Reduced order methods for laminar and turbulent flows in a finite volume setting: projection-based methods and data-driven techniques

This dissertation presents a family of Reduced Order Models (ROMs) which is specifically designed to deal with both laminar and turbulent flows in a finite volume full order setting. Several aspects associated with the reduction of the incompressible Navier\u2013Stokes equations have been investigated. The first of them is related to the need of an accurate reduced pressure reconstruction. This issue has been studied with the help of two main approaches which consist in the use of the Pressure Poisson Equation (PPE) at the reduced order level and also the employment of the supremizer stabilization method. A second aspect is connected with the enforcement of non-homogeneous Dirichlet boundary conditions at the inlet boundary at the reduced order level. The solutions to address this aspect include two methods, namely, the lifting function method and the penalty method. Different solutions for the treatment of turbulence at the reduced order level have been proposed. We have developed a unified reduction approach which is capable of dealing with turbulent flows based on the Reynolds Averaged Navier\u2013Stokes (RANS) equations complemented by any Eddy Viscosity Model (EVM). The turbulent ROM developed is versatile in the sense that it may be applied on the FOM solutions obtained by different turbulent closure models or EVMs. This is made possible thanks to the formulation of the ROM which merges projection-based techniques with data-driven reduction strategies. In particular, the work presents a mixed strategy that exploits a data-driven reduction method to approximate the eddy viscosity solution manifold and a classical POD-Galerkin projection approach for the velocity and the pressure fields. The newly proposed turbulent ROM has been validated on benchmark test cases in both steady and unsteady settings with Reynolds up to Re 10 to 5

The Dirac operator on untrapped surfaces

We establish a sharp extrinsic lower bound for the first eigenvalue of the Dirac operator of an untrapped surface in initial data sets without apparent horizon in terms of the norm of its mean curvature vector. The equality case leads to rigidity results for the constraint equations with spherical boundary as well as uniqueness results for constant mean curvature surfaces in Minkowski space.Comment: 16 page

On a spin conformal invariant on manifolds with boundary

On a n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric, a spin structure and a chirality operator, we study some properties of a spin conformal invariant defined from the first eigenvalue of the Dirac operator under the chiral bag boundary condition. More precisely, we show that we can derive a spinorial analogue of Aubin's inequality.Comment: 26 page

A Reilly formula and eigenvalue estimates for differential forms

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a Riemannian manifold. The equality case of our inequality gives rise to a number of rigidity results, when the geometry of the boundary has special properties and the domain is non-negatively curved. Finally we also obtain, as a by-product of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.Comment: 22 page

Antimicrobial Synergy Testing : Comparing the Tobramycin and Ceftazidime Gradient Diffusion Methodology Used in Assessing Synergy in Cystic Fibrosis-Derived

Funding: This research was funded by the NHS Grampian Endowment fund, grant number EA9431, and the NHS Grampian Clinical Microbiology Fund (NHS Grampian Endowment Funds, Registered Charity Number SC017296). Acknowledgments: The authors would like to thank the laboratories and clinicians who use the Cystic Fibrosis Susceptibility Testing Service. CFASS is an adult patient-testing facility, funded by the National Services Division of the Common Services Agency of the Scottish Executive.Peer reviewedPublisher PD

eEF2K Activity Determines Synergy to Cotreatment of Cancer Cells With PI3K and MEK Inhibitors

