On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

Parametric preference functionals under risk in the gain domain: a Bayesian analysis

The performance of rank dependent preference functionals under risk is comprehensively evaluated using Bayesian model averaging. Model comparisons are made at three levels of heterogeneity plus three ways of linking deterministic and stochastic models: the differences in utilities, the differences in certainty equivalents and contextualutility. Overall, the"bestmodel", which is conditional on the form of heterogeneity is a form of Rank Dependent Utility or Prospect Theory that cap tures the majority of behaviour at both the representative agent and individual level. However, the curvature of the probability weighting function for many individuals is S-shaped, or ostensibly concave or convex rather than the inverse S-shape commonly employed. Also contextual utility is broadly supported across all levels of heterogeneity. Finally, the Priority Heuristic model, previously examined within a deterministic setting, is estimated within a stochastic framework, and allowing for endogenous thresholds does improve model performance although it does not compete well with the other specications considered.

A causal role for posterior medial prefrontal cortex in choice-induced preference change

After a person chooses between two items, preference for the chosen item will increase and preference for the unchosen item will decrease because of the choice made. In other words, we tend to justify or rationalize our past behavior by changing our attitude. This phenomenon of choice-induced preference change has been traditionally explained by cognitive dissonance theory. Choosing something that is disliked or not choosing something that is liked are both cognitively inconsistent, and in order to reduce this inconsistency, people tend to change their subsequently stated preference in accordance with their past choices. Previously, neuroimaging studies identified posterior medial frontal cortex (pMFC) as a key brain region involved in cognitive dissonance. However, it still remains unknown whether the pMFC plays a causal role in inducing preference change following cognitive dissonance. Here, we demonstrate that 25-min 1-Hz repetitive transcranial magnetic stimulation (TMS) applied over the pMFC significantly reduces choice-induced preference change compared to sham stimulation, or control stimulation over a different brain region, demonstrating a causal role for the pMFC.

Observations on the flight paths of the day-flying moth Virbia lamae during periods of mate location: do males have a strategy for contacting the pheromone plume?

1. To maximize the probability of rapid contact with a female’s pheromone plume, the trajectories of male foraging flights might be expected to be directed with respect to wind flow and also to be energetically efficient. 2. Flights directed either upwind, downwind, or crosswind have been proposed as optimal strategies for rapid and/or energetically efficient plume contact. Other possible strategies are random and Lévy walks, which have trajectories and turn frequencies that are not dictated by the direction of wind flow. 3. The planar flight paths of males of the day-active moth Virbia lamae were recorded during the customary time of its sexual activity. 4. We found no directional preference in these foraging flights with respect to the direction of contemporaneous wind flow, but, because crosswind encompasses twice the possible orientations of either upwind or downwind, a random orientation is in effect a de facto crosswind strategy. 5. A crosswind preference should be favoured when the plume extends farther downwind than crosswind, and this strategy is realized by V. lamae males by a random orientation of their trajectories with respect to current wind direction

Organic and conventional fertilizer effects on a tritrophic interaction: parasitism, performance and preference of Cotesia vestalis

Interest in sustainable farming methods that rely on alternatives to conventional synthetic fertilizers and pesticides is increasing. Sustainable farming methods often utilize natural populations of predatory and parasitic species to control populations of herbivores, which may be potential pest species. We investigated the effects of several types of fertilizer, including those typical of sustainable and conventional farming systems, on the interaction between a herbivore and parasitoid. The effects of fertilizer type on percentage parasitism, parasitoid performance, parasitoid attack behaviour and responses to plant volatiles were examined using a model Brassica system, consisting of Brassica oleracea var capitata, Plutella xylostella (Lepidoptera) larvae and Cotesia vestalis (parasitoid). Percentage parasitism was greatest for P. xylostella larvae feeding on plants that had received either a synthetic ammonium nitrate fertilizer or were unfertilized, in comparison to those receiving a composite fertilizer containing hoof and horn. Parasitism was intermediate on plants fertilized with an organically produced animal manure. Male parasitoid tibia length showed the same pattern as percentage parasitism, an indication that offspring performance was maximized on the treatments preferred by female parasitoids for oviposition. Percentage parasitism and parasitoid size were not correlated with foliar nitrogen concentration. The parasitoids did not discriminate between hosts feeding on plants in the four fertilizer treatments in parasitoid behaviour assays, but showed a preference for unfertilized plants in olfactometer experiments. The percentage parasitism and tibia length results provide support for the preference–performance hypothesis

A stated preference valuation of the non-market benefits of pollination services in the UK

Using a choice experiment survey this study examines the UK public's willingness to pay to conserve insect pollinators in relation to the levels of two pollination service benefits: maintaining local produce supplies and the aesthetic benefits of diverse wildflower assemblages. Willingness to pay was estimated using a Bayesian mixed logit with two contrasting controls for attribute non-attendance, exclusion and shrinkage. The results suggest that the UK public have an extremely strong preference to avoid a status quo scenario where pollinator populations and pollination services decline. Total willingness to pay was high and did not significantly vary between the two pollination service outputs, producing a conservative total of £379M over a sample of the tax-paying population of the UK, equivalent to £13.4 per UK taxpayer. Using a basic production function approach, the marginal value of pollination services to these attributes is also extrapolated. The study discusses the implications of these findings and directions for related future research into the non-market value of pollination and other ecosystem services.

