Gaussian elimination as an iterative algorithm

Gaussian elimination (GE) for solving an $n \times n$ linear system of equations $Ax=b$ is the archetypical direct method of numerical linear algebra, as opposed to iterative. In this note we want to point out that GE has an iterative side too

Anatomical errors in the lapidary of the Co-Cathedral of St. John at Valletta

The co-Cathedral of St. John of Valletta was the Conventual Church of the Knights of St. John of Jerusalem from 1573 till the end of their domination of Malta in 1798. During this period the pavement of the church became covered with inlaid marble funereal slabs under which were buried highly placed personages of that order of chivalry. This paper is a review of sixty slabs bearing skulls and skeletons covering a period of over two hundred years from 1602 to 1814. Its aim is to call attention to the more conspicuous osteological errors in this funereal iconography and to relate this to the wider medical and artistic milieu of Malta from the seventeenth to the early nineteenth centuries. The greatest number of the slabs arc from the eighteenth century; four of them (nos. 17, 22, 97 and 238) seem to have been stock designs by the same hand or from the same workshop. Only a small number belong to the seventeenth and the early nineteenth centuries.peer-reviewe

Kronecker-product approximations for some function-related matrices

AbstractA new approximation tool such as sums of Kronecker products is recently found to provide a superb compression property on a series of numerical examples of quite a general nature. The purpose of the paper is explanation of this phenomenon in the form of “existence theorems” for matrix approximations of low Kronecker rank for some classes of function-related matrices including important specimens from potential theory. This lays the grounds for development of new approximation algorithms, for example, in the cases when a matrix is associated with a shift-invariant function on the Cartesian product of nonunform grids, which is of great practical interest in the solution of integral equations on plates or screens

Multiple-Genome Annotation of Genome Fragments Using Hidden Markov Model Profiles

To learn more about microbes and overcome the limitations of standard cultured methods, microbial communities are being studied in an uncultured state. In such metagenomic studies, genetic material is sampled from the environment and sequenced using the whole-genome shotgun sequencing technique. This results in thousands of DNA fragments that need to be identified, so that the composition and inner workings of the microbial community can begin to be understood. Those fragments are then assembled into longer portions of sequences. However the high diversity present in an environment and the often low level of genome coverage achieved by the sequencing technology result in a low number of assembled fragments (contigs) and many unassembled fragments (singletons). The identification of contigs and singletons is usually done using BLAST, which finds sequences similar to the contigs and singletons in a database. An expert may then manually read these results and determine if the function and taxonomic origins of each fragment can be determined. In this report, an automated system called Anacle is developed to annotate, following a taxonomy, the unassembled fragments before the assembly process. Knowledge of what proteins can be found in each taxon is built into Anacle by clustering all known proteins of that taxon. The annotation performances from using Markov clustering (MCL) and Self- Organizing Maps (SOM) are investigated and compared. The resulting protein clusters can each be represented by a Hidden Markov Model (HMM) profile. Thus a “skeleton” of the taxon is generated with the profile HMMs providing a summary of the taxon’s genetic content. The experiments show that (1) MCL is superior to SOMs in annotation and in running time performance, (2) Anacle achieves good performance in taxonomic annotation, and (3) Anacle has the ability to generalize since it can correctly annotate fragments from genomes not present in the training dataset. These results indicate that Anacle can be very useful to metagenomics projects

Dinosaurs and pterosaurs in Greek and Roman art and literature? An investigation of young-earth creationist claims

Many young-Earth creationist (YEC) authors claim that ancient Greek and Roman writings describe dinosaurs and pterosaurs, and that Greco-Roman art illustrates Mesozoic reptiles. Such claims are used as evidence against evolutionary theory in an attempt to cast doubt on the separation of humans and such animals by millions of years. However, examination of the Greco-Roman materials in question reveals that none of them actually depict Mesozoic reptiles. In descriptions of dragons (Greek drakōn; Latin draco) in Greco-Roman literature—which YEC authors claim are dinosaurs—coils and the epithets ophis, serpens, and anguis reveal that the ancient authors are describing snakes, often large constrictors. This is the case for the draco described by Pliny, Phrygian dragons described by Aelian, the Vatican Hill child-eater mentioned by Pliny, the Bagradas River dragon, the legendary dragons that Alexander the Great supposedly encountered, and dragons in Greek mythology. An alleged theropod dinosaur in the Nile Mosaic of Palestrina is a mammal, possibly an otter. An alleged dinosaur in a Pompeii fresco is a crocodile. Herodotus\u27 description of winged snakes is anatomically incompatible with pterosaurs and possibly refers to cobras. Alleged pterosaurs on an Alexandrian coin are winged snakes. An alleged Etruscan pterosaur head sculpture depicts a mammal. Two alleged Tanystropheus in a Roman mosaic from Lydney Park, England are mythical sea monsters. These YEC claims now join the ranks of discredited evidence against evolutionary theory

Spartan Daily, November 1, 2005

Volume 125, Issue 38https://scholarworks.sjsu.edu/spartandaily/10181/thumbnail.jp