In the present study, we analyze the multi-channel service system with ordered entry from finite source and finite storage at each channel. The arrival and service rates are assumed to be State dependent. The steady State probabilities of the system are obtained by using Chapmann-Kolmogorov equations. Some other performance indices viz. utilization of servers, expected number of units in the system and expected number of units at each channel has been derived. A computational algorithm is developed to determine the optimal allocation of storage space facilitated in front of three heterogeneous servers. Sensitivity analysis has been carried out to study the effect of variation of different parameters on the system performance.

In this paper, the secrecy problem in the State dependent causal cognitive interference channel is studied. The channel State is non-causally known at the cognitive encoder. The message of the cognitive encoder must be kept secret from the primary receiver. We use a coding scheme which is a combination of compress-and-forward strategy with Marton coding, Gel’ fand-Pinsker coding and Wyner’ s wiretap coding at the cognitive encoder. We use rate splitting for messages at both transmitters. Furthermore, the cognitive user compresses its channel observation using Wyner-Ziv coding and splits the index of its compressed signal. By using this scheme we derive an achievable secrecy rate region for this channel and extend the results to the Gaussian case and provide some numerical results.

Gaussian interference known at the transmitter can be fully canceled in a Gaussian communication channel employing dirty paper coding, as Costa shows, when interference is independent of the channel noise and when the channel input designed independently of the interference. In this paper, a new and general version of the Gaussian channel in presence of two-sided State information correlated to the channel input and noise is considered. Determining a general achievable rate for the channel and obtaining the capacity in a non-limiting case, we try to analyze and solve the Gaussian version of the Cover-Chiang theorem mathematically and information-theoretically. Our capacity theorem, while including all previous theorems as its special cases, explains situations that can not be analyzed by them; for example, the effect of the correlation between the side information and the channel input on the capacity of the channel that can not be analyzed with Costa’ s ― writing on dirty paper" theorem. Meanwhile, we try to exemplify the concept of ― cognition" of the transmitter or the receiver on a variable (here, the channel noise) with the information-theoretic concept of ― side information" correlated to that variable and known at the transmitter or at the receiver. According to our theorem, the channel capacity is an increasing function of the mutual information of the side information and the channel noise.

In this paper the secrecy problem in the cognitive State-dependent interference channel is considered. In this scenario we have a primary and a cognitive transmitter-receiver pairs. The cognitive transmitter has the message of the primary sender as side information. In addition, the State of the channel is known at the cognitive encoder. Hence, the cognitive encoder uses this side information to cooperate with the primary transmitter. The message of the cognitive encoder must be secret at the primary receiver, i.e., the primary receiver act as an eavesdropper for the cognitive transmitter. An achievable rate region and an outer bound on the rate region in this channel are derived. The results are extended to the previous works as special cases.

Cardiac sodium channels are integral membrane proteins whose structure is not known at atomic level yet and their molecular kinetics is still being studied through mathematical modeling. This study has focused on adapting an existing model of cardiac Na channel to analyze molecular kinetics of channels at 9-37oC. Irvine et al developed a Markov model for Na channel using Neuronal Network Model as a framework. They produced State diagram for channel with 5 close, 2 open, and 5 close-inactivated and one inactivated States. Transitions are expressed as DH and DS and an effective valence (z) terms. Almost all of rate constants are voltage and temperature dependent. The model fails to reproduce kinetics at temperature higher than 25oC. A practical approach would be to scale up each rate constant by its own Q10. As temperature is increased, time constants and recovery rate decrease and increase respectively. First latencies decrease with temperature at (–100)-20 mV. Open probability of channels does not follow temperature suggesting that at higher temperature a larger fraction of channels are inactivated before they reach open State. This study exhibits a reasonable model for single channel ionic current and its recovery from inactivation for a voltage range of (–100)-20 mV at 9-37oC. Our approach may lead to more detailed molecular kinetics of Na channels resulting in better understanding of arrhythmias and Na channel based nervous system malfunction.

In this paper, we deal with the State-dependent nonconvex sweeping process motivated through quasi-variational inequalities arising in the evolution of sandpiles, quasistatic evolution problems with friction, micromechanical damage models for iron materials. We prove the existence of absolutely continuous solution for the problem in presence of a perturbation, that is an external force applied on the system. The perturbation considered here is general and take the form of a sum of a single-valued Carath\'eodory mapping and a set-valued unbounded mapping.