Packet Reordering Metrics to Enable Performance Comparison in IP-Networks

Despite the existence of several metrics to perform measurements on out-of-order packets, few works have used these metrics for comparative purposes. A potential reason for this is that the use of these simple singleton metrics makes it difficult to analyze all the effects of packet reordering. On the other hand, more complete metrics are represented in a vectorial manner, making comparative analysis challenging. In this paper, we present a scenario for testing and describe a methodology for conducting experiments to compare network paths with respect to unordered packets. The results of several simulations explore simple packet reordering metrics derived from vector metric that may allow future work to be benchmarked against. We demonstrated the behaviour of some TCP congestion control algorithms by adjusting different levels of reordering. We highlight good results with the Entropy reorder metric.

Prescribed Schouten Tensor in Locally Conformally Flat Manifolds

We consider the pseudo-Euclidean space $$({\mathbb {R}}^n,g)$$(Rn,g), with $$n \ge 3$$n≥3 and $$g_{ij} = \delta _{ij} \varepsilon _{i}$$gij=δijεi, where $$\varepsilon _{i} = \pm 1$$εi=±1, with at least one positive $$\varepsilon _{i}$$εi and non-diagonal symmetric tensors $$T = \sum \nolimits _{i,j}f_{ij}(x) dx_i \otimes dx_{j} $$T=∑i,jfij(x)dxi⊗dxj. Assuming that the solutions are invariant by the action of a translation $$(n-1)$$(n-1)- dimensional group, we find the necessary and sufficient conditions for the existence of a metric $$\bar{g}$$g¯ conformal to g, such that the Schouten tensor $$\bar{g}$$g¯, is equal to T. From the obtained results, we show that for certain functions h, defined in $$\mathbb {R}^{n}$$Rn, there exist complete metrics $$\bar{g}$$g¯, conformal to the Euclidean metric g, whose curvature $$\sigma _{2}(\bar{g}) = h$$σ2(g¯)=h.

Boundary Behaviour of Weil–Petersson and Fibre Metrics for Riemann Moduli Spaces

The Weil–Petersson and Takhtajan–Zograf metrics on the Riemann moduli spaces of complex structures for an $n$-fold punctured oriented surface of genus $g,$ in the stable range $g+2n>2,$ are shown here to have complete asymptotic expansions in terms of Fenchel–Nielsen coordinates at the exceptional divisors of the Knudsen–Deligne–Mumford compactification. This is accomplished by finding a full expansion for the hyperbolic metrics on the fibres of the universal curve as they approach the complete metrics on the nodal curves above the exceptional divisors and then using a push-forward theorem for conormal densities. This refines a two-term expansion due to Obitsu–Wolpert for the conformal factor relative to the model plumbing metric which in turn refined the bound obtained by Masur. A similar expansion for the Ricci metric is also obtained.

An elementary proof of MinVol(Rn) = 0 for n > 3

In this paper, we give an elementary proof of the result that the minimal volumes of R³ and R4 are zero. The approach is to construct a sequence of explicit complete metrics on them such that the sectional curvatures are bounded in absolute value by 1 and the volumes tend to zero. As a direct consequence, we get that MinVol (Rn) = 0 for n > 3.

On automorphism groups of countable structures

Strengthening a theorem of D. W. Kueker, this paper completely charaterizes which countable structures do not admit uncountable Lω1ω-elementarily equivalent models. In particular, it is shown that if the automorphism group of a countable structure M is abelian, or even just solvable, then there is no uncountable model of the Scott sentence of M. These results arise as part of a study of Polish groups with compatible left-invariant complete metrics.