We strengthen the non-deterministic time hierarchy theorem of [5,15,18] to show that the lower bound holds against sublinear advice. More formally, we show that for any constants c and d such that 1 6 c < d, there is a language in NTIME(n) which is not in NTIME(n)/n. The best known earlier separation [8] could only handle o(log(n)) bits of advice in the lower bound. We generalize our hierarchy ...

Although integral and differential nonlinearity may not be the most important parameters for high-speed, high dynamic performance data converters, they gain significance when it comes to highresolution imaging applications. The following application note serves as a refresher course for their definitions and details two different, yet commonly used techniques to measure INL and DNL in highspeed...

Properties of increasing-weakly lower semicontinuous (LSC) sublinear functionals on the positive cone L 1 + are of importance for study miscellaneous non-controlled factors from a uniied viewpoint based on the notion of sublinear expectation 3, 4 and 5]. For every such functional N there are deened the class is proved and their description is given. The orders induced in L 11 by convex cones co...

We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that mean-uncertainty can be also described. W present our new result of central limit theorem under sublinear expectation. This theorem can be also regarded as a ge...

We consider the problem of testing whether (a large part of) a given string X of length n over some finite alphabet is covered by multiple occurrences of some (unspecified) pattern Y of arbitrary length in the combinatorial property testing model. Our algorithms randomly query a sublinear number of positions of X, and run in sublinear time in n. We first focus on finding patterns of a given len...

In this paper, we show that minimization problems involving sublinear regularizing terms are ill-posed, in general, although numerical experiments in image processing give very good results. The energies studied here are inspired by image restoration and image decomposition. Rewriting the nonconvex sublinear regularizing terms as weighted total variations, we give a new approach to perform mini...

We consider the problem of the presence of short cycles in the graphs of nonzero elements of matrices which have sublinear rank and nonzero entries on the main diagonal, and analyze the connection of these properties to the rigidity of matrices. In particular, we exhibit a family of matrices which shows that sublinear rank does not imply the existence of triangles. This family can also be used ...

We consider the problem of the presence of short cycles in the graphs of nonzero elements of matrices which have sublinear rank and nonzero entries on the main diagonal, and analyze the connection between these properties and the rigidity of matrices. In particular, we exhibit a family of matrices which shows that sublinear rank does not imply the existence of triangles. This family can also be...

We describe algorithms for point multiplication on Koblitz curves using multiple-base expansions of the form k = ∑ ±τ(τ − 1) and k = ∑ ±τ(τ −1)(τ− τ −1). We prove that the number of terms in the second type is sublinear in the bit length of k, which leads to the first provably sublinear point multiplication algorithm on Koblitz curves. For the first type, we conjecture that the number of terms ...

The zero-entropy-density conjecture states that the entropy density defined as s ≔ lim N→∞ S N /N vanishes for all translation-invariant pure states on the spin chain. Or equivalently, S N , the von Neumann entropy of such a state restricted to N consecutive spins, is sublinear. In this paper it is proved that this conjecture cannot be sharpened, i.e., translation-invariant states give rise to ...