Heuristic Approximation Research Articles

Color-avoiding percolation.

Many real world networks have groups of similar nodes which are vulnerable to the same failure or adversary. Nodes can be colored in such a way that colors encode the shared vulnerabilities. Using multiple paths to avoid these vulnerabilities can greatly improve network robustness, if such paths exist. Color-avoiding percolation provides a theoretical framework for analyzing this scenario, focusing on the maximal set of nodes which can be connected via multiple color-avoiding paths. In this paper we extend the basic theory of color-avoiding percolation that was published in S. M. Krause et al. [Phys. Rev. X 6, 041022 (2016)]2160-330810.1103/PhysRevX.6.041022. We explicitly account for the fact that the same particular link can be part of different paths avoiding different colors. This fact was previously accounted for with a heuristic approximation. Here we propose a better method for solving this problem which is substantially more accurate for many avoided colors. Further, we formulate our method with differentiated node functions, either as senders and receivers, or as transmitters. In both functions, nodes can be explicitly trusted or avoided. With only one avoided color we obtain standard percolation. Avoiding additional colors one by one, we can understand the critical behavior of color-avoiding percolation. For unequal color frequencies, we find that the colors with the largest frequencies control the critical threshold and exponent. Colors of small frequencies have only a minor influence on color-avoiding connectivity, thus allowing for approximations.

Thermodynamic Constraints Improve Metabolic Networks

In pursuit of establishing a realistic metabolic phenotypic space, the reversibility of reactions is thermodynamically constrained in modern metabolic networks. The reversibility constraints follow from heuristic thermodynamic poise approximations that take anticipated cellular metabolite concentration ranges into account. Because constraints reduce the feasible space, draft metabolic network reconstructions may need more extensive reconciliation, and a larger number of genes may become essential. Notwithstanding ubiquitous application, the effect of reversibility constraints on the predictive capabilities of metabolic networks has not been investigated in detail. Instead, work has focused on the implementation and validation of the thermodynamic poise calculation itself. With the advance of fast linear programming-based network reconciliation, the effects of reversibility constraints on network reconciliation and gene essentiality predictions have become feasible and are the subject of this study. Networks with thermodynamically informed reversibility constraints outperformed gene essentiality predictions compared to networks that were constrained with randomly shuffled constraints. Unconstrained networks predicted gene essentiality as accurately as thermodynamically constrained networks, but predicted substantially fewer essential genes. Networks that were reconciled with sequence similarity data and strongly enforced reversibility constraints outperformed all other networks. We conclude that metabolic network analysis confirmed the validity of the thermodynamic constraints, and that thermodynamic poise information is actionable during network reconciliation.

Transient VRM Response From a Large Circular Loop Over a Conductive and Magnetically Viscous Half-Space

To effectively characterize the impact of viscous remanent magnetization (VRM) on the transient electromagnetic response, we present a set of analytical expressions for the vertical and radial VRM responses generated by a large circular loop over a magnetically viscous half-space. For a step-off excitation, Neel relaxation theory is used to express the VRM within the half-space as the product of a static on-time magnetization and a time-dependent aftereffect function. Through heuristic and empirical approximations to the elliptic integral of the second kind, we are able to convert Hankel integral-based expressions for static fields into simplified analytical expressions. These were validated with a numerical 1-D forward modeling code. Analytical expressions show that VRM responses are largest near the transmitter wire, and that at the center of a large loop, the strength of the VRM response is inversely proportional to the loop’s radius. We also present an estimate of the crossover time from which the VRM signal starts to dominate the transient response. We found that later crossover times were observed near the centers of large loops and that crossover times were much earlier near the transmitter wire. Also, the magnetic flux density has an earlier crossover time compared with its time derivative. To lower or remove the VRM response in an anticipated survey, our analytical expressions can be used straightforwardly to choose an appropriate loop size, identify the VRM response time window, and select an optimal set of time channels.

