Revisiting special relativity: A natural algebraic alternative to Minkowski spacetime

Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension $i c t$, with the unit imaginary producing the correct spacetime distance $x^2 - c^2 t^2$, and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary $i = \sqrt{-1}$, with the Clifford bivector $\iota = e_1 e_2$ for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis $e_1$ and $e_2$. We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane.Comment: 29 pages, 2 figure

Eight common genetic variants associated with serum dheas levels suggest a key role in ageing mechanisms

Dehydroepiandrosterone sulphate (DHEAS) is the most abundant circulating steroid secreted by adrenal glands-yet its function is unknown. Its serum concentration declines significantly with increasing age, which has led to speculation that a relative DHEAS deficiency may contribute to the development of common age-related diseases or diminished longevity. We conducted a meta-analysis of genome-wide association data with 14,846 individuals and identified eight independent common SNPs associated with serum DHEAS concentrations. Genes at or near the identified loci include ZKSCAN5 (rs11761528; p = 3.15×10-36), SULT2A1 (rs2637125; p = 2.61×10-19), ARPC1A (rs740160; p = 1.56×10-16), TRIM4 (rs17277546; p = 4.50×10-11), BMF (rs7181230; p = 5.44×10-11), HHEX (rs2497306; p = 4.64×10-9), BCL2L11 (rs6738028; p = 1.72×10-8), and CYP2C9 (rs2185570; p = 2.29×10-8). These genes are associated with type 2 diabetes, lymphoma, actin filament assembly, drug and xenobiotic metabolism, and zinc finger proteins. Several SNPs were associated with changes in gene expression levels, and the related genes are connected to biological pathways linking DHEAS with ageing. This study provides much needed insight into the function of DHEAS

Design and Characterization of an Electrically Powered Single Molecule on Gold

The surface diffusion of individual molecules is of paramount importance in self-assembly processes and catalytic processes. However, the fundamental understanding of molecule diffusion peculiarities considering conformations and adsorption sites remain poorly known at the atomic scale. Here, we probe the 4′-(4-tolyl)-2,2′:6′,2″-terpyridine adsorbed on the Au(111) herringbone structure combining scanning tunneling microscopy and atomic force microscopy. Molecules are controllably translated by electrons excitations over the reconstruction, except at elbows acting as pinning centers. Experimental data supported by theoretical calculations show the formation of coordination bonds between the molecule and Au atoms of the surface. Using force spectroscopy, we quantify local variation of the surface potential and the lateral force required to move the molecule. We found an elevation of the diffusion barrier at elbows of the reconstruction of ∼100 meV compared to the rest of the surface

Efficient Coding and Statistically Optimal Weighting of Covariance among Acoustic Attributes in Novel Sounds

To the extent that sensorineural systems are efficient, redundancy should be extracted to optimize transmission of information, but perceptual evidence for this has been limited. Stilp and colleagues recently reported efficient coding of robust correlation (r = .97) among complex acoustic attributes (attack/decay, spectral shape) in novel sounds. Discrimination of sounds orthogonal to the correlation was initially inferior but later comparable to that of sounds obeying the correlation. These effects were attenuated for less-correlated stimuli (r = .54) for reasons that are unclear. Here, statistical properties of correlation among acoustic attributes essential for perceptual organization are investigated. Overall, simple strength of the principal correlation is inadequate to predict listener performance. Initial superiority of discrimination for statistically consistent sound pairs was relatively insensitive to decreased physical acoustic/psychoacoustic range of evidence supporting the correlation, and to more frequent presentations of the same orthogonal test pairs. However, increased range supporting an orthogonal dimension has substantial effects upon perceptual organization. Connectionist simulations and Eigenvalues from closed-form calculations of principal components analysis (PCA) reveal that perceptual organization is near-optimally weighted to shared versus unshared covariance in experienced sound distributions. Implications of reduced perceptual dimensionality for speech perception and plausible neural substrates are discussed

Accurate path integration in continuous attractor network models of grid cells

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of ~10–100 meters and ~1–10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other

The benzene metabolite para-benzoquinone is genotoxic in human, phorbol-12-acetate-13-myristate induced, peripheral blood mononuclear cells at low concentrations

