Labeling of Polymer Nanostructures for Medical Imaging: Importance of crosslinking extent, spacer length, and charge density

Radiolabeling studies were employed to investigate the influence of structure on the efficiency of surface functionalization for poly(acrylic acid)-coated shell crosslinked nanoparticles (SCKs) with two types of amine-terminated DOTA chelators. An intricate interplay between the chemical and physical properties of both the DOTA derivative and the SCK nanostructures was revealed, demonstrating the importance of structural control.     

Up a gear? The significance of an elevated mutation rate in tumorigenesis

Mutations involved in many cancers have been identified, but with some cancers requiring six or more mutations to take on their fully metastatic forms, the question remains whether all of these mutations can be acquired via a process of successive mutation, at a normal rate, and clonal expansion or whether heightened mutation rates are required. This issue has been debated for decades. Recently there has been much interest in forms of genomic instability such as chromosomal instability and microsatellite instability. It remains to definitively show whether or not these instabilities are very early causal events in tumorigenesis. This article reviews the evidence for and against genomic instability being an early causal event in tumorigenesis and surveys the mathematical modelling literature in this area. The focus is on chromosomal instability and microsatellite instability in colorectal cancer.     

Linear Systems of Cubics Singular at General Points of Projective Space

We present an elementary proof that given a general collection of d points in Pⁿ the linear system of cubics singular on each point has the expected codimension except when n=4 and d=7. In that case the cubic is unique. This, together with previous work of the author, gives a proof of the Alexander–Hirschowitz interpolation theorem.     

Planar lattices are lexicographically shellable

The special properties of planar posets have been studied, particularly in the 1970's by I. Rival and others. More recently, the connection between posets, their corresponding polynomial rings and corresponding simplicial complexes has been studied by Stanley and others. This paper, using work of Björner, provides a connection between the two bodies of work, by characterizing when planar posets are Cohen-Macaulay. Planar posets are lattices when they contain a greatest and a least element. We show that a finite planar lattice is lexicographically shellable and therefore Cohen-Macaulay iff it is rank-connected.     

On the connection between harmonic maps and the self-dual Yang—Mills and the sine-Gordon equations

This is an algebraic paper which demonstrates some algebraic connections between the Yang—Mills and the sine-Gordon equation.     

Monotone factors of I.I.D. processes

LetB(p) andB(q) be Bernoulli shifts on {0, 1,...,d - 1}^ℤ. Ifh(p)>h(q), it is a classical theorem of Sinai that there is a factor map takingB(p) toB(q). If, in addition,p stochastically dominatesq, we can ask whether there is such a factor map ϕ which is monotone: ϕ(x) _i≤x_i for each coordinatei of almost every pointx. Here we show that there is a monotone finitary code fromB(p) toB(q) in the case whereB(q) is a shift on two symbols.     

Simulation of Printed Circuit-Board Manufacturing

The paper describes a simulation model that was built to predict the production output of a printed circuit-board manufacturer. Such a prediction with traditional forecasting tools is difficult owing to varying lot sizes, designs, processing time, product mix, machining capacity and fluctuating work-force. The model was built with discrete-event orientation using SIMPLE_1 simulation language. Model-validation was made over a period of 1 month by comparing the simulation and actual outputs as well as the supervisor's predictions. The model was later used to study the effects of varying manning levels and equipment capacities on output, as well as to evaluate proposed changes to the existing system.     

Binaural weighting of monaural spectral cues for sound localization

For human listeners, cues for vertical-plane localization are provided by direction-dependent pinna filtering. This study quantified listeners' weighting of the spectral cues from each ear as a function of stimulus lateral angle, interaural time difference (ITD), and interaural level difference (ILD). Subjects indicated the apparent position of headphone-presented noise bursts synthesized in virtual auditory space. The synthesis filters for the two ears either corresponded to the same location or to two different locations separated vertically by 20 deg. Weighting of each ear's spectral information was determined by a multiple regression between the elevations to which each ear's spectrum corresponded and the vertical component of listeners' responses. The apparent horizontal source location was controlled either by choosing synthesis filters corresponding to locations on or 30 deg left or right of the median plane or by attenuating or delaying the signal at one ear. For broadband stimuli, spectral weighting and apparent lateral angle were determined primarily by ITD. Only for high-pass stimuli were weighting and lateral angle determined primarily by ILD. The results suggest that the weighting of monaural spectral cues and the perceived lateral angle of a sound source depend similarly on ITD, ILD, and stimulus spectral range.     

Shapes of semiflexible polymer rings

The shape of semiflexible polymer rings is studied over their whole range of flexibility. Investigating the joint distribution of asphericity and the nature of asphericity as well as their respective averages, we find two distinct shape regimes depending on the flexibility of the polymer. For a small perimeter to persistence length the fluctuating rings exhibit only planar, elliptical configurations. At higher flexibilities three-dimensional, crumpled structures arise. Analytic calculations confirm the qualitative behavior of the averaged shape parameters and the elliptical shape in the stiff regime.