Space Representation Research Articles

Magnetic structure of the noncentrosymmetric magnet Sr2MnSi2O7 through irreducible representation and magnetic space group analyses.

Magnetic structures of the noncentrosymmetric magnet Sr2MnSi2O7 were examined through neutron diffraction for powder and single-crystalline samples, as well as magnetometry measurements. All allowed magnetic structures for space group P421m with the magnetic wavevector qm = (0, 0, ½) were refined via irreducible representation and magnetic space group analyses. The compound was refined to have in-plane magnetic moments within the magnetic space group Cmc21.1'c (No. 36.177) under zero field, which can be altered to P212121.1'c (No.19.28) above μ0H = 0.067 (5) T to align induced weak-ferromagnetic components within one layer on the ab plane. All refined parameters are provided following the recent framework based upon the magnetic space group, which better conveys when exchanging crystallographic information for commensurate magnetic structures.

Spaces of mathematical chemistry.

In an effort to expand the domain of mathematical chemistry and inspire research beyond the realms of graph theory and quantum chemistry, we explore five mathematical chemistry spaces and their interconnectedness. These spaces comprise the chemical space, which encompasses substances and reactions; the space of reaction conditions, spanning the physical and chemical aspects involved in chemical reactions; the space of reaction grammars, which encapsulates the rules for creating and breaking chemical bonds; the space of substance properties, covering all documented measurements regarding substances; and the space of substance representations, composed of the various ontologies for characterising substances.

Fast mobility analysis for generative design applications through a real vector space representation of mobilities

During the early stages of design, mechanisms are commonly modeled as perfect joints assembled with infinitely rigid bodies. This representation enables the prediction of the system’s mobilities through a mobility analysis. However, traditional mobility analysis tools can be computationally expensive or lack critical information, such as the type or direction of mobilities. It hinders the generation of topology and configuration through generative design schemes.In this paper, we propose an alternative approach to mobility analysis based on a real vector space representation of mobilities. Our method provides relevant information for early design steps while being computationally effective through a novel formulation of series and parallel assembly topological operations. A benchmark on four selected use cases highlights an acceleration of 3 to 4 orders of magnitude compared to traditional approaches. Additionally, design rules on the joints’ positions can be automatically generated with our approach. It enables the automation of the complete design process, including topology and configuration. As such, we provide guidelines to develop a generative design scheme dedicated to the synthesis of guiding mechanisms.

Data-Driven Radial Compressor Design Space Mapping

Abstract Estimates of turbomachinery performance trends inform system-level compromises during preliminary design. Existing empirical correlations for efficiency use limited experimental data, while analytical loss models require calibration to yield predictive results. From a set of 3708 radial compressor computations, this paper maps efficiency as a function of mean-line aerodynamics, and determines the governing loss mechanisms. An open-source turbomachinery design code creates annulus and blade geometry, then runs a Reynolds-averaged Navier–Stokes simulation for compressors sampled from the mean-line design space. Polynomial surface fits yield a continuous eight-dimensional representation of the design space for analysis, predicting efficiency with a root-mean-square error of 1.2% points. The results show a balance between surface dissipation in boundary layers and mixing loss due to casing separations sets optimum values for inlet Mach number, hub-to-tip ratio, de Haller number, and backsweep angle. Surface dissipation drives the effect of flow coefficient, with high surface areas at low values, and high velocities at high values. Compact compressor designs are achieved by increasing inlet Mach number, reducing hub-to-tip ratio, and minimizing the radial loading coefficient—all of which reduce efficiency approaching design space boundaries. An interactive web-based tool makes the results available to practising engineers, demonstrating large ensembles of automated designs and simulations as a higher-fidelity replacement for legacy empirical correlations in preliminary design.

The primacy model and the structure of olfactory space.

