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The rich get richer principle, manifested by the Preferential attachment (PA) mechanism, is widely considered one of the major factors in the growth of real-world networks. PA stipulates that popular nodes are bound to be more attractive than less popular nodes; for example, highly cited papers are more likely to garner further citations. However, it overlooks the transient nature of popularity, which is often governed by trends. Here, we show that in a wide range of real-world networks the recent popularity of a node, i.e., the extent by which it accumulated links recently, significantly influences its attractiveness and ability to accumulate further links. We proceed to model this observation with a natural extension to PA, named Trending Preferential Attachment (TPA), in which edges become less influential as they age. TPA quantitatively parametrizes a fundamental network property, namely the network’s tendency to trends. Through TPA, we find that real-world networks tend to be moderately to highly trendy. Networks are characterized by different susceptibilities to trends, which determine their structure to a large extent. Trendy networks display complex structural traits, such as modular community structure and degree-assortativity, occurring regularly in real-world networks. In summary, this work addresses an inherent trait of complex networks, which greatly affects their growth and structure, and develops a unified model to address its interaction with preferential attachment. [ABSTRACT FROM AUTHOR]

In this paper, by taking full consideration of distributed delay, demographics and contact heterogeneity of the individuals, we present a detailed analytical study of the Susceptible-Infected-Removed (SIR) epidemic model on complex population networks. The basic reproduction number of the model is dominated by the topology of the underlying network, the properties of individuals which include birth rate, death rate, removed rate and infected rate, and continuously distributed time delay. By constructing suitable Lyapunov functional and employing Kirchhoff’s matrix tree theorem, we investigate the globally asymptotical stability of the disease-free and endemic equilibrium points. Specifically, the system shows threshold behaviors: if , then the disease-free equilibrium is globally asymptotically stable, otherwise the endemic equilibrium is globally asymptotically stable. Furthermore, the obtained results show that SIR models with different types of delays have different converge time in the process of contagion: if , then the system with distributed time delay stabilizes fastest; while , the system with distributed time delay converges most slowly. The validness and effectiveness of these results are demonstrated through numerical simulations. [ABSTRACT FROM AUTHOR]

The world is still recovering from the financial crisis peaking in September 2008. The triggering event was the bankruptcy of Lehman Brothers. To detect such turmoils, one can investigate the time-dependent behaviour of correlations between assets or indices. These cross-correlations have been connected to the systemic risks within markets by several studies in the aftermath of this crisis. We study 37 different US indices which cover almost all aspects of the US economy and show that monitoring an average investor’s behaviour can be used to quantify times of increased risk. In this paper the overall investing strategy is approximated by the ground-states of the mean-variance model along the efficient frontier bound to real world constraints. Changes in the behaviour of the average investor is utlilized as a early warning sign. [ABSTRACT FROM AUTHOR]

Privacy-preserving profile matching, a challenging task in mobile social networks, is getting more attention in recent years. In this paper, we propose a novel scheme that is based on ciphertext-policy attribute-based encryption to tackle this problem. In our scheme, a user can submit a preference-profile and search for users with matching-profile in decentralized mobile social networks. In this process, no participant’s profile and the submitted preference-profile is exposed. Meanwhile, a secure communication channel can be established between the pair of successfully matched users. In contrast to existing related schemes which are mainly based on the secure multi-party computation, our scheme can provide verifiability (both the initiator and any unmatched user cannot cheat each other to pretend to be matched), and requires few interactions among users. We provide thorough security analysis and performance evaluation on our scheme, and show its advantages in terms of security, efficiency and usability over state-of-the-art schemes. [ABSTRACT FROM AUTHOR]

Professional association football is a game of talent. The success of a professional club hinges largely on its ability of assembling the best team. Building on a dataset of player transfer records among more than 400 clubs in 24 world-wide top class leagues from 2011 to 2015, this study aims to relate a club’s success to its activities in the player transfer market from a network perspective. We confirm that modern professional football is indeed a money game, in which larger investment spent on the acquisition of talented players generally yields better team performance. However, further investigation shows that professional football clubs can actually play different strategies in surviving or even excelling this game, and the success of strategies is strongly associated to their network properties in the football player transfer network. [ABSTRACT FROM AUTHOR]

