A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs

Individuals who interact with each other in social networks often exchange ideas and influence each other’s opinions. A popular approach to study the spread of opinions on networks is by examining bounded-confidence models (BCMs), in which the nodes of a network have continuous-valued states that encode their opinions and are receptive to other nodes’ opinions when they lie within some confidence bound of their own opinion. In this article, we extend the Deffuant–Weisbuch (DW) model, which is a well-known BCM, by examining the spread of opinions that coevolve with network structure. We propose an adaptive variant of the DW model in which the nodes of a network can (1) alter their opinions when they interact with neighbouring nodes and (2) break connections with neighbours based on an opinion tolerance threshold and then form new connections following the principle of homophily. This opinion tolerance threshold determines whether or not the opinions of adjacent nodes are sufficiently different to be viewed as ‘discordant’. Using numerical simulations, we find that our adaptive DW model requires a larger confidence bound than a baseline DW model for the nodes of a network to achieve a consensus opinion. In one region of parameter space, we observe ‘pseudo-consensus’ steady states, in which there exist multiple subclusters of an opinion cluster with opinions that differ from each other by a small amount. In our simulations, we also examine the roles of early-time dynamics and nodes with initially moderate opinions for achieving consensus. Additionally, we explore the effects of coevolution on the convergence time of our BCM.

We consider problems that can be formulated as a task of finding an optimal triangulation of a graph w.r.t. some notion of optimality. We present algorithms parameterized by the size of a minimum edge clique cover (texttt {cc}) to such problems. This parameterization occurs naturally in many problems in this setting, e.g., in the perfect phylogeny problem texttt {cc} is at most the number of taxa, in fractional hypertreewidth texttt {cc} is at most the number of hyperedges, and in treewidth of Bayesian networks texttt {cc} is at most the number of non-root nodes. We show that the number of minimal separators of graphs is at most 2^texttt {cc}, the number of potential maximal cliques is at most 3^texttt {cc}, and these objects can be listed in times O^*(2^texttt {cc}) and O^*(3^texttt {cc}), respectively, even when no edge clique cover is given as input; the O^*(cdot ) notation omits factors polynomial in the input size. These enumeration algorithms imply O^*(3^texttt {cc}) time algorithms for problems such as treewidth, weighted minimum fill-in, and feedback vertex set. For generalized and fractional hypertreewidth we give O^*(4^m) time and O^*(3^m) time algorithms, respectively, where m is the number of hyperedges. When an edge clique cover of size texttt {cc}' is given as a part of the input we give O^*(2^{texttt {cc}'}) time algorithms for treewidth, minimum fill-in, and chordal sandwich. This implies an O^*(2^n) time algorithm for perfect phylogeny, where n is the number of taxa. We also give polynomial space algorithms with time complexities O^*(9^{texttt {cc}'}) and O^*(9^{texttt {cc}+ O(log ^2 texttt {cc})}) for problems in this framework.

Convergence of a fluid–structure interaction problem decoupled by a Neumann control over a single time step

Despite the recently exhibited importance of higher-order interactions for various processes, few flexible (null) models are available. In particular, most studies on hypergraphs focus on a small set of theoretical models. Here, we introduce a class of models for random hypergraphs which displays a similar level of flexibility of complex network models and where the main ingredient is the probability that a node belongs to a hyperedge. When this probability is a constant, we obtain a random hypergraph in the same spirit as the Erdos-Renyi graph. This framework also allows us to introduce different ingredients such as the preferential attachment for hypergraphs, or spatial random hypergraphs. In particular, we show that for the Erdos-Renyi case there is a transition threshold scaling as 1/sqrt[EN] where N is the number of nodes and E the number of hyperedges. We also discuss a random geometric hypergraph which displays a percolation transition for a threshold distance scaling as r_{c}^{*}∼1/sqrt[E]. For these various models, we provide results for the most interesting measures, and also introduce new ones in the spatial case for characterizing the geometrical properties of hyperedges. These different models might serve as benchmarks useful for analyzing empirical data.

We consider a consensus algorithm in which every node in a time-varying undirected connected graph assigns equal weight to each of its neighbors. Under the assumption that the degree of any given node is constant in time, we show that the algorithm achieves consensus within a given accuracy ∈ on n nodes in time O(n3ln(n=∈)). Because there is a direct relation between consensus algorithms in time-varying environments and inhomogeneous random walks, our result also translates into a general statement on such random walks. Moreover, we give simple proofs that the convergence time becomes exponentially large in the number of nodes n under slight relaxations of the above assumptions. We prove that exponential convergence time is possible for consensus algorithms on fixed directed graphs, and we use an example of Cao, Spielman, and Morse to give a simple argument that the same is possible if the constant degrees assumption is even slightly relaxed.

