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Independent component analysis (ICA) is now a widely used solution for the analysis of multi-subject functional magnetic resonance imaging (fMRI) data. Independent vector analysis (IVA) generalizes ICA to multiple datasets, i.e., to multi-subject data, and in addition to higher-order statistical information in ICA, it leverages the statistical dependence across the datasets as an additional type of statistical diversity. As such, it preserves variability in the estimation of single-subject maps but its performance might suffer when the number of datasets increases. Constrained IVA is an effective way to bypass computational issues and improve the quality of separation by incorporating available prior information. Existing constrained IVA approaches often rely on user-defined threshold values to define the constraints. However, an improperly selected threshold can have a negative impact on the final results. This paper proposes two novel methods for constrained IVA: one using an adaptive-reverse scheme to select variable thresholds for the constraints and a second one based on a threshold-free formulation by leveraging the unique structure of IVA. We demonstrate that our solutions provide an attractive solution to multi-subject fMRI analysis both by simulations and through analysis of resting state fMRI data collected from 98 subjects -- the highest number of subjects ever used by IVA algorithms. Our results show that both proposed approaches obtain significantly better separation quality and model match while providing computationally efficient and highly reproducible solutions., Comment: 11 pages

Resting-state functional magnetic resonance imaging (rsfMRI) is a powerful tool for investigating the relationship between brain function and cognitive processes as it allows for the functional organization of the brain to be captured without relying on a specific task or stimuli. In this paper, we present a novel modeling architecture called BrainRGIN for predicting intelligence (fluid, crystallized, and total intelligence) using graph neural networks on rsfMRI derived static functional network connectivity matrices. Extending from the existing graph convolution networks, our approach incorporates a clustering-based embedding and graph isomorphism network in the graph convolutional layer to reflect the nature of the brain sub-network organization and efficient network expression, in combination with TopK pooling and attention-based readout functions. We evaluated our proposed architecture on a large dataset, specifically the Adolescent Brain Cognitive Development Dataset, and demonstrated its effectiveness in predicting individual differences in intelligence. Our model achieved lower mean squared errors and higher correlation scores than existing relevant graph architectures and other traditional machine learning models for all of the intelligence prediction tasks. The middle frontal gyrus exhibited a significant contribution to both fluid and crystallized intelligence, suggesting their pivotal role in these cognitive processes. Total composite scores identified a diverse set of brain regions to be relevant which underscores the complex nature of total intelligence.

Benchmarking drug efficacy is a critical step in clinical trial design and planning. The challenge is that much of the data on efficacy endpoints is stored in scientific papers in free text form, so extraction of such data is currently a largely manual task. Our objective is to automate this task as much as possible. In this study we have developed and optimised a framework to extract efficacy endpoints from text in scientific papers, using a machine learning approach. Our machine learning model predicts 25 classes associated with efficacy endpoints and leads to high F1 scores (harmonic mean of precision and recall) of 96.4% on the test set, and 93.9% and 93.7% on two case studies. These methods were evaluated against - and showed strong agreement with - subject matter experts and show significant promise in the future of automating the extraction of clinical endpoints from free text. Clinical information extraction from text data is currently a laborious manual task which scales poorly and is prone to human error. Demonstrating the ability to extract efficacy endpoints automatically shows great promise for accelerating clinical trial design moving forwards.

The joint analysis of multimodal neuroimaging data is critical in the field of brain research because it reveals complex interactive relationships between neurobiological structures and functions. In this study, we focus on investigating the effects of structural imaging (SI) features, including white matter micro-structure integrity (WMMI) and cortical thickness, on the whole brain functional connectome (FC) network. To achieve this goal, we propose a network-based vector-on-matrix regression model to characterize the FC-SI association patterns. We have developed a novel multi-level dense bipartite and clique subgraph extraction method to identify which subsets of spatially specific SI features intensively influence organized FC sub-networks. The proposed method can simultaneously identify highly correlated structural-connectomic association patterns and suppress false positive findings while handling millions of potential interactions. We apply our method to a multimodal neuroimaging dataset of 4,242 participants from the UK Biobank to evaluate the effects of whole-brain WMMI and cortical thickness on the resting-state FC. The results reveal that the WMMI on corticospinal tracts and inferior cerebellar peduncle significantly affect functional connections of sensorimotor, salience, and executive sub-networks with an average correlation of 0.81 (p<0.001)., Comment: 20 pages, 5 figures, 2 tables

