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.

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

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

Rapamycin Pharmacokinetic and Pharmacodynamic Relationships in Osteosarcoma: A Comparative Oncology Study in Dogs

Signaling through the mTOR pathway contributes to growth, progression and chemoresistance of several cancers. Accordingly, inhibitors have been developed as potentially valuable therapeutics. Their optimal development requires consideration of dose, regimen, biomarkers and a rationale for their use in combination with other agents. Using the infrastructure of the Comparative Oncology Trials Consortium many of these complex questions were asked within a relevant population of dogs with osteosarcoma to inform the development of mTOR inhibitors for future use in pediatric osteosarcoma patients.This prospective dose escalation study of a parenteral formulation of rapamycin sought to define a safe, pharmacokinetically relevant, and pharmacodynamically active dose of rapamycin in dogs with appendicular osteosarcoma. Dogs entered into dose cohorts consisting of 3 dogs/cohort. Dogs underwent a pre-treatment tumor biopsy and collection of baseline PBMC. Dogs received a single intramuscular dose of rapamycin and underwent 48-hour whole blood pharmacokinetic sampling. Additionally, daily intramuscular doses of rapamycin were administered for 7 days with blood rapamycin trough levels collected on Day 8, 9 and 15. At Day 8 post-treatment collection of tumor and PBMC were obtained. No maximally tolerated dose of rapamycin was attained through escalation to the maximal planned dose of 0.08 mg/kg (2.5 mg/30 kg dog). Pharmacokinetic analysis revealed a dose-dependent exposure. In all cohorts modulation of the mTOR pathway in tumor and PBMC (pS6RP/S6RP) was demonstrated. No change in pAKT/AKT was seen in tumor samples following rapamycin therapy.Rapamycin may be safely administered to dogs and can yield therapeutic exposures. Modulation pS6RP/S6RP in tumor tissue and PBMCs was not dependent on dose. Results from this study confirm that the dog may be included in the translational development of rapamycin and potentially other mTOR inhibitors. Ongoing studies of rapamycin in dogs will define optimal schedules for their use in cancer and evaluate the role of rapamycin use in the setting of minimal residual disease

Ising model for exchange bias in ferromagnetic/antiferromagnetic bilayers

We propose a Random Anisotropy Ising Model (RAIM) to describe exchange bias in a ferromagnetic(F)/antiferromagnetic(AF) system. The F and AF spins are arranged in a square lattice permitting to control the interface between the two layers. The AF film is quenched and exhibit negative exchange interactions, while interactions in the F film are positives. An anisotropy term is introduced in both layers. The influence of the AF spin arrangement at the interface on exchange bias field is analyzed for compensated, uncompensated or rough interfaces

Web Usage Mining: Sequential Pattern Extraction with a Very Low Support

Abstract. The goal of this work is to increase the relevance and the interestingness of patterns discovered by a Web Usage Mining process. Indeed, the sequential patterns extracted on web log files, unless they are found under constraints, often lack interest because of their obvious content. Our goal is to discover minority users ’ behaviors having a coherence which we want to be aware of (like hacking activities on the Web site or a users ’ activity limited to a specific part of the Web site). By means of a clustering method on the extracted sequential patterns, we propose a recursive division of the problem. The developed clustering method is based on patterns summaries and neural networks. Our experiments show that we obtain the targeted patterns whereas their extraction by means of a classical process is impossible because of a very weak support (down to 0.006%). The diversity of users ’ behaviors is so large that the minority ones are both numerous and difficult to locate

Preisach model for systems with asymmetric First order reversal curve (FORC) distribution

This paper addresses the problem of asymmetry of the First-order Reversal Curve (FORC) diagram in correlation with the symmetry of the Preisach distribution. Only in a few cases, for the exchange-bias materials for example, an asymmetric distribution in the demagnetized state has to be considered in the Preisach model. In relation to the case of exchange bias materials a correlation between the distribution of interactions and that of the coercivities was considered. The FORCs starting on the ascending and descendent branches of the major loop are calculated with a Moving Preisach Model. The results show a good resemblance with typical experimental results on exchange bias materials