Collective Modes of Tri-Nuclear Molecules

A geometrical model for tri-nuclear molecules is presented. An analytical solution is obtained provided the nuclei, which are taken to be prolately deformed, are connected in line to each other. Furthermore, the tri-nuclear molecule is composed of two heavy and one light cluster, the later sandwiched between the two heavy clusters. A basis is constructed in which Hamiltonians of more general configurations can be diagonalized. In the calculation of the interaction between the clusters higher multipole deformations are taken into account, including the hexadecupole one. A repulsive nuclear core is introduced in the potential in order to insure a quasi-stable configuration of the system. The model is applied to three nuclear molecules, namely $^{96}$Sr + $^{10}$Be + $^{146}$Ba, $^{108}$Mo + $^{10}$Be + $^{134}$Te and $^{112}$Ru + $^{10}$Be + $^{130}$Sn.Comment: 24 pages, 9 figure

Elements of mathematics in problems. Through olympiads and circles to profession

This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important mathematical ideas and theories. The materials can be used by pupils and students for self-study, and by teachers. This is an abridged pre-copyedit version of the published book submitted with the permission of the publisher. Each included individual material is self-contained and ready-for-use. Solutions to problems are not included intentionally. This collection consolidates updates of several arXiv submissions, e.g., arXiv:1305.2598.Comment: Edited by A. Skopenkov, M. Skopenkov, A. Zaslavsky. In Russian. Optimized for printing on A5 paper. Moscow Center for Continuous Mathematical Education, 2018, 592pp (in Russian

Role of apoptosis genes in aggression revealed using combined analysis of ANDSystem gene networks, expression and genomic data in grey rats with aggressive behavior

Aggressive behavior in animals plays an important role in protecting the territory, offspring, establishing social hierarchical relations, etc. Increased aggression is observed in a number of diseases ( schizophrenia, bipolar disorder, brain degenerative disorders). Neuronal apoptosis is crucial in the maintenance of developmental processes during neurogenesis. Alterations in neuronal apoptosis are observed in aging and neuropathologies accompanied by changes in psycho­emo­ tional state (epilepsy, Alzheimer’s disease, neurotrauma). The expression of key neuronal apoptosis genes (Casp3, Bax and Bcl-xl) in the brain of highly aggressive rats is significantly altered. The aim of this work was to analyze associative networks that describe genetic interactions between genes/proteins involved in neuronal apoptosis, differentially expressed genes and genes with polymorphisms in grey rats with aggressive behavior. Analysis revealed 819 differentially expressed genes in the hypothalamus, ventral tegmental region and periaqueductus Sylvii grey matter in grey rats with aggressive and tame behavior. The Stx1a, Mbp and Th genes have the highest index of betweenness centrality in the associative network of differentially expressed genes. Genome analysis revealed 137 polymorphic genes. Three of them (Lig4, Parp1 and Pigt) were involved in neuronal apoptosis. It was shown that polymorphic and differentially expressed genes were statistically significantly overrepresented among ge nes interacting with neuronal apoptosis genes (p value < 0.01). Three molecular­genetic chains describing connections between polymorphic and neuronal apoptosis genes mediated by differentially expressed genes were reconstructed. Chains included the polymorphic genes Tsc1, Adamts4 and Lgals3, differentially expressed genes Ezr, Acan, Th and 19 neuronal apoptosis genes. It was shown that neuronal apoptosis is closely related to aggressive behavior in animals

Measurement of the e+e−→K+K−π+π−e^+e^- \to K^+K^-\pi^+\pi^- cross section with the CMD-3 detector at the VEPP-2000 collider

The process $e^+e^- \to K^+K^-\pi^+\pi^-$ has been studied in the center-of-mass energy range from 1500 to 2000\,MeV using a data sample of 23 pb$^{-1}$ collected with the CMD-3 detector at the VEPP-2000 $e^+e^-$ collider. Using about 24000 selected events, the $e^+e^- \to K^+K^-\pi^+\pi^-$ cross section has been measured with a systematic uncertainty decreasing from 11.7\% at 1500-1600\,MeV to 6.1\% above 1800\,MeV. A preliminary study of $K^+K^-\pi^+\pi^-$ production dynamics has been performed

Study of the process e+e−→ppˉe^+e^-\to p\bar{p} in the c.m. energy range from threshold to 2 GeV with the CMD-3 detector

