Multifractal spectrum of phase space related to generalized thermostatistics

We consider a self-similar phase space with specific fractal dimension $d$ being distributed with spectrum function $f(d)$. Related thermostatistics is shown to be governed by the Tsallis formalism of the non-extensive statistics, where the non-additivity parameter is equal to ${\bar\tau}(q)\equiv 1/\tau(q)>1$, and the multifractal function $\tau(q)= qd_q-f(d_q)$ is the specific heat determined with multifractal parameter $q\in [1,\infty)$. In this way, the equipartition law is shown to take place. Optimization of the multifractal spectrum function $f(d)$ derives the relation between the statistical weight and the system complexity. It is shown the statistical weight exponent $\tau(q)$ can be modeled by hyperbolic tangent deformed in accordance with both Tsallis and Kaniadakis exponentials to describe arbitrary multifractal phase space explicitly. The spectrum function $f(d)$ is proved to increase monotonically from minimum value $f=-1$ at $d=0$ to maximum one $f=1$ at $d=1$. At the same time, the number of monofractals increases with growth of the phase space volume at small dimensions $d$ and falls down in the limit $d\to 1$.Comment: 16 pages, 7 figure

Forecasting the surface roughness of the workpiece in the round external grinding

The article gives an analysis of the influence of technological factors on the parameters of the surface roughness during the machining of workpieces with the abrasive tools, based on the use of the modern mathematical apparatus of the theory of probability. It is shown that when processing with abrasive tools, the formation of surface microrelief is directly related to the mechanism of material removal in the area of contact between the workpiece and the tool. The main parameters of the contact zone are its dimensions and parameters of the material removal processes, which are characterized by the probabilities of removal or non-removal of the material. The obtained dependences take into account the parameters of the state of the working surface of the tool and can be used to calculate the basic parameters of the surface roughness in round external grinding. The made estimation of the influence of technological factors on the roughness of the surface of the workpiece being processed allows for the selection of the most significant ones, the changes of which must be taken into account when designing grinding operations

Mathematical model of the mechanical properties of Ti-alloyed hypoeutectic cast iron for mixer blades

The object of research is hypoeutectic cast iron intended for cast parts operating under abrasive friction conditions. Such parts are mixer blades, the operational properties of which include durability, assessed by abrasion resistance and strength. To give the blades such properties, cast irons, which are materials of the blades, are alloyed with elements that contribute to the formation of carbides of various compositions. The main problem that impedes the targeted selection of materials for mixer blades or finished blades from different materials or different chemical composition is the lack of substantiated selection criteria. If the shipment is carried out only with the provision of data on the chemical composition of the alloy, it is necessary to be able to evaluate the expected mechanical properties, in particular abrasion resistance and strength. Using the methods of regression analysis, a mathematical model has been obtained that includes two regression equations, which allows for a targeted selection of the chemical composition that provides the maximum possible value of mechanical properties – ultimate strength and coefficient of wear resistance. Optimization of the chemical composition, carried out according to this model, made it possible to determine the following chemical composition: C=2.94 %, Ceq=3.3 %, Ti=1.56 %, providing the maximum ultimate strength σb=391 MPa; C=2.78 %, Ceq=3.14 %, Ti=1.61 %, providing a maximum wear resistance coefficient Kwr=12 %. In the case of priority of the strength criterion, the calculated optimal chemical composition makes it possible to reduce the mass-dimensional characteristics of the mixing units of the mixers. A procedure is proposed for using this model to select a batch of blades with the expected best performance propertie

DIAL measurements of the vertical ozone distribution at the Siberian lidar station

The paper presents the results of DIAL measurements of the vertical ozone distribution at the Siberian lidar station. Sensing is performed according to the method of differential absorption and scattering at wavelength pair of 299/341 nm, which are, respectively, the first and second Stokes components of SRS conversion of 4th harmonic of Nd:YAG laser (266 nm) in hydrogen. Lidar with receiving mirror 0.5 m in diameter is used to implement sensing of vertical ozone distribution in altitude range of 6-16 km. The temperature correction of zone absorption coefficients is introduced in the software to reduce the retrieval errors

Acceleration of GNSS applications development and facilitation of their broad acceptance in Ukraine through international cooperation and own experience

GNSS are used around the globe in a variety of applications and the number of GNSS enabled devices tends to grow dramatically in the nearest years. This article aims to present the experience of NAU in development and research of GNSS applications and technologies together with international cooperationHorizon 202

Novel Budesonide Suppository and Standard Budesonide Rectal Foam Induce High Rates of Clinical Remission and Mucosal Healing in Active Ulcerative Proctitis : a Randomised, Controlled, Non-inferiority Trial

