taxicab correspondence analysis taxicab correspondence analysis is based on the taxicab singular value decomposition of a contingency table and it shares some similar properties with correspondence analysis it is more robust than the ordinary correspondence analysis because it gives uniform weights to all the points the visual map constructed by taxicab correspondence analysis has a larger sweep and clearer perspective than the map obtained by correspondence analysis two examples are provided

analysis of a nonautonomous nicholson blowfly model abstract most dynamic models describing population evolution contain one or more parameters the parameters are treated as fixed constants and qualitative results such as stability of equilibria are calculated using this assumption in reality however the parameters are mathematically evaluated by statistical methods in which the error is decreased over a number of calculations therefore the parameter is a sequence converging to the actual parameter value as time goes to infinity in this article we consider the k th order discrete nicholson blowfly model n n 1 f p n n n n k where and p are parameters for a particular range of parameter values global stability results are well known the general form of the discrete dynamical system is now rewritten as n n 1 f p n n n n n n k where p n and n converge to the parametric values p and we show that when the parameters are replaced by sequences the stability results of the original system still hold this technique may be of general interest to those studying evolutionary systems in which the parameters are not fundamental constants but sequences

an exact test of fit for the gaussian linear model using optimal nonbipartite matching abstractfisher tested the fit of gaussian linear models using replicated observations we refine this method by 1 constructing near replicates using an optimal nonbipartite matching and 2 defining a distance that focuses on predictors important to the model s predictions near replicates may not exist unless the predictor set is low dimensional the test addresses dimensionality by betting that model failures involve a subset of predictors important in the old fit despite using the old fit to pair observations the test has exactly its stated level under the null hypothesis simulations show the test has reasonable power even when many spurious predictors are present

oscillation of continuous and discrete diffusive delay nicholson s blowflies models in this paper we consider the continuous and the discrete delay diffusive nicholson s blowflies models with different types of boundary conditions our aim is to give some sufficient conditions for oscillation of all positive solutions about the positive steady state we show that these conditions have essentially first order character by reducing the problem of oscillation of the boundary value problem to that of first order delay differential or difference equation

on the stability and uniform persistence of a discrete model of nicholson s blowflies abstract consider the delay difference equation n n 1 nn n n pn n k e an n k n 0 1 2 1 which is a discrete analogue of the delay differential equation n t n t pn t e an t t 0 cf 8 we show that when p the zero solution of 1 is uniformly asymptotically stable and every non negative solution of 1 tends to zero as n while for p 1 is uniformly persistent moreover if in addition to p we also have 1 k 1 1 ln p 1 then every positive solution of 1 tends to the positive equilibrium n 1 a ln p

complex scale free networks with tunable power law exponent and clustering abstract we introduce a network evolution process motivated by the network of citations in the scientific literature in each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already in the network this set includes m ambassador nodes and l of each ambassador s descendants where m and l are random variables selected from any choice of distributions p l and q m the process mimics the tendency of authors to cite varying numbers of papers included in the bibliographies of the other papers they cite we show that the degree distributions of the networks generated after a large number of iterations are scale free and derive an expression for the power law exponent in a particular case of the model where the number of ambassadors is always the constant m and the number of selected descendants from each ambassador is the constant l the power law exponent is 2 l 1 l for this example we derive expressions for the degree distribution and clustering coefficient in terms of l and m we conclude that the proposed model can be tuned to have the same power law exponent and clustering coefficient of a broad range of the scale free distributions that have been studied empirically

the best parameter subset using the chebychev curve fitting criterion the chebychev also minimax andl norm criterion has been widely studied as a method for curve fitting published computer codes are available to obtain the optimal parameter estimates to fit a linear function to a set of given points under the chebychev criterion the purpose of this paper is to study procedures for obtaining the best subset ofq parameters from a given set ofm parameters whereq is less than or equal tom

tests of significance in forward selection regression with an f to enter stopping rule a monte carlo simulation is used to estimate the upper percentage points of the null distribution of the sample squared multiple correlation coefftcient r 2 when the number of predictors selected is determined by a stopping rule in the study the sample size n and the number of candidate predictors m satisfy 2 m 20 and 10 n m 1 200 while the f threshold ranges from two to four tables of the upper five percent and upper one percent sample r values are presented and an example is given to illustrate the use of the tables