Understanding sensory processing relies on the establishment of a consistent relationship between the stimulus space, its neural representation, and perceptual quality. In olfaction, the difficulty in establishing these links lies partly in the complexity of the underlying odor input space and perceptual responses. Based on the recently proposed primacy model for concentration invariant odor identity representation and a few assumptions, we have developed a theoretical framework for mapping the odor input space to the response properties of olfactory receptors. We analyze a geometrical structure containing odor representations in a multidimensional space of receptor affinities and describe its low-dimensional implementation, the primacy hull. We propose the implications of the primacy hull for the structure of feedforward connectivity in early olfactory networks. We test the predictions of our theory by comparing the existing receptor-ligand affinity and connectivity data obtained in the fruit fly olfactory system. We find that the Kenyon cells of the insect mushroom body integrate inputs from the high-affinity (primacy) sets of olfactory receptors in agreement with the primacy theory.

Magnetic space groups versus representation analysis in the investigation of magnetic structures: the happy end of a strained relationship.

In recent decades, sustained theoretical and software developments have clearly established that representation analysis and magnetic symmetry groups are complementary concepts that should be used together in the investigation and description of magnetic structures. Historically, they were considered alternative approaches, but currently, magnetic space groups and magnetic superspace groups can be routinely used together with representation analysis, aided by state-of-the-art software tools. After exploring the historical antagonism between these two approaches, we emphasize the significant advancements made in understanding and formally describing magnetic structures by embracing their combined use.

Reinforcement learning as a robotics-inspired framework for insect navigation: from spatial representations to neural implementation.

Bees are among the master navigators of the insect world. Despite impressive advances in robot navigation research, the performance of these insects is still unrivaled by any artificial system in terms of training efficiency and generalization capabilities, particularly considering the limited computational capacity. On the other hand, computational principles underlying these extraordinary feats are still only partially understood. The theoretical framework of reinforcement learning (RL) provides an ideal focal point to bring the two fields together for mutual benefit. In particular, we analyze and compare representations of space in robot and insect navigation models through the lens of RL, as the efficiency of insect navigation is likely rooted in an efficient and robust internal representation, linking retinotopic (egocentric) visual input with the geometry of the environment. While RL has long been at the core of robot navigation research, current computational theories of insect navigation are not commonly formulated within this framework, but largely as an associative learning process implemented in the insect brain, especially in the mushroom body (MB). Here we propose specific hypothetical components of the MB circuit that would enable the implementation of a certain class of relatively simple RL algorithms, capable of integrating distinct components of a navigation task, reminiscent of hierarchical RL models used in robot navigation. We discuss how current models of insect and robot navigation are exploring representations beyond classical, complete map-like representations, with spatial information being embedded in the respective latent representations to varying degrees.

Load Frequency Optimal Active Disturbance Rejection Control of Hybrid Power System

The widespread adoption of the power grid has led to increased attention to load frequency control (LFC) in power systems. The LFC strategy of multi-source hybrid power systems, including hydroelectric generators, Wind Turbine Generators (WTGs), and Photovoltaic Generators (PVGs), with thermal generators is more challenging. Existing methods for LFC tasks pose challenges in achieving satisfactory outcomes in hybrid power systems. In this paper, a novel method for the multi-source hybrid power system LFC task by using an optimal active disturbance rejection control (ADRC) strategy is proposed, which is based on the combination of the improved linear quadratic regulator (LQR) and the ADRC controller. Firstly, an established model of a hybrid power system is presented, which incorporates multiple regions and multiple sources. Secondly, utilizing the state space representation, a novel control strategy is developed by integrating improved LQR and ARDC. Finally, a series of comparative simulation experiments has been conducted using the Simulink model. Compared with the LQR with ESO, the maximum relative error of the maximum peaks of frequency deviation and tie-line exchanged power of the hybrid power system is reduced by 96% and 83%, respectively, by using the proposed strategy. The experimental results demonstrate that the strategy proposed in this paper exhibits a substantial enhancement in control performance.