Using a data sample of 6.8 pb$^{-1}$ collected with the CMD-3 detector at the VEPP-2000 $e^+e^-$ collider we select about 2700 events of the $e^+e^- \to p\bar{p}$ process and measure its cross section at 12 energy ponts with about 6\% systematic uncertainty. From the angular distribution of produced nucleons we obtain the ratio $|G_{E}/G_{M}| = 1.49 \pm 0.23 \pm 0.30$

Chaotic Scattering in Heavy--Ion Reactions

We discuss the relevance of chaotic scattering in heavy--ion reactions at energies around the Coulomb barrier. A model in two and three dimensions which takes into account rotational degrees of freedom is discussed both classically and quantum-mechanically. The typical chaotic features found in this description of heavy-ion collisions are connected with the anomalous behaviour of several experimental data.Comment: 35 pages in RevTex (version 3.0) plus 27 PostScript figures obtainable by anonymous ftp from VAXFCT.CT.INFN.IT in directory kaos. Fig. 1 upon request to the authors. To be published in the October Focus issue on chaotic scattering of CHAO

Роль позитронной эмиссионной и компьютерной томографии с 18F-флуоро-2-дезокси-D-глюкозой в оценке эффективности терапии и прогнозе лимфом

 Aim. To determine the diagnostic value of positron emission tomography (PET)/computed tomography (CT) with F-18 fluorodeoxyglucose (18F-FDG) for monitoring the effectiveness and prognosis of lymphoma therapy.Materials and methods. Retrospective data of 18F-FDG PET/CT (before treatment (PET1), after two cycles (PET2), and after completion of chemotherapy (PET3)) in 30 people with lymphomas were analyzed.Results. A complete metabolic response in PET2 (PET2–) was observed in 21 patients (70%). In 9 patients in PET2–, a partial metabolic response (6 people), lack of metabolic response (2 people), or metabolic progression (1person) were detected. These patients comprised the PET2+ group.After chemotherapy, a complete metabolic response (PET3–) was diagnosed in 26 patients (87%). This effect was achieved in 21 patients (100%) with PET2– and in 5 patients (66%) with PET2+. Of the 9 patients in the PET2+ group, in 4 (44%) patients, a partial metabolic response or no metabolic response was diagnosed. Further monitoring of these patients showed that progression was diagnosed in 2 cases, and in 2 patients, further treatment resulted in complete remission. A two-year follow-up of patients revealed that remission was observed in 20 (67%) patients. The analysis of the results of PET2 showed that a relapse of the disease was observed in 6 (67%) PET2+ patients and remission was noted in 3 (33%) patients. In PET2– patients, a relapse was diagnosed in 4 (19%) persons, and remission was established in 17 (81%) patients.Conclusion. Early PET/CT with 18F-FDG allows to predict the effect of  lymphoma treatment. The method can be recommended for monitoring lymphoma therapy.  Цель. Определение диагностической значимости позитронной эмиссионной и компьютерной томографии (ПЭТ/КТ) с меченной 18F-флуоро-2-дезокси-D-глюкозой  (18F-ФДГ) в оценке эффективности и прогнозе лечения  лимфом.Материалы и методы. Проанализированы  ретроспективные данные ПЭТ/КТ с 18F-ФДГ 30 человек со  злокачественными лимфомами: до лечения (ПЭТ1), через  два курса (ПЭТ2) и после завершения полихимиотерапии  (ПЭТ3).Результаты. При анализе результатов ПЭТ2 полный  метаболический ответ на два курса химиотерапии (ПЭТ2–)  наблюдался у 21 (70%) пациента. У 9 пациентов через два  цикла химиотерапии были установлены: частичный метаболический ответ (6 человек), отсутствие метаболического ответа (2 человека) или метаболическое прогрессировании (1 человек). Эти больные составили группу ПЭТ2+. После окончания химиотерапии полный метаболический ответ (ПЭТ3–) был диагностирован у 26 (87%) пациентов. Такой эффект был достигнут у 21 (100%) больного с ПЭТ2– и 5 (66%) человек с ПЭТ2+. Из 9 пациентов группы ПЭТ2+ у 4 (44%) пациентов после  завершения химиотерапии был диагностирован частичный метаболический ответ или его отсутствие. Дальнейшее  наблюдение за этими пациентами показало, что в двух  случаях было диагностировано прогрессирование, а у 2  больных последующее лечение привело к полной ремиссии. При двухлетнем наблюдении за пациентами обнаружено, что ремиссия наблюдалась у 20 (67%)  пациентов. Анализ результатов ПЭТ2 показал, что при ПЭТ2+ рецидив заболевания наблюдался в 6 (67%) случаях, ремиссия – в 3 (33%). В то время как при ПЭТ2– рецидив  диагностирован у 4 (19%) человек, ремиссия установлена у 17 (81%).Заключение. ПЭТ/КТ с 18F-ФДГ, выполненная на ранних этапах химиотерапии, позволяет предсказать эффект лечения у пациентов со злокачественными лимфомами.  Метод показан к широкому использованию в клинической практике на этапах терапии этой патологии.

