Canonical Integral Research Articles

NOTUM-mediated WNT silencing drives extravillous trophoblast cell lineage development

Trophoblast stem (TS) cells have the unique capacity to differentiate into specialized cell types, including extravillous trophoblast (EVT) cells. EVT cells invade into and transform the uterus where they act to remodel the vasculature facilitating the redirection of maternal nutrients to the developing fetus. Disruptions in EVT cell development and function are at the core of pregnancy-related disease. WNT-activated signal transduction is a conserved regulator of morphogenesis of many organ systems, including the placenta. In human TS cells, activation of canonical WNT signaling is critical for maintenance of the TS cell stem state and its downregulation accompanies EVT cell differentiation. We show that aberrant WNT signaling undermines EVT cell differentiation. Notum, palmitoleoyl-protein carboxylesterase (NOTUM), a negative regulator of canonical WNT signaling, was prominently expressed in first-trimester EVT cells developing in situ and up-regulated in EVT cells derived from human TS cells. Furthermore, NOTUM was required for optimal human TS cell differentiation to EVT cells. Activation of NOTUM in EVT cells is driven, at least in part, by endothelial Per-Arnt-Sim (PAS) domain 1 (also called hypoxia-inducible factor 2 alpha). Collectively, our findings indicate that canonical Wingless-related integration site (WNT) signaling is essential for maintenance of human trophoblast cell stemness and regulation of human TS cell differentiation. Downregulation of canonical WNT signaling via the actions of NOTUM is required for optimal EVT cell differentiation.

Уравнения Лакса на супералгебрах Ли

It is demonstrated that the standard construction of Lax equations on Lie algebras can be extended to Lie superalgebras, with the even subspace carrying the usual Lax equations. The extended equations inherit the existence of the canonical trace polynomial integrals of motion. An extra set of integrals exists in the odd subspace, with a nontrivial homological structure of the orbit space. This establishes a curious algebraic link between integrable evolution equations, supersymmetry and the deformation theory.

Label-free multiphoton imaging reveals volumetric shifts across development in sensory-related brain regions of a miniature transparent vertebrate.

Animals integrate information from different sensory modalities as they mature and perform increasingly complex behaviors. This may parallel differential investment in specific brain regions depending on the demands of changing sensory inputs. To investigate developmental changes in the volume of canonical sensory integration brain regions, we used third harmonic generation imaging for morphometric analysis of forebrain and midbrain regions from 5 to 90 days post fertilization (dpf) in Danionella dracula , a transparent, miniature teleost fish whose brain is optically accessible throughout its lifespan. Relative to whole brain volume, increased volume or investment in telencephalon, a higher order sensory integration center, and torus longitudinalis (TL), a midbrain visuomotor integration center, is relatively consistent from 5 to 30 dpf, until it increases at 60 dpf, followed by another increase at 90 dpf, as animals reach adulthood. In contrast, investment in midbrain optic tectum (TeO), a retinal-recipient target, progressively decreases from 30-90 dpf, whereas investment is relatively consistent across all stages for the midbrain torus semicircularis (TS), a secondary auditory and mechanosensory lateral line center, and the olfactory bulb (OB), a direct target of the olfactory epithelium. In sum, increased investment in higher order integration centers (telencephalon, TL) occurs as juveniles reach adulthood and exhibit more complex cognitive tasks, whereas investment in modality-dominant regions occurs in earlier stages (TeO) or is relatively consistent across development (TS, OB). Complete optical access throughout Danionella 's lifespan provides a unique opportunity to investigate how changing brain structure over development correlates with changes in connectivity, microcircuitry, or behavior.

Efficient Sampling of Cavity Hydration in Proteins with Nonequilibrium Grand Canonical Monte Carlo and Polarizable Force Fields.

Prediction of the hydration levels of protein cavities and active sites is important to both mechanistic analysis and ligand design. Due to the unique microscopic environment of these buried water molecules, a polarizable model is expected to be crucial for an accurate treatment of protein internal hydration in simulations. Here we adapt a nonequilibrium candidate Monte Carlo approach for conducting grand canonical Monte Carlo simulations with the Drude polarizable force field. The GPU implementation enables the efficient sampling of internal cavity hydration levels in biomolecular systems. We also develop an enhanced sampling approach referred to as B-walking, which satisfies detailed balance and readily combines with grand canonical integration to efficiently calculate quantitative binding free energies of water to protein cavities. Applications of these developments are illustrated in a solvent box and the polar ligand binding site in trypsin. Our simulation results show that including electronic polarization leads to a modest but clear improvement in the description of water position and occupancy compared to the crystal structure. The B-walking approach enhances the range of water sampling in different chemical potential windows and thus improves the accuracy of water binding free energy calculations.

