Bounding Embeddings of VC Classes into Maximum Classes

One of the earliest conjectures in computational learning theory-the Sample Compression conjecture-asserts that concept classes (equivalently set systems) admit compression schemes of size linear in their VC dimension. To-date this statement is known to be true for maximum classes---those that possess maximum cardinality for their VC dimension. The most promising approach to positively resolving the conjecture is by embedding general VC classes into maximum classes without super-linear increase to their VC dimensions, as such embeddings would extend the known compression schemes to all VC classes. We show that maximum classes can be characterised by a local-connectivity property of the graph obtained by viewing the class as a cubical complex. This geometric characterisation of maximum VC classes is applied to prove a negative embedding result which demonstrates VC-d classes that cannot be embedded in any maximum class of VC dimension lower than 2d. On the other hand, we show that every VC-d class C embeds in a VC-(d+D) maximum class where D is the deficiency of C, i.e., the difference between the cardinalities of a maximum VC-d class and of C. For VC-2 classes in binary n-cubes for 4 <= n <= 6, we give best possible results on embedding into maximum classes. For some special classes of Boolean functions, relationships with maximum classes are investigated. Finally we give a general recursive procedure for embedding VC-d classes into VC-(d+k) maximum classes for smallest k.Comment: 22 pages, 2 figure

Some effects of y-axis vibration on visual acuity Final report, Jul. 1966 - Nov. 1967

Side to side head vibration effects on visual acuity measurement

Alignment of cryo-EM movies of individual particles by optimization of image translations

Direct detector device (DDD) cameras have revolutionized single particle electron cryomicroscopy (cryo-EM). In addition to an improved camera detective quantum efficiency, acquisition of DDD movies allows for correction of movement of the specimen, due both to instabilities in the microscope specimen stage and electron beam-induced movement. Unlike specimen stage drift, beam-induced movement is not always homogeneous within an image. Local correlation in the trajectories of nearby particles suggests that beam-induced motion is due to deformation of the ice layer. Algorithms have already been described that can correct movement for large regions of frames and for > 1 MDa protein particles. Another algorithm allows individual < 1 MDa protein particle trajectories to be estimated, but requires rolling averages to be calculated from frames and fits linear trajectories for particles. Here we describe an algorithm that allows for individual < 1 MDa particle images to be aligned without frame averaging or linear trajectories. The algorithm maximizes the overall correlation of the shifted frames with the sum of the shifted frames. The optimum in this single objective function is found efficiently by making use of analytically calculated derivatives of the function. To smooth estimates of particle trajectories, rapid changes in particle positions between frames are penalized in the objective function and weighted averaging of nearby trajectories ensures local correlation in trajectories. This individual particle motion correction, in combination with weighting of Fourier components to account for increasing radiation damage in later frames, can be used to improve 3-D maps from single particle cryo-EM.Comment: 11 pages, 4 figure

Studies of iron impurities in YxPr1-xBa2Cu3O7-delta

Pr is the only rare earth which, when substituted for Y in YBa2Cu3O7, significantly alters the superconducting transition temperature T(sub c) without changing the crystal structure. For YxPr1-xBa2Cu3O7-delta with delta approx. equal to 0, T(sub c) is reduced rapidly as x is increased, reaching zero for x about 0.5. For x above 0.5 the compound is antiferromagnetic with a Neel temperature that increases with increasing x, rising to above room temperature for x near 1. A similar behavior is observed when the oxygen deficit delta is increased from zero to 1 with x=0. For the case of Pr substitution, the drop in T(sub c) is believed due to magnetic interactions. For the case of varying delta with x=0, the drop can be attributed to a combination of magnetic interactions, band filling, and changes in crystal structure. To study these effects, the Mossbauer effect of 57 Fe atoms substituted for the Cu atoms has been observed as a function of delta, x, and temperature. The observed spectra are all well described by a two quadrupole-split pairs, a central singlet, and a six-line magnetic hyperfine field pattern. For several Pr compositions both delta and temperature were varied, and the results support the hypothesis that a magnetic interaction exists between the Fe in the Cu lattice and the substitutional Pr atoms

Volatility and dividend risk in perpetual American options

American options are financial instruments that can be exercised at any time before expiration. In this paper we study the problem of pricing this kind of derivatives within a framework in which some of the properties --volatility and dividend policy-- of the underlaying stock can change at a random instant of time, but in such a way that we can forecast their final values. Under this assumption we can model actual market conditions because some of the most relevant facts that may potentially affect a firm will entail sharp predictable effects. We will analyse the consequences of this potential risk on perpetual American derivatives, a topic connected with a wide class of recurrent problems in physics: holders of American options must look for the fair price and the optimal exercise strategy at once, a typical question of free absorbing boundaries. We present explicit solutions to the most common contract specifications and derive analytical expressions concerning the mean and higher moments of the exercise time.Comment: 21 pages, 5 figures, iopart, submitted for publication; deep revision, two new appendice

Ethnicity and Lifetimes: Self Concepts and Situational Contexts of Ethnic Identity in Late Life

This chapter reports on finding from a study of ethnic older men, aged 65 an older (Jewish, Irish, and Italian) who were widowed from 2 to 8 years after a long-term study. It focuses on life reorganization after the initial bereavement period. It identifies key issues in the process concerning continuity and change in identity reformulation, changes in health and activity patterns, ethnic identity and lingering attachment to the deceased spouse. Ethnicity as a dynamic life course process, shaped by contextual and historical dimensions, and personal meaning processes are highlighted. Supported by NIH# R01-AG00520

Thermal Fluctuations and Rubber Elasticity

The effects of thermal elastic fluctuations in rubber materials are examined. It is shown that, due to an interplay with the incompressibility constraint, these fluctuations qualitatively modify the large-deformation stress-strain relation, compared to that of classical rubber elasticity. To leading order, this mechanism provides a simple and generic explanation for the peak structure of Mooney-Rivlin stress-strain relation, and shows a good agreement with experiments. It also leads to the prediction of a phonon correlation function that depends on the external deformation.Comment: 4 RevTeX pages, 1 figure, submitted to PR