Multiple Decompositions Research Articles

Service Referral Patterns Among Black and White Families Involved With Child Protective Services

Racial disproportionality in child protective services is widely studied, yet the role of race in caseworkers' service referral decisions remains less understood. Using the National Survey of Child and Adolescent Well-Being II, multiple regression models and Blinder-Oaxaca decompositions assess whether the intersection of caseworker and child race predicts differences in service referral decisions, and whether service disparities were primarily explained by racial differences in case characteristics or by differential treatment of families. While many raw differences in service referrals were explained by case characteristics, unexplained differences were found in the types of services to which families were referred.

A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel Times

Heavy and uncertain traffic conditions exacerbate the commuting experience of millions of people across the globe. When planning important trips, commuters typically add an extra buffer to the expected trip duration to ensure on-time arrival. Motivated by this, we propose a new traffic assignment model that takes into account the stochastic nature of travel times. Our model extends the traditional model of Wardrop competition when uncertainty is present in the network. The focus is on strategic risk-averse users who capture the trade-off between travel times and their variability in a mean-standard deviation objective, defined as the mean travel time plus a risk-aversion factor times the standard deviation of travel time along a path. We consider both infinitesimal users, leading to a nonatomic game, and atomic users, leading to a discrete finite game. We establish conditions that characterize an equilibrium traffic assignment and find when it exists. The main challenge is posed by the users' risk aversion, since the mean-standard deviation objective is nonconvex and nonseparable, meaning that a path cannot be split as a sum of edge costs. As a result, even an individual user's subproblem—a stochastic shortest path problem—is a nonconvex optimization problem for which no polynomial time algorithms are known. In turn, the mathematical structure of the traffic assignment model with stochastic travel times is fundamentally different from the deterministic counterpart. In particular, an equilibrium characterization requires exponentially many variables, one for each path in the network, since an edge flow has multiple possible path-flow decompositions that are not equivalent. Because of this, characterizing the equilibrium and the socially optimal assignment, which minimizes the total user cost, is more challenging than in the traditional deterministic setting. Nevertheless, we prove that both can be encoded by a representation with just polynomially many paths. Finally, under the assumption that the standard deviations of travel times are independent from edge loads, we show that the worst-case ratio between the social cost of an equilibrium and that of an optimal solution is not higher than the analogous ratio in the deterministic setting. In other words, uncertainty does not further degrade the system performance in addition to strategic user behavior alone.

A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel Times

Heavy and uncertain traffic conditions exacerbate the commuting experience of millions of people across the globe. When planning important trips, commuters typically add an extra buffer to the expected trip duration to ensure on-time arrival. Motivated by this, we propose a new traffic assignment model that takes into account the stochastic nature of travel times. Our model extends the traditional model of Wardrop competition when uncertainty is present in the network. The focus is on strategic risk-averse users who capture the tradeoff between travel times and their variability in a mean-standard deviation (mean-stdev) objective, defined as the mean travel time plus a risk-aversion factor times the standard deviation of travel time along a path. We consider both infinitesimal users, leading to a non-atomic game, and atomic users, leading to a discrete finite game.We establish conditions that characterize an equilibrium traffic assignment and find when it exists. The main challenge is posed by the users’ risk aversion, since the mean-stdev objective is non-convex and non-separable, meaning that a path cannot be split as a sum of edge costs. As a result, even an individual user’s sub-problem — a stochastic shortest path problem — is a non-convex optimization problem for which no polynomial time algorithms are known. In turn, the mathematical structure of the traffic assignment model with stochastic travel times is fundamentally different from the deterministic counterpart. In particular, an equilibrium characterization requires exponentially many variables, one for each path in the network, since an edge-flow has multiple possible path-flow decompositions that are not equivalent. Because of this, characterizing the equilibrium and the socially-optimal assignment, which minimizes the total user cost, is more challenging than in the traditional deterministic setting. Nevertheless, we prove that both can be encoded by a representation with just polynomially-many paths. Finally, for the case of uncertainty parameters that are independent from edge loads, we show that although an equilibrium assignment results in a total user cost that is higher than that of the socially-optimal one, it is not higher than the analogous ratio in the deterministic setting. In other words, uncertainty does not further degrade the system performance in addition to strategic user behavior alone.

