The categorical theory of relations and quantizations

In this paper we develope a categorical theory of relations and use this formulation to define the notion of quantization for relations. Categories of relations are defined in the context of symmetric monoidal categories. They are shown to be symmetric monoidal categories in their own right and are found to be isomorphic to certain categories of $A-A$ bicomodules. Properties of relations are defined in terms of the symmetric monoidal structure. Equivalence relations are shown to be commutative monoids in the category of relations. Quantization in our view is a property of functors between monoidal categories. This notion of quantization induce a deformation of all algebraic structures in the category, in particular the ones defining properties of relations like transitivity and symmetry.Comment: corrected typo

The Dafny Integrated Development Environment

In recent years, program verifiers and interactive theorem provers have become more powerful and more suitable for verifying large programs or proofs. This has demonstrated the need for improving the user experience of these tools to increase productivity and to make them more accessible to non-experts. This paper presents an integrated development environment for Dafny-a programming language, verifier, and proof assistant-that addresses issues present in most state-of-the-art verifiers: low responsiveness and lack of support for understanding non-obvious verification failures. The paper demonstrates several new features that move the state-of-the-art closer towards a verification environment that can provide verification feedback as the user types and can present more helpful information about the program or failed verifications in a demand-driven and unobtrusive way.Comment: In Proceedings F-IDE 2014, arXiv:1404.578

Theory of linear G-difference equations

We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of difference equations are introduced as invariants of the symmetry group. Linear equations are modules over the skew group algebra, solutions are morphisms relating a given equation to other equations,symmetries of an equation are module endomorphisms and conserved structures are invariants in the tensor algebra of the given equation. We show that the equations and their solutions can be described through representations of the isotropy group of the symmetry group of the underluing set. We relate our notion of difference equations and solutions to systems of classical difference equations and their solutions and show that our notions include these as a special case.Comment: 34 page

The quasi-classical model of the spherical configuration in general relativity

We consider the quasi-classical model of the spin-free configuration on the basis of the self-gravitating spherical dust shell in General Relativity. For determination of the energy spectrum of the stationary states on the basis of quasi-classical quantization rules it is required to carry out some regularization of the system. It is realized by an embedding of the initial system in the extended system with rotation. Then, the stationary states of the spherical shells are S-states of the system with the intrinsic momentum. The quasi-classical treatment of a stability of the configuration is associated with the Langer modification of a square of the quantum mechanical intrinsic momentum. It gives value of critical bare mass of the shell determining threshold of stability. For the shell with the bare mass smaller or equal to the Planck's mass, the energy spectra of bound states are found. We obtain the expression for tunneling probability of the shell and construct the quasi-classical model of the pair creation and annihilation of the shells.Comment: 22 pages, sprocl.sty, 3 figure

Quarkonium production in the LHC era: a polarized perspective

Polarization measurements are usually considered as the most difficult challenge for the QCD description of quarkonium production. In fact, global data fits for the determination of the non-perturbative parameters of bound-state formation traditionally exclude polarization observables and use them as a posteriori verifications of the predictions, with perplexing results. With a change of perspective, we move polarization data to the centre of the study, advocating that they actually provide the strongest fundamental indications about the production mechanisms, even before we explicitly consider perturbative calculations. Considering psi(2S) and Y(3S) measurements from LHC experiments and state-of-the-art NLO short-distance calculations in the framework of non-relativistic QCD factorization (NRQCD), we perform a search for a kinematic domain where the polarizations can be correctly reproduced together with the cross sections, by systematically scanning the phase space and accurately treating the experimental uncertainties. This strategy provides a straightforward solution to the "quarkonium polarization puzzle" and reassuring signs that the theoretical framework is reliable. At the same time, the results expose unexpected hierarchies in the non-perturbative NRQCD parameters, that open new paths towards the understanding of bound-state formation in QCD.Comment: Submitted to Phys. Lett.

