Update or Wait: How to Keep Your Data Fresh

In this work, we study how to optimally manage the freshness of information updates sent from a source node to a destination via a channel. A proper metric for data freshness at the destination is the age-of-information, or simply age, which is defined as how old the freshest received update is since the moment that this update was generated at the source node (e.g., a sensor). A reasonable update policy is the zero-wait policy, i.e., the source node submits a fresh update once the previous update is delivered and the channel becomes free, which achieves the maximum throughput and the minimum delay. Surprisingly, this zero-wait policy does not always minimize the age. This counter-intuitive phenomenon motivates us to study how to optimally control information updates to keep the data fresh and to understand when the zero-wait policy is optimal. We introduce a general age penalty function to characterize the level of dissatisfaction on data staleness and formulate the average age penalty minimization problem as a constrained semi-Markov decision problem (SMDP) with an uncountable state space. We develop efficient algorithms to find the optimal update policy among all causal policies, and establish sufficient and necessary conditions for the optimality of the zero-wait policy. Our investigation shows that the zero-wait policy is far from the optimum if (i) the age penalty function grows quickly with respect to the age, (ii) the packet transmission times over the channel are positively correlated over time, or (iii) the packet transmission times are highly random (e.g., following a heavy-tail distribution)

Real-time information processing of environmental sensor network data using Bayesian Gaussian processes

In this article, we consider the problem faced by a sensor network operator who must infer, in real time, the value of some environmental parameter that is being monitored at discrete points in space and time by a sensor network. We describe a powerful and generic approach built upon an efficient multi-output Gaussian process that facilitates this information acquisition and processing. Our algorithm allows effective inference even with minimal domain knowledge, and we further introduce a formulation of Bayesian Monte Carlo to permit the principled management of the hyperparameters introduced by our flexible models. We demonstrate how our methods can be applied in cases where the data is delayed, intermittently missing, censored, and/or correlated. We validate our approach using data collected from three networks of weather sensors and show that it yields better inference performance than both conventional independent Gaussian processes and the Kalman filter. Finally, we show that our formalism efficiently reuses previous computations by following an online update procedure as new data sequentially arrives, and that this results in a four-fold increase in computational speed in the largest cases considered

Planning Against Fictitious Players in Repeated Normal Form Games

Planning how to interact against bounded memory and unbounded memory learning opponents needs different treatment. Thus far, however, work in this area has shown how to design plans against bounded memory learning opponents, but no work has dealt with the unbounded memory case. This paper tackles this gap. In particular, we frame this as a planning problem using the framework of repeated matrix games, where the planner's objective is to compute the best exploiting sequence of actions against a learning opponent. The particular class of opponent we study uses a fictitious play process to update her beliefs, but the analysis generalizes to many forms of Bayesian learning agents. Our analysis is inspired by Banerjee and Peng's AIM framework, which works for planning and learning against bounded memory opponents (e.g an adaptive player). Building on this, we show how an unbounded memory opponent (specifically a fictitious player) can also be modelled as a finite MDP and present a new efficient algorithm that can find a way to exploit the opponent by computing in polynomial time a sequence of play that can obtain a higher average reward than those obtained by playing a game theoretic (Nash or correlated) equilibrium

A record-driven growth process

We introduce a novel stochastic growth process, the record-driven growth process, which originates from the analysis of a class of growing networks in a universal limiting regime. Nodes are added one by one to a network, each node possessing a quality. The new incoming node connects to the preexisting node with best quality, that is, with record value for the quality. The emergent structure is that of a growing network, where groups are formed around record nodes (nodes endowed with the best intrinsic qualities). Special emphasis is put on the statistics of leaders (nodes whose degrees are the largest). The asymptotic probability for a node to be a leader is equal to the Golomb-Dickman constant omega=0.624329... which arises in problems of combinatorical nature. This outcome solves the problem of the determination of the record breaking rate for the sequence of correlated inter-record intervals. The process exhibits temporal self-similarity in the late-time regime. Connections with the statistics of the cycles of random permutations, the statistical properties of randomly broken intervals, and the Kesten variable are given.Comment: 30 pages,5 figures. Minor update

Internal Displacement in Ukraine: Where the Government Went Wrong

The purpose of this project was to show how the Ukrainian government has delegitimized itself currently in the eyes of the Ukrainian People through its handling of the internal displacement problem. To show this, this thesis analyzes Ukrainian legislation passed pertaining to internally displaced people and how these pieces of legislation have been ineffective at producing any significant change in the IDP problem. In certain cases, this legislation is correlated with an increase in the number of IDPs. Further, this thesis analyzes the decline in public opinion of Ukrainian citizens with the government. Through interviews of different human rights organizations and displaced people, evidence is provided for this decline. Due to the contemporary nature of this topic, it would be preemptive to make any final conclusions at this point in time. Rather, this thesis is intended to give an update on present events and provide possible solutions to a current problem

Saltwater intrusion simulation in heterogeneous aquifer using lattice Boltzmann method

This study develops a saltwater intrusion simulation model using a lattice Boltzmann method (LBM) in a two-dimensional coastal confined aquifer. The saltwater intrusion is described by density-dependent groundwater flow and mass transport equations, where a freshwater-saltwater mixing zone is considered. The problem is formulated in terms of hydraulic head instead of pressure, which is recommended in those cases where static pressures dominate to reduce computational cost. The aquifer heterogeneity is explicitly a function of the speed of sound, relaxation parameter and time steps in the LBM. This study explores the equivalent squared sound speed to deal with the spatial-temporal heterogeneity arising from the inhomogeneous hydraulic conductivity and fluid density to update the equilibrium distribution functions in each time step. The Henry problem and its variants are used to demonstrate the LBM applicability to solve the saltwater intrusion problem. The inverse relationship between the time step and diffusion coefficient results in a very small time step for the groundwater flow problem due to the high hydraulic diffusion coefficient. The study demonstrates the ease of implementing the LBM to different salt concentration boundary conditions at the seaside and shows that the isochlors distributions are significantly different. Due to doubts regarding the validity of the Henry problem to test variable-density flows, numerical simulation of freshwater injection into a sediment saturated with saltwater have been carried out, showing the capability of the LBM to represent strong buoyancy effects. Some examples with correlated and uncorrelated random hydraulic conductivity (K) distributions show reasonable flow fields and isochlors distributions. It was found in the Henry problem that completely random heterogeneity in K is insignificant in changing the scale of the saltwater intrusion from that predicted using the mean K value. However, the correlated K field may have significant impact on the saltwater intrusion, resulting different from that obtained by the mean K field