The human brain has a complex, intricate functional architecture. While many studies primarily emphasize pairwise interactions, delving into high-order associations is crucial for a comprehensive understanding of how functional brain networks intricately interact beyond simple pairwise connections. Analyzing high-order statistics allows us to explore the nuanced and complex relationships across the brain, unraveling the heterogeneity and uncovering patterns of multilevel overlap on the psychosis continuum. Here, we employed high-order independent component analysis (ICA) plus multivariate information-theoretical metrics ($O$-information and $S$-information) to estimate high-order interaction to examine schizophrenia using resting-state fMRI. The results show that multiple brain regions networks may be altered in schizophrenia, such as temporal, subcortical, and higher-cognitive brain regions, and meanwhile, it also shows that revealed synergy gives more information than redundancy in diagnosing schizophrenia. All in all, we showed that high-order dependencies were altered in schizophrenia. Identification of these aberrant patterns will give us a new window to diagnose schizophrenia., Comment: 7 pages, 4 figures, Accepted to InfoCog@NeurIPS 2023 (https://sites.google.com/view/infocog-neurips-2023/home)

In 2022 the BL Lac object S4 0954+65 underwent a major variability phase, reaching its historical maximum brightness in the optical and $\gamma$-ray bands. We present optical photometric and polarimetric data acquired by the Whole Earth Blazar Telescope (WEBT) Collaboration from 2022 April 6 to July 6. Many episodes of unprecedented fast variability were detected, implying an upper limit to the size of the emitting region as low as $10^{-4}$ parsec. The WEBT data show rapid variability in both the degree and angle of polarization. We analyse different models to explain the polarization behaviour in the framework of a twisting jet model, which assumes that the long-term trend of the flux is produced by variations in the emitting region viewing angle. All the models can reproduce the average trend of the polarization degree, and can account for its general anticorrelation with the flux, but the dispersion of the data requires the presence of intrinsic mechanisms, such as turbulence, shocks, or magnetic reconnection. The WEBT optical data are compared to $\gamma$-ray data from the Fermi satellite. These are analysed with both fixed and adaptive binning procedures. We show that the strong correlation between optical and $\gamma$-ray data without measurable delay assumes different slopes in faint and high brightness states, and this is compatible with a scenario where in faint states we mainly see the imprint of the geometrical effects, while in bright states the synchrotron self-Compton process dominates., Comment: 12 pages, 13 figures, in press for MNRAS

The orbital stability of contact binary systems has been receiving considerable attention recently. Theoretical studies indicate that merger is likely to occur at very low mass ratios, but the actual mass ratio at which merger may take place is likely to be variable and dependent on the mass of the primary. We consider the effects of metal content on the orbital stability of contact binary systems by modelling the gyration radius of a rotating and tidally distorted primary component at various values of metallicity in the range -1.25 to +0.5. We determine the instability mass ratio range for contact binary systems with a low mass primary in the range 0.6M(sun) to 1.4M(sun) at various metallicity levels and show that systems with low metallicity have an instability mass ratio lower than those with higher metal content and therefore are likely to be more stable. We illustrate the effect through light curve analysis of two otherwise very similar contact binary systems, except for different metallicity. While both would be considered unstable if metallicity was not taken into consideration, only one remains in that category after appropriate adjustments based on metallicity have been made., Comment: 9 pages, 7 Figures and 5 Tables Accepted Monthly Notices of Royal Astronomical Society (MNRAS)