Away With SWOT Analysis: Use Defensive/Offensive Evaluation Instead

SWOT analysis, which delves into a business' strengths, weaknesses, opportunities, and threats, is used widely in firms and classrooms to distill fragmentary facts and figures into concise depictions of the strategic landscape.  Yet despite its popularity and longevity, the SWOT approach to situation assessment often is ineffective.  This article begins with a brief critique of the SWOT framework ­and typical SWOT analysis guidelines.  Thereafter, Defensive/Offensive Evaluation (DOE) is advanced as an effective alternative to SWOT analysis.  Because DOE is more theory-driven, it poses keener questions and promises more illuminating answers

Micromagnetic Simulation of Nanoscale Films with Perpendicular Anisotropy

A model is studied for the theoretical description of nanoscale magnetic films with high perpendicular anisotropy. In the model the magnetic film is described in terms of single domain magnetic grains with Ising-like behavior, interacting via exchange as well as via dipolar forces. Additionally, the model contains an energy barrier and a coupling to an external magnetic field. Disorder is taken into account in order to describe realistic domain and domain wall structures. The influence of a finite temperature as well as the dynamics can be modeled by a Monte Carlo simulation. Many of the experimental findings can be investigated and at least partly understood by the model introduced above. For thin films the magnetisation reversal is driven by domain wall motion. The results for the field and temperature dependence of the domain wall velocity suggest that for thin films hysteresis can be described as a depinning transition of the domain walls rounded by thermal activation for finite temperatures.Comment: Revtex, Postscript Figures, to be published in J. Appl.Phy

Her4 Promotes a Stem-like Phenotype in Osteosarcoma

Metastatic disease to the lungs is the primary cause of death for patients with pediatric osteosarcoma (OS). OS has a high degree of heterogeneity and genomic instability, making understanding the pathogenesis and drivers of metastasis of this disease challenging. In an effort to explain tumoral heterogeneity, the tumor initiating cell model (TIC) states that tumors are composed of cells that form the majority of the tumor and are terminally differentiated. This model however, attributes tumorigenesis, metastasis and chemoresistance to a distinct cell population with a stem-like phenotype that can be identified using selective markers. OS appears to follow this model where OS cells with tumor initiating potential can be identified by expression of Stro1, CD117 and embryonic stem cell transcription factors such as Sox2, Nanog and Oct3/4. Additionally, OS stem-like cells display high aldehyde dehydrogenase activity and sarcosphere formation under limited nutrient media and anchorage independence. These markers are not feasible targets for therapy due to their expression on normal tissue stem cells; however, upstream regulators of this phenotype may be targetable. Therefore, we investigated other modulators of the stem-like phenotype. Her4, a transmembrane receptor of the EGFR family, has been recently studied for its role in cancer. Previously, we demonstrated that Her4 is highly expressed in neuroblastoma, and OS, while others have shown its importance in Ewing sarcoma. This receptor is induced and required to survive stressors, like anchorage independence, serum starvation and chemotherapy treatment, which are similar in vitro conditions used to enrich for cells with tumor initiating potential. Therefore, we hypothesized that Her4 expression is an important regulator of a stem-like phenotype in OS. In sarcosphere culture, Her4 expression is induced and precedes the induction of CD117 and Stro1. OS cells with Her4 deleted by CRISPR/Cas9 have decreased aldehyde dehydrogenase activity and cannot upregulate the pluripotency transcription factors Sox2, Oct3/4 and Nanog even when in sarcospheres. Overexpression of exogenous Her4 was able to cause upregulation of these transcription factors and increase expression of CD117 in monolayer culture. We examined Her4 expression in OS diagnostic biopsies and determined the correlation with metastasis free survival. Tumors with high Her4 expression have higher probability of developing metastatic disease. In this dissertation, we demonstrate that Her4 expression is induced by conditions that enrich stem-like cells and its expression correlates with the ability to upregulate various OS TIC markers. Therefore, Her4 may contribute to pathogenesis of OS by conferring a stem-like phenotype

Card-Contingent Discounts As Sources Of Customer Satisfaction And Dissatisfaction: An Exploratory Inquiry

The reported exploratory study was undertaken to illuminate the effects of card-contingent discounts (CCDs) on customer satisfaction and dissatisfaction.  CCDs are price reductions on certain items that are given only to customers who present a card issued by the seller.  Results from our survey of 953 grocery store patrons indicate that shoppers tend to frame CCDs as price reductions to which they are entitled; denying discounts is judged unfair.  Typical customers are content, rather than delighted, when CCDs are granted and are disappointed or annoyed when CCDs are withheld.  CCDs, therefore, seem more likely to engender dissatisfaction than enhance satisfaction