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The ring Z_k(+,.) mod p^k with prime power modulus (prime p>2) is analysed. Its cyclic group G_k of units has order (p-1)p^{k-1}, and all p-th power n^p residues form a subgroup F_k with |F_k|=|G_k|/p. The subgroup of order p-1, the core…
The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and the representations of these algebras are…
We introduce a novel neural network architecture for encoding and synthesis of 3D shapes, particularly their structures. Our key insight is that 3D shapes are effectively characterized by their hierarchical organization of parts, which…
We show how one can use non-prime-power, composite moduli for computing representations of the product of two $n\times n$ matrices using only $n^{2+o(1)}$ multiplications.
In recent years, deep neural network (DNN) compression systems have proved to be highly effective for designing source codes for many natural sources. However, like many other machine learning systems, these compressors suffer from…
The optimal branch number of MDS matrices makes them a preferred choice for designing diffusion layers in many block ciphers and hash functions. However, in lightweight cryptography, Near-MDS (NMDS) matrices with sub-optimal branch numbers…
While deep neural networks extract rich features from the input data, the current trade-off between depth and computational cost makes it difficult to adopt deep neural networks for many industrial applications, especially when computing…
This technical note describes the design and modular implementation of a one-dimensional convolutional neural network (1D CNN) adapted from residual networks (ResNet), developed for photometric regression tasks with an emphasis on low star…
High energy physics has a constant demand for random number generators (RNGs) with high statistical quality. In this paper, we present ROOT's implementation of the RANLUX++ generator. We discuss the choice of relying only on standard C++…
Recent developments in storage -- especially in the area of resistive random access memory (ReRAM) -- are attempting to scale the storage density by regarding the information data as two-dimensional (2D), instead of one-dimensional (1D).…
For h=3 or 4, Egyptian decompositions into h unit fractions, like 2/D = 1/D1 + ... +1/Dh, were given by using (h-1) divisors (di) of D1. This ancient modus operandi, well recognized today, provides Di=DD1/di for i greater than 1.…
A delayed feedback reservoir (DFR) is a reservoir computing system well-suited for hardware implementations. However, achieving high accuracy in DFRs depends heavily on selecting appropriate hyperparameters. Conventionally, due to the…
Regenerating codes are a class of distributed storage codes that optimally trade the bandwidth needed for repair of a failed node with the amount of data stored per node of the network. Minimum Storage Regenerating (MSR) codes minimize…
Sorting is a fundamental operation in computer systems and is widely used in applications such as databases, data analytics, and hardware accelerators. Unary computing has recently emerged as a low-cost and power-efficient paradigm for…
Large statically indeterminate truss and frame structures exhibit complex load-bearing behavior, and redundancy matrices are helpful for their analysis and design. Depending on the task, the full redundancy matrix or only its diagonal…
Array codes have been widely employed in storage systems, such as Redundant Arrays of Inexpensive Disks (RAID). The row-diagonal parity (RDP) codes and EVENODD codes are two popular double-parity array codes. As the capacity of hard disks…
We present Unified PDE Solvers (UPS), a data- and compute-efficient approach to developing unified neural operators for diverse families of spatiotemporal PDEs from various domains, dimensions, and resolutions. UPS embeds different PDEs…
High-speed long polynomial multiplication is important for applications in homomorphic encryption (HE) and lattice-based cryptosystems. This paper addresses low-latency hardware architectures for long polynomial modular multiplication using…
This paper investigates deep neural network (DNN) compression from the perspective of compactly representing and storing trained parameters. We explore the previously overlooked opportunity of cross-layer architecture-agnostic…
Given n polynomials in n variables with a finite number of complex roots, for any of their roots there is a local residue operator assigning a complex number to any polynomial. This is an algebraic, but generally not rational, function of…