Добірка наукової літератури з теми "Center manifold projection"

We show that the global aspects of Abelian and center projection of a SU (2) gauge theory on an arbitrary manifold are naturally described in terms of smooth Deligne cohomology. This is achieved through the introduction of a novel type of differential topological structure, called Cho structure. Half integral monopole charges appear naturally in this framework.

Conditions for vegetation spreading and pattern formation are mathematically framed through an analysis encompassing three fundamental processes: flow stochasticity, vegetation dynamics, and sediment transport. Flow unsteadiness is included through Poisson stochastic processes whereby vegetation dynamics appears as a secondary instability, which is addressed by Floquet theory. Results show that the model captures the physical conditions heralding the transition between bare and vegetated fluvial states where the nonlinear formation and growth of finite alternate bars are accounted for by Center Manifold Projection. This paves the way to understand changes in biogeomorphological styles induced by man in the Anthropocene and of natural origin since the Paleozoic (Devonian plant hypothesis).

Malignant chromophobe renal cancer (chRCC) and benign oncocytoma (RO) are two renal tumor types difficult to differentiate using histology and immunohistochemistry-based methods because of their similarity in appearance. We previously developed a transcriptomics-based classification pipeline with “Chromophobe-Oncocytoma Gene Signature” (COGS) on a single-molecule counting platform. Renal cancer patients (n = 32, chRCC = 17, RO = 15) were recruited from Augusta University Medical Center (AUMC). Formalin-fixed paraffin-embedded (FFPE) blocks from their excised tumors were collected. We created a custom single-molecule counting code set for COGS to assay RNA from FFPE blocks. Utilizing hematoxylin-eosin stain, pathologists were able to correctly classify these tumor types (91.8%). Our unsupervised learning with UMAP (Uniform manifold approximation and projection, accuracy = 0.97) and hierarchical clustering (accuracy = 1.0) identified two clusters congruent with their histology. We next developed and compared four supervised models (random forest, support vector machine, generalized linear model with L2 regularization, and supervised UMAP). Supervised UMAP has shown to classify all the cases correctly (sensitivity = 1, specificity = 1, accuracy = 1) followed by random forest models (sensitivity = 0.84, specificity = 1, accuracy = 1). This pipeline can be used as a clinical tool by pathologists to differentiate chRCC from RO.

We continue to study of the Grassmann-like manifold of -centered planes. A special case is considered when the center de­scribes an -dimensional surface . We will denote this mani­fold by . An analogue of the strong Norden normalization of the manifold is realized. It is proved that this normalization induces a connection in the bundle associated with the manifold . A geometric characteristic of this connection is given with the help of parallel displacements. In our research we use the Cartan method of external forms and the group-theoretical method of Laptev. These methods are used by many geometers and physicists. The Grassmann-like manifold is closely related to such a well-known and popular manifold as the Grassmann manifold. The Grassmann mani­fold is an example of a homogeneous space and forms an important fun­damental class of projective manifolds, and the projective space itself can be represented as a Grassmann manifold.

