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Classical Euclidean geometry effectively characterizes regular-shaped structures but often falls short when attempting to describe the intricate, irregular-shaped objects, commonly found in biological systems. Multifractal spectrum, a hump function, captures the variability of scaling behavior across an object and provides an alternative approach for analyzing complex biological structures. It is increasingly being used to link structural disorganization of biological tissues to the risk for chronic diseases. Therefore, enhancing the accuracy of existing methods for multifractal analysis may further the understanding of diseases. The box counting method which is often used for computing the multifractal spectrum requires partitioning the object in order to compute the multifractal spectrum. This study proposes a polar partitioning method for the multifractal analysis of complex structures embedded in two-dimensional (2D) space. Its performance is compared with existing methods, including radial and rectangular partitioning. The accuracy of multifractal spectrum computed by polar, radial and rectangular partitioning methods was evaluated using theoretically-derived multifractal structures for which the analytical multifractal spectra exist. The results from this study demonstrate that the polar partitioning method greatly outperforms the rectangular and radial partitioning method when analyzing objects with circular support. The radial partitioning method performs well only when analyzing objects whose scaling rate vary solely along the radial direction. This study identifies the most suitable use cases for each partitioning method to minimize errors in the computations. Instead of the rectangular and radial partitioning methods, the polar partitioning method should be used for computing the multifractal spectrum for complex objects with circular support. 

Integer-order calculus fails to capture the long-range dependence (LRD) and memory effects found in many complex systems. Fractional calculus addresses these gaps through fractional-order integrals and derivatives, but fractional-order dynamical systems pose substantial challenges in system identification and optimal control tasks. In this paper, we theoretically derive the optimal control via linear quadratic regulator (LQR) for fractional-order linear time-invariant (FOLTI) systems and develop an end-to-end deep learning framework based on this theoretical foundation. Our approach establishes a rigorous mathematical model, derives analytical solutions, and incorporates deep learning to achieve data-driven optimal control of FOLTI systems. Our key contributions include: (i) proposing a novel method for system identification and optimal control strategy in FOLTI systems, (ii) developing the first end-to-end data-driven learning framework, Fractional-Order Learning for Optimal Control (FOLOC), that learns control policies from observed trajectories, and (iii) deriving theoretical bounds on the sample complexity for learning accurate control policies under fractional-order dynamics. Experimental results indicate that our method accurately approximates fractional-order system behaviors without relying on Gaussian noise assumptions, pointing to promising avenues for advanced optimal control. 

Being intermediate in scale between molecules and colloids, nanoparticles combine characteristics of both. The structure of their self-assembled states combining order and disorder is difficult to quantify using traditional symmetry-based descriptors. Here, we applied graph theory (GT) to analyze assemblies of 400 to 10,000 nanoparticles across three material systems. We show that GT metrics, augmented Forman-Ricci curvature (AFRC) and Ollivier-Ricci curvature (ORC), capture local and global structural transitions from small clusters to extended networks. AFRC reflects the energetic state of the assembly, whereas ORC quantifies structural complexity and reveals a “Goldilocks” regime that maximizes plasmonic response. The generality of this approach is demonstrated for gold nanocubes, gold nanoprisms, and indium tin oxide nanospheres, providing a unified framework for describing and optimizing complex nanoparticle assemblies. 

Today’s generative models can synthesize magnetic resonance images (MRIs) of the brain at specific ages. However, such models can neither map the aging process longitudinally within subjects, nor accommodate its variability across subjects. Such approaches also cannot predict anatomic features of aging in ways that can be validated retrospectively or trusted prospectively. We introduce a three-dimensional hybrid ControlNet + diffusion model that uses the baseline T1-weighted MRIs of healthy adults to predict individual neuroanatomic aging trajectories, as reflected by follow-up MRIs. The approach captures individual anatomical changes with an average predicted voxelwise intensity error of 15% and structural similarity index of 93%. Unlike methods relying on qualitative validation, our approach quantifies the fidelity of prospective MRI synthesis using FreeSurfer volumetrics. Because brain atrophy reflects risk for Alzheimer’s disease (AD), our model’s ability to generate individual-specific prospective MRIs suggests its clinical potential to assist AD risk estimation. 

