Space-time Measurements of Oceanic Sea States

Stereo video techniques are effective for estimating the space–time wave dynamics over an area of the ocean. Indeed, a stereo camera view allows retrieval of both spatial and temporal data whose statistical content is richer than that of time series data retrieved from point wave probes. We present an application of the Wave Acquisition Stereo System (WASS) for the analysis of offshore video measurements of gravity waves in the Northern Adriatic Sea and near the southern seashore of the Crimean peninsula, in the Black Sea. We use classical epipolar techniques to reconstruct the sea surface from the stereo pairs sequentially in time, viz. a sequence of spatial snapshots. We also present a variational approach that exploits the entire data image set providing a global space–time imaging of the sea surface, viz. simultaneous reconstruction of several spatial snapshots of the surface in order to guarantee continuity of the sea surface both in space and time. Analysis of the WASS measurements show that the sea surface can be accurately estimated in space and time together, yielding associated directional spectra and wave statistics at a point in time that agrees well with probabilistic models. In particular, WASS stereo imaging is able to capture typical features of the wave surface, especially the crest-to-trough asymmetry due to second order nonlinearities, and the observed shape of large waves are fairly described by theoretical models based on the theory of quasi-determinism (Boccotti, 2000). Further, we investigate space–time extremes of the observed stationary sea states, viz. the largest surface wave heights expected over a given area during the sea state duration. The WASS analysis provides the first experimental proof that a space–time extreme is generally larger than that observed in time via point measurements, in agreement with the predictions based on stochastic theories for global maxima of Gaussian fields.

Congruent Docking of Dimeric Kinesin and ncd into Three-dimensional Electron Cryomicroscopy Maps of Microtubule–Motor ADP Complexes

We present a new map showing dimeric kinesin bound to microtubules in the presence of ADP that was obtained by electron cryomicroscopy and image reconstruction. The directly bound monomer (first head) shows a different conformation from one in the more tightly bound empty state. This change in the first head is amplified as a movement of the second (tethered) head, which tilts upward. The atomic coordinates of kinesin·ADP dock into our map so that the tethered head associates with the bound head as in the kinesin dimer structure seen by x-ray crystallography. The new docking orientation avoids problems associated with previous predictions; it puts residues implicated by proteolysis-protection and mutagenesis studies near the microtubule but does not lead to steric interference between the coiled-coil tail and the microtubule surface. The observed conformational changes in the tightly bound states would probably bring some important residues closer to tubulin. As expected from the homology with kinesin, the atomic coordinates of nonclaret disjunctional protein (ncd)·ADP dock in the same orientation into the attached head in a map of microtubules decorated with dimeric ncd·ADP. Our results support the idea that the observed direct interaction between the two heads is important at some stages of the mechanism by which kinesin moves processively along microtubules.

Growing Neural Gas approach for obtaining homogeneous maps by restricting the insertion of new nodes

The Growing Neural Gas model is used widely in artificial neural networks. However, its application is limited in some contexts by the proliferation of nodes in dense areas of the input space. In this study, we introduce some modifications to address this problem by imposing three restrictions on the insertion of new nodes. Each restriction aims to maintain the homogeneous values of selected criteria. One criterion is related to the square error of classification and an alternative approach is proposed for avoiding additional computational costs. Three parameters are added that allow the regulation of the restriction criteria. The resulting algorithm allows models to be obtained that suit specific needs by specifying meaningful parameters.

Abiel Holmes's book: bought Decem'r 23'd anno domini 1780 : manuscript, 1780-1783 and undated

Commonplace book containing excerpts on religion, philosophy, geometry and other subjects; with two fold-out tables, one concerning the "partition of sciences" and the other "grand divisions of Europe."

Commonplace book : manuscript, [16--]

Notes concerning verses of the Bible, and moral and religious issues.

A journall of our expedition agt. Canada ... : manuscript, 1711 and 1722-1723

1. Diary with entries dated 30 July-13 Oct. 1711; concerning the Quebec expedition (ff. 1r-16r) -- 2. Notes on books of the Bible (18r-92v).

Sermons : manuscript, 1694-1695

Autograph manuscript, signed, probably written in Boston.

Mathematics notebook : manuscript, 1782

With sections on numeration, surveying, trigonometry and other topics, accompanied by diagrams and hand-colored illustrations.

A plan of Cambridge Green, 1780 September 14

Small pen-and-ink and watercolor drawing of Cambridge Green created by Harvard senior John Davis, presumably as part of his undergraduate mathematical coursework. The map surveys Cambridge Commons and includes a few rough outlines of College buildings and the Episcopal church, and notes the burying ground, and the roads to Charlestown, Menotomy, the pond, Watertown, and the bridge. The original handwritten text is faded and was annotated with additional text by Davis including the note "[taken in my Senior year at H. College Septr 1780] Surveyed in concert with classmates, Atkins, Hall 1st, Howard, Payne, &c.- J. Davis." There is a note that "Atkins afterwards took the name of Tying." Davis refers to Dudley Atkins Tyng, Joseph Hall, Bezaleel Howard, and Elijah Paine, all members of the Harvard Class of 1781.

A copy of the general map the most part compiled from the actual survey by order of the commisioners appointed to settle the partition line between the provinces of New York and New Jersey : manuscript map, 1769

Map showing the whole of New Jersey and its borders with as well as part of Pennsylvania and New York. Map is drawn in black ink with green, pink, and yellow watercolors used to show features such as waterways, borders, and places of interest. Notes on map concern border disputes between New Jersey and New York.

Un receuil: containing painting, penmanship, algebra and pieces selected from various authors in prose and verse, with a few pieces in French with their translation / by Phebe Folger of Nantucket : manuscript, 1797-1806

Written mostly in a copperplate hand in black ink, and illustrated with watercolor drawings.

Notebook concerning mathematical equations : manuscript, 1769-1774

Notes on measuring height and distance, trigonometry, spherical projection, and other mathematical equations. Probably William Winthrop (1753-1825; Harvard AB 1770).

Essays : manuscript, [17--]

Essays on the dispersion of mankind, the Council of Trent, the invention of writing, and other topics.

Response to remarks by Charles Mordaunt on United States trade with England,

"Lines occasioned by the assertion of Sir Charles Mordaunt in debate, that the Americans could not catch a mouse or shave themselves without having recourse to Birmingham." Undated, unsigned poem, likely by Tudor, in response to remarks made by Mordaunt during a debate on the Orders in Council in the English Parliament.