Probabilistic Analysis of Optimization Problems on Generalized Random Shortest Path Metrics

Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis often falls short of explaining this performance. Because of this, "beyond worst-case analysis" of algorithms has recently gained a lot of attention, including probabilistic analysis of algorithms. The instances of many optimization problems are essentially a discrete metric space. Probabilistic analysis for such metric optimization problems has nevertheless mostly been conducted on instances drawn from Euclidean space, which provides a structure that is usually heavily exploited in the analysis. However, most instances from practice are not Euclidean. Little work has been done on metric instances drawn from other, more realistic, distributions. Some initial results have been obtained by Bringmann et al. (Algorithmica, 2013), who have used random shortest path metrics on complete graphs to analyze heuristics. The goal of this paper is to generalize these findings to non-complete graphs, especially Erd\H{o}s-R\'enyi random graphs. A random shortest path metric is constructed by drawing independent random edge weights for each edge in the graph and setting the distance between every pair of vertices to the length of a shortest path between them with respect to the drawn weights. For such instances, we prove that the greedy heuristic for the minimum distance maximum matching problem, the nearest neighbor and insertion heuristics for the traveling salesman problem, and a trivial heuristic for the $k$-median problem all achieve a constant expected approximation ratio. Additionally, we show a polynomial upper bound for the expected number of iterations of the 2-opt heuristic for the traveling salesman problem.Comment: An extended abstract appeared in the proceedings of WALCOM 201

Radiocarbon Chronologies and Extinction Dynamics of the Late Quaternary Mammalian Megafauna of the Taimyr Peninsula, Russian Federation

This paper presents 75 new radiocarbon dates based on late Quaternary mammal remains recovered from eastern Taimyr Peninsula and adjacent parts of the northern Siberian lowlands, Russian Federation, including specimens of woolly mammoth (Mammuthus primigenius), steppe bison (Bison priscus), muskox (Ovibos moschatus), moose (Alces alces), reindeer (Rangifer tarandus), horse (Equus caballus) and wolf (Canis lupus). New evidence permits reanalysis of megafaunal extinction dynamics in the Asian high Arctic periphery. Increasingly, radiometric records of individual species show evidence of a gap at or near the Pleistocene/Holocene boundary (PHB). In the past, the PHB gap was regarded as significant only when actually terminal, i.e., when it marked the apparent ‘‘last’’ occurrence of a species (e.g., current ‘‘last’’ occurrence date for woolly mammoth in mainland Eurasia is 9600 yr BP). However, for high Arctic populations of horses and muskoxen the gap marks an interruption rather than extinction, because their radiocarbon records resume, nearly simultaneously, much later in the Holocene. Taphonomic effects, ΔC14 flux, and biased sampling are unlikely explanations for these hiatuses. A possible explanation is that the gap is the signature of an event, of unknown nature, that prompted the nearly simultaneous crash of many megafaunal populations in the high Arctic and possibly elsewhere in Eurasia.

Probabilistic Analysis of Facility Location on Random Shortest Path Metrics

The facility location problem is an NP-hard optimization problem. Therefore, approximation algorithms are often used to solve large instances. Such algorithms often perform much better than worst-case analysis suggests. Therefore, probabilistic analysis is a widely used tool to analyze such algorithms. Most research on probabilistic analysis of NP-hard optimization problems involving metric spaces, such as the facility location problem, has been focused on Euclidean instances, and also instances with independent (random) edge lengths, which are non-metric, have been researched. We would like to extend this knowledge to other, more general, metrics. We investigate the facility location problem using random shortest path metrics. We analyze some probabilistic properties for a simple greedy heuristic which gives a solution to the facility location problem: opening the $\kappa$ cheapest facilities (with $\kappa$ only depending on the facility opening costs). If the facility opening costs are such that $\kappa$ is not too large, then we show that this heuristic is asymptotically optimal. On the other hand, for large values of $\kappa$, the analysis becomes more difficult, and we provide a closed-form expression as upper bound for the expected approximation ratio. In the special case where all facility opening costs are equal this closed-form expression reduces to $O(\sqrt[4]{\ln(n)})$ or $O(1)$ or even $1+o(1)$ if the opening costs are sufficiently small.Comment: A preliminary version accepted to CiE 201

The uncertainty principle and classical amplitudes

We study the variance in the measurement of observables during scattering events, as computed using amplitudes. The classical regime, characterised by negligible uncertainty, emerges as a consequence of an infinite set of relationships among multileg, multiloop amplitudes in a momentum-transfer expansion. We discuss two non-trivial examples in detail: the six-point tree and the five-point one-loop amplitudes in scalar QED. We interpret these relationships in terms of a coherent exponentiation of radiative effects in the classical limit which generalises the eikonal formula, and show how to recover the impulse, including radiation reaction, from this generalised eikonal. Finally, we incorporate the physics of spin into our framework

