Ball arithmetic

33 pagesThe Mathemagix project aims at the development of a ''computer analysis'' system, in which numerical computations can be done in a mathematically sound manner. A major challenge for such systems is to conceive algorithms which are both efficient, reliable and available at any working precision. In this paper, we survey several older and newer such algorithms. We mainly concentrate on the automatic and efficient computation of high quality error bounds, based on a variant of interval arithmetic which we like to call ''ball arithmetic''

Synthetic aperture radar/LANDSAT MSS image registration

Algorithms and procedures necessary to merge aircraft synthetic aperture radar (SAR) and LANDSAT multispectral scanner (MSS) imagery were determined. The design of a SAR/LANDSAT data merging system was developed. Aircraft SAR images were registered to the corresponding LANDSAT MSS scenes and were the subject of experimental investigations. Results indicate that the registration of SAR imagery with LANDSAT MSS imagery is feasible from a technical viewpoint, and useful from an information-content viewpoint

Indirect measurement of flow of liquid pumped with pump packages

This paper discusses some research results for indirect measurement methods for pump packagesbased on their head-capacity curves. The paper shows the results of experimental research intoindirect measurement by approximation of vertical lift performance of a pump package with algebraicpolynomials of 2nd and 3rd order illustrating their applicability to solution of tasks pertaining toretrospective estimation of polynomial coefficients for the vertical lift performance approximation.Values of relative errors for indirect measurement of transferred liquid flow with such polynomialsare given

Advanced Centaur explicit guidance equation study Final report

Generalized equations and in-flight computer requirements for Centaur guidance and control and advanced mission plannin

Quantum Circuit Optimization of Arithmetic circuits using ZX Calculus

Quantum computing is an emerging technology in which quantum mechanical properties are suitably utilized to perform certain compute-intensive operations faster than classical computers. Quantum algorithms are designed as a combination of quantum circuits that each require a large number of quantum gates, which is a challenge considering the limited number of qubit resources available in quantum computing systems. Our work proposes a technique to optimize quantum arithmetic algorithms by reducing the hardware resources and the number of qubits based on ZX calculus. We have utilised ZX calculus rewrite rules for the optimization of fault-tolerant quantum multiplier circuits where we are able to achieve a significant reduction in the number of ancilla bits and T-gates as compared to the originally required numbers to achieve fault-tolerance. Our work is the first step in the series of arithmetic circuit optimization using graphical rewrite tools and it paves the way for advancing the optimization of various complex quantum circuits and establishing the potential for new applications of the same

Splines in Compressed Sensing

It is well understood that in any data acquisition system reduction in the amount of data reduces the time and energy, but the major trade-off here is the quality of outcome normally, lesser the amount of data sensed, lower the quality. Compressed Sensing (CS) allows a solution, for sampling below the Nyquist rate. The challenging problem of increasing the reconstruction quality with less number of samples from an unprocessed data set is addressed here by the use of representative coordinate selected from different orders of splines. We have made a detailed comparison with 10 orthogonal and 6 biorthogonal wavelets with two sets of data from MIT Arrhythmia database and our results prove that the Spline coordinates work better than the wavelets. The generation of two new types of splines such as exponential and double exponential are also briefed here .We believe that this is one of the very first attempts made in Compressed Sensing based ECG reconstruction problems using raw data.

Analogue neuromorphic systems.

This thesis addresses a new area of science and technology, that of neuromorphic systems, namely the problems and prospects of analogue neuromorphic systems. The subject is subdivided into three chapters. Chapter 1 is an introduction. It formulates the oncoming problem of the creation of highly computationally costly systems of nonlinear information processing (such as artificial neural networks and artificial intelligence systems). It shows that an analogue technology could make a vital contribution to the creation such systems. The basic principles of creation of analogue neuromorphic systems are formulated. The importance will be emphasised of the principle of orthogonality for future highly efficient complex information processing systems. Chapter 2 reviews the basics of neural and neuromorphic systems and informs on the present situation in this field of research, including both experimental and theoretical knowledge gained up-to-date. The chapter provides the necessary background for correct interpretation of the results reported in Chapter 3 and for a realistic decision on the direction for future work. Chapter 3 describes my own experimental and computational results within the framework of the subject, obtained at De Montfort University. These include: the building of (i) Analogue Polynomial Approximator/lnterpolatoriExtrapolator, (ii) Synthesiser of orthogonal functions, (iii) analogue real-time video filter (performing the homomorphic filtration), (iv) Adaptive polynomial compensator of geometrical distortions of CRT- monitors, (v) analogue parallel-learning neural network (backpropagation algorithm). Thus, this thesis makes a dual contribution to the chosen field: it summarises the present knowledge on the possibility of utilising analogue technology in up-to-date and future computational systems, and it reports new results within the framework of the subject. The main conclusion is that due to its promising power characteristics, small sizes and high tolerance to degradation, the analogue neuromorphic systems will playa more and more important role in future computational systems (in particular in systems of artificial intelligence)

Expressive variational quantum circuits provide inherent privacy in federated learning

Federated learning has emerged as a viable distributed solution to train machine learning models without the actual need to share data with the central aggregator. However, standard neural network-based federated learning models have been shown to be susceptible to data leakage from the gradients shared with the server. In this work, we introduce federated learning with variational quantum circuit model built using expressive encoding maps coupled with overparameterized ans\"atze. We show that expressive maps lead to inherent privacy against gradient inversion attacks, while overparameterization ensures model trainability. Our privacy framework centers on the complexity of solving the system of high-degree multivariate Chebyshev polynomials generated by the gradients of quantum circuit. We present compelling arguments highlighting the inherent difficulty in solving these equations, both in exact and approximate scenarios. Additionally, we delve into machine learning-based attack strategies and establish a direct connection between overparameterization in the original federated learning model and underparameterization in the attack model. Furthermore, we provide numerical scaling arguments showcasing that underparameterization of the expressive map in the attack model leads to the loss landscape being swamped with exponentially many spurious local minima points, thus making it extremely hard to realize a successful attack. This provides a strong claim, for the first time, that the nature of quantum machine learning models inherently helps prevent data leakage in federated learning.Comment: 24 pages, 13 figure