Generalised Graph Laplacians and Canonical Feynman Integrals with Kinematics

To any graph with external half-edges and internal masses, we associate canonical integrals which depend non-trivially on particle masses and momenta, and are always finite. They are generalised Feynman integrals which satisfy graphical relations obtained from contracting edges in graphs, and a coproduct involving both ultra-violet and infra-red subgraphs. Their integrands are defined by evaluating bi-invariant forms, which represent stable classes in the cohomology of the general linear group, on a generalised graph Laplacian matrix which depends on the external kinematics of a graph.

Numerical evaluation of oscillatory integrals via automated steepest descent contour deformation

Steepest descent methods combining complex contour deformation with numerical quadrature provide an efficient and accurate approach for the evaluation of highly oscillatory integrals. However, unless the phase function governing the oscillation is particularly simple, their application requires a significant amount of a priori analysis and expert user input, to determine the appropriate contour deformation, and to deal with the non-uniformity in the accuracy of standard quadrature techniques associated with the coalescence of stationary points (saddle points) with each other, or with the endpoints of the original integration contour. In this paper we present a novel algorithm for the numerical evaluation of oscillatory integrals with general polynomial phase functions, which automates the contour deformation process and avoids the difficulties typically encountered with coalescing stationary points and endpoints. The inputs to the algorithm are simply the phase and amplitude functions, the endpoints and orientation of the original integration contour, and a small number of numerical parameters. By a series of numerical experiments we demonstrate that the algorithm is accurate and efficient over a large range of frequencies, even for examples with a large number of coalescing stationary points and with endpoints at infinity. As a particular application, we use our algorithm to evaluate cuspoid canonical integrals from scattering theory. A Matlab implementation of the algorithm is made available and is called PathFinder.

A Single Cell Atlas of Diffuse Large B Cell Lymphomas Reveals Distinct Cellular States Predictive of Outcomes

Diffuse large B-cell lymphoma (DLBCL) is the most common aggressive B-cell lymphoma with high clinical and biological heterogeneity. Despite current effective immunochemotherapy, up to 40% of patients do not respond or develop refractory disease. DLBCL is characterized by two major cell-of-origin (COO) subtypes, germinal center B cell-like (GCB) and activated B cell-like (ABC), with recent research uncovering additional molecular subgroups based on genomic alterations or tumor microenvironment (TME) features. However, current classifiers use bulk or deconvolution profiling which blurs intra-tumor heterogeneity, hindering the discovery of true functional cell states underlying clinical diversity. Here, we constructed a multimodal single-cell atlas of 62 DLBCL cases, integrating single-cell transcriptomes, immune repertoire and genetic features, to decrypt recurrent B cell states and TME ecosystems while identifying clinically relevant prognostic biomarkers (Fig.1). We performed simultaneous 5'-end single-cell RNA, B-cell receptor (BCR) and T-cell receptor sequencing on 63 DLBCL lymph node biopsies, recovering 109,294 cells after stringent quality controls. These biopsies were obtained from the real-world, clinically-annotated, multicentric CeVi collection and included 43 patient samples at diagnosis (ABC = 17, GCB = 11, Unclassified = 6, Not Evaluated = 9; 21 of which did not achieve event-free survival at 24 months (EFS24) after R-chemotherapy regimens), 11 relapsed/refractory DLBCL and 8 DLBCL transformed from indolent lymphoma. We distinguished malignant B-cells from TME using canonical markers and BCR sequence, exploring heterogeneity in both components. We developed an original bioinformatic approach to define malignant B cell transcriptional archetypes shared across patients. To assess whether subclonal genetics are associated with transcriptional states, we inferred copy number variations (CNV) and studied BCR intraclonal variations of malignant cells. We also integrated TME data (39,674 cells) to quantify subpopulations and clonally expanded T-cell subsets, and performed robust statistical analyses to identify clinically relevant features linked to patient outcomes. To circumvent interpatient heterogeneity in malignant B cells, we defined transcriptional cellular archetypes conserved across patients by combining 3 unsupervised methods: rank-biased overlap meta-clustering, variational autoencoder and canonical correlation analysis integration. We identified 5 cellular archetypes (Arch.1-5): Arch.1 was characterized by plasma cell identity, Arch.2 by MYC and NFKB pathways, Arch.3 by MYC pathway only, Arch.4 by quiescence markers, and Arch.5 by GC markers. Several archetypes co-existed in each tumor sample, and archetype identity was superimposed to the transcriptional profile conferred by COO molecular class as an additional layer of transcriptional heterogeneity. Cell state-specific CNV and BCR subclones were very rare, suggesting that subclonal genetic changes were not the main drivers of malignant B cell plasticity and archetypes. Kaplan-Meier analysis showed a significant negative association between proportion of Arch.4 cells and continuous EFS in our diagnosis cohort. Unsupervised analysis of archetype composition further distinguished ABC patients who achieved EFS24 (enriched in Arch.3 cells) from those with a particularly poor prognosis (enriched in Arch.4 cells). Integrated analysis of the TME revealed three major ecosystems, including one enriched for effector and cytotoxic T cells. In diagnosis samples, pseudo-temporal trajectory analysis revealed the enrichment of clonally-expanded hyperactivated CD8+ T cells expressing canonical exhaustion markers in patients achieving EFS24, suggesting a positive link between the extent of CD8+ T cell differentiation and response to R-CHOP based regimens. Shedding new light on DLBCL biological and clinical heterogeneity, our comprehensive single-cell atlas of DLBCL uncovered recurrent tumor cell states and TME features crucial for stratifying non-responsive ABC patients and guiding treatment decisions. Ongoing single-cell spatial transcriptomics analyses will be used to further validate our findings and elucidate archetype-TME interactions that may drive malignant B cell plasticity, with the potential to uncover novel therapeutic targets.

