Information Processing by Neuron Populations in the Central Nervous System: Mathematical Structure of Data and Operations

In the intricate architecture of the mammalian central nervous system, neurons form populations. Axonal bundles communicate between these clusters using spike trains as their medium. However, these neuron populations' precise encoding and operations have yet to be discovered. In our analysis, the starting point is a state-of-the-art mechanistic model of a generic neuron endowed with plasticity. From this simple framework emerges a profound mathematical construct: The representation and manipulation of information can be precisely characterized by an algebra of finite convex cones. Furthermore, these neuron populations are not merely passive transmitters. They act as operators within this algebraic structure, mirroring the functionality of a low-level programming language. When these populations interconnect, they embody succinct yet potent algebraic expressions. These networks allow them to implement many operations, such as specialization, generalization, novelty detection, dimensionality reduction, inverse modeling, prediction, and associative memory. In broader terms, this work illuminates the potential of matrix embeddings in advancing our understanding in fields like cognitive science and AI. These embeddings enhance the capacity for concept processing and hierarchical description over their vector counterparts.Comment: 34 pages, 12 figure

Spinorial cohomology and maximally supersymmetric theories

Fields in supersymmetric gauge theories may be seen as elements in a spinorial cohomology. We elaborate on this subject, specialising to maximally supersymmetric theories, where the superspace Bianchi identities, after suitable conventional constraints are imposed, put the theories on shell. In these cases, the spinorial cohomologies describe in a unified manner gauge transformations, fields and possible deformations of the models, e.g. string-related corrections in an alpha' expansion. Explicit cohomologies are calculated for super-Yang-Mills theory in D=10, for the N=(2,0) tensor multiplet in D=6 and for supergravity in D=11, in the latter case from the point of view of both the super-vielbein and the super-3-form potential. The techniques may shed light on some questions concerning the alpha'-corrected effective theories, and result in better understanding of the role of the 3-form in D=11 supergravity.Comment: 23 pp, plain tex. v2: Minor changes, references adde

Using force covariance to derive effective stochastic interactions in dissipative particle dynamics

There exist methods for determining effective conservative interactions in coarse grained particle based mesoscopic simulations. The resulting models can be used to capture thermal equilibrium behavior, but in the model system we study do not correctly represent transport properties. In this article we suggest the use of force covariance to determine the full functional form of dissipative and stochastic interactions. We show that a combination of the radial distribution function and a force covariance function can be used to determine all interactions in dissipative particle dynamics. Furthermore we use the method to test if the effective interactions in dissipative particle dynamics (DPD) can be adjusted to produce a force covariance consistent with a projection of a microscopic Lennard-Jones simulation. The results indicate that the DPD ansatz may not be consistent with the underlying microscopic dynamics. We discuss how this result relates to theoretical studies reported in the literature.Comment: 10 pages, 10 figure

D=3, N=8 conformal supergravity and the Dragon window

We give a superspace description of D=3, N=8 supergravity. The formulation is off-shell in the sense that the equations of motion are not implied by the superspace constraints (but an action principle is not given). The multiplet structure is unconventional, which we connect to the existence of a "Dragon window", that is modules occurring in the supercurvature but not in the supertorsion. According to Dragon's theorem this cannot happen above three dimensions. We clarify the relevance of this window for going on the conformal shell, and discuss some aspects of coupling to conformal matter.Comment: plain tex, 24 pp v2: minor change

Spinorial cohomology of abelian d=10 super-Yang-Mills at alpha'^3

We compute the spinorial cohomology of ten-dimensional abelian SYM at order alpha'^3 and we find that it is trivial. Consequently, linear supersymmetry alone excludes the presence of alpha'^3-order corrections. Our result lends support to the conjecture that there may be a unique supersymmetric deformation of ordinary ten-dimensional abelian SYM.Comment: 13 pages, 1 figure, harvma

Unified description of magic numbers of metal clusters in terms of the 3-dimensional q-deformed harmonic oscillator

Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3)>SOq(3) symmetry are compared to experimental data for atomic clusters of alkali metals (Li, Na, K, Rb, Cs), noble metals (Cu, Ag, Au), divalent metals (Zn, Cd), and trivalent metals (Al, In), as well as to theoretical predictions of jellium models, Woods-Saxon and wine bottle potentials, and to the classification scheme using the 3n+l pseudo quantum number. In alkali metal clusters and noble metal clusters the 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), while in addition it gives satisfactory results for the magic numbers of clusters of divalent metals and trivalent metals, thus indicating that Uq(3), which is a nonlinear extension of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry of systems of several metal clusters. The Taylor expansions of angular momentum dependent potentials approximately producing the same spectrum as the 3-dimensional q-deformed harmonic oscillator are found to be similar to the Taylor expansions of the symmetrized Woods-Saxon and wine-bottle symmetrized Woods-Saxon potentials, which are known to provide successful fits of the Ekardt potentials.Comment: 23 pages including 7 table

