Miracle-dz/UniFAR-FTUs huggingface dataset:
l2Match: Optimization Techniques on Subgraph Matching Algorithm Using Label Pair, Neighboring Label Index, and Jump-Redo Method

Graph database is designed to store bidirectional relationships between objects and facilitate the traversal process to extract a subgraph. However, the subgraph matching process is an NP-Complete problem. Existing solutions to this problem usually employ a filter-and-verification framework and a divide-and-conquer method. The filter-and-verification framework minimizes the number of inputs to the verification stage by filtering and pruning invalid candidates as much as possible. Meanwhile, subgraph matching is performed on the substructure decomposed from the larger graph to yield partial embedding. Subsequently, the recursive traversal or set intersection technique combines the partial embedding into a complete subgraph. In this paper, we first present a comprehensive literature review of the state-of-the-art solutions. l2Match, a sub graph isomorphism algorithm for small queries utilizing a Label-Pair Index and filtering method, is then proposed and presented as a proof of concept. Empirical experimentation shows that l2Match outperforms related state-of-the-art solutions, and the proposed methods optimize the existing algorithms.
Stability estimates of Nyström discretizations of Helmholtz decomposition boundary integral equation formulations for the solution of Navier scattering problems in two dimensions with Dirichlet boundary conditions

Helmholtz decompositions of elastic fields is a common approach for the solution of Navier scattering problems. Used in the context of Boundary Integral Equations (BIE), this approach affords solutions of Navier problems via the simpler Helmholtz boundary integral operators (BIOs). Approximations of Helmholtz Dirichlet-to-Neumann (DtN) can be employed within a regularizing combined field strategy to deliver BIE formulations of the second kind for the solution of Navier scattering problems in two dimensions with Dirichlet boundary conditions, at least in the case of smooth boundaries. Unlike the case of scattering and transmission Helmholtz problems, the approximations of the DtN maps we use in the Helmholtz decomposition BIE in the Navier case require incorporation of lower order terms in their pseudodifferential asymptotic expansions. The presence of these lower order terms in the Navier regularized BIE formulations complicates the stability analysis of their Nystr\"om discretizations in the framework of global trigonometric interpolation and the Kussmaul-Martensen kernel singularity splitting strategy. The main difficulty stems from compositions of pseudodifferential operators of opposite orders, whose Nystr\"om discretization must be performed with care via pseudodifferential expansions beyond the principal symbol. The error analysis is significantly simpler in the case of arclength boundary parametrizations and considerably more involved in the case of general smooth parametrizations which are typically encountered in the description of one dimensional closed curves.
No Representation Rules Them All in Category Discovery

In this paper we tackle the problem of Generalized Category Discovery (GCD). Specifically, given a dataset with labelled and unlabelled images, the task is to cluster all images in the unlabelled subset, whether or not they belong to the labelled categories. Our first contribution is to recognize that most existing GCD benchmarks only contain labels for a single clustering of the data, making it difficult to ascertain whether models are using the available labels to solve the GCD task, or simply solving an unsupervised clustering problem. As such, we present a synthetic dataset, named 'Clevr-4', for category discovery. Clevr-4 contains four equally valid partitions of the data, i.e based on object shape, texture, color or count. To solve the task, models are required to extrapolate the taxonomy specified by the labelled set, rather than simply latching onto a single natural grouping of the data. We use this dataset to demonstrate the limitations of unsupervised clustering in the GCD setting, showing that even very strong unsupervised models fail on Clevr-4. We further use Clevr-4 to examine the weaknesses of existing GCD algorithms, and propose a new method which addresses these shortcomings, leveraging consistent findings from the representation learning literature to do so. Our simple solution, which is based on 'mean teachers' and termed $\mu$GCD, substantially outperforms implemented baselines on Clevr-4. Finally, when we transfer these findings to real data on the challenging Semantic Shift Benchmark (SSB), we find that $\mu$GCD outperforms all prior work, setting a new state-of-the-art. For the project webpage, see https://www.robots. ox.ac. uk/~vgg/data/clevr4/
Neural Crystals

