We present a tensor-network formulation for the strong-coupling expansion of QCD with staggered quarks at nonzero chemical potential, for arbitrary number of dimensions, colors, and flavors. We integrate out the gauge and quark degrees of freedom and rewrite the partition function as the complete trace of a tensor network. This network consists of local tensors that contain a numerical and a Grassmann part. We truncate the initial tensor at a fixed order in the inverse coupling beta and compute analytical results for the partition function, the free energy, and the chiral condensate on a 2 & times; 2 lattice up to order beta 4. In a follow-up paper we will introduce an enhanced tensor-network method, order-separated GHOTRG, to explicitly compute the expansion coefficients of the partition function for larger lattices. To demonstrate its potential, first results obtained with this new method are already presented here.

Abstract Multiple sclerosis (MS) is a progressive neuroinflammatory demyelinating disease of the central nervous system (CNS) that remains incurable. Autoreactive myelin-specific T cells contribute to immunopathology by directly targeting and damaging oligodendrocytes in situ . In oligodendrocytes, several immune-modulatory functions have been described that can ameliorate immune damage. However, a systematic discovery of cell-intrinsic mechanisms that protect oligodendrocytes against T cell-derived cytotoxic mechanisms has not been performed. We used human MO3.13 oligodendrocytic cells and human antigen-specific cytotoxic T cells to conduct a high-throughput (HTP) RNAi-based screen with altogether 4155 genes to identify oligodendrocyte-intrinsic immune resistance genes (IRGs). The screen revealed 133 candidate IRGs. Among them, we validated 32, which exerted a strong immuno-protective phenotype. We studied IRG expression landscapes in human brain cell subsets from postmortem brain tissues of MS and control individuals. This revealed clustered expression of IRGs in a cell-type and oligodendrocyte subset-specific manner and differential IRG expression between MS patients and controls in distinct oligodendrocyte subclusters. ChEA3 analysis revealed cell type-specific expression of transcription factors that can drive expression of respective IRGs. Explorative molecular mode of action analyses of five selected IRGs, STK11 , KCNH8 , ABCA2 , SLC1A3 and CHRNA1 revealed that these prevented death receptor-mediated apoptosis induced by T cell-derived cytotoxic molecules. In particular, they controlled TRAIL-induced apoptosis by suppressing JNK1 activation through interfering with several upstream pathways regulating metabolic, potassium, cholesterol, glutamate and acetylcholine homeostasis. In addition, STK11, ABCA2, and CHRNA1 regulated TRAIL-R2 surface expression contributing to increased TRAIL-sensitivity whereas KCNH8 expression in oligodendrocytes inhibited secretion of inflammatory cytokines by cytotoxic T cells. Taken together, we here demonstrate the existence of multiple co-expressed IRGs in human oligodendrocytes that regulate multifaceted mechanisms of T cell resistance and are dysregulated in oligodendrocyte subsets of MS patients.

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.

We present a tensor-network approach for the strong-coupling expansion of two-dimensional QCD with staggered quarks at non-zero chemical potential. After expanding the Boltzmann factor in the gauge and fermion actions, all gauge fields can be integrated out exactly and the partition function can be evaluated using the Grassmann higher-order tensor renormalization group approach. The method is modified to compute the μ dependence of the quark number density and the chiral condensate up to order β^3 with complete absence of higher-order terms infiltrating the result. Although the expansion itself is only a good approximation to the full theory at small β<0.1, the range can be extended, by using judiciously chosen fits. Moreover, these fits also yield a valuable expansion in β for the critical chemical potential.

We propose SpaCeNet as a method for analyzing patterns of correlation in spatial transcriptomics data. SpaCeNet extends the concept of conditional independence to spatially distributed information, and disentangles conditional independence relations between inter- and intra-cellular variables. Moreover, SpaCeNet addresses the various length scales over which intercellular communication occurs via flexible interaction potentials in combination with appropriate regularization strategies.

Advances in omics technologies have allowed spatially resolved molecular profiling of single cells, providing a window not only into the diversity and distribution of cell types within a tissue, but also into the effects of interactions between cells in shaping the transcriptional landscape. Cells send chemical and mechanical signals which are received by other cells, where they can subsequently initiate context-specific gene regulatory responses. These interactions and their responses shape the individual molecular phenotype of a cell in a given microenvironment. RNAs or proteins measured in individual cells, together with the cells' spatial distribution, provide invaluable information about these mechanisms and the regulation of genes beyond processes occurring independently in each individual cell. "SpaCeNet" is a method designed to elucidate both the intracellular molecular networks (how molecular variables affect each other within the cell) and the intercellular molecular networks (how cells affect molecular variables in their neighbors). This is achieved by estimating conditional independence (CI) relations between captured variables within individual cells and by disentangling these from CI relations between variables of different cells.

