Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory

The present paper studies the large-j asymptotics of the Lorentzian EPRL spinfoam amplitude on a 4d simplicial complex with an arbitrary number of simplices. The asymptotics of the spinfoam amplitude is determined by the critical configurations. Here we show that, given a critical configuration in general, there exists a partition of the simplicial complex into three type of regions R_{Nondeg}, R_{Deg-A}, R_{Deg-B}, where the three regions are simplicial sub-complexes with boundaries. The critical configuration implies different types of geometries in different types of regions, i.e. (1) the critical configuration restricted into R_{Nondeg}$implies a nondegenerate discrete Lorentzian geometry, (2) the critical configuration restricted into R_{Deg-A}$ is degenerate of type-A in our definition of degeneracy, but implies a nondegenerate discrete Euclidean geometry on R_{Deg-A}, (3) the critical configuration restricted into R_{Deg-B} is degenerate of type-B, and implies a vector geometry on R_{Deg-B}. With the critical configuration, we further make a subdivision of the regions R_{Nondeg} and R_{Deg-A} into sub-complexes (with boundary) according to their Lorentzian/Euclidean oriented 4-simplex volume V_4(v), such that sgn(V_4(v)) is a constant sign on each sub-complex. Then in the each sub-complex, the spinfoam amplitude at the critical configuration gives the Regge action in Lorentzian or Euclidean signature respectively on R_{Nondeg} or R_{Deg-A}. The Regge action reproduced here contains a sign factor sgn(V_4(v)) of the oriented 4-simplex volume. Therefore the Regge action reproduced here can be viewed a discretized Palatini action with on-shell connection. Finally the asymptotic formula of the spinfoam amplitude is given by a sum of the amplitudes evaluated at all possible critical configurations, which are the products of the amplitudes associated to different type of geometries.Comment: 54 pages, 2 figures, reference adde

Feynman diagrammatic approach to spin foams

"The Spin Foams for People Without the 3d/4d Imagination" could be an alternative title of our work. We derive spin foams from operator spin network diagrams} we introduce. Our diagrams are the spin network analogy of the Feynman diagrams. Their framework is compatible with the framework of Loop Quantum Gravity. For every operator spin network diagram we construct a corresponding operator spin foam. Admitting all the spin networks of LQG and all possible diagrams leads to a clearly defined large class of operator spin foams. In this way our framework provides a proposal for a class of 2-cell complexes that should be used in the spin foam theories of LQG. Within this class, our diagrams are just equivalent to the spin foams. The advantage, however, in the diagram framework is, that it is self contained, all the amplitudes can be calculated directly from the diagrams without explicit visualization of the corresponding spin foams. The spin network diagram operators and amplitudes are consistently defined on their own. Each diagram encodes all the combinatorial information. We illustrate applications of our diagrams: we introduce a diagram definition of Rovelli's surface amplitudes as well as of the canonical transition amplitudes. Importantly, our operator spin network diagrams are defined in a sufficiently general way to accommodate all the versions of the EPRL or the FK model, as well as other possible models. The diagrams are also compatible with the structure of the LQG Hamiltonian operators, what is an additional advantage. Finally, a scheme for a complete definition of a spin foam theory by declaring a set of interaction vertices emerges from the examples presented at the end of the paper.Comment: 36 pages, 23 figure

Operator Spin Foam Models

The goal of this paper is to introduce a systematic approach to spin foams. We define operator spin foams, that is foams labelled by group representations and operators, as the main tool. An equivalence relation we impose in the set of the operator spin foams allows to split the faces and the edges of the foams. The consistency with that relation requires introduction of the (familiar for the BF theory) face amplitude. The operator spin foam models are defined quite generally. Imposing a maximal symmetry leads to a family we call natural operator spin foam models. This symmetry, combined with demanding consistency with splitting the edges, determines a complete characterization of a general natural model. It can be obtained by applying arbitrary (quantum) constraints on an arbitrary BF spin foam model. In particular, imposing suitable constraints on Spin(4) BF spin foam model is exactly the way we tend to view 4d quantum gravity, starting with the BC model and continuing with the EPRL or FK models. That makes our framework directly applicable to those models. Specifically, our operator spin foam framework can be translated into the language of spin foams and partition functions. We discuss the examples: BF spin foam model, the BC model, and the model obtained by application of our framework to the EPRL intertwiners.Comment: 19 pages, 11 figures, RevTex4.

Euclidean three-point function in loop and perturbative gravity

We compute the leading order of the three-point function in loop quantum gravity, using the vertex expansion of the Euclidean version of the new spin foam dynamics, in the region of gamma<1. We find results consistent with Regge calculus in the limit gamma->0 and j->infinity. We also compute the tree-level three-point function of perturbative quantum general relativity in position space, and discuss the possibility of directly comparing the two results.Comment: 16 page

