Spatial organization

Spatial organization can be observed when components of an abiotic or biological group are arranged non-randomly in space. Abiotic patterns, such as the ripple formations in sand dunes or the oscillating wave patterns of the Belousov–Zhabotinsky reaction emerge after thousands of particles interact millions of times. On the other hand, individuals in biological groups may be arranged non-randomly due to selfish behavior, dominance interactions, or cooperative behavior. W. D. Hamilton (1971) proposed that in a non-related "herd" of animals, the spatial organization is likely a result of the selfish interests of individuals trying to acquire food or avoid predation. On the other hand, spatial arrangements have also been observed among highly related members of eusocial groups, suggesting that the arrangement of individuals may provide advantages for the group. Spatial organization can be defined as how something is organized internally as well as externally concerning its surroundings.

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Multivalent Pattern Recognition Through Engineering of Spatial Tolerance in DNA-Based Nanomaterials

Hale Bila

Strength in numbers, combining many weak interactions into an overall strong connection, is the fundamental principle of multivaleny. This concept has been exploiting for the engineering of super-selective cell-targeting materials, which generally display high number of flexible ligands to enhance the systems' avidity. Many biological processes, however, function through a temporal spatial organization of receptors in patterns, matching with a controlled number of ligands to create a specific interaction. In this low-valency regime, the mechanics e.g. rigidity of the ligand-presenting architecture plays a critical role in the selectivity of the multivalent complex. Exploiting the precision in spatial design inherent to DNA nanotechnology, we engineered a library of scaffolds to explore how valency, affinity, and rigidity control the balance of super-selective multivalent binding. Depending on the affinity between the ligand and receptor, a pattern-dependent binding behavior was achieved when spatial tolerance of ligands matches the spatial organization of the target. We label this new form of mechanics-controlled multivalent binding "multivalent pattern recognition" (MPR). The main parameter controlling MPR is the rigidity of the ligand, which controls the over spatial tolerance of binding. Our findings contribute to the rational design of selective targeting with nanomaterials.

EPFL2022

Poly-NL: Linear Complexity Non-local Layers With 3rd Order Polynomials

Grigorios Chrysos, Filippos Kokkinos

Spatial self-attention layers, in the form of Non-Local blocks, introduce long-range dependencies in Convolutional Neural Networks by computing pairwise similarities among all possible positions. Such pairwise functions underpin the effectiveness of non-local layers, but also determine a complexity that scales quadratically with respect to the input size both in space and time. This is a severely limiting factor that practically hinders the applicability of non-local blocks to even moderately sized inputs. Previous works focused on reducing the complexity by modifying the underlying matrix operations, however in this work we aim to retain full expressiveness of non-local layers while keeping complexity linear. We overcome the efficiency limitation of non-local blocks by framing them as special cases of 3rd order polynomial functions. This fact enables us to formulate novel fast Non-Local blocks, capable of reducing the complexity from quadratic to linear with no loss in performance, by replacing any direct computation of pairwise similarities with element-wise multiplications. The proposed method, which we dub as "Poly-NL", is competitive with state-of-the-art performance across image recognition, instance segmentation, and face detection tasks, while having considerably less computational overhead.

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