Abstract Introduction: Multiple myeloma (MM) is a complex hematological malignancy with the heterogenous immune bone marrow (BM) environment contributing to tumor growth, drug resistance, and immune escape. T-Cells play a critical role in the clearance of malignant plasma cells from the tumor environment. However, T-Cells in multiple myeloma demonstrate impaired cytotoxicity, proliferation, and cytokine production due to the activation of immune inhibitory receptors from ligands produced by the myeloma cells. In this study, we investigate the behavior of T-Cells in MM patients by using single-cell RNA-Seq (scRNA-Seq) to compare the transcriptomic profiles of BM T-Cells of patients with rapid progressing (FP; PFS < 18mo) and non-progressing (NP; PFS > 4yrs) disease. Methods: Newly diagnosed MM patients (n=18) from the Multiple Myeloma Research Foundation (MMRF) CoMMpass study (NCT01454297) were identified as either rapid progressors or non-progressors based on their progression free survival since diagnosis. To capture transcriptomic data, scRNA-Seq was performed on 48 aliquots of frozen CD138-negative BM cells at three medical centers/universities (Beth Israel Deaconess Medical Center, Boston, Washington University in St. Louis, and Mount Sinai School of Medicine, NYC). Samples were collected at diagnosis prior to treatment. Surface marker expression for 29 proteins was captured for at least one sample per patient using CITE-Seq. After integration and batch correction, clustering was performed to identify cells of T or NK lineage. Uniform Manifold Approximation and Projection (UMAP) and differential expression were used to identify T-Lymphoid subtypes, and differences in NP and FP samples. Results: In this study, single cell transcriptomic profiles were identified for ~102,207 cells from 48 samples of 18 MM patients. 40,328 T (CD3+) and NK (CD3-, NKG7+) cells were isolated, and subclustered for further analysis (Fig 1A). Using differentially expressed markers for each cluster, the T-Lymphoid subset was refined into seven subtypes, consisting of various CD4+ T-Cells, CD8+ T-Cells, and NK cells (Fig 1B). The CD8+ cells were divided into three distinct phenotypes, namely a GZMK-, GZMB- CD8+ T-Cell cluster, a GZMK+ CD8+ Exhausted T-Cell cluster enriched in TIGIT and multiple chemokines (CCL3, CCL4, XCL2), and a GZMB+ NkT cluster enriched in cytolytic markers (PRF1, GNLY, NKG7) (Fig 1C). Differential expression between NP and FP samples in this CD8+ subset showed enrichment of the NkT cytotoxic markers in NP samples, while FP samples were enriched in the CD8+ Exhausted chemokine markers (Fig 1D). Furthermore, the proportion of CD8+ Exhausted T-Cells was enriched in FP samples (p.val < 0.05) (Fig 1E). Exhaustion markers were measured through both RNA and surface marker levels. In RNA, TIGIT was uniquely associated with the FP-enriched CD8+ Exhausted T-Cell cluster, and CD160 was uniquely expressed in FP samples (Fig 1F). CITE-Seq surface marker expression confirms enrichment of both TIGIT and PD1 in the CD8+ Exhausted T-Cell cluster, and along with more exhaustion in FP samples (p.val < 0.01). Conclusion: In this study, we have identified significant differences in T-Cell activity in patients with non-progressing and rapid-progressing multiple myeloma. T-Cells in rapid progressing patients appear to be in a suppressed state, with low cytolytic activity and enriched exhaustion markers. This GZMK+ T-Cell population shows strong similarities with an aging-associated subtype of effector memory T-Cells found to be enriched in older populations (Mogilenko et al, Immunity 54, 2021). These findings will be further validated in an expanded study, consisting both of a larger number of samples, and multiple samples at different timepoints from the same patient. Figure 1 Figure 1. Disclosures Jayasinghe: MMRF: Consultancy; WUGEN: Consultancy. Vij: BMS: Research Funding; Takeda: Honoraria, Research Funding; Sanofi: Honoraria, Research Funding; BMS: Honoraria; GSK: Honoraria; Oncopeptides: Honoraria; Karyopharm: Honoraria; CareDx: Honoraria; Legend: Honoraria; Biegene: Honoraria; Adaptive: Honoraria; Harpoon: Honoraria. Kumar: Carsgen: Research Funding; KITE: Consultancy, Membership on an entity's Board of Directors or advisory committees, Research Funding; Beigene: Consultancy; Bluebird Bio: Consultancy; Janssen: Consultancy, Membership on an entity's Board of Directors or advisory committees, Research Funding; Tenebio: Research Funding; Oncopeptides: Consultancy; Antengene: Consultancy, Honoraria; Roche-Genentech: Consultancy, Research Funding; Merck: Research Funding; Astra-Zeneca: Consultancy, Membership on an entity's Board of Directors or advisory committees, Research Funding; Celgene: Membership on an entity's Board of Directors or advisory committees, Research Funding; Takeda: Consultancy, Membership on an entity's Board of Directors or advisory committees, Research Funding; Novartis: Research Funding; Amgen: Consultancy, Research Funding; Abbvie: Consultancy, Membership on an entity's Board of Directors or advisory committees, Research Funding; BMS: Consultancy, Research Funding; Adaptive: Membership on an entity's Board of Directors or advisory committees, Research Funding; Sanofi: Research Funding. Avigan: Celgene: Membership on an entity's Board of Directors or advisory committees, Research Funding; Pharmacyclics: Research Funding; Kite Pharma: Consultancy, Research Funding; Juno: Membership on an entity's Board of Directors or advisory committees; Partner Tx: Membership on an entity's Board of Directors or advisory committees; Karyopharm: Membership on an entity's Board of Directors or advisory committees; Bristol-Myers Squibb: Membership on an entity's Board of Directors or advisory committees; Aviv MedTech Ltd: Membership on an entity's Board of Directors or advisory committees; Takeda: Membership on an entity's Board of Directors or advisory committees; Legend Biotech: Membership on an entity's Board of Directors or advisory committees; Chugai: Membership on an entity's Board of Directors or advisory committees; Janssen: Consultancy; Parexcel: Consultancy; Takeda: Consultancy; Sanofi: Consultancy.

