Tilo Wettig

A bstract: We introduce the order-separated Grassmann higher-order tensor renormalization group (OS-GHOTRG) method for QCD with staggered quarks in the strong-coupling expansion. The method allows us to determine the expansion coefficients of the partition function, from which we can obtain the strong-coupling expansions of thermodynamical observables. We use the method in two dimensions to compute the free energy, the particle-number density, and the chiral condensate as a function of the chemical potential up to third order in the inverse coupling β . Although near the phase transition the expansion is only a good approximation to the full theory at small β , we show that the range of applicability can be greatly extended by fits to judiciously chosen transition functions.

Motivation: Cancer progresses through the accumulation of genomic events. Cancer progression models such as Mutual Hazard Networks (MHNs) describe this dynamic, enabling prediction of temporal event positions and patient-specific risks of acquiring mutations. However, current MHN analyses rely on single most likely models and do not quantify the uncertainty inherent to parameter estimation. Assessing forecast stability is essential before using them to anticipate treatment-relevant mutations, adapt targeted therapies, or prioritize monitoring of patients at elevated progression risk. Results: We address a key prerequisite for the responsible clinical use of cancer progression models by making MHN-derived predictions uncertainty-aware. We present a Bayesian framework for MHN that uses Markov Chain Monte Carlo to sample from the posterior distributions of model parameters and derived predictions. For practical use we implemented the Random-Walk Metropolis, Metropolis-Adjusted Langevin Algorithm (MALA), and simplified manifold MALA samplers as part of the existing mhn Python package. Only MALA and smMALA were successful in sampling from MHN posteriors, with MALA performing best. While most MHN parameters and predictions showed low posterior variance, a small subset displayed greater variability across the posterior distribution. This differentiation cannot be obtained from a single most likely model, emphasizing the need for uncertainty quantification, especially in clinical contexts. As an illustrative example, posterior sampling identified a subgroup of STK11$-$, KRAS$+$ lung adenocarcinoma patients with a high predicted short-term risk—with low variance across posterior samples—to develop an STK11 mutation. This subgroup exhibited poorer survival under immunotherapy, resembling patterns observed in STK11+ patients. Availability and implementation: Our implementation is part of version 1.2.0 of the mhn package (https://github.com/spang-lab/LearnMHN). All analyses including the code to produce all figures in this article can be found under https://github.com/huy29433/MCMC-sampling-for-MHN (https://doi.org/10.5281/zenodo.21160219).

Motivation: Cancer progression is driven by the stochastic accumulation of interacting genetic alterations, and tumors from different tissues can share common evolutionary patterns despite distinct anatomical origins. While simplified progression models can be applied at scale, the use of expressive models that capture complex inter-event dependencies remains challenging in pan-cancer settings due to their computational demands. Results: We present fastMHN, a scalable approximation to Mutual Hazard Network-based cancer progression models, that enables pan-cancer analysis of large genomic datasets with the explicit aim of enabling transfer of progression mechanisms across tumor entities. Applying fastMHN to a large clinical cohort, we identify a tumor-progression group spanning multiple tissues that is characterized by a link between STK11 mutations and poor patient survival. While the clinical relevance of STK11 mutations is well established in non-small cell lung cancer, our results suggest that a similar progression mechanism is present in molecularly defined subgroups of other cancer types. These findings illustrate how scalable pan-cancer progression modeling can facilitate cross-entity transfer of biological and potentially clinical insights. Availability and implementation: The pan-cancer classification workflow and all data are available at github.com/simon-pfahler/fastMHN-classification .

We demonstrate that gauge-equivariant pooling and unpooling layers can perform as well as traditional restriction and prolongation layers in multigrid preconditioner models for lattice QCD. These layers introduce a gauge degree of freedom on the coarse grid, allowing for the use of explicitly gauge-equivariant layers on the coarse grid. We investigate the construction of coarse-grid gauge fields and study their efficiency in the preconditioner model. We show that a combined multigrid neural network using a Galerkin construction for the coarse-grid gauge field eliminates critical slowing down. Published by the American Physical Society 2024

Workflow management has become an important topic in many research communities. Here, we focus on the particular aspect of provenance tracking. We follow the W3C PROV standard and formulate a provenance model for Lattice QCD that includes the ensemble-generation and measurement parts of the Lattice QCD workflow. Since many important provenance questions in our community require extensions of this model, we propose a multi-layered provenance approach that combines prospective and retrospective elements.

We show how multigrid preconditioners for the Wilson-clover Dirac operator can be constructed using gauge-equivariant neural networks. For the multigrid solve we employ parallel-transport convolution layers. For the multigrid setup we consider two versions: the standard construction based on the near-null space of the operator and a gauge-equivariant construction using pooling and subsampling layers. We show that both versions eliminate critical slowing down. We also show that transfer learning works and that our approach allows for communication-avoiding algorithms on large machines. In the outlook we discuss how the multigrid setup can be accelerated using gauge-invariant properties of the gauge field.

We demonstrate that a state-of-the-art multigrid preconditioner can be learned efficiently by gauge-equivariant neural networks. We show that the models require minimal retraining on different gauge configurations of the same gauge ensemble and to a large extent remain efficient under modest modifications of ensemble parameters. We also demonstrate that important paradigms such as communication avoidance are straightforward to implement in this framework.