Unraveling Hidden Major Factors by Breaking Heterogeneity into Homogeneous Parts within Many-System Problems

For a large ensemble of complex systems, a Many-System Problem (MSP) studies how heterogeneity constrains and hides structural mechanisms, and how to uncover and reveal hidden major factors from homogeneous parts. All member systems in an MSP share common governing principles of dynamics, but differ in idiosyncratic characteristics. A typical dynamic is found underlying response features with respect to covariate features of quantitative or qualitative data types. Neither all-system-as-one-whole nor individual system-specific functional structures are assumed in such response-vs-covariate (Re–Co) dynamics. We developed a computational protocol for identifying various collections of major factors of various orders underlying Re–Co dynamics. We first demonstrate the immanent effects of heterogeneity among member systems, which constrain compositions of major factors and even hide essential ones. Secondly, we show that fuller collections of major factors are discovered by breaking heterogeneity into many homogeneous parts. This process further realizes Anderson’s “More is Different” phenomenon. We employ the categorical nature of all features and develop a Categorical Exploratory Data Analysis (CEDA)-based major factor selection protocol. Information theoretical measurements—conditional mutual information and entropy—are heavily used in two selection criteria: C1—confirmable and C2—irreplaceable. All conditional entropies are evaluated through contingency tables with algorithmically computed reliability against the finite sample phenomenon. We study one artificially designed MSP and then two real collectives of Major League Baseball (MLB) pitching dynamics with 62 slider pitchers and 199 fastball pitchers, respectively. Finally, our MSP data analyzing techniques are applied to resolve a scientific issue related to the Rosenberg Self-Esteem Scale.     

The solution for axisymmetrical shells with abrupt curvature change (corrugated shells) by the finite element method

It has been noted in the present paper that the finite element method using linear elements for solving axisymmetrical shells cannot be applied to the analysis of axisymmetrical shells with abrupt curvature change, owing to the fact that the influence of the curvature upon the angular displacements has been neglected. The present paper provides a finite element method using linear elements in which the influence of curvature is considered and the angular displacements are treated as continuous parameters. This method has been applied to the calculation of corrugated shells of the type C, and compared with the experimental results obtained by Turner-Ford as well as with the analytical solution given by Prof. Chien Wei-zang. The comparisons have been proved that this theory is correct.     

Light-emitting diodes based on poly(2,3-diphenyl-1,4-phenylene vinylene)

In this paper we report polymer light-emitting diodes based on (2,3-diphenyl-1,4-phenylene vinylene) (DP-PPV), a novel π-conjugated polymer made by using the chlorine precursor route (CPR). Thin films of the precursor polymer were formed by spin-casting on indium-tin oxide (ITO) coated glass substrates, followed by thermal conversion to give DP-PPV thin films. Single layer DP-PPV LEDs were completed by thermally evaporating magnesium (Mg) electrodes. The electroluminescent characteristics of ITO/DP-PPV/Mg devices as well as variations between precursor polymer batches are presented. Bilayer LEDs were also made, for which tris(8-hydroxyquinoline)aluminum (Alq₃) was thermally sublimed on the fully converted DP-PPV films in vacuum, followed by Mg deposition. Both significant improvement in the quantum efficiency (up to 0.7% ph/el) and a reduction in the turn-on voltage of the device were found upon incorporation of the Alq₃ layer. These observations suggest that Alq₃ enhances the injection of electrons and also participates in the recombination process. © 1997 John Wiley & Sons, Ltd.     

Categorical Nature of Major Factor Selection via Information Theoretic Measurements

Without assuming any functional or distributional structure, we select collections of major factors embedded within response-versus-covariate (Re-Co) dynamics via selection criteria [C1: confirmable] and [C2: irrepaceable], which are based on information theoretic measurements. The two criteria are constructed based on the computing paradigm called Categorical Exploratory Data Analysis (CEDA) and linked to Wiener–Granger causality. All the information theoretical measurements, including conditional mutual information and entropy, are evaluated through the contingency table platform, which primarily rests on the categorical nature within all involved features of any data types: quantitative or qualitative. Our selection task identifies one chief collection, together with several secondary collections of major factors of various orders underlying the targeted Re-Co dynamics. Each selected collection is checked with algorithmically computed reliability against the finite sample phenomenon, and so is each member’s major factor individually. The developments of our selection protocol are illustrated in detail through two experimental examples: a simple one and a complex one. We then apply this protocol on two data sets pertaining to two somewhat related but distinct pitching dynamics of two pitch types: slider and fastball. In particular, we refer to a specific Major League Baseball (MLB) pitcher and we consider data of multiple seasons.     