Genetic inactivation of β-catenin is salubrious, whereas its activation is deleterious in desmoplakin cardiomyopathy.

Mutations in the DSP gene encoding desmoplakin, a constituent of the desmosomes at the intercalated discs (IDs), cause a phenotype that spans arrhythmogenic cardiomyopathy (ACM) and dilated cardiomyopathy. It is typically characterized by biventricular enlargement and dysfunction, myocardial fibrosis, cell death, and arrhythmias. The canonical wingless-related integration (cWNT)/β-catenin pathway is implicated in the pathogenesis of ACM. The β-catenin is an indispensable co-transcriptional regulator of the cWNT pathway and a member of the IDs. We genetically inactivated or activated β-catenin to determine its role in the pathogenesis of desmoplakin cardiomyopathy. The Dsp gene was conditionally deleted in the 2-week-old post-natal cardiac myocytes using tamoxifen-inducible MerCreMer mice (Myh6-McmTam:DspF/F). The cWNT/β-catenin pathway was markedly dysregulated in the Myh6-McmTam:DspF/F cardiac myocytes, as indicated by a concomitant increase in the expression of cWNT/β-catenin target genes, isoforms of its key co-effectors, and the inhibitors of the pathway. The β-catenin was inactivated or activated upon inducible deletion of its transcriptional or degron domain, respectively, in the Myh6-McmTam:DspF/F cardiac myocytes. Genetic inactivation of β-catenin in the Myh6-McmTam:DspF/F mice prolonged survival, improved cardiac function, reduced cardiac arrhythmias, and attenuated myocardial fibrosis, and cell death caused by apoptosis, necroptosis, and pyroptosis, i.e. PANoptosis. In contrast, activation of β-catenin had the opposite effects. The deleterious and the salubrious effects were independent of changes in the expression levels of the cWNT target genes and were associated with changes in several molecular and biological pathways, including cell death programmes. The cWNT/β-catenin was markedly dysregulated in the cardiac myocytes in a mouse model of desmoplakin cardiomyopathy. Inactivation of β-catenin attenuated, whereas its activation aggravated the phenotype, through multiple molecular pathways, independent of the cWNT transcriptional activity. Thus, suppression but not activation of β-catenin might be beneficial in desmoplakin cardiomyopathy.

Matsubara dynamics approximation for generalized multi-time correlation functions.

We introduce a semi-classical approximation for calculating generalized multi-time correlation functions based on Matsubara dynamics, a classical dynamics approach that conserves the quantum Boltzmann distribution. This method is exact for the zero time and harmonic limits and reduces to classical dynamics when only one Matsubara mode is considered (i.e., the centroid). Generalized multi-time correlation functions can be expressed as canonical phase-space integrals, involving classically evolved observables coupled through Poisson brackets in a smooth Matsubara space. Numerical tests on a simple potential show that the Matsubara approximation exhibits better agreement with exact results than classical dynamics, providing a bridge between the purely quantum and classical descriptions of multi-time correlation functions. Despite the phase problem that prevents practical applications of Matsubara dynamics, the reported work provides a benchmark theory for the future development of quantum-Boltzmann-preserving semi-classical approximations for studies of chemical dynamics in condensed phase systems.

