Minkowski Tensors of Anisotropic Spatial Structure

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalisations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations, and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The article further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic method more readily accessible for future application in the physical sciences

Local Anisotropy of Fluids using Minkowski Tensors

Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based on strong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices $0\leq \beta_\nu^{a,b}\leq 1$ of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurations of simple liquid models, including the ideal gas (Poisson point process), the hard disks and hard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowski tensors provide a robust characterization of local anisotropy, which ranges from $\beta_\nu^{a,b}\approx 0.3$ for vapor phases to $\beta_\nu^{a,b}\to 1$ for ordered solids. We find that for fluids, local anisotropy decreases monotonously with increasing free volume and randomness of particle positions. Furthermore, the local anisotropy indices $\beta_\nu^{a,b}$ are sensitive to structural transitions in these simple fluids, as has been previously shown in granular systems for the transition from loose to jammed bead packs

Use of Artificial Enclosures to Determine the Survival of Rana pipiens Larvae in Upper Midwestern Agricultural Ponds

Amphibians in the upper Midwest use agricultural ponds for breeding. Unfortunately, the risks (both direct and indirect) associated with using these ponds are poorly understood in both amphibian adults and larvae. In order to quantify these risks, we performed a comparison of larval survival rates between agricultural and natural ponds in southeastern Minnesota during the spring and summer of 2001. During this time, larval survival was observed in Rana pipiens tadpoles raised through metamorphosis in enclosures placed in agricultural and natural ponds. In addition, we measured the levels of nutrients commonly linked with agricultural ponds (i.e., ammonia, total phosphorous, and total nitrogen), and whether or not nutrient concentration was associated with larval survival. No differences were detected in nutrient levels or survival of larvae reared in agricultural and natural ponds. Furthermore, neither nutrient levels nor pond type significantly predicted larval survival. Our data were highly variable, making the interpretation of our results difficult. The enclosures used to rear tadpoles were highly effective and can be easily incorporated into future studies

Minkowski tensors and local structure metrics: Amorphous and crystalline sphere packings

Robust and sensitive tools to characterise local structure are essential for investigations of granular or particulate matter. Often local structure metrics derived from the bond network are used for this purpose, in particular Steinhardt's bond-orientational order parameters ql . Here we discuss an alternative method, based on the robust characterisation of the shape of the particles' Voronoi cells, by Minkowski tensors and derived anisotropy measures. We have successfully applied these metrics to quantify structural changes and the onset of crystallisation in random sphere packs. Here we specifically discuss the expectation values of these metrics for simple crystalline unimodal packings of spheres, consisting of single spheres on the points of a Bravais lattice. These data provide an important reference for the discussion of anisotropy values of disordered structures that are typically of relevance in granular systems. This analysis demonstrates that, at least for sufficiently high packing fractions above φ > 0.61, crystalline sphere packs exist whose Voronoi cells are more anisotropic with respect to a volumetric moment tensor than the average value of Voronoi cell anisotropy in random sphere packs

Cell shape analysis of random tessellations based on Minkowski tensors

To which degree are shape indices of individual cells of a tessellation characteristic for the stochastic process that generates them? Within the context of stochastic geometry and the physics of disordered materials, this corresponds to the question of relationships between different stochastic models. In the context of image analysis of synthetic and biological materials, this question is central to the problem of inferring information about formation processes from spatial measurements of resulting random structures. We address this question by a theory-based simulation study of shape indices derived from Minkowski tensors for a variety of tessellation models. We focus on the relationship between two indices: an isoperimetric ratio of the empirical averages of cell volume and area and the cell elongation quantified by eigenvalue ratios of interfacial Minkowski tensors. Simulation data for these quantities, as well as for distributions thereof and for correlations of cell shape and volume, are presented for Voronoi mosaics of the Poisson point process, determinantal and permanental point processes, and Gibbs hard-core and random sequential absorption processes as well as for Laguerre tessellations of polydisperse spheres and STIT- and Poisson hyperplane tessellations. These data are complemented by mechanically stable crystalline sphere and disordered ellipsoid packings and area-minimising foam models. We find that shape indices of individual cells are not sufficient to unambiguously identify the generating process even amongst this limited set of processes. However, we identify significant differences of the shape indices between many of these tessellation models. Given a realization of a tessellation, these shape indices can narrow the choice of possible generating processes, providing a powerful tool which can be further strengthened by density-resolved volume-shape correlations.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jense

Millisecond-Timescale Optical Control of Neural Dynamics in the Nonhuman Primate Brain

