Kakeya sets over non-archimedean local rings

In a recent paper of Ellenberg, Oberlin, and Tao, the authors asked whether there are Besicovitch phenomena in F_q[[t]]^n. In this paper, we answer their question in the affirmative by explicitly constructing a Kakeya set in F_q[[t]]^n of measure 0. Furthermore, we prove that any Kakeya set in F_q[[t]]^2 or Z_p^2 is of Minkowski dimension 2.Comment: 10 page

Oribatid assemblies of tropical high mountains on some points of the “Gondwana-Bridge” – a case study

This work is the first part of a series of studies, which introduces the methodological possibilities of coenological and zoogeographical indication and – following the climate, vegetation and elevation zones – the pattern-describing analysis of the main Oribatid sinusia of the world explored till our days.This current work is a case-study, which displays the comparison of 9 examination sites from 3 different geographical locations. On each location, three vegetation types have been examined: a plain rain-forest, a mossforest and a mountainous paramo. Analyses are based on the hitherto non-published genus-level database and coenological tables of the deceased János Balogh professor. Occurrence of 18 genera is going to be published as new data for the given zoogeographical region

Explicit computations of Hida families via overconvergent modular symbols

In [Pollack-Stevens 2011], efficient algorithms are given to compute with overconvergent modular symbols. These algorithms then allow for the fast computation of $p$-adic $L$-functions and have further been applied to compute rational points on elliptic curves (e.g. [Darmon-Pollack 2006, Trifkovi\'c 2006]). In this paper, we generalize these algorithms to the case of families of overconvergent modular symbols. As a consequence, we can compute $p$-adic families of Hecke-eigenvalues, two-variable $p$-adic $L$-functions, $L$-invariants, as well as the shape and structure of ordinary Hida-Hecke algebras.Comment: 51 pages. To appear in Research in Number Theory. This version has added some comments and clarifications, a new example, and further explanations of the previous example

On Linear Codes with Random Multiplier Vectors and the Maximum Trace Dimension Property

Let $C$ be a linear code of length $n$ and dimension $k$ over the finite field $\mathbb{F}_{q^m}$. The trace code $\mathrm{Tr}(C)$ is a linear code of the same length $n$ over the subfield $\mathbb{F}_q$. The obvious upper bound for the dimension of the trace code over $\mathbb{F}_q$ is $mk$. If equality holds, then we say that $C$ has maximum trace dimension. The problem of finding the true dimension of trace codes and their duals is relevant for the size of the public key of various code-based cryptographic protocols. Let $C_{\mathbf{a}}$ denote the code obtained from $C$ and a multiplier vector $\mathbf{a}\in (\mathbb{F}_{q^m})^n$. In this paper, we give a lower bound for the probability that a random multiplier vector produces a code $C_{\mathbf{a}}$ of maximum trace dimension. We give an interpretation of the bound for the class of algebraic geometry codes in terms of the degree of the defining divisor. The bound explains the experimental fact that random alternant codes have minimal dimension. Our bound holds whenever $n\geq m(k+h)$, where $h\geq 0$ is the Singleton defect of $C$. For the extremal case $n=m(h+k)$, numerical experiments reveal a closed connection between the probability of having maximum trace dimension and the probability that a random matrix has full rank

Understanding Enemy Images in Central and Eastern European Politics. Towards an Interdisciplinary Approach

Europe has experienced a rise in politics based on antagonism, often discussed from the perspectives of populism and the mainstreaming of the ideologies of the radical right. In this study, we argue that there is a need for an interdisciplinary, theoretically broader and more empirically focused approach that fosters understanding of these developments. To explore the causal factors, we focus on the enemy images that are constructed and diffused by politicians, and their specific historical and structural contexts.V předchozích letech Evropa zažívá vzestup politiky založené na antagonismu, často diskutovaném v kontextu populismu a mainstreamingu ideologie radikální pravice. V tomto textu tvrdíme, že je třeba multidisciplinárního, teoreticky širšího a více empiricky zaměřeného přístupu pro porozumění tohoto vývoje. Pro zjištění kauzálních příčin se soustředíme na zobrazení nepřítele prezentované politiky a též na strukturální a specifické historické faktory

Multiscale Analysis of Spreading in a Large Communication Network

In temporal networks, both the topology of the underlying network and the timings of interaction events can be crucial in determining how some dynamic process mediated by the network unfolds. We have explored the limiting case of the speed of spreading in the SI model, set up such that an event between an infectious and susceptible individual always transmits the infection. The speed of this process sets an upper bound for the speed of any dynamic process that is mediated through the interaction events of the network. With the help of temporal networks derived from large scale time-stamped data on mobile phone calls, we extend earlier results that point out the slowing-down effects of burstiness and temporal inhomogeneities. In such networks, links are not permanently active, but dynamic processes are mediated by recurrent events taking place on the links at specific points in time. We perform a multi-scale analysis and pinpoint the importance of the timings of event sequences on individual links, their correlations with neighboring sequences, and the temporal pathways taken by the network-scale spreading process. This is achieved by studying empirically and analytically different characteristic relay times of links, relevant to the respective scales, and a set of temporal reference models that allow for removing selected time-domain correlations one by one

Variation for carbon isotope ratio in a set of emmer (Triticum dicoccum Schrank) and bread wheat (Triticum aestivum L.) accessions

A high level of drought tolerance is an important objective in breeding new generation wheat varieties. A group of six landraces of the emmer wheat (Triticum diccocum Schrank), as well as two landraces, two old cultivars and two modern varieties of bread wheat (Triticum aestivum L.) were evaluated for their ability to discriminate 13C, a trait related to stomatal closure and consequently, an important component tolerance to drought. Three emmer wheat landraces and one of the bread wheat landraces has the lowest. Therefore, emmer wheat may play the role of a donor of the tolerance to drought in wheat breeding programs targetting drought prone conditions.Key words: Emmer wheat, bread wheat, drought tolerance, carbon isotope ratio, discrimination

Circadian pattern and burstiness in mobile phone communication

The temporal communication patterns of human individuals are known to be inhomogeneous or bursty, which is reflected as the heavy tail behavior in the inter-event time distribution. As the cause of such bursty behavior two main mechanisms have been suggested: a) Inhomogeneities due to the circadian and weekly activity patterns and b) inhomogeneities rooted in human task execution behavior. Here we investigate the roles of these mechanisms by developing and then applying systematic de-seasoning methods to remove the circadian and weekly patterns from the time-series of mobile phone communication events of individuals. We find that the heavy tails in the inter-event time distributions remain robustly with respect to this procedure, which clearly indicates that the human task execution based mechanism is a possible cause for the remaining burstiness in temporal mobile phone communication patterns.Comment: 17 pages, 12 figure