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We show that the time-resolved dynamics of an underdamped harmonic oscillator can be used to do multifunctional computation, performing distinct computations at distinct times within a single dynamical trajectory. We consider the amplitude…

Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…

We present the design of an analog circuit which solves linear programming (LP) problems. In particular, the steady-state circuit voltages are the components of the LP optimal solution. The paper shows how to construct the circuit and…

Oscillator based Ising machines are non-von-Neumann machines ideally suited for solving combinatorial problems otherwise intractable on classic stored-program digital computers due to their run-time complexity. Possible future applications…

Many combinatorial problems can be mapped to Ising machines, i.e., networks of coupled oscillators that settle to a minimum-energy ground state, from which the problem solution is inferred. This work proposes DROID, a novel event-driven…

In this paper we briefly discuss \Rings --- an efficient lightweight library for commutative algebra. Polynomial arithmetic, GCDs, polynomial factorization and Gr\"obner bases are implemented with the use of modern asymptotically fast…

We develop a custom printed circuit board (PCB) for a low-power and high-speed accelerator of NP-Hard graph problems. The architecture implements an annealing-based computing paradigm using a network of nonlinear electronic oscillators…

Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…

Algebraic multigrid (AMG) methods are powerful solvers with linear or near-linear computational complexity for certain classes of linear systems, Ax=b. Broadening the scope of problems that AMG can effectively solve requires the development…

In-memory computing with crosspoint resistive memory arrays has been shown to accelerate data-centric computations such as the training and inference of deep neural networks, thanks to the high parallelism endowed by physical rules in the…

Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to…

Analog integrated circuit (IC) floorplanning is typically a manual process with the placement of components (devices and modules) planned by a layout engineer. This process is further complicated by the interdependence of floorplanning and…

The rapidly increasing size of deep-learning models has caused renewed and growing interest in alternatives to digital computers to dramatically reduce the energy cost of running state-of-the-art neural networks. Optical matrix-vector…

In this paper, we derive a variational integrator for certain highly oscillatory problems in mechanics. To do this, we take a new approach to the splitting of fast and slow potential forces: rather than splitting these forces at the level…

With an increasing number of power-states, finer- grained power management and larger dynamic ranges of digital circuits, the integration of compact, scalable linear-regulators embedded deep within logic blocks has become important. While…

The slowing of Moore's law and the increasing energy demands of machine learning present critical challenges for both the hardware and machine learning communities, and drive the development of novel computing paradigms. Of particular…

The frenetic growth of the need for computation performance and efficiency, along with the intrinsic limitations of the current main solutions, is pushing the scientific community towards unconventional, and sometimes even exotic,…

Model order reduction (MOR) is crucial for the design process of integrated circuits. Specifically, the vast amount of passive RLCk elements in electromagnetic models extracted from physical layouts exacerbates the extraction time, the…

We develop two classes of composite moment-free numerical quadratures for computing highly oscillatory integrals having integrable singularities and stationary points. The first class of the quadrature rules has a polynomial order of…

The growing demand for edge computing and AI drives research into analog in-memory computing using memristors, which overcome data movement bottlenecks by computing directly within memory. However, device failures and variations critically…