We derive multi-bladed polyhedron propellers after a new principle. The remarkable structures of Coxsackievirus a21 and Human Rhinovirus Complexed with ICAM-1 are given as examples.

C-fibers, unmyelinated afferent axons, convey information from the periphery of the nervous system to the spinal cord. They transmit signals originating from noxious stimulation evoking the sensations of itch and pain in the central nervous system. Different classes of C-fibers are characterized by functional, morphological and biochemical characteristics. In pain studies, a classification into mechano-insensitive (CMi) and mechano responsive fibers (CM) has proven useful as changes in proportions and response characteristics of these fibers have been observed in neuropathy patients (Weidner et al. 1999, 2000; Orstavik 2003, 2010). In this study, using computational modeling of a C-fiber, we have studied the possible contribution of different ion channel subtypes (Na-TTXs, Nav1.8, Nav1.9, Kdr, KA, KM, K(Na), h) as well as the Na/K-ATPase pump to conductive properties of C-fibers. In particular we investigated mechanisms that could generate the fiber-specific differences between CM and CMi fibers with regard to activity dependent slowing (ADS) and recovery cycles (RC). In our study we represent the axon by three cylindrical sections, one representing the peripheral thin end (branch, 2.5 cm), one the central part (parent, 10 cm) and a conical section between these (0.5 cm). In total 730 compartments are used. Temperature is set to 32 degrees C in branch and 37 degrees in parent sections. We represent variable ion concentrations of Na and K intra axonally, periaxonally and extracellularly, from which reversal potentials are calculated. We use ion channel models based on Hodgkin Huxley formalism. An ion pump (Na/K-ATPase) is included. We find that TTX-sensitive Na and Nav1.8 have the strongest influence on action potential conduction velocity as is expected since these are the major components of the rising phase of the action potential. Preliminary observations indicate that a small subset of Na and K currents play a key role in determining differences in activity dependent velocity changes (ADS) in the two fiber classes. We plan to also study contributions from morphological characteristics (superficial branch lengths) to activity dependent differences between the fiber classes (Schmidt et al. 2002). We further intend to investigate candidate ion channels which could play a role in changing the functional characteristics of a CMi fiber to that of a CM fiber. Our studies may provide insights into ionic changes underlying changes in the excitability of C-fibers associated with pain.

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We derive many generalized polyhedra of dodecahedron type with analytic mathematics.The findings are compared with the structures of the Adeno Herpes series of viruses.

Abstract We describe generalized polyhedra of icosahedron type with analytic mathematics (exponential summation method) using the ordinary (Platon and Archimedes) polyhedra and their interpenetrations (mixed polyhedra). To this we add the Hardy devation for enhancing the topology within each structure type. The findings are compared with the structures of some viruses.

Simple rod packings of new kinds are used to circumscribe the Platonic and the Archimedean polyhedra. The geometry is chiral and describes a spherical propeller and differences in the Echoviruses 7 and 12 structures. A cubic version of such a chiral virus is discussed for the early evolution.

The organizations of neurons, axons and dendrites in brain space are described with structures of infinite types of rods using Gauss distribution mathematics. Hermitian wavelets are used to describe mechanisms of thought.

New polyhedra are derived with symmetry codes and variables.

We assume the pentagonal viruses are relatively late and Search for models of an earlier evolution. A possible start from the beginning billions of years ago would be cubic mathematics describing hypothetical virus structures. The proposed shift from cubic pentagonal symmetry is unique and methods from inorganic solid-stage chemistry are very important in our description of structure.

We show that the spike structures of viruses accurately can be described as stellations of polyhedra using exponential GD functions and also the fundamental theorem of algebra. The structures of foot-and-mouth disease virus, human Coxsackie viruses B3 and A21, polio virus, human rhinovirus 16 (common cold), human hepatitis B virus, herpes virus, Sindbis virus, Semliki virus, and echoviruses 1, 7 and 12 are discussed. Again methods from inorganic solid-state chemistry are very useful in the descriptions.

The fundamental theorern of algebra and the Hermites provide unique methods to describe virus capsids. Giant virus structures are described in the Rossmann's series that contains the PBCV-1. and also a hypothetical Mimi virus structure. The HIV core structure given by Mark Yeager and Barbie Ganser-Pornillos is described as composed of capsid members of the Blue Tongue series.

With the new periodic exponential mathematics, with new structure building principles (morphotropic, bilateral and disk), with the plural concept and the volume variations, we have a good understanding of the evolution of the structure of viruses. A massive demonstration of this is the simple Blue Tongue series. The structures of nine viruses from the smallest to the very big capsids are described as closely related: Parvovius (m=1), Coxsackie (m=2), Semliki (m=3), Simian (m=4), Cowpea mosaic (m=5), Blue Tongue (m=6), Herpes (m=7), Vacant (m=8), Human Adenovirus Type 5 (m=9), Archaeal (m=10).

The report presents a platform for further research and development (R&D) work from a perspective grounded in the sociology of knowledge. Municipalities are viewed as potential active knowledge producers rather than mediators merely implementing national R&D policies, or utilizing knowledge imported from traditionally organized research. Three dimensions of future inquiry are suggested.