In this article we investigate some modifications of the total variation inpainting model and discuss the existence as well as the smoothness of solutions to these new variational problems. We emphasize that our variant of a linear growth regulariza-tion is completely discussed in the Sobolev space W 1 1 without passing to a relaxed version in the space of functions with bounded variation.

We prove that each perfect Frobenius field is algebraically bounded and hence has a dimension function in the sense of v.d. Dries on the collection of all definable sets. Given a definable set S over Q (resp. Fp) we can effectively determine for each k ∈ {−∞, 0, 1, . . .} whether there exists a perfect Frobenius fieldM of characteristic 0 (resp., of characteristic p) such that the dimension of ...

The absolute loss is the absolute difference between the desired and predicted outcome. I demonstrate worst-case upper bounds on the absolute loss for the perceptron algorithm and an exponentiated update algorithm related to the Weighted Majority algorithm. The bounds characterize the behavior of the algorithms over any sequence of trials, where each trial consists of an example and a desired o...

this paper presents a new approach which is based on quality control in order to optimize supplier selection. using inspections, removing the defected materials and considering penalties for low quality materials are the main factors which we have considered in modeling. in this model costs are divided to three parts: 1- costs of purchasing 2- costs of inspection policy 3- costs of quality and ...

We obtain estimation error rates and sharp oracle inequalities for regularization procedures of the form f̂ ∈ argmin f∈F ( 1 N N ∑ i=1 `(f(Xi), Yi) + λ ‖f‖ ) when ‖·‖ is any norm, F is a convex class of functions and ` is a Lipschitz loss function satisfying a Bernstein condition over F . We explore both the bounded and subgaussian stochastic frameworks for the distribution of the f(Xi)’s, with ...

The nonparametric problem of estimating a variance based on a sample of size n from a univariate distribution which has a known bounded range but is otherwise arbitrary is treated. For squared error loss, a certain linear function of the sample variance is seen to be minimax for each n from 2 through 13, except n = 4. For squared error loss weighted by the reciprocal of the variance, a constant...

We consider a cryptographically motivated framework for quantum metrology in the presence of malicious adversary. begin by devising an estimation strategy (potentially) altered resource (due to adversary) and quantify amount bias loss precision as function introduced uncertainty resource. By incorporating appropriate cryptographic protocol, can be bounded with respect soundness protocol. Thus e...

In this paper, we initiate a systematic investigation of differentially private algorithms for convex empirical risk minimization. Various instantiations of this problem have been studied before. We provide new algorithms and matching lower bounds for private ERM assuming only that each data point’s contribution to the loss function is Lipschitz bounded and that the domain of optimization is bo...

In this paper, we initiate a systematic investigation of differentially private algorithms for convex empirical risk minimization. Various instantiations of this problem have been studied before. We provide new algorithms and matching lower bounds for private ERM assuming only that each data point’s contribution to the loss function is Lipschitz bounded and that the domain of optimization is bo...

Letting {δn} be a refining sequence of Rademacher functions on the interval [0, T ], we introduce a functional on processes in the G-expectation space by d(K) = lim sup n Ê[ ∫ T 0 δn(s)dKs]. We prove that d(K) > 0 if Kt = ∫ t 0 ηsd〈B〉s with nontrivial η ∈ M G(0, T ) and that d(K) = 0 if Kt = ∫ t 0 ηsds with η ∈ M G(0, T ). This implies the uniqueness of the representation for G-martingales with...