While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis. We introduce a representation of stabilizer codes as graphs with certain structures, and prove via the ZX calculus that this representation is related to stabilizer tableaus by an efficiently computable bijection. This gives a new universal recipe for code construction by way of finding graphs with nice properties. The graph representation gives insight into both code construction and algorithms. We construct as examples families of ⟦ n , Θ ( n log  n ) , Θ ( log  n ) ⟧ and ⟦ n , Ω ( n 4 / 5 ) , Θ ( n 1 / 5 ) ⟧ codes. We use graphs in a probabilistic analysis to extend the quantum Gilbert-Varshamov bound into a three-way distance-rate-weight trade-off. Moreover, code properties such as distance and encoding circuit depth are bounded by simple functions of the graph degree. We prove that key coding algorithms—distance approximation, minimum-weight generator selection, and decoding—are unified as instances of one optimization game on a graph. By studying this game, we construct an efficient greedy decoder and prove that it corrects all recoverable errors for all graphs with cycle lengths no shorter than 13 (reducible to 5 with mild extra constraints); these include the above two families. Our results suggest that graphs are generically useful for the study of stabilizer codes.

Foreground-aware Universe Graph Matching for Domain Adaptive Object Detection.

Graphs are the primary means of describing the relation between individuals in society, and have been extensively used for analysing various types of networks, such as social networks, biological networks, and electric networks. Many practical problems can be abstracted to graph problems, and cannot be solved efficiently due to their NP-hard nature. DNA computing, leveraging the vast parallelism and high-density storage of DNA molecules, provides a new way for solving intractable problems. However, existing DNA computing models are limited by single computing function. This paper proposed a novel DNA computing model with two DNA modules-a graph representation module (GRM) and a detection module (DM)-that can solve a variety of NP-hard problems. To show the feasibility of the proposed model, we conducted simulation and biochemical experiments on multiple NP-hard problems, such as the minimum dominating set, maximum independent set, and minimum vertex cover. Experimental results showed that the GRM is a universal graph representation module, based on which multiple graph problems can be solved by cascading a proper designed detection module. Our method also highlighted the potential for DNA strand displacement to act as a computation tool to solve intractable graph problems.

We initiate the focused study of constant-cost randomized communication, with emphasis on its connection to graph representations. We observe that constant-cost randomized communication problems are equivalent to hereditary (i.e. closed under taking induced subgraphs) graph classes which admit constant-size adjacency sketches and probabilistic universal graphs (PUGs), which are randomized versions of the well-studied adjacency labeling schemes and induced-universal graphs. This gives a new perspective on long-standing questions about the existence of these objects, including new methods of constructing adjacency labeling schemes. We ask three main questions about constant-cost communication, or equivalently, constant-size PUGs: (1) Are there any natural, non-trivial problems aside from Equality and k-Hamming Distance which have constant-cost communication? We provide a number of new examples, including deciding whether two vertices have path-distance at most k in a planar graph, and showing that constant-size PUGs are preserved by the Cartesian product operation. (2) What structures of a problem explain the existence or non-existence of a constant-cost protocol? We show that in many cases a Greater-Than subproblem is such a structure. (3) Is the Equality problem complete for constant-cost randomized communication? We show that it is not: there are constant-cost problems which do not reduce to Equality.81 pages. This is the TheoretiCS journal version

Conformational transitions are central to protein function, yet their mechanistic analysis remains challenging due to the multi-dimensionality and timescales underlying the molecular motions. While interpretable network models such as Bayesian networks have advanced the identification of key residue interactions in molecular dynamics (MD) data, they lack temporal resolution and cannot capture the sequence of events during transitions. Here, we introduce Dynamically Resolved Universal Model for BayEsiAn network Tracking or DRUMBEAT, a machine learning approach that combines a universal graph topology with sliding-window rescoring to generate interpretable, time-resolved maps of cooperative events in MD trajectories. Applying DRUMBEAT to the benchmark Fip35 WW domain folding trajectories from DE Shaw Research Group, we recover both major folding pathways and critical residues previously highlighted by experiment. Importantly, DRUMBEAT provides new insight in two ways: (1) uncover unknown protein features important for transition, and (2) dissect the order and timing of conformational changes, revealing the precise sequence of residue contact closures during individual folding events. Robustness analysis demonstrates that both the universal graph and time-resolved results are highly consistent across multiple sampling replicates. These findings establish DRUMBEAT as a scalable and interpretable machine learning framework for dissecting the dynamics of protein folding and other conformational transitions, offering a generalizable tool for the mechanistic study of biomolecular dynamics.

