Dynamic Range Majority Data Structures

Given a set $P$ of coloured points on the real line, we study the problem of answering range $\alpha$-majority (or "heavy hitter") queries on $P$. More specifically, for a query range $Q$, we want to return each colour that is assigned to more than an $\alpha$-fraction of the points contained in $Q$. We present a new data structure for answering range $\alpha$-majority queries on a dynamic set of points, where $\alpha \in (0,1)$. Our data structure uses O(n) space, supports queries in $O((\lg n) / \alpha)$ time, and updates in $O((\lg n) / \alpha)$ amortized time. If the coordinates of the points are integers, then the query time can be improved to $O(\lg n / (\alpha \lg \lg n) + (\lg(1/\alpha))/\alpha))$. For constant values of $\alpha$, this improved query time matches an existing lower bound, for any data structure with polylogarithmic update time. We also generalize our data structure to handle sets of points in d-dimensions, for $d \ge 2$, as well as dynamic arrays, in which each entry is a colour.Comment: 16 pages, Preliminary version appeared in ISAAC 201

Impact of processed earwigs and their faeces on the aroma and taste of 'Chasselas' and 'Pinot Noir' wines

The abundance of the European earwig Forficula auricularia L. (Dermaptera, Forficulidae) in European vineyards increased considerably over the last few years. Although earwigs are omnivorous predators that prey on viticultural pests such as grape moths, they are also known to erode berries and to transfer fungal spores. Moreover, they are suspected to affect the human perception of wines both directly by their processing with the grapes and indirectly by the contamination of grape clusters with their faeces. In this study we artificially contaminated grapes with F. auricularia adults and/or their faeces and determined the impact on aroma and taste of white 'Chasselas' and red 'Pinot noir' wines. Whereas the addition of five living adults/kg grapes affected the olfactory sensation of 'Chasselas' wines only marginally, 0.6 gram of earwig faeces/kg grapes had a strong effect on colour, aroma and the general appreciation of 'Chasselas' wines. Faeces-contaminated wines were less fruity and less floral, the aroma was described as faecal and they were judged to be of lower quality. The contamination of 'Pinot noir' grapes with four different densities of living earwig adults (e.g. 0, 5, 10 and 20 individuals/kg grapes) showed that only wines contaminated with more than 10 earwigs/kg grapes smelled and tasted significantly different than the uncontaminated control wine. Earwig-contaminated 'Pinot noir' wines were judged to be of lower quality. The descriptors “animal”, “reductive”, “vegetal”, “acidic”, “bitter” and “tannic” characterised their sensory perception. In conclusion, our results show that there is a real risk of wine contamination by F. auricularia. In particular, earwig faeces and earwig adults at densities above a threshold of 5 to 10 individuals/kg grapes have the potential to reduce the quality of wines. The evolution of earwig populations in vineyards should therefore be monitored carefully in order to anticipate problems during vinification.

Nondeterministic Instance Complexity and Proof Systems with Advice

Motivated by strong Karp-Lipton collapse results in bounded arithmetic, Cook and Krajíček [1] have recently introduced the notion of propositional proof systems with advice. In this paper we investigate the following question: Given a language L , do there exist polynomially bounded proof systems with advice for L ? Depending on the complexity of the underlying language L and the amount and type of the advice used by the proof system, we obtain different characterizations for this problem. In particular, we show that the above question is tightly linked with the question whether L has small nondeterministic instance complexity

Geometric gauge potentials and forces in low-dimensional scattering systems

We introduce and analyze several low-dimensional scattering systems that exhibit geometric phase phenomena. The systems are fully solvable and we compare exact solutions of them with those obtained in a Born-Oppenheimer projection approximation. We illustrate how geometric magnetism manifests in them, and explore the relationship between solutions obtained in the diabatic and adiabatic pictures. We provide an example, involving a neutral atom dressed by an external field, in which the system mimics the behavior of a charged particle that interacts with, and is scattered by, a ferromagnetic material. We also introduce a similar system that exhibits Aharonov-Bohm scattering. We propose some practical applications. We provide a theoretical approach that underscores universality in the appearance of geometric gauge forces. We do not insist on degeneracies in the adiabatic Hamiltonian, and we posit that the emergence of geometric gauge forces is a consequence of symmetry breaking in the latter.Comment: (Final version, published in Phy. Rev. A. 86, 042704 (2012

Functional screening of willow alleles in Arabidopsis combined with QTL mapping in willow (Salix) identifies SxMAX4 as a coppicing response gene.

