Related papers: Wave-Shaped Round Functions and Primitive Groups
Diffusion-weighted magnetic resonance imaging allows for reconstruction of models for structural connectivity in the brain, such as fiber orientation distribution functions (ODFs) that describe the distribution, direction, and volume of…
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
In the desire to quantify the success of neural networks in deep learning and other applications, there is a great interest in understanding which functions are efficiently approximated by the outputs of neural networks. By now, there…
Following [14] and [12], we formalize the notion of an oscillatory integral interpreted as a functional on the amplitudes supported near a fixed critical point $x_0$ of the phase function with zero critical value. We relate to an…
We seek to develop network algorithms for function computation in sensor networks. Specifically, we want dynamic joint aggregation, routing, and scheduling algorithms that have analytically provable performance benefits due to in-network…
Modern quantum chemistry can make quantitative predictions on an immense array of chemical systems. However, the interpretation of those predictions is often complicated by the complex wave function expansions used. Here we show that an…
We further elaborate on a phase-space picture for a system of $N$ qubits and explore the structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves satisfying certain additional properties and…
We study diffusion and wave equations in networks. Combining semigroup and variational methods we obtain well-posedness and many nice properties of the solutions in general L^p -context. Following earlier articles of other authors, we…
Group convolutional layers with respect to some group $G$ are modeled by convolutions or cross-correlations with a filter, and they provide the fundamental building block for group convolutional neural networks. For entirely unconstrained…
Intrinsic random functions (IRF) provide a versatile approach when the assumption of second-order stationarity is not met. Here, we develop the IRF theory on the circle with its universal kriging application. Unlike IRF in Euclidean spaces,…
The XCRUSH family of non-Feistel, ARX block ciphers is designed to make efficient use of modern 64-bit general-purpose processors using a small number of encryption rounds which are simple to implement in software. The avalanche function,…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the sixth paper, exact analysis of the wave propagation in a beam with rectangular…
Cryptography is always very important in data origin authentications, entity authentication, data integrity and confidentiality. In recent years, a variety of chaotic cryptographic schemes have been proposed. These schemes have typical…
This thesis aims to use intelligent systems to extend and improve performance and security of cryptographic techniques. Genetic algorithms framework for cryptanalysis problem is addressed. A novel extension to the differential cryptanalysis…
Photons, acting as ``flying qubits'' in propagation geometries such as waveguides, appear unavoidably in the form of wavepackets (pulses). The actual shape of the photonic wavepacket, as well as possible temporal/spectral correlations…
We propose a novel type of a spin wave computing device, based on a bilayer structure which includes a bias layer, made from a hard magnetic material and a propagation layer, made from a magnetic material with low damping, for example,…
Fractional Fourier transform and chaos functions play a key role in many of encryption-decryption algorithms. In this work performance of image encryption-decryption algorithms is quantified and compared using the computation time i.e. the…
An exploratory study of two-particle wave function is carried out with a four dimensional simple model. The wave functions not only for two-particle ground and first excited states but also for an unstable state are calculated from three-…
While granular segregation in partially filled containers has been studied extensively, granular dynamics in densely filled spheres is not fully understood. Here, surface band segregation and granular convection are reported in a rotating…
Permutations over $F_{2^{2k}}$ with low differential uniform, high algebraic degree and high nonlinearity are of great cryptographical importance since they can be chosen as the substitution boxes (S-boxes) for many block ciphers. A well…