.) we obtain an upper bound for the derivatives of the Poisson kernel for \(\mathcal{L}_\alpha.\) During the course of the proof we also get an upper estimate for the derivatives of the transition probabilities of the evolution on N generated by L ^σ(t), where σ is a continuous function from [0,?∞?) to ? ^k .     

Support vector machine regression (SVR/LS-SVM)--an alternative to neural networks (ANN) for analytical chemistry? Comparison of nonlinear methods on near infrared (NIR) spectroscopy data

In this study, we make a general comparison of the accuracy and robustness of five multivariate calibration models: partial least squares (PLS) regression or projection to latent structures, polynomial partial least squares (Poly-PLS) regression, artificial neural networks (ANNs), and two novel techniques based on support vector machines (SVMs) for multivariate data analysis: support vector regression (SVR) and least-squares support vector machines (LS-SVMs). The comparison is based on fourteen (14) different datasets: seven sets of gasoline data (density, benzene content, and fractional composition/boiling points), two sets of ethanol gasoline fuel data (density and ethanol content), one set of diesel fuel data (total sulfur content), three sets of petroleum (crude oil) macromolecules data (weight percentages of asphaltenes, resins, and paraffins), and one set of petroleum resins data (resins content). Vibrational (near-infrared, NIR) spectroscopic data are used to predict the properties and quality coefficients of gasoline, biofuel/biodiesel, diesel fuel, and other samples of interest. The four systems presented here range greatly in composition, properties, strength of intermolecular interactions (e.g., van der Waals forces, H-bonds), colloid structure, and phase behavior. Due to the high diversity of chemical systems studied, general conclusions about SVM regression methods can be made. We try to answer the following question: to what extent can SVM-based techniques replace ANN-based approaches in real-world (industrial/scientific) applications? The results show that both SVR and LS-SVM methods are comparable to ANNs in accuracy. Due to the much higher robustness of the former, the SVM-based approaches are recommended for practical (industrial) application. This has been shown to be especially true for complicated, highly nonlinear objects.     

Optimization of immunoaffinity enrichment and detection: toward a comprehensive characterization of the phosphotyrosine proteome of K562 cells by liquid chromatography-mass spectrometry

Phosphorylation of protein tyrosine residues regulates many cell functions and has also been proved to be involved in oncogenesis. Thus, the identification of the phosphotyrosine (pTyr) proteome of cells is a very important task. Since tyrosine phosphorylation represents only around 1% of the total human phosphoproteome, the study of pTyr proteins is rather challenging. Here we report the optimization study of the phosphotyrosine proteome using K562 cells as a model system. A substantial segment of the phosphotyrosine proteome of K562 cells was characterized by immunoaffinity enrichment with 4G10 and PYKD1 antibodies followed by LC-MS/MS analysis. 480 non-redundant pTyr peptides corresponding to 342 pTyr proteins were found. 141 pTyr peptides were not described elsewhere. The mass spectrometry approach involving high-resolving FTMS analysis of precursor ions and subsequent detection of CID fragments in a linear ion trap was considered as optimal. For detection of low abundant pTyr peptides pooling of individual immunoaffinity enrichments for one LC-MS/MS analysis was crucial. The enrichment properties of the monoclonal PYKD1 antibody were presented for the first time, also in comparison to the 4G10 antibody. PYKD1 was found to be more effective for protein enrichment (1.2 and 5% efficiency at peptide and protein level correspondingly), while 4G10 showed better results when peptide enrichment was performed (15% efficiency versus 3.6% at protein level). Substantially different subsets of the phosphoproteome were enriched by these antibodies. This finding together with previous studies demonstrates that comprehensive pTyr proteome characterization by immunoprecipitation requires multiple antibodies to be used for the affinity enrichment.     

