Algorithmic Randomness

We consider algorithmic randomness in the Cantor space C of the infinite binary sequences. By an algorithmic randomness concept one specifies a set of elements of C, each of which is assigned the property of being random. Miscellaneous notions from computability theory are used in the definitions of randomness concepts that are essentially rooted in the following three intuitive randomness requirements: the initial segments of a random sequence should be effectively incompressible, no random sequence should be an element of an effective measure null set containing sequences with an “exceptional property”, and finally, considering betting games, in which the bits of a sequence are guessed successively, there should be no effective betting strategy that helps a player win an unbounded amount of capital on a random sequence. For various formalizations of these requirements one uses versions of Kolmogorov complexity, of tests, and of martingales, respectively. In case any of these notions is used in the definition of a randomness concept, one may ask in general for fundamental equivalent definitions in terms of the respective other two notions. This was a long-standing open question w.r.t. computable randomness, a central concept that had been introduced by Schnorr via martingales. In this thesis, we introduce bounded tests that we use to give a characterization of computable randomness in terms of tests. Our result was obtained independently of the prior test characterization of computable randomness due to Downey, Griffiths, and LaForte, who defined graded tests for their result. Based on bounded tests, we define bounded machines which give rise to a version of Kolmogorov complexity that we use to prove another characterization of computable randomness. This result, as in analog situations, allows for the introduction of interesting lowness and triviality properties that are, roughly speaking, “anti-randomness” properties. We define and study the notions lowness for bounded machines and bounded triviality. Using a theorem due to Nies, it can be shown that only the computable sequences are low for bounded machines. Further we show some interesting properties of bounded machines, and we demonstrate that every boundedly trivial sequence is K-trivial. Furthermore we define lowness for computable machines, a lowness notion in the setting of Schnorr randomness. We prove that a sequence is low for computable machines if and only if it is computably traceable. Gacs and independently Kucera proved a central theorem which states that every sequence is effectively decodable from a suitable Martin-Löf random sequence. We present a somewhat easier proof of this theorem, where we construct a sequence with the required property by diagonalizing against appropriate martingales. By a variant of that construction we prove that there exists a computably random sequence that is weak truth-table autoreducible. Further, we show that a sequence is computably enumerable self-reducible if and only if its associated real is computably enumerable. Finally we investigate interrelations between the Lebesgue measure and effective measures on C. We prove the following extension of a result due to Book, Lutz, and Wagner: A union of Pi-0-1 classes that is closed under finite variations has Lebesgue measure zero if and only if it contains no Kurtz random real. However we demonstrate that even a Sigma-0-2 class with Lebesgue measure zero need not be a Kurtz null class. Turning to Almost classes, we show among other things that every Almost class with respect to a bounded reducibility has computable packing dimension zero

VARIJABILNOST SESKVITERPENA ETARSKIH ULJA VRSTE TEUCRIUM MONTANUM L

The aim of this study is to determine the qualitative variability and relative presence of sesquiterpene hydrocarbons in essential oils samples of Teucrium montanum L. collected from two different substrate types. Four samples of essential oils from serpentinite and four from calcareous were obtained by the method of hydrodistillation from aboveground plant parts. Based on the results, it was shown that populations from serpentinite habitats synthesize 2 times more sesquiterpenes than from calcareous ones, while the compound 6-epi-β-cubeben was detected only in populations from calcareous. Edaphic characteristics of habitats affect the qualitative composition and relative presence of sesquiterpenes in essential oils, which has a significant application in biotechnology.Publishe

Serum albumin binding analysis and toxicological screening of novel chroman-2,4-diones as oral anticoagulants

Two chroman-2,4-dione derivatives, namely 2a and 2f, were tested as in vivo anticoagulants by seven days of continuous per os application to adult male Wistar rats in a concentration of 20 mg/kg of body weight. Derivatives were selected from a group of six previously intraperitoneally applied compounds on the basis of presenting remarkable activity in a concentration of 2 mg/kg of body weight. The derivatives 2a and 2f are VKORC1 inhibitors, and comparison of the absorption spectra, association, and dissociation constants suggested that the compounds will be bound to serum albumin in the same manner as warfarin is, leading to transfer towards the molecular target VKORC1. After oral administration, the compounds proved to be anticoagulants comparable with warfarin, inasmuch as the measured prothrombin times for 2a and 2f were 56.63 and 60.08 s, respectively. The INR values of 2a and 2f ranged from 2.6 to 2.8, recommending them as useful therapeutics in the treatment of patients suffering from thromboembolic events and atrial fibrillation. The high percentage of binding and high binding affinity of 2a and 2f towards serum albumin reduced the risk of induced internal bleeding. Several kinds of toxicity studies were performed to investigate whether or not 2a and 2f can cause pathological changes in the liver, kidneys, and DNA. The catalytic activity of serum enzymes, concentration and catalytic activity of liver and kidney oxidative stress markers and enzymes, respectively, as well as the observed hepatic and renal morphological changes indicated that the compounds in relation to warfarin induced irrelevant hepatic toxicity, no increment of necrosis, and inconsiderable oxidative damage in the liver and kidneys. Estimation of DNA damage using the comet assay confirmed that 2a and 2f caused no clinically significant genotoxicity. The higher activity and lower toxicity of 2f recommended this compound as a better drug candidate than 2a. (C) 2014 Elsevier Ireland Ltd. All rights reserved.Ministry of Education, Science and Technological Development, Republic of Serbia {[}III 43004, III 41010, OI 173020

Variable neuroprotective role of Filipendula ulmaria extract in rat hippocampus

We evaluated the influence of an antioxidant-rich extract of Filipendula ulmaria L. on anxiety levels induced by nano-sized particles of different calcium phosphates. Rats in experimental groups were administered with either nano-sized hydroxyapatite, tricalcium phosphate, or amorphous calcium phosphate in the presence of Filipendula ulmaria extract. Appropriate behavioral tests were performed to assess anxiety levels, while oxidative status and apoptosis parameters were determined in the hippocampus samples. The applied calcium phosphates increased oxidative stress markers in hippocampal tissue, accompanied by an enhanced pro-apoptotic mechanism. Moreover, the hippocampal immunoreactivity for brain-derived neurotrophic factor and GABAergic-A receptors was significantly lower following calcium phosphate nanoparticles intake. The observed functional and morphological alterations in the rat hippocampus occurred simultaneously with the anxiogenic response estimated in behavioral testing. The neuroprotective effect of Filipendulaulmariawas markedly manifested by the attenuation of oxidative damage induced by amorphous calcium phosphate and enhanced anti-apoptotic action in the rat hippocampus. The increased hippocampal immunoreactivity for brain-derived neurotrophic factor, GABAergic-A receptors and significant anxiolytic-like effects of Filipendula ulmaria may suggest a beneficial role of antioxidant supplementation in preventing anxiogenic response to nano-sized calcium phosphates