Liquid relaxation: A new Parodi-like relation for nematic liquid crystals

We put forward a hydrodynamic theory of nematic liquid crystals that includes both anisotropic elasticity and dynamic relaxation. Liquid remodeling is encompassed through a continuous update of the shear-stress free configuration. The low-frequency limit of the dynamical theory reproduces the classical Ericksen-Leslie theory, but it predicts two independent identities between the six Leslie viscosity coefficients. One replicates Parodi's relation, while the other-which involves five Leslie viscosities in a nonlinear way-is new. We discuss its significance, and we test its validity against evidence from physical experiments, independent theoretical predictions, and molecular-dynamics simulations.Comment: 6 pages, 1 figure, 2 table

Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays

The goal of this paper is to introduce a new method in computer-aided geometry of solid modeling. We put forth a novel algebraic technique to evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with regularized operators of union, intersection, and difference, i.e., any CSG tree. The result is obtained in three steps: first, by computing an independent set of generators for the d-space partition induced by the input; then, by reducing the solid expression to an equivalent logical formula between Boolean terms made by zeros and ones; and, finally, by evaluating this expression using bitwise operators. This method is implemented in Julia using sparse arrays. The computational evaluation of every possible solid expression, usually denoted as CSG (Constructive Solid Geometry), is reduced to an equivalent logical expression of a finite set algebra over the cells of a space partition, and solved by native bitwise operators.Comment: revised version submitted to Computer-Aided Geometric Desig

Chain-Based Representations for Solid and Physical Modeling

In this paper we show that the (co)chain complex associated with a decomposition of the computational domain, commonly called a mesh in computational science and engineering, can be represented by a block-bidiagonal matrix that we call the Hasse matrix. Moreover, we show that topology-preserving mesh refinements, produced by the action of (the simplest) Euler operators, can be reduced to multilinear transformations of the Hasse matrix representing the complex. Our main result is a new representation of the (co)chain complex underlying field computations, a representation that provides new insights into the transformations induced by local mesh refinements. Our approach is based on first principles and is general in that it applies to most representational domains that can be characterized as cell complexes, without any restrictions on their type, dimension, codimension, orientability, manifoldness, connectedness

Algebraic filtering of surfaces from 3d medical images with julia

In this paper we introduce a novel algebraic filter, based on algebraic topology methods, to extract and smooth the boundary surface of any subset of voxels arising from the segmentation of a 3D medical image. The input of the Linear Algebraic Representation (lar) Surface extraction filter (lar-surf) is defined as a chain, i.e., an element of a linear space of chains here subsets of voxels represented in coordinates as a sparse binary vector. The output is produced by a linear mapping between spaces of 3-and 2-chains, given by the boundary operator ∂3: C3 → C2. The only data structures used in this approach are sparse arrays with one or two indices, i.e., sparse vectors and sparse matrices. This work is based on lar algebraic methods and is implemented in Julia language, natively supporting parallel computing on hybrid hardware architectures

Minimally invasive multimode optical fiber microendoscope for deep brain fluorescence imaging.

A major open challenge in neuroscience is the ability to measure and perturb neural activity in vivo from well defined neural sub-populations at cellular resolution anywhere in the brain. However, limitations posed by scattering and absorption prohibit non-invasive multi-photon approaches for deep (>2mm) structures, while gradient refractive index (GRIN) endoscopes are relatively thick and can cause significant damage upon insertion. Here, we present a novel micro-endoscope design to image neural activity at arbitrary depths via an ultra-thin multi-mode optical fiber (MMF) probe that has 5-10X thinner diameter than commercially available micro-endoscopes. We demonstrate micron-scale resolution, multi-spectral and volumetric imaging. In contrast to previous approaches, we show that this method has an improved acquisition speed that is sufficient to capture rapid neuronal dynamics in-vivo in rodents expressing a genetically encoded calcium indicator (GCaMP). Our results emphasize the potential of this technology in neuroscience applications and open up possibilities for cellular resolution imaging in previously unreachable brain regions

Salience-driven overestimation of total somatosensory stimulation

Psychological characterisation of sensory systems often focusses on minimal units of perception, such as thresholds, acuity, selectivity and precision. Research on how these units are aggregated to create integrated, synthetic experiences is rarer. We investigated mechanisms of somatosensory integration by asking volunteers to judge the total intensity of stimuli delivered to two fingers simultaneously. Across four experiments, covering physiological pathways for tactile, cold and warm stimuli, we found that judgements of total intensity were particularly poor when the two simultaneous stimuli had different intensities. Total intensity of discrepant stimuli was systematically overestimated. This bias was absent when the two stimulated digits were on different hands. Taken together, our results showed that the weaker stimulus of a discrepant pair was not extinguished, but contributed less to the perception of the total than the stronger stimulus. Thus, perception of somatosensory totals is biased towards the most salient element. ‘Peak’ biases in human judgements are well-known, particularly in affective experience. We show that a similar mechanism also influences sensory experience