Dynamic Transitions for Quasilinear Systems and Cahn-Hilliard equation with Onsager mobility

The main objectives of this article are two-fold. First, we study the effect of the nonlinear Onsager mobility on the phase transition and on the well-posedness of the Cahn-Hilliard equation modeling a binary system. It is shown in particular that the dynamic transition is essentially independent of the nonlinearity of the Onsager mobility. However, the nonlinearity of the mobility does cause substantial technical difficulty for the well-posedness and for carrying out the dynamic transition analysis. For this reason, as a second objective, we introduce a systematic approach to deal with phase transition problems modeled by quasilinear partial differential equation, following the ideas of the dynamic transition theory developed recently by Ma and Wang

New approaches to regression in financial mathematics and life sciences by generalized additive models

This paper introduces into and improves the theoretical research done by the authors in the last two years in the applied area of GAMs (generalized additive models) which belong to the modern statistical learning, important in many areas of prediction, e.g., in financial mathematics and life sciences, e.g., computational biology and ecology. These models have the form ψ(x) = β0 + Σj=1^m fj(xj), where ψ are functions of the predictors, and they are fitted through local scoring algorithm using a scatterplot smoother as building blocks proposed by Hastie and Tibshirani (1987). Aerts, Claeskens and Wand (2002) studied penalized spline generalized additive models to derive some approximations. We present a mathematical modeling by splines based on a new clustering approach for the input data x, their density, and the variation of the output data y. We bounding (penalizing) second order terms (curvature) of the splines, we include a regularization of the inverse problem, contributing to a more robust approximation. In a first step, we present a refined modification and investigation of the backfitting algorithm previously applied to additive models. Then, by using the language of optimization theory, we initiate future research on solution methods with mathematical programming.Описываются теоретические результаты, полученные авторами за последние два года в прикладной области GAM (обобщенных аддитивных моделей), которые принадлежат к статистическому обучению и важны во многих случаях получения предсказаний, например, в финансовой математике или в науках о жизни (например, в вычислительной биологии и экологии). Эти модели имеют вид ψ(x) = β0 + Σj=1^m fj(xj) где ψ — предсказывающие функции. Они фильтруются алгоритмами локального выигрыша с использованием рассеянного сглаживания, предложенного Hastie и Tibshirani (1987 г.). Aerts, Claeskеns і Wand (2002 г.) использовали сплайновые обобщенные аддитивные модели со штрафом, чтобы получить некоторые аппроксимации. Мы предлагаем математическое моделирование со сплайнами, основанное на новом кластерном подходе к входным данным х, их плотности и вариации выходных данных у. Ограничивая (штрафом) члены второго порядка (кривизну) сплайнов, включаем регуляризацию обратных задач, получая более грубую аппроксимацию. На первом этапе представляем улучшенную модификацию и исследуем алгоритм обратных шагов, который ранее применялся к аддитивным модулям. Затем с использованием языка теории оптимизации инициируем будущие исследования методов решения с использованием математического программирования.Описано теоретичні результати, отримані авторами за останні два роки у прикладній області GAM (узагальнених адитивних моделей), що належать до статистичного навчання і важливі для багатьох випадків одержання прогнозу, наприклад, у фінансовій математиці або у науках про життя (наприклад, у обчислювальній біології та екології). Ці моделі мають вигляд ψ(x) = β0 + Σj=1^m fj(xj), де ψ — прогнозуючі функції. Вони фільтруються алгоритмами локального виграшу із використанням розсіяного згладжування, запропонованого Hastie і Tibshirani (1987 р.). Aerts, Claeskеns і Wand (2002 р.) використали сплайнові узагальнені адитивні моделі із штрафом, аби одержати деякі апроксимації. Ми пропонуємо математичне моделювання із сплайнами, яке базується на новому кластерному підході до вхідних даних х, їх густини та варіації вихідних даних у. Обмеживши (штрафом) члени другого порядку (кривизну) сплайнів, включаємо регуляризацію зворотних задач одержуючи більш грубу апроксимацію. На першому етапі пропонуємо покращену модифікацію і досліджуємо алгоритм зворотних кроків, який раніше застосовувався до адитивних модулей. Потім із використанням мови теорії оптимізації, ініціюємо майбутні дослідженя методів розв’язання із використанням математичного програмування

CLUSTERnGO: a user-defined modelling platform for two-stage clustering of time-series data.

