Optimal resource allocation in survey designs

Resource allocation is a relatively new research area in survey designs and has not been fully addressed in the literature. Recently, the declining participation rates and increasing survey costs have steered research interests towards resource planning. Survey organizations across the world are considering the development of new mathematical models in order to improve the quality of survey results while taking into account optimal resource planning. In this paper, we address the problem of resource allocation in survey designs and we discuss its impact on the quality of the survey results. We propose a novel method in which the optimal allocation of survey resources is determined such that the quality of survey results, i.e., the survey response rate, is maximized. We demonstrate the effectiveness of our method by extensive numerical experiments.     

Structuring public utility functions

Public von Neumann-Morgenstern utility functions are constructed using assumptions about individual and subgroup sovereignty and equality of individuals. These public utility functions require knowledge of one value parameter about equity and the average of individual utility functions. The latter can be obtained by sampling.     

Optimal design of non-equilibrium experiments for genetic network interrogation

Many experimental systems in biology, especially synthetic gene networks, are amenable to perturbations that are controlled by the experimenter. We developed an optimal design algorithm that calculates optimal observation times in conjunction with optimal experimental perturbations in order to maximize the amount of information gained from longitudinal data derived from such experiments. We applied the algorithm to a validated model of a synthetic Brome Mosaic Virus (BMV) gene network and found that optimizing experimental perturbations may substantially decrease uncertainty in estimating BMV model parameters.     

Comments to “Quantification of network structural dissimilarities” published by Schieber et al

Recently, we came across the paper entitled “Quantification of network structural dissimilarities” published by Nature Communications. In this paper, Schieber et al claimed to propose a novel technique for measuring the structural similarity of networks. The authors of this commentary are familiar with this special area of network analysis. After reading the paper, we doubt that the graph similarity (distance) measure due to Schieber et al is entirely novel. Instead, parts thereof are very similar to contributions we have authored. Unfortunately, they have not been cited nor acknowledged in Schieber et al.     

Optimal designs with respect to Elfving's partial minimax criterion in polynomial regression

For the polynomial regression model on the interval [a, b] the optimal design problem with respect to Elfving's minimax criterion is considered. It is shown that the minimax problem is related to the problem of determining optimal designs for the estimation of the individual parameters. Sufficient conditions are given guaranteeing that an optimal design for an individual parameter in the polynomial regression is also minimax optimal for a subset of the parameters. The results are applied to polynomial regression on symmetric intervals [–b, b] (b1) and on nonnegative or nonpositive intervals where the conditions reduce to very simple inequalities, involving the degree of the underlying regression and the index of the maximum of the absolute coefficients of the Chebyshev polynomial of the first kind on the given interval. In the most cases the minimax optimal design can be found explicitly.Research supported in part by the Deutsche Forschungsgemeinschaft.Research supported in part by NSF Grant DMS 9101730.     

Classes of network connectivity and dynamics

Many kinds of complex systems exhibit characteristic patterns of temporal correlations that emerge as the result of functional interactions within a structured network. One such complex system is the brain, composed of numerous neuronal units linked by synaptic connections. The activity of these neuronal units gives rise to dynamic states that are characterized by specific patterns of neuronal activation and co‐activation. These patterns, called functional connectivity, are possible neural correlates of perceptual and cognitive processes. Which functional connectivity patterns arise depends on the anatomical structure of the underlying network, which in turn is modified by a broad range of activity‐dependent processes. Given this intricate relationship between structure and function, the question of how patterns of anatomical connectivity constrain or determine dynamical patterns is of considerable theoretical importance. The present study develops computational tools to analyze networks in terms of their structure and dynamics. We identify different classes of network, including networks that are characterized by high complexity. These highly complex networks have distinct structural characteristics such as clustered connectivity and short wiring length similar to those of large‐scale networks of the cerebral cortex. © 2002 Wiley Periodicals, Inc.     

Minimalist designs

The iterative absorption method has recently led to major progress in the area of (hyper‐)graph decompositions. Among other results, a new proof of the existence conjecture for combinatorial designs, and some generalizations, was obtained. Here, we illustrate the method by investigating triangle decompositions: We give a simple proof that a triangle‐divisible graph of large minimum degree has a triangle decomposition and prove a similar result for quasi‐random host graphs.     

Bayesian network management

We formulate some general network (and risk) management problems in a Bayesian context, and point out some of the essential features. We argue and demonstrate that, when one is interested in rare events, the Bayesian and frequentist approaches can lead to very different strategies: the former typically leads to strategies which are more conservative. We also present an asymptotic formula for the predictive probability of ruin (for a random walk with positive drift) for large initial capital and large number of past observations. This is a preliminary investigation which raises many interesting questions for future research. This revised version was published online in June 2006 with corrections to the Cover Date.     

Optimal designs for nonparametric kernel regression

We consider the fixed design regression model Y_i = g(t_i) + ξ_i, i = 1, …, n, where ξ_i are (not necessarily i.i.d.) no variables, t_i constitute the design points where nonrepeatable measurements are to be taken and Y_i are the observations from which g and its derivatives are to be estimated. The dependency of the Integrated Mean Squared Error of two different types of kernel estimates on the design {t₁, …, t_n} is established. This allows the derivation of asymptotically optimal designs.     