IL-32 expression is important for pathogen clearance but detrimental in chronic inflammation, autoimmunity, and cancer. T cells are major IL-32 producers in these diseases and key mediators of pathogen and tumor elimination but also autoimmune destruction. However, their contribution to IL-32 biology during immune responses is hardly understood due to several isoforms with divergent inflammatory properties. Here, we identified IL-32β as the predominant isoform in various T cell subsets of healthy individuals and breast cancer patients with the highest levels detected in intratumoral regulatory T cells. We show that IL-32β is induced by IL-2 but IL-32β release requires T Cell Receptor rather than IL2R stimulation. Using inhibitors of protein secretion pathways and serial (ultra)centrifugation of T cell supernatants, we demonstrate that T cells actively secrete IL-32β unconventionally, as a free protein and, to a minor degree, through exosomes. Thus, our data identify activated T cells as major IL-32β secretors in health and cancer.

Abstract Immunological diseases are typically heterogeneous in clinical presentation, severity and response to therapy. Biomarkers of immune diseases often reflect this variability, especially compared to their regulated behaviour in health. This leads to a common difficulty that frustrates biomarker discovery and interpretation – namely, unequal dispersion of immune disease biomarker expression between patient classes necessarily limits a biomarker’s informative range. To solve this problem, we introduce dataset restriction, a procedure that splits datasets into classifiable and unclassifiable samples. Applied to synthetic flow cytometry data, restriction identifies biomarkers that are otherwise disregarded. In advanced melanoma, restriction finds biomarkers of immune-related adverse event risk after immunotherapy and enables us to build multivariate models that accurately predict immunotherapy-related hepatitis. Hence, dataset restriction augments discovery of immune disease biomarkers, increases predictive certainty for classifiable samples and improves multivariate models incorporating biomarkers with a limited informative range. This principle can be directly extended to any classification task.

The tensor renormalization group is a promising numerical method used to study lattice statistical field theories. However, this approach is computationally expensive in 2+1 and 3+1 dimensions. Here we use tensor renormalization group methods to study an effective three-dimensional $\mathbb{Z}_{3}$ model for the heavy-quark, high-temperature, strong-coupling limit of single-flavor 3+1 dimensional quantum chromodynamics. Our results are cross-checked using the worm Monte Carlo algorithm. We present the phase diagram of the model through the measurement of the Polyakov loop, the nearest-neighbor Polyakov loop correlator, and their susceptibilities. The tensor renormalization group results are in good agreement with the literature

The higher-order tensor renormalization group is a tensor-network method providing estimates for the partition function and thermodynamical observables of classical and quantum systems in thermal equilibrium. At every step of the iterative blocking procedure, the coarse-grid tensor is truncated to keep the tensor dimension under control. For a consistent tensor blocking procedure, it is crucial that the forward and backward tensor modes are projected on the same lower-dimensional subspaces. In this paper we present two methods, the SuperQ and the iterative SuperQ method, to construct tensor truncations that reduce or even minimize the local approximation errors, while satisfying this constraint.

We present a tensor-network approach for two-dimensional strong-coupling QCD with staggered quarks at nonzero chemical potential. After integrating out the gauge fields at infinite coupling, the partition function can be written as a full contraction of a tensor network consisting of coupled local numeric and Grassmann tensors. To evaluate the partition function and to compute observables, we develop a Grassmann higher-order tensor renormalization group method, specifically tailored for this model. During the coarsening procedure, the blocking of adjacent Grassmann tensors is performed analytically, and the total number of Grassmann variables in the tensor network is reduced by a factor of two at each coarsening step. The coarse-site numeric tensors are truncated using higher-order singular value decompositions. The method is validated by comparing the partition function, the chiral condensate and the baryon density computed with the tensor method with exact analytical results on small lattices up to volumes of 4×4. For larger volumes, we present first tensor results for the chiral condensate as a function of the mass and volume, and observe that the chiral symmetry is not broken dynamically in two dimensions. We also present tensor results for the number density as a function of the chemical potential, which hint at a first-order phase transition.

We apply tensor network methods to study the strong-coupling 𝑈(𝑁) model in its dimer formulation. In three and four dimensions, we investigate the chiral condensate as a function of the quark mass and the degree of the symmetry group, and find good agreement with Monte Carlo simulations. Particularly interesting is the study of chiral symmetry breaking as a function of the mass and the volume, which clearly shows that this symmetry is spontaneously broken in the limit of infinite volume and zero mass.