Clipping in linear planetary gears is considered, as a result of which the contact of teeth and teeth is disrupted in the section of the active profile of the satellite. The conditions for the occurrence of clipping are determined, and a universal graph (analogous to the blocking contour for an involute transmission) is shown, which shows the presence or absence of clipping. Keywords mechanism of motion transformation, planetary gear, cycloidal gear, clipping mkpandurov@gmail.com

The screening and discovery of magnetic materials are hindered by the computational cost of first-principles density-functional theory (DFT) calculations required to find the ground state magnetic ordering. Although universal machine-learning interatomic potentials (uMLIPs), also known as atomistic foundation models, offer high-fidelity models of many atomistic systems with significant speedup, they currently lack the inputs required for predicting magnetic ordering. In this work, we present a data-efficient, spin-informed graph neural network framework that incorporates spin degrees of freedom as inputs and preserves physical symmetries, extending the functionality of uMLIPs to simulate magnetic orderings. This framework speeds up DFT calculations through better initial guesses for magnetic moments, determines the ground-state ordering of bulk materials and even generalizes to magnetic ordering in surfaces. Furthermore, we implement a closed-loop anomaly detection approach that effectively addresses the classic "chicken-and-egg" problem of creating a high-quality dataset while developing a uMLIP, unearthing anomalies in large benchmark datasets and boosting model accuracy.

Abstract The electron density is a fundamental observable of an atomic system from which all ground-state properties can be computed. As a prediction target for machine learning (ML) models, electron density is often represented on a dense real space grid, which is data heavy, or through density fitting approximations. In this work, we show the power of targeting the density matrix (DM), a linear-scaling sparse SE(3) equivariant matrix that encodes the exact density. We introduce Graph2Mat, a universal function for converting molecular graphs into equivariant matrices. We demonstrate how a ML model that combines this Graph2Mat approach with state-of-the-art molecular graph representations can accurately predict the DM of molecular systems. The models achieve state-of-the-art performance on electron density prediction by matching the accuracy of grid-based methods, while using datasets that are at least one order of magnitude smaller. Accurately predicted electron densities can also accelerate density functional theory (DFT) calculations by reducing the number of self-consistent field (SCF) iterations needed to converge. In this work, we get an average 40% reduction on the number of SCF steps in DFT calculations of QM9 molecules with SIESTA. The novel prediction model also allows for two new and promising measures of uncertainty (total charge error and self-consistency error) that will facilitate its practical usage, e.g. within active learning workflows. These results open the door for many applications using hybrid ML-accelerated DFT methodologies, and uncertainty aware single iteration ab initio molecular dynamics.

This paper is concerned with games of infinite duration played over potentially infinite graphs. Recently, Ohlmann (LICS 2022) presented a characterisation of objectives admitting optimal positional strategies, by means of universal graphs: an objective is positional if and only if it admits well-ordered monotone universal graphs. We extend Ohlmann's characterisation to encompass (finite or infinite) memory upper bounds. We prove that objectives admitting optimal strategies with $\varepsilon$-memory less than $m$ (a memory that cannot be updated when reading an $\varepsilon$-edge) are exactly those which admit well-founded monotone universal graphs whose antichains have size bounded by $m$. We also give a characterisation of chromatic memory by means of appropriate universal structures. Our results apply to finite as well as infinite memory bounds (for instance, to objectives with finite but unbounded memory, or with countable memory strategies). We illustrate the applicability of our framework by carrying out a few case studies, we provide examples witnessing limitations of our approach, and we discuss general closure properties which follow from our results.

