Scaled Toda-like flows

AbstractThis paper discusses the class of isospectral flows Ẋ = [X, A ∘ X], where ∘ denotes the Hadamard product and [., .] is the Lie bracket. The presence of A allows arbitrary and independent scaling for each element in the matrix X. The time-1 mapping of the scaled Toda-like flow still enjoys a QR-like iteration. The scaled structure includes the classical Toda flow, Brockett's double bracket flow, and other interesting flows as special cases. Convergence proof is thus unified and simplified. The effect of scaling on a variety of applications is demonstrated by examples

Legal Research--Computer Retrieval of Statutory Law and Decisional Law

Legal research presently involves a considerable amount of any lawyer\u27s time and efforts largely because it is a slow and tedious process. Searching for a pertinent legal point can prove to be time-consuming and often fruitless. Moreover, it is here that chance plays one of its largest roles in the law.\u27 An important legal point may exist,yet the researcher may fail to find it although he exercises a great degree of diligence. All lawyers must recognize this problem and the fact that it is becoming more acute with the passage of time. Something needs to be done to facilitate legal research in order to preserve the efficient development and administration of law by the courts, legislatures and, more importantly, by the lawyers in their day-to-day practice

The Medicinal Chemistry of Imidazotetrazine Prodrugs

YesTemozolomide (TMZ) is the standard first line treatment for malignant glioma, reaching “blockbuster” status in 2010, yet it remains the only drug in its class. The main constraints on the clinical effectiveness of TMZ therapy are its requirement for active DNA mismatch repair (MMR) proteins for activity, and inherent resistance through O6-methyl guanine-DNA methyl transferase (MGMT) activity. Moreover, acquired resistance, due to MMR mutation, results in aggressive TMZ-resistant tumour regrowth following good initial responses. Much of the attraction in TMZ as a drug lies in its PK/PD properties: it is acid stable and has 100% oral bioavailability; it also has excellent distribution properties, crosses the blood-brain barrier, and there is direct evidence of tumour localisation. This review seeks to unravel some of the mysteries of the imidazotetrazine class of compounds to which TMZ belongs. In addition to an overview of different synthetic strategies, we explore the somewhat unusual chemical reactivity of the imidazotetrazines, probing their mechanisms of reaction, examining which attributes are required for an active drug molecule and reviewing the use of this combined knowledge towards the development of new and improved anti-cancer agents

Coherent Excitonic Coupling in an Asymmetric Double InGaAs Quantum Well Arises from Many-Body Effects

We study an asymmetric double InGaAs quantum well using optical two-dimensional coherent spectroscopy. The collection of zero-quantum, one-quantum, and two-quantum two-dimensional spectra provides a unique and comprehensive picture of the double well coherent optical response. Coherent and incoherent contributions to the coupling between the two quantum well excitons are clearly separated. An excellent agreement with density matrix calculations reveals that coherent interwell coupling originates from many-body interactions

The rings of n-dimensional polytopes

Points of an orbit of a finite Coxeter group G, generated by n reflections starting from a single seed point, are considered as vertices of a polytope (G-polytope) centered at the origin of a real n-dimensional Euclidean space. A general efficient method is recalled for the geometric description of G- polytopes, their faces of all dimensions and their adjacencies. Products and symmetrized powers of G-polytopes are introduced and their decomposition into the sums of G-polytopes is described. Several invariants of G-polytopes are found, namely the analogs of Dynkin indices of degrees 2 and 4, anomaly numbers and congruence classes of the polytopes. The definitions apply to crystallographic and non-crystallographic Coxeter groups. Examples and applications are shown.Comment: 24 page

Concentration and Extraction of Phosphorous from Swine Manure Slurries (as Struvite)

Excessive loading of phosphorus (P) onto agricultural lands has been recognized as a threat to surface water quality. Forced precipitation of struvite (MgNH4PO4•6H2O) from animal waste slurries prior to land application can reduce dissolved reactive P levels in manure slurries. It also offers the potential to recover excess phosphorus from manures and move it to cropping areas that require phosphorus fertilizer inputs. Past work indicates that ~90% of the soluble phosphorus can be concentrated into a precipitate following chemical amendment. This study will provide important information regarding the feasibility of phosphorus recovery as a means of balancing swine manure nutrient content with crop needs. Given the expanding regulations regarding phosphorus management, it is important to develop and test phosphorus management strategies. The sustainability of many animal operations in their current locations will depend upon their ability to meet new regulations requiring phosphorus management as well as nitrogen management

Deferring the learning for better generalization in radial basis neural networks

Proceeding of: International Conference Artificial Neural Networks — ICANN 2001. Vienna, Austria, August 21–25, 2001The level of generalization of neural networks is heavily dependent on the quality of the training data. That is, some of the training patterns can be redundant or irrelevant. It has been shown that with careful dynamic selection of training patterns, better generalization performance may be obtained. Nevertheless, generalization is carried out independently of the novel patterns to be approximated. In this paper, we present a learning method that automatically selects the most appropriate training patterns to the new sample to be predicted. The proposed method has been applied to Radial Basis Neural Networks, whose generalization capability is usually very poor. The learning strategy slows down the response of the network in the generalisation phase. However, this does not introduces a significance limitation in the application of the method because of the fast training of Radial Basis Neural Networks