Branching processes with immigration in atypical random environment

Motivated by a seminal paper of Kesten et al. (Ann. Probab., 3(1), 1–31, 1975) we consider a branching process with a conditional geometric offspring distribution with i.i.d. random environmental parameters An, n ≥ 1 and with one immigrant in each generation. In contrast to above mentioned paper we assume that the environment is long-tailed, that is that the distribution F of $\xi _{n}:=\log ((1-A_{n})/A_{n})$ ξ n : = log ( ( 1 − A n ) / A n ) is long-tailed. We prove that although the offspring distribution is light-tailed, the environment itself can produce extremely heavy tails of the distribution of the population size in the n th generation which becomes even heavier with increase of n. More precisely, we prove that, for all n, the distribution tail $\mathbb {P}(Z_{n} \ge m)$ ℙ ( Z n ≥ m ) of the n th population size Zn is asymptotically equivalent to $n\overline F(\log m)$ n F ¯ ( log m ) as m grows. In this way we generalise Bhattacharya and Palmowski (Stat. Probab. Lett., 154, 108550, 2019) who proved this result in the case n = 1 for regularly varying environment F with parameter α > 1. Further, for a subcritical branching process with subexponentially distributed ξn, we provide the asymptotics for the distribution tail $\mathbb {P}(Z_{n}>m)$ ℙ ( Z n > m ) which are valid uniformly for all n, and also for the stationary tail distribution. Then we establish the “principle of a single atypical environment” which says that the main cause for the number of particles to be large is the presence of a single very small environmental parameter Ak.

Recurrent Neural Network-based Path Planning for an Excavator Arm under Varying Environment

This paper proposes an algorithm to generate the reference trajectory based on recurrent neural networks for an excavator arm working in a dynamic environment. Firstly, the dynamic of the plant which includes the tracking controller, the arm, and the pile is appropriated by a recurrent neural network. Next, the recurrent neural network combined with a Model Reference Adaptive Controller (MRAC) is used to calculate the reference trajectory for the system. In this paper, the generated trajectory is changed depending on the variation of the pile to maximize the dug weight. This algorithm is simple but effective because it only needs information about the weight at each duty cycle of the excavator. The efficiency of the overall system is verified through simulations. The results show that the proposed scheme gives a good performance, i.e. the dug weight always remains at the desired value (nominal load) as the pile changes its shape during working time.

Modeling and Optimization of Mobile Signal Strength in challenging Atmospheric Conditions

For the network planning in the field of telecommunication networks received signal strength plays an important role. The received signal strength gets affected due to the varying environment condition through which the signal propagates and it also depends on the distance between the location of signal transmitter and the receiver. So complete information about these parameters are very much requires for proper mobile network planning. By keeping all these challenges in mind, this study was aimed to determine the received signal strength for Long-Term Evolution (LTE), Second Generation (2G) and Third Generation (3G) wireless technologies with challenging environment conditions. All the experiments were conducted at Lajpat Nagar residential area which is located in New Delhi. During the experiments received signal strength for all the three above mentioned wireless technologies were monitored with respect to varying environment conditions (Temperature, Relative Humidity and Air quality index for Particulate Matter 2.5) and distance from the base station. Later the optimization of received signal strength was carried out by using response surface methodology. Measurement results showed that Second Generation (2G) signal strengths was significantly higher than Third Generation (3G) and Long-Term Evolution (LTE) and the best values obtained for received signal strength for Long-Term Evolution (LTE), Third Generation (3G) and Second Generation (2G) were -77.9264dBm, -60.0345dBm and -58.1280dBm respectively. ANOVA results shows good mathematical modeling between input and output responses.

Proteins moonlighting in tumor metabolism and epigenetics

Cancer development is a complicated process controlled by the interplay of multiple signaling pathways and restrained by oxygen and nutrient accessibility in the tumor microenvironment. High plasticity in using diverse nutrients to adapt to metabolic stress is one of the hallmarks of cancer cells. To respond to nutrient stress and to meet the requirements for rapid cell proliferation, cancer cells reprogram metabolic pathways to take up more glucose and coordinate the production of energy and intermediates for biosynthesis. Such actions involve gene expression and activity regulation by the moonlighting function of oncoproteins and metabolic enzymes. The signal — moonlighting protein — metabolism axis facilitates the adaptation of tumor cells under varying environment conditions and can be therapeutically targeted for cancer treatment.