(1) Sn = S0 + n ∑ i=1 Xi When S0 = 0 the renewal process is an ordinary renewal process; when S0 is a nonnegative random variable the renewal process is a delayed renewal process. In either case, the individual terms Sn of this sequence are called renewals, or sometimes occurrences. With each renewal process is associated a renewal counting process N (t ) that tracks the total number of renewal...

We determine the impact of resource renewal on the lifetime of a forager that depletes its environment and starves if it wanders too long without eating. In the framework of a minimal starving random-walk model with resource renewal, there are three universal classes of behavior as a function of the renewal time. For sufficiently rapid renewal, foragers are immortal, while foragers have a finit...

This article describes the Key renewal theorem and the Blackwell’s renewaltheorem. These two limit theorems for renewal processes are equivalent but of different forms.They are particularly useful for characterizing the asymptotic behavior of a probabilisticquantity of interest in a renewal process. We present two applications of these limit theorems:the limiting distributions o...

The paper is dusted to an evaluation methodology for urban renewal plans. A central rol e is played by the concept of supply profil es of urban facilities. Urban renewal is considered to be a qualitative improvement of these profil es. Many urban renewal plans are characterized by the availability of soft (ordinal or qualitative) information. Therefore, the paper gives an overview óf soft muUi ...

The alternating renewal process is one of the renewal processes in renewal theory. It is widely used in inventory systems and queueing systems. In classical alternating renewal processes, one of the assumptions is that the on times and off times are independent random variables. The notion of a fuzzy set was introduced by Zadeh [1] who defined it as a generalized characteristic function. Recent...

ATP-dependent chromatin remodeling complexes are a notable group of epigenetic modifiers that use the energy of ATP hydrolysis to change the structure of chromatin, thereby altering its accessibility to nuclear factors. BAF250a (ARID1a) is a unique and defining subunit of the BAF chromatin remodeling complex with the potential to facilitate chromosome alterations critical during development. Ou...

In sensor networks, sensors are likely to be captured by attackers because they are usually deployed in an unprotected or even a hostile environment. If an adversarial compromises a sensor, he/she uses the keys from the compromised sensor to uncover the keys of others sensors. Therefore, it is very important to renew the keys of sensors in a proactive or reactive manner. Even though many group ...