A scalable expressive ensemble learning using Random Prism: a MapReduce approach

The induction of classification rules from previously unseen examples is one of the most important data mining tasks in science as well as commercial applications. In order to reduce the influence of noise in the data, ensemble learners are often applied. However, most ensemble learners are based on decision tree classifiers which are affected by noise. The Random Prism classifier has recently been proposed as an alternative to the popular Random Forests classifier, which is based on decision trees. Random Prism is based on the Prism family of algorithms, which is more robust to noise. However, like most ensemble classification approaches, Random Prism also does not scale well on large training data. This paper presents a thorough discussion of Random Prism and a recently proposed parallel version of it called Parallel Random Prism. Parallel Random Prism is based on the MapReduce programming paradigm. The paper provides, for the first time, novel theoretical analysis of the proposed technique and in-depth experimental study that show that Parallel Random Prism scales well on a large number of training examples, a large number of data features and a large number of processors. Expressiveness of decision rules that our technique produces makes it a natural choice for Big Data applications where informed decision making increases the user’s trust in the system.

A moment problem for random discrete measures

Let X be a locally compact Polish space. A random measure on X is a probability measure on the space of all (nonnegative) Radon measures on X. Denote by K(X) the cone of all Radon measures η on X which are of the form η =

Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of ℝ d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.

Recurrence for quenched random Lorentz tubes

We consider the billiard dynamics in a striplike set that is tessellated by countably many translated copies of the same polygon. A random configuration of semidispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global choice of scatterers, is called quenched random Lorentz tube. We prove that under general conditions, almost every system in the ensemble is recurrent.

Systematic and random errors between collocated satellite ice water path observations

There remains large disagreement between ice-water path (IWP) in observational data sets, largely because the sensors observe different parts of the ice particle size distribution. A detailed comparison of retrieved IWP from satellite observations in the Tropics (!30 " latitude) in 2007 was made using collocated measurements. The radio detection and ranging(radar)/light detection and ranging (lidar) (DARDAR) IWP data set, based on combined radar/lidar measurements, is used as a reference because it provides arguably the best estimate of the total column IWP. For each data set, usable IWP dynamic ranges are inferred from this comparison. IWP retrievals based on solar reflectance measurements, in the moderate resolution imaging spectroradiometer (MODIS), advanced very high resolution radiometer–based Climate Monitoring Satellite Applications Facility (CMSAF), and Pathfinder Atmospheres-Extended (PATMOS-x) datasets, were found to be correlated with DARDAR over a large IWP range (~20–7000 g m -2 ). The random errors of the collocated data sets have a close to lognormal distribution, and the combined random error of MODIS and DARDAR is less than a factor of 2, which also sets the upper limit for MODIS alone. In the same way, the upper limit for the random error of all considered data sets is determined. Data sets based on passive microwave measurements, microwave surface and precipitation products system (MSPPS), microwave integrated retrieval system (MiRS), and collocated microwave only (CMO), are largely correlated with DARDAR for IWP values larger than approximately 700 g m -2 . The combined uncertainty between these data sets and DARDAR in this range is slightly less MODIS-DARDAR, but the systematic bias is nearly an order of magnitude.

Self-concept clarity and compulsive Internet use: the role of preference for virtual interactions and employment status in British and North-American samples

Background and Aims Compulsive Internet Use (CIU) describes a maladaptive relationship with the Internet characterised by loss of control and conflict. Although also affecting adults, most studies use teenage samples, and theoretical development on risk factors is scarce. According to Davis (2001), the social connectivity function of the Internet is key in identifying traits associated with CIU. Since Self-Concept Clarity (SCC) is strongly related to social anxiety, and virtual interactions allow “self-edition”, we hypothesized that individuals low in SCC could choose virtual interactions as safer alternative to satisfy their social needs. This could in turn increase the risk of CIU. Building on a previous study, we also expected CIU to be more harmful in the unemployed. Methods We collected samples from the UK (N = 532) and US (N = 502) with equal distribution of employed and unemployed individuals. We ran Measurement Invariance tests to confirm that the constructs were equivalent across countries. Subsequently, we conducted mediation and moderation analysis to test our hypothesis with Multigroup Confirmatory Factor Analysis. Results Measurement Invariance was confirmed. The relationship between SCC and CIU was partially mediated by preference of virtual interactions in both countries. This preference was significantly related to lower social support. Short term unemployment seemed to accentuate the negative impact of CIU on life satisfaction in both countries, although only marginally significantly in the US. The unemployed reported significantly lower levels of life satisfaction. Conclusion We demonstrated that SCC is a key vulnerability factor to CIU in adults, and confirmed the additional risks for the unemployed.