Willows (Salix spp.) are important biomass crops due to their ability to grow rapidly with low fertilizer inputs and ease of cultivation in short-rotation coppice cycles. They are relatively undomesticated and highly diverse, but functional testing to identify useful allelic variation is time-consuming in trees and transformation is not yet possible in willow. Arabidopsis is heralded as a model plant from which knowledge can be transferred to advance the improvement of less tractable species. Here, knowledge and methodologies from Arabidopsis were successfully used to identify a gene influencing stem number in coppiced willows, a complex trait of key biological and industrial relevance. The strigolactone-related More AXillary growth (MAX) genes were considered candidates due to their role in shoot branching. We previously demonstrated that willow and Arabidopsis show similar response to strigolactone and that transformation rescue of Arabidopsis max mutants with willow genes could be used to detect allelic differences. Here, this approach was used to screen 45 SxMAX1, SxMAX2, SxMAX3 and SxMAX4 alleles cloned from 15 parents of 11 mapping populations varying in shoot-branching traits. Single-nucleotide polymorphism (SNP) frequencies were locus dependent, ranging from 29.2 to 74.3 polymorphic sites per kb. SxMAX alleles were 98%-99% conserved at the amino acid level, but different protein products varying in their ability to rescue Arabidopsis max mutants were identified. One poor rescuing allele, SxMAX4D, segregated in a willow mapping population where its presence was associated with increased shoot resprouting after coppicing and colocated with a QTL for this trait

A Two-loop Test of Buscher's T-duality I

We study the two loop quantum equivalence of sigma models related by Buscher's T-duality transformation. The computation of the two loop perturbative free energy density is performed in the case of a certain deformation of the SU(2) principal sigma model, and its T-dual, using dimensional regularization and the geometric sigma model perturbation theory. We obtain agreement between the free energy density expressions of the two models.Comment: 28 pp, Latex, references adde

The Combinatorial World (of Auctions) According to GARP

Revealed preference techniques are used to test whether a data set is compatible with rational behaviour. They are also incorporated as constraints in mechanism design to encourage truthful behaviour in applications such as combinatorial auctions. In the auction setting, we present an efficient combinatorial algorithm to find a virtual valuation function with the optimal (additive) rationality guarantee. Moreover, we show that there exists such a valuation function that both is individually rational and is minimum (that is, it is component-wise dominated by any other individually rational, virtual valuation function that approximately fits the data). Similarly, given upper bound constraints on the valuation function, we show how to fit the maximum virtual valuation function with the optimal additive rationality guarantee. In practice, revealed preference bidding constraints are very demanding. We explain how approximate rationality can be used to create relaxed revealed preference constraints in an auction. We then show how combinatorial methods can be used to implement these relaxed constraints. Worst/best-case welfare guarantees that result from the use of such mechanisms can be quantified via the minimum/maximum virtual valuation function

Smoothed Analysis of the Minimum-Mean Cycle Canceling Algorithm and the Network Simplex Algorithm

The minimum-cost flow (MCF) problem is a fundamental optimization problem with many applications and seems to be well understood. Over the last half century many algorithms have been developed to solve the MCF problem and these algorithms have varying worst-case bounds on their running time. However, these worst-case bounds are not always a good indication of the algorithms' performance in practice. The Network Simplex (NS) algorithm needs an exponential number of iterations for some instances, but it is considered the best algorithm in practice and performs best in experimental studies. On the other hand, the Minimum-Mean Cycle Canceling (MMCC) algorithm is strongly polynomial, but performs badly in experimental studies. To explain these differences in performance in practice we apply the framework of smoothed analysis. We show an upper bound of $O(mn^2\log(n)\log(\phi))$ for the number of iterations of the MMCC algorithm. Here $n$ is the number of nodes, $m$ is the number of edges, and $\phi$ is a parameter limiting the degree to which the edge costs are perturbed. We also show a lower bound of $\Omega(m\log(\phi))$ for the number of iterations of the MMCC algorithm, which can be strengthened to $\Omega(mn)$ when $\phi=\Theta(n^2)$. For the number of iterations of the NS algorithm we show a smoothed lower bound of $\Omega(m \cdot \min \{ n, \phi \} \cdot \phi)$.Comment: Extended abstract to appear in the proceedings of COCOON 201