Survival mediation analysis with the death-truncated mediator: The completeness of the survival mediation parameter

In medical research, the development of mediation analysis with a survival outcome has facilitated investigation into causal mechanisms. However, studies have not discussed the death-truncation problem for mediators, the problem being that conventional mediation parameters cannot be well-defined in the presence of a truncated mediator. In the present study, we systematically defined the completeness of causal effects to uncover the gap, in conventional causal definitions, between the survival and nonsurvival settings. We proposed three approaches to redefining the natural direct and indirect effects, which are generalized forms of the conventional causal effects for survival outcomes. Furthermore, we developed three statistical methods for the binary outcome of the survival status and formulated a Cox model for survival time. We performed simulations to demonstrate that the proposed methods are unbiased and robust. We also applied the proposed method to explore the effect of hepatitis C virus infection on mortality, as mediated through hepatitis B viral load

Smoothed Analysis of Dynamic Networks

We generalize the technique of smoothed analysis to distributed algorithms in dynamic network models. Whereas standard smoothed analysis studies the impact of small random perturbations of input values on algorithm performance metrics, dynamic graph smoothed analysis studies the impact of random perturbations of the underlying changing network graph topologies. Similar to the original application of smoothed analysis, our goal is to study whether known strong lower bounds in dynamic network models are robust or fragile: do they withstand small (random) perturbations, or do such deviations push the graphs far enough from a precise pathological instance to enable much better performance? Fragile lower bounds are likely not relevant for real-world deployment, while robust lower bounds represent a true difficulty caused by dynamic behavior. We apply this technique to three standard dynamic network problems with known strong worst-case lower bounds: random walks, flooding, and aggregation. We prove that these bounds provide a spectrum of robustness when subjected to smoothing---some are extremely fragile (random walks), some are moderately fragile / robust (flooding), and some are extremely robust (aggregation).Comment: 20 page

Evolving graphs: dynamical models, inverse problems and propagation

Applications such as neuroscience, telecommunication, online social networking, transport and retail trading give rise to connectivity patterns that change over time. In this work, we address the resulting need for network models and computational algorithms that deal with dynamic links. We introduce a new class of evolving range-dependent random graphs that gives a tractable framework for modelling and simulation. We develop a spectral algorithm for calibrating a set of edge ranges from a sequence of network snapshots and give a proof of principle illustration on some neuroscience data. We also show how the model can be used computationally and analytically to investigate the scenario where an evolutionary process, such as an epidemic, takes place on an evolving network. This allows us to study the cumulative effect of two distinct types of dynamics

Braess's Paradox in Wireless Networks: The Danger of Improved Technology

When comparing new wireless technologies, it is common to consider the effect that they have on the capacity of the network (defined as the maximum number of simultaneously satisfiable links). For example, it has been shown that giving receivers the ability to do interference cancellation, or allowing transmitters to use power control, never decreases the capacity and can in certain cases increase it by $\Omega(\log (\Delta \cdot P_{\max}))$, where $\Delta$ is the ratio of the longest link length to the smallest transmitter-receiver distance and $P_{\max}$ is the maximum transmission power. But there is no reason to expect the optimal capacity to be realized in practice, particularly since maximizing the capacity is known to be NP-hard. In reality, we would expect links to behave as self-interested agents, and thus when introducing a new technology it makes more sense to compare the values reached at game-theoretic equilibria than the optimum values. In this paper we initiate this line of work by comparing various notions of equilibria (particularly Nash equilibria and no-regret behavior) when using a supposedly "better" technology. We show a version of Braess's Paradox for all of them: in certain networks, upgrading technology can actually make the equilibria \emph{worse}, despite an increase in the capacity. We construct instances where this decrease is a constant factor for power control, interference cancellation, and improvements in the SINR threshold ($\beta$), and is $\Omega(\log \Delta)$ when power control is combined with interference cancellation. However, we show that these examples are basically tight: the decrease is at most O(1) for power control, interference cancellation, and improved $\beta$, and is at most $O(\log \Delta)$ when power control is combined with interference cancellation

A Statistical Mechanical Load Balancer for the Web

The maximum entropy principle from statistical mechanics states that a closed system attains an equilibrium distribution that maximizes its entropy. We first show that for graphs with fixed number of edges one can define a stochastic edge dynamic that can serve as an effective thermalization scheme, and hence, the underlying graphs are expected to attain their maximum-entropy states, which turn out to be Erdos-Renyi (ER) random graphs. We next show that (i) a rate-equation based analysis of node degree distribution does indeed confirm the maximum-entropy principle, and (ii) the edge dynamic can be effectively implemented using short random walks on the underlying graphs, leading to a local algorithm for the generation of ER random graphs. The resulting statistical mechanical system can be adapted to provide a distributed and local (i.e., without any centralized monitoring) mechanism for load balancing, which can have a significant impact in increasing the efficiency and utilization of both the Internet (e.g., efficient web mirroring), and large-scale computing infrastructure (e.g., cluster and grid computing).Comment: 11 Pages, 5 Postscript figures; added references, expanded on protocol discussio