An Efficient Matrix Factorization Method for Tensor Completion

Most recent low-rank tensor completion algorithms are based on tensor nuclear norm minimization problems. The convex relaxation problem of tensor <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> -rank minimization has to be solved iteratively and involves multiple singular value decompositions (SVDs) at each iteration, and thus such algorithms suffer from high computation cost. In this letter, we propose an efficient low-rank tensor completion approach. First, we introduce a matrix factorization idea into the tensor nuclear norm model, and then can achieve a much smaller scale matrix nuclear norm minimization problem. Moreover, we develop an efficient iterative scheme for solving the proposed model with orthogonality constraint. Our extensive evaluation results validate both the effectiveness and efficiency of the proposed approach.

Low complexity bit and power allocation for MIMO-OFDM systems using space-frequency beamforming

This paper presents a new bit and power allocation algorithm for multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. The optimal power allocation algorithm in terms of maximum capacity in MIMO-OFDM systems is given by the joint space-frequency water-filling (JSF-WF)11JSF-WF stands for Joint Space-Frequency Water-Filling. algorithm. This algorithm involves multiple singular value decompositions and an iterative water-filling calculation over the subchannels, and therefore, has a high computational complexity. We present an algorithm with reduced bit and power allocation complexity. The proposed algorithm is based on a geometric channel model consisting of several clusters of subpaths, characterized by a set of physical parameters. It performs beamforming with null-steering towards the clusters' directions-of-departure, such that the frequency-selective MIMO channel is transformed into a flat fading MIMO channel. Thus, constant bit and power allocation over the frequency domain can be performed, which is simple to compute and implement. The performance of the proposed algorithm is evaluated and compared to the JSF-WF algorithm in terms of bit-error-rate, for known and misspecified channel model parameters. It is demonstrated that the proposed algorithm performance is slightly lower than the JSF-WF performance, while it significantly reduces the complexity of the allocation algorithm.

Fast Algorithms for the Approximation of the Pseudospectral Abscissa and Pseudospectral Radius of a Matrix

The $\varepsilon$-pseudospectral abscissa and radius of an $n\times n$ matrix are, respectively, the maximal real part and the maximal modulus of points in its $\varepsilon$-pseudospectrum, defined using the spectral norm. Existing techniques compute these quantities accurately, but the cost is multiple singular value decompositions and eigenvalue decompositions of order n, making them impractical when n is large. We present new algorithms based on computing only the spectral abscissa or radius of a sequence of matrices, generating a sequence of lower bounds for the pseudospectral abscissa or radius. We characterize fixed points of the iterations, and we discuss conditions under which the sequence of lower bounds converges to local maximizers of the real part or modulus over the pseudospectrum, proving a locally linear rate of convergence for $\varepsilon$ sufficiently small. The convergence results depend on a perturbation theorem for the normalized eigenprojection of a matrix as well as a characterization of the group inverse (reduced resolvent) of a singular matrix defined by a rank-one perturbation. The total cost of the algorithms is typically only a constant times the cost of computing the spectral abscissa or radius, where the value of this constant usually increases with $\varepsilon$, and may be less than 10 in many practical cases of interest.

Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems

The shuffle product plays an important role in the study of multiple zeta values (MZVs). This is expressed in terms of multiple integrals, and also as a product in a certain non-commutative polynomial algebra over the rationals in two indeterminates. In this paper, we give a new interpretation of the shuffle product. In fact, we prove that the procedure of shuffle products essentially coincides with that of partial fraction decompositions of MZVs of root systems. As an application, we give a proof of extended double shuffle relations without using Drinfel’d integral expressions for MZVs. Furthermore, our argument enables us to give some functional relations which include double shuffle relations.

