We present a probabilistic construction of $\mathbb{R}^d$ -valued non-linear affine processes with jumps. Given set $\Theta$ parameters, we define family sublinear expectations on the Skorokhod space under which canonical process X is (sublinear) Markov generator. This yields tractable model for Knightian uncertainty expectation Markovian functional can be calculated via partial integro-differe...

We consider randomized encodings (RE) that enable encoding a Turing machine Π and input x into its “randomized encoding” Π̂(x) in sublinear, or even polylogarithmic, time in the running-time of Π(x), independent of its output length. We refer to the former as sublinear RE and the latter as compact RE. For such efficient RE, the standard simulation-based notion of security is impossible, and we t...

background and objective: one way to promote education quality is to evaluate faculty activities by students, departmental heads, and the dean. the degree of correspondence between students' and departmental heads' evaluation shows how honest they are in their assessment. the current paper intends to find the truth.     materials and methods : questionnaires were used to conduct the s...

It has recently been observed that sparse and compressible signals can be sketched using very few nonadaptive linear measurements in comparison with the length of the signal. This sketch can be viewed as an embedding of an entire class of compressible signals into a low-dimensional space. In particular, d-dimensional signals with m nonzero entries (m-sparse signals) can be embedded in O(m log d...

The output scores of a neural network classifier are converted to probabilities via normalizing over the scores of all competing categories. Computing this partition function, Z, is then linear in the number of categories, which is problematic as real-world problem sets continue to grow in categorical types, such as in visual object recognition or discriminative language modeling. We propose th...

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 ...

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...