A Monte Carlo (MC) simulation is performed on peroxide induced branching reactions in a linear low density polyethylene (LLDPE) melt processed with different dicumyl peroxide (DCP) concentrations at various processing times and temperatures. The MC simulation can successfully monitor the microstructural changes due to the induced long chain branching (LCB), decreased terminal double bonds, and increased trans vinyl bonds in LLDPE during peroxide modification. The induced structural changes are in good agreement with the experimental results obtained by rheometery and SEC analysis. The changes in the gel content, , and MWD as a result of the peroxide modification are also determined. The simulation results also reveal that the chemical mechanism by which the modification proceeded is closely related to the changes in concentrations of reactive vinyl species of the PE molecules. Moreover, the results indicate that the degree of induced LCB increases almost linearly with the DCP concentrations. The findings of this paper indicate that the MC simulation method is able to predict the suitable processing conditions needed for inducing desirable structural changes in a LLDPE.

The US Air Force (USAF) Flight Test Center has made recent advancements in its system identification capabilities. The most recent project from the USAF Test Pilot School (TPS) was to implement a near real-time parameter identification curriculum sortie. This sortie development entailed automatic parsing of input doublets and then analyzing these doublets using equation error. The Global Vigilance Combined Test Force would like to take the next step toward more rapid parameter identification, specifically by extending beyond the previous equation error techniques and advancing towards trajectory reconstruction, i.e. data compatibility and output error. The paper herein demonstrates how to solve for aerodynamic stability and control derivatives via dynamic optimization using pseudospectral methods. Future research may include time delay which can be added as another optimization parameter, thus resolving issues with heavily filtered instrumentation data. The inherent implicit integration within the pseudospectral method has already shown improved stability over traditional explicit integration within shooting methods (1) . Also, by optimizing the solution using a smaller finite number of nodes, the convergence time may drastically improve over explicit or sequential integration. Lastly, by using segmented adaptive node distribution, vice a single segment, a more accurate solution may be obtained using the same number of nodes. The work herein introduces a new method for system identification algorithms. This is intended to be an extension, or improvement, upon the existing accomplishments within the System Identification Programs for Aircraft (SIDPAC) software documented in Aircraft System Identification: Theory and Practice by V. Klein and E.A. Morelli. The pseudospectral method and the General Pseudospectral Optimal Control Software (GPOPS) to solve dynamic optimization problems are already established. This paper extends these established techniques towards this new application. These results are modeled after textbook examples for output error. This technique is motivated by the desire to develop a practical real time parameter estimation capability.

Active grain growth control with distributed heating

This paper describes an alternate method to Monte Carlo for calculating circuit node voltage and branch current variances due to random process variability. Recent results show that the complex models traditionally used to describe random process variations of a transistor can be replaced by a single independent current noise source with a variance dependent on the transistor's size and operating points. As a result, each transistor affected by random process variability can be modeled as a deterministic device in parallel with a current noise source. By replacing all the transistors in a circuit with this model, the spatial voltage variances of circuit nodes can be calculated through linear small-signal analysis. The idea is presented in this paper and a tool implemented for Berkeley SPICE is described. The results of the variability SPICE tool match the results from Monte Carlo run in SPECTRE, with an accuracy determined by the accuracy of the random process variability model. For example, the standard deviations computed by the tool are within a 5.0% accuracy of those calculated through measured silicon data which has a fitting error of 5.4%. The Monte Carlo method computes node variances in a time proportional to the number of circuit nodes and the number of iterations, whereas the computation time required by the variability tool is only a function of the number of circuit nodes. For large analog designs this results in a significant speed-up in the amount of time required to calculate circuit node variances.

The influence of the concatenation of arbitrary optical multiplexers/demultiplexers (MUX/DEMUXs) on the probability density function (PDF) of the output current of a transparent optical network is assessed. All PDF results obtained analytically are compared with estimates from Monte Carlo simulation and an excellent agreement is achieved. The non-Gaussian behavior of the PDFs, previously reported by other authors for square-law detectors, is significantly enhanced with the number of nodes increase due to the noise accumulation along the cascade of MUX/DEMUXs. The increase of the MUX/DEMUXs bandwidth and detuning also enhances the PDFs non-Gaussian behavior. The PDF shape variation with the detuning depends strongly on the number of nodes. Explanations for the Gaussian approximation (GA) accuracy on the assessment of the performance of a concatenation of optical MUX/DEMUXs are also provided. For infinite extinction ratio and tuned MUX/DEMUXs, the GA error probabilities are, in general, pessimistic, due to the inaccurate estimation of the error probability for both bits. For low extinction ratio, the GA is very accurate due to a balance between the error probabilities estimated for the bits “1” and “0.” With the detuning increase, the GA estimates can become optimistic.