The current paper continues consideration of geometry of projective frame orbits started in the author’s article in the previous issue. The ndimensional projective space with a distinguished point (the center) is considered. The action of matrix affine group of order n on the adapted projective frame manifold is given. It is shown that the linear frames, i. e., bases of the tangent space, can be identified with the orbits of adapted projective frames under the action of some normal subgroup of this group. Two adapted frames are said to be equivalent if they belong to the same orbit. The strict perspectivity relation between two adapted frames is introduced. The proofs of the theorem on the Desargues hyperplane and of the criterion of equivalence are simplified. According to this criterion, two adapted frames in strict perspective are equivalent if and only if the Desargues hyperplane generated by these frames is passing through the center.

We prove the existence and uniqueness of equilibrium states for a family of partially hyperbolic systems, with respect to Hölder continuous potentials with small variation. The family comes from the projection, on the center-unstable direction, of a family of partially hyperbolic horseshoes introduced by Díaz et al [Destroying horseshoes via heterodimensional cycles: generating bifurcations inside homoclinic classes. Ergod. Th. & Dynam. Sys.29 (2009), 433–474]. For the original three-dimensional system we consider potentials with small variation, constant on local stable manifolds, obtaining existence and uniqueness of equilibrium states.

Introduction: Multiple myeloma (MM) is a genetically complex and clinically heterogeneous disease. Disease biology and phenotype is heavily influenced by the tumor microenvironment and the interaction between the immune milieu and malignant plasma cell population. Understanding the molecular profile of tumor along with the immune ecosystem can provide insights into key pathways that are important in disease pathobiology. Therefore, in this study, we have used single-cell RNA-Seq (scRNA-Seq) to compare the detailed maps of the bone marrow microenvironment of patients with rapid progressing disease (PFS < 18 months) with those whose disease had not progressed at the time of analysis (PFS < 4 years) Methods: MM patients (n=18) with rapid and no progression were identified from the Multiple Myeloma Research Foundation (MMRF) CoMMpass study, a longitudinal genomic study of patients with newly diagnosed, active multiple myeloma (NCT01454297). To generate a robust scRNA-Seq profile with minimal false positive, we profiled multiple technical replicates/aliquots of viably frozen CD138-negative bone marrow cells from each patient at three medical centers/universities (Beth Israel Deaconess Medical Center, Boston, Washington University in St. Louis and Mount Sinai School of Medicine, NYC using droplet-based single-cell barcoding technique. After batch correction and normalization, the cellular clusters were identified using principal component analysis and Uniform Manifold Approximation and Projection (UMAP) approach (Becht et al, 2018). Differential expression, pathways and systems biology analysis between rapid and non-progressors revealed differences for specific cell clusters (Panigrahy, Gartung et al. 2019). To determine association of plasma cell overexpressed genes with survival in CoMMpass study, survival analysis was performed using Kaplan-Meier (K-M) approach. Results: In this study, comparative analysis was performed of the bone marrow microenvironment of patients with aggressive and indolent disease by generating single-cell profiles of ~102,207 cells from 48 samples of 18 patients with MM. The UMAP approach identified multiple transcriptionally diverse clusters of plasma (CD138+), immune (PTPRC+) and erythroid (GYPA1/2+) cells (Fig 1a). Interestingly, the analysis identified CD138+ plasma/tumors cells clusters in a subset of samples from patients with rapid -progression and these clusters depicted a high degree of inter-patient heterogeneity (Fig 1a). Further characterization of plasma tumor cells depicted significant activation (Z score >2 and P-value <.001) of pathway related to "Unfolded protein response", epithelial-mesenchymal transition (EMT), and "p38 MAPK Signaling". These rapid progressions associated with plasma cells overexpressing multiple genes (e.g., Hazard ratio (HR) CCL3=1.9 95% CI= (1.5-3.9) log-rank P=0.0004, HSPA5 HR=1.4 (1-2.6), P=0.03) that are associated with poor outcome in multiple myeloma based CoMMpass data. The bone