Global Behavior of Solutions to Two Classes of Second Order Rational Difference Equations

For nonnegative real numbers $\alpha$, $\beta$, $\gamma$, $A$, $B$ and $C$ such that $B+C>0$ and $\alpha+\beta+\gamma >0$, the difference equation \begin{equation*} x_{n+1}=\displaystyle\frac{\alpha +\beta x_{n}+\gamma x_{n-1}}{A+B x_{n}+C x_{n-1}}, \quad n=0,1,2,... %, \quad x_{-1},x_{0}\in [0,\infty) \end{equation*} has a unique positive equilibrium. A proof is given here for the following statements: \medskip \noindent Theorem 1. {\it For every choice of positive parameters $\alpha$, $\beta$, $\gamma$, $A$, $B$ and $C$, all solutions to the difference equation \begin{equation*} x_{n+1}=\displaystyle\frac{\alpha +\beta x_{n}+\gamma x_{n-1}}{A+B x_{n}+C x_{n-1}}, \quad n=0,1,2,..., \quad x_{-1},x_{0}\in [0,\infty) \end{equation*} converge to the positive equilibrium or to a prime period-two solution.} \medskip \noindent Theorem 2. {\it For every choice of positive parameters $\alpha$, $\beta$, $\gamma$, $A$, $B$ and $C$, all solutions to the difference equation \begin{equation*} x_{n+1}= \displaystyle\frac{\alpha +\beta x_{n}+\gamma x_{n-1}}{B x_{n}+C x_{n-1}}, \quad n=0,1,2,..., \quad x_{-1},x_{0}\in (0,\infty) \end{equation*} converge to the positive equilibrium or to a prime period-two solution.}Comment: 23 page

Perceptions of park visitors on access to urban parks and benefits of green spaces

There has been limited research on understanding access to public green spaces in cities of the global South. In a study in Hyderabad, India, we interview visitors in four parks to understand their perceptions of and access to ecosystem services. Of these, two parks charge entry fees and two provide free entry or entry at minimal cost. Most users value the park as a recreational space, but are largely unable to access provisioning services such as food and fodder. This poses a particular challenge for low income residents. In the large parks with high vegetation cover, visitors could identify a variety of trees, plants, and birds, while in the smallest neighbourhood park which has the least amount of greenery, they could only identify a small number of species. Parks were visited more by men than by women, who cited challenges of lack of time, and lack of safety. Park entry fees also acted as barriers, for low income groups. The two parks located in wealthy and gentrifying neighbourhoods were almost exclusively accessed by middle class and wealthy visitors, because of the entry fee. Surveys of willingness to pay found that wealthy visitors were keen to pay an entry fee and did not seem to understand the implications of such a fee on exclusion, low income visitors expressed negative views. A central role of the urban park as a ‘public space’ within a city is to nourish the sense of community. Yet some parks have been converted into landscaped and designed areas with high public investment, and entry charges, with limited provision for harvesting ecosystem services. Thus even in public spaces like parks, we observe stark gender and income inequalities, leading to the uneven access to green space

Nature-based solutions and mental health

This chapter demonstrates the mental health benefits of nature-based solutions in cities. First, factors that determine urban mental health and adverse health effects of environmental stressors in cities are explained. Second, it is demonstrated that green spaces as nature-based solutions for many societal challenges provide co-benefits for mental health by reducing these stressors. It is further discussed how nature-based solutions may target supporting mental health by providing resources for human–nature interaction, enhancing social interaction and strengthening mental resilience. Nature-based interventions that are originally intended to support persons with psychiatric illness are introduced as models for the design of mentally supportive cities. And third, two case studies illustrate the mental health benefits of urban parks with the example of Leipzig, Germany and of street trees by the example of Hyderabad, India. The two case studies were used as application cases for a recent conceptual framework as a guide for putting science into practice

Actin Cytoskeleton Regulation by the Yeast NADPH Oxidase Yno1p Impacts Processes Controlled by MAPK Pathways