A note on universal graphs for spanning trees

Detecting Defects in Multicomponent Software Using a Set of Universal Graph Representations of the Code

Molecular representation learning has remarkably accelerated the development of drug analysis and discovery. It implements machine learning methods to encode molecule embeddings for diverse downstream drug-related tasks. Due to the scarcity of labeled molecular data, self-supervised molecular pre-training is promising as it can handle large-scale unlabeled molecular data to prompt representation learning. Although many universal graph pre-training methods have been successfully introduced into molecular learning, there still exist some limitations. Many graph augmentation methods, such as atom deletion and bond perturbation, tend to destroy the intrinsic properties and connections of molecules. In addition, identifying subgraphs that are important to specific chemical properties is also challenging for molecular learning. To address these limitations, we propose the self-supervised Molecular Graph Information Bottleneck (MGIB) model for molecular pre-training. MGIB observes molecular graphs from the atom view and the motif view, deploys a learnable graph compression process to extract the core subgraphs, and extends the graph information bottleneck into the self-supervised molecular pre-training framework. Model analysis validates the contribution of the self-supervised graph information bottleneck and illustrates the interpretability of MGIB through the extracted subgraphs. Extensive experiments involving molecular property prediction, including 7 binary classification tasks and 6 regression tasks demonstrate the effectiveness and superiority of our proposed MGIB.

Understanding the mechanical properties of silicon oxynitride (a-SiON), a key insulating material, is vital for electronic device design and reliability. Though the effects of fabrication conditions on a-SiON have been studied, the underlying relationship between its atomic-scale structure and mechanical properties remains unclear. This study investigates the relationship between elasticity and atomic-scale structures in a-SiON by molecular dynamics simulations with a universal graph neural network interatomic potential. The bulk modulus increases from 49 to 150 GPa with higher N content. N atoms form N2 molecules under O-rich conditions, hindering bulk modulus increase, and form an Si3N4-like network under O-poor conditions, enhancing bulk modulus. Formation energy calculations indicate N2 formation is preferable under O-rich conditions. Meanwhile, under O-poor conditions, Si–N bond formation is preferable, which reinforces a-SiON by increasing bond density. The findings suggest realizing O-poor conditions is crucial for highly elastic insulating films.

Abstract Let be any wheel graph and the class of all countable graphs not containing as a minor. We show that there exists a graph in which contains every graph in as an induced subgraph.

Abstract Intelligent metasurfaces, as the next‐generation of metasurfaces, have emerged as a versatile artificial electromagnetic (EM) medium capable of adaptively manipulating wave‐matter interactions, especially in the construction of EM space integration and the analogy of wave‐based neural networks. However, current computational landscape for intelligent metasurfaces relies either on time‐consuming full‐wave numerical simulations with excessive computational complexity or on application‐limited physical models that are difficult to consider the coupling effects. Here, a universal graph neural network (GNN) framework is introduced, incorporating the elusive coupling effects inside metasurfaces, enabling rapid and precise characterization with arbitrary‐large size. This framework exhibits exceptional compatibility with physical models, thereby significantly expanding the realm of potential design scenarios. By harnessing the principles of diffraction theory and near‐to‐far transformation algorithms, highly accurate modeling of the scattered fields emanating from metasurfaces is achieved. Through microwave experiments on intelligent metasurfaces, the efficacy of GNN in real‐world scenarios is effectively demonstrated. The utilization of topological strategies to characterize intelligent metasurfaces marks a major leap toward the next‐generation metasurfaces, promising transformative advancements across various applications.

Due to the vast chemical space, discovering materials with a specific function is challenging. Chemical formulas are obligated to conform to a set of exacting criteria, such as charge neutrality, balanced electronegativity, synthesizability, and mechanical stability. In response to this formidable task, we introduce a deep-learning-based generative model for material composition and structure design by learning and exploiting explicit and implicit chemical knowledge. Our pipeline first uses deep diffusion language models as the generator of compositions and then applies a template-based crystal structure prediction algorithm to predict their corresponding structures, which is then followed by structure relaxation using a universal graph neural network-based potential. Density functional theory (DFT) calculations of the formation energies and energy-above-the-hull analysis are used to validate new structures generated through our pipeline. Based on the DFT calculation results, six new materials, including Ti2HfO5, TaNbP, YMoN2, TaReO4, HfTiO2, and HfMnO2, with formation energy less than zero have been found. Remarkably, among these, four materials, namely, Ti2HfO5, TaNbP, YMoN2, and TaReO4, exhibit an e-above-hull energy of less than 0.3 eV. These findings have proved the effectiveness of our approach.