So(3) ⊂ su(3) revisited

This paper reproduces the result of Elliot, namely that the irreducible finite dimensional representation of the Lie algebra su(3) of highest weight (m, n) is decomposed according to the embedding so(3) ⊂ su(3). First, a realisation (a representation in terms of vector fields) of the Lie algebra su(3) is constructed on a space of polynomials of three variables. The special polynomial basis of the representation space is given. In this basis, we find the highest weight vectors of the representation of the Lie subalgebra so(3) and in this way the representation space is decomposed to the direct sum of invariant subspaces. The process is illustrated by the example of the decomposition of the representation of highest weight (2, 2). As an additional result, the generating function of the decomposition is given.

An ecological approach to understanding transitions and tensions in complex learning contexts

The move away from transmission-based lecturing toward a more student-centred active learning approach is well evidenced in STEM higher education. However, the examination of active learning has generally remained confined to formal timetabled contexts, with assumptions made that students independently manage the transition between timetabled and non-timetabled learning. This paper introduces research findings from a mixed methods study that used an ecological approach when investigating student transitions between a formal lecture theatre and adjacent informal breakout space in a UK STEM university. Using quantitative occupancy monitoring data to analyse usage patterns of both spaces, in combination with qualitative ethnographic observations and field interviews, permitted a purposeful exploration of student engagement with transitions within and between the two learning spaces. The ecological approach aided the discovery of spatial, pedagogic and agentic transitions and tensions, which subsequently informed strategic modification of space across the institution to facilitate the adoption of active learning pedagogy.

Agglomerator++: Interpretable part-whole hierarchies and latent space representations in neural networks

Deep neural networks achieve outstanding results in a large variety of tasks, often outperforming human experts. However, a known limitation of current neural architectures is the poor accessibility in understanding and interpreting the network’s response to a given input. This is directly related to the huge number of variables and the associated non-linearities of neural models, which are often used as black boxes. This lack of transparency, particularly in crucial areas like autonomous driving, security, and healthcare, can trigger skepticism and limit trust, despite the networks’ high performance. In this work, we want to advance the interpretability in neural networks. We present Agglomerator++, a framework capable of providing a representation of part-whole hierarchies from visual cues and organizing the input distribution to match the conceptual-semantic hierarchical structure between classes. We evaluate our method on common datasets, such as SmallNORB, MNIST, FashionMNIST, CIFAR-10, and CIFAR-100, showing that our solution delivers a more interpretable model compared to other state-of-the-art approaches. Our code is available at https://mmlab-cv.github.io/Agglomeratorplusplus/.

Integration and competition between space and time in the hippocampus

Episodic memory is organized in both spatial and temporal contexts. The hippocampus is crucial for episodic memory and has been demonstrated to encode spatial and temporal information. However, how the representations of space and time interact in the hippocampal memory system is still unclear. Here, we recorded the activity of hippocampal CA1 neurons in mice in a variety of one-dimensional navigation tasks while systematically varying the speed of the animals. For all tasks, we found neurons simultaneously represented space and elapsed time. There was a negative correlation between the preferred space and lap duration, e.g., the preferred spatial position shifted more toward the origin when the lap duration became longer. A similar relationship between the preferred time and traveled distance was also observed. The results strongly suggest a competitive and integrated representation of space-time by single hippocampal neurons, which may provide the neural basis for spatiotemporal contexts.

Inclusivity in Physical and Digital Theater Environments

Today, there is a problem with the organization of inclusivity in theatrical institutions, which becomes very significant for groups of people with increased needs, when the lack of certain solutions and the inability, for one reason or another, directly affects the attendance of people with limited mobility.Purpose: The aim of this work is to explore the possibility and methods of organizing inclusivity in theatrical space using up-to-date technologies such as VR, AR, metauniverse, etc. Methodology: The analysis of modern research projects related to reorientation of design and construction to the inclusivity and well-being of the architectural environment of buildings and identification of the main criteria, tools and alternative solutions. The use of high technologies in theaters are considered using real-life projects.Research findings: The main criteria are identified for reorientation of design to architecture that consider increased needs of citizens. Focusing on existing theater projects, the possibility of using virtual and augmented reality technologies and metaverses, is determined for the theater space.