Approximation algorithms in partitioning real-time tasks with replications

Today is an era where multiprocessor technology plays a major role in designs of modern computer architecture. While multiprocessor systems offer extra computing power, it also opens a new range of opportunities to improve fault-robustness. This paper focuses on a problem of achieving fault-tolerance using replications in real-time, multiprocessor systems. In the problem, multiple replicas, or copies, of a computing task are executed on distinct processors to resist potential processor failures and computing faults. Two greedy, approximation heuristics, named Worst Fit Increasing K-Replication and First Fit Increasing K-Replication, are studied to maximise the number of real-time tasks assigned on a system with identical processors, respecting to the tasks’ replicating and timely requirements. Worst case performance is analysed by using an approximation ratio between the algorithms and an optimal solution. We mathematically prove that the ratios of using both algorithms are infinitely close to 2. Simulations are performed on a large set of testing cases which can be used to bring to light the average performance of using the algorithms in practice. The results show that both heuristic algorithms provide simple but fast and effective solutions to solve the problem.

A high-fidelity multiresolution digital elevation model for Earth systems

Abstract. The impact of topography on Earth systems variability is well recognised. As numerical simulations evolved to incorporate broader scales and finer processes, accurately assimilating or transforming the topography to produce more exact land–atmosphere–ocean interactions, has proven to be quite challenging. Numerical schemes of Earth systems often use empirical parameterisation at sub-grid scale with downscaling to express topographic endogenous processes, or rely on insecure point interpolation to induce topographic forcing, which creates bias and input uncertainties. Digital elevation model (DEM) generalisation provides more sophisticated systematic topographic transformation, but existing methods are often difficult to be incorporated because of unwarranted grid quality. Meanwhile, approaches over discrete sets often employ heuristic approximation, which are generally not best performed. Based on DEM generalisation, this article proposes a high-fidelity multiresolution DEM with guaranteed grid quality for Earth systems. The generalised DEM surface is initially approximated as a triangulated irregular network (TIN) via selected feature points and possible input features. The TIN surface is then optimised through an energy-minimised centroidal Voronoi tessellation (CVT). By devising a robust discrete curvature as density function and exact geometry clipping as energy reference, the developed curvature CVT (cCVT) converges, the generalised surface evolves to a further approximation to the original DEM surface, and the points with the dual triangles become spatially equalised with the curvature distribution, exhibiting a quasi-uniform high-quality and adaptive variable resolution. The cCVT model was then evaluated on real lidar-derived DEM datasets and compared to the classical heuristic model. The experimental results show that the cCVT multiresolution model outperforms classical heuristic DEM generalisations in terms of both surface approximation precision and surface morphology retention.

An Efficient Approximate Algorithm for the 1-Median Problem on a Graph

We propose a heuristic approximation algorithm for the 1-median problem. The 1-median problem is the problem of finding a vertex with the highest closeness centrality. Starting from a randomly selected vertex, our algorithm repeats to find a vertex with higher closeness centrality by approximately calculating closeness centrality of each vertex using simpler spanning subgraphs, which are called k-neighbor dense shortest path graphs with shortcuts. According to our experimental results using real networks with more than 10,000 vertices, our algorithm is more than 100 times faster than the exhaustive search and more than 20 times faster than the state-of-the-art approximation algorithm using annotated information to the vertices while the solutions output by our algorithm have higher approximation ratio.

Multi-model approach based on parametric sensitivities – A heuristic approximation for dynamic optimization of semi-batch processes with parametric uncertainties

Abstract Optimal processes often exhibit active path constraints. Parametric uncertainties in the process model might thus lead to constraint violations. A heuristic approach is presented to overcome this challenge. The nominal model is optimized with additional path constraints due to worst-case models. A heuristic method of choosing these models is proposed based on sensitivities of the constraints with respect to the uncertain parameters. The presented approximation does not guarantee robust feasibility, but path constraint violations are less likely to occur compared to the optimization using the nominal model solely. Two case studies are presented: a complex emulsion copolymerization process (DAE with 139 equations) and the penicillin formation (four differential equations and two algebraic equations). The results of both case studies show that, in contrast to the optimization in the nominal case, the multi-model approach does not violate the path constraints for different scenarios of the parametric uncertainty set.

