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Recent years have witnessed an emerging trend in neuromorphic computing that centers around the use of brain connectomics as a blueprint for artificial neural networks. Connectomics-based neuromorphic computing has primarily focused on embedding human brain large-scale structural connectomes (SCs), as estimated from diffusion Magnetic Resonance Imaging (dMRI) modality, to echo-state networks (ESNs). A critical step in ESN embedding requires pre-determined read-in and read-out layers constructed by the induced subgraphs of the embedded reservoir. As \textit{a priori} set of functional sub-circuits are derived from functional MRI (fMRI) modality, it is unknown, till this point, whether the embedding of fMRI-induced sub-circuits/networks onto SCs is well justified from the neuro-physiological perspective and ESN performance across a variety of tasks. This paper proposes a pipeline to implement and evaluate ESNs with various embedded topologies and processing/memorization tasks. To this end, we showed that different performance optimums highly depend on the neuro-physiological characteristics of these pre-determined fMRI-induced sub-circuits. In general, fMRI-induced sub-circuit-embedded ESN outperforms simple bipartite and various null models with feed-forward properties commonly seen in MLP for different tasks and reservoir criticality conditions. We provided a thorough analysis of the topological properties of pre-determined fMRI-induced sub-circuits and highlighted their graph-theoretical properties that play significant roles in determining ESN performance., Comment: 10 pages, 12 figures

Predicting phenotypes with complex genetic bases based on a small, interpretable set of variant features remains a challenging task. Conventionally, data-driven approaches are utilized for this task, yet the high dimensional nature of genotype data makes the analysis and prediction difficult. Motivated by the extensive knowledge encoded in pre-trained LLMs and their success in processing complex biomedical concepts, we set to examine the ability of LLMs in feature selection and engineering for tabular genotype data, with a novel knowledge-driven framework. We develop FREEFORM, Free-flow Reasoning and Ensembling for Enhanced Feature Output and Robust Modeling, designed with chain-of-thought and ensembling principles, to select and engineer features with the intrinsic knowledge of LLMs. Evaluated on two distinct genotype-phenotype datasets, genetic ancestry and hereditary hearing loss, we find this framework outperforms several data-driven methods, particularly on low-shot regimes. FREEFORM is available as open-source framework at GitHub: https://github.com/PennShenLab/FREEFORM.

Recently, there has been a revived interest in system neuroscience causation models due to their unique capability to unravel complex relationships in multi-scale brain networks. In this paper, our goal is to verify the feasibility and effectiveness of using a causality-based approach for fMRI fingerprinting. Specifically, we propose an innovative method that utilizes the causal dynamics activities of the brain to identify the unique cognitive patterns of individuals (e.g., subject fingerprint) and fMRI tasks (e.g., task fingerprint). The key novelty of our approach stems from the development of a two-timescale linear state-space model to extract 'spatio-temporal' (aka causal) signatures from an individual's fMRI time series data. To the best of our knowledge, we pioneer and subsequently quantify, in this paper, the concept of 'causal fingerprint.' Our method is well-separated from other fingerprint studies as we quantify fingerprints from a cause-and-effect perspective, which are then incorporated with a modal decomposition and projection method to perform subject identification and a GNN-based (Graph Neural Network) model to perform task identification. Finally, we show that the experimental results and comparisons with non-causality-based methods demonstrate the effectiveness of the proposed methods. We visualize the obtained causal signatures and discuss their biological relevance in light of the existing understanding of brain functionalities. Collectively, our work paves the way for further studies on causal fingerprints with potential applications in both healthy controls and neurodegenerative diseases.

Higher-order properties of functional magnetic resonance imaging (fMRI) induced connectivity have been shown to unravel many exclusive topological and dynamical insights beyond pairwise interactions. Nonetheless, whether these fMRI-induced higher-order properties play a role in disentangling other neuroimaging modalities' insights remains largely unexplored and poorly understood. In this work, by analyzing fMRI data from the Human Connectome Project Young Adult dataset using persistent homology, we discovered that the volume-optimal persistence homological scaffolds of fMRI-based functional connectomes exhibited conservative topological reconfigurations from the resting state to attentional task-positive state. Specifically, while reflecting the extent to which each cortical region contributed to functional cycles following different cognitive demands, these reconfigurations were constrained such that the spatial distribution of cavities in the connectome is relatively conserved. Most importantly, such level of contributions covaried with powers of aperiodic activities mostly within the theta-alpha (4-12 Hz) band measured by magnetoencephalography (MEG). This comprehensive result suggests that fMRI-induced hemodynamics and MEG theta-alpha aperiodic activities are governed by the same functional constraints specific to each cortical morpho-structure. Methodologically, our work paves the way toward an innovative computing paradigm in multimodal neuroimaging topological learning., Comment: The code for our analyses is provided in https://github.com/ngcaonghi/scaffold_noise

