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•Our ECViT-GAN is an innovative and effective framework for synthesizing functional connectivity from 3D gray matter data.•Our approach accurately predicts brain function based on structural gray matter brain scans with amazing precision.•Our model effectively established a connection between structural and functional brain imaging data through the utilization of generative AI.•We ascertain the crucial anatomical brain areas that have considerable relevance to the functional aspects of schizophrenia. Brain disorders are often associated with changes in brain structure and function, where functional changes may be due to underlying structural variations. Gray matter (GM) volume segmentation from 3D structural MRI offers vital structural information for brain disorders like schizophrenia, as it encompasses essential brain tissues such as neuronal cell bodies, dendrites, and synapses, which are crucial for neural signal processing and transmission; changes in GM volume can thus indicate alterations in these tissues, reflecting underlying pathological conditions. In addition, the use of the ICA algorithm to transform high-dimensional fMRI data into functional network connectivity (FNC) matrices serves as an effective carrier of functional information. In our study, we introduce a new generative deep learning architecture, the conditional efficient vision transformer generative adversarial network (cEViT-GAN), which adeptly generates FNC matrices conditioned on GM to facilitate the exploration of potential connections between brain structure and function. We developed a new, lightweight self-attention mechanism for our ViT-based generator, enhancing the generation of refined attention maps critical for identifying structural biomarkers based on GM. Our approach not only generates high quality FNC matrices with a Pearson correlation of 0.74 compared to real FNC data, but also uses attention map technology to identify potential biomarkers in GM structure that could lead to functional abnormalities in schizophrenia patients. Visualization experiments within our study have highlighted these structural biomarkers, including the medial prefrontal cortex (mPFC), dorsolateral prefrontal cortex (DL-PFC), and cerebellum. In addition, through cross-domain analysis comparing generated and real FNC matrices, we have identified functional connections with the highest correlations to structural information, further validating the structure-function connections. This comprehensive analysis helps to understand the intricate relationship between brain structure and its functional manifestations, providing a more refined insight into the neurobiological research of schizophrenia.

Multimodal neuroimaging is an emerging field that leverages multiple sources of information to diagnose specific brain disorders, especially when deep learning‐based AI algorithms are applied. The successful combination of different brain imaging modalities using deep learning remains a challenging yet crucial research topic. The integration of structural and functional modalities is particularly important for the diagnosis of various brain disorders, where structural information plays a crucial role in diseases such as Alzheimer's, while functional imaging is more critical for disorders such as schizophrenia. However, the combination of functional and structural imaging modalities can provide a more comprehensive diagnosis. In this work, we present MultiViT, a novel diagnostic deep learning model that utilizes vision transformers and cross‐attention mechanisms to effectively fuse information from 3D gray matter maps derived from structural MRI with functional network connectivity matrices obtained from functional MRI using the ICA algorithm. MultiViT achieves an AUC of 0.833, outperforming both our unimodal and multimodal baselines, enabling more accurate classification and diagnosis of schizophrenia. In addition, using vision transformer's unique attentional maps in combination with cross‐attentional mechanisms and brain function information, we identify critical brain regions in 3D gray matter space associated with the characteristics of schizophrenia. Our research not only significantly improves the accuracy of AI‐based automated imaging diagnostics for schizophrenia, but also pioneers a rational and advanced data fusion approach by replacing complex, high‐dimensional fMRI information with functional network connectivity, integrating it with representative structural data from 3D gray matter images, and further providing interpretative biomarker localization in a 3D structural space. The MultiViT model combines structural and functional neuroimaging data for the prediction of schizophrenia and integrates vision transformers with cross‐attention layers in order to preserve mutual information. The pipeline generates highly interpretable cross‐attention‐based brain saliency maps and emphasizes functional network connectivity patterns related to the disorder.

Deep learning has become a prominent computational modeling tool in the areas of computer vision and image processing in recent years. This research comprehensively analyzes the different deep-learning methods used for image-to-image translation and reconstruction in the natural and medical imaging domains. We examine the famous deep learning frameworks, such as convolutional neural networks and generative adversarial networks, and their variants, delving into the fundamental principles and difficulties of each. In the field of natural computer vision, we investigate the development and extension of various deep-learning generative models. In comparison, we investigate the possible applications of deep learning to generative medical imaging problems, including medical image translation, MRI reconstruction, and multi-contrast MRI synthesis. This thorough review provides scholars and practitioners in the areas of generative computer vision and medical imaging with useful insights for summarizing past works and getting insight into future research paths.

Existing RNA 3D structure quality assessment (QA) methods rely on local geometric descriptors or statistical potentials that evaluate atomic-level contacts but are blind to global topological coherence. This creates a critical failure mode-structures that are \"locally correct but globally wrong\"-where well-formed local helices mask misplaced domains and incorrect overall packing. We introduce SpecRNA-QA, a lightweight RNA QA method based on multiscale graph-Laplacian features of inter-nucleotide contact networks. In CASP16 leave-one-out cross-validation, it achieves median per-target Spearman (target-clustered bootstrap 95% CI [0.64,0.73]) versus 0.47 for an internal geometry baseline-a +0.22 gap that is significant at = 1.2 × 10 (one-sided Wilcoxon signed-rank) and reflects a per-target win rate of 93%. The gain is concentrated on large, multi-domain RNAs, where global coherence is poorly captured by local descriptors. In a contextual comparison with established statistical potentials, local energy-based scores remain strongest on compact RNAs, while SpecRNA-QA yields the strongest signal we observed on targets longer than 200 nt; within the single-threaded runtime budget used here, the strongest local-energy comparator, rsRNASP, timed out on 22 of 26 large targets, and we report an explicit paired head-to-head on the four commonly scored targets in Section 4.2. A training-free heuristic variant further shows that the spectral prior carries intrinsic quality information even in the absence of labeled QA data.