Identification of microsatellite loci according to BAC sequencing data and their physical mapping to the bread wheat 5B chromosome

The shortage of polymorphic markers for the regions of wheat chromosomes that encode commercially valuable traits determined the need for studying wheat microsatellite loci. In this work, SSR markers for individual regions in the short arm of bread wheat chromosome 5B (5BS) were designed based on sequencing data for BAC clones, and the regions of the corresponding chromosome were saturated with these markers. Totally, 130 randomly selected BAC clones from the 5BS library were sequenced on the Ion Torrent platform and assembled in contigs using MIRA software. The assembly characteristics (N50 = 4 136 bp) are comparable to the recently obtained data for wheat and relative species and acceptable for identification of microsatellite loci. An algorithm utilizing the properties of complexity decompositions in  he sliding-window mode was used to detect DNA sequences with a repeat unit of 2–4 bp. Analysis of 17 770 contigs with the total length of 25 879 921 bp allowed for designing 113, 79, and 67 microsatellite (SSR) loci with a repeat unit of 2, 3, and 4 bp, respectively. The SSR markers with a motif of 3 bp were tested using nullitetrasomic lines of Chinese Spring wheat homoeologous group 5. Thus, 21 markers specific for chromosome 5B were detected. Eight of these markers were mapped to the distal region of this chromosome (bin 5BS6) using a set of Chinese Spring deletion lines for 5BS. Eight and four markers were mapped to the interstitial region (bins 5BS5 and 5BS4, respectively). One marker was mapped to a pericentromeric bin. A comparative analysis of the distribution of trinucleotide microsatellites over wheat chromosome 5B and in different cereal species suggests that the (AAG)n repeat has proliferated and has been maintained during the evolution of cereals

Representation of Time-Varying Stimuli by a Network Exhibiting Oscillations on a Faster Time Scale

Sensory processing is associated with gamma frequency oscillations (30–80 Hz) in sensory cortices. This raises the question whether gamma oscillations can be directly involved in the representation of time-varying stimuli, including stimuli whose time scale is longer than a gamma cycle. We are interested in the ability of the system to reliably distinguish different stimuli while being robust to stimulus variations such as uniform time-warp. We address this issue with a dynamical model of spiking neurons and study the response to an asymmetric sawtooth input current over a range of shape parameters. These parameters describe how fast the input current rises and falls in time. Our network consists of inhibitory and excitatory populations that are sufficient for generating oscillations in the gamma range. The oscillations period is about one-third of the stimulus duration. Embedded in this network is a subpopulation of excitatory cells that respond to the sawtooth stimulus and a subpopulation of cells that respond to an onset cue. The intrinsic gamma oscillations generate a temporally sparse code for the external stimuli. In this code, an excitatory cell may fire a single spike during a gamma cycle, depending on its tuning properties and on the temporal structure of the specific input; the identity of the stimulus is coded by the list of excitatory cells that fire during each cycle. We quantify the properties of this representation in a series of simulations and show that the sparseness of the code makes it robust to uniform warping of the time scale. We find that resetting of the oscillation phase at stimulus onset is important for a reliable representation of the stimulus and that there is a tradeoff between the resolution of the neural representation of the stimulus and robustness to time-warp. Author Summary Sensory processing of time-varying stimuli, such as speech, is associated with high-frequency oscillatory cortical activity, the functional significance of which is still unknown. One possibility is that the oscillations are part of a stimulus-encoding mechanism. Here, we investigate a computational model of such a mechanism, a spiking neuronal network whose intrinsic oscillations interact with external input (waveforms simulating short speech segments in a single acoustic frequency band) to encode stimuli that extend over a time interval longer than the oscillation's period. The network implements a temporally sparse encoding, whose robustness to time warping and neuronal noise we quantify. To our knowledge, this study is the first to demonstrate that a biophysically plausible model of oscillations occurring in the processing of auditory input may generate a representation of signals that span multiple oscillation cycles.National Science Foundation (DMS-0211505); Burroughs Wellcome Fund; U.S. Air Force Office of Scientific Researc