Reactive oxygen species (ROS) that exceed the antioxidative capacity of the cell can be harmful and are termed oxidative stress. Increasing evidence suggests that ROS are not exclusively detrimental, but can fulfill important signaling functions. Recently, we have been able to demonstrate that a NADPH oxidase-like enzyme (termed Yno1p) exists in the single-celled organism Saccharomyces cerevisiae. This enzyme resides in the peripheral and perinuclear endoplasmic reticulum and functions in close proximity to the plasma membrane. Its product, hydrogen peroxide, which is also produced by the action of the superoxide dismutase, Sod1p, influences signaling of key regulatory proteins Ras2p and Yck1p/2p. In the present work, we demonstrate that Yno1p-derived H2O2 regulates outputs controlled by three MAP kinase pathways that can share components: the filamentous growth (filamentous growth MAPK (fMAPK)), pheromone response, and osmotic stress response (hyperosmolarity glycerol response, HOG) pathways. A key structural component and regulator in this process is the actin cytoskeleton. The nucleation and stabilization of actin are regulated by Yno1p. Cells lacking YNO1 showed reduced invasive growth, which could be reversed by stimulation of actin nucleation. Additionally, under osmotic stress, the vacuoles of a ∆yno1 strain show an enhanced fragmentation. During pheromone response induced by the addition of alpha-factor, Yno1p is responsible for a burst of ROS. Collectively, these results broaden the roles of ROS to encompass microbial differentiation responses and stress responses controlled by MAPK pathway

Some Computational Challenges in Analyzing Global Dynamics of Certain Nonlinear Discrete Dynamical Systems

I will present some computational challenges involved in analyzing global behavior of solutions to certain classes of nonlinear discrete dynamical systems which appear in mathematical modeling of natural and physical phenomena such as, for example, population models in Theoretical Ecology. I will also suggest some innovative geometrical and iterative approaches to overcome these challenges

Household labor supply and intermarriage of immigrants: differences by gender

Abstract Intermarriage between a native and immigrant can affect the household’s supply of labor hours. Spouse selectivity on the basis of human capital, distribution of bargaining power, and labor supply coordination within the household can differ by type of marriage and gender of the immigrant—and, consequently, affect how spouses supply labor to the market. Using the 2010 American Community Survey, a household labor market specialization index is created. Raw two-limit Tobit estimates show lower specialization in intermarried households for both genders, compared to their intra-married counterparts. The finding for intermarried female households is reversed, and gender-based specialization increases, when controls for human capital are introduced. The role of immigrant education for both intermarried men and women is underscored—specialization differences, by type of marriage, are insignificant when the immigrant has post-college education. At lower levels of immigrant education, native spouses supply more market labor. Intermarriage may also skew bargaining power in favor of native husbands in immigrant female households

Some Computational Challenges in Analyzing Global Dynamics of Certain Nonlinear Discrete Dynamical Systems

We present some computational challenges involved in analyzing global behavior of solutions to certain classes of nonlinear discrete dynamical systems which have applications in mathematical biology and ecology. We also suggest some innovative geometric and computer-based approaches to overcome these challenges

On the Connection between a Class of Discrete Dynamical Systems and Some Plane Algebraic Curves

We will analyze the global behavior of solutions to a class of nonlinear discrete dynamical systems with applications in the natural sciences. In particular, we will show that the global dynamics of these solutions are determined by certain plane algebraic curves

Investigating Notch and Kurtz Interaction Networks

Notch is a transmembrane receptor that plays a crucial role in cell fate determination during development. Previous work identified Kurtz (Krz), a Drosophila homolog of mammalian β-arrestins, as a component of the Notch protein interaction network. In this study, I extended the characterization of the Notch and Krz interaction networks. For Notch, I undertook a novel in vivo approach that will allow me to follow the dynamics of Notch signaling and its interactions by expressing tagged Notch receptor at its endogenous level. Investigation of the Krz interacting proteins revealed a surprising connection with Ulp1 which is involved in regulation of SUMO conjugation