Attainable Knowledge

The article investigates an evidence-based semantics for epistemic logics in which pieces of evidence are interpreted as equivalence relations on the epistemic worlds. It is shown that the properties of knowledge obtained from potentially infinitely many pieces of evidence are described by modal logic S5. At the same time, the properties of knowledge obtained from only a finite number of pieces of evidence are described by modal logic S4. The main technical result is a sound and complete bi-modal logical system that describes properties of these two modalities and their interplay

Blameworthiness in Strategic Games

There are multiple notions of coalitional responsibility. The focus of this paper is on the blameworthiness defined through the principle of alternative possibilities: a coalition is blamable for a statement if the statement is true, but the coalition had a strategy to prevent it. The main technical result is a sound and complete bimodal logical system that describes properties of blameworthiness in one-shot games

Knowledge and Blameworthiness

Blameworthiness of an agent or a coalition of agents is often defined in terms of the principle of alternative possibilities: for the coalition to be responsible for an outcome, the outcome must take place and the coalition should have had a strategy to prevent it. In this article we argue that in the settings with imperfect information, not only should the coalition have had a strategy, but it also should have known that it had a strategy, and it should have known what the strategy was. The main technical result of the article is a sound and complete bimodal logic that describes the interplay between knowledge and blameworthiness in strategic games with imperfect information

Marketing Impact on Diffusion in Social Networks

The paper proposes a way to add marketing into the standard threshold model of social networks. Within this framework, the paper studies logical properties of the influence relation between sets of agents in social networks. Two different forms of this relation are considered: one for promotional marketing and the other for preventive marketing. In each case a sound and complete logical system describing properties of the influence relation is proposed. Both systems could be viewed as extensions of Armstrong's axioms of functional dependency from the database theory

Applications of Little's Law to stochastic models of gene expression

The intrinsic stochasticity of gene expression can lead to large variations in protein levels across a population of cells. To explain this variability, different sources of mRNA fluctuations ('Poisson' and 'Telegraph' processes) have been proposed in stochastic models of gene expression. Both Poisson and Telegraph scenario models explain experimental observations of noise in protein levels in terms of 'bursts' of protein expression. Correspondingly, there is considerable interest in establishing relations between burst and steady-state protein distributions for general stochastic models of gene expression. In this work, we address this issue by considering a mapping between stochastic models of gene expression and problems of interest in queueing theory. By applying a general theorem from queueing theory, Little's Law, we derive exact relations which connect burst and steady-state distribution means for models with arbitrary waiting-time distributions for arrival and degradation of mRNAs and proteins. The derived relations have implications for approaches to quantify the degree of transcriptional bursting and hence to discriminate between different sources of intrinsic noise in gene expression. To illustrate this, we consider a model for regulation of protein expression bursts by small RNAs. For a broad range of parameters, we derive analytical expressions (validated by stochastic simulations) for the mean protein levels as the levels of regulatory small RNAs are varied. The results obtained show that the degree of transcriptional bursting can, in principle, be determined from changes in mean steady-state protein levels for general stochastic models of gene expression.Comment: Accepted by Physical Review

Stochastic modeling of regulation of gene expression by multiple small RNAs

A wealth of new research has highlighted the critical roles of small RNAs (sRNAs) in diverse processes such as quorum sensing and cellular responses to stress. The pathways controlling these processes often have a central motif comprising of a master regulator protein whose expression is controlled by multiple sRNAs. However, the regulation of stochastic gene expression of a single target gene by multiple sRNAs is currently not well understood. To address this issue, we analyze a stochastic model of regulation of gene expression by multiple sRNAs. For this model, we derive exact analytic results for the regulated protein distribution including compact expressions for its mean and variance. The derived results provide novel insights into the roles of multiple sRNAs in fine-tuning the noise in gene expression. In particular, we show that, in contrast to regulation by a single sRNA, multiple sRNAs provide a mechanism for independently controlling the mean and variance of the regulated protein distribution