Prompt learning methods are gaining increasing attention due to their ability to customize large vision-language models to new domains using pre-trained contextual knowledge and minimal training data. However, existing works typically rely on optimizing unified prompt inputs, often struggling with fine-grained classification tasks due to insufficient discriminative attributes. To tackle this, we consider a new framework based on a dual context of both domain-shared and class-specific contexts, where the latter is generated by Large Language Models (LLMs) such as GPTs. Such dual prompt methods enhance the model's feature representation by joining implicit and explicit factors encoded in LLM knowledge. Moreover, we formulate the Unbalanced Optimal Transport (UOT) theory to quantify the relationships between constructed prompts and visual tokens. Through partial matching, UOT can properly align discrete sets of visual tokens and prompt embeddings under different mass distributions, which is particularly valuable for handling irrelevant or noisy elements, ensuring that the preservation of mass does not restrict transport solutions. Furthermore, UOT's characteristics integrate seamlessly with image augmentation, expanding the training sample pool while maintaining a reasonable distance between perturbed images and prompt inputs. Extensive experiments across few-shot classification and adapter settings substantiate the superiority of our model over current state-of-the-art baselines., Comment: Version 1

In systems and network neuroscience, many common practices in brain connectomic analysis are often not properly scrutinized. One such practice is mapping a predetermined set of sub-circuits, like functional networks (FNs), onto subjects' functional connectomes (FCs) without adequately assessing the information-theoretic appropriateness of the partition. Another practice that goes unchallenged is thresholding weighted FCs to remove spurious connections without justifying the chosen threshold. This paper leverages recent theoretical advances in Stochastic Block Models (SBMs) to formally define and quantify the information-theoretic fitness (e.g., prominence) of a predetermined set of FNs when mapped to individual FCs under different fMRI task conditions. Our framework allows for evaluating any combination of FC granularity, FN partition, and thresholding strategy, thereby optimizing these choices to preserve important topological features of the human brain connectomes. By applying to the Human Connectome Project with Schaefer parcellations at multiple levels of granularity, the framework showed that the common thresholding value of 0.25 was indeed information-theoretically valid for group-average FCs despite its previous lack of justification. Our results pave the way for the proper use of FNs and thresholding methods and provide insights for future research in individualized parcellations.

In recent years, a study by environmental organizations in the world and Vietnam shows that weather change is quite complex. global warming has become a serious problem in the modern world, which is a concern for scientists. last century, it was difficult to forecast the weather due to missing weather monitoring stations and technological limitations. this made it hard to collect data for building predictive models to make accurate simulations. in Vietnam, research on weather forecast models is a recent development, having only begun around 2000. along with advancements in computer science, mathematical models are being built and applied with machine learning techniques to create more accurate and reliable predictive models. this article will summarize the research and solutions for applying recurrent neural networks to forecast urban temperatures., Comment: 6 pages

Nowadays, engineers need to tackle many unprecedented challenges that are often complex, and, most importantly, cannot be exhaustively compartmentalized into a single engineering discipline. In other words, most engineering problems need to be solved from a multidisciplinary approach. However, conventional engineering programs usually adopt pedagogical approaches specifically tailored to traditional, niched engineering disciplines, which become increasingly deviated from the industry needs as those programs are typically designed and taught by instructors with highly specialized engineering training and credentials. To reduce the gap, more multidisciplinary engineering programs emerge by systematically stretching across all engineering fibers, and challenge the sub-optimal traditional pedagogy crowded in engineering classrooms. To further advance future-oriented pedagogy, in this work, we hypothesized neuro-induced linkages between how cognitively different learners are and how the linkages would affect learners in the knowledge acquisition process. We situate the neuro-induced linkages in the context of multidisciplinary engineering education and propose possible pedagogical approaches to actualize the implications of this conceptual framework. Our study, based on the innovative concept of brain fingerprint, would serve as a pioneer model to theorize key components of learner-centered multidisciplinary engineering pedagogy which centers on the key question: how do we motivate engineering students of different backgrounds from a neuro-inspired perspective?, Comment: 10 pages, 2 figures