The BL Lac 1ES 2344+514 is known for temporary extreme properties (e.g., a shift of the synchrotron SED peak energy $\nu_{synch,p}$ above 1keV). While those extreme states were so far observed only during high flux levels, additional multi-year observing campaigns are required to achieve a coherent picture. Here, we report the longest investigation of the source from radio to VHE performed so far, focusing on a systematic characterisation of the intermittent extreme states. While our results confirm that 1ES 2344+514 typically exhibits $\nu_{synch,p}>$1keV during elevated flux periods, we also find periods where the extreme state coincides with low flux activity. A strong spectral variability thus happens in the quiescent state, and is likely caused by an increase of the electron acceleration efficiency without a change in the electron injection luminosity. We also report a strong X-ray flare (among the brightest for 1ES 2344+514) without a significant shift of $\nu_{synch,p}$. During this particular flare, the X-ray spectrum is among the softest of the campaign. It unveils complexity in the spectral evolution, where the common harder-when-brighter trend observed in BL Lacs is violated. During a low and hard X-ray state, we find an excess of the UV flux with respect to an extrapolation of the X-ray spectrum to lower energies. This UV excess implies that at least two regions contribute significantly to the infrared/optical/ultraviolet/X-ray emission. Using the simultaneous MAGIC, XMM-Newton, NuSTAR, and AstroSat observations, we argue that a region possibly associated with the 10 GHz radio core may explain such an excess. Finally, we investigate a VHE flare, showing an absence of simultaneous variability in the 0.3-2keV band. Using a time-dependent leptonic modelling, we show that this behaviour, in contradiction to single-zone scenarios, can instead be explained by a two-component model., Comment: Accepted for publication in Astronomy & Astrophysics

The LogRank conjecture of Lov\'asz and Saks from 1988 is the most famous open problem in the communication complexity theory. The statement is as follows: Suppose that two players intend to compute a Boolean function $f(x,y)$ when $x$ is known for the first and $y$ for the second player, and they may send and receive messages encoded with bits, then they can compute $f(x,y)$ with exchanging $(\log \rank (M_f))^c $ bits, where $M_f$ is a Boolean matrix, determined by function $f$. The problem is widely open and very popular, and it has resisted numerous attacks in the last 35 years. The best upper bound is still exponential in the bound of the conjecture. Unfortunately, we cannot prove the conjecture, but we present a communication protocol with $(\log \rank (M_f))^c $ bits, which computes a -- somewhat -- related quantity to $f(x,y)$. The relation is characterized by a representation of low-degree, multi-linear polynomials modulo composite numbers. This result of ours may help to settle this long-time open conjecture., Comment: Some typos were corrected in this version

We use CANUCS JWST/NIRCam imaging of galaxies behind the gravitationally-lensing cluster MACS J0417.5-1154 to investigate star formation burstiness in low-mass ($M_\star\sim10^8\ M_\odot$) galaxies at $z\sim4.7-6.5$. Our sample of 123 galaxies is selected using the Lyman break selection and photometric emission-line excess methods. Sixty per cent of the 123 galaxies in this sample have H$\alpha$-to-UV flux ratios that deviate significantly from the range of $\eta_{1500}$ values consistent with smooth and steady star formation histories. This large fraction indicates that the majority of low-mass galaxies is experiencing bursty star formation histories at high redshift. We also searched for interacting galaxies in our sample and found that they are remarkably common ($\sim40$ per cent of the sample). Compared to non-interacting galaxies, interacting galaxies are more likely to have very low H$\alpha$-to-UV ratios, suggesting that galaxy-galaxy interactions enhance star formation burstiness and enable faster quenching (with timescales of $\lesssim100$ Myr) that follows the rapid rise of star formation activity. Given the high frequency of galaxy-galaxy interactions and the rapid SFR fluctuations they appear to cause, we conclude that galaxy-galaxy interactions could be a leading cause of bursty star formation in low-mass, high-$z$ galaxies. They could thus play a significant role in the evolution of the galaxy population at early cosmological times., Comment: 20 pages, 15 figures, and 1 table. Accepted for publication in MNRAS

Artificial intelligence (AI) has shown great promise in revolutionizing the field of digital health by improving disease diagnosis, treatment, and prevention. This paper describes the Health Guardian platform, a non-commercial, scientific research-based platform developed by the IBM Digital Health team to rapidly translate AI research into cloud-based microservices. The platform can collect health-related data from various digital devices, including wearables and mobile applications. Its flexible architecture supports microservices that accept diverse data types such as text, audio, and video, expanding the range of digital health assessments and enabling holistic health evaluations by capturing voice, facial, and motion bio-signals. These microservices can be deployed to a clinical cohort specified through the Clinical Task Manager (CTM). The CTM then collects multi-modal, clinical data that can iteratively improve the accuracy of AI predictive models, discover new disease mechanisms, or identify novel biomarkers. This paper highlights three microservices with different input data types, including a text-based microservice for depression assessment, a video-based microservice for sit-to-stand mobility assessment, and a wearable-based microservice for functional mobility assessment. The CTM is also discussed as a tool to help design and set up clinical studies to unlock the full potential of the platform. Today, the Health Guardian platform is being leveraged in collaboration with research partners to optimize the development of AI models by utilizing a multitude of input sources. This approach streamlines research efforts, enhances efficiency, and facilitates the development and validation of digital health applications., Comment: 10 pages, 6 figures