We consider the distributed detection problem of a temporally correlated random radio source signal using a wireless sensor network capable of measuring the energy of the received signals. It is well-known that optimal tests in the Neyman-Pearson setting are based on likelihood ratio tests (LRT), which, in this set-up, evaluate the quotient between the probability density functions (PDF) of the measurements when the source signal is present and absent. When the source is present, the computation of the joint PDF of the energy measurements at the nodes is a challenging problem. This is due to the statistical dependence introduced to the received signals by the propagation through fading channels of the radio signal emitted by the source. We deal with this problem using the characteristic function of the (intractable) joint PDF, and proposing an approximation to it. We derive bounds for the approximation error in two wireless propagation scenarios, slow and fast fading, and show that the proposed approximation is exponentially tight with the number of nodes when the time-bandwidth product is sufficiently high. The approximation is used as a substitute of the exact joint PDF for building an approximate LRT, which performs better than other well-known detectors, as verified by Monte Carlo simulations.

This paper presents a general statistical treatment for power flow analysis in a complex structure. The nominal power flow is computed using the characteristic constraint (CC) modes of the component structures. These CC modes are built from component mode synthesis (CMS) of finite element models, and they form a highly-reduced order basis for capturing the motion of the interface between components — and thus the power flow. The power flow statistics are then calculated over an ensemble of systems due to the variation of structural system parameters. Each modal response is expanded in a basis of quadrature polynomials or locally linear interpolation (LLI) functions in these uncertain parameters. The system equations for the reduced order CMS model with uncertainties are derived using Galerkin's method. These equations have the same form as the nominal power flow equations, but the number of equations is increased by a factor equal to the order of the polynomials (when using quadrature polynomials) or the number of nodes in the parameter space (when using LLI functions). Thus, the ensemble-averaged power flow can be calculated by solving this new set of equations, instead of using Monte Carlo simulations. A cantilever plate and a L-shaped plate are used as example structures for the demonstration of these statistical approximations. In general, this statistical treatment provides efficient and accurate modeling of parameter uncertainties, which is critical for mid-frequency vibration analysis.

Purpose: To provide an efficient cloud computing infrastructure for VMAT and IMRT inverse planning. Methods: Amazon Elastic Compute Cloud (EC2) with a master node (17.1 GB memory, 2 virtual cores, 420 GB instance storage, 64‐bit platform) is used as the backbone of cloud computing for VMAT and IMRT dose optimization. The master node is scalable on an “on‐demand” basis. It can lunch more workers if the CPU usage exceeds the upper limit for given time (e.g., over 90% usage for 2 minutes), or terminate the workers if there are finished tasks. A quadratic objective function with volumetric constraints is expressed as a function of the aperture shapes and weights of the incident beams. A Monte Carlo simulation is employed to generate accurate dose kernel by parallel tasks. The number of parallel tasks is approximately the same as or less than the total number of beamlets in iterative simulation for all beams. The cloud optimization is implemented for a Varian TrueBeam STX linac beams with and without flattening filters available. The filed output from EC2 is sent down to the Simple Storage Service (S3). Three clinical cases have been studied for the purpose of evaluating the performance of the new planning platform. Results: A cloud computing environment leads to speedups of 150–300 times for the cases considered in this study. The speedup scales approximately linearly with the number of nodes used for computing. The resultant plans from the cloud computing are found almost identical to that obtained using a desktop PC, indicating the reliability of the cloud computing platform. Conclusions: A cloud computing infrastructure has been established for VMAT and IMRT inverse planning with different beam characteristics. The cloud computing environment substantially improves the speed of inverse planning and makes future on‐treatment adaptive replanning possible.This work was supported by grants from the National Research Foundation of Korea (NRFK) of the Korea Government (MEST) (Grant No. K20901000001‐09E0100‐ 00110)

Monte Carlo Methods for Node Self-Localization and Nonlinear Target Tracking in Wireless Sensor Networks

Numerical solution methods for option pricing fall into two broad classes, either the lattice framework or Monte Carlo simulation. Monte Carlo simulation is problematic for American options, while the Binomial and Trinomial approaches have difficulty incorporating stochastic jumps. The probability density at expiration that is generated by a lattice typically has different skewness and kurtosis than is embedded in option market prices. The Binomial can be fitted imposing a terminal density with the right moments, using the Johnson system of distributions for example, but the problem still remains that the number of distinct nodes to calculate increases quadratically with the number of time steps. This article proposes the “Willow Tree” method, which combines a small number of large time steps that connect to many possible next period nodes, with the constraint that the terminal density, constructed from the Johnson system, has the same mean, volatility, skewness, and kurtosis as the risk neutral density extracted from prices in the options market. The result is a much faster and more accurate valuation than may be achieved through existing approaches. <b>TOPICS:</b>Options, simulations