Are we seeing the beginnings of Inflation?

Phantom Cosmology provides an unique opportunity to "connect" the phantom driven (low en- ergy meV scale) dark energy phase to the (high energy GUT scale) inflationary era. This is possible because the energy density increases in phantom cosmology. We present a concrete model where the energy density, but not the scale factor, cycles through phases of standard radiation/matter domi- nation followed by dark energy/inflationary phases, and the pattern repeating itself. An interesting feature of the model is that once we include interactions between the "phantom fluid" and ordinary matter, the Big rip singularity is avoided with the phantom phase naturally giving way to a near exponential inflationary expansion.Comment: 17 pages, 1 figur

An efficient algorithm for computing the distance between close partitions

A K -partition of a set S is a splitting of S into K non-overlapping classes that cover all elements of S . Numerous practical applications dealing with data partitioning or clustering require computing the distance between two partitions. Previous articles proved that one can compute it in polynomial time—minimum O ( | S | + K 2 ) and maximum O ( | S | + K 3 ) —using a reduction to the linear assignment problem. We propose several conditions for which the partition distance can be computed in O ( | S | ) time. In practical terms, this computation can be done in O ( | S | ) time for any two relatively resembling partitions (i.e. with distance less than | S | 5 ) except specially constructed cases. Finally, we prove that, even if there is a bounded number of classes for which the proposed conditions are not satisfied, one can still preserve the linear complexity by exploiting decomposition properties of the similarity matrix

Multiplicative functions that are close to their mean

We introduce a simple approach to study partial sums of multiplicative functions which are close to their mean value. As a first application, we show that a completely multiplicative function f : N→C satisfies ∑ f(n)_ (n≤x) = cx+O(1) with c ≠ 0 if and only if f(p) = 1 for all but finitely many primes and |f(p)| < 1 for the remaining primes. This answers a question of Imre Ruzsa. For the case c = 0, we show, under the additional hypothesis ∑_(p:|f(p)|<1)1/p < ∞, that f has bounded partial sums if and only if f(p) = χ(p)p^(it) for some non-principal Dirichlet character χ modulo q and t ∈ ℝ except on a finite set of primes that contains the primes dividing q, wherein |f(p)| < 1. This essentially resolves another problem of Ruzsa and generalizes previous work of the first and the second author on Chudakov's conjecture. We also consider some other applications, which include a proof of a recent conjecture of Aymone concerning the discrepancy of square-free supported multiplicative functions

Effect of cecal microbiota transplantation between different broiler breeds on the chick flora in the first week of life

The cecal microbiota plays numerous roles in chicken health and nutrition. Where such microbiota differs between lines exhibiting distinct phenotypes, microbiota transplantation offers scope to dissect the role of gut microbial communities in those traits. However, the composition and stability of transplants over time is relatively ill-defined and varying levels of success have been reported. In this study, we transplanted cecal contents from adult Roslin broilers into chicks from a different broiler line. Within 0.1% abundant (average) in the donor sample, 137 were detected in the treated group (75 were >0.1% abundant (average)) while only 88 were detected in the control group (29 were >0.1% abundant (average)). Our data therefore suggests that stable transplantation of the cecal microbiota between lines is achievable using the methods described in this paper

Informed Reactive Tabu Search for Graph Coloring

Tabu search (TS) has always been a very popular algorithm for graph coloring, both as a stand-alone optimizer as well as a subroutine inside population-based hybrid methods. We present two TS extensions that could allow previous TS algorithms to improve their behavior at almost no additional computational cost. First, we integrate two new evaluation functions which employ supplementary (structural or dynamic) information in addition to the conventional objective function (the number of edges with both ends of the same color). These new evaluation functions allow the search process to differentiate configurations not distinguished by the conventional evaluation function. The second extension concerns a reactive mechanism for improving the tabu list management. Theoretical arguments show that this reactive component completely eliminates the risk of getting blocked looping on plateaus. Numerical experiments show that the two proposed TS extensions can be very useful inside a stand-alone TS optimizer, as well as inside TS subroutines of state-of-the-art hybrid methods.