We discuss D-dimensional scalar field interacting with a scale invariant random metric which is either a Gaussian field or a square of a Gaussian field. The metric depends on d dimensional coordinates (where d < D). By a projection to a lower dimensional subspace we obtain a scale invariant non-Gaussian model of Euclidean quantum field theory in D − d or d dimensions.

We consider subsemimodules and convex subsets of semimodules over semirings with an idempotent addition. We introduce a nonlinear projection on subsemimodules: the projection of a point is the maximal approximation from below of the point in the subsemimodule. We use this projection to separate a point from a convex set. We also show that the projection minimizes the analogue of Hilbert’s proje...

Berwald metrics are particular Finsler metrics which still have linear Berwald connections. Their complete classification is established in an earlier work, [Sz1], of this author. The main tools in these classification are the Simons-Berger holonomy theorem and the Weyl-group theory. It turnes out that any Berwald metric is a perturbed-Cartesian product of Riemannian, Minkowski, and such non-Ri...

Doust and Weston [5] introduced a new method called “enhanced negative type” for calculating a non trivial lower bound ℘T on the supremal strict p-negative type of any given finite metric tree (T, d). (In the context of finite metric trees any such lower bound ℘T > 1 is deemed to be non trivial.) In this paper we refine the technique of enhanced negative type and show how it may be applied more...

Doust and Weston [8] introduced a new method called “enhanced negative type” for calculating a non trivial lower bound ℘T on the supremal strict p-negative type of any given finite metric tree (T, d). (In the context of finite metric trees any such lower bound ℘T > 1 is deemed to be non trivial.) In this paper we refine the technique of enhanced negative type and show how it may be applied more...

It has been reported repeatedly that discriminative learning of distance metric boosts the pattern recognition performance. A weak point of ITML-based methods is that the distance threshold for similarity/dissimilarity constraints must be determined manually and it is sensitive to generalization performance, although the ITML-based methods enjoy an advantage that the Bregman projection framewor...

We construct a natural L-metric on the perturbed Seiberg-Witten moduli spaces Mμ+ of a compact 4-manifold M , and we study the resulting Riemannian geometry of Mμ+ . We derive a formula which expresses the sectional curvature of Mμ+ in terms of the Green operators of the deformation complex of the Seiberg-Witten equations. In case M is simply connected, we construct a Riemannian metric on the S...

Many-objective optimization problems (MaOPs) are challenging in scientific research. Research has tended to focus on algorithms rather than algorithm frameworks. In this paper, we introduce a projection-based evolutionary algorithm, MOEA/PII. Applying the idea of dimension reduction and decomposition, it divides objective space into projection plane free dimension(s). The balance between conver...

We show that an algebraic subvariety of the moduli space genus g Riemann surfaces is coarsely dense with respect to Teichmüller metric (or Thurston metric) if and only it has full dimension. apply this determine which strata abelian differentials have projection space. Furthermore, we prove a result on coarse density projections GL 2 (ℝ)-orbit closures in differentials.