Applications of the Owa-Srivastava Operator to the Class of K-Uniformly Convex Functions

2000 Mathematics Subject Classification: Primary 30C45, 26A33; Secondary 33C15

Some Notes about a Class of Univalent Functions with Negative Coefficients

MSC 2010: 30C45, 30C50

Some Distortion Theorems for Starlike Harmonic Functions

MSC 2010: 30C55, 30C45

On a Class of Univalent Functions with Negative Coefficients

Донка Пашкулева - Предмет на тази статия е получаването на точни оценки за коефициентите и ръста на функциите за някои класове еднолистни функции с отрицателни коефициенти.

Singular Solutions with Exponential Growth for the (3+1)-D Wave Equation

Недю И. Попиванов, Тодор П. Попов, Рудолф Шерер - Разглеждат се четиримерни гранични задачи за нехомогенното вълново уравнение. Те са предложени от М. Протер като многомерни аналози на задачата на Дарбу в равнината. Известно е, че единственото обобщено решение може да има силна степенна особеност само в една гранична точка. Тази сингулярност е изолирана във върха на характеристичния конус и не се разпространява по конуса. Друг аспект на проблема е, че задачата не е фредхолмова, тъй като има безкрайномерно коядро. Предишни резултати сочат, че решението може да има най-много експоненциален ръст, но оставят открит въпроса дали наистина съществуват такива решения. Показваме, че отговора на този въпрос е положителен и строим обобщено решение на задачата на Протер с експоноциална особеност.

Recent Results for Supercritical Controlled Branching Processes with Control Random Functions

2000 Mathematics Subject Classification: 60J80, 60F05

Loss of p38δ mitogen-activated protein kinase expression promotes oesophageal squamous cell carcinoma proliferation, migration and anchorage-independent growth.

Oesophageal cancer is an aggressive tumour which responds poorly to both chemotherapy and radiation therapy and has a poor prognosis. Thus, a greater understanding of the biology of oesophageal cancer is needed in order to identify novel therapeutic targets. Among these targets p38 MAPK isoforms are becoming increasingly important for a variety of cellular functions. The physiological functions of p38α and -β are now well documented in contrast to -γ and -δ which are comparatively under-studied and ill-defined. A major obstacle to deciphering the role(s) of the latter two p38 isoforms is the lack of specific chemical activators and inhibitors. In this study, we analysed p38 MAPK isoform expression in oesophageal cancer cell lines as well as human normal and tumour tissue. We observed specifically differential p38δ expression. The role(s) of p38δ and active (phosphorylated) p38δ (p-p38δ) in oesophageal squamous cell carcinoma (OESCC) was delineated using wild-type p38δ as well as active p-p38δ, generated by fusing p38δ to its upstream activator MKK6b(E) via a decapeptide (Gly-Glu)5 linker. OESCC cell lines which are p38δ-negative (KE-3 and -8) grew more quickly than cell lines (KE-6 and -10) which express endogenous p38δ. Re-introduction of p38δ resulted in a time-dependent decrease in OESCC cell proliferation which was exacerbated with p-p38δ. In addition, we observed that p38δ and p-p38δ negatively regulated OESCC cell migration in vitro. Finally both p38δ and p-p38δ altered OESCC anchorage-independent growth. Our results suggest that p38δ and p-p38δ have a role in the suppression of OESCC. Our research may provide a new potential target for the treatment of oesophageal cancer.

