Hidden regret in insurance markets: adverse and advantageous selection

We examine insurance markets with two types of customers: those who regret suboptimal decisions and those who don.t. In this setting, we characterize the equilibria under hidden information about the type of customers and hidden action. We show that both pooling and separating equilibria can exist. Furthermore, there exist separating equilibria that predict a positive correlation between the amount of insurance coverage and risk type, as in the standard economic models of adverse selection, but there also exist separating equilibria that predict a negative correlation between the amount of insurance coverage and risk type, i.e. advantageous selection. Since optimal choice of regretful customers depends on foregone alternatives, any equilibrium includes a contract which is o¤ered but not purchased

Hidden Regret and Advantageous Selection in Insurance Markets

We examine insurance markets in which there are two types of customers: those who regret suboptimal decisions and those who don\u27t. In this setting, we characterize the equilibria under hidden information about the type of customers and hidden action. We show that both pooling and separating equilibria can exist. Furthermore, there exist separating equilibria that predict a positive correlation between the amount of insurance coverage and risk type, as in the standard economic models of adverse selection, but there also exist separating equilibria that predict a negative correlation between the amount of insurance coverage and risk type, i.e. advantageous selection. Since optimal choice of regretful customers depends on foregone alternatives, any equilibrium includes a contract which is not purchased

The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary

We consider the dimer-monomer problem for the rectangular lattice. By mapping the problem into one of close-packed dimers on an extended lattice, we rederive the Tzeng-Wu solution for a single monomer on the boundary by evaluating a Pfaffian. We also clarify the mathematical content of the Tzeng-Wu solution by identifying it as the product of the nonzero eigenvalues of the Kasteleyn matrix.Comment: 4 Pages to appear in the Physical Review E (2006

Theory of resistor networks: The two-point resistance

The resistance between arbitrary two nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network. Explicit formulas for two-point resistances are deduced for regular lattices in one, two, and three dimensions under various boundary conditions including that of a Moebius strip and a Klein bottle. The emphasis is on lattices of finite sizes. We also deduce summation and product identities which can be used to analyze large-size expansions of two-and-higher dimensional lattices.Comment: 30 pages, 5 figures now included; typos in Example 1 correcte

Exploring quantum phase transitions by the cross derivative of the ground state energy

In this work, the cross derivative of the Gibbs free energy, initially proposed for phase transitions in classical spin models [Phys. Rev. B 101, 165123 (2020)], is extended for quantum systems. We take the spin-1 XXZ chain with anisotropies as an example to demonstrate its effectiveness and convenience for the Gaussian-type quantum phase transitions therein. These higher-order transitions are very challenging to determine by conventional methods. From the cross derivative with respect to the two anisotropic strengths, a single valley structure is observed clearly in each system size. The finite-size extrapolation of the valley depth shows a perfect logarithmic divergence, signaling the onset of a phase transition. Meanwhile, the critical point and the critical exponent for the correlation length are obtained by a power-law fitting of the valley location in each size. The results are well consistent with the best estimations in the literature. Its application to other quantum systems with continuous phase transitions is also discussed briefly.Comment: 7 pages, 7 figure

Synthetic poly(ester amine) and poly(amido amine) nanoparticles for efficient DNA and siRNA delivery to human endothelial cells

Biodegradable poly(ester amine) (PEA)-based and poly(amido amine) (PAA)-based nanoparticles were developed for efficient in vitro siRNA delivery to human umbilical vein endothelial cells (HUVECs). They were screened, characterized, and compared with traditionally studied DNA-containing particles. Several of the polymeric nanoparticles tested were found to be effective for delivering functional siRNA to green fluorescent protein (GFP) + HUVECs, achieving 60%–75% GFP knockdown while maintaining high viability. While PEAs have been used previously to form polyplexes or nanoparticles for DNA delivery, highly effective siRNA delivery in hard-to-transfect human cell types has not been previously reported. PEAs and linear nondendrimeric PAAs were also found to be effective for DNA delivery to HUVECs using GFP-encoding plasmid DNA (up to 50%–60% transfection efficiency). PEAs and PAAs can be separated into groups that form polymeric nanoparticles effective for siRNA delivery, for DNA delivery, or for both

Theory of impedance networks: The two-point impedance and LC resonances

We present a formulation of the determination of the impedance between any two nodes in an impedance network. An impedance network is described by its Laplacian matrix L which has generally complex matrix elements. We show that by solving the equation L u_a = lambda_a u_a^* with orthonormal vectors u_a, the effective impedance between nodes p and q of the network is Z = Sum_a [u_{a,p} - u_{a,q}]^2/lambda_a where the summation is over all lambda_a not identically equal to zero and u_{a,p} is the p-th component of u_a. For networks consisting of inductances (L) and capacitances (C), the formulation leads to the occurrence of resonances at frequencies associated with the vanishing of lambda_a. This curious result suggests the possibility of practical applications to resonant circuits. Our formulation is illustrated by explicit examples.Comment: 21 pages, 3 figures; v4: typesetting corrected; v5: Eq. (63) correcte

Spanning Trees on Graphs and Lattices in d Dimensions

The problem of enumerating spanning trees on graphs and lattices is considered. We obtain bounds on the number of spanning trees $N_{ST}$ and establish inequalities relating the numbers of spanning trees of different graphs or lattices. A general formulation is presented for the enumeration of spanning trees on lattices in $d\geq 2$ dimensions, and is applied to the hypercubic, body-centered cubic, face-centered cubic, and specific planar lattices including the kagom\'e, diced, 4-8-8 (bathroom-tile), Union Jack, and 3-12-12 lattices. This leads to closed-form expressions for $N_{ST}$ for these lattices of finite sizes. We prove a theorem concerning the classes of graphs and lattices ${\cal L}$ with the property that $N_{ST} \sim \exp(nz_{\cal L})$ as the number of vertices $n \to \infty$, where $z_{\cal L}$ is a finite nonzero constant. This includes the bulk limit of lattices in any spatial dimension, and also sections of lattices whose lengths in some dimensions go to infinity while others are finite. We evaluate $z_{\cal L}$ exactly for the lattices we considered, and discuss the dependence of $z_{\cal L}$ on d and the lattice coordination number. We also establish a relation connecting $z_{\cal L}$ to the free energy of the critical Ising model for planar lattices ${\cal L}$.Comment: 28 pages, latex, 1 postscript figure, J. Phys. A, in pres