MOTIVATION: Simple bioinformatic tools are frequently used to analyse time-series datasets regardless of their ability to deal with transient phenomena, limiting the meaningful information that may be extracted from them. This situation requires the development and exploitation of tailor-made, easy-to-use and flexible tools designed specifically for the analysis of time-series datasets. RESULTS: We present a novel statistical application called CLUSTERnGO, which uses a model-based clustering algorithm that fulfils this need. This algorithm involves two components of operation. Component 1 constructs a Bayesian non-parametric model (Infinite Mixture of Piecewise Linear Sequences) and Component 2, which applies a novel clustering methodology (Two-Stage Clustering). The software can also assign biological meaning to the identified clusters using an appropriate ontology. It applies multiple hypothesis testing to report the significance of these enrichments. The algorithm has a four-phase pipeline. The application can be executed using either command-line tools or a user-friendly Graphical User Interface. The latter has been developed to address the needs of both specialist and non-specialist users. We use three diverse test cases to demonstrate the flexibility of the proposed strategy. In all cases, CLUSTERnGO not only outperformed existing algorithms in assigning unique GO term enrichments to the identified clusters, but also revealed novel insights regarding the biological systems examined, which were not uncovered in the original publications. AVAILABILITY AND IMPLEMENTATION: The C++ and QT source codes, the GUI applications for Windows, OS X and Linux operating systems and user manual are freely available for download under the GNU GPL v3 license at http://www.cmpe.boun.edu.tr/content/CnG. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.This work was supported by the Turkish State Planning Organization [DPT09K120520 to B.K.]; the Bogazici University Research Fund [10A05D4 to B.K., 08A506 to B.K., 6882-12A01D5 to A.T.C.]; TUBITAK [106M444 to B.K., 110E292 to A.T.C.], Biotechnology and Biological Sciences Research Council [BRIC2.2 grant BB/K011138/1 to S.G.O.]; and EU 7th Framework Programme [BIOLEDGE Contract No: 289126 to S.G.O.].This is the final version of the article. It first appeared from Oxford University Press via http://dx.doi.org/10.1093/bioinformatics/btv53

Rice Straw Geotextile As Ground Cover ForSoil Erosion Mitigation

Generally, the study aimed to mitigate soil erosion using rice straw geotextile as ground cover. Specifically, it attempted to: evaluate the effect of RSM and RSN as ground cover in mitigating soil erosion at varying slope gradients and different rainfall intensities, and; determine the relationship of slope gradient versus sediment concentration, sediment yield and quantity of soil loss at different levels of rainfall intensity. Results revealed that RSGT as ground cover greatly affected soil erosion. Under rainfall intensities of 75, 100 and 125 mm/hr, RSM had significantly lower soil loss as compared to RSN, CCN And NGC. However, RSN and CCN were comparable with each other but differ significantly with NGC.  Sediment concentration, sediment yield and soil erosion exhibited a nonlinear relationship with slope gradient. At any given level of rainfall intensity, the three indicators increased correspondingly as the slope was increased from 10 to 35o and then  declined when  the slope was further  increased from 35 to 60o. Sediment concentration best fitted (R2 = 0.977) in a quadratic model in the form of a second-degree polynomial equation: SC = 0.551 + 0.626S - 0.008S2 Likewise, observed sediment yield best fitted (R2 = 0.954) a second degree polynomial equation as expressed by a quadratic model: SY = 356.0 + 61.70S – 0.972S2 Moreover, the observed soil erosion was best modeled with R2 = 97.1% confidence by a second degree polynomial equation. The regression model is quadratic in form and is given by the equation: SE = 68.92 + 11.11S - 0.174S2. Keywords: rice straw, geotextile, ground cover, soil erosion, mitigation, rainfall simulatio