Due to the ever-growing popularity mobile devices of various kinds have received worldwide, the demands on large-scale wireless network infrastructure development and enhancement have been rapidly swelling in recent years. A mobile device holder can get online at a wireless network access point, which covers a limited area. When the client leaves the access point, there will be a temporary disconnection until he/she enters the coverage of another access point. Even when the coverages of two neighboring access points overlap, there is still work to do to make the wireless connection smoothly continue. The action of one wireless network access point passing a client to another access point is referred to as the handover. During handover, for security concerns, the client and the new access point should perform mutual authentication before any Internet access service is practically gained/provided. If the handover protocol is inefficient, in some cases discontinued Internet service will happen. In 2013, Li et al. proposed a fast handover authentication mechanism for wireless mesh network (WMN) based on tickets. Unfortunately, Li et al.’s work came with some weaknesses. For one thing, some sensitive information such as the time and date of expiration is sent in plaintext, which increases security risks. For another, Li et al.’s protocol includes the use of high-quality tamper-proof devices (TPDs), and this unreasonably high equipment requirement limits its applicability. In this paper, we shall propose a new efficient handover authentication mechanism. The new mechanism offers a higher level of security on a more scalable ground with the client’s privacy better preserved. The results of our performance analysis suggest that our new mechanism is superior to some similar mechanisms in terms of authentication delay. [ABSTRACT FROM AUTHOR]

Information transmission in cells occurs quite accurately even when concentration changes are “read” by individual binding sites. In this paper we study ligand number and site occupancy fluctuations when ligands diffuse and react going beyond the analyses that focus on their asymptotic decay. In this way we show that, for immobile binding sites, fluctuations in the number of bound molecules decay on a relatively fast scale before the asymptotic behavior kicks in. This result can explain the observed co-existence of highly fluctuating instantaneous transcriptional activities with accumulated mRNA concentrations that have relatively small noise levels. We also show that the initial stages of the decay in the bound molecule number fluctuations have one or two characteristic timescales depending on the concentration of free molecules. This transition can explain the changes in enzyme activity observed at the single molecule level. [ABSTRACT FROM AUTHOR]

In this paper, a novel method for selecting a navigation satellite subset for a global positioning system (GPS) based on a genetic algorithm is presented. This approach is based on minimizing the factors in the geometric dilution of precision (GDOP) using a modified genetic algorithm (MGA) with an elite conservation strategy, adaptive selection, adaptive mutation, and a hybrid genetic algorithm that can select a subset of the satellites represented by specific numbers in the interval (4 ∼ n) while maintaining position accuracy. A comprehensive simulation demonstrates that the MGA-based satellite selection method effectively selects the correct number of optimal satellite subsets using receiver autonomous integrity monitoring (RAIM) or fault detection and exclusion (FDE). This method is more adaptable and flexible for GPS receivers, particularly for those used in handset equipment and mobile phones. [ABSTRACT FROM AUTHOR]

The misalignment between recorded in-focus and out-of-focus images using the Phase Diversity (PD) algorithm leads to a dramatic decline in wavefront detection accuracy and image recovery quality for segmented active optics systems. This paper demonstrates the theoretical relationship between the image misalignment and tip-tilt terms in Zernike polynomials of the wavefront phase for the first time, and an efficient two-step alignment correction algorithm is proposed to eliminate these misalignment effects. This algorithm processes a spatial 2-D cross-correlation of the misaligned images, revising the offset to 1 or 2 pixels and narrowing the search range for alignment. Then, it eliminates the need for subpixel fine alignment to achieve adaptive correction by adding additional tip-tilt terms to the Optical Transfer Function (OTF) of the out-of-focus channel. The experimental results demonstrate the feasibility and validity of the proposed correction algorithm to improve the measurement accuracy during the co-phasing of segmented mirrors. With this alignment correction, the reconstructed wavefront is more accurate, and the recovered image is of higher quality. [ABSTRACT FROM AUTHOR]

Time delay due to maturation time, capturing time or other reasons widely exists in biological systems. In this paper, a predator-prey system of Leslie type with diffusion and time delay is studied based on mathematical analysis and numerical simulations. Conditions for both delay induced and diffusion induced Turing instability are obtained by using bifurcation theory. Furthermore, a series of numerical simulations are performed to illustrate the spatial patterns, which reveal the information of density changes of both prey and predator populations. The obtained results show that the interaction between diffusion and time delay may give rise to rich dynamics in ecosystems. [ABSTRACT FROM AUTHOR]