Loop quantum gravity: the first twenty five years

This is a review paper invited by the journal "Classical ad Quantum Gravity" for a "Cluster Issue" on approaches to quantum gravity. I give a synthetic presentation of loop gravity. I spell-out the aims of the theory and compare the results obtained with the initial hopes that motivated the early interest in this research direction. I give my own perspective on the status of the program and attempt of a critical evaluation of its successes and limits.Comment: 24 pages, 3 figure

t→bWt \to b W in NonCommutative Standard Model

We study the top quark decay to b quark and W boson in the NonCommutative Standard Model (NCSM). The lowest contribution to the decay comes from the terms quadratic in the matrix describing the noncommutative (NC) effects while the linear term is seen to identically vanish because of symmetry. The NC effects are found to be significant only for low values of the NC characteristic scale.Comment: 11 page Latex file containing 2 eps figures (redrawn). More discussion included. To appear in PR

Bcl-2 protein family: Implications in vascular apoptosis and atherosclerosis

Apoptosis has been recognized as a central component in the pathogenesis of atherosclerosis, in addition to the other human pathologies such as cancer and diabetes. The pathophysiology of atherosclerosis is complex, involving both apoptosis and proliferation at different phases of its progression. Oxidative modification of lipids and inflammation differentially regulate the apoptotic and proliferative responses of vascular cells during progression of the atherosclerotic lesion. Bcl-2 proteins act as the major regulators of extrinsic and intrinsic apoptosis signalling pathways and more recently it has become evident that they mediate the apoptotic response of vascular cells in response to oxidation and inflammation either in a provocative or an inhibitory mode of action. Here we address Bcl-2 proteins as major therapeutic targets for the treatment of atherosclerosis and underscore the need for the novel preventive and therapeutic interventions against atherosclerosis, which should be designed in the light of molecular mechanisms regulating apoptosis of vascular cells in atherosclerotic lesions

Suppression of Mcl-1 via RNA interference sensitizes human hepatocellular carcinoma cells towards apoptosis induction

BACKGROUND: Hepatocelluar carcinoma (HCC) is one of the most common cancers worldwide and a major cause of cancer-related mortality. HCC is highly resistant to currently available chemotherapeutic drugs. Defects in apoptosis signaling contribute to this resistance. Myeloid cell leukemia-1 (Mcl-1) is an anti-apoptotic member of the Bcl-2 protein family which interferes with mitochondrial activation. In a previous study we have shown that Mcl-1 is highly expressed in tissues of human HCC. In this study, we manipulated expression of the Mcl-1 protein in HCC cells by RNA interference and analyzed its impact on apoptosis sensitivity of HCC cells in vitro. METHODS: RNA interference was performed by transfecting siRNA to specifically knock down Mcl-1 expression in HCC cells. Mcl-1 expression was measured by quantitative real-time PCR and Western blot. Induction of apoptosis and caspase activity after treatment with chemotherapeutic drugs and different targeted therapies were measured by flow cytometry and fluorometric analysis, respectively. RESULTS: Here we demonstrate that Mcl-1 expressing HCC cell lines show low sensitivity towards treatment with a panel of chemotherapeutic drugs. However, treatment with the anthracycline derivative epirubicin resulted in comparatively high apoptosis rates in HCC cells. Inhibition of the kinase PI3K significantly increased apoptosis induction by chemotherapy. RNA interference efficiently downregulated Mcl-1 expression in HCC cells. Mcl-1 downregulation sensitized HCC cells to different chemotherapeutic agents. Sensitization was accompanied by profound activation of caspase-3 and -9. In addition, Mcl-1 downregulation also increased apoptosis rates after treatment with PI3K inhibitors and, to a lower extent, after treatment with mTOR, Raf I and VEGF/PDGF kinase inhibitors. TRAIL-induced apoptosis did not markedly respond to Mcl-1 knockdown. Additionally, knockdown of Mcl-1 efficiently enhanced apoptosis sensitivity towards combined treatment modalities: Mcl-1 knockdown significantly augmented apoptosis sensitivity of HCC cells towards chemotherapy combined with PI3K inhibition. CONCLUSION: Our data suggest that specific downregulation of Mcl-1 by RNA interference is a promising approach to sensitize HCC cells towards chemotherapy and molecularly targeted therapies

Manufacturing and Supply Chain Flexibility: Building an Integrative Conceptual Model Through Systematic Literature Review and Bibliometric Analysis

The purpose of this study is twofold: first, to establish the current themes on the topic of manufacturing and supply chain flexibility (MSCF), assess their level of maturity in relation to each other, identify the emerging ones and reflect on how they can inform each other, and second, to develop a conceptual model of MSCF that links different themes connect and highlight future research opportunities. The study builds on a sample of 222 articles published from 1996 to 2018 in international, peer-reviewed journals. The analysis of the sample involves two complementary approaches: the co-word technique to identify the thematic clusters as well as their relative standing and a critical reflection on the papers to explain the intellectual content of these thematic clusters. The results of the co-word analysis show that MSCF is a dynamic topic with a rich and complex structure that comprises five thematic clusters. The value chain, capability and volatility clusters showed research topics that were taking a central role in the discussion on MSCF but were not mature yet. The SC purchasing practices and SC planning clusters involved work that was more focused and could be considered more mature. These clusters were then integrated in a framework that built on the competence–capability perspective and identified the major structural and infrastructural elements of MSCF as well as its antecedents and consequences. This paper proposes an integrative framework helping managers keep track the various decisions they need to make to increase flexibility from the viewpoint of the entire value chain