Prescribed-time zero-error active disturbance rejection control for uncertain wheeled mobile robots subject to skidding and slipping

This paper investigates the prescribed-time control problem for a class of wheeled mobile robot (WMR) subject to nonparametric skidding, slipping and input disturbance in an inner-outer loop framework. First, by backstepping approach, the virtual linear and angular velocities are acquired to follow the reference path to one special point. Then, different from the conventional ones for canonical integral cascade model, a novel prescribed-time extended state observer (PTESO) is designed for WMR such that the unknown skidding and slipping can be observed and compensated. By developing the active disturbance rejection control technique, the zero-error control is achieved for WMR in prescribed time instead of ultimately uniform boundedness. Moreover, the influence of the uncertainty is attenuated by the compensation scheme based on the PTESO estimation. Finally, some simulation results are presented to demonstrate the superiority and effectiveness of the developed method.

Asymptotic approximation of a highly oscillatory integral with application to the canonical catastrophe integrals

AbstractWe consider the highly oscillatory integral for large positive values of w, , K and p positive integers with , and an entire function. The standard saddle point method is complicated and we use here a simplified version of this method introduced by López et al. We derive an asymptotic approximation of this integral when for general values of K and p in terms of elementary functions, and determine the Stokes lines. For , the asymptotic behavior of this integral may be classified in four different regions according to the even/odd character of the couple of parameters K and p; the special case requires a separate analysis. As an important application, we consider the family of canonical catastrophe integrals for large values of one of its variables, say , and bounded values of the remaining ones. This family of integrals may be written in the form for appropriate values of the parameters w, θ and the function . Then, we derive an asymptotic approximation of the family of canonical catastrophe integrals for large . The approximations are accompanied by several numerical experiments. The asymptotic formulas presented here fill up a gap in the NIST Handbook of Mathematical Functions by Olver et al.

Therapeutic approaches to activate the canonical Wnt pathway for bone regeneration.

Activation of the canonical Wingless-related integration site (Wnt) pathway has been shown to increase bone formation and therefore has therapeutic potential for use in orthopedic conditions. However, attempts at developing an effective strategy to achieve Wnt activation has been met with several challenges. The inherent hydrophobicity of Wnt ligands makes isolating and purifying the protein difficult. To circumvent these challenges, many have sought to target extracellular inhibitors of the Wnt pathway, such as Wnt signaling pathway inhibitors Sclerostin and Dickkopf-1, or to use small molecules, ions and proteins to increase target Wnt genes. Here, we review systemic and localized bioactive approaches to enhance bone formation or improve bone repair through antibody-based therapeutics, synthetic Wnt surrogates and scaffold doping to target canonical Wnt. We conclude with a brief review of emerging technologies, such as mRNA therapy and Clustered Regularly Interspaced Short Palindromic Repeats technology, which serve as promising approaches for future clinical translation.

Single-cell multimodal analysis identifies common regulatory programs in synovial fibroblasts of rheumatoid arthritis patients and modeled TNF-driven arthritis

BackgroundSynovial fibroblasts (SFs) are specialized cells of the synovium that provide nutrients and lubricants for the proper function of diarthrodial joints. Recent evidence appreciates the contribution of SF heterogeneity in arthritic pathologies. However, the normal SF profiles and the molecular networks that govern the transition from homeostatic to arthritic SF heterogeneity remain poorly defined.MethodsWe applied a combined analysis of single-cell (sc) transcriptomes and epigenomes (scRNA-seq and scATAC-seq) to SFs derived from naïve and hTNFtg mice (mice that overexpress human TNF, a murine model for rheumatoid arthritis), by employing the Seurat and ArchR packages. To identify the cellular differentiation lineages, we conducted velocity and trajectory analysis by combining state-of-the-art algorithms including scVelo, Slingshot, and PAGA. We integrated the transcriptomic and epigenomic data to infer gene regulatory networks using ArchR and custom-implemented algorithms. We performed a canonical correlation analysis-based integration of murine data with publicly available datasets from SFs of rheumatoid arthritis patients and sought to identify conserved gene regulatory networks by utilizing the SCENIC algorithm in the human arthritic scRNA-seq atlas.ResultsBy comparing SFs from healthy and hTNFtg mice, we revealed seven homeostatic and two disease-specific subsets of SFs. In healthy synovium, SFs function towards chondro- and osteogenesis, tissue repair, and immune surveillance. The development of arthritis leads to shrinkage of homeostatic SFs and favors the emergence of SF profiles marked by Dkk3 and Lrrc15 expression, functioning towards enhanced inflammatory responses and matrix catabolic processes. Lineage inference analysis indicated that specific Thy1+ SFs at the root of trajectories lead to the intermediate Thy1+/Dkk3+/Lrrc15+ SF states and culminate in a destructive and inflammatory Thy1− SF identity. We further uncovered epigenetically primed gene programs driving the expansion of these arthritic SFs, regulated by NFkB and new candidates, such as Runx1. Cross-species analysis of human/mouse arthritic SF data determined conserved regulatory and transcriptional networks.ConclusionsWe revealed a dynamic SF landscape from health to arthritis providing a functional genomic blueprint to understand the joint pathophysiology and highlight the fibroblast-oriented therapeutic targets for combating chronic inflammatory and destructive arthritic disease.

