In embedded systems, efficient implementations of numerical algorithms typically use the fixed-point arithmetic rather than the standardized and costly floating-point arithmetic. But, fixed-point programmers face two difficulties: First, writing fixed-point codes is tedious and error prone. Second, the low dynamic range of fixed-point numbers leads to the persistent belief that fixedpoint compu...

Numerical software, common in scientific computing or embedded systems, inevitably uses a finiteprecision approximation of the real arithmetic in which most algorithms are designed. In many applications, the roundoff errors introduced by finite-precision arithmetic are not the only source of inaccuracy, and measurement and other input errors further increase the uncertainty of the computed resu...

Queuing is a common phenomenon in theme parks which negatively affects visitor experience and revenue yields. There is thus a need for park operators to infer the real queuing delays without expensive investment in human effort or complex tracking infrastructure. In this paper, we depart from the classical queuing theory approach and provide a data-driven and online approach for estimating the ...

A grove theory is a Lawvere algebraic theory T for which each hom-set T (n, p) is a commutative monoid; composition on the right distrbutes over all finite sums: ( ∑ i∈F fi) ·h = ∑ i∈F fi ·h. A matrix theory is a grove theory in which composition on the left and right distributes over finite sums. A matrix theory M is isomorphic to a theory of all matrices over the semiring S = M(1, 1). Example...

A special final coalgebra theorem, in the style of Aczel (1988), is proved within standard Zermelo-Fraenkel set theory. Aczel’s Anti-Foundation Axiom is replaced by a variant definition of function that admits non-well-founded constructions. Variant ordered pairs and tuples, of possibly infinite length, are special cases of variant functions. Analogues of Aczel’s solution and substitution lemma...

̈ find x ∈ R s. t. x i ≥ 0, Fi(x)≥ 0, x iFi(x) = 0, for i = 1, · · · ,n, where F(x) : R → R is assumed to be continuously differentiable. There have been extensive studies for complementarity problems, see for example [5] and a recent review paper [7]. The NCP was introduced by Cottle [4] in his Ph.D. thesis in 1964. At the beginning, it was recognized that the NCP is a special case of a variati...

Signal processing theory and practice are enabling and driving forces behind multimedia devices, communications systems, and even such diverse fields as automotive and medical systems. Over 90% of the signal processing systems on the market used fixed-point arithmetic because of the cost, power, and area savings that fixed-point systems provide. However, most colleges and universities do not te...

In The Revision Theory of Truth (MIT Press), Gupta and Belnap (1993) claim as an advantage of their approach to truth “its consequence that truth behaves like an ordinary classical concept under certain conditions— conditions that can roughly be characterized as those in which there is no vicious reference in the language.” To clarify this remark, they define Thomason models, nonpathological mo...

This two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derive a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model is stated for both meshed and radial networks, and is parameterized by several graph-theoretic matrices – the power network stiffness matrices – which quantify...

A special final coalgebra theorem, in the style of Aczel’s [2], is proved within standard Zermelo-Fraenkel set theory. Aczel’s AntiFoundation Axiom is replaced by a variant definition of function that admits non-well-founded constructions. Variant ordered pairs and tuples, of possibly infinite length, are special cases of variant functions. Analogues of Aczel’s Solution and Substitution Lemmas ...