Fluctuations of the free energy in the REM and the p-spin SK models

We consider the random fluctuations of the free energy in the $p$-spin version of the Sherrington-Kirkpatrick model in the high temperature regime. Using the martingale approach of Comets and Neveu as used in the standard SK model combined with truncation techniques inspired by a recent paper by Talagrand on the $p$-spin version, we prove that (for $p$ even) the random corrections to the free energy are on a scale $N^{-(p-2)/4}$ only, and after proper rescaling converge to a standard Gaussian random variable. This is shown to hold for all values of the inverse temperature, \b, smaller than a critical \b_p. We also show that \b_p\to \sqrt{2\ln 2} as $p\uparrow +\infty$. Additionally we study the formal $p\uparrow +\infty$ limit of these models, the random energy model. Here we compute the precise limit theorem for the partition function at {\it all} temperatures. For \b<\sqrt{2\ln2}, fluctuations are found at an {\it exponentially small} scale, with two distinct limit laws above and below a second critical value $\sqrt{\ln 2/2}$: For \b up to that value the rescaled fluctuations are Gaussian, while below that there are non-Gaussian fluctuations driven by the Poisson process of the extreme values of the random energies. For \b larger than the critical $\sqrt{2\ln 2}$, the fluctuations of the logarithm of the partition function are on scale one and are expressed in terms of the Poisson process of extremes. At the critical temperature, the partition function divided by its expectation converges to 1/2.Comment: 40pp, AMSTe

tt-Martin boundary of killed random walks in the quadrant

We compute the $t$-Martin boundary of two-dimensional small steps random walks killed at the boundary of the quarter plane. We further provide explicit expressions for the (generating functions of the) discrete $t$-harmonic functions. Our approach is uniform in $t$, and shows that there are three regimes for the Martin boundary.Comment: 18 pages, 2 figures, to appear in S\'eminaire de Probabilit\'e

On the functions counting walks with small steps in the quarter plane

Models of spatially homogeneous walks in the quarter plane ${\bf Z}_+^{2}$ with steps taken from a subset $\mathcal{S}$ of the set of jumps to the eight nearest neighbors are considered. The generating function $(x,y,z)\mapsto Q(x,y;z)$ of the numbers $q(i,j;n)$ of such walks starting at the origin and ending at $(i,j) \in {\bf Z}_+^{2}$ after $n$ steps is studied. For all non-singular models of walks, the functions $x \mapsto Q(x,0;z)$ and $y\mapsto Q(0,y;z)$ are continued as multi-valued functions on ${\bf C}$ having infinitely many meromorphic branches, of which the set of poles is identified. The nature of these functions is derived from this result: namely, for all the 51 walks which admit a certain infinite group of birational transformations of ${\bf C}^2$, the interval $]0,1/|\mathcal{S}|[$ of variation of $z$ splits into two dense subsets such that the functions $x \mapsto Q(x,0;z)$ and $y\mapsto Q(0,y;z)$ are shown to be holonomic for any $z$ from the one of them and non-holonomic for any $z$ from the other. This entails the non-holonomy of $(x,y,z)\mapsto Q(x,y;z)$, and therefore proves a conjecture of Bousquet-M\'elou and Mishna.Comment: 40 pages, 17 figure

Современное состояние антимикробной резистентности Streptococcus pneumoniae и специфической вакцинопрофилактики пневмококковой инфекции

The constant increase in the level of resistance of Streptococcus pneumoniae to antimicrobial drugs significantly affects the algorithms for the pharmacotherapy of pneumococcal infection, reduces the effectiveness of the therapy and increases the healthcare costs. In this regard, specific vaccine prevention of pneumococcal diseases is a socially significant and economically promising and profitable area.The aim of the study is to analyze the current status of antimicrobial resistance of S. pneumoniae in healthy carriers and patients with non-invasive and invasive pneumococcal infections, as well as specific vaccine prevention of pneumococcal infection.Conclusion. An increase in the number of pneumococcal strains resistant to macrolides and tetracycline has been noted, as well as a trend toward an increase in resistance to beta-lactam antibiotics. Given the spread of resistant strains of S. pneumoniae, a continuous epidemiological surveillance of pneumococcal infection with an assessment of the dynamics of pneumococcal serotype resistance and the effectiveness of vaccination is needed on a global scale.Постоянный рост уровня устойчивости Streptococcus pneumoniae к антимикробным препаратам существенно влияет на алгоритмы фармакотерапии пневмококковой инфекции, снижая эффективность проводимой терапии и увеличивая экономические затраты системы здравоохранения. В связи с этим специфическая вакцинопрофилактика заболеваний пневмококковой этиологии является социально значимым и экономически перспективным и выгодным направлением.Цель работы – проанализировать современное состояние антимикробной резистентности S. pneumoniae у здоровых носителей и пациентов с неинвазивной и инвазивной пневмококковой инфекцией, а также специфической вакцинопрофилактики пневмококковой инфекции.Заключение. Выявлено увеличение количества штаммов пневмококка, резистентных к макролидам и тетрациклину, а также обнаружена тенденция к росту устойчивости к бета-лактамным антибактериальным препаратам. Учитывая распространение резистентных штаммов S. pneumoniae, необходимо проведение непрерывного эпидемиологического мониторинга пневмококковой инфекции с оценкой динамики устойчивости серотипов пневмококка и эффективности вакцинопрофилактики во всем мире