A New Theory of Potential Step Chronoamperometry at Hemispheroidal Electrodes: Complete Explicit Semi-Analytical Formulae for the Faradaic Current Density and the Faradaic Current

The recently described theory of potential step chronoamperometry at inlaid microdisk electrodes [L. K. Bieniasz, Electrochim. Acta 199(2016)1] is extended to hemispheroidal electrodes, assuming diffusional transport under limiting current conditions. Both oblate and prolate hemispheroids are discussed. The theory provides previously unknown, rigorous, complete, and explicit expressions for the concentration, the Faradaic current density, and the Faradaic current. The expressions are in the form of inverse Laplace transforms of infinite series involving spheroidal wave functions. Numerical Laplace transform inversion, applied to the series, yields highly accurate solution values. Hence, the present solutions are advantageous over formerly used low-accurate and/or heuristic approximations, for the purposes of experimental data analysis, and for testing of modelling/simulation techniques.

A degree based approach to find Steiner Trees

In this paper, we introduce a heuristic approximation algorithm for The Steiner Tree problem which is known to be NP Hard. It is based on the concept of degree of each node in the given graph. The Steiner Tree problem is similar to the Minimum Spanning Tree problem with a subset of vertices. The complexity analysis tells us that this method has an approximation ratio of n/4, where n is the number of nodes in the given graph.

A Novel QoS Provisioning Algorithm for Optimal Multicast Routing in WMNs

The problem of optimal multicast routing in Wireless Mess Networks (WMNs) with Quality-of-Service (QoS) provisioning, which is Non-Deterministic Polynomial (NP)-complete, is studied in this paper. The existing algorithms are not very efficient or effective. In order to find an approximation optimal solution for WMNs in feasible time from source to the set of destination nodes, combining the previous deterministic algorithm with the well-known Minimum Path Cost Heuristic (MPH) algorithm, a novel multicast heuristic approximation (NMHA) algorithm with QoS provisioning is proposed in this paper to deal with it. The theoretical validations for the proposed algorithm are presented to show its performance and efficiency. After that, the random static networks with different destination nodes are evaluated. Simulations in these networks show that the proposed algorithm can achieve the approximate optimal solution with the approximation factor of 2(1 + ε)(1 − 1/q) and the time complexity of O(qmn2τK−1).

Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation

Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d(1≤d≤3) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.097801], a good agreement being observed.

A New Theory of Potential Step Chronoamperometry at a Microdisk Electrode: Complete Explicit Semi-Analytical Formulae for the Faradaic Current Density and the Faradaic Current

A novel theory is presented, of potential step chronoamperometry at a microdisk electrode, assuming a purely diffusional transport under limiting current conditions. The theory provides previously unknown, rigorous, complete, and explicit expressions for the concentration, the Faradaic current density, and the Faradaic current. The microdisk is considered as a limiting case of an oblate microhemispheroidal electrode, when the smallest radius of the hemispheroid tends to zero. The method of separation of variables in the Laplace space is used, resulting in two spheroidal differential equations. The concentration of the depolarizer, the Faradaic current density, and the Faradaic current, are then expressed as inverse Laplace transforms of infinite series involving spheroidal wave functions. Numerical Laplace transform inversion, applied to the series, yields highly accurate solution values. The series are also amenable to analytical examinations. Hence, the present solutions should be preferred over formerly used low-accurate and/or heuristic approximations, for the purposes of experimental data analysis, and for the testing of modelling/simulation techniques. The formula derived for the concentration can also be used to develop a theory of chronoamperometry at oblate microhemispheroidal electrodes.

A new theory, and automatic computation of reversible cyclic voltammograms at a microband electrode

By generalising the recent theory of chronoamperometry [L. K. Bieniasz, Electrochim. Acta 178 (2015) 25], a new, semi-analytical description of reversible cyclic voltammetry at a microband electrode is obtained, assuming equal diffusion coefficients of the species involved in a redox reaction. In contrast to the formerly proposed model [K. Aoki, K. Tokuda, J. Electroanal. Chem. 237 (1987) 163], the new theory does not involve any heuristic approximations. It is based on the formalism of Mathieu equations and functions, and provides rigorous and complete expressions for the voltammetric current, in the form of either a convolution integral or an integral equation. The voltammograms are calculated automatically with a prescribed accuracy, by using either the adaptive integrator dqags from the QUADPACK package, or the adaptive Huber method for integral equations. The two methods are compared, and dqags is found to be more efficient. A highly accurate (relative error about 10−16) procedure for calculating the kernel function of the integral equation, and its moment integrals, is also described.