Static charged spheres with anisotropic pressure in general relativity

We report a generalization of our earlier formalism [Pramana, 54, 663 (1998)] to obtain exact solutions of Einstein-Maxwell’s equations for static spheres filled with a charged fluid having anisotropic pressure and of null conductivity. Defining new variables: w=(4π/3)(ρ+ε)r ², u=4πξr ², v _r=4πp _r r ², v _⊥=4πp _⊥ r ²[ρ, ξ(=−(1/2)F ₁₄ F ¹⁴), p _r, p _⊥ being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas ε denotes the eigenvalue of the conformal Weyl tensor and interpreted as the energy density of the free gravitational field], we have recast Einstein’s field equations into a form easy to integrate. Since the system is underdetermined we make the following assumptions to solve the field equations (i) u=v _r=(a ²/2κ)r ⁿ⁺², v _⊥=k ₁ v _r, w=k ₂ v _r; a ², n(>0), k ₁, k ₂ being constants with κ=((k ₁+2)/3+k ₂) and (ii) w+u=(b ²/2)r ⁿ⁺², u=v _r, v _⊥−v _r=k, with b and k as constants. In both cases the field equations are integrated completely. The first solution is regular in the metric as well as physical variables for all values of n>0. Even though the second solution contains terms like k/r ² since Q(0)=0 it is argued that the pressure anisotropy, caused by the electric flux near the centre, can be made to vanish reducing it to the generalized Cooperstock-de la Cruz solution given in [14]. The interior solutions are shown to match with the exterior Reissner-Nordstrom solution over a fixed boundary. Dedicated to Prof. F A E Pirani.     

A short range many-body potential for modelling bcc metals

The problem considered is the fitting of a many-body interaction potential to bulk crystal data. A parameterisation of the potential is assumed which is based on physical considerations. The free parameters are determined by using global optimization to perform a least squares fit, to a large number of crystal properties. This has been achieved for body centered cubic (bcc) materials. The approach adopted here fits the bcc crystal structure, as the preferred minimum energy configuration for tungsten, and also fits the dimer energetics and the elastic properties of crystalline tungsten.     

Synthesis and X-ray investigation of liquid crystalline polymers containing laterally methyl-substituted tolane-based mesogenic side groups

A series of polymethacrylates containing laterally methyl-substituted 4-alkoxy-4-nitrotolane, 4-alkoxy-4'-cyanotolane, and 4-alkoxy-4'-trifluoromethyltolane as mesogenic side groups are presented. The thermal behaviours of the prepared compounds were characterized by differential scanning calorimetry, optical polarized microscopy and X-ray diffraction. All of the obtained methacrylate monomers exhibit no mesophase, while most of the synthesized polymers reveal enantiotropic mesomorphism. The polymer containing 4-propyloxy-2'-methyl-4'-nitrotolane side groups was the only one to show no mesomorphic behaviour. The spacer length and the nature of terminal group have a profound influence on the type of mesophase formed and the thermal stability. Incorporation of a lateral methyl-substituent into the mesogenic groups reduces the thermal stabilities of the mesophases. X-ray diffraction reveals that polymers with a smectic A or smectic E phase have the inclination to form a bilayer structure. Increasing the temperature within the smectic phase range, the intermolecular spacing increases while the layer spacing decreases. On the other hand, introducing a lateral substituent into the mesogenic side groups leads to increase in both layer and intermolecular spacing.     

Copolymerization of butadiene and styrene by initiation with alkyllithium and alkali metal tert-butoxides

Combinations of the various alkali metal tert-butoxides with organolithium initiators give homogeneous copolymers of butadiene and styrene. The unprecedented flexibility of this initiator system allowed preparation of random copolymers with various amounts of vinyl unsaturation and various degrees of randomness. The butyllithium–potassium tert-butoxide initiator system was more efficient than phenylpotassium.     

Dual temperature‐ and pH‐sensitive hydrogels from interpenetrating networks and copolymerization of N‐isopropylacrylamide and sodium acrylate

Hydrogels responsive to both temperature and pH have been synthesized in the forms of sequential interpenetrating networks (IPNs) of N‐isopropylacrylamide (NIPAAm) and sodium acrylate (SA) and compared with the crosslinked random copolymers of N‐isopropylacrylamide and SA. Whereas the stimuli‐sensitive behaviors of copolymer hydrogels were strongly dependent on the ionic SA contents, the IPN hydrogels exhibited independent swelling and thermal behaviors of each network component. The sequences and media in the synthesis of IPNs influenced the swelling capacities of the IPNs, but not the temperature or pH ranges at which the swelling changes occurred. In IPNs, a more expanded primary gel network during the synthesis of the secondary network contributed to the better swelling of the final IPNs. Both the swelling and thermal behaviors of the IPNs suggest that poly(N‐isopropylacrylamide) and poly(sodium acrylate) are phase separated regardless of their synthesis conditions. The presence of the poly(sodium acrylate) network did not influence the temperature or the extent of phase transition of the poly(N‐isopropylacrylamide) network in the IPNs, but did improve the thermal stability of the IPNs. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3293–3301, 2004     

High-performance capillary electrophoretic analysis of synthetic food colorants

Summary A high-performance capillary electrophoresis method with diode-array detection has been developed for analysis of synthetic food colorants. The influence of buffer composition on the separation of the food colorants was examined, as were the effects of α-, β- and γ-c-yclodextrins on analyte migration behavior. Eight food colorants were completely separated within 10 min using pH 9.5 borax—NaOH buffer containing 5 mM β-cyclodextrin. Experimental results indicate that the relative standard deviations of analyte migration times were<0.88% under the optimized separation condition. Correlation coefficients of the linear calibration plots of the analytes exceeded 0.998. The method was suitable for determination of the quantities of synthetic food colorantsi in ice cream bars and fruit soda drinks.