This paper presents extensions to Alpha, a language based upon the formalism of affine recurrence equations (AREs). These extensions address the need for parametric and structured systems of such AREs. Similar to, but more general as the map operator of classical functional languages, the Alpha structuration techniques provide a dense and powerful description of complex systems referencing each...

The affine synthesis operator Sc = P j>0 P k∈Zd cj,kψj,k is shown to map the mixed-norm sequence space `(`) surjectively onto L(R), 1 ≤ p < ∞, under mild conditions on the synthesizer ψ ∈ L(R) (say, having a radially decreasing L majorant near infinity) and assuming R Rd ψ dx = 1. Here ψj,k(x) = | det aj |ψ(ajx− k), for some dilation matrices aj that expand. Therefore the standard norm on f ∈ L...

Let Uq(Ĝ) be a quantized affine Lie algebra. It is proven that the universal R-matrix R of Uq(Ĝ) satisfies the celebrated conjugation relation R = TR with T the usual twist map. As applications, braid generators are shown to be diagonalizable on arbitrary tensor product modules of integrable irreducible highest weight Uq(Ĝ)-module and a spectral decomposition formula for the braid generators is...

‎Highest weight modules of the double affine Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎Singular vectors of Verma modules are‎ ‎determined using a similar condition with horizontal affine Lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

This paper presents a methodology for historical map registration with a multi-image affine transformation estimated with a simultaneous Least Squares independent model adjustment. The method is based on two set of equations for (i) image-to-ground and (ii) image-to-image points and provides the rectification parameters with a global approach where all the unknowns are simultaneously estimated....

Let Γ0 ⊂ O(2, 1) be a Schottky group, and let Σ = H2/Γ0 be the corresponding hyperbolic surface. Let C(Σ) denote the space of geodesic currents on Σ. The cohomology group H1(Γ0, V) parametrizes equivalence classes of affine deformations Γu of Γ0 acting on an irreducible representation V of O(2, 1). We define a continuous biaffine map C(Σ)×H1(Γ0, V) Ψ −→ R which is linear on the vector space H1(...

In secret quantum communications the best eavesdropping attacks on quantum cryptography are based on imperfect cloning machines. The incoherent attack, based on quantum cloning, is the most common eavesdropping strategy. Using a probe, the eavesdropper imperfectly clones the sender’s quantum state which keeps one copy and sends the other. The physically allowed transformations of Eve’s quantum ...

In this paper we characterize the group of affine transformations a flat simply connected manifold whose developing map is diffeomorphism. This proved by making use some simple facts about homeomorphisms $\mathbb{R}^n$ preserving open sets. We show examples where characterization useful.

Non-malleable code is a relaxed version of errorcorrection codes and the decoding of modified codewords results in the original message or a completely unrelated value. Thus, if an adversary corrupts a codeword then he cannot get any information from the codeword. This means that non-malleable codes are useful to provide a security guarantee in such situations that the adversary can overwrite t...

Prior work on diagnosing Alzheimer’s disease from magnetic resonance images of the brain established that convolutional neural networks (CNNs) can leverage high-dimensional image information for classifying patients. However, little research focused how these models utilize usually low-dimensional tabular information, such as patient demographics or laboratory measurements. We introduce Dynamic...