The Stochastic Solution to a Cauchy Problem for Degenerate Parabolic Equations

We study the stochastic solution to a Cauchy problem for a degenerate parabolic equation arising from option pricing. When the diffusion coefficient of the underlying price process is locally H\"older continuous with exponent $\delta\in (0, 1]$, the stochastic solution, which represents the price of a European option, is shown to be a classical solution to the Cauchy problem. This improves the standard requirement $\delta\ge 1/2$. Uniqueness results, including a Feynman-Kac formula and a comparison theorem, are established without assuming the usual linear growth condition on the diffusion coefficient. When the stochastic solution is not smooth, it is characterized as the limit of an approximating smooth stochastic solutions. In deriving the main results, we discover a new, probabilistic proof of Kotani's criterion for martingality of a one-dimensional diffusion in natural scale.Comment: Keywords: local martingales, local stochastic solutions, degenerate Cauchy problems, Feynman-Kac formula, necessary and sufficient condition for uniqueness, comparison principl

Maxwell's two-demon engine under pure dephasing noise

The interplay between thermal machines and quantum correlations is of great interest in both quantum thermodynamics and quantum information science. Recently, a quantum Szil\'ard engine has been proposed, showing that the quantum steerability between a Maxwell's demon and a work medium can be beneficial to a work extraction task. Nevertheless, this type of quantum-fueled machine is usually fragile in the presence of decoherence effects. We provide an example of the pure dephasing process, showing that the engine's quantumness can be degraded. Therefore, in this work, we tackle this question by introducing a second demon who can access a control system and make the work medium pass through two dephasing channels in a manner of quantum superposition. Furthermore, we provide a quantum circuit to simulate our proposed concept and test it on IBMQ and IonQ quantum computers.Comment: 10 pages, 7 figures, 2 table

On-shell approach to (spinning) gravitational absorption processes

We utilize three point amplitudes with (spinning) particles of unequal mass and a graviton to capture the dynamics of absorption processes. We demonstrate that the construction can represent the spheroidal harmonics appearing in the Teukolsky equations. The absolute square of the ``Wilson coefficients'' in this effective description can be fixed by matching to the known absorptive cross-sections. As an application, we compute corrections to the gravitational Compton amplitude from the exchange of states corresponding to such absorption effects. In the super-extremal limit, the corrections generate the non-analytic $|a|$-dependent contribution of the Compton amplitude found in ref.\cite{Bautista:2022wjf}.Comment: 32 pages, 2 figure

Improvement of n-butanol tolerance in Escherichia coli by membrane-targeted tilapia metallothionein

Background: Though n-butanol has been proposed as a potential transportation biofuel, its toxicity oftencauses oxidative stress in the host microorganism and is considered one of the bottlenecks preventing itsefficient mass production.Results: To relieve the oxidative stress in the host cell, metallothioneins (MTs), which are known as scavengersfor reactive oxygen species (ROS), were engineered in E. coli hosts for both cytosolic and outer-membrane-targeted (osmoregulatory membrane protein OmpC fused) expression. Metallothioneins from human (HMT),mouse (MMT), and tilapia fish (TMT) were tested. The host strain expressing membrane-targeted TMT showed thegreatest ability to reduce oxidative stresses induced by n-butanol, ethanol, furfural, hydroxymethylfurfural, andnickel. The same strain also allowed for an increased growth rate of recombinant E. coli under n-butanol stress.Further experiments indicated that the TMT-fused OmpC protein could not only function in ROS scavenging butalso regulate either glycine betaine (GB) or glucose uptake via osmosis, and the dual functional fusion proteincould contribute in an enhancement of the host microorganism’s growth rate.Conclusions: The abilities of scavenging intracellular or extracellular ROS by these engineering E. coli wereexamined, and TMT show the best ability among three MTs. Additionally, the membrane-targeted fusion protein,OmpC-TMT, improved host tolerance up to 1.5% n-butanol above that of TMT which is only 1%. These resultspresented indicate potential novel approaches for engineering stress tolerant microorganism strains

A 128-point Multi-Path SC FFT Architecture

This paper presents a new radix-2^k multi-path FFT architecture, named MSC FFT, which is based on a single-path radix-2 serial commutator (SC) FFT architecture. The proposed multi-path architecture has a very high hardware utilization that results in a small chip area, while providing high throughput. In addition, the adoption of radix-2^k FFT algorithms allows for simplifying the rotators even further. It is achieved by optimizing the structure of the processing element (PE). The implemented architecture is a 128-point 4-parallel multi-path SC FFT using 90 nm process. Its area and power consumption at 250 MHz are only 0.167 mm2 and 14.81 mW, respectively. Compared with existing works, the proposed design reduces significantly the chip rea and the power consumption, while providing high throughput.Comment: Conference paper, ISCAS 2020, 5 page

THE ACUTE EFFECT OF UPPER EXTREMITY PLYOMETRIC TRAINING

The purpose of this study was to probe the acute effect of the performance of upper extremity muscle groups after the plyometric training intervention. The participants were 13 healthy male college students. The force transducers (300kg, 200 Hz) and EMG sensor (1000 Hz) were taken to diagnose the acute effects of strength and muscle activation done by upper extremity pre and post plyometric training (load :24kg, 12 repetiiion times Iset, 3 set), and pair t-test was taken to test the significance(a=.05). The result showed that the strength after the upper extremity plyometric training intervention obviously had decreased 8% (

ELEMENTARY SCHOOL BOYS’ SOCCER KICK SKILL ANALYSIS

The purpose of this study is aimed to analyze elementary school boys’ kicking skills on the perspective of motor skills. The data is collected by Vicon Motion Analysis System (250Hz). The parameters include the compare of the instant joint angles and the time proportion during the process of the kicking toward the different kick performance groups. The participants are 36 elementary boy soccer players (age: 11.7±0.3 yrs; height: 1.42±0.13 m; weight: 37.5±13.0 kg). The subjects were divided to two groups according to the instance kicking ball speed. The result indicated that the high ball speed group players have greater extremity joint angles than the low ball speed group. No difference was found on the time proportion during the process of the kicking. We suggest that the learning of kicking skill can start with the lower speed in the beginner stage

Social Capital and Technological Literacy in Taiwan

The burgeoning interest in social capital within the technology community represents a welcome move towards a concern for the social elements of technological adaptation and capacity. Since technology plays an ever larger role in our daily life, it is necessary to articulate social capital and its relationship to technological literacy. A nationwide data was collected by area sampling, and position generator was used to measure social capital. Regression model was constructed for technological literacy. Age, gender, education, income, web access, and social capital were included as independent variables. The results show that age, gender, education, web access, and social capital were good predictors of technological literacy. It is concluded that social capital is helpful in coping with rapid technological change. Theoretical and empirical implications and future research are discussed