This paper presents a data-centric and security-focused data fabric designed for digital health applications. With the increasing interest in digital health research, there has been a surge in the volume of Internet of Things (IoT) data derived from smartphones, wearables, and ambient sensors. Managing this vast amount of data, encompassing diverse data types and varying time scales, is crucial. Moreover, compliance with regulatory and contractual obligations is essential. The proposed data fabric comprises an architecture and a toolkit that facilitate the integration of heterogeneous data sources, across different environments, to provide a unified view of the data in dashboards. Furthermore, the data fabric supports the development of reusable and configurable data integration components, which can be shared as open-source or inner-source software. These components are used to generate data pipelines that can be deployed and scheduled to run either in the cloud or on-premises. Additionally, we present the implementation of our data fabric in a home-based telemonitoring research project involving older adults, conducted in collaboration with the University of California, San Diego (UCSD). The study showcases the streamlined integration of data collected from various IoT sensors and mobile applications to create a unified view of older adults' health for further analysis and research.

State machines are used in engineering many types of software-intensive systems. UML State Machines extend simple finite state machines with powerful constructs. Among the many extensions, there is one seemingly simple and innocent language construct that fundamentally changes state machines' reactive model of computation: doActivity behaviors. DoActivity behaviors describe behavior that is executed independently from the state machine once entered in a given state, typically modeling complex computation or communication as background tasks. However, the UML specification or textbooks are vague about how the doActivity behavior construct should be appropriately used. This lack of guidance is a severe issue as, when improperly used, doActivities can cause concurrent, non-deterministic bugs that are especially challenging to find and could ruin a seemingly correct software design. The Precise Semantics of UML State Machines (PSSM) specification introduced detailed operational semantics for state machines. To the best of our knowledge, there is no rigorous review yet of doActivity's semantics as specified in PSSM. We analyzed the semantics by collecting evidence from cross-checking the text of the specification, its semantic model and executable test cases, and the simulators supporting PSSM. We synthesized insights about subtle details and emergent behaviors relevant to tool developers and advanced modelers. We reported inconsistencies and missing clarifications in more than 20 issues to the standardization committee. Based on these insights, we studied 11 patterns for doActivities detailing the consequences of using a doActivity in a given situation and discussing countermeasures or alternative design choices. We hope that our analysis of the semantics and the patterns help vendors develop conformant simulators or verification tools and engineers design better state machine models.

The cross-modal synthesis between structural magnetic resonance imaging (sMRI) and functional network connectivity (FNC) is a relatively unexplored area in medical imaging, especially with respect to schizophrenia. This study employs conditional Vision Transformer Generative Adversarial Networks (cViT-GANs) to generate FNC data based on sMRI inputs. After training on a comprehensive dataset that included both individuals with schizophrenia and healthy control subjects, our cViT-GAN model effectively synthesized the FNC matrix for each subject, and then formed a group difference FNC matrix, obtaining a Pearson correlation of 0.73 with the actual FNC matrix. In addition, our FNC visualization results demonstrate significant correlations in particular subcortical brain regions, highlighting the model's capability of capturing detailed structural-functional associations. This performance distinguishes our model from conditional CNN-based GAN alternatives such as Pix2Pix. Our research is one of the first attempts to link sMRI and FNC synthesis, setting it apart from other cross-modal studies that concentrate on T1- and T2-weighted MR images or the fusion of MRI and CT scans.

The Brain Imaging Data Structure (BIDS) is a community-driven standard for the organization of data and metadata from a growing range of neuroscience modalities. This paper is meant as a history of how the standard has developed and grown over time. We outline the principles behind the project, the mechanisms by which it has been extended, and some of the challenges being addressed as it evolves. We also discuss the lessons learned through the project, with the aim of enabling researchers in other domains to learn from the success of BIDS.