a branch and bound algorithm for fitting anti robinson structures to symmetric dissimilarity matrices the seriation of proximity matrices is an important problem in combinatorial data analysis and can be conducted using a variety of objective criteria some of the most popular criteria for evaluating an ordering of objects are based on anti robinson forms which reflect the pattern of elements within each row and or column of the reordered matrix when moving away from the main diagonal this paper presents a branch and bound algorithm that can be used to seriate a symmetric dissimilarity matrix by identifying a reordering of rows and columns of the matrix optimizing an anti robinson criterion computational results are provided for several proximity matrices from the literature using four different anti robinson criteria the results suggest that with respect to computational efficiency the branch and bound algorithm is generally competitive with dynamic programming further because it requires much less storage than dynamic programming the branch and bound algorithm can provide guaranteed optimal solutions for matrices that are too large for dynamic programming implementations

mixed integer second order cone programming formulations for variable selection in linear regression abstract this study concerns a method of selecting the best subset of explanatory variables in a multiple linear regression model goodness of fit measures for example adjusted r2 aic and bic are generally used to evaluate a subset regression model although variable selection with regard to these measures is usually performed with a stepwise regression method it does not always provide the best subset of explanatory variables in this paper we propose mixed integer second order cone programming formulations for selecting the best subset of variables with respect to adjusted r2 aic and bic computational experiments show that in terms of these measures the proposed formulations yield better solutions than those provided by common stepwise regression methods

permutation tests for joinpoint regression with applications to cancer rates the identification of changes in the recent trend is an important issue in the analysis of cancer mortality and incidence data we apply a joinpoint regression model to describe such continuous changes and use the grid search method to fit the regression function with unknown joinpoints assuming constant variance and uncorrelated errors we find the number of significant joinpoints by performing several permutation tests each of which has a correct significance level asymptotically each p value is found using monte carlo methods and the overall asymptotic significance level is maintained through a bonferroni correction these tests are extended to the situation with non constant variance to handle rates with poisson variation and possibly autocorrelated errors the performance of these tests are studied via simulations and the tests are applied to u s prostate cancer incidence and mortality rates

from regular to growing small world networks abstract we propose a growing model which interpolates between one dimensional regular lattice and small world networks the model undergoes an interesting phase transition from large to small worlds we investigate the structural properties by both theoretical predictions and numerical simulations our growing model is a complementarity for the important static watts strogatz network model

time structure of the activity in neural network models several neural network models in continuous time are reconsidered in the framework of a general mean field theory which is exact in the limit of a large and fully connected network the theory assumes pointlike spikes which are generated by a renewal process the effect of spikes on a receiving neuron is described by a linear response kernel which is the dominant term in a weak coupling expansion it is shown that the resulting spike response model is the most general renewal model with linear inputs the standard integrate and fire model forms a special case in a network structure with several pools of identical spiking neurons the global states and the dynamic evolution are determined by a nonlinear integral equation which describes the effective interaction within and between different pools we derive explicit stability criteria for stationary incoherent and oscillatory coherent solutions it is shown that the stationary state of noiseless systems is almost always unstable noise suppresses fast oscillations and stabilizes the system furthermore collective oscillations are stable only if the firing occurs while the synaptic potential is increasing in particular collective oscillations in a network with delayless excitatory interaction are at most semistable inhibitory interactions with short delays or excitatory interactions with long delays lead to stable oscillations our general results allow a straightforward application to different network models with spiking neurons furthermore the theory allows an estimation of the errors introduced in firing rate or graded response models

variable neighborhood search heuristics for selecting a subset of variables in principal component analysis the selection of a subset of variables from a pool of candidates is an important problem in several areas of multivariate statistics within the context of principal component analysis pca a number of authors have argued that subset selection is crucial for identifying those variables that are required for correct interpretation of the components in this paper we adapt the variable neighborhood search vns paradigm to develop two heuristics for variable selection in pca the performances of these heuristics were compared to those obtained by a branch and bound algorithm as well as forward stepwise backward stepwise and tabu search heuristics in the first experiment which considered candidate pools of 18 to 30 variables the vns heuristics matched the optimal subset obtained by the branch and bound algorithm more frequently than their competitors in the second experiment which considered candidate pools of 54 to 90 variables the vns heuristics provided better solutions than their competitors for a large percentage of the test problems an application to a real world data set is provided to demonstrate the importance of variable selection in the context of pca

