Loop and Path Spaces and Four-Dimensional BF Theories: Connections, Holonomies and Observables

We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A,B), where A is a connection for a fixed principal bundle P(M,G) and B is a 2-form on M. The relevant curvatures, parallel transports and holonomies are computed and their expressions in local coordinates are exhibited. When the 2-form B is given by the curvature of A, then the so-called non-abelian Stokes formula follows. For a generic 2-form B, we distinguish the cases when the parallel transport depends on the whole path of paths and when it depends only on the spanned surface. In particular we discuss generalizations of the non-abelian Stokes formula. We study also the invariance properties of the (trace of the) holonomy under suitable transformation groups acting on the pairs (A,B). In this way we are able to define observables for both topological and non-topological quantum field theories of the BF type. In the non topological case, the surface terms may be relevant for the understanding of the quark-confinement problem. In the topological case the (perturbative) four-dimensional quantum BF-theory is expected to yield invariants of imbedded (or immersed) surfaces in a 4-manifold M.Comment: TeX, 39 page

Euthanasia and physician-assisted suicide for patients with depression. Thought-provoking remarks

Euthanasia and medical assistance in dying entail daunting ethical and moral challenges, in addition to a host of medical and clinical issues, which are further complicated in cases of patients whose decision-making skills have been negatively affected or even impaired by psychiatric disorders. The authors closely focus on clinical depression and relevant European laws that have over the years set firm standards in such a complex field. Pertaining to the mental health realm specifically, patients are required to undergo a mental competence assessment in order to request aid in dying. The way psychiatrists deal and interact with decisionally capable patients who have decided to end their own lives, on account of sufferings which they find to be unbearable, may be influenced by subjective elements such as ethical and cultural biases on the part of the doctors involved. Moreover, critics of medical aid in dying claim that acceptance of such practices might gradually lead to the acceptance or practice of involuntary euthanasia for those deemed to be nothing more than a burden to society, a concept currently unacceptable to the vast majority of observers. Ultimately, the authors conclude, the key role of clinicians should be to provide alternatives to those who feel so hopeless as to request assistance in dying, through palliative care and effective social and health care policies for the weakest among patients: lonely, depressed or ill-advised people

A nonmonotone GRASP

A greedy randomized adaptive search procedure (GRASP) is an itera- tive multistart metaheuristic for difficult combinatorial optimization problems. Each GRASP iteration consists of two phases: a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Repeated applications of the con- struction procedure yields different starting solutions for the local search and the best overall solution is kept as the result. The GRASP local search applies iterative improvement until a locally optimal solution is found. During this phase, starting from the current solution an improving neighbor solution is accepted and considered as the new current solution. In this paper, we propose a variant of the GRASP framework that uses a new “nonmonotone” strategy to explore the neighborhood of the current solu- tion. We formally state the convergence of the nonmonotone local search to a locally optimal solution and illustrate the effectiveness of the resulting Nonmonotone GRASP on three classical hard combinatorial optimization problems: the maximum cut prob- lem (MAX-CUT), the weighted maximum satisfiability problem (MAX-SAT), and the quadratic assignment problem (QAP)

Cheating and the evolutionary stability of mutualisms

Interspecific mutualisms have been playing a central role in the functioning of all ecosystems since the early history of life. Yet the theory of coevolution of mutualists is virtually nonexistent, by contrast with well-developed coevolutionary theories of competition, predator–prey and host–parasite interactions. This has prevented resolution of a basic puzzle posed by mutualisms: their persistence in spite of apparent evolutionary instability. The selective advantage of 'cheating', that is, reaping mutualistic benefits while providing fewer commodities to the partner species, is commonly believed to erode a mutualistic interaction, leading to its dissolution or reciprocal extinction. However, recent empirical findings indicate that stable associations of mutualists and cheaters have existed over long evolutionary periods. Here, we show that asymmetrical competition within species for the commodities offered by mutualistic partners provides a simple and testable ecological mechanism that can account for the long-term persistence of mutualisms. Cheating, in effect, establishes a background against which better mutualists can display any competitive superiority. This can lead to the coexistence and divergence of mutualist and cheater phenotypes, as well as to the coexistence of ecologically similar, but unrelated mutualists and cheaters

Four-Dimensional Yang-Mills Theory as a Deformation of Topological BF Theory

The classical action for pure Yang--Mills gauge theory can be formulated as a deformation of the topological $BF$ theory where, beside the two-form field $B$, one has to add one extra-field $\eta$ given by a one-form which transforms as the difference of two connections. The ensuing action functional gives a theory that is both classically and quantistically equivalent to the original Yang--Mills theory. In order to prove such an equivalence, it is shown that the dependency on the field $\eta$ can be gauged away completely. This gives rise to a field theory that, for this reason, can be considered as semi-topological or topological in some but not all the fields of the theory. The symmetry group involved in this theory is an affine extension of the tangent gauge group acting on the tangent bundle of the space of connections. A mathematical analysis of this group action and of the relevant BRST complex is discussed in details.Comment: 74 pages, LaTeX, minor corrections; to be published in Commun. Math. Phy

The Birman-Schwinger Operator for a Parabolic Quantum Well in a Zero-Thickness Layer in the Presence of a Two-Dimensional Attractive Gaussian Impurity

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Model Fisik Kincir Air untuk Irigasi Pertanian

Physical model research of water wheel for agricultural irrigation is executed at Hidrotechnic's Laboratory University of Riau. Model that is utilized doesn't utilize model scale, but phenomenon of prototype will be represented by model that made. Water wheel bases executed field study previous, having alone uniqueness. Paddle wheel lap speed one every minute (RPM) and debit who can be lifted by waters jacking tube visual's are relative stable. Even so was known it must be water wheel condition be still get improved debit that can be lifted by waters jacking tube. Water wheel model is undershoot water wheel made bases prototype aught at the site or at agricultural location. This waterwheel is made at Technicals Engineering Material Laboratory. This Waterwheel model specification with diameter 55 cm, broad 6 cm, long fan 6 cm, total fan 18 numbers and heavy 1,764 kg. The research did by variated foots up and tube dimension so gotten by water wheel model with tubed optimal one. Variation of tube is 3, 6, 9 and 18 numbers with each volume saves 3,4 ml, 8,0 ml, and 16,8 ml whereas debit flows are not variated.Result of this experiment showing that Waterwheel speed regarde by flow speed that punches waterwheel fans, but relationship both is not linear. Total tube and tube volume regard paddle wheel lap. Diameter 0,8 cm tube can't lift waters because the diameter of tube are too small but diameter 1,3 cm and 1,7 cm tube both can lift flows.Maximum debits which diameter 1,3 tube can be lifted by jacking tube is 6,39 ml/dt, it happens upon tube amount 18 numbers whereas on diameter tube 1,7 cm maximum debits is 5,38 ml / dt happens upon tubed amount 6 numbers