Insulin-like growth factor receptor activity in cancer biology & therapy responses

The Insulin-like Growth Factor 1 Receptor (IGF-1R) has an essential function in normal cell growth and in cancer progression. However, anti-IGF-1R therapies have mostly been withdrawn from clinical trials owing to a lack of efficacy and predictive biomarkers. IGF-1R activity and signalling in cancer cells is regulated by its C-terminal tail, and in particular, by a motif that encompasses tyrosines 1250 and 1251 flanked by serines 1248 and 1252 (1248- SFYYS-1252). Mutation of Y1250/1251 greatly reduces IGF-1-promoted cell migration, interaction with the scaffolding protein RACK1 in the context Integrin signalling, and IGF- 1R kinase activity. Here we investigated the phosphorylation of the SFYYS motif and characterise the conditions under which this motif may be phosphorylated under. As phosphorylated residues, the SFYYS motif may also serve to recruit interacting proteins to the IGF-1R. To this end we identified a novel IGF-1R interacting partner which requires phosphorylated residues in the SFYYS motif to interact with the IGF-1R. This interaction was found to be IGF-1-dependent, and required the scaffold protein RACK1. The interaction of this binding protein with the IGF-1R likely functions to promote maximal phosphorylation of Shc and ERK in IGF-1-stimulated cell migration, and may be important for IGF-1 signalling in cancer cells. Lastly, we have investigated possible kinases that may confer resistance or sensitivity to the IGF-1R kinase inhibitor BMS-754807. In this screen we identified ATR as a mediator of resistance and showed that suppression or chemical inhibition of ATR synergised with BMS-754807 to reduce colony formation. This work has contributes to our understanding of IGF-1R kinase regulation and signalling and suggests that administration of anti-IGF-1R drugs with ATR inhibitors may have therapeutic benefit.

Effects of hypercapnia on aspects of feeding, nutrition, and growth in the edible sea urchin Lytechinus variegatus held in culture

Land-based aquaculture facilities experience occasional hypercapnic conditions due to the accumulation of the metabolic waste product carbon dioxide. Pre-gonadal Lytechinus variegatus (horizontal diameter=20 mm) were exposed to control (608 µatm pCO2, pH 8.1) or hypercapnic conditions (1738 µatm pCO2, pH 7.7) in synthetic seawater for 14 weeks. Sea urchins exposed to hypercapnic conditions exhibited significantly slower growth (reduced dry matter production), primarily due to reduced test production. Higher fecal production rates and lower ash absorption efficiency (%) in individuals exposed to hypercapnic conditions suggest the ability to process or retain dietary carbonates may have been affected. Significant increases in neutral lipid storage in the gut and increased soluble protein storage in the gonads of individuals exposed to hypercapnic conditions suggest alterations in nutrient metabolism and storage. Furthermore, organic production and energy allocation increased in the lantern of those individuals exposed to hypercapnic conditions. These results suggest chronic exposure to hypercapnic conditions alters nutrient allocation to organ systems and functions, leading to changes in somatic and reproductive production.

Role of fibroblast growth factors and their receptors in prostate cancer

Prostate cancer (PCa) is the most common non-cutaneous malignant disease among males in the developed countries. Radical prostatectomy (RP) is an effective therapy for most PCa patients with localized or locally invaded tumors but in some cases the cancer recurs after RP. PCa is a heterogeneous disease, which is regulated by many factors, such as androgen receptor (AR), estrogen receptors and  (ER and ER), fibroblast growth factors (FGFs) and their receptors (FGFRs). In this study, the role of ERβ, FGF8, FGF13 and FGFRL1 was investigated in PCa. Previous studies have suggested that ER is protective against PCa whereas FGF8 has been shown to induce PCa in transgenic mice. FGF13 and FGFRL1 are poorly understood members of the FGF and FGFR families, respectively. Transgenic mouse models were used to investigate the ability of inactivated ERβ to facilitate FGF8-induced prostate tumorigenesis. Human PCa tissue microarrays (TMAs) were used to study the expression pattern of FGF13 and FGFRL1 in PCa and the results were correlated to corresponding patient data. The targets and biological functions of FGF13 and FGFRL1 were characterized using experimental in vivo and in vitro models. The results show that deficiency of ERβ, which had been expected to have tumor suppressing capacity, seemed to influence epithelial differentiation but did not affect FGF8-induced prostate tumorigenesis. Analysis of the TMAs showed increased expression of FGF13 in PCa. The level of cytoplasmic FGF13 was associated with the PCa biochemical recurrence (BCR), demonstrated by increasing serum PSA value, and was able to act as an independent prognostic biomarker for PCa patients after RP. Expression of FGFRL1, the most recently identified FGFR, was also elevated in PCa. Cytoplasmic and nuclear FGFRL1 was associated with high Gleason score and Ki67 level whereas the opposite was true for the cell membrane FGFRL1. Silencing of FGFRL1 in PC-3M cells led to a strongly decreased growth rate of these cells as xenografts in nude mice and the experiments with PCa cell lines showed that FGFRL1 is able to modulate the FGF2- and FGF8-induced signaling pathways. The next generation sequencing (NGS) experiments with FGFRL1-silenced PC-3M cells revealed candidates for FGFRL1 target genes. In summary, these studies provide new data on the FGF/FGFR signaling pathways in normal and malignant prostate and suggest a potential role for FGF13 and FGFRL1 as novel prognostic markers for PCa patients. Keywords: FGF8, FGF13, FGFRL1, ERβ, prostate cancer, prognostic marker

