On training feedforward neural networks

A new algorithm that mapsn-dimensional binary vectors intom-dimensional binary vectors using 3-layered feedforward neural networks is described. The algorithm is based on a representation of the mapping in terms of the corners of then-dimensional signal cube. The weights to the hidden layer are found by a corner classification algorithm and the weights to the output layer are all equal to 1. Two corner classification algorithms are described. The first one is based on the perceptron algorithm and it performs generalization. The computing power of this algorithm may be gauged from the example that the exclusive-Or problem that requires several thousand iterative steps using the backpropagation algorithm was solved in 8 steps. Another corner classification algorithm presented in this paper does not require any computations to find the weights. However, in its basic form it does not perform generalization.     

LINEAR MAPPINGS THAT PRESERVE THE DERIVATIONAL STRUCTURE OF C*-ALGEBRAS

Abstract

Given a C*-algebra A and a suitable set of derivations on A, we consider the algebras A _n of n-differentiable elements of A as described in [B], before passing to an analysis of important classes of bounded linear maps between two such spaces. We show that even in this general framework, all the main features of the theory for the case C^(m)(U) → C ^(p) (V) where U and V are open balls in suitable Banach spaces, are preserved (see for example [A-G-L], [Gu-L], [Ja] and [L]). As part of the theory developed we obtain a non-trivial extension of the Kleinecke-Shirokov theorem in the category of C*-algebras to unbounded partially defined *-derivations. This indicates the existence of a single mathematical principle governing both the non-increasibility of differentiability by continuous homomorphisms and the untenability of the Heisenberg Uncertainty Principle for bounded observables.     

Über die Verwendung von 40K und 87Rb in der Radionuklid-Metrologie

Anhand kernphysikalischer Charakteristika wird die Möglichkeit, einige natürliche instabile Nuklide in der Metrologie zu verwenden, diskutiert. Als Standards sind ⁴⁰K und ⁸⁷Rb sehr gut geeignet. Unter Berücksichtigung der Kriterien für Standards wurden die geeignetsten Kalium- und Rubidiumsalze ausgewählt, und an einigen Beispielen wird ihre praktische Anwendung gezeigt.     

Does faecal matter reflect location? An initial assessment of isotopic variability between consumed prey remains and faecal matter for wild jaguars*

ABSTRACT

Faecal isotopic analysis may complement other non-invasive wildlife survey tools for monitoring landscape use by carnivores, such as motion-detecting cameras and non-invasive genetic sampling. We analysed carbon, nitrogen, and strontium isotopes in faecal matter produced by jaguars (Panthera onca) as well as bones from consumed prey at the Mountain Pine Ridge Forest Reserve (MPR) in Belize, Central America. The MPR is ideally suited for a spatial isotope study as vegetation and geology both vary considerably. The isotopic composition of faecal matter should reflect the habitat and geology where consumed prey lived. We used bone from consumed prey recovered from jaguar scats as a proxy for diet. Faecal matter and bone showed comparable spatial isotopic trends, suggesting that the isotopic composition of jaguar faeces can be used to detect foraging in different habitats (pine forest versus broadleaf forest) or on different geologies (Mesozoic carbonates; Palaeozoic granite, contact metamorphics, and metasediments). This result is reassuring as bones are not always present in carnivore scats. Studying landscape use by cryptic and wide-ranging carnivore species like jaguars remains challenging. Isotopic analysis of faecal matter complements the existing array of non-invasive spatial monitoring tools.     

Spin geometry on quantum groups via covariant differential calculi

Let 870802000440-si1.gif"> be a cosemisimple Hopf ∗-algebra with antipode S and let Γ be a left-covariant first-order differential ∗-calculus over 870802000440-si4.gif"> such that Γ is self-dual (see Section 2) and invariant under the Hopf algebra automorphism S². A quantum Clifford algebra Cl(Γ,σ,g) is introduced which acts on Woronowicz’ external algebra Γ^∧. A minimal left ideal of Cl(Γ,σ,g) which is an 870802000440-si5.gif">-bimodule is called a spinor module. Metrics on spinor modules are investigated. The usual notion of a linear left connection on Γ is extended to quantum Clifford algebras and also to spinor modules. The corresponding Dirac operator and connection Laplacian are defined. For the quantum group SL_q(2) and its bicovariant 4D_±-calculi these concepts are studied in detail. A generalization of Bochner's theorem is given. All invariant differential operators over a given spinor module are determined. The eigenvalues of the Dirac operator are computed.     

南海东部柱样沉积物锶同位素变化特征及其地质意义

Sr同位素比值可提供有关物质来源的重要信息,南海东部海域的3个柱样沉积物采用二端元组分混合模型,得到南部陆坡区69柱中陆源物质质量分数为42．48％～92．95％,平均为78．33％;中部深海区149柱中陆源物质质量分数为74．29％～85．04％,平均为81．63％;南部深海区294柱中陆源物质质量分数为53．55％～76．74％,平均为67．01％,3个柱样中陆源组分质量分数变化表明南海东部海域沉积物中陆源物质由北至南逐渐减少,而幔源物质逐渐增多,结合沉积柱样的δ^13C、δ^18O同位素数据分析反映南海15万年来经历了2次较大规模的冰期和3次间冰期。     

Approximation of quantum tori by finite quantum tori for the quantum Gromov-Hausdorff distance

We establish that, given a compact Abelian group G endowed with a continuous length function l and a sequence (H_n)_n∈N of closed subgroups of G converging to G for the Hausdorff distance induced by l, then is the quantum Gromov-Hausdorff limit of any sequence for the natural quantum metric structures and when the lifts of σ_n to converge pointwise to σ. This allows us in particular to approximate the quantum tori by finite-dimensional C^*-algebras for the quantum Gromov-Hausdorff distance. Moreover, we also establish that if the length function l is allowed to vary, we can collapse quantum metric spaces to various quotient quantum metric spaces.     

Rates of -statistical convergence of positive linear operators

In this paper we study the rates of A-statistical convergence of sequences of positive linear operators mapping the weighted space C_ρ1 into the weighted space B_ρ2.     

Gravity and the Noncommutative Residue for Manifolds with Boundary

We prove a Kastler–Kalau–Walze type theorem for the Dirac operator and the signature operator for 3,4-dimensional manifolds with boundary. As a corollary, we give two kinds of operator-theoretic explanations of the gravitational action in the case of 4-dimensional manifolds with flat boundary.      

Photoacoustic studies and selective ablation of vascular tissue using a pulsed dye laser

The optical attenuation coefficient for human aorta has been measured in the 440–500 nm spectral region using the transient photoacoustic (thermoelastic) response produced by an excimer-laser-pumped dye laser. It is confirmed that diseased tissue has a significantly higher attenuation than normal samples in this spectral region. The maximum difference occurs at 8764.gif" alt="sim" align="MIDDLE" BORDER="0">480 nm and there is a lowering of the ablation threshold fluence for diseased tissue by a factor of 8764.gif" alt="sim" align="MIDDLE" BORDER="0">1.5 for dye laser ablation at this wavelength.