HTRCI and Channel Ranking Based Joint Symbols Detection for MQRD-PCM/MIMO-OFDM

MIMO-OFDM is considered a key technology in emerging high-data rate systems. In MIMO-OFDM systems, channel estimation and signal detection are important to distinguish transmit signals from multiple transmit antennas. Previously, we have proposed a parallel detection algorithm using multiple QR decompositions (Q is an orthogonal square matrix, R is upper triangular matrix) with permuted channel matrix (MQRD-PCM) to reduce the system complexity of MIMO-OFDM. This method achieves a good BER performance with a low system complexity. However, since MQRD-PCM is a kind of parallel detection method, the wrong detection probability is increased due to the bad channel signal-to-interference plus noise power ratio (SINR) of the transmitted signals. As a result, the average BER performance is influenced by the wrong detection probability of the bad channel SINR. To overcome the above-mentioned problems, in this paper, we propose the high time resolution carrier interferometry and channel ranking based joint signal detection for MQRD-PCM/MIMO-OFDM.

Performance Enhancement of MQRD-PCM/MIMO-OFDM Using Channel Ranking Based Joint Symbols Detection

MIMO-OFDM is considered a key technology in emerging high-data rate systems. With MIMO techniques, the transmission quality deteriorates due to inter-antenna interference (IAI). Several signal detection schemes have been proposed to mitigate this problem. However, it is impractical to use the conventional methods without reducing theirs computational complexity. Previously, we have proposed a parallel detection algorithm using multiple QR decompositions with permuted channel matrix (MQRD-PCM) for MIMO-OFDM to reduce the system complexity. This method achieves a good BER performance with low system complexity. However, since MQRD-PCM is a kind of parallel detection method, the wrong detection probability is increased due to the bad channel SINR of the transmitted signal. As a result, the average BER performance is influenced by the wrong detection probability of the bad channel SINR. To overcome this problem, in this paper, we propose the channel ranking based joint symbols detection for MQRD-PCM/MIMO-OFDM.

Centimeter-size BiFeO3 single crystals grown by flux method

A narrow part of Fe2O3–Bi2O3 phase diagram was re-investigated in order to elaborate single crystals of the multiferroic BiFeO3 (BFO). Centimeter-size single crystals were successfully obtained by flux method, and present a preferred growth direction. X-ray diffraction studied have highlighted that the growth direction is along the polar axis [111] r of the structure. The stability of BFO versus temperature (reversible ferroelectric transition followed by multiple irreversible decompositions) is discussed in the light of Differential Scanning Calorimetry (DSC) analysis performed between 25 and 1400°C.

DEA models for two‐stage processes: Game approach and efficiency decomposition

AbstractData envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). This tool has been utilized by a number of authors to examine two‐stage processes, where all the outputs from the first stage are the only inputs to the second stage. The current article examines and extends these models using game theory concepts. The resulting models are linear, and imply an efficiency decomposition where the overall efficiency of the two‐stage process is a product of the efficiencies of the two individual stages. When there is only one intermediate measure connecting the two stages, both the noncooperative and centralized models yield the same results as applying the standard DEA model to the two stages separately. As a result, the efficiency decomposition is unique. While the noncooperative approach yields a unique efficiency decomposition under multiple intermediate measures, the centralized approach is likely to yield multiple decompositions. Models are developed to test whether the efficiency decomposition arising from the centralized approach is unique. The relations among the noncooperative, centralized, and standard DEA approaches are investigated. Two real world data sets and a randomly generated data set are used to demonstrate the models and verify our findings. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008

Throughput Improvement with Discrete Pilot Signal Assignment and Iterative Channel Identification for MQRD-PCM/OFDM

In MIMO systems, the channel identification is important to distinguish transmitted signals from multiple transmit antennas. One of the most typical channel identification schemes is to employ a code division multiplexing (CDM) based scheme in which a unique spreading code is assigned to distinguish both BS and MS antenna elements. However, by increasing the number of base stations and transmit antenna elements, large spreading codes and pilot symbols are required to distinguish the received power from all the connectable BS, as well as to identify all the CSI for the combination of transmitter and receiver antenna elements. Furthermore, the complexity of maximum likelihood detection (MLD) for implementation of MIMO is a considerable work. To reduce these problems, in this paper, we propose the parallel detection algorithm using multiple QR decompositions with permuted channel matrix (MQRD-PCM) with discrete pilot signal assignment and iterative channel identification for MIMO/OFDM.