We face up to the challenge of explainability in Multimodal Artificial Intelligence (MMAI). At the nexus of neuroscience-inspired and quantum computing, interpretable and transparent spin-geometrical neural architectures for early fusion of large-scale, heterogeneous, graph-structured data are envisioned, harnessing recent evidence for relativistic quantum neural coding of (co-)behavioral states in the self-organizing brain, under competitive, multidimensional dynamics. The designs draw on a self-dual classical description – via special Clifford-Lipschitz operations – of spinorial quantum states within registers of at most 16 qubits for efficient encoding of exponentially large neural structures. Formally ‘trained’, Lorentz neural architectures with precisely one lateral layer of exclusively inhibitory interneurons accounting for anti-modalities, as well as their co-architectures with intra-layer connections are highlighted. The approach accommodates the fusion of up to 16 time-invariant interconnected (anti-)modalities and the crystallization of latent multidimensional patterns. Comprehensive insights are expected to be gained through applications to Multimodal Big Data, under diverse real-world scenarios.
Onedata4Sci: Life science data management solution based on Onedata

Life-science experimental methods generate vast and ever-increasing volumes of data, which provide highly valuable research resources. However, management of these data is nontrivial and applicable software solutions are currently subject to intensive development. The solutions mainly fall into one of the two groups: general data management systems (e.g. Onedata, iRODS, B2SHARE, CERNBox) or very specialised data management solutions (e.g. solutions for biomolecular simulation data, biological imaging data, genomic data). To bridge this gap between them, we provide Onedata4Sci, a prototype data management solution, which is focused on the management of life science data and covers four key steps of the data life cycle, i.e. data acquisition, user access, computational processing and archiving. Onedata4Sci is based on the Onedata data management system. It is written in Python, fully containerised, with the support for processing the stored data in Kubernetes. The applicability of Onedata4Sci is shown in three distinct use cases -- plant imaging data, cellular imaging data, and cryo-electron microscopy data. Despite the use cases covering very different types of data and user patterns, Onedata4Sci demonstrated an ability to successfully handle all these conditions. Complete source codes of Onedata4Sci are available on GitHub (https://github.com/CERIT-SC/onedata4sci), and its documentation and manual for installation are also provided.
The Space of Vectored Hyperbolic Surfaces is Path-Connected

In the space $\mathcal{H}^2$ of hyperbolic surfaces decorated with a base unit vector, the topology induced by the Gromov-Hausdorff convergence coincides with the Chabauty topology on the space of discrete torsion-free subgroups of $\text{PSL}_2(\mathbb{R})$. Using paths constructed from changing the Fenchel-Nielsen coordinates and shrinking curves to cusps, we show path-connectivity of $\mathcal{H}^2$ and some of its subspaces.
Two-step dynamic obstacle avoidance

Dynamic obstacle avoidance (DOA) is a fundamental challenge for any autonomous vehicle, independent of whether it operates in sea, air, or land. This paper proposes a two-step architecture for handling DOA tasks by combining supervised and reinforcement learning (RL). In the first step, we introduce a data-driven approach to estimate the collision risk of an obstacle using a recurrent neural network, which is trained in a supervised fashion and offers robustness to non-linear obstacle movements. In the second step, we include these collision risk estimates into the observation space of an RL agent to increase its situational awareness. ~We illustrate the power of our two-step approach by training different RL agents in a challenging environment that requires to navigate amid multiple obstacles. The non-linear movements of obstacles are exemplarily modeled based on stochastic processes and periodic patterns, although our architecture is suitable for any obstacle dynamics. The experiments reveal that integrating our collision risk metrics into the observation space doubles the performance in terms of reward, which is equivalent to halving the number of collisions in the considered environment. Furthermore, we show that the architecture's performance improvement is independent of the applied RL algorithm.
Analytic solution of Markovian epidemics without re-infections on heterogeneous networks

