Local stability implies global stability for the 2-dimensional Ricker map

Consider the difference equation $x_{k+1}=x_k e^{\alpha-x_{n-d}}$ where $\alpha$ is a positive parameter and d is a non-negative integer. The case d = 0 was introduced by W.E. Ricker in 1954. For the delayed version d >= 1 of the equation S. Levin and R. May conjectured in 1976 that local stability of the nontrivial equilibrium implies its global stability. Based on rigorous, computer aided calculations and analytical tools, we prove the conjecture for d = 1.Comment: for associated C++ program, mathematica worksheet and output, see http://www.math.u-szeged.hu/~krisztin/ricke

A new quantum version of f-divergence

This paper proposes and studies new quantum version of $f$-divergences, a class of convex functionals of a pair of probability distributions including Kullback-Leibler divergence, Rnyi-type relative entropy and so on. There are several quantum versions so far, including the one by Petz. We introduce another quantum version ($\mathrm{D}_{f}^{\max}$, below), defined as the solution to an optimization problem, or the minimum classical $f$- divergence necessary to generate a given pair of quantum states. It turns out to be the largest quantum $f$-divergence. The closed formula of $\mathrm{D}_{f}^{\max}$ is given either if $f$ is operator convex, or if one of the state is a pure state. Also, concise representation of $\mathrm{D}_{f}^{\max}$ as a pointwise supremum of linear functionals is given and used for the clarification of various properties of the quality. Using the closed formula of $\mathrm{D}_{f}^{\max}$, we show: Suppose $f$ is operator convex. Then the\ maximum $f\,$- divergence of the probability distributions of a measurement under the state $\rho$ and $\sigma$ is strictly less than $\mathrm{D}_{f}^{\max}\left( \rho\Vert\sigma\right)$. This statement may seem intuitively trivial, but when $f$ is not operator convex, this is not always true. A counter example is $f\left( \lambda\right) =\left\vert 1-\lambda\right\vert$, which corresponds to total variation distance. We mostly work on finite dimensional Hilbert space, but some results are extended to infinite dimensional case.Comment: The proof of dual representation of the former version was misstated. An alternative proof is presente

Stationary quantum source coding

In this paper the quantum source coding theorem is obtained for a completely ergodic source. This results extends Shannon's classical theorem as well as Schumacher's quantum noiseless coding theorem for memoryless sources. The control of the memory effects requires earlier results of Hiai and Petz on high probability subspaces.Comment: 8 page

Equilibrium states and their entropy densities in gauge-invariant C*-systems

A gauge-invariant C*-system is obtained as the fixed point subalgebra of the infinite tensor product of full matrix algebras under the tensor product unitary action of a compact group. In the paper, thermodynamics is studied on such systems and the chemical potential theory developed by Araki, Haag, Kastler and Takesaki is used. As a generalization of quantum spin system, the equivalence of the KMS condition, the Gibbs condition and the variational principle is shown for translation-invariant states. The entropy density of extremal equilibrium states is also investigated in relation to macroscopic uniformity.Comment: 20 pages, revised in March 200

Wild plants used for food by Hungarian ethnic groups living in the Carpathian Basin

A list of plant species used for food in Hungary and among Hungarian ethnic groups of the Carpathian Basin during the 19th and 20th centuries was compiled from 71 ethnographic and ethnobotanical sources and a survey among contemporary Hungarian botanists. Species used as food, spice, beverage or occasional snacks were collected. Sources mention 236 plant species belonging to 68 families. Most wild fleshy fruits (mostly Rosa, Rubus, Cornus, Ribes, Vaccinium spp.), dry fruits and seeds (Fagus, Quercus, Corylus, Castanea, Trapa spp.), several green vegetables (e.g. Rumex, Urtica, Humulus, Chenopodiaceae spp., Ranunculus ficaria), bulbs and tubers (Lathyrus tuberosus, Helianthus tuberosus, Chaerophyllum bulbosum, Allium spp.) used for food in Europe, are also known to be consumed in Hungary. A characteristic feature of Hungarian plant use was the mass consumption of the underground parts of several marsh (e.g. Typha, Phragmites, Sagittaria, Alisma, Butomus, Bolboschoenus spp., as well as the endemic Armoracia macrocarpa) and steppe species (e.g. Crambe tataria, Rumex pseudonatronatus). Consuming wild food plants is still important among Hungarians living in Transylvania: even nowadays more than 40 species are gathered and used at some locations

Tularemia - possible increase and new risk factors

Purpose: Tularemia is a zoonotic disease caused by the bacterium Francisella tularensis. In Europe each year approximately 1200 human cases are reported. Four subspecies are currently known: tularensis (the most virulent form), holarctica (the most widespread form), mediasiatic, and novicida. In Austria Francisella tularensis supsp. holarctica is endemic in the eastern part of the country (Lower Austria and Burgenland), and is known to have a 5-year cycle. Zoonotic transmission from pet species in Europe has only been described in Norway due to a cat bite, as well as after an accidental exposure to the disease while spaying a cat. In 2014 first reports of clinically ill dogs were reported from Norway. Methods & Materials: As hunting with dogs has a long tradition in Austria, and as there are endemic areas for the disease a first serological screening of 80 hunting dogs used in the hunt for European brown hares (Lepus europaeus) was conducted. Results: Of these 80 dogs 5 tested positive for tularemia (6.25%, CI 2.1% - 14%). One positive dog had shown some clinical symptoms, however this female dog also tested positive for Brucella canis. Conclusion: This result shows that dogs not only have contact to the pathogen, but also seroconvert. The occurrence of the disease is thought to increase in the next years due to our changing climate, and this year there is a new hotspot of the disease in Austria (i.e. Salzburg). These changes, as well as the result of this study highlight the need to raise the awareness level of the disease, its possible increase and new risk factors