Constructing banking networks under decreasing costs of link formation

The structure of networks plays a central role in the behavior of financial systems and their response to policy. Real-world networks, however, are rarely directly observable: banks’ assets and liabilities are typically known, but not who is lending how much and to whom. This paper adds to the existing literature in two ways. First, it shows how to simulate realistic networks that are based on balance-sheet information. To do so, we introduce a model where links cause fixed-costs, independent of contract size; but the costs per link decrease the more connected a bank is (scale economies). Second, to approach the optimization problem, we develop a new algorithm inspired by the transportation planning literature and research in stochastic search heuristics. Computational experiments find that the resulting networks are not only consistent with the balance sheets, but also resemble real-world financial networks in their density (which is sparse but not minimally dense) and in their core-periphery and disassortative structure.

     

Packing Measure Analysis of Harmonic Measure

We show that, for any Jordan domain J in R², harmonic measureis supported by a Borel set of packing dimension 1. We alsoobtain incomplete analogs to the results of Makarov, which connectthe almost everywhere behavior of the derivative near the boundaryfor the conformal mapping function from the unit disk J withthe Hausdorff measure properties of sets supporting the harmonicmeasure.     

Symmetry reductions and exact solutions of shallow water wave equations

In this paper we study symmetry reductions and exact solutions of the shallow water wave (SWW) equation $$u_{xxxt} + \alpha u_x u_{xt} + \beta u_t u_{xx} - u_{xt} - u_{xx} = 0,$$ whereα andβ are arbitrary, nonzero, constants, which is derivable using the so-called Boussinesq approximation. Two special cases of this equation, or the equivalent nonlocal equation obtained by settingu _x =U, have been discussed in the literature. The caseα=2β was discussed by Ablowitz, Kaup, Newell and Segur (Stud. Appl. Math.,53 (1974), 249), who showed that this case was solvable by inverse scattering through a second-order linear problem. This case and the caseα=β were studied by Hirota and Satsuma (J. Phys. Soc. Japan,40 (1976), 611) using Hirota's bi-linear technique. Further, the caseα=β is solvable by inverse scattering through a third-order linear problem. In this paper, a catalogue of symmetry reductions is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole (J. Math. Mech,18 (1969), 1025). The classical Lie method yields symmetry reductions of (1) expressible in terms of the first, third and fifth Painlevé transcendents and Weierstrass elliptic functions. The nonclassical method yields a plethora of exact solutions of (1) withα=β which possess a rich variety of qualitative behaviours. These solutions all like a two-soliton solution fort < 0 but differ radically fort > 0 and may be viewed as a nonlinear superposition of two solitons, one travelling to the left with arbitrary speed and the other to the right with equal and opposite speed. These families of solutions have important implications with regard to the numerical analysis of SWW and suggests that solving (1) numerically could pose some fundamental difficulties. In particular, one would not be able to distinguish the solutions in an initial-value problem since an exponentially small change in the initial conditions can result in completely different qualitative behaviours. We compare the two-soliton solutions obtained using the nonclassical method to those obtained using the singular manifold method and Hirota's bi-linear method. Further, we show that there is an analogous nonlinear superposition of solutions for two (2+1)dimensional generalisations of the SWW Equation (1) withα=β. This yields solutions expressible as the sum of two solutions of the Korteweg-de Vries equation.     

Pulsed fluorescence measurements of trapped molecular ions with zero background detection

Sensitive methods have been developed to measure laser-induced fluorescence from trapped ions by reducing the detection of background scattering to zero levels during the laser excitation pulse. The laser beam diameter has been reduced to approximately 150 microm to eliminate scattering on trap apertures and the resulting laser-ion interaction is limited to a volume of approximately 10(-5) cm which is approximately 0.03-0.15 of the total ion cloud volume depending on experimental conditions. The detection optics collected fluorescence only from within the solid angle defined by laser-ion interaction volume. Rhodamine 640 and Alexa Fluor 350 ions, commonly used as fluorescence resonance energy transfer (FRET) fluorophores, were generated in the gas phase by using electrospray ionization and injected into a radiofrequency Paul trap where they were stored and exposed to Nd:YAG laser pulses at 532 and 355 nm for times up to 10 m. Fluorescence emitted by these ions was investigated for several trap q(z) values and ion cloud temperatures. Analysis of photon statistics indicated an average of approximately 10 photons were incident on the PMT detector per 15 ns pulse for approximately 10(3) trapped ions in the interaction volume. Fluorescence measurements displayed a dependence on trapped ion number which were consistent with calculations of the space charge limited ion density. To investigate the quantitative capability of these fluorescence techniques, the laser-induced fragmentation of trapped Alexa Fluor 350 ions was measured and compared with a rate equation model of the dynamics. Decay of the fluorescence signal as well as the parent ion number compared closely with quantitative predictions of the photofragmentation model.     

