Fractional jumps: complete characterisation and an explicit infinite family

In this paper we provide a complete characterisation of transitive fractional jumps by showing that they can only arise from transitive projective automorphisms. Furthermore, we prove that such construction is feasible for arbitrarily large dimension by exhibiting an infinite class of projectively primitive polynomials whose companion matrix can be used to define a full orbit sequence over an affine space

On lattice profile of the elliptic curve linear congruential generators

Lattice tests are quality measures for assessing the intrinsic structure of pseudorandom number generators. Recently a new lattice test has been introduced by Niederreiter and Winterhof. In this paper, we present a general inequality that is satisfied by any periodic sequence. Then, we analyze the behavior of the linear congruential generators on elliptic curves (EC-LCG) under this new lattice test and prove that the EC-LCG passes it up to very high dimensions. We also use a result of Brandstätter and Winterhof on the linear complexity profile related to the correlation measure of order k to present lower bounds on the linear complexity profile of some binary sequences derived from the EC-LCG

IL-4 Deficiency Is Associated with Mechanical Hypersensitivity in Mice

Interleukin-4 (IL-4) is an anti-inflammatory and analgesic cytokine that induces opioid receptor transcription. We investigated IL-4 knockout (ko) mice to characterize their pain behavior before and after chronic constriction injury (CCI) of the sciatic nerve as a model for neuropathic pain. We investigated opioid responsivity and measured cytokine and opioid receptor gene expression in the peripheral and central nervous system (PNS, CNS) of IL-4 ko mice in comparison with wildtype (wt) mice. Naïve IL-4 ko mice displayed tactile allodynia (wt: 0.45 g; ko: 0.18 g; p<0.001), while responses to heat and cold stimuli and to muscle pressure were not different. No compensatory changes in the gene expression of tumor necrosis factor-alpha (TNF), IL-1β, IL-10, and IL-13 were found in the PNS and CNS of naïve IL-4 ko mice. However, IL-1β gene expression was stronger in the sciatic nerve of IL-4 ko mice (p<0.001) 28 days after CCI and only IL-4 ko mice had elevated IL-10 gene expression (p = 0.014). Remarkably, CCI induced TNF (p<0.01), IL-1β (p<0.05), IL-10 (p<0.05), and IL-13 (p<0.001) gene expression exclusively in the ipsilateral spinal cord of IL-4 ko mice. The compensatory overexpression of the anti-inflammatory and analgesic cytokines IL-10 and IL-13 in the spinal cord of IL-4 ko mice may explain the lack of genotype differences for pain behavior after CCI. Additionally, CCI induced gene expression of μ, κ, and δ opioid receptors in the contralateral cortex and thalamus of IL-4 ko mice, paralleled by fast onset of morphine analgesia, but not in wt mice. We conclude that a lack of IL-4 leads to mechanical sensitivity; the compensatory hyperexpression of analgesic cytokines and opioid receptors after CCI, in turn, protects IL-4 ko mice from enhanced pain behavior after nerve lesion

Extracellular vesicles in psychiatry research in the context of RDoC criteria

The analysis of extracellular vesicles has been accelerated because of the technological advancements in omics methods in recent decades. Extracellular vesicles provide multifaceted information regarding the functional status of the cells. This information would be critical in case of central nervous system cells, which are confined in a relatively sealed biological compartment. This obstacle is more dramatic in psychiatric disorders since their diagnosis primarily depend on the symptoms and signs of the patients. In this paper, we reviewed this rapidly advancing field by discussing definition of extracellular vesicles, their biogenesis and potential use as clinical biomarkers. Then we focused on their potential use in psychiatric disorders in the context of diagnosis and treatment of these disorders. Finally, we tried to combine the RDoC (Research Domain Criteria) with the use of extracellular vesicles in psychiatry research and practice. This review may offer new insights in both basic and translational research focusing on psychiatri

On the correlation of pseudorandom numbers generated by inversive methods

10.1007/s00605-007-0503-3Monatshefte fur Mathematik1533251-26

Quadratic functions with prescribed spectra

We study a class of quadratic p-ary functions Fp,n from \F_p^n to F_p, p ≥ 2, which are well-known to have plateaued Walsh spectrum; i.e., for each b ∈ F_p^n the Walsh transform fˆ(b) satisfies |fˆ(b)|^2 ∈ {0, p^(n+s)} for some integer 0 ≤ s ≤ n − 1. For various types of integers n, we determine possible values of s, construct Fp,n with prescribed spectrum, and present enumeration results. Our work generalizes some of the earlier results, in characteristic two, of Khoo et. al. (Des Codes Cryptogr, 38, 279–295, 2006) and Charpin et al. (IEEE Trans Inf Theory 51, 4286–4298, 2005) on semi-bent functions, and of Fitzgerald (Finite Fields Appl 15, 69–81, 2009) on quadratic forms