Benzene is one of the most prominent occupational and environmental pollutants. The substance is a proven human carcinogen that induces hematologic malignancies in humans, probably at even low doses. Yet knowledge of the mechanisms leading to benzene-induced carcinogenesis is still incomplete. Benzene itself is not genotoxic. The generation of carcinogenic metabolites involves the production of oxidized intermediates such as catechol, hydroquinone and para-benzoquinone (p-BQ) in the liver. Further activation to the ultimate carcinogenic intermediates is most probably catalyzed by myeloperoxidase (MPO). Yet the products of the MPO pathway have not been identified. If an oxidized benzene metabolite such as p-BQ was actually the precursor for the ultimate carcinogenic benzene metabolite and further activation proceeds via MPO mediated reactions, it should be possible to activate p-BQ to a genotoxic compound in vitro. We tested this hypothesis with phorbol-12-acetate-13-myristate (PMA) activated peripheral blood cells exposed to p-BQ, using the cytokinesis-block micronucleus test. Addition of 20–28 ng/ml PMA caused a significant increase of micronuclei at low and non-cytotoxic p-BQ concentrations between 0.04 and 0.2 μg/ml (0.37–1.85 μM). Thus with PMA or p-BQ alone no reproducible elevation of micronuclei was seen up to toxic concentrations. PMA and p-BQ induce micronuclei when administered jointly. Our results add further support to the hypothesis that MPO is a key enzyme in the activation of benzene

Movement and habitat use of the snapping turtle in an urban landscape

In order to effectively manage urban habitats, it is important to incorporate the spatial ecology and habitat use of the species utilizing them. Our previous studies have shown that the distribution of upland habitats surrounding a highly urbanized wetland habitat, the Central Canal (Indianapolis, IN, USA) influences the distribution of map turtles (Graptemys geographica) and red-eared sliders (Trachemys scripta) during both the active season and hibernation. In this study we detail the movements and habitat use of another prominent member of the Central Canal turtle assemblage, the common snapping turtle, Chelydra serpentina. We find the same major upland habitat associations for C. serpentina as for G. geographica and T. scripta, despite major differences in their activity (e.g., C. serpentina do not regularly engage in aerial basking). These results reinforce the importance of recognizing the connection between aquatic and surrounding terrestrial habitats, especially in urban ecosystems

Influence of ischemic core muscle fibers on surface depolarization potentials in superfused cardiac tissue preparations: a simulation study

Thin-walled cardiac tissue samples superfused with oxygenated solutions are widely used in experimental studies. However, due to decreased oxygen supply and insufficient wash out of waste products in the inner layers of such preparations, electrophysiological functions could be compromised. Although the cascade of events triggered by cutting off perfusion is well known, it remains unclear as to which degree electrophysiological function in viable surface layers is affected by pathological processes occurring in adjacent tissue. Using a 3D numerical bidomain model, we aim to quantify the impact of superfusion-induced heterogeneities occurring in the depth of the tissue on impulse propagation in superficial layers. Simulations demonstrated that both the pattern of activation as well as the distribution of extracellular potentials close to the surface remain essentially unchanged. This was true also for the electrophysiological properties of cells in the surface layer, where most relevant depolarization parameters varied by less than 5.5 %. The main observed effect on the surface was related to action potential duration that shortened noticeably by 53 % as hypoxia deteriorated. Despite the known limitations of such experimental methods, we conclude that superfusion is adequate for studying impulse propagation and depolarization whereas repolarization studies should consider the influence of pathological processes taking place at the core of tissue sample

Neural network model of the primary visual cortex: From functional architecture to lateral connectivity and back

The role of intrinsic cortical dynamics is a debatable issue. A recent optical imaging study (Kenet et al., 2003) found that activity patterns similar to orientation maps (OMs), emerge in the primary visual cortex (V1) even in the absence of sensory input, suggesting an intrinsic mechanism of OM activation. To better understand these results and shed light on the intrinsic V1 processing, we suggest a neural network model in which OMs are encoded by the intrinsic lateral connections. The proposed connectivity pattern depends on the preferred orientation and, unlike previous models, on the degree of orientation selectivity of the interconnected neurons. We prove that the network has a ring attractor composed of an approximated version of the OMs. Consequently, OMs emerge spontaneously when the network is presented with an unstructured noisy input. Simulations show that the model can be applied to experimental data and generate realistic OMs. We study a variation of the model with spatially restricted connections, and show that it gives rise to states composed of several OMs. We hypothesize that these states can represent local properties of the visual scene