Green method for ultrasensitive determination of Hg in natural waters by electrothermal-atomic absorption spectrometry following sono-induced cold vapor generation and ‘in-atomizer trapping’

Sono-induced cold vapor generation (SI-CVG) has been used for the first time in combination with a graphite furnace atomizer for determination of Hg in natural waters by electrothermal-atomic absorption spectrometry after in situ trapping onto a noble metal-pretreated platform (Pd, Pt or Rh) inserted into a graphite tube. The system allows ‘in-atomizer trapping’ of Hg without the use of conventional reduction reactions based on sodium borohydride or tin chloride in acid medium for cold vapor generation. The sono-induced reaction is accomplished by applying ultrasound irradiation to the sample solution containing Hg(II) in the presence of an organic compound such as formic acid. As this organic acid is partly degraded upon ultrasound irradiation to yield CO, CO₂, H₂ and H₂O, the amount of lab wastes is minimized and a green methodology is achieved.     

Antimony(III) Oxide Film on a Cellulose Fiber Surface: Preparation and Characterization of the Composite

Cellulose/antimony(III) oxide composites, Cel/Sb(2)O(3), with oxide loadings of 1.7, 5.4, and 9.2 wt% were prepared by reacting the precursor SbCl(3) reagent with cellulose in dry ethanol solution. The reaction of the Lewis acid and the cellulose fibers occurred at the~amorphous domains of the biopolymer, increasing the crystallinity degree of the composite compared with that of the untreated cellulose. The scanning electron microscopy images and metal mapping for all samples showed that the oxide film layer uniformly covered the fiber surfaces with no detectable agglomerates of the oxide particles. The synchrotron X-ray diffraction patterns indicated that the antimony oxide film was obtained as a crystalline phase with orthorombic structure. The atomic ratios of O/Sb, determined by X-ray photoelectron spectroscopy, indicated that, for Cel/Sb(2)O(3) samples with 9.3 wt% loading, the fiber surface is nearly saturated by the oxide layer. The thermal stability of Cel/Sb(2)O(3) compared to that of untreated cellulose is practically unaffected. Copyright 2000 Academic Press.     

Time-Resolved Fluorescence and Transient Spectroscopy in Determining Photochemical and Photophysical Channels in Reacting Systems in Solutions and Microheterogeneous Media

Abstract— Characterization of short-lived intermediates in homogeneous and microheterogeneous systems has been carried out using time-resolved spectroscopic techniques. The data obtained from these techniques have been analyzed in a relatively unconventional manner to elucidate complex transient behavior for two reactive systems. The highly nonexponential fluorescence decay for a series of fraws-stilbene-derivatized amphiphiles that readily form bilayer systems in aqueous media has been analyzed using a distribution of lifetimes analysis (DLA). The utility of DLA for quantitative studies was first determined by simulation of artificial decay data. Despite some limitations in DLA, qualitative conclusions as to the nature of the fluorescing species may be drawn when supplementary information such as steady-state spectroscopic data are also considered. The results indicate that the observed fluorescence originates from different types of excited-state species that consist of two or more trans-stilbene units; one of the emissions is attributed to the excited state of a ground-state aggregate while the other is assigned to an excimer that may arise from a 'defect'in the bilayer. The nonexponential nature of the decays is attributed to distributions of environments experienced by the fluorescing species. Electron transfer (ET) reactions between several excited pinacols and carbon tetrachloride in solution have been found to yield products with quantum yields that are higher than unity in the presence of oxygen, suggesting a chain mechanism for product formation. In these systems both the donor and the acceptor undergo bond fragmentation following the initial ET step. The individual steps involved in the proposed mechanism for these systems have been investigated in part using different steady-state and time-resolved laser spectroscopic techniques. However, it was also necessary to utilize pulse radiolysis in order to confirm the involvement of certain radical intermediates that were not observable by the usual flash photolysis techniques.