While the basic greedy algorithm gives a semi-streaming algorithm with an approximation guarantee of 2 for the
unweighted
matching problem, it was only recently that Paz and Schwartzman obtained an ...analogous result for weighted instances. Their approach is based on the versatile local ratio technique and also applies to generalizations such as weighted hypergraph matchings. However, the framework for the analysis fails for the related problem of weighted matroid intersection and as a result the approximation guarantee for weighted instances did not match the factor 2 achieved by the greedy algorithm for unweighted instances.Our main result closes this gap by developing a semi-streaming algorithm with an approximation guarantee of
2
+
ε
for
weighted
matroid intersection, improving upon the previous best guarantee of
4
+
ε
. Our techniques also allow us to generalize recent results by Levin and Wajc on submodular maximization subject to matching constraints to that of matroid-intersection constraints. While our algorithm is an adaptation of the local ratio technique used in previous works, the analysis deviates significantly and relies on structural properties of matroid intersection, called kernels. Finally, we also conjecture that our algorithm gives a
(
k
+
ε
)
approximation for the intersection of
k
matroids but prove that new tools are needed in the analysis as the structural properties we use fail for
k
≥
3
.
An instance of
colorful
k
-
center
consists of points in a metric space that are colored red or blue, along with an integer
k
and a coverage requirement for each color. The goal is to find the ...smallest radius
ρ
such that there exist balls of radius
ρ
around
k
of the points that meet the coverage requirements. The motivation behind this problem is twofold. First, from fairness considerations: each color/group should receive a similar service guarantee, and second, from the algorithmic challenges it poses: this problem combines the difficulties of clustering along with the subset-sum problem. In particular, we show that this combination results in strong integrality gap lower bounds for several natural linear programming relaxations. Our main result is an efficient approximation algorithm that overcomes these difficulties to achieve an approximation guarantee of 3, nearly matching the tight approximation guarantee of 2 for the classical
k
-center problem which this problem generalizes. algorithms either opened more than
k
centers or only worked in the special case when the input points are in the plane.
The effects of a TRPV1 antagonist (AZD1386) were investigated in patients with acute pain. After removal of a mandibular third molar and at request of analgesia 103 patients randomly received 95 mg ...AZD1386 (n = 40), placebo (n = 40) or 500 mg naproxen (n = 23) in a double-blind manner. Plasma samples were drawn, and pain intensity and body temperature were measured during 8 h after drug administration. The pain intensity difference from drug intake was calculated as a percentage (PID%) and as a weighted sum over the 8 h (SPID%0-8 h). The time to first perceptible and first meaningful pain relief was recorded. SPID%(0-8) h showed no significant difference between AZD1386 and placebo (P = .132) but between naproxen and placebo (P = .038). AZD1386 had a rapid short-lasting analgesia and compared to placebo, PID% was significantly higher (P ≤ .026) at 0.25, 0.50, 0.75 and 1.00 h after drug administration. Correspondingly, for naproxen significantly higher PID% (P ≤ .021) was seen at 2.5, 3, 4, 5, 6, 7 and 8 h. The frequency of patients obtaining perceptible and meaningful pain relief was about 85% and 48% after AZD1386 and about 53% and 25% after placebo. The occurrence of perceptible and meaningful pain relief was significantly faster (P = .002 and P = .031) for AZD1386 compared to placebo. Adverse events were similar to placebo with the exception of 2 patients reporting chills. The highest individual body temperature after AZD1386 was 38.1°C, recorded in 2 patients. In summary, AZD1386 was well tolerated with a rapid analgesia that was short lasting despite sustained plasma concentration.
Anthropogenic underwater noise is a global pollutant of increasing concern but its impact on reproduction in fish is largely unknown. Hence, a better understanding of its consequences for this ...important link to fitness is crucial. Working in aquaria, we experimentally tested the impact of broadband noise exposure (added either continuously or intermittently), compared to a control, on the behaviour and reproductive success of the common goby (Pomatoschistus microps), a vocal fish with exclusive paternal care. Compared to the intermittent noise and control treatments, the continuous noise treatment increased latency to female nest inspection and spawning and decreased spawning probability. In contrast, many other female and male pre-spawning behaviours, and female ventilation rate (proxies for stress levels) did not differ among treatments. Therefore, it is likely that female spawning decisions were delayed by a reduced ability to assess male acoustic signals, rather than due to stress per se and that the silent periods in the intermittent noise treatment provided a respite where the females could assess the males. Taken together, we show that noise (of similar frequency range as anthropogenic boat noise) negatively affects reproductive success, particularly under a continuous noise exposure.
Studies of colonization of new habitats that appear from rapidly changing environments are interesting and highly relevant to our understanding of divergence and speciation. Here, we analyse ...phenotypic and genetic variation involved in the successful establishment of a marine fish (sand goby, Pomatoschistus minutus) over a steep salinity drop from 35 PSU in the North Sea (NE Atlantic) to two PSU in the inner parts of the post‐glacial Baltic Sea. We first show that populations are adapted to local salinity in a key reproductive trait, the proportion of motile sperm. Thereafter, we show that genome variation at 22,190 single nucleotide polymorphisms (SNPs) shows strong differentiation among populations along the gradient. Sequences containing outlier SNPs and transcriptome sequences, mapped to a draft genome, reveal associations with genes with relevant functions for adaptation in this environment but without overall evidence of functional enrichment. The many contigs involved suggest polygenic differentiation. We trace the origin of this differentiation using demographic modelling and find the most likely scenario is that at least part of the genetic differentiation is older than the Baltic Sea and is a result of isolation of two lineages prior to the current contact over the North Sea–Baltic Sea transition zone.