PI3K-mammalian target of rapamycin and MAPK/ERK kinase (MEK)/mitogen-activated protein kinase (MAPK) are the most frequently dysregulated signaling pathways in cancer. A problem that limits the success of therapies that target individual PI3K-MAPK members is that these pathways converge to regulate downstream functions and often compensate each other, leading to drug resistance and transient responses to therapy. In order to overcome resistance, therapies based on cotreatments with PI3K/AKT and MEK/MAPK inhibitors are now being investigated in clinical trials, but the mechanisms of sensitivity to cotreatment are not fully understood. Using LC-MS/MS-based phosphoproteomics, we found that eukaryotic elongation factor 2 kinase (eEF2K), a key convergence point downstream of MAPK and PI3K pathways, mediates synergism to cotreatment with trametinib plus pictilisib (which target MEK1/2 and PI3Kα/δ, respectively). Inhibition of eEF2K by siRNA or with a small molecule inhibitor reversed the antiproliferative effects of the cotreatment with PI3K plus MEK inhibitors in a cell model–specific manner. Systematic analysis in 12 acute myeloid leukemia cell lines revealed that eEF2K activity was increased in cells for which PI3K plus MEKi cotreatment is synergistic, while PKC potentially mediated resistance to such cotreatment. Together, our study uncovers eEF2K activity as a key mediator of responses to PI3Ki plus MEKi and as a potential biomarker to predict synergy to cotreatment in cancer cells

Computational design of dynamic receptor-peptide signaling complexes applied to chemotaxis.

Engineering protein biosensors that sensitively respond to specific biomolecules by triggering precise cellular responses is a major goal of diagnostics and synthetic cell biology. Previous biosensor designs have largely relied on binding structurally well-defined molecules. In contrast, approaches that couple the sensing of flexible compounds to intended cellular responses would greatly expand potential biosensor applications. Here, to address these challenges, we develop a computational strategy for designing signaling complexes between conformationally dynamic proteins and peptides. To demonstrate the power of the approach, we create ultrasensitive chemotactic receptor-peptide pairs capable of eliciting potent signaling responses and strong chemotaxis in primary human T cells. Unlike traditional approaches that engineer static binding complexes, our dynamic structure design strategy optimizes contacts with multiple binding and allosteric sites accessible through dynamic conformational ensembles to achieve strongly enhanced signaling efficacy and potency. Our study suggests that a conformationally adaptable binding interface coupled to a robust allosteric transmission region is a key evolutionary determinant of peptidergic GPCR signaling systems. The approach lays a foundation for designing peptide-sensing receptors and signaling peptide ligands for basic and therapeutic applications

Generic metrics and the mass endomorphism on spin three-manifolds

Let $(M,g)$ be a closed Riemannian spin manifold. The constant term in the expansion of the Green function for the Dirac operator at a fixed point $p\in M$ is called the mass endomorphism in $p$ associated to the metric $g$ due to an analogy to the mass in the Yamabe problem. We show that the mass endomorphism of a generic metric on a three-dimensional spin manifold is nonzero. This implies a strict inequality which can be used to avoid bubbling-off phenomena in conformal spin geometry.Comment: 8 page

Prediction of Signed Protein Kinase Regulatory Circuits.

Complex networks of regulatory relationships between protein kinases comprise a major component of intracellular signaling. Although many kinase-kinase regulatory relationships have been described in detail, these tend to be limited to well-studied kinases whereas the majority of possible relationships remains unexplored. Here, we implement a data-driven, supervised machine learning method to predict human kinase-kinase regulatory relationships and whether they have activating or inhibiting effects. We incorporate high-throughput data, kinase specificity profiles, and structural information to produce our predictions. The results successfully recapitulate previously annotated regulatory relationships and can reconstruct known signaling pathways from the ground up. The full network of predictions is relatively sparse, with the vast majority of relationships assigned low probabilities. However, it nevertheless suggests denser modes of inter-kinase regulation than normally considered in intracellular signaling research. A record of this paper's transparent peer review process is included in the Supplemental Information

Extended Formulations in Mixed-integer Convex Programming

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable with standard symmetric and nonsymmetric cones. Conic reformulations are shown to be effective extended formulations themselves because they encode separability structure. For mixed-integer conic-representable problems, we provide the first outer approximation algorithm with finite-time convergence guarantees, opening a path for the use of conic solvers for continuous relaxations. We then connect the popular modeling framework of disciplined convex programming (DCP) to the existence of extended formulations independent of conic representability. We present evidence that our approach can yield significant gains in practice, with the solution of a number of open instances from the MINLPLIB2 benchmark library.Comment: To be presented at IPCO 201