Scaling of transverse nuclear magnetic relaxation due to magnetic nanoparticle aggregation

The aggregation of superparamagnetic iron oxide (SPIO) nanoparticles decreases the transverse nuclear magnetic resonance (NMR) relaxation time of adjacent water molecules measured by a Carr-Purcell-Meiboom-Gill (CPMG) pulse-echo sequence. This effect is commonly used to measure the concentrations of a variety of small molecules. We perform extensive Monte Carlo simulations of water diffusing around SPIO nanoparticle aggregates to determine the relationship between and details of the aggregate. We find that in the motional averaging regime scales as a power law with the number N of nanoparticles in an aggregate. The specific scaling is dependent on the fractal dimension d of the aggregates. We find for aggregates with d=2.2, a value typical of diffusion limited aggregation. We also find that in two-nanoparticle systems, is strongly dependent on the orientation of the two nanoparticles relative to the external magnetic field, which implies that it may be possible to sense the orientation of a two-nanoparticle aggregate. To optimize the sensitivity of SPIO nanoparticle sensors, we propose that it is best to have aggregates with few nanoparticles, close together, measured with long pulse-echo times.     

Direct Likelihood Evaluation for the Renewal Hawkes Process

An interesting extension of the widely applied Hawkes self-exiting point process, the renewal Hawkes (RHawkes) process, was recently proposed by Wheatley, Filimonov, and Sornette, which has the potential to significantly widen the application domains of the self-exciting point processes. However, they claimed that computation of the likelihood of the RHawkes process requires exponential time and therefore is practically impossible. They proposed two expectation–maximization (EM) type algorithms to compute the maximum likelihood estimator (MLE) of the model parameters. Because of the fundamental role of likelihood in statistical inference, a practically feasible method for likelihood evaluation is highly desirable. In this article, we provide an algorithm that evaluates the likelihood of the RHawkes process in quadratic time, a drastic improvement from the exponential time claimed by Wheatley, Filimonov, and Sornette. We demonstrate the superior performance of the resulting MLEs of the model relative to the EM estimators through simulations. We also present a computationally efficient procedure to calculate the Rosenblatt residuals of the process for goodness-of-fit assessment, and a simple yet efficient procedure for future event prediction. The proposed methodologies were applied on real data from seismology and finance. An R package implementing the proposed methodologies is included in the supplementary materials.     

A hybrid rank-based evolutionary algorithm applied to multi-mode resource-constrained project scheduling problem

We consider the multi-mode resource-constrained project scheduling problem (MRCPSP), where a task has different execution modes characterized by different resource requirements. Due to the nonrenewable resources and the multiple modes, this problem is NP-hard; therefore, we implement an evolutionary algorithm looking for a feasible solution minimizing the makespan.     

Variations on the theme of slacks-based measure of efficiency in DEA

In DEA, there are typically two schemes for measuring efficiency of DMUs; radial and non-radial. Radial models assume proportional change of inputs/outputs and usually remaining slacks are not directly accounted for inefficiency. On the other hand, non-radial models deal with slacks of each input/output individually and independently, and integrate them into an efficiency measure, called slacks-based measure (SBM). In this paper, we point out shortcomings of the SBM and propose four variants of the SBM model. The original SBM model evaluates efficiency of DMUs referring to the furthest frontier point within a range. This results in the hardest score for the objective DMU and the projection may go to a remote point on the efficient frontier which may be inappropriate as the reference. In an effort to overcome this shortcoming, we first investigate frontier (facet) structure of the production possibility set. Then we propose Variation I that evaluates each DMU by the nearest point on the same frontier as the SBM found. However, there exist other potential facets for evaluating DMUs. Therefore we propose Variation II that evaluates each DMU from all facets. We then employ clustering methods to classify DMUs into several groups, and apply Variation II within each cluster. This Variation III gives more reasonable efficiency scores with less effort. Lastly we propose a random search method (Variation IV) for reducing the burden of enumeration of facets. The results are approximate but practical in usage.     

Simultaneous Model Selection via Rate-Distortion Theory,With Applications to Cluster and Significance Analysis of Gene Expression Data

High-dimensional data are prevalent across many application areas, and generate an ever-increasing demand for statistical methods of dimension reduction, such as cluster and significance analysis. One application area that has recently received much interest is the analysis of microarray gene expression data.