Most epidemic processes on networks can be modelled by a compartmental model, that specifies the spread of a disease in a population. The corresponding compartmental graph describes how the viral state of the nodes (individuals) changes from one compartment to another. If the compartmental graph does not contain directed cycles (e.g. the famous SIR model satisfies this property), then we provide an analytic, closed-form solution of the continuous-time Markovian compartmental model on heterogeneous networks. The eigenvalues of the Markovian process are related to cut sets in the contact graph between nodes with different viral states. We illustrate our finding by analytically solving the continuous-time Markovian SI and SIR processes on heterogeneous networks. We show that analytic extensions to e.g. non-Markovian dynamics, temporal networks, simplicial contagion and more advanced compartmental models are possible. Our exact and explicit formula contains sums over all paths between two states in the SIR Markov graph, which prevents the computation of the exact solution for arbitrary large graphs.
A large-scale particle system with independent jumps and distributed synchronization

We study a system consisting of $n$ particles, moving forward in jumps on the real line. Each particle can make both independent jumps, whose sizes have some distribution, or ``synchronization'' jumps, which allow it to join a randomly chosen other particle if the latter happens to be ahead of it. System state is the empirical distribution of particle locations. The mean-field asymptotic regime, where $n\to\infty$, is considered. We prove that $v_n$, the steady-state speed of the particle system advance, converges, as $n\to\infty$, to a limit $v_{**}$ which can be easily found from a {\em minimum speed selection principle. } Also, as $n\to\infty$, we prove the convergence of the system dynamics to that of a deterministic mean-field limit (MFL). We show that the average speed of advance of any MFL is lower bounded by $v_{**}$, and the speed of a ``benchmark'' MFL, resulting from all particles initially co-located, is equal to $v_{**}$. In the special case of exponentially distributed independent jump sizes, we prove that a traveling wave MFL with speed $v$ exists if and only if $v\ge v_{**}$, with $v_{**}$ having simple explicit form; we also show the existence of traveling waves for the modified systems, with a left or right boundary moving at a constant speed $v$. Using these traveling wave existence results, we provide bounds on an MFL average speed of advance, depending on the right tail exponent of its initial state. We conjecture that these results for exponential jump sizes generalize to general jump sizes.
Learning Multi-Pattern Normalities in the Frequency Domain for Efficient Time Series Anomaly Detection

Anomaly detection significantly enhances the robustness of cloud systems. While neural network-based methods have recently demonstrated strong advantages, they encounter practical challenges in cloud environments: the contradiction between the impracticality of maintaining a unique model for each service and the limited ability to deal with diverse normal patterns by a unified model, as well as issues with handling heavy traffic in real time and short-term anomaly detection sensitivity. Thus, we propose MACE, a multi-normal-pattern accommodated and efficient anomaly detection method in the frequency domain for time series anomaly detection. There are three novel characteristics of it: (i) a pattern extraction mechanism excelling at handling diverse normal patterns with a unified model, which enables the model to identify anomalies by examining the correlation between the data sample and its service normal pattern, instead of solely focusing on the data sample itself; (ii) a dualistic convolution mechanism that amplifies short-term anomalies in the time domain and hinders the reconstruction of anomalies in the frequency domain, which enlarges the reconstruction error disparity between anomaly and normality and facilitates anomaly detection; (iii) leveraging the sparsity and parallelism of frequency domain to enhance model efficiency. We theoretically and experimentally prove that using a strategically selected subset of Fourier bases can not only reduce computational overhead but is also profitable to distinguish anomalies, compared to using the complete spectrum. Moreover, extensive experiments demonstrate MACE's effectiveness in handling diverse normal patterns with a unified model and it achieves state-of-the-art performance with high efficiency.
Enhancing Sentiment Analysis Results through Outlier Detection Optimization

