The concept of Internet of Things (IoT) was proposed by Professor Kevin Ashton of the Massachusetts Institute of Technology (MIT) in 1999. IoT is an environment that people understand in many different ways depending on their requirement, point of view and purpose. When transmitting data in IoT environment, distribution of network traffic fluctuates frequently. If links of the network or nodes fail randomly, then automatically new nodes get added frequently. Heavy network traffic affects the response time of all system and it consumes more energy continuously. Minimization the network traffic/ by finding the shortest path from source to destination minimizes the response time of all system and also reduces the energy consumption cost. The ant colony optimization (ACO) and K-Means clustering algorithms characteristics conform to the auto-activator and optimistic response mechanism of the shortest route searching from source to destination. In this article, ACO and K-Means clustering algorithms are studied to search the shortest route path from source to destination by optimizing the Quality of Service (QoS) constraints. Resources are assumed in the active and varied IoT network atmosphere for these two algorithms. This work includes the study and comparison between ant colony optimization (ACO) and K-Means algorithms to plan a response time aware scheduling model for IoT. It is proposed to divide the IoT environment into various areas and a various number of clusters depending on the types of networks. It is noticed that this model is more efficient for the suggested routing algorithm in terms of response time, point-to-point delay, throughput and overhead of control bits.

-Evolution of membrane potential and spiking activity for a single leaky integrate-and-fire (LIF) neuron in distributed delay framework (DDF) is investigated. DDF provides a mechanism to incorporate memory element in terms of delay (kernel) function into a single neuron models. This investigation includes LIF neuron model with two different kinds of delay kernel functions, namely, gamma distributed delay kernel function and hypo-exponential distributed delay kernel function. Evolution of membrane potential for considered models is studied in terms of stationary state probability distribution (SPD). Stationary state probability distribution of membrane potential (SPDV) for considered neuron models are found asymptotically similar which is Gaussian distributed. In order to investigate the effect of membrane potential delay, rate code scheme for neuronal information processing is applied. Firing rate and Fano-factor for considered neuron models are calculated and standard LIF model is used for comparative study. It is noticed that distributed delay increases the spiking activity of a neuron. Increase in spiking activity of neuron in DDF is larger for hypo-exponential distributed delay function than gamma distributed delay function. Moreover, in case of hypo-exponential delay function, a LIF neuron generates spikes with Fano-factor less than 1.Keywords -Distributed Delay Framework, Fokker-Planck Equation, Gamma Distribution, Hypo-exponential Distribution, Stationary Probability Distribution, Spiking Activity. I. InTRoducTIonT heRe are a number of neuron models depending on biophysical and electrical properties of a neuron suggested in literature [1][2][3][4][5]. Among these neuron models, Leaky integrate-and-fire (LIF) model has become a backbone for theoretical as well as experimental investigation of neuronal dynamics due to its simplicity and analytical solvable capability [5,6,7]. This model is an RC-circuit equivalent representation of a neuron with additional spiking constraint and is widely used for mathematical explanation of bio-physical mechanism and information processing of neurons [1,2,4,8,9]. Based on some specific properties, many variants of LIF model are suggested in literature [1,5,7,8]. These neuron models explain neuronal dynamics adequately, but when we talk about memory, we have to rely on group of few neurons or neural networks. None of these single neuron models capture memory element. Recently, Karmeshu et. al. [10] have suggested a distributed delay framework for incorporating the effect of previous values of membrane potential (memory) on neuronal dynamics, in which, a kernel function is included in LIF model to capture the aggregate effect of previous values of membrane potential on its further evolution. It is a challenging problem to find an appropriate kernel function so that the resulting model can explain most of the variability in neuronal responses. To this end, Karmeshu et. al. [10] have investigated their proposed framework with exponential distributed delay kernel and...

Background: Distributed Delay Framework (DDF) has suggested a mechanism to incorporate the delay factor in the evolution of the membrane potential of a neuron model in terms of distributed delay kernel functions. Incorporation of delay in neural networks provide comparatively more efficient output. Depending on the parameter of investigation, there exist a number of choices of delay kernel function for a neuron model. Objective: We investigate the Leaky integrate-and-fire (LIF) neuron model in DDF with hypoexponential delay kernel. LIF neuron with hypo-exponential distributed delay (LIFH) model is capable to regenerate almost all possible empirically observed spiking patterns. Methods: In this article, we perform the detailed analytical and simulation based study of the LIFH model. We compute the explicit expressions for the membrane potential and its first two moment viz. mean and variance, in analytical study. Temporal information processing functionality of the LIFH model is investigated during simulation based study. Results: We find that the LIFH model is capable to reproduce unimodal, bimodal and multimodal inter-spike- interval distributions which are qualitatively similar with the experimentally observed ISI distributions. Conclusion: We also notice the neurotransmitter imbalance situation, where a noisy neuron exhibits long tail behavior in aforementioned ISI distributions which can be characterized by power law behavior.

-Implementation of a neuron like information processing structure at hardware level is a burning research problem. In this article, we analyze the modified hybrid spiking neuron model (the MHSN model) in distributed delay framework (DDF) for hardware level implementation point of view. We investigate its temporal information processing capability in term of inter-spike-interval (ISI) distribution. We also perform the stability analysis of the MHSN model, in which, we compute nullclines, steady state solution, eigenvalues corresponding the MHSN model. During phase plane analysis, we notice that the MHSN model generates limit cycle oscillations which is an important phenomenon in many biological processes. Qualitative behavior of these limit cycle does not changes due to the variation in applied input stimulus, however, delay effect the spiking activity and duration of cycle get altered.

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