Master integrals for mixed QCD-QED corrections to charged-current Drell-Yan production of a massive charged lepton

The master integrals for the mixed QCD-QED two-loop virtual corrections to the charged-current Drell-Yan process qoverline{q} ′ → ℓν are computed analytically by using the differential equation method. A suitable choice of master integrals makes it successful to cast the differential equation system into the canonical form. We keep the dependence on charged lepton mass in the building of differential equations and then expand the system against the ratio of small charged lepton mass to large W-boson mass. In such a way the final results will contain large logarithms of the form log( {m}_{ell}^2 / {m}_W^2 ). Finally, all the canonical master integrals are given as Taylor series around d = 4 spacetime dimensions up to order four, with coefficients expressed in terms of Goncharov polylogarithms up to weight four.

Biophysical Survey of Small-Molecule β-Catenin Inhibitors: A Cautionary Tale.

The canonical Wingless-related integration site signaling pathway plays a critical role in human physiology, and its dysregulation can lead to an array of diseases. β-Catenin is a multifunctional protein within this pathway and an attractive yet challenging therapeutic target, most notably in oncology. This has stimulated the search for potent small-molecule inhibitors binding directly to the β-catenin surface to inhibit its protein–protein interactions and downstream signaling. Here, we provide an account of the claimed (and some putative) small-molecule ligands of β-catenin from the literature. Through in silico analysis, we show that most of these molecules contain promiscuous chemical substructures notorious for interfering with screening assays. Finally, and in line with this analysis, we demonstrate using orthogonal biophysical techniques that none of the examined small molecules bind at the surface of β-catenin. While shedding doubts on their reported mode of action, this study also reaffirms β-catenin as a prominent target in drug discovery.

Signal transduction pathway activity in high-grade serous carcinoma, its precursors and Fallopian tube epithelium

ObjectiveTo determine the activity of key signal transduction pathways in serous tubal intraepithelial carcinoma (STIC) and concurrent high-grade serous carcinoma (HGSC) and compare this to pathway activity in normal Fallopian tube epithelium (FTE). MethodsWe assessed mRNA expression levels of pathway-specific target genes with RT-qPCR in STIC and concurrent HGSC (n = 8) and normal FTE (n = 8). Subsequently, signal transduction pathway assays were used to assess functional activity of the androgen (AR) and estrogen receptor (ER), phosphoinositide-3-kinase (PI3K), Hedgehog (HH), transforming growth factor beta (TGF-β) and canonical wingless-type MMTV integration site (Wnt) pathways. ResultsThere were no statistically significant differences in pathway activity between STIC and HGSC, but STIC and HGSC demonstrated significantly lower ER and higher PI3K and HH pathway activity in comparison to normal FTE, suggesting these pathways as putative early drivers. In addition, we determined FOXO3a protein expression by immunohistochemistry and found loss of FOXO3a protein expression in STIC and HGSC compared to normal FTE. This observation confirmed that activation of PI3K signaling by loss of FOXO is an early hallmark of serous carcinogenesis. Furthermore, HGSC demonstrated significant loss of AR and Wnt pathway activity in relation to FTE, suggesting these pathways contribute to disease progression. ConclusionOur observations, together with the previously described associations between p53 signaling and both PI3K and HH pathway activity, provide evidence that increased PI3K and HH pathway activity and loss of ER pathway activity may be underlying events contributing to neoplastic transformation of FTE into STIC.

