Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.

Probability on Trees and Networks

Applied Probability and Queues.

PMMA: A key macromolecular component for dielectric low-κ hybrid inorganic–organic polymer films

Synthetic control of the mutual arrangement of the cyclometalated ligands (C^N) in Ir(III) dimers, [Ir(C^N)(2)Cl](2), and cationic bis-cyclometalated Ir(III) complexes, [Ir(C^N)(2)(L^L)](+) (L^L = neutral ligand), is described for the first time. Using 1-benzyl-4-(2,4-difluorophenyl)-1H-1,2,3-triazole (HdfptrBz) as a cyclometalating ligand, two different Ir(III) dimers, [Ir(dfptrBz)(2)Cl](2), are synthesized depending on the reaction conditions. At 80 °C, the dimer with an unusual mutual cis-C,C and cis-N,N configuration of the C^N ligands is isolated. In contrast, at higher temperature (140 °C), the geometrical isomer with the common cis-C,C and trans-N,N arrangement of the C^N ligand is obtained. In both cases, an asymmetric bridge, formed by a chloro ligand and two adjacent nitrogens of the triazole ring of one of the cyclometalated ligands, is observed. The dimers are cleaved in coordinating solvents to give the solvento complexes [Ir(dfptrBz)(2)Cl(S)] (S = DMSO or acetonitrile), which maintain the C^N arrangement of the parent dimers. Controlling the C^N ligand arrangement in the dimers allows for the preparation of the first example of geometrical isomers of a cationic bis-cyclometalated Ir(III) complex. Thus, N,N-trans-[Ir(dfptrBz)(2)(dmbpy)](+) (dmbpy = 4,4'-dimethyl-2,2'-bipyridine), with cis-C,C and trans-N,N arrangement of the C^N ligands, as well as N,N-cis-[Ir(dfptrBz)(2)(dmbpy)](+), with cis-C,C and cis-N,N C^N ligand orientation, are synthesized and characterized. Interestingly, both isomers show significantly different photophysical and electroluminescent properties, depending on the mutual arrangement of the C^N ligands. Furthermore, quantum chemical calculations give insight into the observed photophysical experimental data.

Control of the mutual arrangement of cyclometalated ligands in cationic iridium(III) complexes. Synthesis, spectroscopy, and electroluminescence of the different isomers.

Transparent nano composite PVA–TiO2 and PMMA–TiO2 thin films: Optical and dielectric properties

That there exist two losing games that can be combined, either by random mixture or by nonrandom alternation, to form a winning game is known as Parrondo's paradox. We establish a strong law of large numbers and a central limit theorem for the Parrondo player's sequence of profits, both in a one-parameter family of capital-dependent games and in a two-parameter family of history-dependent games, with the potentially winning game being either a random mixture or a nonrandom pattern of the two losing games. We derive formulas for the mean and variance parameters of the central limit theorem in nearly all such scenarios; formulas for the mean permit an analysis of when the Parrondo effect is present.

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Limit theorems for Parrondo's paradox

This study explored the conceptual framework of dieticians' intentions to recommend functional food and the mediating role of consumption frequency. A web-based survey was designed using a self-administered questionnaire. A sample of Korean dieticians (N=233) responded to the questionnaire that included response efficacy, risk perception, consumption frequency, and recommendation intention for functional foods. A structural equation model was constructed to analyze the data. We found that response efficacy was positively related to frequency of consumption of functional foods and to recommendation intention. Consumption frequency also positively influenced recommendation intention. Risk perception had no direct influence on recommendation intention; however, the relationship was mediated completely by consumption frequency. Dieticians' consumption frequency and response efficacy were the crucial factors in recommending functional foods. Dieticians may perceive risks arising from the use of functional foods in general, but the perceived risks do not affect ratings describing dieticians' intentions to recommend them. The results also indicated that when dieticians more frequently consume functional foods, the expression of an intention to recommend functional foods may be controlled by the salience of past behaviors rather than by attitudes.

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Dieticians' intentions to recommend functional foods: The mediating role of consumption frequency of functional foods

Let game B be Toral's cooperative Parrondo game with (one-dimensional) spatial dependence, parameterized by N ≥ 3 and p0, p1, p2, p3 ∈ [0, 1], and let game A be the special case p0 = p1 = p2 = p3 = 1/2. In previous work we investigated μB and μ(1/2, 1/2), the mean profits per turn to the ensemble of N players always playing game B and always playing the randomly mixed game (1/2)(A + B). These means were computable for 3 ≤ N ≤ 19, at least, and appeared to converge as N → ∞, suggesting that the Parrondo region (i.e., the region in which μB ≤ 0 and μ(1/2, 1/2) > 0) has nonzero volume in the limit. The convergence was established under certain conditions, and the limits were expressed in terms of a parameterized spin system on the one-dimensional integer lattice. In this paper we replace the random mixture with the nonrandom periodic pattern Ar Bs, where r and s are positive integers. We show that μ[r, s], the mean profit per turn to the ensemble of N players repeatedly playing the pattern Ar Bs, is computable for 3 ≤ N ≤ 18 and r + s ≤ 4, at least, and appears to converge as N → ∞, albeit more slowly than in the random-mixture case. Again this suggests that the Parrondo region (μB ≤ 0 and μ[r, s] > 0) has nonzero volume in the limit. Moreover, we can prove this convergence under certain conditions and identify the limits.

Parrondo Games with Spatial Dependence, III

Two luminescent iridium(III) tris-cyclometalated complexes with isomeric 2,4-diphenyloxazolato and 2,5-diphenyloxazolato ligands, fac-Ir(24dpo)3 and fac-Ir(25dpo)3, are reported. The molecular structure for Ir(24dpo)3 was determined by X-ray diffraction. Electrochemical and spectroscopic studies supported by structures are discussed so as to demonstrate how the ligand structure influences the luminescent properties.

Iridium(III) Tris-cyclometalated Complexes with Diphenyloxazolic Ligands: Influence of Ligand Structure on Electrochemical and Photophysical Properties

In Toral's games, at each turn one member of an ensemble of $N\ge2$ players is selected at random to play.  He plays either game $A'$, which involves transferring one unit of capital to a second randomly chosen player, or game $B$, which is an asymmetric game of chance whose rules depend on the player's current capital, and which is fair or losing.  Game $A'$ is fair (with respect to the ensemble's total profit), so the \textit{Parrondo effect} is said to be present if the random mixture $\gamma A'+(1-\gamma)B$ (i.e., play game $A'$ with probability $\gamma$ and play game $B$ otherwise) is winning.  Toral demonstrated the Parrondo effect for $\gamma=1/2$ using computer simulation.  We prove it, establishing a strong law of large numbers and a central limit theorem for the sequence of profits of the ensemble of players for each $\gamma\in(0,1)$.  We do the same for the nonrandom pattern of games $(A')^r B^s$ for all integers $r,s\ge1$.  An unexpected relationship between the random-mixture case and the nonrandom-pattern case occurs in the limit as $N\to\infty$.

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Jiyeon Lee

Papers

Limit theorems for Parrondo's paradox

Dieticians' intentions to recommend functional foods: The mediating role of consumption frequency of functional foods

Parrondo Games with Spatial Dependence, III

Iridium(III) Tris-cyclometalated Complexes with Diphenyloxazolic Ligands: Influence of Ligand Structure on Electrochemical and Photophysical Properties

Parrondo's paradox via redistribution of wealth