We present a tensor-network method for strong-coupling QCD with staggered quarks at nonzero chemical potential. After integrating out the gauge fields at infinite coupling, the partition function can be written as a full contraction of a tensor network consisting of coupled local numeric and Grassmann tensors. To evaluate the partition function and to compute observables, we develop a Grassmann higher-order tensor renormalization group method, specifically tailored for this model. We apply the method to the two-dimensional case and validate it by comparing results for the partition function, the chiral condensate and the baryon density with exact analytical expressions on small lattices up to volumes of $4\times4$. For larger two-dimensional volumes, we present tensor results for the chiral condensate as a function of the mass and volume, and observe that the chiral symmetry is not broken dynamically in two dimensions. Furthermore, our results for the number density as a function of the chemical potential hint at a first-order phase transition. Finally, we present some preliminary tensor results for three-dimensional strong-coupling QCD.

We present results of tensor-network simulations of the three-dimensional $O(2)$ model at non-zero chemical potential and temperature, which were computed using the higher-order tensor-renormalization-group method (HOTRG). This necessitated enhancements to the HOTRG blocking procedure to reduce the truncation error in the case of anisotropic tensors. Moreover, the construction of the truncated vector spaces was adapted to strongly reduce the effect of systematic errors in the computation of observables using the finite-difference method. Our (improved) HOTRG results for the evolution of the number density with the chemical potential are in agreement with results obtained with the worm algorithm, and both the Silver Blaze phenomenon at zero temperature and the temperature dependence of the number density can be adequately reproduced.

Estimating the effects of interventions on patient outcome is one of the key aspects of personalized medicine. Their inference is often challenged by the fact that the training data comprises only the outcome for the administered treatment, and not for alternative treatments (the so-called counterfactual outcomes). Several methods were suggested for this scenario based on observational data, i.e.~data where the intervention was not applied randomly, for both continuous and binary outcome variables. However, patient outcome is often recorded in terms of time-to-event data, comprising right-censored event times if an event does not occur within the observation period. Albeit their enormous importance, time-to-event data is rarely used for treatment optimization. We suggest an approach named BITES (Balanced Individual Treatment Effect for Survival data), which combines a treatment-specific semi-parametric Cox loss with a treatment-balanced deep neural network; i.e.~we regularize differences between treated and non-treated patients using Integral Probability Metrics (IPM). We show in simulation studies that this approach outperforms the state of the art. Further, we demonstrate in an application to a cohort of breast cancer patients that hormone treatment can be optimized based on six routine parameters. We successfully validated this finding in an independent cohort. BITES is provided as an easy-to-use python implementation.

We apply tensor network methods to study the strong-coupling $U(N)$ model in its dimer formulation. In three and four dimensions, we investigate the chiral condensate as a function of the quark mass and the degree of the symmetry group, and find good agreement with Monte Carlo simulations. Particularly interesting is the study of chiral symmetry breaking as a function of the mass and the volume, which clearly shows that this symmetry is spontaneously broken in the limit of infinite volume and zero mass.

We calculate thermodynamic potentials and their derivatives for the three-dimensional $O(2)$ model using tensor-network methods to investigate the well-known second-order phase transition. We also consider the model at non-zero chemical potential to study the Silver Blaze phenomenon, which is related to the particle number density at zero temperature. Furthermore, the temperature dependence of the number density is explored using asymmetric lattices. Our results for both zero and non-zero magnetic field, temperature, and chemical potential are consistent with those obtained using other methods.

We calculate thermodynamic potentials and their derivatives for the three-dimensional $O(2)$ model using tensor-network methods to investigate the well-known second-order phase transition. We also consider the model at non-zero chemical potential to study the Silver Blaze phenomenon, which is related to the particle number density at zero temperature. Furthermore, the temperature dependence of the number density is explored using asymmetric lattices. Our results for both zero and non-zero magnetic field, temperature, and chemical potential are consistent with those obtained using other methods.

Regulatory CD4 + T cells (Treg) prevent tumor clearance by conventional T cells (Tconv) comprising a major obstacle of cancer immune-surveillance. Hitherto, the mechanisms of Treg repertoire formation in human cancers remain largely unclear. Here, we analyze Treg clonal origin in breast cancer patients using T-Cell Receptor and single-cell transcriptome sequencing. While Treg in peripheral blood and breast tumors are clonally distinct, Tconv clones, including tumor-antigen reactive effectors (Teff), are detected in both compartments. Tumor-infiltrating CD4 + cells accumulate into distinct transcriptome clusters, including early activated Tconv, uncommitted Teff, Th1 Teff, suppressive Treg and pro-tumorigenic Treg. Trajectory analysis suggests early activated Tconv differentiation either into Th1 Teff or into suppressive and pro-tumorigenic Treg. Importantly, Tconv, activated Tconv and Treg share highly-expanded clones contributing up to 65% of intratumoral Treg. Here we show that Treg in human breast cancer may considerably stem from antigen-experienced Tconv converting into secondary induced Treg through intratumoral activation.