Lafont 11] gives an elegant proof of nite model property (fmp) for Multiplicative-Additive Linear Logic (MALL) and suggests it can be adapted to noncommutative linear logics of Abrusci 1]. In 4, 6, 9], fmp for certain fragments of MALL (e.g. BCI, BCII^]) and weaker systems (e.g. the product-free Lambek calculus) has been proven by a diierent method; whereas Lafont uses phase space models and qu...

A stable discrete-time control system may become unstable when the discrete-time control law is implemented with a xed-point digital control processor (DCP) due to the nite word length (FWL) eeects which depend on the control law structures and the discrete-time representations (e.g., delta operator or forward-shift representations) used to represent the control laws. To improve closed-loop sta...

Photon-Counting CT is an emerging imaging technology that promises higher spatial resolution and the possibility for material decomposition in reconstruction. A major difficulty to efficiently model cross-talk between detectors. In this work, we accelerate image reconstruction tasks by modelling with appropriately trained deep convolutional neural network. The main result relates proving conver...

interpretation: Domains and surroundings. Abstract interpretation is a general theory for specifying and designing approximate semantics of program languages [10]. Approximation can be equivalently formulated either in terms of Galois connections or closure operators [11]. An upper closure operator ρ : C → C on a poset C (uco(C ) for short), representing concrete objects, is monotone, idempoten...

The convexity of numerical domains such as polyhedra, octagons, intervals and linear equalities enables tractable analysis of software for buffer overflows, null pointer dereferences and floating point errors. However, convexity also causes the analysis to fail in many common cases. Powerset extensions can remedy this shortcoming by considering disjunctions of predicates. Unfortunately, analysi...

We discuss the implications of the desire to augment a functionalprogramming language with a derivative-taking operator using forward-mode automatic differentiation (AD). The primary technical difficulty in doing so lies in ensuring correctness in the face of nested invocation of that operator, due to the need to distinguish perturbations introduced by distinct invocations. We exhibit a series ...

We show that projected-gradient methods for the distributed computation of generalized Nash equilibria in aggregative games are preconditioned forward-backward splitting methods applied to the KKT operator of the game. Specifically, we adopt the preconditioned forward-backward design, recently conceived by Yi and Pavel in the manuscript “A distributed primal-dual algorithm for computation of ge...

This paper deals with a broad question—to what extent is topology algebraic—using two specific questions: (1) what are the algebraic conditions on the underlying membership lattices which insure that categories for topology and fuzzy topology are indeed topological categories; and (2) what are the algebraic conditions which insure that algebraic theories in the sense of Manes are a foundation f...

This talk aims at presenting a new way of approaching topological structures, induced by recent developments in the eld of lattice-valued topology, and deemed to incorporate in itself both crisp and many-valued settings. Based on category theory and universal algebra, the new framework is called categorically-algebraic (catalg) [9-12], to underline its motivating theories, on one hand, and to d...

We examine double successive approximations on a set, which we denote by L2L1, U2U1, U2L1, L2U1 where L1, U1 and L2, U2 are based on generally non-equivalent equivalence relations E1 and E2 respectively, on a finite non-empty set V. We consider the case of these operators being given fully defined on its powerset P(V ). Then, we investigate if we can reconstruct the equivalence relations which ...