marrow microenvironment cells formed 22 clusters, comprising of cells from myeloid, macrophages, T cells, B cells, dendritic cells, Natural Killer T (NKT) cells, and erythroid lineages. The Non-progressive patients depicted enrichment of GZMB+ T and NKT cells with overexpression of genes associated with "Natural Killer Cell Signaling", "CD28 Signaling in T Helper Cells", "NF-kB Signaling" and "Th17 Activation Pathway" (Fig1b, c). Systems biology analysis depicted significant activation of TNF, STAT4, and NFATC2 regulatory signatures in NKT cells. The analysis also observed enrichment of macrophages, several types of monocytes, and myeloid cells in the samples from patients with non-progressive disease (Fig 1d). The myeloid/monocytes cluster depicted significant activation of multiple metabolic (i.e., Glycolysis, Gluconeogenesis) and immune response (i.e. IL8) pathways (Fig 1e). In summary, this multi-site study provides insights into potentially significant differences in the transcriptomic landscape of multiple myeloma patients with rapid and non-progression of disease. The non-progressive patients depict significant enrichment of activated T cells and myeloid lineage populations, suggesting their role toward better outcomes. These findings will be further expanded by ongoing single cell analyses of the CoMMpass tissue bank under the MMRF Immune Atlas initiative. Figure 1 Disclosures Bhasin: Canomiiks Inc: Current equity holder in private company, Other: Co-Founder. Dhodapkar:Roche/Genentech: Membership on an entity's Board of Directors or advisory committees, Other; Amgen: Membership on an entity's Board of Directors or advisory committees, Other; Celgene/BMS: Membership on an entity's Board of Directors or advisory committees, Other; Janssen: Membership on an entity's Board of Directors or advisory committees, Other; Kite: Membership on an entity's Board of Directors or advisory committees, Other; Lava Therapeutics: Membership on an entity's Board of Directors or advisory committees, Other. Kumar:Merck: Consultancy, Research Funding; Adaptive Biotechnologies: Consultancy; Genecentrix: Consultancy; Tenebio: Other, Research Funding; Celgene/BMS: Other: Research funding for clinical trials to the institution, Consulting/Advisory Board participation with no personal payments; Genentech/Roche: Other: Research funding for clinical trials to the institution, Consulting/Advisory Board participation with no personal payments; Oncopeptides: Consultancy, Other: Independent Review Committee; IRC member; Kite Pharma: Consultancy, Research Funding; Novartis: Research Funding; Sanofi: Research Funding; MedImmune: Research Funding; Karyopharm: Consultancy; BMS: Consultancy, Research Funding; Cellectar: Other; Carsgen: Other, Research Funding; Dr. Reddy's Laboratories: Honoraria; Janssen Oncology: Other: Research funding for clinical trials to the institution, Consulting/Advisory Board participation with no personal payments; Takeda: Other: Research funding for clinical trials to the institution, Consulting/Advisory Board participation with no personal payments; AbbVie: Other: Research funding for clinical trials to the institution, Consulting/Advisory Board participation with no personal payments; Amgen: Consultancy, Other: Research funding for clinical trials to the institution, Consulting/Advisory Board participation with no personal payments, Research Funding.

Design of active suspension systems is well known, however the notion of control bifurcations for the design of such systems has been introduced recently. A nonlinear active suspension system consisting of a magneto-rheological damper is analyzed in this work. It is well known that a parameterized nonlinear differential equation can have multiple equilibria as the parameter is varied. A local bifurcation of a parameterized nonlinear system typically happens because some eigenvalues of the parameterized linear approximating differential equation cross the imaginary axis and there is a change in stability of the equilibrium. The qualitative change in the equilibrium point can be characterized by investigating the projection of the flow on the center manifold. A control bifurcation of a nonlinear system typically occurs when its linear approximation loses stabilizability. In this work the control bifurcations of a magneto-rheological fluid based active suspension system is analyzed. Some parametric results are presented with suggestions on how to design nonlinear control based on the parametric control bifurcation analysis as applied to the design of an active suspension system.