The results of cluster analysis are open to subjective interpretation. To facilitate the objective inference of such analyses, we use flexible parameterizations of the cluster means, paired with model selection, to generate sparse and easy-to-interpret representations of each cluster. Model selection in cluster analysis is combinatorial in the numbers of clusters and data dimensions, and thus presents a computationally challenging task.

In this article we introduce a model selection method based on rate-distortion theory, which allows us to turn the combinatorial model selection problem into a fast and simultaneous selection across clusters. The method is also applicable to model selection in significance analysis

We show that simultaneous model selection for cluster analysis generates objectively interpretable cluster models, and that the selection performance is competitive with a combinatorial search, at a fraction of the computational cost. Moreover, we show that the rate-distortion based significance analysis substantially increases the power compared with standard methods.

This article has supplementary material online.     

固定合作规模网络的平均路径长度

本文提出了一种特殊的合作网络,称之为固定合作规模网络．我们重点研究了这类网络的平均路径长度,通过建立微分方程,得到平均路径长度的增加速度近似与网络规模的对数成正比．     

Formalizing and solving the problem of clustering in MCDA

The topic of clustering has been widely studied in the field of Data Analysis, where it is defined as an unsupervised process of grouping objects together based on notions of similarity. Clustering in the field of Multi-Criteria Decision Aid (MCDA) has seen a few adaptations of methods from Data Analysis, most of them however using concepts native to that field, such as the notions of similarity and distance measures. As in MCDA we model the preferences of a decision maker over a set of decision alternatives, we can find more diverse ways of comparing them than in Data Analysis. As a result, these alternatives may also be arranged into different potential structures. In this paper we wish to formally define the problem of clustering in MCDA using notions that are native to this field alone, and highlight the different structures which we may try to uncover through this process. Following this we propose a method for finding these structures. As in any clustering problem, finding the optimal result in an exact manner is impractical, and so we propose a stochastic heuristic approach, which we validate through tests on a large set of artificially generated benchmarks.     

EPR study of the diluted magnetic semiconductor CuGa1−xMnxTe2

Electron paramagnetic resonance (EPR) experiments were made in the diluted magnetic semiconductor CuGa_1−xMn_xTe₂, in the temperature range 70<T<300 K. The samples were synthesized by direct fusion of stoichiometric mixtures of the elements, with Mn composition from x=0.0 to 0.25. The EPR spectra were measured as function of temperature, Mn composition, and field orientation. The temperature variation of the resonance field shows a critical point at about 235 K, and is associated with a transition from the ferromagnetic to the superparamagnetic state. The resonance field was also measured as a function of the field angle, and displays a well-defined uniaxial symmetry. This uniaxial field depends on the Mn concentration and is due to tetragonal distortions induced by Mn²⁺ at Ga sites, and the demagnetizing effects due to formation of ferromagnetism (FM) Mn-clusters.     

Prediction of drug-target interaction by integrating diverse heterogeneous information source with multiple kernel learning and clustering methods

BackgroundIdentification of potential drug-target interaction pairs is very important for pharmaceutical innovation and drug discovery. Numerous machine learning-based and network-based algorithms have been developed for predicting drug-target interactions. However, large-scale pharmacological, genomic and chemical datum emerged recently provide new opportunity for further heightening the accuracy of drug-target interactions prediction.ResultsIn this work, based on the assumption that similar drugs tend to interact with similar proteins and vice versa, we developed a novel computational method (namely MKLC-BiRW) to predict new drug-target interactions. MKLC-BiRW integrates diverse drug-related and target-related heterogeneous information source by using the multiple kernel learning and clustering methods to generate the drug and target similarity matrices, in which the low similarity elements are set to zero to build the drug and target similarity correction networks. By incorporating these drug and target similarity correction networks with known drug-target interaction bipartite graph, MKLC-BiRW constructs the heterogeneous network on which Bi-random walk algorithm is adopted to infer the potential drug-target interactions.ConclusionsCompared with other existing state-of-the-art methods, MKLC-BiRW achieves the best performance in terms of AUC and AUPR. MKLC-BiRW can effectively predict the potential drug-target interactions.