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

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

Dynamic multilateral markets

We study dynamic multilateral markets, in which players' payoffs result from intra-coalitional bargaining. The latter is modeled as the ultimatum game with exogenous (time-invariant) recognition probabilities and unanimity acceptance rule. Players in agreeing coalitions leave the market and are replaced by their replicas, which keeps the pool of market participants constant over time. In this infinite game, we establish payoff uniqueness of stationary equilibria and the emergence of endogenous cooperation structures when traders experience some degree of (heterogeneous) bargaining frictions. When we focus on market games with different player types, we derive, under mild conditions, an explicit formula for each type's equilibrium payoff as the market frictions vanish

Sliding friction between an elastomer network and a grafted polymer layer: the role of cooperative effects

We study the friction between a flat solid surface where polymer chains have been end-grafted and a cross-linked elastomer at low sliding velocity. The contribution of isolated grafted chains' penetration in the sliding elastomer has been early identified as a weakly velocity dependent pull-out force. Recent experiments have shown that the interactions between the grafted chains at high grafting density modify the friction force by grafted chain. We develop here a simple model that takes into account those interactions and gives a limit grafting density beyond which the friction no longer increases with the grafting density, in good agreement with the experimental dataComment: Submitted to Europhys. Letter

Baryon magnetic moments in the external field method

We present a calculation of the magnetic moments of the baryon octet and decuplet using the external field method and standard Wilson gauge and fermion actions in the quenched approximation. Progressively smaller static magnetic fields are introduced on a $24^4$ latticeat beta=6.0 and the pion mass is probed down to about 500 MeV. Magnetic moments are extracted from the linear response of the masses to the external field.Comment: Lattice2004 (weak matrix elements), 3 pages, 8 figure

Conditioned place preference and locomotor activity in response to methylphenidate, amphetamine and cocaine in mice lacking dopamine D4 receptors

Methylphenidate (MP) and amphetamine (AMPH) are the most frequently prescribed medications for the treatment of attention-deficit/hyperactivity disorder (ADHD). Both drugs are believed to derive their therapeutic benefit by virtue of their dopamine (DA)-enhancing effects, yet an explanation for the observation that some patients with ADHD respond well to one medication but not to the other remains elusive. The dopaminergic effects of MP and AMPH are also thought to underlie their reinforcing properties and ultimately their abuse. Polymorphisms in the human gene that codes for the DA D4 receptor (D4R) have been repeatedly associated with ADHD and may correlate with the therapeutic as well as the reinforcing effects of responses to these psychostimulant medications. Conditioned place preference (CPP) for MP, AMPH and cocaine were evaluated in wild-type (WT) mice and their genetically engineered littermates, congenic on the C57Bl/6J background, that completely lack D4Rs (knockout or KO). In addition, the locomotor activity in these mice during the conditioning phase of CPP was tested in the CPP chambers. D4 receptor KO and WT mice showed CPP and increased locomotor activity in response to each of the three psychostimulants tested. D4R differentially modulates the CPP responses to MP, AMPH and cocaine. While the D4R genotype affected CPP responses to MP (high dose only) and AMPH (low dose only) it had no effects on cocaine. Inasmuch as CPP is considered an indicator of sensitivity to reinforcing responses to drugs these data suggest a significant but limited role of D4Rs in modulating conditioning responses to MP and AMPH. In the locomotor test, D4 receptor KO mice displayed attenuated increases in AMPH-induced locomotor activity whereas responses to cocaine and MP did not differ. These results suggest distinct mechanisms for D4 receptor modulation of the reinforcing (perhaps via attenuating dopaminergic signalling) and locomotor properties of these stimulant drugs. Thus, individuals with D4 receptor polymorphisms might show enhanced reinforcing responses to MP and AMPH and attenuated locomotor response to AMPH.Fil: Thanos, P. K.. NIAAA Intramural Program; Estados Unidos. Brookhaven National Laboratory; Estados Unidos. Universidad de Buenos Aires; ArgentinaFil: Bermeo, C.. Brookhaven National Laboratory; Estados UnidosFil: Rubinstein, Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; ArgentinaFil: Suchland, K. L.. Oregon Health & Science University; Estados UnidosFil: Wang, G. J.. Brookhaven National Laboratory; Estados UnidosFil: Grandy, David K.. Oregon Health & Science University; Estados UnidosFil: Volkow, N. D.. NIAAA Intramural Program; Estados Unido

Phase transition in nanomagnetite

Recently, the application of nanosized magnetite particles became an area of growing interest for their potential practical applications. Nanosized magnetite samples of 36 and 9 nm sizes were synthesized. Special care was taken on the right stoichiometry of the magnetite particles. Mössbauer spectroscopy measurements were made in 4.2–300 K temperature range. The temperature dependence of the intensities of the spectral components indicated size dependent transition taking place in a broad temperature range. For nanosized samples, the hyperfine interaction values and their relative intensities changed above the Verwey transition temperature value of bulk megnetite. The continuous transition indicated the formation of dendritelike granular assemblies formed during the preparation of the samples