Interactions between a Trawl Fishery and Spatial Closures for Biodiversity Conservation in the Great Barrier Reef World Heritage Area, Australia

Background\ud The Queensland East Coast Otter Trawl Fishery (ECOTF) for penaeid shrimp fishes within Australia's Great Barrier Reef World Heritage Area (GBRWHA). The past decade has seen the implementation of conservation and fisheries management strategies to reduce the impact of the ECOTF on the seabed and improve biodiversity conservation. New information from electronic vessel location monitoring systems (VMS) provides an opportunity to review the interactions between the ECOTF and spatial closures for biodiversity conservation.\ud \ud Methodology and Results\ud We used fishing metrics and spatial information on the distribution of closures and modelled VMS data in a geographical information system (GIS) to assess change in effort of the trawl fishery from 2001–2009 and to quantify the exposure of 70 reef, non-reef and deep water bioregions to trawl fishing. The number of trawlers and the number of days fished almost halved between 2001 and 2009 and new spatial closures introduced in 2004 reduced the area zoned available for trawl fishing by 33%. However, we found that there was only a relatively minor change in the spatial footprint of the fishery as a result of new spatial closures. Non-reef bioregions benefited the most from new spatial closures followed by deep and reef bioregions.\ud \ud Conclusions/Significance\ud Although the catch of non target species remains an issue of concern for fisheries management, the small spatial footprint of the ECOTF relative to the size of the GBRWHA means that the impact on benthic habitats is likely to be negligible. The decline in effort as a result of fishing industry structural adjustment, increasing variable costs and business decisions of fishers is likely to continue a trend to fish only in the most productive areas. This will provide protection for most benthic habitats without any further legislative or management intervention

Protein crystals in adenovirus type 5-infected cells: requirements for intranuclear crystallogenesis, structural and functional analysis

Intranuclear crystalline inclusions have been observed in the nucleus of epithelial cells infected with Adenovirus serotype 5 (Ad5) at late steps of the virus life cycle. Using immuno-electron microscopy and confocal microscopy of cells infected with various Ad5 recombinants modified in their penton base or fiber domains, we found that these inclusions represented crystals of penton capsomers, the heteromeric capsid protein formed of penton base and fiber subunits. The occurrence of protein crystals within the nucleus of infected cells required the integrity of the fiber knob and part of the shaft domain. In the knob domain, the region overlapping residues 489–492 in the FG loop was found to be essential for crystal formation. In the shaft, a large deletion of repeats 4 to 16 had no detrimental effect on crystal inclusions, whereas deletion of repeats 8 to 21 abolished crystal formation without altering the level of fiber protein expression. This suggested a crucial role of the five penultimate repeats in the crystallisation process. Chimeric pentons made of Ad5 penton base and fiber domains from different serotypes were analyzed with respect to crystal formation. No crystal was found when fiber consisted of shaft (S) from Ad5 and knob (K) from Ad3 (heterotypic S5-K3 fiber), but occurred with homotypic S3K3 fiber. However, less regular crystals were observed with homotypic S35-K35 fiber. TB5, a monoclonal antibody directed against the Ad5 fiber knob was found by immunofluorescence microscopy to react with high efficiency with the intranuclear protein crystals in situ. Data obtained with Ad fiber mutants indicated that the absence of crystalline inclusions correlated with a lower infectivity and/or lower yields of virus progeny, suggesting that the protein crystals might be involved in virion assembly. Thus, we propose that TB5 staining of Ad-infected 293 cells can be used as a prognostic assay for the viability and productivity of fiber-modified Ad5 vectors

Dirac electrons in graphene-based quantum wires and quantum dots

In this paper we analyse the electronic properties of Dirac electrons in finite-size ribbons and in circular and hexagonal quantum dots made of graphene.Comment: Contribution for J. Phys.: Cond. Mat. special issue on graphene physic

NMR investigations of the interaction between the azo-dye sunset yellow and Fluorophenol

The interaction of small molecules with larger noncovalent assemblies is important across a wide range of disciplines. Here, we apply two complementary NMR spectroscopic methods to investigate the interaction of various fluorophenol isomers with sunset yellow. This latter molecule is known to form noncovalent aggregates in isotropic solution, and form liquid crystals at high concentrations. We utilize the unique fluorine-19 nucleus of the fluorophenol as a reporter of the interactions via changes in both the observed chemical shift and diffusion coefficients. The data are interpreted in terms of the indefinite self-association model and simple modifications for the incorporation of a second species into an assembly. A change in association mode is tentatively assigned whereby the fluorophenol binds end-on with the sunset yellow aggregates at low concentration and inserts into the stacks at higher concentrations