A Computationally-Realizable Rigorous Canonical Numbering Algorithm for Chemical Graphs with its Open-Source Implementation in Rust

Canonical numbering of the vertices from a graph has been a challenging open issue for decades not only in the domain of graph theory but also in the cheminformatic applications. This paper presents an efficient, fast and rigorous approach for canonical numbering and symmetry perception as the first workable solution with theoretical completeness. The methodology is composed of a set of algorithms including extendable representation of vertex, high-performance sorting and graph reduction, etc. The canonical numbering of vertices can be generated in a short time through the novel vertex representation method. Furthermore, a new concept of graph reduction decreases the amount of computation to determine constitutional symmetry of complex graphs into the range of hardware capability. An open-source version of algorithms overall is implemented in Rust thanks to the features of safety, performance and robust abstraction of this modern programming language. The results of experiments on more than 2 million molecules from ChEMBL database has been given at the end.

The human visual system preserves the hierarchy of two-dimensional pattern regularity

Symmetries are present at many scales in natural scenes. Humans and other animals are highly sensitive to visual symmetry, and symmetry contributes to numerous domains of visual perception. The four fundamental symmetries—reflection, rotation, translation and glide reflection—can be combined into exactly 17 distinct regular textures. These wallpaper groups represent the complete set of symmetries in two-dimensional images. The current study seeks to provide a more comprehensive description of responses to symmetry in the human visual system, by collecting both brain imaging (steady-state visual evoked potentials measured using high-density EEG) and behavioural (symmetry detection thresholds) data using the entire set of wallpaper groups. This allows us to probe the hierarchy of complexity among wallpaper groups, in which simpler groups are subgroups of more complex ones. We find that both behaviour and brain activity preserve the hierarchy almost perfectly: subgroups consistently produce lower-amplitude symmetry-specific responses in visual cortex and require longer presentation durations to be reliably detected. These findings expand our understanding of symmetry perception by showing that the human brain encodes symmetries with a high level of precision and detail. This opens new avenues for research on how fine-grained representations of regular textures contribute to natural vision.

Symmetry perception with spiking neural networks

Mirror symmetry is an abundant feature in both nature and technology. Its successful detection is critical for perception procedures based on visual stimuli and requires organizational processes. Neuromorphic computing, utilizing brain-mimicked networks, could be a technology-solution providing such perceptual organization functionality, and furthermore has made tremendous advances in computing efficiency by applying a spiking model of information. Spiking models inherently maximize efficiency in noisy environments by placing the energy of the signal in a minimal time. However, many neuromorphic computing models ignore time delay between nodes, choosing instead to approximate connections between neurons as instantaneous weighting. With this assumption, many complex time interactions of spiking neurons are lost. Here, we show that the coincidence detection property of a spiking-based feed-forward neural network enables mirror symmetry. Testing this algorithm exemplary on geospatial satellite image data sets reveals how symmetry density enables automated recognition of man-made structures over vegetation. We further demonstrate that the addition of noise improves feature detectability of an image through coincidence point generation. The ability to obtain mirror symmetry from spiking neural networks can be a powerful tool for applications in image-based rendering, computer graphics, robotics, photo interpretation, image retrieval, video analysis and annotation, multi-media and may help accelerating the brain-machine interconnection. More importantly it enables a technology pathway in bridging the gap between the low-level incoming sensor stimuli and high-level interpretation of these inputs as recognized objects and scenes in the world.

In plain sight: implicit priming of patterns and faces using change symmetry

Aksentijevic–Gibson complexity is an original complexity measure based on the amount of change in a string or 2D array that has been successfully implemented on data from psychology to physics. The key ingredient to computing the measure is a change symmetry (CS)—a novel form of structure (also known as generalised palindrome) which represents a central or mirror symmetry based on the redundant arrangement not of symbols but of changes. This results in patterns that although globally symmetrical do not appear as such when inspected locally. We used this property to (a) affect the registration of a target, (b) prime the symmetry judgment of 2D arrays and (c) faces using 1D patterns possessing change symmetry. In Experiment 2, we applied the lock and key principle to complete the prime without showing its structure at once. In Experiments 3 and 4, we presented subjects with fast sequences of CSs such that the configuration of an individual pattern was masked by the subsequent pattern leaving only the structural “essence” of the prime symmetry. The results strongly support the contention that higher-level hidden structure of change symmetry successfully primes the symmetry perception of 2D arrays as well as facial attractiveness.