Managing data and code in open scientific research is complicated by two key problems: large datasets often cannot be stored alongside code in repository platforms like GitHub, and iterative analysis can lead to unnoticed changes to data, increasing the risk that analyses are based on older versions of data. Here, I introduce SciDataFlow: a fast, concurrent command-line tool paired with a simple Data Manifest specification. SciDataFlow streamlines tracking data changes, uploading data to remote repositories, and pulling in all data necessary to reproduce a computational analysis., Comment: 3 pages, no figures

Hexapeptides are increasingly applied as model systems for studying the amyloidogenecity properties of oligo- and polypeptides. It is possible to construct 64 million different hexapeptides from the twenty proteinogenic amino acid residues. Today's experimental amyloid databases contain only a fraction of these annotated hexapeptides. For labeling all the possible hexapeptides as "amyloidogenic" or "non-amyloidogenic" there exist several computational predictors with good accuracies. It may be of interest to define and study a simple graph structure on the 64 million hexapeptides as nodes when two hexapeptides are connected by an edge if they differ by only a single residue. For example, in this graph, HIKKLM is connected to AIKKLM, or HIKKNM, or HIKKLC, but it is not connected with an edge to VVKKLM or HIKNPM. In the present contribution, we consider our previously published artificial intelligence-based tool, the Budapest Amyloid Predictor (BAP for short), and demonstrate a spectacular property of this predictor in the graph defined above. We show that for any two hexapeptides predicted to be "amyloidogenic" by the BAP predictor, there exists an easily constructible path of length at most 6 that passes through neighboring hexapeptides all predicted to be "amyloidogenic" by BAP. For example, the predicted amyloidogenic ILVWIW and FWLCYL hexapeptides can be connected through the length-6 path ILVWIW-IWVWIW-IWVCIW-IWVCIL-FWVCIL-FWLCIL-FWLCYL in such a way that the neighbors differ in exactly one residue, and all hexapeptides on the path are predicted to be amyloidogenic by BAP. The symmetric statement also holds for non-amyloidogenic hexapeptides. It is noted that the mentioned property of the Budapest Amyloid Predictor \url{https://pitgroup.org/bap} is not proprietary; it is also true for any linear Support Vector Machine (SVM)-based predictors.

Robots must make and break contact with the environment to perform useful tasks, but planning and control through contact remains a formidable challenge. In this work, we achieve real-time contact-implicit model predictive control with a surprisingly simple method: inverse dynamics trajectory optimization. While trajectory optimization with inverse dynamics is not new, we introduce a series of incremental innovations that collectively enable fast model predictive control on a variety of challenging manipulation and locomotion tasks. We implement these innovations in an open-source solver and present simulation examples to support the effectiveness of the proposed approach. Additionally, we demonstrate contact-implicit model predictive control on hardware at over 100 Hz for a 20-degree-of-freedom bi-manual manipulation task. Video and code are available at https://idto.github.io.

Polycyclic aromatic hydrocarbons (PAHs) are highly toxic, carcinogenic substances. On soils contaminated with PAHs, crop cultivation, animal husbandry and even the survival of microflora in the soil are greatly perturbed, depending on the degree of contamination. Most microorganisms cannot tolerate PAH-contaminated soils, however, some microbial strains can adapt to these harsh conditions and survive on contaminated soils. Analysis of the metagenomes of contaminated environmental samples may lead to discovery of PAH-degrading enzymes suitable for green biotechnology methodologies ranging from biocatalysis to pollution control. In the present study, our goal was to apply a metagenomic data search to identify efficient novel enzymes in remediation of PAH-contaminated soils. The metagenomic hits were further analyzed using a set of bioinformatics tools to select protein sequences predicted to encode well-folded soluble enzymes. Three novel enzymes (two dioxygenases and one peroxidase) were cloned and used in soil remediation microcosms experiments. The novel enzymes were found to be efficient for degradation of naphthalene and phenanthrene. Adding the inorganic oxidant CaO2 further increased the degrading potential of the novel enzymes for anthracene and pyrene. We conclude that metagenome mining paired with bioinformatic predictions, structural modelling and functional assays constitutes a powerful approach towards novel enzymes for soil remediation.

