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1. The small-world effect for interferometer networks

   https://doi.org/10.1088/2632-072x/ad4c45  

   Krawciw, Benjamin; Carr, Lincoln D; Diniz_Behn, Cecilia (May 2024, Journal of Physics: Complexity)

   Abstract Complex network theory has focused on properties of networks with real-valued edge weights. However, in signal transfer networks, such as those representing the transfer of light across an interferometer, complex-valued edge weights are needed to represent the manipulation of the signal in both magnitude and phase. These complex-valued edge weights introduce interference into the signal transfer, but it is unknown how such interference affects network properties such as small-worldness. To address this gap, we have introduced a small-world interferometer network model with complex-valued edge weights and generalized existing network measures to define theinterferometric clustering coefficient, theapparent path length, and theinterferometric small-world coefficient. Using high-performance computing resources, we generated a large set of small-world interferometers over a wide range of parameters in system size, nearest-neighbor count, and edge-weight phase and computed their interferometric network measures. We found that the interferometric small-world coefficient depends significantly on the amount of phase on complex-valued edge weights: for small edge-weight phases, constructive interference led to a higher interferometric small-world coefficient; while larger edge-weight phases induced destructive interference which led to a lower interferometric small-world coefficient. Thus, for the small-world interferometer model, interferometric measures are necessary to capture the effect of interference on signal transfer. This model is an example of the type of problem that necessitates interferometric measures, and applies to any wave-based network including quantum networks. 

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2. Latent Weight-Based Pruning for Small Binary Neural Networks

   https://doi.org/10.1145/3566097.3567873  

   Chen, Tianen; Anderson, Noah; Kim, Younghyun (January 2023, ASPDAC '23: Proceedings of the 28th Asia and South Pacific Design Automation Conference)

   Binary neural networks (BNNs) substitute complex arithmetic operations with simple bit-wise operations. The binarized weights and activations in BNNs can drastically reduce memory requirement and energy consumption, making it attractive for edge ML applications with limited resources. However, the severe memory capacity and energy constraints of low-power edge devices call for further reduction of BNN models beyond binarization. Weight pruning is a proven solution for reducing the size of many neural network (NN) models, but the binary nature of BNN weights make it difficult to identify insignificant weights to remove. In this paper, we present a pruning method based on latent weight with layer-level pruning sensitivity analysis which reduces the over-parameterization of BNNs, allowing for accuracy gains while drastically reducing the model size. Our method advocates for a heuristics that distinguishes weights by their latent weights, a real-valued vector used to compute the pseudogradient during backpropagation. It is tested using three different convolutional NNs on the MNIST, CIFAR-10, and Imagenette datasets with results indicating a 33%--46% reduction in operation count, with no accuracy loss, improving upon previous works in accuracy, model size, and total operation count. 

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3. Controlling the Multifractal Generating Measures of Complex Networks

   https://doi.org/10.1038/s41598-020-62380-6  

   Yang, Ruochen; Bogdan, Paul (March 2020, Scientific reports)

   Mathematical modelling of real complex networks aims to characterize their architecture and decipher their underlying principles. Self-repeating patterns and multifractality exist in many real-world complex systems such as brain, genetic, geoscience, and social networks. To better comprehend the multifractal behavior in the real networks, we propose the weighted multifractal graph model to characterize the spatiotemporal complexity and heterogeneity encoded in the interaction weights. We provide analytical tools to verify the multifractal properties of the proposed model. By varying the parameters in the initial unit square, the model can reproduce a diverse range of multifractal spectrums with different degrees of symmetry, locations, support and shapes. We estimate and investigate the weighted multifractal graph model corresponding to two real-world complex systems, namely (i) the chromosome interactions of yeast cells in quiescence and in exponential growth, and (ii) the brain networks of cognitively healthy people and patients exhibiting late mild cognitive impairment leading to Alzheimer disease. The analysis of recovered models show that the proposed random graph model provides a novel way to understand the self-similar structure of complex networks and to discriminate different network structures. Additionally, by mapping real complex networks onto multifractal generating measures, it allows us to develop new network design and control strategies, such as the minimal control of multifractal measures of real systems under different functioning conditions or states. 

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4. Controlling the Multifractal Generating Measures of Complex Networks

   https://doi.org/10.1038/s41598-020-62380-6  

   Yang, Ruochen Yang; Bogdan, Paul (March 2020, Scientific reports)

   Mathematical modelling of real complex networks aims to characterize their architecture and decipher their underlying principles. Self-repeating patterns and multifractality exist in many real-world complex systems such as brain, genetic, geoscience, and social networks. To better comprehend the multifractal behavior in the real networks, we propose the weighted multifractal graph model to characterize the spatiotemporal complexity and heterogeneity encoded in the interaction weights. We provide analytical tools to verify the multifractal properties of the proposed model. By varying the parameters in the initial unit square, the model can reproduce a diverse range of multifractal spectrums with different degrees of symmetry, locations, support and shapes. We estimate and investigate the weighted multifractal graph model corresponding to two real-world complex systems, namely (i) the chromosome interactions of yeast cells in quiescence and in exponential growth, and (ii) the brain networks of cognitively healthy people and patients exhibiting late mild cognitive impairment leading to Alzheimer disease. The analysis of recovered models show that the proposed random graph model provides a novel way to understand the self-similar structure of complex networks and to discriminate different network structures. Additionally, by mapping real complex networks onto multifractal generating measures, it allows us to develop new network design and control strategies, such as the minimal control of multifractal measures of real systems under different functioning conditions or states. 

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5. Collective Noise Filtering in Complex Networks

   Zhao, Tingyu; Kovács, István A (January 2026, arXivorg)

   Complex networks are powerful representations of complex systems across scales and domains, and the field is experiencing unprecedented growth in data availability. However, real-world network data often suffer from noise, biases, and missing data in the edge weights, which undermine the reliability of downstream network analyses. Standard noise filtering approaches, whether treating individual edges one-by-one or assuming a uniform global noise level, are suboptimal, because in reality both signal and noise can be heterogeneous and correlated across multiple edges. As a solution, we introduce the Network Wiener Filter, a principled method for collective edge-level noise filtering that leverages both network topology and noise characteristics, to reduce error in the observed edge weights and to infer missing edge weights. We demonstrate the broad practical efficacy of the Network Wiener Filter in two distinct settings, the genetic interaction network of the yeast S. cerevisiae and the Enron Corpus email network, noting compelling evidence of successful noise suppression in both applications. With the Network Wiener Filter, we advocate for a shift toward error-aware network science, one that embraces data imperfection as an inherent feature and learns to navigate it effectively. 

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