Recent advancements in large language models (LLMs) have achieved promising performances across various applications. Nonetheless, the ongoing challenge of integrating long-tail knowledge continues to impede the seamless adoption of LLMs in specialized domains. In this work, we introduce DALK, a.k.a. Dynamic Co-Augmentation of LLMs and KG, to address this limitation and demonstrate its ability on studying Alzheimer's Disease (AD), a specialized sub-field in biomedicine and a global health priority. With a synergized framework of LLM and KG mutually enhancing each other, we first leverage LLM to construct an evolving AD-specific knowledge graph (KG) sourced from AD-related scientific literature, and then we utilize a coarse-to-fine sampling method with a novel self-aware knowledge retrieval approach to select appropriate knowledge from the KG to augment LLM inference capabilities. The experimental results, conducted on our constructed AD question answering (ADQA) benchmark, underscore the efficacy of DALK. Additionally, we perform a series of detailed analyses that can offer valuable insights and guidelines for the emerging topic of mutually enhancing KG and LLM. We will release the code and data at https://github.com/David-Li0406/DALK., Comment: Accepted by EMNLP 2024 Findings; revise format problem

In this paper, we examine Yangjun Chen's technical report titled ``The 2-MAXSAT Problem Can Be Solved in Polynomial Time'' [Che23], which revises and expands upon their conference paper of the same name [Che22]. Chen's paper purports to build a polynomial-time algorithm for the ${\rm NP}$-complete problem 2-MAXSAT by converting a 2-CNF formula into a graph that is then searched. We show through multiple counterexamples that Chen's proposed algorithms contain flaws, and we find that the structures they create lack properly formalized definitions. Furthermore, we elaborate on how the author fails to prove the correctness of their algorithms and how they make overgeneralizations in their time analysis of their proposed solution. Due to these issues, we conclude that Chen's technical report [Che23] and conference paper [Che22] both fail to provide a proof that ${\rm P}={\rm NP}$., Comment

In this paper, we take a closer look at Czerwinski's "${\rm P}\neq{\rm NP}$ relative to a ${\rm P}$-complete oracle" [Cze23]. There are (uncountably) infinitely-many relativized worlds where ${\rm P}$ and ${\rm NP}$ differ, and it is well-known that for any ${\rm P}$-complete problem $A$, ${\rm P}^A \neq {\rm NP}^A \iff {\rm P}\neq {\rm NP}$. The paper defines two sets ${\rm D}_{\rm P}$ and ${\rm D}_{\rm NP}$ and builds the purported proof of their main theorem on the claim that an oracle Turing machine with ${\rm D}_{\rm NP}$ as its oracle and that accepts ${\rm D}_{\rm P}$ must make $\Theta(2^n)$ queries to the oracle. We invalidate the latter by proving that there is an oracle Turing machine with ${\rm D}_{\rm NP}$ as its oracle that accepts ${\rm D}_{\rm P}$ and yet only makes one query to the oracle. We thus conclude that Czerwinski's paper [Cze23] fails to establish that ${\rm P} \neq {\rm NP}$.

The paper is devoted to an invariance principle for Kemperman's model of oscillating random walk on $\mathbb{Z}$. This result appears as an extension of the invariance principal theorem for classical random walks on $\mathbb{Z}$ or reflected random walks on $\mathbb{N}_0$. Relying on some natural Markov sub-process which takes into account the oscillation of the random walks between $\mathbb{Z}^-$ and $\mathbb{Z}^+$, we first construct an aperiodic sequence of renewal operators acting on a suitable Banach space and then apply a powerful theorem proved by S. Gou\"ezel.

We establish an analogy between the Fokker-Planck equation describing evolutionary landscape dynamics and the Schr\"{o}dinger equation which characterizes quantum mechanical particles, showing how a population with multiple genetic traits evolves analogously to a wavefunction under a multi-dimensional energy potential in imaginary time. Furthermore, we discover within this analogy that the stationary population distribution on the landscape corresponds exactly to the ground-state wavefunction. This mathematical equivalence grants entry to a wide range of analytical tools developed by the quantum mechanics community, such as the Rayleigh-Ritz variational method and the Rayleigh-Schr\"{o}dinger perturbation theory, allowing us to not only make reasonable quantitative assessments but also explore fundamental biological inquiries. We demonstrate the effectiveness of these tools by estimating the population success on landscapes where precise answers are elusive, and unveiling the ecological consequences of stress-induced mutagenesis -- a prevalent evolutionary mechanism in pathogenic and neoplastic systems. We show that, even in a unchanging environment, a sharp mutational burst resulting from stress can always be advantageous, while a gradual increase only enhances population size when the number of relevant evolving traits is limited. Our interdisciplinary approach offers novel insights, opening up new avenues for deeper understanding and predictive capability regarding the complex dynamics of evolving populations.

We have developed a mathematical model that captures stress-induced mutagenesis, a fundamental aspect of pathogenic and neoplastic evolutionary dynamics, on the fitness landscape with multiple relevant genetic traits as a high-dimensional Euclidean space. In this framework, stress-induced mutagenesis manifests as a heterogeneous diffusion process. We show how increasing mutations, and thus reducing exploitation, in a static ecology with fixed carrying capacity and maximum growth rates, can paradoxically boost population size. Remarkably, this unexpected biophysical phenomenon applies universally to any number of traits.