Realization of geodesic flows with a linear first integral by billiards with slipping

An arbitrary geodesic flow on the projective plane or Klein bottle with an additional, linear in the momentum, first integral is modelled using billiards with slipping on table complexes. The requisite table of a circular topological billiard with slipping is constructed algorithmically. Furthermore, linear integrals of geodesic flows can be reduced to the same canonical integral of a circular planar billiard. Bibliography: 36 titles.

Invariant Differential Forms on Complexes of Graphs and Feynman Integrals

We study differential forms on an algebraic compactification of a moduli space of metric graphs. Canonical examples of such forms are obtained by pulling back invariant differentials along a tropical Torelli map. The invariant differential forms in question generate the stable real cohomology of the general linear group, as shown by Borel. By integrating such invariant forms over the space of metrics on a graph, we define canonical period integrals associated to graphs, which we prove are always finite and take the form of generalised Feynman integrals. Furthermore, canonical integrals can be used to detect the non-vanishing of homology classes in the commutative graph complex. This theory leads to insights about the structure of the cohomology of the commutative graph complex, and new connections between graph complexes, motivic Galois groups and quantum field theory.

Survival Is Related to Estrogen Signal Transduction Pathway Activity in Postmenopausal Women Diagnosed with High-Grade Serous Ovarian Carcinoma.

Simple SummaryAll cells have a complex internal network of ‘communication chains’ called signal transduction pathways (STPs). Through interaction of different proteins in STPs, they are partly responsible for the behavior of a cell. In our study, we investigated the activity of six STPs in 85 women with advanced stage high-grade serous ovarian cancer (HGSC). To investigate the relation between and differences in survival and STP activity, women with a short disease-free survival (below 12 months) and a long disease-free survival (above 24 months) were included. We found no differences in mean STP activity between short-term survivors (52 women) and long-term survivors (33 women). However, when we analyzed postmenopausal women, we found that both disease-free and overall survival were related to estrogen receptor (ER) pathway signaling. This indicates that a better survival outcome was related to a more active ER pathway in this subgroup.High-grade serous ovarian carcinoma (HGSC), the most common subtype of ovarian cancer, has a high mortality rate. Although there are some factors associated with survival, such as stage of disease, there are remarkable differences in survival among women diagnosed with advanced stage disease. In this study, we investigate possible relations between survival and signal transduction pathway (STP) activity. We assessed the functional activity of the androgen receptor (AR), estrogen receptor (ER), phosphoinositide-3-kinase (PI3K), Hedgehog (HH), transforming growth factor beta (TGF-β) and canonical wingless-type MMTV integration site (Wnt) pathway in 85 primary tumor samples of patients with FIGO stage IIIC to IVB HGSC and disease-free survival (DFS) below 12 (n = 52) or over 24 months (n = 33). There were no significant differences in median pathway activity between patients with a short and long DFS. In univariate Cox proportional hazards analysis, ER pathway activity was related to a favorable DFS and overall survival (OS) in postmenopausal women (p = 0.033 and p = 0.041, respectively), but not in premenopausal women. We divided the postmenopausal group into subgroups based on ER pathway activity quartiles. Survival analysis revealed that postmenopausal women in the lowest ER quartile had a shorter DFS and OS (log-rank p = 0.006 and p < 0.001, respectively). Furthermore, we were able to form subgroups of patients based on an inverse relation between ER and PI3K pathway activity. In conclusion, in postmenopausal patients with advanced stage HGSC, a poorer survival outcome was associated with low functional ER pathway activity.

Next-to-leading power two-loop soft functions for the Drell-Yan process at threshold

We calculate the generalized soft functions at mathcal{O} ( {alpha}_s^2 ) at next-to-leading power accuracy for the Drell-Yan process at threshold. The operator definitions of these objects contain explicit insertions of soft gauge and matter fields, giving rise to a dependence on additional convolution variables with respect to the leading power result. These soft functions constitute the last missing ingredient for the validation of the bare factorization theorem to NNLO accuracy. We carry out the calculations by reducing the soft squared amplitudes into a set of canonical master integrals and we employ the method of differential equations to evaluate them. We retain the exact d-dimensional dependence of the convolution variables at the integration boundaries in order to regulate the fixed-order convolution integrals. After combining the soft functions with the relevant collinear functions, we perform checks of the results at the cross-section level against the literature and expansion-by-regions calculations, at NNLO and partly at N3LO, finding agreement.