Periodic behavior in families of numerical and affine semigroups via parametric Presburger arithmetic

Semigroup Forum - Let $$f_1(n), \ldots , f_k(n)$$ be polynomial functions of n. For fixed $$n\in \mathbb {N}$$ , let $$S_n\subseteq \mathbb {N}$$ be the numerical semigroup generated by...     

Cellular Buckling in Long Structures

A long structural system with an unstable (subcritical)post-buckling response that subsequently restabilizes typically deformsin a cellular manner, with localized buckles first forming and thenlocking up in sequence. As buckling continues over a growing number ofcells, the response can be described by a set of lengthening homoclinicconnections from the fundamental equilibrium state to itself. In thelimit, this leads to a heteroclinic connection from the fundamentalunbuckled state to a post-buckled state that is periodic. Under suchprogressive displacement the load tends to oscillate between twodistinct values.The paper is both a review and a pointer tofuture research. The response is described via a typical system, asimple but ubiquitous model of a strut on a foundation which includesinitially-destabilizing and finally-restabilizing nonlinear terms. Anumber of different structural forms, including the axially-compressedcylindrical shell, a typical sandwich structure, a model of geologicalfolding and a simple link model are shown to display such behaviour. Amathematical variational argument is outlined for determining the globalminimum postbuckling state under controlled end displacement (rigidloading). Finally, the paper stresses the practical significance of aMaxwell-load instability criterion for such systems. This criterion,defined under dead loading to be where the pre-buckled and post-buckledstate have the same energy, is shown to have significance in the presentsetting under rigid loading also. Specifically, the Maxwell load isargued to be the limit of minimum energy localized solutions asend-shortening tends to infinity.     

Validation of the anisotropy index ellipsoidal area ratio in diffusion tensor imaging

A new diffusion anisotropy index, ellipsoidal area ratio (EAR), was described recently and proved to be less noise-sensitive than fractional anisotropy (FA) by theory and simulation. Here we show that EAR has higher signal-to-noise ratios than FA in average diffusion tensor imaging data from 40 normal subjects. EAR was also more sensitive than FA in detecting white matter abnormalities in a patient with widespread diffuse axonal injury. Monte Carlo simulation showed that EAR's mean values are more biased by noise than FA when anisotropy is small, both for single fiber tracts and when fiber tracts cross. However, the improved signal-to-noise ratio of EAR relative to FA suggests that EAR may be a superior measure of anisotropy both in quantifying both deep white matter with relatively uniform fiber tracts and pericortical white matter structure with relatively low anisotropy and fiber crossings.     

A photoactivated trans-diammine platinum complex as cytotoxic as cisplatin

The synthesis and X-ray structure (as the tetrahydrate) of the platinum(IV) complex trans,trans,trans-[Pt(N(3))(2)(OH)(2)(NH(3))(2)] 3 are described and its photochemistry and photobiology are compared with those of the cis isomer cis,trans,cis-[Pt(N(3))(2)(OH)(2)(NH(3))(2)] 4. Complexes 4 and 3 are potential precursors of the anticancer drug cisplatin and its inactive trans isomer transplatin, respectively. The trans complex 3 is octahedral, contains almost linear azide ligands, and adopts a layer structure with extensive intermolecular hydrogen bonding. The intense azide-to-platinum(IV) charge-transfer band of complex 3 (285 nm; epsilon=19 500 M(-1) cm(-1)) is more intense and bathochromically shifted relative to that of the cis isomer 4. In contrast to transplatin, complex 3 rapidly formed a platinum(II) bis(5'-guanosine monophosphate) (5'-GMP) adduct when irradiated with UVA light, and did not react in the dark. Complexes 3 and 4 were non-toxic to human skin cells (keratinocytes) in the dark, but were as cytotoxic as cisplatin on irradiation for a short time (50 min). Damage to the DNA of these cells was detected by using the "comet" assay. Both trans- and cis-diammine platinum(IV) diazide complexes therefore have potential as photochemotherapeutic agents.     

Phonemes, intensity and attention: differential effects on the mismatch negativity (MMN)

Auditory event-related potentials (ERPs) to speech sounds were recorded in a demanding selective attention task to measure how the mismatch negativity (MMN) was affected by attention, deviant feature, and task relevance, i.e., whether the feature was target or nontarget type. With vowel-consonant-vowel (VCV) disyllables randomly presented to the right and left ears, subjects attended to the VCVs in one ear. In different conditions, the subjects responded to either intensity or phoneme deviance in the consonant. The position of the deviance within the VCV also varied, being in the first (VC), second (CV), or both (VC and CV) formant-transition regions. The MMN amplitudes were larger for deviants in the attended ear. Task relevance affected the MMNs to intensity and phoneme deviants differently. Target-type intensity deviants yielded larger MMNs than nontarget types. For phoneme deviants there was no main effect of task relevance, but there was a critical interaction with deviance position. The both position gave the largest MMN amplitudes for target-type phoneme deviants, as it did for target- and nontarget-type intensity deviants. The MMN for nontarget-type phoneme deviants, however, showed an inverse pattern such that the MMN for the both position had the smallest amplitude despite its greater spectro-temporal deviance and its greater detectability when it was the target. These data indicate that the MMN reflects differences in phonetic structure as well as differences in acoustic spectral-energy structure of the deviant stimuli. Furthermore, the task relevance effects demonstrate that top-down controls not only affect the amplitude of the MMN, but can reverse the pattern of MMN amplitudes among different stimuli.     

Short rational generating functions for lattice point problems

We prove that for any fixed the generating function of the projection of the set of integer points in a rational -dimensional polytope can be computed in polynomial time. As a corollary, we deduce that various interesting sets of lattice points, notably integer semigroups and (minimal) Hilbert bases of rational cones, have short rational generating functions provided certain parameters (the dimension and the number of generators) are fixed. It follows then that many computational problems for such sets (for example, finding the number of positive integers not representable as a non-negative integer combination of given coprime positive integers ) admit polynomial time algorithms. We also discuss a related problem of computing the Hilbert series of a ring generated by monomials.

     

Fabrication of assembled virus nanostructures on templates of chemoselective linkers formed by scanning probe nanolithography

We have developed a multistep route to the fabrication of virus assembled nanostructures with chemoselective protein-to-surface linkers synthesized by an efficient solid-phase method. These linkers were used to create patterns of 30-to-50-nm-width-lines by scanning probe nanolithography. Genetically modified cow pea mosaic virus with unique cysteine residues at specific locations on their capsomers were assembled through covalent linkage on these patterns. The morphology of the assembled structures on these line patterns characterized by atomic force microscopy was found to be strongly influenced by the intervirion interactions.