Martin boundary of a reflected random walk on a half-space

The complete representation of the Martin compactification for reflected random walks on a half-space $\Z^d\times\N$ is obtained. It is shown that the full Martin compactification is in general not homeomorphic to the ``radial'' compactification obtained by Ney and Spitzer for the homogeneous random walks in $\Z^d$ : convergence of a sequence of points $z_n\in\Z^{d-1}\times\N$ to a point of on the Martin boundary does not imply convergence of the sequence $z_n/|z_n|$ on the unit sphere $S^d$. Our approach relies on the large deviation properties of the scaled processes and uses Pascal's method combined with the ratio limit theorem. The existence of non-radial limits is related to non-linear optimal large deviation trajectories.Comment: 42 pages, preprint, CNRS UMR 808

ПАРАМЕТРЫ ЭКОЛОГИЧЕСКОЙ ПЛАСТИЧНОСТИ СОРТОВ И СОРТООБРАЗЦОВ ЯРОВОГО ЯЧМЕНЯ АМУРСКОЙ СЕЛЕКЦИИ

The article is concerned with increasing of crop yield and explores that production quality is influenced by the variety adjusted to local conditions. This variety is most productive for plant production and important in agricultural production. New cultivar should be highly productive, highly adaptive and environmentally plastic (to form steady crop yield in different conditions). The article explores estimation of cultivars and varieties of Amur spring barley on environmental plasticity and stability. The researchers estimated environmental plasticity and stability for 3 years (2012–2014), which differed in vegetation conditions. The authors apply regression co-efficient (bi), which characterize cultivars response to agricultural changes and stability variance (s2di), which shows cultivar response to environmental changes and its stability. New Amur variety included into the State List of Selection Inventions is not stable, which is proved by estimation in 2008–2011. Earlier it was not stable but responded well to the changes; now it is not stable but more productive in favorable conditions. The authors make the idea that varieties, which belong to the group of well-responding to the changes and stable ones are the most significant varieties. The researchers define Mishka variety as a stable and well-responding. Огромную роль в повышении урожайности и улучшении качества продукции играет сорт, приспособленный к местным условиям. Он является основой производства любой растениеводческой продукции и его роль в сельскохозяйственном производстве постоянно возрастает. Новый сорт должен быть не только высокоурожайным, но обладать высокой адаптивной способностью и широкой экологической пластичностью (формировать стабильный урожай в различных условиях). Статья посвящена вопросу оценки сортов и сортообразцов ярового ячменя амурской селекции по параметрам экологической пластичности и стабильности. Расчет экологической пластичности и стабильности проводили в среднем за 3 года (2012–2014 гг.), сильно отличающиеся по условиям вегетации. Для определения данных параметров приведен расчет коэффициента регрессии (bi ), характеризующего реакцию сортов на изменение условий выращивания, и вариансы стабильности (s 2 di), которая указывает, насколько сорт отзывчив на условия среды и стабилен ли в этих условиях. Новый сорт амурской селекции Амур, внесенный в Государственный реестр селекционных достижений в 2015 г., является нестабильным, что также подтверждается и ранее проведенными расчетами (в 2008–2011 гг.). Если он ранее был нестабильным, но хорошо отзывчивым на изменение условий, то в данный момент он характеризуется как нестабильный и показывающий лучшие результаты в благоприятных условиях. Наибольшее значение имеют сорта, которые относятся к группе хорошо отзывчивых на изменение условий и являются стабильными. Из изученных нами 12 сортообразцов к этой группе можно отнести один – сортообразец Мишка

Dislocation of the ozurdex implant into the anterior chamber (case of reposition)

The purpose of the study is to report a case of migration of the dexamethasone Ozurdex implant into the anterior chamber in a patient with pseudophakia and avitria and the method of reposition.Цель исследования – cообщить о случае миграции имплантата дексаметазона Озурдекс в переднюю камеру у пациента с артифакией и авитрией и способе репозиции

Analysis of the Karmarkar-Karp Differencing Algorithm

The Karmarkar-Karp differencing algorithm is the best known polynomial time heuristic for the number partitioning problem, fundamental in both theoretical computer science and statistical physics. We analyze the performance of the differencing algorithm on random instances by mapping it to a nonlinear rate equation. Our analysis reveals strong finite size effects that explain why the precise asymptotics of the differencing solution is hard to establish by simulations. The asymptotic series emerging from the rate equation satisfies all known bounds on the Karmarkar-Karp algorithm and projects a scaling $n^{-c\ln n}$, where $c=1/(2\ln2)=0.7213...$. Our calculations reveal subtle relations between the algorithm and Fibonacci-like sequences, and we establish an explicit identity to that effect.Comment: 9 pages, 8 figures; minor change