CAUSAL INFERENCE WITH A CONTINUOUS TREATMENT AND OUTCOME: ALTERNATIVE ESTIMATORS FOR PARAMETRIC DOSE-RESPONSE FUNCTIONS WITH APPLICATIONS.

Causal inference with a continuous treatment is a relatively under-explored problem. In this dissertation, we adopt the potential outcomes framework. Potential outcomes are responses that would be seen for a unit under all possible treatments. In an observational study where the treatment is continuous, the potential outcomes are an uncountably infinite set indexed by treatment dose. We parameterize this unobservable set as a linear combination of a finite number of basis functions whose coefficients vary across units. This leads to new techniques for estimating the population average dose-response function (ADRF). Some techniques require a model for the treatment assignment given covariates, some require a model for predicting the potential outcomes from covariates, and some require both. We develop these techniques using a framework of estimating functions, compare them to existing methods for continuous treatments, and simulate their performance in a population where the ADRF is linear and the models for the treatment and/or outcomes may be misspecified. We also extend the comparisons to a data set of lottery winners in Massachusetts. Next, we describe the methods and functions in the R package causaldrf using data from the National Medical Expenditure Survey (NMES) and Infant Health and Development Program (IHDP) as examples. Additionally, we analyze the National Growth and Health Study (NGHS) data set and deal with the issue of missing data. Lastly, we discuss future research goals and possible extensions.

Analysis of the role of the transcription factor C/EBPβ in controlling uterine functions during early pregnancy

Embryo implantation into the endometrium is a complex biological process involving the integration of steroid hormone signaling, endometrial tissue remodeling and maternal- fetal communications. A successful pregnancy is the outcome of the timely integration of these events during the early stages of implantation. The involvement of ovarian steroid hormones, estrogen (E) and progesterone (P), acting through their cognate receptors, is essential for uterine functions during pregnancy. The molecular mechanisms that control the process of implantation are undergoing active exploration. Through our recent efforts, we identified the transcription factor, CCAAT Enhancer Binding Protein Beta (C/EBPb) as a prominent target of estrogen and progesterone signaling in the uterus. The development of a C/EBPb-null mouse model, which is infertile, presented us with an opportunity to analyze the role of this molecule in uterine function. We discovered that C/EBPb functions in two distinct manners: (i) by acting as a mediator of E-induced proliferation of the uterine epithelium and (ii) by controlling uterine stromal cell differentiation, a process known as decidualization, during pregnancy. My studies have delineated important mechanisms by which E regulates C/EBPb expression to induce DNA replication and prevent apoptosis of uterine epithelial cells during E-induced epithelial growth. In subsequent studies, I analyzed the role of C/EBPb in decidualization and uncovered a unique mechanism by which C/EBPb regulates the synthesis of a unique laminin-containing extracellular matrix (ECM) that supports stromal cell differentiation and embryo invasion. In order to better define the role of laminin in implantation, we developed a laminin gamma 1-conditional knockout mouse model. This is currently an area of ongoing investigation. The information gained from our analysis of C/EBPb function in the uterus provides new insights into the mechanisms of steroid hormone action during early pregnancy. Ultimately, our findings may aid in the understanding of dysregulation of hormone-controlled pathways that underlie early pregnancy loss and infertility in women.

