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1. Chemical master equation parameter exploration using DMRG

   https://doi.org/10.1063/5.0276591  

   Zima, John P; Nicholson, Schuyler B; Gingrich, Todd R (August 2025, The Journal of Chemical Physics)

   Well-mixed chemical reaction networks (CRNs) contain many distinct chemical species with copy numbers that fluctuate in correlated ways. While those correlations are typically monitored via Monte Carlo sampling of stochastic trajectories, there is interest in systematically approximating the joint distribution over the exponentially large number of possible microstates using tensor networks or tensor trains. We exploit the tensor network strategy to determine when the steady state of a seven-species gene toggle switch CRN model supports bistability as a function of two decomposition rates, both parameters of the kinetic model. We highlight how the tensor network solution captures the effects of stochastic fluctuations, going beyond mean field and indeed deviating meaningfully from a mean-field analysis. The work furthermore develops and demonstrates several technical advances that will allow steady-states of broad classes of CRNs to be computed in a manner conducive to parameter exploration. We show that the steady-state distributions can be computed via the ordinary density matrix renormalization group (DMRG) algorithm, despite having a non-Hermitian rate operator with a small spectral gap, we illustrate how that steady-state distribution can be efficiently projected to an order parameter that identifies bimodality, and we employ excited-state DMRG to calculate a relaxation timescale for the bistability. 

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2. Complexity of Mesoscale Eddy Diffusivity in the Ocean

   https://doi.org/10.1029/2020GL091719  

   Kamenkovich, Igor; Berloff, Pavel; Haigh, Michael; Sun, Luolin; Lu, Yueyang (March 2021, Geophysical Research Letters)

   Abstract Stirring of water by mesoscale currents (“eddies”) leads to large‐scale transport of many important oceanic properties (“tracers”). These eddy‐induced transports can be related to the large‐scale tracer gradients, using the concept of turbulent diffusion. The concept is widely used to describe these transports in the real ocean and to represent them in climate models. This study focuses on the inherent complexity of the corresponding coefficient tensor (“K‐tensor”) and its components, defined here in all its spatio‐temporal complexity. Results demonstrate that this comprehensiveK‐tensor is space‐, time‐, direction‐ and tracer‐dependent. Using numerical simulations with both idealized and comprehensive models of the Atlantic circulation, we show that these properties lead to upgradient eddy fluxes and the potential importance of all tensor components. The uncovered complexity of the eddy transports calls for reconsideration of how they are estimated in practice, included in the general circulation models and theoretically interpreted. 

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3. Doping asymmetry in the three-band Hamiltonian for cuprate ladders: Failure of the standard model of superconductivity in cuprates

   https://doi.org/10.1103/PhysRevB.107.L241108  

   Song, Jeong-Pil; Mazumdar, Sumit; Clay, R. Torsten (June 2023, Physical Review B)

   Stephen E. Nagler (Ed.)

   The relevance of the single-band two-dimensional Hubbard model to superconductivity in the doped cuprates has recently been questioned, based on density matrix renormalization group (DMRG) computations that found superconductivity over an unrealistically broad doping region upon electron-doping, yet a complete absence of superconductivity for hole-doping. We report very similar results from DMRG calculations on a Cu2O3 twoleg ladder within the parent three-band correlated-electron Hamiltonian. The strong asymmetry found in our calculations are in contradiction to the deep and profound symmetry in the experimental phase diagrams of electron- and hole-doped cuprate superconductors, as seen from the occurrence of quantum critical points within the superconducting domes in both cases that are characterized by Fermi surface reconstruction, large jumps in carrier density, and strange metal behavior. 

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4. A Conceptual Framework for Investigating and Mitigating Machine-Learning Measurement Bias (MLMB) in Psychological Assessment

   https://doi.org/10.1177/25152459211061337  

   Tay, Louis; Woo, Sang Eun; Hickman, Louis; Booth, Brandon M.; D’Mello, Sidney (January 2022, Advances in Methods and Practices in Psychological Science)

   Given significant concerns about fairness and bias in the use of artificial intelligence (AI) and machine learning (ML) for psychological assessment, we provide a conceptual framework for investigating and mitigating machine-learning measurement bias (MLMB) from a psychometric perspective. MLMB is defined as differential functioning of the trained ML model between subgroups. MLMB manifests empirically when a trained ML model produces different predicted score levels for different subgroups (e.g., race, gender) despite them having the same ground-truth levels for the underlying construct of interest (e.g., personality) and/or when the model yields differential predictive accuracies across the subgroups. Because the development of ML models involves both data and algorithms, both biased data and algorithm-training bias are potential sources of MLMB. Data bias can occur in the form of nonequivalence between subgroups in the ground truth, platform-based construct, behavioral expression, and/or feature computing. Algorithm-training bias can occur when algorithms are developed with nonequivalence in the relation between extracted features and ground truth (i.e., algorithm features are differentially used, weighted, or transformed between subgroups). We explain how these potential sources of bias may manifest during ML model development and share initial ideas for mitigating them, including recognizing that new statistical and algorithmic procedures need to be developed. We also discuss how this framework clarifies MLMB but does not reduce the complexity of the issue. 

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5. Dynamic Graph Convolutional Networks Using the Tensor M-Product

   https://doi.org/10.1137/1.9781611976700  

   Malik, O. A.; Ubaru, S.; Horesh, L.; Kilmer, M. E.; Avron, H. (January 2021, Proceedings of the 2021 SIAM International Conference on Data Mining (SDM))

   Demeniconi, C.; Davidson, I (Ed.)

   Many irregular domains such as social networks, financial transactions, neuron connections, and natural language constructs are represented using graph structures. In recent years, a variety of graph neural networks (GNNs) have been successfully applied for representation learning and prediction on such graphs. In many of the real-world applications, the underlying graph changes over time, however, most of the existing GNNs are inadequate for handling such dynamic graphs. In this paper we propose a novel technique for learning embeddings of dynamic graphs using a tensor algebra framework. Our method extends the popular graph convolutional network (GCN) for learning representations of dynamic graphs using the recently proposed tensor M-product technique. Theoretical results presented establish a connection between the proposed tensor approach and spectral convolution of tensors. The proposed method TM-GCN is consistent with the Message Passing Neural Network (MPNN) framework, accounting for both spatial and temporal message passing. Numerical experiments on real-world datasets demonstrate the performance of the proposed method for edge classification and link prediction tasks on dynamic graphs. We also consider an application related to the COVID-19 pandemic, and show how our method can be used for early detection of infected individuals from contact tracing data. 

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