A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope

A derivation of the Ces\`aro-Fedorov relation from the Selberg trace formula on an orbifolded 2-sphere is elaborated and extended to higher dimensions using the known heat-kernel coefficients for manifolds with piecewise-linear boundaries. Several results are obtained that relate the coefficients, $b_i$, in the Shephard-Todd polynomial to the geometry of the fundamental domain. For the 3-sphere we show that $b_4$ is given by the ratio of the volume of the fundamental tetrahedron to its Schl\"afli reciprocal.Comment: Plain TeX, 26 pages (eqn. (86) corrected

Ground-state properties of tubelike flexible polymers

In this work we investigate structural properties of native states of a simple model for short flexible homopolymers, where the steric influence of monomeric side chains is effectively introduced by a thickness constraint. This geometric constraint is implemented through the concept of the global radius of curvature and affects the conformational topology of ground-state structures. A systematic analysis allows for a thickness-dependent classification of the dominant ground-state topologies. It turns out that helical structures, strands, rings, and coils are natural, intrinsic geometries of such tubelike objects

Local biases drive, but do not determine, the perception of illusory trajectories

When a dot moves horizontally across a set of tilted lines of alternating orientations, the dot appears to be moving up and down along its trajectory. This perceptual phenomenon, known as the slalom illusion, reveals a mismatch between the veridical motion signals and the subjective percept of the motion trajectory, which has not been comprehensively explained. In the present study, we investigated the empirical boundaries of the slalom illusion using psychophysical methods. The phenomenon was found to occur both under conditions of smooth pursuit eye movements and constant fixation, and to be consistently amplified by intermittently occluding the dot trajectory. When the motion direction of the dot was not constant, however, the stimulus display did not elicit the expected illusory percept. These findings confirm that a local bias towards perpendicularity at the intersection points between the dot trajectory and the tilted lines cause the illusion, but also highlight that higher-level cortical processes are involved in interpreting and amplifying the biased local motion signals into a global illusion of trajectory perception

Local biases drive, but do not determine, the perception of illusory trajectories

When a dot moves horizontally across a set of tilted lines of alternating orientations, the dot appears to be moving up and down along its trajectory. This perceptual phenomenon, known as the slalom illusion, reveals a mismatch between the veridical motion signals and the subjective percept of the motion trajectory, which has not been comprehensively explained. In the present study, we investigated the empirical boundaries of the slalom illusion using psychophysical methods. The phenomenon was found to occur both under conditions of smooth pursuit eye movements and constant fixation, and to be consistently amplified by intermittently occluding the dot trajectory. When the motion direction of the dot was not constant, however, the stimulus display did not elicit the expected illusory percept. These findings confirm that a local bias towards perpendicularity at the intersection points between the dot trajectory and the tilted lines cause the illusion, but also highlight that higher-level cortical processes are involved in interpreting and amplifying the biased local motion signals into a global illusion of trajectory perception

Generation and characterization of standardized forms of trehalose dihydrate and their associated solid-state behavior

Trehalose dihydrate is a nonreducing disaccharide which has generated great interest in the food and pharmaceutical industries. However, it is well recognized that considerable batch to batch variation exists for supposedly identical samples, particularly in terms of the thermal response. In this investigation, two standardized forms of trehalose dihydrate were generated using two distinct crystallization pathways. The two batches were characterized using scanning electron microscopy, X-ray powder diffraction, and FTIR. The thermal responses of the two forms were then studied using modulated temperature differential scanning calorimetry (MTDSC) and thermogravimetric analysis (TGA). In particular, we describe the technique of quasi-isothermal MTDSC as a means of studying the change in equilibrium heat capacity as a function of temperature. Finally, variable temperature FTIR was utilized to assess the change in bonding configuration as a function of temperature. SEM revealed significant differences in the continuity and grain structure of the two batches. The TGA, MTDSC, and quasi-isothermal MTDSC studies all indicated significant differences in the thermal response and water loss profile. This was confirmed using variable temperature FTIR which indicated differences in bond reconfiguration as a function of temperature. We ascribe these differences to variations in the route by which water may leave the structure, possibly associated with grain size. The study has therefore demonstrated that chemically identical dihydrate forms may show significant differences in thermal response. We believe that this may assist in interpreting and hence controlling interbatch variation for this material