The Fundamental Gap For Hyperbolic Triangles

In 1983, M. van den Berg made his Fundamental Gap Conjecture about the difference between the first two Dirichlet eigenvalues (the fundamental gap) of any convex domain in the Euclidean plane. Recently, progress has been made in the case where the domains are polygons and, in particular, triangles. We examine the conjecture for triangles in hyperbolic geometry, though we seek an for an upper bound for the fundamental gap rather than a lower bound.

Implementing fisher Black's simple discounting rule

We propose a simple implementation of Black’s (1988) elegant rule for discounting uncertain future cash flows. Black’s rule avoids the thorny problem of estimating an appropriate risk-adjusted discount rate. Instead, the rule calls for discounting conditional mean cash flows at appropriate riskless interest rates. Our contribution in this article is to describe and illustrate a method of estimating the conditional mean cash flows called for in Black’s rule. The method is quite flexible with respect to the types of information available concerning the distributions of future cash flows. We argue that this approach to computing present values offers a theoretically sound and generally feasible addition to the toolbox of financial managers.

Delay discounting task in pigs reveals response strategies related to dopamine metabolite.

We developed a novel delay discounting task to investigate outcome impulsivity in pigs. As impulsivity can affect aggression, and might also relate to proactive and reactive coping styles, eight proactive (HR) and eight reactive (LR) pigs identified in a manual restraint test ("Backtest", after Bolhuis et al., 2003) were weaned and mixed in four pens of four unfamiliar pigs, so that each pen had two HR and two LR pigs, and aggression was scored in the 9h after mixing. In the delay discounting task, each pig chose between two levers, one always delivering a small immediate reward, the other a large delayed reward with daily increasing delays, impulsive individuals being the ones discounting the value of the large reward quicker. Two novel strategies emerged: some pigs gradually switched their preference towards the small reward ('Switchers') as predicted, but others persistently preferred the large reward until they stopped making choices ('Omitters'). Outcome impulsivity itself was unrelated to these strategies, to urinary serotonin metabolite (5-HIAA) or dopamine metabolite (HVA) levels, aggression at weaning, or coping style. However, HVA was relatively higher in Omitters than Switchers, and positively correlated with behavioural measures of indecisiveness and frustration during choosing. The delay discounting task thus revealed two response strategies that seemed to be related to the activity of the dopamine system and might indicate a difference in execution, rather than outcome, impulsivity.

Comparing the performance of hyperbolic and circular rod quadrupole mass spectrometers with applied higher order auxiliary excitation

This work applies higher order auxiliary excitation techniques to two types of quadrupole mass spectrometers (QMSs): commercial systems and spaceborne instruments. The operational settings of a circular rod geometry commercial system and an engineering test-bed for a hyperbolic rod geometry spaceborne instrument were matched, with the relative performance of each sensor characterized with and without applied excitation using isotopic measurements of Kr+. Each instrument was operated at the limit of the test electronics to determine the effect of auxiliary excitation on extending instrument capabilities. For the circular rod sensor, with applied excitation, a doubling of the mass resolution at 1% of peak transmission resulted from the elimination of the low-mass side peak tail typical of such rod geometries. The mass peak stability and ion rejection efficiency were also increased by factors of 2 and 10, respectively, with voltage scan lines passing through the center of stability islands formed from auxiliary excitation. Auxiliary excitation also resulted in factors of 6 and 2 in peak stability and ion rejection efficiency, respectively, for the hyperbolic rod sensor. These results not only have significant implications for the use of circular rod quadrupoles with applied excitation as a suitable replacement for traditional hyperbolic rod sensors, but also for extending the capabilities of existing hyperbolic rod QMSs for the next generation of spaceborne instruments and low-mass commercial systems.

A note on three factor model of discounting

In Montiel Olea and Strzalecki (2014), authors have axiomatically developed an algorithm to infer the parameters of beta-delta model of cognitive bias (present and future biases). While this is extremely useful, it allows the implied beta to become very large when the response is impatient in the future choices relative to present choices, i.e., when there is a strong future bias. I modify the model to further exponentiate the functional form to get more reasonable beta values.

Analysis of human cytochrome P450 3A4 cooperativity: Construction and characterization of a site-directed mutant that displays hyperbolic steroid hydroxylation kinetics

Cytochrome P450 3A4 is generally considered to be the most important human drug-metabolizing enzyme and is known to catalyze the oxidation of a number of substrates in a cooperative manner. An allosteric mechanism is usually invoked to explain the cooperativity. Based on a structure–activity study from another laboratory using various effector–substrate combinations and on our own studies using site-directed mutagenesis and computer modeling of P450 3A4, the most likely location of effector binding is in the active site along with the substrate. Our study was designed to test this hypothesis by replacing residues Leu-211 and Asp-214 with the larger Phe and Glu, respectively. These residues were predicted to constitute a portion of the effector binding site, and the substitutions were designed to mimic the action of the effector by reducing the size of the active site. The L211F/D214E double mutant displayed an increased rate of testosterone and progesterone 6β-hydroxylation at low substrate concentrations and a decreased level of heterotropic stimulation elicited by α-naphthoflavone. Kinetic analyses of the double mutant revealed the absence of homotropic cooperativity with either steroid substrate. At low substrate concentrations the steroid 6β-hydroxylase activity of the wild-type enzyme was stimulated by a second steroid, whereas L211F/D214E displayed simple substrate inhibition. To analyze L211F/D214E at a more mechanistic level, spectral binding studies were carried out. Testosterone binding by the wild-type enzyme displayed homotropic cooperativity, whereas substrate binding by L211F/D214E displayed hyperbolic behavior.

Dyakonons in hyperbolic metamaterials

We have analyzed surface-wave propagation that takes place at the boundary between an isotropic medium and a semi-infinite metal-dielectric periodic medium cut normally to the layers. In the range of frequencies where the periodic medium shows hyperbolic space dispersion, hybridization of surface waves (dyakonons) occurs. At low to moderate frequencies, dyakonons enable tighter confinement near the interface in comparison with pure SPPs. On the other hand, a distinct regime governs dispersion of dyakonons at higher frequencies.

Engineered surface waves in hyperbolic metamaterials

We analyzed surface-wave propagation that takes place at the boundary between a semi-infinite dielectric and a multilayered metamaterial, the latter with indefinite permittivity and cut normally to the layers. Known hyperbolization of the dispersion curve is discussed within distinct spectral regimes, including the role of the surrounding material. Hybridization of surface waves enable tighter confinement near the interface in comparison with pure-TM surface-plasmon polaritons. We demonstrate that the effective-medium approach deviates severely in practical implementations. By using the finite-element method, we predict the existence of long-range oblique surface waves.

Table of hyperbolic sines and cosines; x=2 to x=10.

Mode of access: Internet.