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In recent work, Darmon, Pozzi and Vonk explicitly construct a modular form whose spectral coefficients are $p$-adic logarithms of Gross-Stark units and Stark-Heegner points. Here we describe how this construction gives rise to a practical…

Recent years have seen a rapid increase in research activity in the field of DRAM-based Processing-In-Memory (PIM) accelerators, where the analog computing capability of DRAM is employed by minimally changing the inherent structure of DRAM…

This paper presents a novel algorithm for the modulus operation for FPGA implementation. The proposed algorithm use only addition, subtraction, logical, and bit shift operations, avoiding the complexities and hardware costs associated with…

In this paper, we propose the Adaptive Physics-Informed Neural Networks (APINNs) for accurate and efficient simulation-free Bayesian parameter estimation via Markov-Chain Monte Carlo (MCMC). We specifically focus on a class of parameter…

The alternating direction method of multipliers (ADMM) is commonly used for distributed model fitting problems, but its performance and reliability depend strongly on user-defined penalty parameters. We study distributed ADMM methods that…

The quality of the part fabricated from the Additive Manufacturing (AM) process depends upon the process parameters used, and therefore, optimization is required for apt quality. A methodology is proposed to set these parameters…

The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…

We present a fast algorithm for modular exponentiation when the factorization of the modulus is known. Let $a,n,m$ be positive integers and suppose $m$ factors canonically as $\prod_{i=1}^k p_i^{e_i}$. Choose integer parameters $t_i\in [1,…

Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…

Polynomial multiplication is a key algorithm underlying computer algebra systems (CAS) and its efficient implementation is crucial for the performance of CAS. In this paper we design and implement algorithms for polynomial multiplication…

Innovative membrane technologies optimally integrated into large separation process plants are essential for economical water treatment and disposal. However, the mass transport through membranes is commonly described by nonlinear…

Generalized Additive Models (GAMs) have quickly become the leading choice for inherently-interpretable machine learning. However, unlike uninterpretable methods such as DNNs, they lack expressive power and easy scalability, and are hence…

Transformers have emerged as a powerful tool for natural language processing (NLP) and computer vision. Through the attention mechanism, these models have exhibited remarkable performance gains when compared to conventional approaches like…

We give an $O(N\cdot \log N\cdot 2^{O(\log^*N)})$ algorithm for multiplying two $N$-bit integers that improves the $O(N\cdot \log N\cdot \log\log N)$ algorithm by Sch\"{o}nhage-Strassen. Both these algorithms use modular arithmetic.…

Photonic computing is a compelling avenue for performing highly efficient matrix multiplication, a crucial operation in Deep Neural Networks (DNNs). While this method has shown great success in DNN inference, meeting the high precision…

Integral linear systems $Ax=b$ with matrices $A$, $b$ and solutions $x$ are also required to be in integers, can be solved using invariant factors of $A$ (by computing the Smith Canonical Form of $A$). This paper explores a new problem…

Adapters are light-weight modules that allow parameter-efficient fine-tuning of pretrained models. Specialized language and task adapters have recently been proposed to facilitate cross-lingual transfer of multilingual pretrained models…

The alternating direction method of multipliers (ADMM) has been widely adopted in low-rank approximation and low-order model identification tasks; however, the performance of nonconvex ADMM is highly reliant on the choice of penalty…

Polynomial preconditioning can improve the convergence of the Arnoldi method for computing eigenvalues. Such preconditioning significantly reduces the cost of orthogonalization; for difficult problems, it can also reduce the number of…

In recent years, the integration of Machine Learning (ML) models with Operation Research (OR) tools has gained popularity across diverse applications, including cancer treatment, algorithmic configuration, and chemical process optimization.…