Interactions between neural representations of the social and spatial environment.

Even in our highly interconnected modern world, geographic factors play an important role in human social connections. Similarly, social relationships influence how and where we travel, and how we think about our spatial world. Here, we review the growing body of neuroscience research that is revealing multiple interactions between social and spatial processes in both humans and non-human animals. We review research on the cognitive and neural representation of spatial and social information, and highlight recent findings suggesting that underlying mechanisms might be common to both. We discuss how spatial factors can influence social behaviour, and how social concepts modify representations of space. In so doing, this review elucidates not only how neural representations of social and spatial information interact but also similarities in how the brain represents and operates on analogous information about its social and spatial surroundings.This article is part of the theme issue 'The spatial-social interface: a theoretical and empirical integration'.

Empowering sign language communication: Integrating sentiment and semantics for facial expression synthesis

Translating written sentences from oral languages to a sequence of manual and non-manual gestures plays a crucial role in building a more inclusive society for deaf and hard-of-hearing people. Facial expressions (non-manual), in particular, are responsible for encoding the grammar of the sentence to be spoken, applying punctuation, pronouns, or emphasizing signs. These non-manual gestures are closely related to the semantics of the sentence being spoken and also to the utterance of the speaker’s emotions. However, most Sign Language Production (SLP) approaches are centered on synthesizing manual gestures and do not focus on modeling the speaker’s expression. This paper introduces a new method focused in synthesizing facial expressions for sign language. Our goal is to improve sign language production by integrating sentiment information in facial expression generation. The approach leverages a sentence’s sentiment and semantic features to sample from a meaningful representation space, integrating the bias of the non-manual components into the sign language production process. To evaluate our method, we extend the Fréchet gesture distance (FGD) and propose a new metric called Fréchet Expression Distance (FED) and apply an extensive set of metrics to assess the quality of specific regions of the face. The experimental results showed that our method achieved state of the art, being superior to the competitors on How2Sign and PHOENIX14T datasets. Moreover, our architecture is based on a carefully designed graph pyramid that makes it simpler, easier to train, and capable of leveraging emotions to produce facial expressions. Our code and pretrained models will be available at: https://github.com/verlab/empowering-sign-language.

Brain structure and activity predicting cognitive maturation in adolescence.

Cognitive abilities of primates, including humans, continue to improve through adolescence 1,2. While a range of changes in brain structure and connectivity have been documented 3,4, how they affect neuronal activity that ultimately determines performance of cognitive functions remains unknown. Here, we conducted a multilevel longitudinal study of monkey adolescent neurocognitive development. The developmental trajectory of neural activity in the prefrontal cortex accounted remarkably well for working memory improvements. While complex aspects of activity changed progressively during adolescence, such as the rotation of stimulus representation in multidimensional neuronal space, which has been implicated in cognitive flexibility, even simpler attributes, such as the baseline firing rate in the period preceding a stimulus appearance had predictive power over behavior. Unexpectedly, decreases in brain volume and thickness, which are widely thought to underlie cognitive changes in humans 5 did not predict well the trajectory of neural activity or cognitive performance changes. Whole brain cortical volume in particular, exhibited an increase and reached a local maximum in late adolescence, at a time of rapid behavioral improvement. Maturation of long-distance white matter tracts linking the frontal lobe with areas of the association cortex and subcortical regions best predicted changes in neuronal activity and behavior. Our results provide evidence that optimization of neural activity depending on widely distributed circuitry effects cognitive development in adolescence.

9D Rotation Representation-SVD Fusion with Deep Learning for Unconstrained Head Pose Estimation

Abstract Accurately estimating human head pose poses a significant challenge across various application domains. To address the inherent limitations of previous approaches, this research proposes an unconstrained head pose estimation strategy. The method combines deep learning with rotation matrices, utilizing nine-dimensional vectors output by the neural network, which are projected back to rotation matrices in SO (3) space through singular value decomposition. This ensures both the smoothness and uniqueness of the rotation representation. The approach demonstrates distinct advantages in handling the rotation estimation task, particularly when the rotated representation is used as the model output. It not only avoids the discontinuity and double-coverage issues associated with prior methods but also enhances the stability of the representation in high-dimensional space, thereby improving the learning process. Additionally, the geodesic loss function is incorporated to train the network. The proposed strategy surpasses previous state-of-the-art methods, as evidenced by experiments conducted on the AFLW2000 and BIWI datasets.