Pliable Index Coding

We formulate a new variant of the index coding problem, where instead of demanding a specific message, clients are pliable, and are interested in receiving any $t$ messages that they do not have. We term this problem pliable index coding or PICOD $(t)$ . We prove that, with this formulation, although some instances of the problem become simple, in general, the problem of finding the optimal linear code remains NP-hard. However, we show that it is possible to construct pliable index codes that are substantially smaller than index codes in many cases. If there are $n$ clients, the server has $m$ messages, and each client has a side information set of cardinality $s\leq m-t$ ; we show that $O(\min \{t\log n, t+\log ^{2} n\})$ broadcast transmissions are sufficient to satisfy all the clients. For $t=1$ , this is an exponential improvement over the $n$ messages required in index coding in the worst case (for $m=n$ ). In addition, for $t\gg \log ^{2} n$ , the number of broadcast transmissions required is only linearly dependent on $t$ . We generalize the results to instances where the side information sets are not necessarily of equal cardinality. When $m = O(n^\delta )$ , for some constant $\delta >0$ , we show that the codes of size $O(\min \{t\log ^{2} n,t\log n+\log ^{3} n\})$ are sufficient in general. We also consider the scenario when the server only knows the cardinality of the side information sets of the clients and each client is interested in receiving any $t$ messages that it does not have. We term this formulation oblivious pliable index coding or OB-PICOD $(t)$ . If the cardinalities of side information sets of all the clients is $s$ (with $s\leq m-t$ ), then we show that $\min \{s+t,m-s\}$ messages are both sufficient and necessary for linear codes. Finally, we develop efficient heuristic approximation algorithms for PICOD $(t)$ and show through simulations on the random instances of PICOD $(t)$ that they perform well in practice.

Thermodynamics-based models of transcriptional regulation with gene sequence.

Quantitative models of gene regulatory activity have the potential to improve our mechanistic understanding of transcriptional regulation. However, the few models available today have been based on simplistic assumptions about the sequences being modeled or heuristic approximations of the underlying regulatory mechanisms. In this work, we have developed a thermodynamics-based model to predict gene expression driven by any DNA sequence. The proposed model relies on a continuous time, differential equation description of transcriptional dynamics. The sequence features of the promoter are exploited to derive the binding affinity which is derived based on statistical molecular thermodynamics. Experimental results show that the proposed model can effectively identify the activity levels of transcription factors and the regulatory parameters. Comparing with the previous models, the proposed model can reveal more biological sense.

SHORT-PERIOD STELLAR ACTIVITY CYCLES WITHKEPLERPHOTOMETRY

We study the short-periodic component of stellar activity with a cycle periods Pcyc up to 1000 days using the Kepler mission photometry of fast-rotating (rotational periods from 1 to 4 days) stars with spectra of M4V to F3V. Applying the originally developed two non-spectral methods, we measured the effective period of stellar cycles in 462 objects. The obtained results are in accordance with previous measurements by Vida et al. (2014), do not seem to result from a beating effect. The performed measurements of Pcyc cluster in a specific branch which covers the previously unstudied region in the Saar-Brandenburg (1999) diagram, and connects the branch of inactive stars with the area populated by super-active objects. It is shown that the formation of the discovered branch is due to the alpha-quenching effect, which saturates the magnetic dynamo and decreases the cycle periods with the increase of inverted Rossby number. This finding is important in the context of the discussion on catastrophic quenching and other heuristic approximations of the non-linear alpha-effect.

