Survey on counting special types of polynomials

Most integers are composite and most univariate polynomials over a finite field are reducible. The Prime Number Theorem and a classical result of Gau{\ss} count the remaining ones, approximately and exactly. For polynomials in two or more variables, the situation changes dramatically. Most multivariate polynomials are irreducible. This survey presents counting results for some special classes of multivariate polynomials over a finite field, namely the the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), the relatively irreducible ones (irreducible but reducible over an extension field), the decomposable ones, and also for reducible space curves. These come as exact formulas and as approximations with relative errors that essentially decrease exponentially in the input size. Furthermore, a univariate polynomial f is decomposable if f = g o h for some nonlinear polynomials g and h. It is intuitively clear that the decomposable polynomials form a small minority among all polynomials. The tame case, where the characteristic p of Fq does not divide n = deg f, is fairly well-understood, and we obtain closely matching upper and lower bounds on the number of decomposable polynomials. In the wild case, where p does divide n, the bounds are less satisfactory, in particular when p is the smallest prime divisor of n and divides n exactly twice. The crux of the matter is to count the number of collisions, where essentially different (g, h) yield the same f. We present a classification of all collisions at degree n = p^2 which yields an exact count of those decomposable polynomials.Comment: to appear in Jaime Gutierrez, Josef Schicho & Martin Weimann (editors), Computer Algebra and Polynomials, Lecture Notes in Computer Scienc

A new ventrops (Diptera: Rhinophoridae) from Ethiopia

A new species of the Afrotropical endemic rhinophorid genus Ventrops is described, illustrated and compared with congeners

Private provision of public goods: Do individual climate protection efforts depend on perceptions of climate policy?

This paper extends the economic literature on the private provision of public goods by examining the relevance of perceptions of climate policy to voluntary contributions to the public good of climate protection. Based on an analytical model which allows for perceptions of climate policy such as justification of international climate policy, procedural trust and procedural justice to affect voluntary climate protection activities, we examined data from representative surveys among citizens in the USA and Germany. Our microeconometric analysis confirmed the prediction that the perceived justification of international climate policy is positively related to voluntary contributions to climate protection in both countries. We also found empirical support (mainly for the USA) that higher perceived procedural justice lowers citizens' propensity to adopt climate protection activities. In contrast, we found no support that higher perceived procedural trust reduces citizens' propensity to adopt such measures. In a broad interpretation, our empirical results imply that individuals' perceptions about the process of providing public goods should also be considered when analyzing the factors explaining voluntary individual contribution to public goods

Learning to Predict Image-based Rendering Artifacts with Respect to a Hidden Reference Image

Image metrics predict the perceived per-pixel difference between a reference image and its degraded (e. g., re-rendered) version. In several important applications, the reference image is not available and image metrics cannot be applied. We devise a neural network architecture and training procedure that allows predicting the MSE, SSIM or VGG16 image difference from the distorted image alone while the reference is not observed. This is enabled by two insights: The first is to inject sufficiently many un-distorted natural image patches, which can be found in arbitrary amounts and are known to have no perceivable difference to themselves. This avoids false positives. The second is to balance the learning, where it is carefully made sure that all image errors are equally likely, avoiding false negatives. Surprisingly, we observe, that the resulting no-reference metric, subjectively, can even perform better than the reference-based one, as it had to become robust against mis-alignments. We evaluate the effectiveness of our approach in an image-based rendering context, both quantitatively and qualitatively. Finally, we demonstrate two applications which reduce light field capture time and provide guidance for interactive depth adjustment.Comment: 13 pages, 11 figure

Consumers' willingness to offset their CO2 emissions from traveling: A discrete choice analysis of framing and provider contributions

This paper identifies potential drivers and individuals' willingness to pay (WTP) for offsetting their emissions from traveling. We focus on the effects of framing the polluting activity with different modes of transportation (i.e. bus and plane) and travel occasions (i.e. holiday and professional training) as well as the effects of contributions from the travel provider. The analyses are based on discrete choice experiments with a representative sample of about 1000 consumers from Germany. Applying mixed logit and latent class logit models, the findings suggest substantial framing effects resulting from the variation in the mode of transportation as well as a significantly higher WTP when offsets are matched by the travel provider 1:1. The findings further indicate that re-/afforestation projects in the participants' region are the preferred mode for compensation. Respondents who are more willing to offset emissions from traveling seem to be younger and female, have a higher income, exhibit stronger environmental and social preferences, and believe that offsetting is effective in protecting the climate

A Leptonic ALP Portal to the Dark Sector

We discuss the leptonic ALP portal as a simple scenario that connects observed discrepancies in anomalous magnetic moments to the Dark Matter relic abundance. In this framework an axion-like particle in the multi-MeV range couples to SM leptons and a DM fermion, with mass above the ALP mass but below a GeV. The ALP contributes to $(g-2)_\mu$ and $(g-2)_e$ dominantly through 2-loop Barr-Zee diagrams, while the DM abundance is generated by $p$-wave annihilation to ALP pairs. Constraints from beam-dump experiments, colliders and CMB probes are very stringent, and restrict the viable parameter space to a rather narrow region that will be tested in the near future.Comment: 12 pages, 5 figure

Taxonomic approach to the tachinid flies Dinera carinifrons (Fallén) (Diptera: Tachinidae) and Dinera fuscata Zhang and Shima using molecular and morphometric data

Molecular phylogenetic and traditional morphometric methods were applied to examine six Palaearctic taxa of the taxonomically difficult tachinid fly genus Dinera Robineau-Desvoidy (Diptera: Tachinidae), with particular reference to D. carinifrons (Fallén) and D. fuscata Zhang and Shima. Results of a phylogenetic analysis based on the mitochondrial markers 12S and 16S rDNA and multivariate statistical analyses of 19 morphometric characters were used to delimit both species. A lectotype was designated for D. carinifrons to stabilize the nomenclature in the group. Dinera carinifrons has a transpalaearctic distribution and is present in Central Europe, especially in high altitudes of the Alps. It differs from the similar and closely related D. fuscata in that it has a slightly larger body size, a dense greyish microtrichosity on the body, and different head proportions. Dinera fuscata, as delimited here, is widespread in the Palaearctic region, including Europe. Slight differences in both molecular and morphometric characters were found between western (Europe and Iran) and eastern (China and Japan) populations of D. fuscata, which are interpreted as an intraspecific variation. Differential diagnosis between D. carinifrons and D. fuscata is provided in the form of a revised portion of the determination key to the Palaearctic Dinera by Zhang and Shima (2006). CETPO project CZ.1.07/2.3.00/20.0166 (partly).Molekulárně fylogenetické a tradiční morfometrické metody byly využity ke studiu šesti palearktických druhů tachin rodu Dinera Robineau-Desvoidy (Diptera: Tachinidae), se zvláštním zřetelem na D. carinifrons (Fallén) a D. fuscata Zhang a Shima. Částečně i CETPO project CZ.1.07/2.3.00/20.0166