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We perform a numerical approximation of coherent sets in finite-dimensional smooth dynamical systems by computing singular vectors of the transfer operator for a stochastically perturbed flow. This operator is obtained by solution of a…

Scientific computing programs often undergo aggressive compiler optimization to achieve high performance and efficient resource utilization. While performance is critical, we also need to ensure that these optimizations are correct. In this…

Verification of programs using floating-point arithmetic is challenging on several accounts. One of the difficulties of reasoning about such programs is due to the peculiarities of floating-point arithmetic: rounding errors, infinities,…

Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…

Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized…

This paper provides an introduction to the design of augmented data structures that offer an efficient representation of a mathematical sequence and fast sequential summation algorithms, which guarantee both logarithmic running time and…

In this survey article we present difference field algorithms for symbolic summation. Special emphasize is put on new aspects in how the summation problems are rephrased in terms of difference fields, how the problems are solved there, and…

We consider distributed stochastic optimization problems that are solved with master/workers computation architecture. Statistical arguments allow to exploit statistical similarity and approximate this problem by a finite-sum problem, for…

Entanglement has shown promise in enhancing information processing tasks in a sensor network, via distributed quantum sensing protocols. As noise is ubiquitous in sensor networks, error correction schemes based on Gottesman, Kitaev and…

Within the past years, hardware vendors have started designing low precision special function units in response to the demand of the Machine Learning community and their demand for high compute power in low precision formats. Also the…

This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…

In this paper, we propose a mixed-precision convolution unit architecture which supports different integer and floating point (FP) precisions. The proposed architecture is based on low-bit inner product units and realizes higher precision…

A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…

Minimizing loss functions is central to machine-learning training. Although first-order methods dominate practical applications, higher-order techniques such as Newton's method can deliver greater accuracy and faster convergence, yet are…

Parallel-across-the method time integration can provide small scale parallelism when solving initial value problems. Spectral deferred corrections (SDC) with a diagonal sweeper, which is closely related to iterated Runge-Kutta methods…

The rapid advancements in high-dimensional statistics and machine learning have increased the use of first-order methods. Many of these methods can be regarded as instances of the proximal point algorithm. Given the importance of the…

We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hoelder or Sobolev spaces. First we discuss optimal deterministic and randomized algorithms. Then we add a new…

Many problems in science and engineering involve, as part of their solution process, the consideration of a separable function which is the sum of two convex functions, one of them possibly non-smooth. Recently a few works have discussed…

In communication networks, optimization is essential in enhancing performance metrics, e.g., network utility. These optimization problems often involve sum-of-products (or ratios) terms, which are typically non-convex and NP-hard, posing…

Building on the previous work of Lee et al. and Ferdinand et al. on coded computation, we propose a sequential approximation framework for solving optimization problems in a distributed manner. In a distributed computation system, latency…