Parallel Detection Algorithm Using Multiple QR Decompositions With Permuted Channel Matrix for SDM/OFDM

Space division multiplexing (SDM)/orthogonal frequency division multiplexing (OFDM) systems transmit different data using the same frequency, so it is necessary to separate the simultaneously received signals in the receiver. Previous studies have shown that maximum likelihood detection (MLD) provides the best bit error rate (BER) performance. However, the complexity of MLD exponentially increases with the constellation size and the number of transmit antenna branches. Therefore, it is impractical to use a full MLD without reducing its computational complexity, because it would be prohibitively large for implementation. Recently, the use of QR decomposition with an M-algorithm (QRD-M) has been proposed to reduce the system complexity while maintaining the performance of the system. However, the QRD-M performance depends on the number of surviving symbol replica candidates. When QRD-M is used with a small number of surviving symbol replica candidates, the performance declines, but when there is a large number of surviving symbol replica candidates and the transmitter antenna branches, QRD-M requires a large memory to maintain their branch metrics, and a long latency time is also required. To reduce these problems, in this paper, we propose a parallel detection algorithm using multiple QR decompositions with permuted channel matrices for SDM/OFDM systems.

Adaptive Two-Player Hierarchical Holographic Modeling Game for Counterterrorism Intelligence Analysis

Intelligence gathering and analysis for countering terrorism is a vital and costly venture; therefore approaches need to be explored that can help determine the scope of collection and improve the efficacy of analysis efforts. The Adaptive Two-Player Hierarchical Holographic Modeling (HHM) Game introduced in this paper is a repeatable, adaptive, and systemic process for tracking terrorism scenarios. It builds on fundamental principles of systems engineering, systems modeling, and risk analysis. The game creates two opposing views of terrorism: one developed by a Blue Team defending against acts of terrorism, and the other by a Red Team planning to carry out a terrorist act. The HHM process identifies the vulnerabilities of potential targets that could be exploited in attack plans. These vulnerabilities can be used by the Blue Team to identify corresponding surveillance capabilities that can help to provide warning of a possible attack. Vulnerability-based scenario structuring, comprehensive risk identification and the identification of surveillance capabilities that can support preemption are all achieved through the deployment of HHM.State variables, which represent the essence of the system, play a pivotal role in the Adaptive Two-Player HHM Game, providing an enabling roadmap to intelligence analysts. Indeed, vulnerabilities are defined in terms of the system's state variables: Vulnerability is the manifestation of the inherent states of a system (e.g., physical, technical, organizational, cultural) that can be exploited by an adversary to cause harm or damage. Threat is a potential adversarial intent to cause harm or damage by adversely changing the states of the system. Threat to a vulnerable system may lead to risk, which is a measure of the probability and severity of adverse effects.Each player in the Adaptive Two-Player HHM Game deploys the same modeling tools. This ensures that the results from different models can be compared and integrated. If the membership of different teams is drawn from groups with different value systems, skills, and experience, it can be expected that modeling results will differ. This should help to identify the appropriate mix of skills for a modeling team to develop a robust model. In addition, Bayesian analysis is central to the adaptive characteristics of the proposed methodology. Not only do new samples of evidence serve as likelihood functions to generate additional probabilities for given scenarios, but the probabilities associated with one scenario can be used as likelihood functions for other scenarios. This cross-updating process is further exploited by the construction of multiple decompositions, each representing a different perspective, e.g., geographical, functional, temporal. A food-poisoning scenario with Red and Blue Teams was developed to demonstrate the approach.