A quasistatic implementation of the concurrent atomistic-continuum method for FCC crystals

In recent years, numerous partitioned-domain methods have been developed to describe dislocation behavior at length scales that are usually inaccessible to most classical atomistic methods. These methods retain full atomistic detail in regions of interest while using a continuum description to reduce the computational burden elsewhere. In most of these methods, however, lattice defects in the continuum are either implemented via constitutive relations, lattice elasticity with dislocation field interactions, or are not permitted at all. In such approaches, the transit of dislocations across the atomistic/continuum interface appeals to approximate heuristics intended to minimize the effects of the interface due to the change from atomistic to continuum degrees of freedom. The concurrent atomistic-continuum (CAC) method, originally developed for addressing dynamic dislocation behavior by Xiong et al. (2011), permits dislocations to propagate in a continuum domain that employs a piecewise continuous finite element description with interelement displacement discontinuities. The method avoids ghost forces at interface between atomistically resolved and coarse-grained domains. CAC has subsequently been used to investigate complex dislocation behavior in face-centered cubic (FCC) metals (Xiong et al., 2012b,a,c, 2015). In this paper, we propose a quasistatic 3-D method to carry out sequential energy-minimized simulations at 0 K. This facilitates study of structure evolution along minimum energy pathways, avoiding over-driven conditions of high rate molecular dynamics. Parallelization steps in code implementation are described. Applications are presented for the quasistatic CAC method in FCC metal plasticity. Comparisons are made with a fully-resolved atomistic method for generalized stacking fault energy, core structure and stress field of a single 60° mixed type dislocation, surface indentation, and 60° mixed type dislocation migration through the interface between atomistic and coarse-grained domains. It is shown that 3-D CAC simulations are useful in substantially reducing the number of degrees of freedom while preserving key characteristics of dislocation structure, stacking faults, and plasticity, including the net Burgers vector and long range fields of interacting dislocations.

An imperialist competitive algorithm for the winner determination problem in combinatorial auction

Winner Determination problem (WDP) in combinatorial auction is an NP-complete problem. The NP-complete problems are often solved by using heuristic methods and approximation algorithms. This paper presents an imperialist competitive algorithm (ICA) for solving winner determination problem. Combinatorial auction (CA) is an auction that auctioneer considers many goods for sale and the bidder bids on the bundle of items. In this type of auction, the goal is finding winning bids that maximize the auctioneer’s income under the constraint that each item can be allocated to at most one bidder. To demonstrate, the postulated algorithm is applied over various benchmark problems. The ICA offers competitive results and finds good-quality solution in compare to genetic algorithm (GA), Memetic algorithm (MA), Nash equilibrium search approach (NESA) and Tabu search.

Modeling of a Dynamic Interaction of Motor Transport and Natural Systems in Order to Minimize the Risks of Project and Management Decisions

Fundamental tasks for the problem of scientific support for the design of transport infrastructure in the ecosystem splits are analyzed. New aspects of simulational application in dynamic interaction of motor transport and natural systems are considered. Method for simulational studies is analyzed. The problems and advantages of the simulation of complex systems are investigated. Mathematical model of the transport infrastructure influence in the environmental situation and A* search algorithm are developed, which guaranteed to find the shortest path till the heuristic approximation, i.e., it never exceeds the real remaining distance to the target and then this algorithm uses the heuristic in the best possible way: No other algorithm will reveal fewer joints disregarding the joints with the same cost. The successful solution of the problem results from the preliminary theoretical research, partly stated in 20 scientific publications and protected intellectual property objects, including certificates of state registration of computer programs.

Agnostic Pointwise-Competitive Selective Classification

Pointwise-competitive classifier from class F is required to classify identically to the best classifier in hindsight from F. For noisy, agnostic settings we present a strategy for learning pointwise-competitive classifiers from a finite training sample provided that the classifier can abstain from prediction at a certain region of its choice. For some interesting hypothesis classes and families of distributions, the measure of this rejected region is shown to be diminishing at a fast rate, with high probability. Exact implementation of the proposed learning strategy is dependent on an ERM oracle that can be hard to compute in the agnostic case. We thus consider a heuristic approximation procedure that is based on SVMs, and show empirically that this algorithm consistently outperforms a traditional rejection mechanism based on distance from decision boundary.