We consider optimization problems of the following type: min{tr(CX) : A(X) = B,X positive semidefinite}. Here, tr(·) denotes the trace operator, C and X are symmetric n× n matrices, B is a symmetric m ×m matrix and A(·) denotes a linear operator. Such problems are called semidefinite programs and have recently become the object of considerable interest due to important connections with max-min ...

In this paper, a smoothing algorithm for training max-min neural networks is proposed. Specifically, we apply a smooth function to approximate functions and use this smoothing technique twice, once to eliminate the inner operator and once to eliminate the operator. In place of actual network output by its approximation function, we use all partial derivatives of the approximation function with ...

The paper explores the polyfunctional word 都 to TO in early Southern Min texts dating back to the sixteenth century or even earlier. Unlike 都 dou in Mandarin, which mainly functions as a maximality operator, 都 to in Southern Min is chiefly used as a modal particle expressing a concessive meaning or meaning of unexpectedness as a type of conventional implicature rather than pragmatic inference. ...

State of the art statistical timing analysis (STA) tools often yield less accurate results when timing variables become correlated due to global source of variations and path reconvergence. To the best of our knowledge, no good solution is available dealing both types of correlations simultaneously. In this paper, we present a novel statistic timing algorithm, AMECT (Asymptotic MAX/MIN approxim...

A second order characterization of functions which have convex level sets (quasiconvex functions) results in the operator L0(Du,Du) = min{v ·D2u vT | |v| = 1, |v ·Du| = 0}. In two dimensions this is the mean curvature operator, and in any dimension L0(Du,Du)/|Du| is the first principal curvature of the surface S = u−1(c). Our main results include a comparison principle for L0(Du,Du) = g when g ...

In our previous study, we defined the semantics of modal μ-calculus on minplus algebra N∞ and developed a model-checking algorithm. N∞ is the set of all natural numbers and infinity (∞), and has two operations min and plus. In the semantics, disjunctions are interpreted by min and conjunctions by plus. This semantics allows interesting properties of a Kripke structure, such as the shortest path...

In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and gen...

Let (M, g, σ) be a closed Riemannian spin manifold of dimension n ≥ 2. We define the two quantities λ±min(M, [g], σ) := infg∈[g] |λ ± 1 (g)|Vol(M, g) , where λ+1 (g) is the smallest positive eigenvalue of the Dirac operator D and λ−1 (g) is its largest negative eigenvalue. If S is the sphere S with the standard metric, it is known that the two inequalities λ±min(M, [g], σ) ≤ λ + min(S ) hold. I...

We introduce a logical language with nullary operators min(n), for each non-negative integer n, which mean ‘the reasoner has at least n different beliefs’. The resulting language allows us to express interesting properties of non-monotonic and resourcebounded reasoners. Other operators, such as ‘the reasoner has at most n different beliefs’ and the operator introduced in [1, 4]: ‘the reasoner k...