A frictionless microswimmer

We investigate the self-locomotion of an elongated microswimmer by virtue of the unidirectional tangential surface treadmilling. We show that the propulsion could be almost frictionless, as the microswimmer is propelled forward with the speed of the backward surface motion, i.e. it moves throughout an almost quiescent fluid. We investigate this swimming technique using the special spheroidal coordinates and also find an explicit closed-form optimal solution for a two-dimensional treadmiler via complex-variable techniques.Comment: 6 pages, 4 figure

A variation of the Azéma martingale and drawdown options

In this paper, we derive a variation of the Azéma martingale using two approaches—a direct probabilistic method and another by projecting the Kennedy martingale onto the filtration generated by the drawdown duration. This martingale links the time elapsed since the last maximum of the Brownian motion with the maximum process itself. We derive explicit formulas for the joint densities of (τ,W τ , M τ ), which are the first time the drawdown period hits a prespecified duration, the value of the Brownian motion, and the maximum up to this time. We use the results to price a new type of drawdown option, which takes into account both dimensions of drawdown risk—the magnitude and the duration

Parisian Option Pricing: A Recursive Solution for the Density of the Parisian Stopping Time

In this paper, we obtain the density function of the single barrier one-sided Parisian stopping time. The problem reduces to that of solving a Volterra integral equation of the first kind, where a recursive solution is consequently obtained. The advantage of this new method as compared to that in previous literature is that the recursions are easy to program as the resulting formula involves only a finite sum and does not require a numerical inversion of the Laplace transform. For long window periods, an explicit formula for the density of the stopping time can be obtained. For shorter window lengths, we derive a recursive equation from which numerical results are computed. From these results, we compute the prices of one-sided Parisian options

Recursive formula for the double-barrier Parisian stopping time

In this paper, we obtain a recursive formula for the density of the double barrier Parisian stopping time. We present a probabilistic proof of the formula for the first few steps of the recursion, and then a formal proof using explicit Laplace inversions. These results provide an efficient computational method for pricing double barrier Parisian options

Scattering of electromagnetic waves by many small perfectly conducting or impedance bodies

A theory of electromagnetic (EM) wave scattering by many small particles of an arbitrary shape is developed. The particles are perfectly conducting or impedance. For a small impedance particle of an arbitrary shape, an explicit analytical formula is derived for the scattering amplitude. The formula holds as a → 0, where a is a characteristic size of the small particle and the wavelength is arbitrary but fixed. The scattering amplitude for a small impedance particle is shown to be proportional to a2−κ, where κ ∈ [0,1) is a parameter which can be chosen by an experimenter as he/she wants. The boundary impedance of a small particle is assumed to be of the form ζ = ha−κ, where h = const, Reh ≥ 0. The scattering amplitude for a small perfectly conducting particle is proportional to a3, and it is much smaller than that for the small impedance particle. The many-body scattering problem is solved under the physical assumptions a ≪ d ≪ λ, where d is the minimal distance between neighboring particles and λ is the wavelength. The distribution law for the small impedance particles is N(∆) ∼ 1/a2−κ∆ N(x)dx as a → 0. Here, N(x) ≥ 0 is an arbitrary continuous function that can be chosen by the experimenter and N(∆) is the number of particles in an arbitrary sub-domain ∆. It is proved that the EM field in the medium where many small particles, impedance or perfectly conducting, are distributed, has a limit, as a → 0 and a differential equation is derived for the limiting field. On this basis, a recipe is given for creating materials with a desired refraction coefficient by embedding many small impedance particles into a given material. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4929965

The Unique Determination of Neuronal Currents in the Brain via Magnetoencephalography

The problem of determining the neuronal current inside the brain from measurements of the induced magnetic field outside the head is discussed under the assumption that the space occupied by the brain is approximately spherical. By inverting the Geselowitz equation, the part of the current which can be reconstructed from the measurements is precisely determined. This actually consists of only certain moments of one of the two functions specifying the tangential part of the current. The other function specifying the tangential part of the current as well as the radial part of the current are completely arbitrary. However, it is also shown that with the assumption of energy minimization, the current can be reconstructed uniquely. A numerical implementation of this unique reconstruction is also presented

Antenatal care and perinatal outcomes of asylum seeking women and their infants.

OBJECTIVES: Asylum seekers have been highlighted as a particularly vulnerable group of expectant mothers due to complex medical and psychosocial needs, as well as the difficulties they may face in accessing care. Our aim was to examine if there were differences in the antenatal care and perinatal outcomes for asylum seeking women when compared to age- and ethnicity-matched controls delivering at the same hospital. METHODS: Two age- and ethnicity-matched non-asylum seeking controls were identified for each asylum-seeking woman. Electronic patient records were analysed to determine the amount of antenatal care received and neonatal outcomes. RESULTS: Thirty-four asylum-seeking women were identified who had term born infants. The median number of antenatal care episodes at the delivering hospital was significantly fewer amongst asylum-seeking women compared to controls (three vs. nine, p<0.0001). The median number of antenatal ultrasound examinations at the delivering hospital amongst asylum-seeking women was one (IQR 1-2), compared to three (IQR 3-4) in the controls (p<0.0001). The postnatal length of stay was significantly longer for infants of asylum-seeking women (median three vs. two days, p=0.002). Thirty-seven percent of asylum seeking women but none of the controls required assistance from social services. There was a significant correlation between antenatal and postnatal costs for asylum seeking women (r=0.373, p=0.042), but not for controls (r=0.171, p=0.181). CONCLUSIONS: The increased postnatal length of stay in the infants of asylum seeking mothers may reflect their mother's reduced antenatal care and hence insufficient discharge planning for mothers and infants with increased social needs