To understand how brain states and behaviors are generated by neural circuits, it would be useful to be able to perturb precisely the activity of specific cell types and pathways in the nonhuman primate nervous system. We used lentivirus to target the light-activated cation channel channelrhodopsin-2 (ChR2) specifically to excitatory neurons of the macaque frontal cortex. Using a laser-coupled optical fiber in conjunction with a recording microelectrode, we showed that activation of excitatory neurons resulted in well-timed excitatory and suppressive influences on neocortical neural networks. ChR2 was safely expressed, and could mediate optical neuromodulation, in primate neocortex over many months. These findings highlight a methodology for investigating the causal role of specific cell types in nonhuman primate neural computation, cognition, and behavior, and open up the possibility of a new generation of ultraprecise neurological and psychiatric therapeutics via cell-type-specific optical neural control prosthetics.Helen Hay Whitney Foundation (Fellowship)National Institutes of Health (U.S.) (NIH-EY002621-31)McGovern Institute for Brain Research at MIT (Neurotechnology Award)National Institutes of Health (U.S.) (Grant NIH-EY12848)National Institutes of Health (U.S.) (Grant NIH-EY017292)National Institutes of Health (U.S.) (NIH Director's New Innovator Award (DP2 OD002002-01))Brain & Behavior Research FoundationUnited States. Dept. of DefenseNational Science Foundation (U.S.)Alfred P. Sloan FoundationDr. Gerald Burnett and Marjorie BurnettSFN Research Award for Innovation in NeuroscienceMassachusetts Institute of Technology. Media LaboratoryBenesse FoundationWallace H. Coulter Foundatio

GrassPlot v. 2.00 – first update on the database of multi-scale plant diversity in Palaearctic grasslands

Abstract: GrassPlot is a collaborative vegetation-plot database organised by the Eurasian Dry Grassland Group (EDGG) and listed in the Global Index of Vegetation-Plot Databases (GIVD ID EU-00-003). Following a previous Long Database Report (Dengler et al. 2018, Phyto- coenologia 48, 331–347), we provide here the first update on content and functionality of GrassPlot. The current version (GrassPlot v. 2.00) contains a total of 190,673 plots of different grain sizes across 28,171 independent plots, with 4,654 nested-plot series including at least four grain sizes. The database has improved its content as well as its functionality, including addition and harmonization of header data (land use, information on nestedness, structure and ecology) and preparation of species composition data. Currently, GrassPlot data are intensively used for broad-scale analyses of different aspects of alpha and beta diversity in grassland ecosystems

A Cortical Attractor Network with Martinotti Cells Driven by Facilitating Synapses

The population of pyramidal cells significantly outnumbers the inhibitory interneurons in the neocortex, while at the same time the diversity of interneuron types is much more pronounced. One acknowledged key role of inhibition is to control the rate and patterning of pyramidal cell firing via negative feedback, but most likely the diversity of inhibitory pathways is matched by a corresponding diversity of functional roles. An important distinguishing feature of cortical interneurons is the variability of the short-term plasticity properties of synapses received from pyramidal cells. The Martinotti cell type has recently come under scrutiny due to the distinctly facilitating nature of the synapses they receive from pyramidal cells. This distinguishes these neurons from basket cells and other inhibitory interneurons typically targeted by depressing synapses. A key aspect of the work reported here has been to pinpoint the role of this variability. We first set out to reproduce quantitatively based on in vitro data the di-synaptic inhibitory microcircuit connecting two pyramidal cells via one or a few Martinotti cells. In a second step, we embedded this microcircuit in a previously developed attractor memory network model of neocortical layers 2/3. This model network demonstrated that basket cells with their characteristic depressing synapses are the first to discharge when the network enters an attractor state and that Martinotti cells respond with a delay, thereby shifting the excitation-inhibition balance and acting to terminate the attractor state. A parameter sensitivity analysis suggested that Martinotti cells might, in fact, play a dominant role in setting the attractor dwell time and thus cortical speed of processing, with cellular adaptation and synaptic depression having a less prominent role than previously thought

Millisecond-Timescale Local Network Coding in the Rat Primary Somatosensory Cortex

Correlation among neocortical neurons is thought to play an indispensable role in mediating sensory processing of external stimuli. The role of temporal precision in this correlation has been hypothesized to enhance information flow along sensory pathways. Its role in mediating the integration of information at the output of these pathways, however, remains poorly understood. Here, we examined spike timing correlation between simultaneously recorded layer V neurons within and across columns of the primary somatosensory cortex of anesthetized rats during unilateral whisker stimulation. We used Bayesian statistics and information theory to quantify the causal influence between the recorded cells with millisecond precision. For each stimulated whisker, we inferred stable, whisker-specific, dynamic Bayesian networks over many repeated trials, with network similarity of 83.3±6% within whisker, compared to only 50.3±18% across whiskers. These networks further provided information about whisker identity that was approximately 6 times higher than what was provided by the latency to first spike and 13 times higher than what was provided by the spike count of individual neurons examined separately. Furthermore, prediction of individual neurons' precise firing conditioned on knowledge of putative pre-synaptic cell firing was 3 times higher than predictions conditioned on stimulus onset alone. Taken together, these results suggest the presence of a temporally precise network coding mechanism that integrates information across neighboring columns within layer V about vibrissa position and whisking kinetics to mediate whisker movement by motor areas innervated by layer V