Howling Detection and Suppression Based on Segmented Notch Filtering

The existing adaptive echo cancellation based howling (typically in hearing aids) removal methods have several drawbacks such as insufficient attenuation of the howling component, slow response and nonlinear distortion. To solve these problems, we propose a segmented notch filtering based scheme. Specifically, firstly, it is proved that the attenuation value can reach −330 dB at any detected howling frequency; secondly, the filter coefficients can be readily calculated by a closed-form formula, yielding a fast response to the sudden howling accident; thirdly, the closed-form formula of this filter is theoretically an even function, indicating that this filter possesses a linear transfer characteristic. In combination with proper segmentation and precisely removing these transient samples arising from FIR (Finite Impulsive Response) filtering, nonlinear distortion can be entirely avoided. Experimental results show that our proposed scheme can not only accurately estimate the howling frequency, but can also completely remove it, which yields a high-quality output waveform with a recovery SNR of about 22 dB. Therefore, the proposed segmented notching based scheme possesses vast potential for hearing aid development and other relevant applications.

Attractors with large complex structure for one-parameter families of Calabi-Yau manifolds

The attractor equations for an arbitrary one-parameter family of Calabi-Yau manifolds are studied in the large complex structure region. These equations are solved iteratively, generating what we term an N-expansion, which is a power series in the Gromov-Witten invariants of the manifold. The coefficients of this series are associated with integer partitions. In important cases we are able to find closed-form expressions for the general term of this expansion. To our knowledge, these are the first generic solutions to attractor equations that incorporate instanton contributions. In particular, we find a simple closed-form formula for the entropy associated to rank two attractor points, including those recently discovered. The applications of our solutions are briefly discussed. Most importantly, we are able to give an expression for the Wald entropy of black holes that includes all genus 0 instanton corrections.

String correlators on AdS3: four-point functions

We propose a closed-form formula for genus 0 four-point functions in AdS3 string theory with pure NS-NS flux including arbitrary amounts of spectral flow. Our formula passes many non-trivial consistency checks and has intriguing connections to Hurwitz theory. This paper is the second in a series with several instalments.

A closed-form pricing formula for catastrophe equity options

In this article, we derive a closed-form pricing formula for catastrophe equity put options under a stochastic interest rate framework. A distinguishing feature of the proposed solution is its simplified form in contrast to several recently published formulae that require evaluating several layers of infinite sums of $n$ -fold convoluted distribution functions. As an application of the proposed formula, we consider two different frameworks and obtain the closed-form formula for the joint characteristic function of the asset price and the losses, which is the only required ingredient in our pricing formula. The prices obtained by the newly derived formula are compared with those obtained using Monte-Carlo simulations to show the accuracy of our formula.

A Mathematical Model for the Analysis of Jet Engine Fuel Consumption during Aircraft Cruise

In this paper we propose a mathematical model for the fuel consumption analysis during aircraft cruise. A closed-form formula that expresses the aircraft’s weight variation over time, and hence, the fuel flow rate, is obtained as a result. Furthermore, a closed-form expression of the aircraft’s main performance parameters is also obtained. We compare the values of such parameters computed by using the Piano-X software and computed by using our mathematical model. Simulation results confirm that our mathematical model provides results very close to reality. Finally, the closed-form formula of the fuel flow rate provided by our model is used to improve the calculation of the carbon dioxide emissions for four example routes, which, unlike here, are usually obtained under the assumption of a constant value of the fuel flow rate.

The Effect of Mean-Reverting Processes in the Pricing of Options in the Energy Market: An Arithmetic Approach

In this paper we study the effect that mean-reverting components in the arithmetic dynamics of electricity spot price have on the price of a call option on a swap. Our model allows for seasonal effects, spikes, and negative values of the price of electricity. We show that for sufficiently large delivery periods of the swap contract, the error that one makes by neglecting some of the mean-reverting processes affecting the spot price evolution converges to zero. The decay rate is explicitly calculated. This is achieved by exploiting the additive structure of the electricity price process in order to determine an explicit closed-form formula for the price of the call on a swap. The theoretical analysis is then illustrated via a numerical example.