Wavelets for Differential Equations and Numerical Operator Calculus

Differential equations are commonplace in engineering, and lots of research have been carried out in developing methods, both efficient and precise, for their numerical solution. Nowadays the numerical practitioner can rely on a wide range of tools for solving differential equations: finite difference methods, finite element methods, meshless, and so on. Wavelets, since their appearance in the early 1990s, have attracted attention for their multiresolution nature that allows them to act as a “mathematical zoom,” a characteristic that promises to describe efficiently the functions involved in the differential equation, especially in the presence of singularities. The objective of this chapter is to introduce the main concepts of wavelets and differential equation, allowing the reader to apply wavelets to the solution of differential equations and in numerical operator calculus

Numerical Problem Encryption for High-Performance Computing Applications

Recent years witnessed the diffusion of cloud-based services. Cloud services have the interesting advantage that they can provide resources (CPU, disk space, etc.) that would be too expensive to deploy and maintain in-house. A major drawback of cloud-based services is the problem of handling private data and—possibly—intellectual property to a third party. With some service (e.g., data storage), cryptography can provide a solution; however, there are some services that are more difficult to protect. An example of such services is the renting of CPU to carry out numerical computation such as differential equation solving. In this chapter, we discuss the problem of encrypting numerical problems so that their solution can be safely outsourced. The idea is to transform (encrypt) a given numerical problem into a different one whose solution can be mapped back to the solution of the original problem if the key used at the encryption stage is known

Analytic and simulation results about a compact, reliable, and unbiased 1-bit physically unclonable constant

Physically unclonable constants (PUC) are circuits used to embed unique secret bit-words in chips. We propose a simple PUC, with a complexity comparable with an SRAM cell. The proposed scheme is studied both theoretically and by means of simulations and it is shown that the proposed PUC is both unbiased and very stable. In particular, its intra-distance is predicted to be from 10 to 100 times smaller than competitor schemes. Simulations allow to conclude that the advantages of the proposed scheme are relevant enough to make it competitive even if the actual performance of a real implementation, not considered in this paper, will turn out to be an order of magnitude worse than predicte

Group-based reduction schemes for streaming applications

Some peer-to-peer streaming systems make use of linear codes to reduce the rate of the data uploaded by peers with limited upload capabilities. Such "data reduction" techniques are based on a vector-space approach and produce the data to be uploaded by means of linear combinations of the content data in a suitable finite field. In this paper, we propose a more general approach based on group theory. The new approach, while including the vector space approach as a special case, allows to design schemes that cannot be modeled as linear codes. We analyze the properties of the schemes based on the new approach, showing also how a group-based scheme can be used to prevent stream poisoning and how a group-based scheme can be converted into a secret-sharing scheme. Examples of group-based schemes that cannot be described in the vector-space framework are also shown

On the Virtualization of Audio Transducers

In audio transduction applications, virtualization can be defined as the task of digitally altering the acoustic behavior of an audio sensor or actuator with the aim of mimicking that of a target transducer. Recently, a digital signal preprocessing method for the virtualization of loudspeakers based on inverse equivalent circuit modeling has been proposed. The method applies Leuciuc’s inversion theorem to obtain the inverse circuital model of the physical actuator, which is then exploited to impose a target behavior through the so called Direct–Inverse–Direct Chain. The inverse model is designed by properly augmenting the direct model with a theoretical two-port circuit element called nullor. Drawing on this promising results, in this manuscript, we aim at describing the virtualization task in a broader sense, including both actuator and sensor virtualizations. We provide ready-to-use schemes and block diagrams which apply to all the possible combinations of input and output variables. We then analyze and formalize different versions of the Direct–Inverse–Direct Chain describing how the method changes when applied to sensors and actuators. Finally, we provide examples of applications considering the virtualization of a capacitive microphone and a nonlinear compression driver

The hunt for cosmic neutrino sources with IceCube

IceCube is a cubic-kilometer neutrino telescope under construction at the geographic South Pole. Once completed it will comprise 4800 optical sensors deployed on 80 vertical strings at depths in the ice between 1450 and 2450 meters. Part of the array is already operational and data was recorded in the configurations with 9 (year 2006/2007), 22 (year 2007/2008) and 40-strings (year 2008/2009) respectively. Here we report preliminary results on the search for point-like neutrino sources using data collected with the first 22 strings (IC-22).Comment: 10 pages, 3 figures, prepared for the Scineghe08 Conference, Padova/Italy (2008