A Study on the Reversed Lack of Memory Property and its Generalizations

In this thesis, the concept of reversed lack of memory property and its generalizations is studied.We we generalize this property which involves operations different than the ”addition”. In particular an associative, binary operator ” * ” is considered. The univariate reversed lack of memory property is generalized using the binary operator and a class of probability distributions which include Type 3 extreme value, power function, reflected Weibull and negative Pareto distributions are characterized (Asha and Rejeesh (2009)). We also define the almost reversed lack of memory property and considered the distributions with reversed periodic hazard rate under the binary operation. Further, we give a bivariate extension of the generalized reversed lack of memory property and characterize a class of bivariate distributions which include the characterized extension (CE) model of Roy (2002a) apart from the bivariate reflected Weibull and power function distributions. We proved the equality of local proportionality of the reversed hazard rate and generalized reversed lack of memory property. Study of uncertainty is a subject of interest common to reliability, survival analysis, actuary, economics, business and many other fields. However, in many realistic situations, uncertainty is not necessarily related to the future but can also refer to the past. Recently, Di Crescenzo and Longobardi (2009) introduced a new measure of information called dynamic cumulative entropy. Dynamic cumulative entropy is suitable to measure information when uncertainty is related to the past, a dual concept of the cumulative residual entropy which relates to uncertainty of the future lifetime of a system. We redefine this measure in the whole real line and study its properties. We also discuss the implications of generalized reversed lack of memory property on dynamic cumulative entropy and past entropy.In this study, we extend the idea of reversed lack of memory property to the discrete set up. Here we investigate the discrete class of distributions characterized by the discrete reversed lack of memory property. The concept is extended to the bivariate case and bivariate distributions characterized by this property are also presented. The implication of this property on discrete reversed hazard rate, mean past life, and discrete past entropy are also investigated.

Muscarinic M1 and M3 Receptors,IP3 and cGMP Functional Regulation in Streptozotocin Induced Diabetic Rats: Insulin and Somatotropin Induced Rejuvenation as a Function of Age

The present study describes that acetylcholine through muscarinic Ml and M3 receptors play an important role in the brain function during diabetes as a function of age. Cholinergic activity as indicated by acetylcholine esterase, a marker for cholinergic function, decreased in the brain regions - the cerebral cortex, brainstem and corpus striatum of old rats compared to young rats. in diabetic condition, it was increased in both young and old rats in cerebral cortex, and corpus striatum while in brainstem it was decreased. The functional changes in the muscarinic receptors were studied in the brain regions and it showed that muscarinic M I receptors of old rats were down regulated in cerebral cortex while in corpus striatum and brainstem it was up regulated. Muscarinic M3 receptors of old rats showed no significant change in cerebral cortex while in corpus striatum and brainstem muscarinic receptors were down regulated. During diabetes, muscarinic M I receptors were down regulated in cerebral cortex and brainstem of young rats while in corpus striatum they were up regulated. In old rats, M I receptors were up regulated in cerebral cortex, corpus striatum and in brainstem they were down regulated. Muscarinic M3 receptors were up regulated in cerebral cortex and brainstem of young rats while in corpus striatum they were down regulated. In old rats, muscarinic M l receptors were up regulated in cerebral cortex, corpus striatum and brainstem. In insulin treated diabetic rats the activity of the receptors were reversed to near control. Pancreatic muscarinic M3 receptor activity increased in the pancreas of both young and old rats during diabetes. In vitro studies using carbachol and antagonists for muscarinic Ml and M3 receptor subtypes confirmed the specific receptor mediated neurotransmitter changes during diabetes. Calcium imaging studies revealed muscarinic M I mediated Ca2 + release from the pancreatic islet cells of young and old rats. Electrophysiological studies using EEG recording in young and old rats showed a brain activity difference during diabetes. Long term low dose STH and INS treated rat brain tissues were used for gene expression of muscarinic Ml, M3, glutamate NMDARl, mGlu-5,alpha2A, beta2, GABAAa1 and GABAB, DAD2 and 5-HT 2C receptors to observe the neurotransmitter receptor functional interrelationship for integrating memory, cognition and rejuvenating brain functions in young and old. Studies on neurotransmitter receptor interaction pathways and gene expression regulation by second messengers like IP3 and cGMP in turn will lead to the development of therapeutic agents to manage diabetes and brain activity.From this study it is suggested that functional improvement of muscarinic Ml, M3, glutamate NMDAR1, mGlu-5, alpha2A, beta2, GABAAa1 and GABAB, DAD2 and 5-HT 2C receptors mediated through IP3 and cGMP will lead to therapeutic applications in the management of diabetes. Also, our results from long term low dose STH and INS treatment showed rejuvenation of the brain function which has clinical significance in maintaining healthy period of life as a function of age.

Withania somnitera and withanolide a mediated restoration of AMPA and NMDA receptor function in pilocarpine induced temporal lobe epilepsy

The onset of spontaneous seizures triggers a cascade of molecular and cellular events that eventually leads to neuronal injury and cognitive decline. The present study investigated the effect of Withania somnifera (WS) root extract and Withanolide A (WA) in restoring behavioural deficit by inhibiting oxidative stress induced alteration in glutamergic neurotransmission. The subdued performance in behavioural tests shows impaired motor coordination and memory. Histopathological investigations revealed significant neuronal loss in hippocampus of epileptic rats indicating glutamate mediated excitotoxicity. The treatment with WS and WA restored behavioural deficit and ameliorated neuronal loss. An altered redox homeostasis leading to oxidative stress is a hallmark of TLE. The antioxidant potential was afflicted in epileptic rats, evident from altered activity of SOD and CAT, down regulation of SOD and GPX expression and enhanced lipid peroxidation. The antioxidant property of WS and WA restored altered antioxidant capacity. Alteration in GDH activity and down regulation of GLAST expression resulted in enhanced glutamate content in the brain regions. The metabolism of glutamate was altered in the form of down regulated GAD expression. The alteration in synthesis, transport and metabolism resulted in further increase of the glutamate concentration at the synapse leading to glutamate mediated excitotoxicity. The decreased NMDA and AMPA receptor binding and down regulated NMDA R1, NMDA 2B and AMPA (GluR2) mRNA expression indicated altered glutamergic receptor function. The treatment with WS and WA reversed altered glutamergic receptor function, synthesis, transport and metabolism. The enhanced levels of second messenger IP3 responsible for Ca2+ mediated toxicity was reversed after treatment with WS and WA. Neurotoxics concentration of glutamate resulted in up regulation of pro apoptotic factors Bax and Caspase 8 and down regulation of anti apoptotic factor Akt resulting in neuronal death. The treatment with WS and WA resulted in activation of Akt and down regulation of Bax and caspase 8 leading to blocking of apoptotic pathway. The treatment with WS and WA resulted in reduced seizure frequency and amelioration of associated alterations suggesting the therapeutic role of Withania somnifera in temporal lobe epilepsy

Message Integrity in the World Wide Web: Use of Nested Hash Function and a Fast Stream Cipher

The focus of this work is to provide authentication and confidentiality of messages in a swift and cost effective manner to suit the fast growing Internet applications. A nested hash function with lower computational and storage demands is designed with a view to providing authentication as also to encrypt the message as well as the hash code using a fast stream cipher MAJE4 with a variable key size of 128-bit or 256-bit for achieving confidentiality. Both nested Hash function and MAJE4 stream cipher algorithm use primitive computational operators commonly found in microprocessors; this makes the method simple and fast to implement both in hardware and software. Since the memory requirement is less, it can be used for handheld devices for security purposes.