Publisher Copyright: © The Author(s) 2022. Published by Oxford University Press on behalf of European Crohn’s and Colitis Organisation.BACKGROUND AND AIMS: Proctitis is the least extensive type of ulcerative colitis, for which rectal therapy is rarely studied and is underused. This study evaluated the efficacy, safety, and patient's preference of a novel formulation of budesonide suppository 4 mg, compared with a commercially available budesonide rectal foam 2 mg, for the treatment of mild to moderate ulcerative proctitis. METHODS: This was a randomised, double-blind, double-dummy, active-controlled trial. Patients were randomly assigned in a 1:1 ratio to receive either budesonide 4 mg suppository or budesonide 2 mg foam once daily for 8 weeks. The co-primary endpoints were changes from baseline to Week 8 in clinical symptoms, for which clinical remission was defined as having a modified Ulcerative Colitis-Disease Activity Index [UC-DAI] subscore for stool frequency of 0 or 1 and a subscore for rectal bleeding of 0, and mucosal healing, defined as having a modified UC-DAI subscore for mucosal appearance of 0 or 1. Using a more stringent criterion, we additionally analysed deepened mucosal healing, which was defined as a mucosal appearance subscore of 0. Patient's preference, physician's global assessment, and quality of life were also assessed and analysed. RESULTS: Overall, 286 and 291 patients were included in the 4 mg suppository and 2 mg foam groups, respectively. Budesonide 4 mg suppository met the prespecified criterion for non-inferiority to the 2 mg foam in both co-primary endpoints of clinical remission and mucosal healing. Secondary endpoints consistently supported the non-inferiority of the suppository. Trends in favour of the suppository were observed in the subgroup of mesalazine non-responders. More patients reported a preference for the suppository over rectal foam. CONCLUSIONS: In patients with ulcerative proctitis, budesonide 4 mg suppository was non-inferior to budesonide 2 mg foam in efficacy, and both were safe and well tolerated.publishersversionPeer reviewe

Predicting nucleosome positions on the DNA: combining intrinsic sequence preferences and remodeler activities

Nucleosome positions on the DNA are determined by the intrinsic affinities of histone proteins to a given DNA sequence and by the ATP-dependent activities of chromatin remodeling complexes that can translocate nucleosomes with respect to the DNA. Here, we report a theoretical approach that takes into account both contributions. In the theoretical analysis two types of experiments have been considered: in vitro experiments with a single reconstituted nucleosome and in vivo genome-scale mapping of nucleosome positions. The effect of chromatin remodelers was described by iteratively redistributing the nucleosomes according to certain rules until a new steady state was reached. Three major classes of remodeler activities were identified: (i) the establishment of a regular nucleosome spacing in the vicinity of a strong positioning signal acting as a boundary, (ii) the enrichment/depletion of nucleosomes through amplification of intrinsic DNA-sequence-encoded signals and (iii) the removal of nucleosomes from high-affinity binding sites. From an analysis of data for nucleosome positions in resting and activated human CD4+ T cells [Schones et al., Cell 132, p. 887] it was concluded that the redistribution of a nucleosome map to a new state is greatly facilitated if the remodeler complex translocates the nucleosome with a preferred directionality

NucTools: analysis of chromatin feature occupancy profiles from high-throughput sequencing data

Background: Biomedical applications of high-throughput sequencing methods generate a vast amount of data in which numerous chromatin features are mapped along the genome. The results are frequently analysed by creating binary data sets that link the presence/absence of a given feature to specific genomic loci. However, the nucleosome occupancy or chromatin accessibility landscape is essentially continuous. It is currently a challenge in the field to cope with continuous distributions of deep sequencing chromatin readouts and to integrate the different types of discrete chromatin features to reveal linkages between them. Results: Here we introduce the NucTools suite of Perl scripts as well as MATLAB- and R-based visualization programs for a nucleosome-centred downstream analysis of deep sequencing data. NucTools accounts for the continuous distribution of nucleosome occupancy. It allows calculations of nucleosome occupancy profiles averaged over several replicates, comparisons of nucleosome occupancy landscapes between different experimental conditions, and the estimation of the changes of integral chromatin properties such as the nucleosome repeat length. Furthermore, NucTools facilitates the annotation of nucleosome occupancy with other chromatin features like binding of transcription factors or architectural proteins, and epigenetic marks like histone modifications or DNA methylation. The applications of NucTools are demonstrated for the comparison of several datasets for nucleosome occupancy in mouse embryonic stem cells (ESCs) and mouse embryonic fibroblasts (MEFs). Conclusions: The typical workflows of data processing and integrative analysis with NucTools reveal information on the interplay of nucleosome positioning with other features such as for example binding of a transcription factor CTCF, regions with stable and unstable nucleosomes, and domains of large organized chromatin K9me2 modifications (LOCKs). As potential limitations and problems we discuss how inter-replicate variability of MNase-seq experiments can be addressed