Multicriteria Modelling of Repair Contract Based on Utility and ELECTRE I Method with Dependability and Service Quality Criteria

A DM faces a choice among several alternatives of repair contract for a system. Each alternative of a repair contract implies specific results regarding the following characteristics or criteria: response time, quality service, dependability and related cost. This problem has been analysed through a multicriteria decision model. The model is based on the ELECTRE method combined with utility functions. Main theoretical aspects and practical implications are presented, including a numerical application.     

Compressing strongly connected subgroups in social networks: An entropy-based approach

To detect and study cohesive subgroups of actors is a main objective in social network analysis. What are the respective relations inside such groups and what separates them from the outside. Entropy-based analysis of network structures is an up-and-coming approach. It turns out to be a powerful instrument to detect certain forms of cohesive subgroups and to compress them to superactors without loss of information about their embeddedness in the net: Compressing strongly connected subgroups leaves the whole net’s and the (super-)actors’ information theoretical indices unchanged; i.e., such compression is information-invariant. The actual article relates on the reduction of networks with hundreds of actors. All entropy-based calculations are realized in an expert system shell.     

Optimal designs for minimax extrapolation

Speckman developed a minimax linear estimator robust against departures from an assumed model. Some concomitant questions of optimal design are investigated.     

Common cold outbreaks: A network theory approach

In this study, at first we evaluated the network structure in social encounters by which respiratory diseases can spread. We considered common-cold and recorded a sample of human population and actual encounters between them. Our results show that the database structure presents a great value of clustering. In the second step, we evaluated dynamics of disease spread with SIR model by assigning a function to each node of the structural network. The rate of disease spread in networks was observed to be inversely correlated with characteristic path length. Therefore, the shortcuts have a significant role in increasing spread rate. We conclude that the dynamics of social encounters’ network stands between the random and the lattice in network spectrum. Although in this study we considered the period of common-cold disease for network dynamics, it seems that similar approaches may be useful for other airborne diseases such as SARS.     

The final answer to the complexity of a basic problem in resilient network design

To provide resilience to failures of the multi-commodity flow network, either in the failure-free state flows can be routed along multiple paths and over-dimensioned, or whenever a failure occurs flows can be restored along unaffected paths. The complexity of the network design depends on the selected method of providing resilience and on a number of design options—whether single or multiple commodities and single- or multi-element failures are considered, if the reaction to failures is dependent or independent on the failure, which mechanism of capacity release and reuse is applied, etc. For almost all combinations of those choices either the corresponding design problem has already been shown to be NP-hard or a compact linear programming formulation of the problem has been provided. The only case that has resisted an answer is when flows are restored in a state-dependent manner using the stub release mechanism. In this paper it is proved that the corresponding network design problem is NP-hard even for a single commodity and for single-element failures. The proof is based on the reduction of the Hamiltonian path problem.     

Incomplete split plot designs

We propose an incomplete split plot design where levels of one factor (say A) are applied to the wholeplots and levels of the other (say B) to subplots, and where the number of subplots in each wholeplot may be less than the number of levels of factor B.The t levels of factor A are arranged in a completely randomized design. The s levels of factor B are arranged in a connected and proper incomplete block design within each level of factor A, by considering the wholeplots as blocks.     

Optimal decision rule in forming an insurance portfolio

The paper is devoted to finding an optimal decision rule for accepting/rejecting potential insureds when the demand for the insurance provision is a stochastic variable. A criterion to be maximized is the mean-variance utility function of the insurer. It is shown that the optimal decision rule is a stopping rule with some finite protection level.     

Common intersection designs

Motivated by an application to sensor networks, Lee and Stinson [ 6 ] defined a new type of set system termed a “common intersection design.” Briefly, a µ‐common intersection design is a 1‐design in which no pair of points occurs in more than one block, and in which any two disjoint blocks intersect at least µ blocks in common. In general, we want to maximize µ as a function of the other parmameters of the design. In this paper, we analyze combinatorial properties of common intersection designs. We determine necessary conditions for “optimal” common intersection designs and provide several existence results. Connections with other types of designs are pointed out. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 251–269, 2006     

Aggregation of utility-based individual preferences for group decision-making

Multi-attribute utility theory (MAUT) elicits an individual decision maker’s preferences for single attributes and develops a utility function by mathematics formulation to add up the preferences of the entire set of attributes when assessing alternatives. A common aggregation method of MAUT for group decisions is the simple additive weighting (SAW) method, which does not consider the different preferential levels and preferential ranks for individual decision makers’ assessments of alternatives in a decision group, and thus seems too intuitive in achieving the consensus and commitment for group decision aggregation. In this paper, the preferential differences denoting the preference degrees among different alternatives and preferential priorities denoting the favorite ranking of the alternatives for each decision maker are both considered and aggregated to construct the utility discriminative values for assessing alternatives in a decision group. A comparative analysis is performed to compare the proposed approach to the SAW model, and a satisfaction index is used to investigate the satisfaction levels of the final two resulting group decisions. In addition, a feedback interview is conducted to understand the subjective perceptions of decision makers while examining the results obtained from these two approaches for the second practical case. Both investigation results show that the proposed approach is able to achieve a more satisfying and agreeable group decision than that of the SAW method.     

Optimum covariate designs in a binary proper equi-replicate block design set-up

The choice of covariates values for a given block design attaining minimum variance for estimation of each of the regression parameters of the model has attracted attention in recent times. In this article, we consider the problem of finding the optimum covariate design (OCD) for the estimation of covariate parameters in a binary proper equi-replicate block (BPEB) design model with covariates, which cover a large class of designs in common use. The construction of optimum designs is based mainly on Hadamard matrices.