This is the second part of our work on Zariski decomposition structures, where we compare two different volume type functions for curve classes. The first function is the polar transform of the volume for ample divisor classes. The second function captures the asymptotic geometry of curves analogously to the volume function for divisors. We prove that the two functions coincide, generalizing Za...

The database PubChem was classified using 42 integer value descriptors of molecular structure, here called molecular quantum numbers (MQNs), which count atoms and bond types, polar groups, and topological features. Principal component analysis of the MQN data set shows that PubChem compounds occupy a partially filled elliptical cone in the (PC1,PC2,PC3) space whose axis is the first principal c...

ultimate limits of an open pit, which define its size and shape at the end of the mine’s life, is the pit with the highest profit value. a number of algorithms such as floating or moving cone method, floating cone method ii and the corrected forms of this method, the korobov algorithm and the corrected form of this method, dynamic programming and the lerchs and grossmann algorithm based on grap...

It is shown that various first and second order derivatives of the Fitzpatrick and Penot representative functions for a maximal monotone operator T , in a reflexive Banach space, can be used to represent differential information associated with the tangent and normal cones to the GraphT . In particular we obtain formula for the Proto-derivative, as well as its polar, the normal cone to the grap...

This study measured the accuracy with which human listeners can localize spoken words. A broadband (300 Hz-16 kHz) corpus of monosyllabic words was created and presented tolisteners using a virtual auditory environment. Localization was examined for 76 locations ona sphere surrounding the listener. Experiment 1 showed that low-pass filtering the speech sounds at 8 kHz degraded performance, caus...

We show that the fundamental objects of the Lp-Brunn-Minkowski theory, namely the Lp-affine surface areas for a convex body, are closely related to information theory: they are exponentials of Rényi divergences of the cone measures of a convex body and its polar. We give geometric interpretations for all Rényi divergences Dα, not just for the previously treated special case of relative entropy ...

In most previous works, histograms are simply treated as n-dimensional arrays or even reshaped into vectors when measuring the distances between them. However many histograms have their intrinsic topologies, such as HSV histogram (cone), shape context (polar), orientation histogram (circle). The topologies are important for so-called cross-bin distance, because they determine the similarities b...

The closely related mitogen-activated protein kinase isoforms extracellular signal-regulated kinase 1 (ERK1) and ERK2 have been implicated in the control of cell proliferation, differentiation and survival. However, the specific in vivo functions of the two ERK isoforms remain to be analysed. Here, we show that disruption of the Erk2 locus leads to embryonic lethality early in mouse development...

A bent-core compound derived from a 4-cyanoresorcinol core unit with two terephthalate based rod-like wings and carrying chiral 3,7-dimethyloctyloxy side chains has been synthesized in racemic and enantiomerically pure form and characterized by polarizing microscopy, differential scanning calorimetry, X-ray diffraction and electro-optical investigations to study the influence of molecular chira...