Creolization and Gender: Island Imaginings in Ananda Devi's Pagli and Its Sequel

Abstract: This essay opens the study of "Archipelagic Asias" to the southwest Indian Ocean archipelagos to explore representations of Indic cultures in the literature of the creolized islands of Mauritius. By combining archipelagic and feminist epistemologies, I examine one of the most successful novels of Ananda Devi, Pagli (2001), in which an Indo-Mauritian woman has an affair with a Creole fisherman, and its little-known short story sequel, "Agalega" (2021). Published in Maudrigosa!, a volume celebrating the Mauritian archipelago, the short story denounces the construction of an Indian military base on the Mauritius Outer Island of Agalega. I argue that literary representations of Mauritius's geographic space form different island imaginings that express Mauritius's affective relation to its creolized culture and the impact it has on women's corporeal and sexual freedom.

Path signatures for diversity in probabilistic trajectory optimisation

Motion planning can be cast as a trajectory optimisation problem where a cost is minimised as a function of the trajectory being generated. In complex environments with several obstacles and complicated geometry, this optimisation problem is usually difficult to solve and prone to local minima. However, recent advancements in computing hardware allow for parallel trajectory optimisation where multiple solutions are obtained simultaneously, each initialised from a different starting point. Unfortunately, without a strategy preventing two solutions to collapse on each other, naive parallel optimisation can suffer from mode collapse diminishing the efficiency of the approach and the likelihood of finding a global solution. In this paper, we leverage on recent advances in the theory of rough paths to devise an algorithm for parallel trajectory optimisation that promotes diversity over the range of solutions, therefore avoiding mode collapses and achieving better global properties. Our approach builds on path signatures and Hilbert space representations of trajectories and connects parallel variational inference for trajectory estimation with diversity-promoting kernels. We empirically demonstrate that this strategy achieves lower average costs than competing alternatives on a range of problems, from 2D navigation to robotic manipulators operating in cluttered environments.

SG-Fusion: A swin-transformer and graph convolution-based multi-modal deep neural network for glioma prognosis

The integration of morphological attributes extracted from histopathological images and genomic data holds significant importance in advancing tumor diagnosis, prognosis, and grading. Histopathological images are acquired through microscopic examination of tissue slices, providing valuable insights into cellular structures and pathological features. On the other hand, genomic data provides information about tumor gene expression and functionality. The fusion of these two distinct data types is crucial for gaining a more comprehensive understanding of tumor characteristics and progression. In the past, many studies relied on single-modal approaches for tumor diagnosis. However, these approaches had limitations as they were unable to fully harness the information from multiple data sources. To address these limitations, researchers have turned to multi-modal methods that concurrently leverage both histopathological images and genomic data. These methods better capture the multifaceted nature of tumors and enhance diagnostic accuracy. Nonetheless, existing multi-modal methods have, to some extent, oversimplified the extraction processes for both modalities and the fusion process. In this study, we presented a dual-branch neural network, namely SG-Fusion. Specifically, for the histopathological modality, we utilize the Swin-Transformer structure to capture both local and global features and incorporate contrastive learning to encourage the model to discern commonalities and differences in the representation space. For the genomic modality, we developed a graph convolutional network based on gene functional and expression level similarities. Additionally, our model integrates a cross-attention module to enhance information interaction and employs divergence-based regularization to enhance the model’s generalization performance. Validation conducted on glioma datasets from the Cancer Genome Atlas unequivocally demonstrates that our SG-Fusion model outperforms both single-modal methods and existing multi-modal approaches in both survival analysis and tumor grading.