A self-contained proof is presented of the fact that any increasing, continuous preferences over contingent payoffs that admit a (possibly state-dependent) additive representation are scale (resp. translation) invariant if and only if they take the form of CRRA (resp. CARA) expected utility, with the probabilities and coeffi cient of risk aversion uniquely determined as part of the representati...

Kernel-target alignment is commonly used to predict the behavior of reproducing kernels in a classification context, without training any kernel machine. In this paper, we show that a poor position of training data in feature space can drastically reduce the value of alignment. This implies that, in a kernel selection setting, the best kernel of a given collection may be characterized by a low ...

After reviewing some basic properties of RT algebras, which appear to be the natural framework to deal with integrable systems in presence of an impurity, we show how any integrable system (including these possessing translation invariance) can be promoted to an integrable system with an impurity which can reflect and transmit particles. The technics allows bulk translation invariant S-matrices...

We study the Moyal commutators and their expectation values between vacuum states and non-vacuum states for noncommutative scalar field theory. For noncommutative φ⋆4 scalar field theory, we derive its energy-momentum tensor from translation transformation and Lagrange field equation. We generalize the Heisenberg and quantum motion equations to the form of Moyal star-products for noncommutative...

A semi-fragile watermarking algorithm for authenticating 2D engineering graphics based on log-polar coordinates mapping is proposed. Firstly, the coordinates of vertices of entities are mapped to the log-polar coordinate system to obtain the invariance of translation, scaling and rotation. Then the watermark is embedded in the mantissa of the real-valued log-polar coordinates via bit substituti...

A new method of image denoising using waveletbased contourlet transform (WBCT) is proposed. Due to the lack of translation invariance of WBCT, image denoising by means of WBCT would lead to Gibbs-like phenomena. In the paper,cycle spinning-based technique is applied to develop translation invariant WBCT denoising scheme. Many simulation experiments with images contaminated by additive white Gau...

We study unfrustrated spin Hamiltonians that consist of commuting tensor products of Pauli matrices. Assuming translation-invariance, we observe that the Hamiltonian is described by a map between modules over the translation group algebra, so homological methods are applicable. We show universal properties of topologically ordered phases in low spatial dimensions. Particularly, we prove that in...

Theorem 1.1. Let G, X, p0, and r be as above. Suppose T is translation invariant, maps L log L to L, and is bounded on L0 . Then T is bounded on L, 1 < p < p0 with an operator norm of O((p − 1) ). This theorem is false without the assumption of translation invariance, since L is not an interpolation space between L log L and L0 . For a concrete counterexample, take E and F be subsets of X of me...