This study investigated the generalizability of Arabidopsis thaliana immune responses across diverse pathogens, including Botrytis cinerea, Sclerotinia sclerotiorum, and Pseudomonas syringae, using a data-driven, machine learning approach. Machine learning models were trained to predict disease development from early transcriptional responses. Feature selection techniques based on network science and topology were used to train models employing only a fraction of the transcriptome. Machine learning models trained on one pathosystem where then validated by predicting disease development in new pathosystems. The identified feature selection gene sets were enriched for pathways related to biotic, abiotic, and stress responses, though the specific genes involved differed between feature sets. This suggests common immune responses to diverse pathogens that operate via different gene sets.The study demonstrates that machine learning can uncover both established and novel components of the plant's immune response, offering insights into disease resistance mechanisms. These predictive models highlight the potential to advance our understanding of multigenic outcomes in plant immunity and can be further refined for applications in disease prediction. 

Computation graphs are Directed Acyclic Graphs (DAGs) where the nodes correspond to mathematical operations and are used widely as abstractions in optimizations of neural networks. The device placement problem aims to identify optimal allocations of those nodes to a set of (potentially heterogeneous) devices. Existing approaches rely on two types of architectures known as grouper-placer and encoder-placer, respectively. In this work, we bridge the gap between encoder-placer and grouper-placer techniques and propose a novel framework for the task of device placement, relying on smaller computation graphs extracted from the OpenVINO toolkit. The framework consists of five steps, including graph coarsening, node representation learning and policy optimization. It facilitates end-to-end training and takes into account the DAG nature of the computation graphs. We also propose a model variant, inspired by graph parsing networks and complex network analysis, enabling graph representation learning and jointed, personalized graph partitioning, using an unspecified number of groups. To train the entire framework, we use reinforcement learning using the execution time of the placement as a reward. We demonstrate the flexibility and effectiveness of our approach through multiple experiments with three benchmark models, namely Inception-V3, ResNet, and BERT. The robustness of the proposed framework is also highlighted through an ablation study. The suggested placements improve the inference speed for the benchmark models by up to over CPU execution and by up to compared to other commonly used baselines. 

Malware represents a significant security concern in today’s digital landscape, as it can destroy or disable operating systems, steal sensitive user information, and occupy valuable disk space. However, current malware detection methods, such as static-based and dynamic-based approaches, struggle to identify newly developed ("zero-day") malware and are limited by customized virtual machine (VM) environments. To overcome these limitations, we propose a novel malware detection approach that leverages deep learning, mathematical techniques, and network science. Our approach focuses on static and dynamic analysis and utilizes the Low-Level Virtual Machine (LLVM) to profile applications within a complex network. The generated network topologies are input into the GraphSAGE architecture to efficiently distinguish between benign and malicious software applications, with the operation names denoted as node features. Importantly, the GraphSAGE models analyze the network’s topological geometry to make predictions, enabling them to detect state-of-the-art malware and prevent potential damage during execution in a VM. To evaluate our approach, we conduct a study on a dataset comprising source code from 24,376 applications, specifically written in C/C++, sourced directly from widely-recognized malware and various types of benign software. The results show a high detection performance with an Area Under the Receiver Operating Characteristic Curve (AUROC) of 99.85%. Our approach marks a substantial improvement in malware detection, providing a notably more accurate and efficient solution when compared to current state-of-the-art malware detection methods. The code is released at https://github.com/HantangZhang/MGN. 

Phase transitions are typically quantified using order parameters, such as crystal lattice distances and radial distribution functions, which can identify subtle changes in crystalline materials or high‐contrast phases with large structural differences. However, the identification of phases with high complexity, multiscale organization and of complex patterns during the structural fluctuations preceding phase transitions, which are essential for understanding the system pathways between phases, is challenging for those traditional analyses. Here, it is shown that for two model systems— thermotropic liquid crystals and a lyotropic water/surfactant mixtures—graph theoretical (GT) descriptors can successfully identify complex phases combining molecular and nanoscale levels of organization that are hard to characterize with traditional methodologies. Furthermore, the GT descriptors also reveal the pathways between the different phases. Specifically, centrality parameters and node‐based fractal dimension quantify the system behavior preceding the transitions, capturing fluctuation‐induced breakup of aggregates and their long‐range cooperative interactions. GT parameterization can be generalized for a wide range of chemical systems and be instrumental for the growth mechanisms of complex nanostructures.