A quantum Bose-Hubbard model with evolving graph as toy model for emergent spacetime

We present a toy model for interacting matter and geometry that explores quantum dynamics in a spin system as a precursor to a quantum theory of gravity. The model has no a priori geometric properties, instead, locality is inferred from the more fundamental notion of interaction between the matter degrees of freedom. The interaction terms are themselves quantum degrees of freedom so that the structure of interactions and hence the resulting local and causal structures are dynamical. The system is a Hubbard model where the graph of the interactions is a set of quantum evolving variables. We show entanglement between spatial and matter degrees of freedom. We study numerically the quantum system and analyze its entanglement dynamics. We analyze the asymptotic behavior of the classical model. Finally, we discuss analogues of trapped surfaces and gravitational attraction in this simple model.Comment: 23 pages, 6 figures; updated to published versio

Trapping in complex networks

We investigate the trapping problem in Erdos-Renyi (ER) and Scale-Free (SF) networks. We calculate the evolution of the particle density $\rho(t)$ of random walkers in the presence of one or multiple traps with concentration $c$. We show using theory and simulations that in ER networks, while for short times $\rho(t) \propto \exp(-Act)$, for longer times $\rho(t)$ exhibits a more complex behavior, with explicit dependence on both the number of traps and the size of the network. In SF networks we reveal the significant impact of the trap's location: $\rho(t)$ is drastically different when a trap is placed on a random node compared to the case of the trap being on the node with the maximum connectivity. For the latter case we find \rho(t)\propto\exp\left[-At/N^\frac{\gamma-2}{\gamma-1}\av{k}\right] for all $\gamma>2$, where $\gamma$ is the exponent of the degree distribution $P(k)\propto k^{-\gamma}$.Comment: Appendix adde

Distributed Symmetry Breaking in Hypergraphs

Fundamental local symmetry breaking problems such as Maximal Independent Set (MIS) and coloring have been recognized as important by the community, and studied extensively in (standard) graphs. In particular, fast (i.e., logarithmic run time) randomized algorithms are well-established for MIS and $\Delta +1$-coloring in both the LOCAL and CONGEST distributed computing models. On the other hand, comparatively much less is known on the complexity of distributed symmetry breaking in {\em hypergraphs}. In particular, a key question is whether a fast (randomized) algorithm for MIS exists for hypergraphs. In this paper, we study the distributed complexity of symmetry breaking in hypergraphs by presenting distributed randomized algorithms for a variety of fundamental problems under a natural distributed computing model for hypergraphs. We first show that MIS in hypergraphs (of arbitrary dimension) can be solved in $O(\log^2 n)$ rounds ($n$ is the number of nodes of the hypergraph) in the LOCAL model. We then present a key result of this paper --- an $O(\Delta^{\epsilon}\text{polylog}(n))$-round hypergraph MIS algorithm in the CONGEST model where $\Delta$ is the maximum node degree of the hypergraph and $\epsilon > 0$ is any arbitrarily small constant. To demonstrate the usefulness of hypergraph MIS, we present applications of our hypergraph algorithm to solving problems in (standard) graphs. In particular, the hypergraph MIS yields fast distributed algorithms for the {\em balanced minimal dominating set} problem (left open in Harris et al. [ICALP 2013]) and the {\em minimal connected dominating set problem}. We also present distributed algorithms for coloring, maximal matching, and maximal clique in hypergraphs.Comment: Changes from the previous version: More references adde

Temporal Network Optimization Subject to Connectivity Constraints

In this work we consider temporal networks, i.e. networks defined by a labeling λ assigning to each edge of an underlying graph G a set of discrete time-labels. The labels of an edge, which are natural numbers, indicate the discrete time moments at which the edge is available. We focus on path problems of temporal networks. In particular, we consider time-respecting paths, i.e. paths whose edges are assigned by λ a strictly increasing sequence of labels. We begin by giving two efficient algorithms for computing shortest time-respecting paths on a temporal network. We then prove that there is a natural analogue of Menger’s theorem holding for arbitrary temporal networks. Finally, we propose two cost minimization parameters for temporal network design. One is the temporality of G, in which the goal is to minimize the maximum number of labels of an edge, and the other is the temporal cost of G, in which the goal is to minimize the total number of labels used. Optimization of these parameters is performed subject to some connectivity constraint. We prove several lower and upper bounds for the temporality and the temporal cost of some very basic graph families such as rings, directed acyclic graphs, and trees

Fast multipole networks

Two prerequisites for robotic multiagent systems are mobility and communication. Fast multipole networks (FMNs) enable both ends within a unified framework. FMNs can be organized very efficiently in a distributed way from local information and are ideally suited for motion planning using artificial potentials. We compare FMNs to conventional communication topologies, and find that FMNs offer competitive communication performance (including higher network efficiency per edge at marginal energy cost) in addition to advantages for mobility