Distance Fibonacci Polynomials—Part II

In this paper we use a graph interpretation of distance Fibonacci polynomials to get a new generalization of Lucas polynomials in the distance sense. We give a direct formula, a generating function and we prove some identities for generalized Lucas polynomials. We present Pascal-like triangles with left-justified rows filled with coefficients of these polynomials, in which one can observe some symmetric patterns. Using a general Q-matrix and a symmetric matrix of initial conditions we also define matrix generators for generalized Lucas polynomials.

Phyllotaxis as geometric canalization during plant development

ABSTRACTWhy living forms develop in a relatively robust manner, despite various sources of internal or external variability, is a fundamental question in developmental biology. Part of the answer relies on the notion of developmental constraints: at any stage of ontogenesis, morphogenetic processes are constrained to operate within the context of the current organism being built. One such universal constraint is the shape of the organism itself, which progressively channels the development of the organism toward its final shape. Here, we illustrate this notion with plants, where strikingly symmetric patterns (phyllotaxis) are formed by lateral organs. This Hypothesis article aims first to provide an accessible overview of phyllotaxis, and second to argue that the spiral patterns in plants are progressively canalized from local interactions of nascent organs. The relative uniformity of the organogenesis process across all plants then explains the prevalence of certain patterns in plants, i.e. Fibonacci phyllotaxis.

Two Distinct Human Medial Temporal Complexes

We had previously discussed that hMT+ should have two distinct regions, one is connected to the central retina, and another is connected to the retinal peripheries; and both of these distinct regions generate different perceived speed. Namely, in the central region, the stimulus appears to move much slower, see references 1 & 2; in the peripheral region however, it appears to move faster and even with reversed direction, see reference 4. This article, however, provides evidence that repeated symmetric patterns are perceived to move much slower than repeated asymmetric patterns (RAP); additionally, asymmetric but not symmetric patterns tends to generate illusory motion reversals. Evidences which conclude that symmetric, but not asymmetric patterns are preferred to be processed by the central retina; an additional characteristic that adds further distinction between the central and the peripheral hMT+ regions.

The engulfment receptor Draper organizes the postsynaptic spectrin cytoskeleton into corrals containing synaptic proteins and promotes synaptic renewal

SummaryThe spectrin cytoskeleton is required for development of the Drosophila neuromuscular junction (NMJ) but its role is unclear. Here we show that the muscle spectrin lattice functions to corral membrane-associated synaptic proteins and limit their lateral mobility. Drosophila adducin, Hts, is required for integrity of the spectrin cytoskeleton and disruption of Hts function results in failure of the corrals. The spectrin cytoskeleton is itself patterned at the muscle membrane by the engulfment receptor Draper (Drpr) through regulation of Hts. We find patches of membrane where the spectrin cytoskeleton is organized into bilaterally symmetric patterns, which coincide with a field of Drpr-dependent structures similar to phagocytic pseudopods. The bilaterally symmetric patterns are likely created by folds of the muscle membrane in the pseudopods. We present evidence that the folds trap nascent boutons of motor neurons, leading to boutons with a bilaterally symmetric organization of the postsynaptic membrane. Drpr thus acts as a sensor of synaptic damage that promotes synaptogenesis.

Multilevel Design for the Interior of 3D Fabrications

This article presents a multilevel design for infill patterns. The method partitions an input model into subareas and each subarea are applied with different scales of infill patterns. The number of subareas can be decided by users. For each subarea, there are different values of the scaling parameter that determines the number of columns and rows of pattern elements, which is useful to change the weight and strength of a certain area by user demands. Subareas can be symmetric or asymmetric to each other depending on the geometry of a 3D model and the application requirements. In each subarea, there are generated symmetric patterns. The proposed method is also applicable to combining different patterns. The aim of our work is to create lightweight 3D fabrications with lighter interior structures to minimize printing materials and supplementary to strengthen thin parts of objects. Our approach allows for the composition of sparse and dense distributions of patterns of interior 3D fabrications in an efficient way so users can fabricate their own 3D designs.