Alternating Projections and Douglas-Rachford for Sparse Affine Feasibility

The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved nonconvex relaxations. In this work we consider elementary methods based on projections for solving a sparse feasibility problem without employing convex heuristics. In a recent paper Bauschke, Luke, Phan and Wang (2014) showed that, locally, the fundamental method of alternating projections must converge linearly to a solution to the sparse feasibility problem with an affine constraint. In this paper we apply different analytical tools that allow us to show global linear convergence of alternating projections under familiar constraint qualifications. These analytical tools can also be applied to other algorithms. This is demonstrated with the prominent Douglas-Rachford algorithm where we establish local linear convergence of this method applied to the sparse affine feasibility problem.Comment: 29 pages, 2 figures, 37 references. Much expanded version from last submission. Title changed to reflect new development

The framing of charitable giving: A field experiment at bottle refund machines in Germany

This article investigates the decision of consumers at bottle refund machines to either reclaim their bottle deposit or to donate the refund to a non-profit organization. The study documents the unique pre-intervention data on donating behaviour and introduces a field experiment to increase donation levels. The design comprised the strategic framing of the situation by highlighting different cues about the normative, descriptive and local expectations of charitable giving as well as cues about the warm glow of donating money. The experiment took place in 20 supermarkets in Germany and lasted for 12 months. By varying the experimental design and using different modelling approaches, the study arrives at the conclusion that individuals largely act consistent with the assumption having self-regarding preferences that are stable and difficult to change. Hence, our pre-test and postintervention data stand in sharp contrast to results from lab experiments

Predicting chemical environments of bacteria from receptor signaling

Sensory systems have evolved to respond to input stimuli of certain statistical properties, and to reliably transmit this information through biochemical pathways. Hence, for an experimentally well-characterized sensory system, one ought to be able to extract valuable information about the statistics of the stimuli. Based on dose-response curves from in vivo fluorescence resonance energy transfer (FRET) experiments of the bacterial chemotaxis sensory system, we predict the chemical gradients chemotactic Escherichia coli cells typically encounter in their natural environment. To predict average gradients cells experience, we revaluate the phenomenological Weber's law and its generalizations to the Weber-Fechner law and fold-change detection. To obtain full distributions of gradients we use information theory and simulations, considering limitations of information transmission from both cell-external and internal noise. We identify broad distributions of exponential gradients, which lead to log-normal stimuli and maximal drift velocity. Our results thus provide a first step towards deciphering the chemical nature of complex, experimentally inaccessible cellular microenvironments, such as the human intestine.Comment: DG and GM contributed equally to this wor

Bounds on the exponent of primitivity which depend on the spectrum and the minimal polynomial

AbstractSuppose A is an n × n nonnegative primitive matrix whose minimal polynomial has degree m. We conjecture that the well-known bound on the exponent of primitivity (n − 1)2 + 1, due to Wielandt, can be replaced by (m − 1)2 + 1. The only case for which we cannot prove the conjecture is when m ⩾ 5, the number of distinct eigenvalues of A is m − 1 or m, and the directed graph of A has no circuits of length shorter than m − 1, but at least one of its vertices lies on a circuit of length not shorter than m. We show that m(m − 1) is always a bound on the exponent, this being an improvement on Wielandt's bound when m < n. For the case in which A is also symmetric, the bound which we obtain is 2(m − 1). To obtain our results we prove a lemma which shows that for a (general) nonnegative matrix, the number of its distinct eigenvalues is an upper bound on the length of the shortest circuit in its directed graph

The Modified Pharaoh Approach: Stingless bees mummify beetle parasites alive

Social insect colonies usually live in nests, which are often invaded by parasitic species^1^. Workers from these colonies use different defence strategies to combat invaders^1^. Nevertheless, some parasitic species are able to bypass primary colony defences due to their morphology and behaviour^1-3^. In particular, some beetle nest invaders cannot be killed or removed by workers of social bees^2-5^, thus creating the need for alternative social defence strategies to ensure colony survival. Here we show, using Diagnostic Radioentomology^6^, that stingless bee workers _Trigona carbonaria_, immediately mummify invading destructive nest parasites _Aethina tumida_ alive, with a mixture of resin, wax and mud, thereby preventing severe damage to the colony. In sharp contrast to the responses of honeybee^7^ and bumblebee colonies^8^, the rapid live mummification strategy of _T. carbonaria_ effectively prevents beetle parasite advancements and removes their ability to reproduce. The convergent evolution of live mummification by stingless bees and social encapsulation by honeybees^3^ suggests that colonies of social bees generally rely on, secondary defence mechanisms when harmful nest intruders cannot be killed or ejected easily. This process is analogous to immune responses in animals

Ingestion of amniotic fluid enhances the facilitative effect of VTA morphine on the onset of maternal behavior in virgin rats

Previous research has shown that injection of morphine into the ventral tegmental area(VTA) facilitates the onset of maternal behavior in virgin female rats, and injection of the opioid antagonist naltrexone into the VTA disrupts the onset of maternal behavior in parturient rats. Placentophagia – ingestion of placenta and amniotic fluid, usually at parturition – modifies central opioid processes. Ingestion of the active substance in placenta and amniotic fluid, Placental Opioid-Enhancing Factor (POEF), enhances the hypoalgesic effect of centrally administered morphine, and more specifically, enhances δ- and κ-opioid-receptor-\ud mediated hypoalgesia and attenuates μ-opioid-receptor-mediated hypoalgesia. POEF (in placenta or amniotic fluid) ingestion does not, by itself, produce hypoalgesia. In the\ud present study, we tested the hypothesis that ingestion of amniotic fluid enhances the facilitative effect of opioid activity (unilateral morphine injection) in the VTA on the rate of onset of maternal behavior. Virgin female Long-Evans rats were given one intra-VTA injection of morphine sulfate (0.0, 0.01, or 0.03 μg, in saline) and an orogastric infusion of 0.25 ml amniotic fluid or saline once each day of the first three days of the 10-day testing\ud period. Subjects were continuously exposed to foster pups that were replaced every 12 h; replacement of pups was followed by a 15-min observation period. Maternal behavior\ud latency was determined by the first of two consecutive tests wherein the subject displayed pup retrieval, pup licking in the nest, and crouching over all foster pups, during the 15-min observation. We confirmed the previous finding that the VTA injection, alone, of 0.03 μg morphine shortened the latency to show maternal behavior and that 0.0 μg and 0.01 μg morphine did not. Ingestion of amniotic fluid (and therefore POEF) facilitated the onset of\ud maternal behavior in rats receiving an intra-VTA microinjection of an otherwise subthreshold dose of morphine (0.01 μg)