When dealing with text data containing subjective labels like speaker emotions, inaccuracies or discrepancies among labelers are not uncommon. Such discrepancies can significantly affect the performance of machine learning algorithms. This study investigates the potential of identifying and addressing outliers in text data with subjective labels, aiming to enhance classification outcomes. We utilized the Deep SVDD algorithm, a one-class classification method, to detect outliers in nine text-based emotion and sentiment analysis datasets. By employing both a small-sized language model (DistilBERT base model with 66 million parameters) and non-deep learning machine learning algorithms (decision tree, KNN, Logistic Regression, and LDA) as the classifier, our findings suggest that the removal of outliers can lead to enhanced results in most cases. Additionally, as outliers in such datasets are not necessarily unlearnable, we experienced utilizing a large language model -- DeBERTa v3 large with 131 million parameters, which can capture very complex patterns in data. We continued to observe performance enhancements across multiple datasets.
An exact mathematical description of computation with transient spatiotemporal dynamics in a complex-valued neural network

We study a complex-valued neural network (cv-NN) with linear, time-delayed interactions. We report the cv-NN displays sophisticated spatiotemporal dynamics, including partially synchronized ``chimera'' states. We then use these spatiotemporal dynamics, in combination with a nonlinear readout, for computation. The cv-NN can instantiate dynamics-based logic gates, encode short-term memories, and mediate secure message passing through a combination of interactions and time delays. The computations in this system can be fully described in an exact, closed-form mathematical expression. Finally, using direct intracellular recordings of neurons in slices from neocortex, we demonstrate that computations in the cv-NN are decodable by living biological neurons. These results demonstrate that complex-valued linear systems can perform sophisticated computations, while also being exactly solvable. Taken together, these results open future avenues for design of highly adaptable, bio-hybrid computing systems that can interface seamlessly with other neural networks.
An Exploration of Left-Corner Transformations

The left-corner transformation (Rosenkrantz and Lewis, 1970) is used to remove left recursion from context-free grammars, which is an important step towards making the grammar parsable top-down with simple techniques. This paper generalizes prior left-corner transformations to support semiring-weighted production rules and to provide finer-grained control over which left corners may be moved. Our generalized left-corner transformation (GLCT) arose from unifying the left-corner transformation and speculation transformation (Eisner and Blatz, 2007), originally for logic programming. Our new transformation and speculation define equivalent weighted languages. Yet, their derivation trees are structurally different in an important way: GLCT replaces left recursion with right recursion, and speculation does not. We also provide several technical results regarding the formal relationships between the outputs of GLCT, speculation, and the original grammar. Lastly, we empirically investigate the efficiency of GLCT for left-recursion elimination from grammars of nine languages.
Rethinking Directional Integration in Neural Radiance Fields

Recent works use the Neural radiance field (NeRF) to perform multi-view 3D reconstruction, providing a significant leap in rendering photorealistic scenes. However, despite its efficacy, NeRF exhibits limited capability of learning view-dependent effects compared to light field rendering or image-based view synthesis. To that end, we introduce a modification to the NeRF rendering equation which is as simple as a few lines of code change for any NeRF variations, while greatly improving the rendering quality of view-dependent effects. By swapping the integration operator and the direction decoder network, we only integrate the positional features along the ray and move the directional terms out of the integration, resulting in a disentanglement of the view-dependent and independent components. The modified equation is equivalent to the classical volumetric rendering in ideal cases on object surfaces with Dirac densities. Furthermore, we prove that with the errors caused by network approximation and numerical integration, our rendering equation exhibits better convergence properties with lower error accumulations compared to the classical NeRF. We also show that the modified equation can be interpreted as light field rendering with learned ray embeddings. Experiments on different NeRF variations show consistent improvements in the quality of view-dependent effects with our simple modification.
Graph theoretic analysis of three-terminal quantum dot thermocouples: Onsager relations and spin-thermoelectric effects