We present Predictive Sparse Manifold Transform (PSMT), a minimalistic, interpretable and biologically plausible framework for learning and predicting natural dynamics. PSMT incorporates two layers where the first sparse coding layer represents the input sequence as sparse coefficients over an overcomplete dictionary and the second manifold learning layer learns a geometric embedding space that captures topological similarity and dynamic temporal linearity in sparse coefficients. We apply PSMT on a natural video dataset and evaluate the reconstruction performance with respect to contextual variability, the number of sparse coding basis functions and training samples. We then interpret the dynamic topological organization in the embedding space. We next utilize PSMT to predict future frames compared with two baseline methods with a static embedding space. We demonstrate that PSMT with a dynamic embedding space can achieve better prediction performance compared to static baselines. Our work establishes that PSMT is an efficient unsupervised generative framework for prediction of future visual stimuli., Comment: Paper presented at the 1st Workshop on High-dimensional Learning Dynamics (HLD) at the 40th International Conference on Machine Learning (ICML) 2023, Honolulu, Hawaii, USA (https://sites.google.com/view/hidimlearning), 10 pages

We present a novel approach for finding multiple noisily embedded template graphs in a very large background graph. Our method builds upon the graph-matching-matched-filter technique proposed in Sussman et al., with the discovery of multiple diverse matchings being achieved by iteratively penalizing a suitable node-pair similarity matrix in the matched filter algorithm. In addition, we propose algorithmic speed-ups that greatly enhance the scalability of our matched-filter approach. We present theoretical justification of our methodology in the setting of correlated Erdos-Renyi graphs, showing its ability to sequentially discover multiple templates under mild model conditions. We additionally demonstrate our method's utility via extensive experiments both using simulated models and real-world dataset, include human brain connectomes and a large transactional knowledge base., Comment: 27 pages, 12 figures, 3 tables

We present measurements of stellar populations properties of a z = 9.1 gravitationally lensed galaxy MACS1149-JD1 using deep JWST NIRISS slitless spectroscopy as well as NIRISS and NIRCam imaging from the CAnadian NIRISS Unbiased Cluster Survey (CANUCS). The galaxy is split into four components. Three magnified (${\mu}$ ~ 17) star-forming components are unresolved, giving intrinsic sizes of < 50pc. In addition, the underlying extended component contains the bulk of the stellar mass, formed the majority of its stars ~ 50Myr earlier than the other three components and is not the site of the most active star formation currently. The NIRISS and NIRCam resolved photometry does not confirm a strong Balmer break previously seen in Spitzer. The NIRISS grism spectrum has been extracted for the entire galaxy and shows a clear continuum and Lyman-break, with no Lyman-${\alpha}$ detected., Comment: This is the version of the article before peer review or editing, as submitted by an author to ApJLetters

Deep learning (DL) models have been popular due to their ability to learn directly from the raw data in an end-to-end paradigm, alleviating the concern of a separate error-prone feature extraction phase. Recent DL-based neuroimaging studies have also witnessed a noticeable performance advancement over traditional machine learning algorithms. But the challenges of deep learning models still exist because of the lack of transparency in these models for their successful deployment in real-world applications. In recent years, Explainable AI (XAI) has undergone a surge of developments mainly to get intuitions of how the models reached the decisions, which is essential for safety-critical domains such as healthcare, finance, and law enforcement agencies. While the interpretability domain is advancing noticeably, researchers are still unclear about what aspect of model learning a post hoc method reveals and how to validate its reliability. This paper comprehensively reviews interpretable deep learning models in the neuroimaging domain. Firstly, we summarize the current status of interpretability resources in general, focusing on the progression of methods, associated challenges, and opinions. Secondly, we discuss how multiple recent neuroimaging studies leveraged model interpretability to capture anatomical and functional brain alterations most relevant to model predictions. Finally, we discuss the limitations of the current practices and offer some valuable insights and guidance on how we can steer our future research directions to make deep learning models substantially interpretable and thus advance scientific understanding of brain disorders., Comment: 109 pages, 21 figures

The subgraph-subgraph matching problem is, given a pair of graphs and a positive integer $K$, to find $K$ vertices in the first graph, $K$ vertices in the second graph, and a bijection between them, so as to minimize the number of adjacency disagreements across the bijection; it is ``seeded" if some of this bijection is fixed. The problem is intractable, and we present the ssSGM algorithm, which uses Frank-Wolfe methodology to efficiently find an approximate solution. Then, in the context of a generalized correlated random Bernoulli graph model, in which the pair of graphs naturally have a core of $K$ matched pairs of vertices, we provide and prove mild conditions for the subgraph-subgraph matching problem solution to almost always be the correct $K$ matched pairs of vertices., Comment: 27 pages, 16 figures