Slower-than-light multi-front solutions of the Sine-Gordon in (1+2) dimensions, constructed through the Hirota algorithm, are mapped onto spatially localized structures, which emulate free, spatially extended, massive relativistic particles. A localized structure is an image of the junctions at which the fronts intersect. It propagates together with the multi-front solution at the velocity of the latter. The profile of the localized structure obeys the linear wave equation in (1+2) dimensions, to which a term that represents interaction with a slower-than-light, Sine-Gordon-multi-front solution has been added. This result can be also formulated in terms of a (1+2)-dimensional Lagrangian system, in which the Sine-Gordon and wave equations are coupled. Expanding the Euler-Lagrange equations in powers of the coupling constant, the zero-order part of the solution reproduces the (1+2)-dimensional Sine-Gordon fronts. The first-order part is the spatially localized structure. : 02.30.Ik, 03.65.Pm, 05.45.Yv, 02.30.Ik. [ABSTRACT FROM AUTHOR]

The wealth of sensory data coming from different modalities has opened numerous opportunities for data analysis. The data are of increasing volume, complexity and dimensionality, thus calling for new methodological innovations towards multimodal data processing. However, multimodal architectures must rely on models able to adapt to changes in the data distribution. Differences in the density functions can be due to changes in acquisition conditions (pose, illumination), sensors characteristics (number of channels, resolution) or different views (e.g. street level vs. aerial views of a same building). We call these different acquisition modes domains, and refer to the adaptation problem as domain adaptation. In this paper, instead of adapting the trained models themselves, we alternatively focus on finding mappings of the data sources into a common, semantically meaningful, representation domain. This field of manifold alignment extends traditional techniques in statistics such as canonical correlation analysis (CCA) to deal with nonlinear adaptation and possibly non-corresponding data pairs between the domains. We introduce a kernel method for manifold alignment (KEMA) that can match an arbitrary number of data sources without needing corresponding pairs, just few labeled examples in all domains. KEMA has interesting properties: 1) it generalizes other manifold alignment methods, 2) it can align manifolds of very different complexities, performing a discriminative alignment preserving each manifold inner structure, 3) it can define a domain-specific metric to cope with multimodal specificities, 4) it can align data spaces of different dimensionality, 5) it is robust to strong nonlinear feature deformations, and 6) it is closed-form invertible, which allows transfer across-domains and data synthesis. To authors’ knowledge this is the first method addressing all these important issues at once. We also present a reduced-rank version of KEMA for computational efficiency, and discuss the generalization performance of KEMA under Rademacher principles of stability. Aligning multimodal data with KEMA reports outstanding benefits when used as a data pre-conditioner step in the standard data analysis processing chain. KEMA exhibits very good performance over competing methods in synthetic controlled examples, visual object recognition and recognition of facial expressions tasks. KEMA is especially well-suited to deal with high-dimensional problems, such as images and videos, and under complicated distortions, twists and warpings of the data manifolds. A fully functional toolbox is available at . [ABSTRACT FROM AUTHOR]

Several variable selection algorithms in multivariate calibration can be accelerated using Graphics Processing Units (GPU). Among these algorithms, the Firefly Algorithm (FA) is a recent proposed metaheuristic that may be used for variable selection. This paper presents a GPU-based FA (FA-MLR) with multiobjective formulation for variable selection in multivariate calibration problems and compares it with some traditional sequential algorithms in the literature. The advantage of the proposed implementation is demonstrated in an example involving a relatively large number of variables. The results showed that the FA-MLR, in comparison with the traditional algorithms is a more suitable choice and a relevant contribution for the variable selection problem. Additionally, the results also demonstrated that the FA-MLR performed in a GPU can be five times faster than its sequential implementation. [ABSTRACT FROM AUTHOR]

In this paper, a randomized numerical approach is used to obtain approximate solutions for a class of nonlinear Fredholm integral equations of the second kind. The proposed approach contains two steps: at first, we define a discretized form of the integral equation by quadrature formula methods and solution of this discretized form converges to the exact solution of the integral equation by considering some conditions on the kernel of the integral equation. And then we convert the problem to an optimal control problem by introducing an artificial control function. Following that, in the next step, solution of the discretized form is approximated by a kind of Monte Carlo (MC) random search algorithm. Finally, some examples are given to show the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, using the Lie group analysis method, we study the invariance properties of the time fractional fifth-order KdV equation. A systematic research to derive Lie point symmetries to time fractional fifth-order KdV equation is performed. In the sense of point symmetry, all of the vector fields and the symmetry reductions of the fractional fifth-order KdV equation are obtained. At last, by virtue of the sub-equation method, some exact solutions to the fractional fifth-order KdV equation are provided. [ABSTRACT FROM AUTHOR]