Spontaneous Ocular Scanning of Visual Symmetry Is Similar During Classification and Evaluation Tasks

Visual symmetry perception and symmetry preference have been studied extensively. However, less is known about how people spontaneously scan symmetrical stimuli with their eyes. We thus examined spontaneous saccadic eye movements when participants ( N = 20) observed patterns with horizontal or vertical mirror reflection. We found that participants tend to make saccades along the axis of reflection and that this oculomotor behaviour was similar during objective classification and subjective evaluation tasks. The axis-scanning behaviour generates a dynamic sequence of novel symmetrical images from a single static stimulus. This could aid symmetry perception and evaluation by enhancing the neural response to symmetry.

Atomic Ring Invariant and Modified CANON Extended Connectivity Algorithm for Symmetry Perception in Molecular Graphs and Rigorous Canonicalization of SMILES

We propose new invariant (the product of the corresponding primes for the ring size of each bond of an atom) as a simple unambiguous ring invariant of an atom that allows distinguishing symmetry classes in the highly symmetrical molecular graphs using traditional local and distance atom invariants. Also, we propose modifications of Weininger’s CANON algorithm to avoid its ambiguities (swapping and leveling ranks, incorrect determination of symmetry classes in non-aromatic annulenes, arbitrary selection of atom for breaking ties). The atomic ring invariant and the Modified CANON algorithm allow us to create a rigorous procedure for the generation of canonical SMILES which can be used for accurate and fast structural searching in large chemical databases.

Atomic Ring Invariant and Modified CANON Extended Connectivity Algorithm for Symmetry Perception in Molecular Graphs and Rigorous Canonicalization of SMILES

We propose new invariant (the product of the corresponding primes for the ring size of each bond of an atom) as a simple unambiguous ring invariant of an atom that allows distinguishing symmetry classes in the highly symmetrical molecular graphs using traditional local and distance atom invariants. Also, we propose modifications of Weininger’s CANON algorithm to avoid its ambiguities (swapping and leveling ranks, incorrect determination of symmetry classes in non-aromatic annulenes, arbitrary selection of atom for breaking ties). The atomic ring invariant and the Modified CANON algorithm allow us to create a rigorous procedure for the generation of canonical SMILES which can be used for accurate and fast structural searching in large chemical databases.

Atomic Ring Invariant and Modified CANON Extended Connectivity Algorithm for Symmetry Perception in Molecular Graphs and Rigorous Canonicalization of SMILES

We propose new invariant (product of corresponding primes for ring size of each bond of an atom) as a simple unambiguous ring invariant of the atom which allows to distinguish symmetry classes in highly symmetrical molecular graphs (with using of traditional local atom invariants). Also, we propose modifications of Weininger’s CANON algorithm which let to avoid its ambiguities (swapping and leveling of ranks, incorrect determination of symmetry classes in non-aromatic annulenes, arbitrary selection of atom for breaking ties). The atomic ring invariant and the Modified CANON algorithm allow us to create a rigorous procedure for the generation of canonical SMILES which can be used for accurate and fast structural search in large chemical databases.

Time for Change: Implementation of Aksentijevic-Gibson Complexity in Psychology

Given that complexity is critical for psychological processing, it is somewhat surprising that the field was dominated for a long time by probabilistic methods that focus on the quantitative aspects of the source/output. Although the more recent approaches based on the Minimum Description Length principle have produced interesting and useful models of psychological complexity, they have not directly defined the meaning and quantitative unit of complexity measurement. Contrasted to these mathematical approaches are various ad hoc measures based on different aspects of structure, which can work well but suffer from the same problem. The present manuscript is composed of two self-sufficient, yet related sections. In Section 1, we describe a complexity measure for binary strings which satisfies both these conditions (Aksentijevic–Gibson complexity; AG). We test the measure on a number of classic studies employing both short and long strings and draw attention to an important feature—a complexity profile—that could be of interest in modelling the psychological processing of structure as well as analysis of strings of any length. In Section 2 we discuss different factors affecting the complexity of visual form and showcase a 2D generalization of AG complexity. In addition, we provide algorithms in R that compute the AG complexity for binary strings and matrices and demonstrate their effectiveness on examples involving complexity judgments, symmetry perception, perceptual grouping, entropy, and elementary cellular automata. Finally, we enclose a repository of codes, data and stimuli for our example in order to facilitate experimentation and application of the measure in sciences outside psychology.