Partial observation is a pervasive obstacle in nonequilibrium physics: coarse graining may absorb hidden forcing into an apparently equilibrium-like reduced description, so a driven system can look reversible through the only variables one can measure. For scalar Gaussian observables of linear stochastic systems, no time-irreversibility statistic can detect the underlying drive. The Lucente--Crisanti ceiling constrains what one channel carries; what two channels carry is a different question, with a sharp closed-form answer. Two simultaneously observed channels retain an off-diagonal cross-spectral sector inaccessible to any scalar reduction; under channel-separable multiplicative structure the observed-channel response factors cancel identically, leaving a closed-form cross-spectral witness controlled only by the hidden spectrum, the loadings, and the innovation scales, strictly positive at every nonzero cross-coupling including at exact timescale coalescence where every scalar reduction is blind. Within general CSM this certifies shared hidden-sector drive; under the additional one-way coupling assumption the witness identifies the total entropy production rate at leading order with a square-root scaling.

We propose the Financial Connectome, a new scientific discipline that models financial markets through the lens of brain functional architecture. Inspired by the foundational work of group independent component analysis (groupICA) in neuroscience, we reimagine markets not as collections of assets, but as high-dimensional dynamic systems composed of latent market modules. Treating stocks as functional nodes and their co-fluctuations as expressions of collective cognition, we introduce dynamic Market Network Connectivity (dMNC), the financial analogue of dynamic functional connectivity (dFNC). This biologically inspired framework reveals structurally persistent market subnetworks, captures regime shifts, and uncovers systemic early warning signals all without reliance on predictive labels. Our results suggest that markets, like brains, exhibit modular, self-organizing, and temporally evolving architectures. This work inaugurates the field of financial connectomics, a principled synthesis of systems neuroscience and quantitative finance aimed at uncovering the hidden logic of complex economies.

Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive. In this work, we show that scaling laws can be formally explained as redundancy laws. Using kernel regression, we show that a polynomial tail in the data covariance spectrum yields an excess risk power law with exponent alpha = 2s / (2s + 1/beta), where beta controls the spectral tail and 1/beta measures redundancy. This reveals that the learning curve's slope is not universal but depends on data redundancy, with steeper spectra accelerating returns to scale. We establish the law's universality across boundedly invertible transformations, multi-modal mixtures, finite-width approximations, and Transformer architectures in both linearized (NTK) and feature-learning regimes. This work delivers the first rigorous mathematical explanation of scaling laws as finite-sample redundancy laws, unifying empirical observations with theoretical foundations.

We address the attribution problem for apparent slow collective dynamics: is the observed persistence intrinsic, or inherited from a persistent driver? For the leading eigenvalue fraction \\(_1=_/N\\) of S\\&P 500 60-day rolling correlation matrices (\\(237\\) stocks, 2004--2023), a VIX-coupled Ornstein--Uhlenbeck model reduces the effective relaxation time from \\(298\\) to \\(61\\) trading days and improves the fit over bare mean reversion by \\(\\)BIC\\(=109\\). On the decomposition sample, an informational residual of \\((VIX)\\) alone retains most of that gain (\\(\\)BIC\\(=78.6\\)), whereas a mechanical VIX proxy alone does not improve the fit. Autocorrelation-matched placebo fields fail (\\(\\)BIC\\(_=2.7\\)), disjoint weekly reconstructions still favor the field-coupled model (\\(\\)BIC\\(=140\\)--\\(151\\)), and six anchored chronological holdouts preserve the out-of-sample advantage. Quiet-regime and field-stripped residual autocorrelation controls show the same collapse of persistence. Stronger hidden-variable extensions remain only partially supported. Within the tested stochastic class, conditioning on the observed VIX proxy absorbs most of the apparent slow dynamics.

Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive. In this work, we show that scaling laws can be formally explained as redundancy laws. Using kernel regression, we show that a polynomial tail in the data covariance spectrum yields an excess risk power law with exponent alpha = 2s / (2s + 1/beta), where beta controls the spectral tail and 1/beta measures redundancy. This reveals that the learning curve's slope is not universal but depends on data redundancy, with steeper spectra accelerating returns to scale. We establish the law's universality across boundedly invertible transformations, multi-modal mixtures, finite-width approximations, and Transformer architectures in both linearized (NTK) and feature-learning regimes. This work delivers the first rigorous mathematical explanation of scaling laws as finite-sample redundancy laws, unifying empirical observations with theoretical foundations.

We propose the Financial Connectome, a new scientific discipline that models financial markets through the lens of brain functional architecture. Inspired by the foundational work of group independent component analysis (groupICA) in neuroscience, we reimagine markets not as collections of assets, but as high-dimensional dynamic systems composed of latent market modules. Treating stocks as functional nodes and their co-fluctuations as expressions of collective cognition, we introduce dynamic Market Network Connectivity (dMNC), the financial analogue of dynamic functional connectivity (dFNC). This biologically inspired framework reveals structurally persistent market subnetworks, captures regime shifts, and uncovers systemic early warning signals all without reliance on predictive labels. Our results suggest that markets, like brains, exhibit modular, self-organizing, and temporally evolving architectures. This work inaugurates the field of financial connectomics, a principled synthesis of systems neuroscience and quantitative finance aimed at uncovering the hidden logic of complex economies.