This paper presents new simple approaches for evaluating determinant and inverse of a matrix. The choice of pivot selection has been kept arbitrary thus they reduce the error while solving an ill conditioned system. Computation of determinant of a matrix has been made more efficient by saving unnecessary data storage and also by reducing the order of the matrix at each iteration, while dictionary notation [1] has been incorporated for computing the matrix inverse thereby saving unnecessary calculations. These algorithms are highly class room oriented, easy to use and implemented by students. By taking the advantage of flexibility in pivot selection, one may easily avoid development of the fractions by most. Unlike the matrix inversion method [2] and [3], the presented algorithms obviate the use of permutations and inverse permutations. [ABSTRACT FROM AUTHOR]

To enrich any model and its dynamics introduction of delay is useful, that models a precise description of real-life phenomena. Differential equations in which current time derivatives count on the solution and its derivatives at a prior time are known as delay differential equations (DDEs). In this study, we are introducing new techniques for finding the numerical solution of fractional delay differential equations (FDDEs) based on the application of neural minimization (NM) by utilizing Chebyshev simulated annealing neural network (ChSANN) and Legendre simulated annealing neural network (LSANN). The main purpose of using Chebyshev and Legendre polynomials, along with simulated annealing (SA), is to reduce mean square error (MSE) that leads to more accurate numerical approximations. This study provides the application of ChSANN and LSANN for solving DDEs and FDDEs. Proposed schemes can be effortlessly executed by using Mathematica or MATLAB software to get explicit solutions. Computational outcomes are depicted, for various numerical experiments, numerically and graphically with error analysis to demonstrate the accuracy and efficiency of the methods. [ABSTRACT FROM AUTHOR]

Quantitative MRI methods have recently gained extensive interest and are seeing substantial developments; however, their application in single patient vs control group comparisons is often limited by inherent statistical difficulties. One such application is detecting malformations of cortical development (MCDs) behind drug resistant epilepsies, a task that, especially when based solely on conventional MR images, may represent a serious challenge. We aimed to develop a novel straightforward voxel-wise evaluation method based on the Mahalanobis-distance, combining quantitative MRI data into a multidimensional parameter space and detecting lesion voxels as outliers. Simulations with standard multivariate Gaussian distribution and resampled DTI-eigenvalue data of 45 healthy control subjects determined the optimal critical value, cluster size threshold, and the expectable lesion detection performance through ROC-analyses. To reduce the effect of false positives emanating from registration artefacts and gyrification differences, an automatic classification method was applied, fine-tuned using a leave-one-out strategy based on diffusion and T1-weighted data of the controls. DWI processing, including thorough corrections and robust tensor fitting was performed with ExploreDTI, spatial coregistration was achieved with the DARTEL tools of SPM12. Additional to simulations, clusters of outlying diffusion profile, concordant with neuroradiological evaluation and independent calculations with the MAP07 toolbox were identified in 12 cases of a 13 patient example population with various types of MCDs. The multidimensional approach proved sufficiently sensitive in pinpointing regions of abnormal tissue microstructure using DTI data both in simulations and in the heterogeneous example population. Inherent limitations posed by registration artefacts, age-related differences, and the different or mixed pathologies limit the generalization of specificity estimation. Nevertheless, the proposed statistical method may aid the everyday examination of individual subjects, ever so more upon extending the framework with quantitative information from other modalities, e.g. susceptibility mapping, relaxometry, or perfusion. [ABSTRACT FROM AUTHOR]

Modern logistics processes and systems can feature extremely complicated dynamics. Agent Based Modeling is emerging as a powerful modeling tool for design, analysis and control of such logistics systems. However, the complexity of the model itself can be overwhelming and mathematical meta-modeling tools are needed that aggregate information and enable fast and accurate decision making and control system design. Here we present Koopman Mode Analysis (KMA) as such a tool. KMA uncovers exponentially growing, decaying or oscillating collective patterns in dynamical data. We apply the methodology to two problems, both of which exhibit a bifurcation in dynamical behavior, but feature very different dynamics: Medical Treatment Facility (MTF) logistics and ship fueling (SF) logistics. The MTF problem features a transition between efficient operation at low casualty rates and inefficient operation beyond a critical casualty rate, while the SF problem features a transition between short mission life at low initial fuel levels and sustained mission beyond a critical initial fuel level. Both bifurcations are detected by analyzing the spectrum of the associated Koopman operator. Mathematical analysis is provided justifying the use of the Dynamic Mode Decomposition algorithm in punctuated linear decay dynamics that is featured in the SF problem. [ABSTRACT FROM AUTHOR]