FlorNExT®, a cloud computing application to estimate growth and yield of maritime pine (Pinus pinaster Ait.) stands in Northeastern Portugal

Aim of the study: To introduce and describe FlorNExT®, a free cloud computing application to estimate growth and yield of maritime pine (Pinus pinaster Ait.) even-aged stands in the Northeast of Portugal (NE Portugal). Area of study: NE Portugal. Material and methods: FlorNExT® implements a dynamic growth and yield modelling framework which integrates transition functions for dominant height (site index curves) and basal area, as well as output functions for tree and stand volume, biomass, and carbon content. Main results: FlorNExT® is freely available from any device with an Internet connection at: http://flornext.esa.ipb.pt/. Research highlights: This application has been designed to make it possible for any stakeholder to easily estimate standing volume, biomass, and carbon content in maritime pine stands from stand data, as well as to estimate growth and yield based on four stand variables: age, density, dominant height, and basal area. FlorNExT® allows planning thinning treatments. FlorNExT® is a fundamental tool to support forest mobilization at local and regional scales in NE Portugal. Material and methods: FlorNExT® implements a dynamic growth and yield modelling framework which integrates transition functions for dominant height (site index curves) and basal area, as well as output functions for tree and stand volume, biomass, and carbon content. Main results: FlorNExT® is freely available from any device with an Internet connection at: http://flornext.esa.ipb.pt/. Research highlights: This application has been designed to make it possible for any stakeholder to easily estimate standing volume, biomass, and carbon content in maritime pine stands from stand data, as well as to estimate growth and yield based on four stand variables: age, density, dominant height, and basal area. FlorNExT® allows planning thinning treatments. FlorNExT® is a fundamental tool to support forest mobilization at local and regional scales in NE Portugal.

Application of an online-biomass sensor in an optical multisensory platform prototype for growth monitoring of biotechnical relevant microorganism and cell lines in single-use shake flasks

In the context of this work we evaluated a multisensory, noninvasive prototype platform for shake flask cultivations by monitoring three basic parameters (pH, pO2 and biomass). The focus lies on the evaluation of the biomass sensor based on backward light scattering. The application spectrum was expanded to four new organisms in addition to E. coli K12 and S. cerevisiae [1]. It could be shown that the sensor is appropriate for a wide range of standard microorganisms, e.g., L. zeae, K. pastoris, A. niger and CHO-K1. The biomass sensor signal could successfully be correlated and calibrated with well-known measurement methods like OD600, cell dry weight (CDW) and cell concentration. Logarithmic and Bleasdale-Nelder derived functions were adequate for data fitting. Measurements at low cell concentrations proved to be critical in terms of a high signal to noise ratio, but the integration of a custom made light shade in the shake flask improved these measurements significantly. This sensor based measurement method has a high potential to initiate a new generation of online bioprocess monitoring. Metabolic studies will particularly benefit from the multisensory data acquisition. The sensor is already used in labscale experiments for shake flask cultivations.

Exact solutions for cluster-growth kinetics with evolving size and shape profiles

In this paper we construct a model for the simultaneous compaction by which clusters are restructured, and growth of clusters by pairwise coagulation. The model has the form of a multicomponent aggregation problem in which the components are cluster mass and cluster diameter. Following suitable approximations, exact explicit solutions are derived which may be useful for the verification of simulations of such systems. Numerical simulations are presented to illustrate typical behaviour and to show the accuracy of approximations made in deriving the model. The solutions are then simplified using asymptotic techniques to show the relevant timescales of the kinetic processes and elucidate the shape of the cluster distribution functions at large times.