Beyond MFV in family symmetry theories of fermion masses

Minimal Flavour Violation (MFV) postulates that the only source of flavour changing neutral currents and CP violation, as in the Standard Model, is the CKM matrix. However it does not address the origin of fermion masses and mixing and models that do usually have a structure that goes well beyond the MFV framework. In this paper we compare the MFV predictions with those obtained in models based on spontaneously broken (horizontal) family symmetries, both Abelian and non-Abelian. The generic suppression of flavour changing processes in these models turns out to be weaker than in the MFV hypothesis. Despite this, in the supersymmetric case, the suppression may still be consistent with a solution to the hierarchy problem, with masses of superpartners below 1 TeV. A comparison of FCNC and CP violation in processes involving a variety of different family quantum numbers should be able to distinguish between various family symmetry models and models satisfying the MFV hypothesis.Comment: 34 pages, no figure

Vacuum Alignment in SUSY A4 Models

In this note we discuss the vacuum alignment in supersymmetric models with spontaneously broken flavour symmetries in the presence of soft supersymmetry (SUSY) breaking terms. We show that the inclusion of soft SUSY breaking terms can give rise to non-vanishing vacuum expectation values (VEVs) for the auxiliary components of the flavon fields. These non-zero VEVs can have an important impact on the phenomenology of this class of models, since they can induce an additional flavour violating contribution to the sfermion soft mass matrix of right-left (RL) type. We carry out an explicit computation in a class of SUSY A4 models predicting tri-bimaximal mixing in the lepton sector. The flavour symmetry breaking sector is described in terms of flavon and driving supermultiplets. We find non-vanishing VEVs for the auxiliary components of the flavon fields and for the scalar components of the driving fields which are of order m_{SUSY} x and m_{SUSY}, respectively. Thereby, m_{SUSY} is the generic soft SUSY breaking scale which is expected to be around 1 TeV and is the VEV of scalar components of the flavon fields. Another effect of these VEVs can be the generation of a mu term.Comment: 23 pages; added a new section on the relation to Supergravity; version accepted for publication in JHE

Ultraviolet Completion of Flavour Models

Effective Flavour Models do not address questions related to the nature of the fundamental renormalisable theory at high energies. We study the ultraviolet completion of Flavour Models, which in general has the advantage of improving the predictivity of the effective models. In order to illustrate the important features we provide minimal completions for two known A4 models. We discuss the phenomenological implications of the explicit completions, such as lepton flavour violating contributions that arise through the exchange of messenger fields.Comment: 18 pages, 8 figure

BPIFB1 (LPLUNC1) is upregulated in cystic fibrosis lung disease

Although the biology the PLUNC (recently renamed BPI fold, BPIF) family of secreted proteins is poorly understood, multiple array based studies have suggested that some are differentially expressed in lung diseases. We have examined the expression of BPIFB1 (LPLUNC1), the prototypic two-domain containing family member, in lungs from CF patients and in mouse models of CF lung disease. BPIFB1 was localized in CF lung samples along with BPIFA1, MUC5AC, CD68 and NE and directly compared to histologically normal lung tissues and that of bacterial pneumonia. We generated novel antibodies to mouse BPIF proteins to conduct similar studies on ENaC transgenic (ENaC-Tg) mice, a model for CF-like lung disease. Small airways in CF demonstrated marked epithelial staining of BPIFB1 in goblet cells but staining was absent from alveolar regions. BPIFA1 and BPIFB1 were not co-localised in the diseased lungs. In ENaC-Tg mice there was strong staining of both proteins in the airways and luminal contents. This was most marked for BPIFB1 and was noted within 2 weeks of birth. The two proteins were present in distinct cells within epithelium. BPIFB1 was readily detected in BAL from ENaC-Tg mice but was absent from wild-type mice. Alterations in the expression of BPIF proteins is associated with CF lung disease in humans and mice. It is unclear if this elevation of protein production, which results from phenotypic alteration of the cells within the diseased epithelium, plays a role in the pathogenesis of the disease

Preliminary genetic evidence of two different populations of Opisthorchis viverrini in Lao PDR

Opisthorchis viverrini is a major public health concern in Southeast Asia. Various reports have suggested that this parasite may represent a species complex, with genetic structure in the region perhaps being dictated by geographical factors and different species of intermediate hosts. We used four microsatellite loci to analyze O. viverrini adult worms originating from six species of cyprinid fish in Thailand and Lao PDR. Two distinct O. viverrini populations were observed. In Ban Phai, Thailand, only one subgroup occurred, hosted by two different fish species. Both subgroups occurred in fish from That Luang, Lao PDR, but were represented to very different degrees among the fish hosts there. Our data suggest that, although geographical separation is more important than fish host specificity in influencing genetic structure, it is possible that two species of Opisthorchis, with little interbreeding, are present near Vientiane in Lao PDR

Cooperative secretions facilitate host range expansion in bacteria

The majority of emergent human pathogens are zoonotic in origin, that is, they can transmit to humans from other animals. Understanding the factors underlying the evolution of pathogen host range is therefore of critical importance in protecting human health. There are two main evolutionary routes to generalism: organisms can tolerate multiple environments or they can modify their environments to forms to which they are adapted. Here we use a combination of theory and a phylogenetic comparative analysis of 191 pathogenic bacterial species to show that bacteria use cooperative secretions that modify their environment to extend their host range and infect multiple host species. Our results suggest that cooperative secretions are key determinants of host range in bacteria, and that monitoring for the acquisition of secreted proteins by horizontal gene transfer can help predict emerging zoonoses