Variable selection in near-infrared spectroscopy: benchmarking of feature selection methods on biodiesel data

In the present work, microwave heating initiated precipitation polymerization was developed to prepare podophyllotoxin (PPT) molecularly imprinted polymers (MIPs), resulting in much shorter polymerization time and better particle morphology. Prior to the polymerization, ultraviolet and FTIR spectroscopy were used to study the interactions between PPT and the functional monomers. The synthesized parameters were respectively optimized and the optimal conditions for the efficient adsorption property were template: PPT, 1 mmol; functional monomer: acrylamide, 6 mmol; bi-crosslinker: ethylene glycol dimethacrylate, 20 mmol and divinylbenzene, 20 mmol; porogen: acetonitrile, 40 mL; initiator: azobisisobutyronitrile, 0.01mol L?1; polymerization temperature: 60°C. FTIR spectroscopy, SEM and thermal analysis were used to characterize the MIPs. The results of the equilibrium rebinding experiments and the competitive adsorption experiments showed that these imprinted polymers exhibited good adsorption ability for the PPT. Scatchard analysis illustrated that two and one types of binding sites were generated in the MIPs and non-imprinted polymers (NIPs), respectively. Using the prepared MIPs as the solid phase extraction (SPE) sorbent, PPT was extracted selectively and efficiently from Dysosma versipellis, Sinopodophyllum hexandrum and Diphylleia sinensis. The regression equation was y=5.873×10?x+17075.659 with the correlation coefficient of 0.9994 in the concentration range of 0.005-0.4 mg mL?1. After washing and eluting the SPE column with methanol and MeOH/acetic acid solution (v/v, 9:1), the limits of detection were 0.12-0.18 μg mL?1 and their recoveries were in the range of 89.5-91.1% with all RSDs lower than 3.7.     

The S1/S2 exciton interaction in 2-pyridone·6-methyl-2-pyridone: Davydov splitting, vibronic coupling, and vibronic quenching

The excitonic splitting between the S(1) and S(2) electronic states of the doubly hydrogen-bonded dimer 2-pyridone[middle dot]6-methyl-2-pyridone (2PY·6M2PY) is studied in a supersonic jet, applying two-color resonant two-photon ionization (2C-R2PI), UV-UV depletion, and dispersed fluorescence spectroscopies. In contrast to the C(2h) symmetric (2-pyridone)(2) homodimer, in which the S(1) ← S(0) transition is symmetry-forbidden but the S(2) ← S(0) transition is allowed, the symmetry-breaking by the additional methyl group in 2PY·6M2PY leads to the appearance of both the S(1) and S(2) origins, which are separated by Δ(exp) = 154 cm(-1). When combined with the separation of the S(1) ← S(0) excitations of 6M2PY and 2PY, which is δ = 102 cm(-1), one obtains an S(1)/S(2) exciton coupling matrix element of V(AB, el) = 57 cm(-1) in a Frenkel-Davydov exciton model. The vibronic couplings in the S(1)/S(2) ← S(0) spectrum of 2PY·6M2PY are treated by the Fulton-Gouterman single-mode model. We consider independent couplings to the intramolecular 6a(') vibration and to the intermolecular σ(') stretch, and obtain a semi-quantitative fit to the observed spectrum. The dimensionless excitonic couplings are C(6a(')) = 0.15 and C(σ(')) = 0.05, which places this dimer in the weak-coupling limit. However, the S(1)/S(2) state exciton splittings Δ(calc) calculated by the configuration interaction singles method (CIS), time-dependent Hartree-Fock (TD-HF), and approximate second-order coupled-cluster method (CC2) are between 1100 and 1450 cm(-1), or seven to nine times larger than observed. These huge errors result from the neglect of the coupling to the optically active intra- and intermolecular vibrations of the dimer, which lead to vibronic quenching of the purely electronic excitonic splitting. For 2PY·6M2PY the electronic splitting is quenched by a factor of ~30 (i.e., the vibronic quenching factor is Γ(exp) = 0.035), which brings the calculated splittings into close agreement with the experimentally observed value. The 2C-R2PI and fluorescence spectra of the tautomeric species 2-hydroxypyridine·6-methyl-2-pyridone (2HP·6M2PY) are also observed and assigned.