Related papers: The 10-point and 12-point Number Theoretic Hilbert…
Solutions to the $n$-dimensional Laplace equation which are constant on a central quadric are found. The associated twistor description of the case $n=3$ is used to characterise Gibbons-Hawking metrics with tri-holomorphic $SL(2, \C)$…
In this project we examine several different quantum key distribution protocols which we divide into ones utilizing qubits whose Hilbert spaces are two dimensional and ones whose Hilbert space dimension is greater than two, these units of…
Can transformers generalize efficiently on problems that require dealing with examples with different levels of difficulty? We introduce a new task tailored to assess generalization over different complexities and present results that…
The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point…
From their inception, quaternions and their division algebra have proven to be advantageous in modelling rotation/orientation in three-dimensional spaces and have seen use from the initial formulation of electromagnetic filed theory through…
The state-of-the-art hardware platforms for training Deep Neural Networks (DNNs) are moving from traditional single precision (32-bit) computations towards 16 bits of precision -- in large part due to the high energy efficiency and smaller…
We apply the Hilbert transform to the physics of internal waves in two-dimensional fluids. Using this demodulation technique, we can discriminate internal waves propagating in different directions: this is very helpful in answering several…
The classical Talbot method for the computation of the inverse Laplace transform is improved for the case where the transform is analytic in the complex plane except for the negative real axis. First, by using a truncated Talbot contour…
Designing privacy-preserving deep learning models is a major challenge within the deep learning community. Homomorphic Encryption (HE) has emerged as one of the most promising approaches in this realm, enabling the decoupling of knowledge…
For a continuous angle-valued map defined on a compact ANR, a fixed field and any degree one proposes a refinement of the Novikov-Betti number and of the Novikov homology of the pair consisting of the ANR and the degree one integral…
This paper presents digital hardware for computing polynomial multiplication using Number Theoretic Transform (NTT), specifically designed for implementation on Field Programmable Gate Arrays (FPGAs). Multiplying two large polynomials…
Numerical integration methods are central to the study of self-gravitating systems, particularly those comprised of many bodies or otherwise beyond the reach of analytical methods. Predictor-corrector schemes, both multi-step methods and…
This paper presents several numerical applications of deep learning-based algorithms that have been introduced in [HPBL18]. Numerical and comparative tests using TensorFlow illustrate the performance of our different algorithms, namely…
Integral transformations are used to estimate high order derivatives of various special functions. Applications are given to numerical integration, where estimates of high order derivatives of the integrand are needed to achieve bounds on…
Neural Machine Translation (NMT) is resource intensive. We design a quantization procedure to compress NMT models better for devices with limited hardware capability. Because most neural network parameters are near zero, we employ…
Iterative algorithms are fundamental tools for approximating fixed-points of nonexpansive operators in real Hilbert spaces. Among them, Krasnosel'ski\u{\i}--Mann iteration and Halpern iteration are two widely used schemes. In this work, we…
A low-complexity 8-point orthogonal approximate DCT is introduced. The proposed transform requires no multiplications or bit-shift operations. The derived fast algorithm requires only 14 additions, less than any existing DCT approximation.…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
A comprehensive approach to the spectrum characterization (derivation of eigenvalues and the corresponding multiplicities) for non-normalized, symmetric discrete trigonometric transforms (DTT) is presented in the paper. Eight types of the…
A multi-domain spectral method is presented to compute the Hilbert transform on the whole compactified real line, with a special focus on piece-wise analytic functions and functions with algebraic decay towards infinity. Several examples of…