Functional connectomes (FCs) contain pairwise estimations of functional couplings based on pairs of brain regions activity. FCs are commonly represented as correlation matrices that are symmetric positive definite (SPD) lying on or inside the SPD manifold. Since the geometry on the SPD manifold is non-Euclidean, the inter-related entries of FCs undermine the use of Euclidean-based distances. By projecting FCs into a tangent space, we can obtain tangent functional connectomes (tangent-FCs). Tangent-FCs have shown a higher predictive power of behavior and cognition, but no studies have evaluated the effect of such projections with respect to fingerprinting. We hypothesize that tangent-FCs have a higher fingerprint than regular FCs. Fingerprinting was measured by identification rates (ID rates) on test-retest FCs as well as on monozygotic and dizygotic twins. Our results showed that identification rates are systematically higher when using tangent-FCs. Specifically, we found: (i) Riemann and log-Euclidean matrix references systematically led to higher ID rates. (ii) In tangent-FCs, Main-diagonal regularization prior to tangent space projection was critical for ID rate when using Euclidean distance, whereas barely affected ID rates when using correlation distance. (iii) ID rates were dependent on condition and fMRI scan length. (iv) Parcellation granularity was key for ID rates in FCs, as well as in tangent-FCs with fixed regularization, whereas optimal regularization of tangent-FCs mostly removed this effect. (v) Correlation distance in tangent-FCs outperformed any other configuration of distance on FCs or on tangent-FCs across the fingerprint gradient (here sampled by assessing test-retest, Monozygotic and Dizygotic twins). (vi)ID rates tended to be higher in task scans compared to resting-state scans when accounting for fMRI scan length., Comment: 31 pages, 10 figures, 2 tables

Functional connectivity quantifies the statistical dependencies between the activity of brain regions, measured using neuroimaging data such as functional MRI BOLD time series. The network representation of functional connectivity, called a Functional Connectome (FC), has been shown to contain an individual fingerprint allowing participants identification across consecutive testing sessions. Recently, researchers have focused on the extraction of these fingerprints, with potential applications in personalized medicine. Here, we show that a mathematical operation denominated degree-normalization can improve the extraction of FC fingerprints. Degree-normalization has the effect of reducing the excessive influence of strongly connected brain areas in the whole-brain network. We adopt the differential identifiability framework and apply it to both original and degree-normalized FCs of 409 individuals from the Human Connectome Project, in resting-state and 7 fMRI tasks. Our results indicate that degree-normalization systematically improves three fingerprinting metrics, namely differential identifiability, identification rate and matching rate. Moreover, the results related to the matching rate metric suggest that individual fingerprints are embedded in a low-dimensional space. The results suggest that low-dimensional functional fingerprints lie in part in weakly connected subnetworks of the brain, and that degree-normalization helps uncovering them. This work introduces a simple mathematical operation that could lead to significant improvements in future FCs fingerprinting studies., Comment: Main: 23 pages, 7 Figures, Supplementary: 3 pages, 3 Figures, 1 Table

It has been well established that Functional Connectomes (FCs), as estimated from functional MRI (fMRI) data, have an individual fingerprint that can be used to identify an individual from a population (subject-identification). Although identification rate is high when using resting-state FCs, other tasks show moderate to low values. Furthermore, identification rate is task-dependent, and is low when distinct cognitive states, as captured by different fMRI tasks, are compared. Here we propose an embedding framework, GEFF (Graph Embedding for Functional Fingerprinting), based on group-level decomposition of FCs into eigenvectors. GEFF creates an eigenspace representation of a group of subjects using one or more task FCs (Learning Stage). In the Identification Stage, we compare new instances of FCs from the Learning subjects within this eigenspace (validation dataset). The validation dataset contains FCs either from the same tasks as the Learning dataset or from the remaining tasks that were not included in Learning. Assessment of validation FCs within the eigenspace results in significantly increased subject-identification rates for all fMRI tasks tested and potentially task-independent fingerprinting process. It is noteworthy that combining resting-state with one fMRI task for GEFF Learning Stage covers most of the cognitive space for subject identification. In addition to subject-identification, GEFF was also used for identification of cognitive states, i.e. to identify the task associated to a given FC, regardless of the subject being already in the Learning dataset or not (subject-independent task-identification). In addition, we also show that eigenvectors from the Learning Stage can be characterized as task-dominant, subject dominant or neither, providing a deeper insight into the extent of variance in functional connectivity across individuals and cognitive states., Comment: 30 pages; 6 figures; 5 supplementary figures