Sequence Of Conditional Probabilities Research Articles

Is Drug Delivery System a Deterministic or Probabilistic Approach? A Theoretical Model Based on the Sequence: Electrodynamics–Diffusion–Bayes

Commonly, it is accepted that oncology treatment would yield outcomes with a certain determinism without any quantitative support or mathematical model that establishes such determinations. Nowadays, with the advent of nanomedicine, the targeting drug delivery scheme has emerged, whose central objective is the uptake of nanoparticles by tumors. Once they are injected into the bloodstream, it is unclear as to which process governs the directing of nanoparticles towards the desired target, deterministic or stochastic. In any scenario, an optimal outcome, small toxicity and minimal dispersion of drugs is expected. Commonly, it is expected that an important fraction of them can be internalized into tumor. In this manner, due to the fraction of nanoparticles that have failed to uptake, the success of the drug delivery scheme might be at risk. In this paper, a theory based on the sequence electrodynamics–diffusion–Bayes theorem is presented. The Bayesian probability that emerges at the end of the sequence might be telling us that dynamical processes based on the injection of electrically charged nanoparticles might be dictated by stochastic formalism. Thus, rather than expecting a deterministic process, the chain of events would convert the drug delivery scheme to be dependent on a sequence of conditional probabilities.

A route-based pathway analysis framework integrating mutation information and gene expression data.

We propose a new way of analyzing biological pathways in which the analysis combines both transcriptome data and mutation information and uses the outcome to identify "routes" of aberrant pathways potentially responsible for the etiology of disease. Each pathway route is encoded as a Bayesian Network which is initialized with a sequence of conditional probabilities which are designed to encode directionality of regulatory relationships encoded in the pathways, i.e. activation and inhibition relationships. First, we demonstrate the effectiveness of our model through simulation in which the model was able to easily separate Test samples from Control samples using fictitiously perturbed pathway routes. Second, we apply our model to analyze the Breast Cancer data set, available from TCGA, against many cancer pathways available from KEGG and rank the significance of identified pathways. The outcome is consistent with what have already been reported in the literature. Third, survival analysis has been carried out on the same data set by using pathway routes as features. Overall, we envision that our model of using pathway routes for analysis can further refine the conventional ways of subtyping cancer patients as it can discover additional characteristics specific to individual's tumor.

Emergence of Information and the Origins of Life a Tentative Physical Model

Life and living systems requires the existence of information. It is no doubt difficult to understand how this information could have spontaneously emerged in the first living cells. In fact spontaneous random association of molecules cannot give birth to information exactly as the random association of letters has a poor probability to generate a word. The idea developed in this paper is that the information required for the building up of the ?primordial cell? does not originate from the association of molecules xi, with p(xi), probability of occurrence, but from the association of xi, molecules possessing conditional probabilities p(xi?yj,yk....). As will be shown in the paper, such a situation implies that molecules of conditional probabilities p(xi?yj,yk....) do not associate randomly but should follow an order defined by the nature of these conditional probabilities. As a conditional information, , is associated with the corresponding conditional probability of occurrence it follows that a sequence of conditional probabilities possesses a global information. Moreover the system can spontaneously generate an information if h(xi?yj,yk....) < h(xi). Hence the global information could have been generated through the ?coupling? of many of these individual mathematical uncertainties. The problem discussed in the present paper is precisely the converse of a transfer of information from a source to a destination in a communication channel, which has been extensively studied but the emergence of new information in a system.

Diffusion approximations and nearly optimal maintenance policies for system breakdown and repair problems

We consider the problem of service system deterioration and maintenance when there are only small statistical differences in the quality (or time required) of each produced item when the system is in the different states of deterioration, but where those marginal differences are economically important. This is somewhat analogous to the situation in the modeling of queues in heavy traffic, where the main effects which are dealt with might also be considered to be “marginal” ones. In our case the production of each item takes a random length of time and the deterioration during any production or sampling period can have a fairly general (and state dependent) statistical relation with this time and with the quality of the production. Due to this generality, there are several continuous parameter interpolations (of the sequence of conditional probabilities of the system states, given the observed data) which are appropriate for purposes of the weak convergence, each with its own advantages. (We can work with the “natural time scales” of the deterioration process, or with that of the sampling process, or with something in between.) The diffusion process limit is obtained when the random sequences (time, quality) are appropriately correlated. The limit process is of the form of a filtering problem for white-noise corrupted observations of a function of a Markov chain, but the limit problem is somewhat nonstandard since the effective noise covariance and the signal part of the effective observation might depend on the current conditional probability, due to the nature of the “scaling.”