Singular cosphere bundle reduction

This paper studies singular contact reduction for cosphere bundles at the zero value of the momentum map. A stratification of the singular quotient, finer than the contact one and better adapted to the bundle structure of the problem, is obtained. The strata of this new stratification are a collection of cosphere bundles and coisotropic or Legendrian submanifolds of their corresponding contact components.

     

Multirate multicast service provisioning II: a tâtonnement process for rate allocation

In multirate multicast different users in the same multicast group can receive services at different rates depending on their own requirements and the congestion level of the network. In this two-part paper we present a general framework for addressing the optimal rate control problem in multirate multicast where the objective is the maximization of a social welfare function expressed by the sum of the users’ utility functions. In Part II we present a market based mechanism and an adjustment process that have the following features. They satisfy the informational constraints imposed by the nature of multirate multicast; and when they are combined with the results of Part I they result in an optimal solution of the corresponding centralized multirate multicast problem.     

Generalized characteristic functions for a single-mode radiation field

We derive simple formulas for the higher-order moments of the quadrature operators operators of a two-field superposition by introducing a new generalized characteristic function depending on two complex variables. Using this formalism we investigate the preservation of higher-order squeezing during weak thermalization of an even coherent state.     

Current trends in lead discovery: are we looking for the appropriate properties?

The new drug discovery paradigm is based on high-throughput technologies, both with respect to synthesis and screening. The progression HTS hits lead series candidate drug marketed drug appears to indicate that the probability of reaching launched status is one in a million. This has shifted the focus from good quality candidate drugs to good quality leads. We examined the current trends in lead discovery by comparing MW (molecular weight), LogP (octanol/water partition coefficient, estimated by Kowwin [17]) and LogSw (intrinsic water solubility, estimated by Wskowwin [18]) for the following categories: 62 leads and 75 drugs [11]; compounds in the development phase (I, II, III and launched), as indexed in MDDR; and compounds indexed in medicinal chemistry journals [ref. 20], categorized according to their biological activity. Comparing the distribution of the above properties, the 62 lead structures show the lowest median with respect to MW (smaller) and LogP (less hydrophobic), and the highest median with respect to LogSw (more soluble). By contrast, over 50% of the medicinal chemistry compounds with activities above 1 nanomolar have MW > 425, LogP > 4.25 and LogSw < -4.75, indicating that the reported active compounds are larger, more hydrophobic and less soluble when compared to time-tested quality leads. In the MDDR set, a progressive constraint to reduce MW and LogP, and to increase LogSw, can be observed when examining trends in the developmental sequence: phase I, II, III and launched drugs. These trends indicate that other properties besides binding affinity, e.g., solubility and hydrophobicity, need to be considered when choosing the appropriate leads.     

A characterization theorem for certain unions of two starshaped sets in R 2

Let S be a compact set in R ². For S simply connected, S is a union of two starshaped sets if and only if for every F finite, F bdry S, there exist a set G bdry S arbitrarily close to F and points s, t depending on G such that each point of G is clearly visible via S from one of s, t. In the case where S has at most finitely many components, the necessity of the condition still holds while the sufficiency fails.     

Euler-Poincaré Approaches to Nematodynamics

Nematodynamics is the orientation dynamics of flowless liquid-crystals. We show how Euler-Poincaré reduction produces a unifying framework for various theories, including Ericksen-Leslie, Luhiller-Rey, and Eringen??s micropolar theory. In particular, we show that these theories are all compatible with each other and some of them allow for more general configurations involving a non vanishing disclination density. All results are also extended to flowing liquid crystals.     

Solving chemical master equations by adaptive wavelet compression

Solving chemical master equations numerically on a large state space is known to be a difficult problem because the huge number of unknowns is far beyond the capacity of traditional methods. We present an adaptive method which compresses the problem very efficiently by representing the solution in a sparse wavelet basis that is updated in each step. The step-size is chosen adaptively according to estimates of the temporal and spatial approximation errors. Numerical examples demonstrate the reliability of the error estimation and show that the method can solve large problems with bimodal solution profiles.