We introduce a simplified model for a three-terminal quantum thermocouple consisting of two strongly-coupled quantum dots. To elucidate spin-dependent Seebeck and Peltier effects, we employ a microscopic Hamiltonian and map the Lindblad master equation onto a quantum transition network, capturing the key working principles for both reciprocal effects. Our analysis reveals quantum thermodynamic networks encompassing both Coulomb interaction and spin-flipping processes, lead to the emergence of spin-thermolectric effects. Using algebraic graph theory, we recover the phenomenological law of irreversible thermodynamics from the stochastic version of the entropy production rate expressed in terms of cycle flux and cycle forces. Remarkably, Onsager reciprocity and Kelvin relation for transport coefficients find their premises in the properties of cycle flux trajectories within the quantum transition network. This underscores the universal generality of thermodynamic principles across classical and quantum realms, despite their fundamentally different basis from classical laws of irreversible thermodynamics relying on local equilibrium assumptions.
Protein domain embeddings for fast and accurate similarity search

Recently developed protein language models have enabled a variety of applications with the protein contextual embeddings they produce. Per-protein representations (each protein is represented as a vector of fixed dimension) can be derived via averaging the embeddings of individual residues, or applying matrix transformation techniques such as the discrete cosine transformation to matrices of residue embeddings. Such protein-level embeddings have been applied to enable fast searches of similar proteins, however limitations have been found; for example, PROST is good at detecting global homologs but not local homologs, and knnProtT5 excels for proteins of single domains but not multi-domain proteins. Here we propose a novel approach that first segments proteins into domains (or subdomains) and then applies the discrete cosine transformation to the vectorized embeddings of residues in each domain to infer domain-level contextual vectors. Our approach, called DCTdomain, utilizes predicted contact maps from ESM-2 for domain segmentation, which is formulated as a domain segmentation problem and can be solved using a recursive cut algorithm (RecCut in short) in quadratic time to the protein length; for comparison, an existing approach for domain segmentation uses a cubic-time algorithm. We showed such domain-level contextual vectors (termed as DCT fingerprints) enable fast and accurate detection of similarity between proteins that share global similarities but with undefined extended regions between shared domains, and those that only share local similarities.
Development of a Next Generation SNP Genotyping Array for Wheat

High throughput genotyping arrays have provided a cost effective, reliable and interoperable system for genotyping hexaploid wheat and its related germplasm pool. Existing, highly cited arrays including our 35K Axiom Wheat Breeder’s genotyping array and the Illumina 90K iSelect array were designed based on a limited amount of varietal sequence diversity and with imperfect knowledge of SNP positions. Recent progress in sequencing wheat varieties and landraces has given us access to a vast pool of SNP diversity, whilst technological improvements in array design has allowed us to fit significantly more probes onto a 384-well format Axiom array than was previously possible. Here we describe a novel High Density Axiom genotyping array, the Triticum aestivum Next Generation array (TaNG), largely derived from whole genome skim sequencing of 204 elite wheat lines and 111 wheat landraces taken from the Watkins “Core Collection”. We use a novel “minimal marker” optimisation approach to select up to six SNPs in each 1.5 MB region of the wheat genome with the highest combined varietal discrimination potential. A design iteration step allowed us to test and replace skim-sequence derived SNPs which failed to convert to reliable Axiom markers, resulting in a final design, designated TaNG1.1 with 43,372 SNPs derived from a haplotype-optimised combination of novel SNPs, DArTAG-derived and legacy wheat Axiom markers. We show that this design has an even distribution of SNPs across chromosomes and sub-genomes compared to previous arrays and can be used to generate genetic maps with a significantly higher number of distinct bins than our previous Axiom array. We also demonstrate the improved performance of TaNG1.1 for Genome Wide Association Studies (GWAS) and its utility for Copy Number Variation (CNV) analysis. The array is commercially available, and the marker annotations, initial genotyping results and software used to generate the optimised marker sets are freely available.