Cumulative receiver operator characteristic (ROC) curve analysis extends classic ROC curve analysis to discriminate three or more ordinal outcome levels on a shared continuous scale. The procedure combines cumulative logit regression with a cumulative extension to the ROC curve and performs as expected with ternary (three-level) ordinal outcomes under a variety of simulated conditions (unbalanced data, proportional and non-proportional odds, areas under the ROC curve [AUCs] from 0.70 to 0.95). Simulations also compared several criteria for selecting cutpoints to discriminate outcome levels: the Youden Index, Matthews Correlation Coefficient, Total Accuracy, and Markedness. Total Accuracy demonstrated the least absolute percent-bias. Cutpoints computed from maximum likelihood regression parameters demonstrated bias that was often negligible. The procedure was also applied to publicly available data related to computer imaging and biomarker exposure science, yielding good to excellent AUCs, as well as cutpoints with sensitivities and specificities of commensurate quality. Implementation of cumulative ROC curve analysis and extension to more than three outcome levels are straightforward. The author’s programs for ternary ordinal outcomes are publicly available. [ABSTRACT FROM AUTHOR]

The thermoanalytical technique differential scanning calorimetry (DSC) has been applied to characterize protein denaturation patterns (thermograms) in blood plasma samples and relate these to a subject's health status. The analysis and classification of thermograms is challenging because of the high-dimensionality of the dataset. There are various methods for group classification using high-dimensional data sets; however, the impact of using high-dimensional data sets for cancer classification has been poorly understood. In the present article, we proposed a statistical approach for data reduction and a parametric method (PM) for modeling of high-dimensional data sets for two- and three- group classification using DSC and demographic data. We compared the PM to the non-parametric classification method K-nearest neighbors (KNN) and the semi-parametric classification method KNN with dynamic time warping (DTW). We evaluated the performance of these methods for multiple two-group classifications: (i) normal versus cervical cancer, (ii) normal versus lung cancer, (iii) normal versus cancer (cervical + lung), (iv) lung cancer versus cervical cancer as well as for three-group classification: normal versus cervical cancer versus lung cancer. In general, performance for two-group classification was high whereas three-group classification was more challenging, with all three methods predicting normal samples more accurately than cancer samples. Moreover, specificity of the PM method was mostly higher or the same as KNN and DTW-KNN with lower sensitivity. The performance of KNN and DTW-KNN decreased with the inclusion of demographic data, whereas similar performance was observed for the PM which could be explained by the fact that the PM uses fewer parameters as compared to KNN and DTW-KNN methods and is thus less susceptible to the risk of overfitting. More importantly the accuracy of the PM can be increased by using a greater number of quantile data points and by the inclusion of additional demographic and clinical data, providing a substantial advantage over KNN and DTW-KNN methods. [ABSTRACT FROM AUTHOR]

We are living in the world of handheld smart devices including smart phones, mini computers, tablets, net-books and others communication devices. The telecommunication standards used in these devices includes error correction codes which are integral part of current and future communication systems. To achieve the higher data rate applications, the turbo and Low Density Parity Check (LDPC) codes are decoded on parallel architecture which in turn raises the memory conflict issue. In order to get the good performance, the simultaneous access to the entire memory bank should be performed without any conflict. In this article we present breadth first technique applied on transportation modeling of the problem for solving the collision issue of Turbo decoders in order to get optimized architecture solution. [ABSTRACT FROM AUTHOR]

Absolute and relative dispersion are fundamental quantities employed in order to assess the mixing strength of a basin. There exists a time scale called Lagrangian Integral Scale associated to absolute dispersion that highlights the occurrence of the transition from a quadratic dependence on time to a linear dependence on time. Such a time scale is commonly adopted as an indicator of the duration needed to lose the influence of the initial conditions. This work aims to show that in a semi-enclosed basin the choice of the formulation in order to calculate the absolute dispersion can lead to different results. Moreover, the influence of initial conditions can persist beyond the Lagrangian Integral Scale. Such an influence can be appreciated by evaluating absolute and relative dispersion recursively by changing the initial conditions. Furthermore, finite-size Lyapunov exponents characterize the different regimes of the basin. [ABSTRACT FROM AUTHOR]