Using a combined experimental, genomic and demographic inference approach, we study the establishment of sand goby over a steep salinity gradient from the North Sea to the Baltic Sea. Sperm motility and outlier SNPs support local adaptation along the gradient, whereas demographic inference suggests that this adaptation involved ancient genetic variants having evolved either in glacial refugia or during ancient expansion wave before the Baltic Sea colonization.
The genetic architecture of mate preferences is likely to affect significant evolutionary processes, including speciation and hybridization. Here, we investigate laboratory hybrids between a pair of ...sympatric Lake Victoria cichlid fish species that appear to have recently evolved from a hybrid population between similar predecessor species. The species demonstrate strong assortative mating in the laboratory, associated with divergent male breeding coloration (red dorsum versus blue). We show in a common garden experiment, using DNA-based paternity testing, that the strong female mate preferences among males of the two species are fully recovered in a large fraction of their F2 hybrid generation. Individual hybrid females often demonstrated consistent preferences in multiple mate choice trials (more than or equal to five) across a year or more. This result suggests that female mate preference is influenced by relatively few major genes or genomic regions. These preferences were not changed by experience of a successful spawning event with a male of the non-preferred species in a no-choice single-male trial. We found no evidence for imprinting in the F2 hybrids, although the F1 hybrid females may have been imprinted on their mothers. We discuss this nearly Mendelian inheritance of consistent innate mate preferences in the context of speciation theory.
One of the classic results in scheduling theory is the $2$-approximation algorithm by Lenstra, Shmoys, and Tardos for the problem of scheduling jobs to minimize makespan on unrelated machines; i.e., ...job $j$ requires time $p_{ij}$ if processed on machine $i$. More than two decades after its introduction it is still the algorithm of choice even in the restricted model where processing times are of the form $p_{ij} \in \{p_j, \infty\}$. This problem, also known as the restricted assignment problem, is NP-hard to approximate within a factor less than $1.5$, which is also the best known lower bound for the general version. Our main result is a polynomial time algorithm that estimates the optimal makespan of the restricted assignment problem within a factor $33/17 + \epsilon \approx 1.9412 + \epsilon$, where $\epsilon > 0$ is an arbitrarily small constant. The result is obtained by upper bounding the integrality gap of a certain strong linear program, known as the configuration LP, that was previously successfully used for the related Santa Claus problem. Similar to the strongest analysis for that problem our proof is based on a local search algorithm that will eventually find a schedule of the mentioned approximation guarantee but is not known to converge in polynomial time. PUBLICATION ABSTRACT
We study minimizing the sum of weighted completion times in a concurrent open shop. We give a primal–dual 2-approximation algorithm for this problem. We also show that several natural linear ...programming relaxations for this problem have an integrality gap of 2. Finally, we show that this problem is inapproximable within a factor strictly less than 6/5 if
P
≠
NP
, or strictly less than 4/3 if the Unique Games Conjecture also holds.
In species with alternative reproductive tactics, there is much empirical support that parasitically spawning males have larger testes and greater sperm numbers as an evolved response to a higher ...degree of sperm competition, but support for higher sperm performance (motility, longevity and speed) by such males is inconsistent. We used the sand goby (Pomatoschistus minutus) to test whether sperm performance differed between breeding‐coloured males (small testes, large mucus‐filled sperm‐duct glands; build nests lined with sperm‐containing mucus, provide care) and parasitic sneaker‐morph males (no breeding colouration, large testes, rudimentary sperm‐duct glands; no nest, no care). We compared motility (per cent motile sperm), velocity, longevity of sperm, gene expression of testes and sperm morphometrics between the two morphs. We also tested if sperm‐duct gland contents affected sperm performance. We found a clear difference in gene expression of testes between the male morphs with 109 transcripts differentially expressed between the morphs. Notably, several mucin genes were upregulated in breeding‐coloured males and two ATP‐related genes were upregulated in sneaker‐morph males. There was a partial evidence of higher sperm velocity in sneaker‐morph males, but no difference in sperm motility. Presence of sperm‐duct gland contents significantly increased sperm velocity, and nonsignificantly tended to increase sperm motility, but equally so for the two morphs. The sand goby has remarkably long‐lived sperm, with only small or no decline in motility and velocity over time (5 min vs. 22 h), but again, this was equally true for both morphs. Sperm length (head, flagella, total and flagella‐to‐head ratio) did not differ between morphs and did not correlate with sperm velocity for either morph. Thus, other than a clear difference in testes gene expression, we found only modest differences between the two male morphs, confirming previous findings that increased sperm performance as an adaptation to sperm competition is not a primary target of evolution.
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