On the uniqueness of stationary points in L2 approximation with a rational polyphase function

The question of uniqueness of L 2 approximation when using a rational polyphase function is of great importance for the practical use of polyphase IIR adaptive filters. As shown in a previous work, the polyphase structure can alleviate the problem of convergence speed in IIR adaptive filters, allowing their computational complexity gain over FIR adaptive filters to be exploited. In that work, however, a demonstration of a uniqueness property was not presented. In this paper, we initially present an example of a practical application and the gain in convergence speed that can be achieved by using a polyphase IIR adaptive filter. We then demonstrate the following uniqueness property of the approximation of a rational function with degree N by a p-phase rational polyphase function with pM+1 and M free coefficients in, respectively, its numerator and denominator: if N is less or equal to M then the two functions are identical at all stationary points of the squared L 2 norm of the error. Following the demonstration of the uniqueness property, we make some remarks on the existence of multiple polyphase decompositions of a rational function. Such situations lead to restrictions on the use of polyphase IIR adaptive filters, in order to avoid slow convergence.

Parallel strategies for crash and impact simulations

We describe a general strategy we have found effective for parallelizing solid mechanics simulations. Such simulations often have several computationally intensive parts, including finite element integration, detection of material contacts, and particle interaction if smoothed particle hydrodynamics is used to model highly deforming materials. The need to balance all of these computations simultaneously is a difficult challenge that has kept many commercial and government codes from being used effectively on parallel supercomputers with hundreds or thousands of processors. Our strategy is to load-balance each of the significant computations independently with whatever balancing technique is most appropriate. The chief benefit is that each computation can be scalably parallelized. The drawback is the data exchange between processors and extra coding that must be written to maintain multiple decompositions in a single code. We discuss these trade-offs and give performance results showing this strategy has led to a parallel implementation of a widely used solid mechanics code that can now be run efficiently on thousands of processors of the Pentium-based Sandia/Intel TFLOPS machine. We illustrate with several examples the kinds of high-resolution, million-element models that can now be simulated routinely. We also look to the future and discuss what possibilities this new capability promises, as well as the new set of challenges it poses in material models, computational techniques, and computing infrastructure.

13C-Selective Infrared Multiple Photon Decomposition of β-Propiolactone, β-Butyrolactone, and Diketene with a CO2 TEA Laser

13C-Selective infrared multiple photon decomposition of lactone compounds has been studied using a CO2 TEA (transversely excited atmospheric) laser. The main decomposition products were ethylene and CO2 in β-propiolactone. We obtained CO2 with a 13C atomic fraction of 55% in the irradiation of 2 Torr (1 Torr = 1 mmHg = 133.322 Pa) β-propiolactone at 1035.47 cm-1. The addition of 100 Torr of N2 to 2 Torr of β-propiolactone resulted in a remarkable increase in selectivity, i.e., 75% 13C in CO2, while the yield was considerably decreased. Respective olefinic products were propylene and allene in the multiple photon decompositions of β-butyrolactone and diketene. The common product CO2 was also found to be significantly enriched with 13C in these lactone compounds.

Multiple Canonical Decompositions of Families of Operators and a Model of Quasinormal Families

Multiple Canonical Decompositions of Families of Operators and a Model of Quasinormal Families

Multiple canonical decompositions of families of operators and a model of quasinormal families

A general method of canonical decompositions of several operatorvalued functions (operators) is presented. A model of a family of doubly commuting quasinormal operators is constructed.

New overlapping coordination methodologies for large-scale optimization problems

We focus on the computational aspects of hierarchical overlapping coordination and propose new coordination methodologies. The overlapping coordination procedure of Macko and Haimes ( IEEE Trans. Syst. Man Cybern., 1978, SMC-8, 745–751) is a feasible decomposition method in that every constraint is always satisfied, and coupling variables are used as the coordination variables. We propose two new methodologies, a nonfeasible decomposition method and a mixed method, and show that coordination procedures similar to those in the conventional large-scale systems which deal with only one decomposition are possible in the overlapping coordination which deals with multiple decompositions. In the nonfeasible decomposition method, the Lagrange or Kuhn-Tucker multipliers of the coupling constraints of each decomposition are used as the coordination variables. The coupling constraints of each decomposition may not be satisfied until the optimal solution is found. In the mixed method, both the coupling variables and the multipliers of the coupling constraints are used as the coordination variables. We also show that those two methods have symmetrical coordination structures, and a simple numerical example is solved. The proposed methodologies will enlarge the application area of hierarchical overlapping coordination.