Observed bimodal tree cover distributions at particular environmental conditions and theoretical models indicate that some areas in the tropics can be in either of the alternative stable vegetation states forest or savanna. However, when including spatial interaction in nonspatial differential equation models of a bistable quantity, only the state with the lowest potential energy remains stable. Our recent reaction-diffusion model of Amazonian tree cover confirmed this and was able to reproduce the observed spatial distribution of forest versus savanna satisfactorily when forced by heterogeneous environmental and anthropogenic variables, even though bistability was underestimated. These conclusions were solely based on simulation results for one set of parameters. Here, we perform an analytical and numerical analysis of the model. We derive the Maxwell point (MP) of the homogeneous reaction-diffusion equation without savanna trees as a function of rainfall and human impact and show that the front between forest and nonforest settles at this point as long as savanna tree cover near the front remains sufficiently low. For parameters resulting in higher savanna tree cover near the front, we also find irregular forest-savanna cycles and woodland-savanna bistability, which can both explain the remaining observed bimodality. [ABSTRACT FROM AUTHOR]

Short-term traffic speed prediction is a key component of proactive traffic control in the intelligent transportation systems. The objective of this study is to investigate the short-term traffic speed prediction under different data collection time intervals. Traffic speed data was collected from an urban freeway in Edmonton, Canada. A seasonal autoregressive integrated moving average plus seasonal discrete grey model structure (SARIMA-SDGM) was proposed to perform the traffic speed prediction. The model performance of SARIMA-SDGM model was compared with that of the seasonal autoregressive integrated moving average (SARIMA) model, seasonal discrete grey model (SDGM), artificial neural network (ANN) model, and support vector regression (SVR) model. The results showed that SARIMA-SDGM model performs best with the lowest mean absolute error (MAE), mean absolute percentage error (MAPE), and the root mean square error (RMSE). The traffic speed prediction accuracy under different time intervals were compared based on the SARIMA-SDGM model. The results showed that the prediction accuracy improves with the increase in time interval. In addition, when the time interval is greater than 10 min, the prediction results yield stable prediction accuracy. [ABSTRACT FROM AUTHOR]

Rockburst is a common dynamic disaster in deep underground engineering. To accurately predict rockburst intensity grade, this study proposes a novel rockburst prediction model based on variable weight and matter-element extension theory. In the proposed model, variable weight theory is used to optimize the weights of prediction indexes. Matter-element extension theory and grade variable method are used to calculate the grade variable interval corresponding to the classification standard of rockburst intensity grade. The rockburst intensity grade of Engineering Rock Mass is predicted by rock burst intensity level variable and the interval. Finally, the model is tested by predicting the rockburst intensity grades of worldwide several projects. The prediction results are compared with the actual rockburst intensity grades and the prediction results of other models. The results indicate that, after using variable weight theory and grade variable method, the correct rate of prediction results of matter-element extension model is improved, and the safety of the prediction results is also enhanced. This study provides a new way to predict rock burst in underground engineering. [ABSTRACT FROM AUTHOR]

SNP datasets are high-dimensional, often with thousands to millions of SNPs and hundreds to thousands of samples or individuals. Accordingly, PCA graphs are frequently used to provide a low-dimensional visualization in order to display and discover patterns in SNP data from humans, animals, plants, and microbes—especially to elucidate population structure. PCA is not a single method that is always done the same way, but rather requires three choices which we explore as a three-way factorial: two kinds of PCA graphs by three SNP codings by six PCA variants. Our main three recommendations are simple and easily implemented: Use PCA biplots, SNP coding 1 for the rare allele and 0 for the common allele, and double-centered PCA (or AMMI1 if main effects are also of interest). We also document contemporary practices by a literature survey of 125 representative articles that apply PCA to SNP data, find that virtually none implement our recommendations. The ultimate benefit from informed and optimal choices of PCA graph, SNP coding, and PCA variant, is expected to be discovery of more biology, and thereby acceleration of medical, agricultural, and other vital applications. [ABSTRACT FROM AUTHOR]