Exact Solution of Photon Equation in Stationary G\"{o}del-type and G\"{o}del Space-Times

In this work the photon equation (massless Duffin-Kemmer-Petiau equation) is written expilicitly for general type of stationary G\"{o}del space-times and is solved exactly for G\"{o}del-type and G\"{o}del space-times. Harmonic oscillator behaviour of the solutions is discussed and energy spectrum of photon is obtained.Comment: 9 pages,RevTeX, no figure, revised for publicatio

Identification of tandem repeat families from long-read sequences of Humulus lupulus

Hop (Humulus lupulus L.) is known for its use as a bittering agent in beer and has a rich history of cultivation, beginning in Europe and now spanning the globe. There are five wild varieties worldwide, which may have been introgressed with cultivated varieties. As a dioecious species, its obligate outcrossing, non-Mendelian inheritance, and genomic structural variability have confounded directed breeding efforts. Consequently, understanding the hop genome represents a considerable challenge, requiring additional resources. In order to facilitate investigations into the transmission genetics of hop, we report here a tandem repeat discovery pipeline developed using k-mer filtering and dot plot analysis of PacBio long-read sequences from the hop cultivar Apollo. From this we identified 17 new and distinct tandem repeat sequence families, which represent candidates for FISH probe development. For two of these candidates, HuluTR120 and HuluTR225, we produced oligonucleotide FISH probes from conserved regions of and demonstrated their utility by staining meiotic chromosomes from wild hop, var. neomexicanus to address, for example, questions about hop transmission genetics. Collectively, these tandem repeat sequence families represent new resources suitable for development of additional cytogenomic tools for hop research

Razvoj i vrednovanje dvoslojnih tableta propranolol hidroklorida

The objective of the present research was to develop a bilayer tablet of propranolol hydrochloride using superdisintegrant sodium starch glycolate for the fast release layer and water immiscible polymers such as ethyl cellulose, Eudragit RLPO and Eudragit RSPO for the sustaining layer. In vitro dissolution studies were carried out in a USP 24 apparatus I. The formulations gave an initial burst effect to provide the loading dose of the drug followed by sustained release for 12 hrs from the sustaining layer of matrix embedded tablets. In vitro dissolution kinetics followed the Higuchi model via a non-Fickian diffusion controlled release mechanism after the initial burst release. FT-IR studies revealed that there was no interaction between the drug and polymers used in the study. Statistical analysis (ANOVA) showed no significant difference in the cumulative amount of drug release after 15 min, but significant difference (p 0.005) in the amount of drug released after 12 h from optimized formulations was observed.U radu je opisan razvoj dvoslojnih tableta propranolol hidroklorida, koristeći superdezintegrator škrob glikolat natrij u sloju za brzo oslobađanje i polimere koji se ne miješaju s vodom (etil celuloza, Eudragit RLPO i Eudragit RSPO) u sloju za usporeno oslobađanje. In vitro oslobađanje praćeno je u USP aparatu I te je uočeno početno naglo oslobađanje ljekovite tvari iza kojeg slijedi polagano oslobađanje tijekom 12 sati. In vitro kinetika oslobađanja prati Higouchijev model, dok mehanizam kontroliranog oslobađanja ne slijedi Fickov zakon poslije početnog naglog oslobađanja. FT-IR studije ukazuju da nema interakcije između ljekovite tvari i polimera upotrebljenih u oblikovanju. Statistička analiza (ANOVA) nije pokazala značajne razlike u kumulativnoj količini oslobođenog lijeka iz optimiranih formulacija poslije 15 minuta i polije 12 h