Posets of copies of countable ultrahomogeneous tournaments

This work is devoted to the algebraic theory of automata, which is one of the branches of mathematical cybernetics, which studies information transformation devices that arise in many applied problems. Depending on a specific problem, automata are considered, in which the main sets are equipped with additional mathematical structures consistent with the functions of an automaton. In this work, we study automata over graphs — graphic automata, that is, automata in which the set of states and the set of output signals are equipped with the mathematical structure of graphs. For graphs 𝐺 and 𝐻 universal graphic automaton Atm(𝐺,𝐻) is a universally attracting object in the category of semigroup automata. The input signalsemigroup of such automaton is 𝑆 = End 𝐺×Hom(𝐺,𝐻). Naturally, interest arises in studying the question of abstract characterization of universal graph automata: under what conditions will the abstract automaton 𝐴 be isomorphic to the universal graph automaton Atm(𝐺,𝐻) over graphs 𝐺 from the class K_1, 𝐻 from class K_2? The purpose of the work is to study the issue of elementary axiomatization of some classes of graphic automata. The impossibility of elementaryaxiomatization by means of the language of restricted predicate calculus of some wide classes of such automata over reflexive graphs is proved.

Metal organic frameworks (MOFs) are crystalline, three-dimensional structures with high surface areas and tunable porosities. Made from metal nodes connected by organic linkers, the exact properties of a given MOF are determined by node and linker choice. MOFs hold promise for numerous applications, including gas capture and storage. M2(4,4'-dioxidobiphenyl-3,3'-dicarboxylate)-henceforth simply M2(dobpdc), with M = Mg, Mn, Fe, Co, Ni, Cu, or Zn-is regarded as one of the most promising structures for CO2 capture applications. Further modification of the MOF with diamines or tetramines can significantly boost gas species selectivity, a necessity for the ultra-dilute CO2 concentrations in the direct-air capture of CO2. There are countless potential diamines and tetramines, paving the way for a vast number of potential sorbents to be probed for CO2 adsorption properties. The number of amines and their configuration in the MOF pore are key drivers of CO2 adsorption capacity and kinetics, and so a validation of computational prediction of these quantities is required to suitably use computational methods in the discovery and screening of amine-functionalized sorbents. In this work, we study the predictive accuracy of density functional theory and related calculations on amine loading and configuration for one diamine and two tetramines. In particular, we explore the Perdew-Burke-Ernzerhof (PBE) functional and its formulation for solids (PBEsol) with and without the Grimme-D2 and Grimme-D3 pairwise corrections (PBE+D2/3 and PBEsol+D2/3), two revised PBE functionals with the Grimme-D2 and Grimme-D3 pairwise corrections (RPBE+D2/3 and revPBE+D2/3), and the nonlocal van der Waals correlation (vdW-DF2) functional. We also investigate a universal graph deep learning interatomic potential's (M3GNet) predictive accuracy for loading and configuration. These results allow us to identify a useful screening procedure for configuration prediction that has a coarse component for quick evaluation and a higher accuracy component for detailed analysis. Our general observation is that the neural network-based potential can be used as a high-level and rapid screening tool, whereas PBEsol+D3 gives a completely qualitatively predictive picture across all systems studied, and can thus be used for high accuracy motif predictions. We close by briefly exploring the predictions of relative thermal stability for the different functionals and dispersion corrections.

The past few years has witnessed the dominance of Graph Convolutional Networks (GCNs) over human motion prediction. Various styles of graph convolutions have been proposed, with each one meticulously designed and incorporated into a carefully-crafted network architecture. This paper breaks the limits of existing knowledge by proposing Universal Graph Convolution (UniGC), a novel graph convolution concept that re-conceptualizes different graph convolutions as its special cases. Leveraging UniGC on network-level, we propose GCNext, a novel GCN-building paradigm that dynamically determines the best-fitting graph convolutions both sample-wise and layer-wise. GCNext offers multiple use cases, including training a new GCN from scratch or refining a preexisting GCN. Experiments on Human3.6M, AMASS, and 3DPW datasets show that, by incorporating unique module-to-network designs, GCNext yields up to 9x lower computational cost than existing GCN methods, on top of achieving state-of-the-art performance. Our code is available at https://github.com/BradleyWang0416/GCNext.