algebraic connectivity of interdependent networks the algebraic connectivity un 1 i e the second smallest eigenvalue of the laplacian matrix plays a crucial role in dynamic phenomena such as diffusion processes synchronization stability and network robustness in this work we study the algebraic connectivity in the general context of interdependent networks or network of networks non the present work shows both analytically and numerically how the algebraic connectivity of nons experiences a transition the transition is characterized by a saturation of the algebraic connectivity upon the addition of suffcient coupling links between the two individual networks of a non in practical terms this shows that non topologies require only a fraction of coupling links in order to achieve optimal diffusivity furthermore we observe a footprint of the transition on the properties of fiedler s spectral bisection

emergence of the small world architecture in neural networks by activity dependent growth abstract in this paper we propose a model describing the growth and development of neural networks based on the latest achievements of experimental neuroscience the model is based on two evolutionary equations the first equation is for the evolution of the neurons state and the second is for the growth of axon tips by using the model we demonstrated the neuronal growth process from disconnected neurons to fully connected three dimensional networks for the analysis of the network s connections structure we used the random graphs theory methods it is shown that the growth in neural networks results in the formation of a well known small world network model the analysis of the connectivity distribution shows the presence of a strictly non gaussian but no scale free degree distribution for the in degree node distribution in terms of the graphs theory this study developed a new model of dynamic graph

regressions by leaps and bounds this paper describes several algorithms for computing the residual sums of squares for all possible regressions with what appears to be a minimum of arithmetic less than six floating point operations per regression and shows how two of these algorithms can be combined to form a simple leap and bound technique for finding the best subsets without examining all possible subsets the result is a reduction of several orders of magnitude in the number of operations required to find the best subsets

joint identification of location and dispersion effects in unreplicated two level factorials most procedures that have been proposed to identify dispersion effects in unreplicated factorial designs assume that location effects have been identified correctly incorrect identification of location effects may impair subsequent identification of dispersion effects we develop a method for joint identification of location and dispersion effects that can reliably identify active effects of both types a normal based model containing parameters for effects in both the mean and variance is used parameters are estimated using maximum likelihood and subsequent effect selection is done using a specially derived information criterion an exhaustive search through a limited version of the space of possible models is conducted both a single model output and model averaging are considered the method is shown to be capable of identifying sensible location dispersion models that are missed by methods that rely on sequential estimation of location and dispersion effects supplementary materials for this articl

almost periodic solutions for an impulsive delay nicholson s blowflies model by means of the contraction mapping principle and gronwall bellman s inequality we prove the existence and exponential stability of positive almost periodic solution for an impulsive delay nicholson s blowflies model the main results are illustrated by an example

preferential attachment in randomly grown networks abstract we reintroduce the model of callaway et al 2001 as a special case of a more general model for random network growth vertices are added to the graph at a rate of 1 while edges are introduced at rate rather than edges being introduced at random we allow for a degree of preferential attachment with a linear attachment kernel parametrised by m the original model is recovered in the limit of no preferential attachment m as expected even weak preferential attachment introduces a power law tail to the degree distribution additionally this generalisation retains a great deal of the tractability of the original along with a surprising range of behaviour although key mathematical features are modified for finite m in particular the critical edge density c which marks the onset of a giant network component is reduced with increasing tendency for preferential attachment the positive degree degree correlation introduced by the unbiased growth process is offset by the skewed degree distribution reducing the network assortativity

taxicab correspondence analysis of contingency tables with one heavyweight column the aim of this paper is to study the analysis of contingency tables with one heavyweight column or one heavyweight entry by taxicab correspondence analysis tca given that the mathematics of tca is simpler than the mathematics of correspondence analysis ca the influence of one heavyweight column on the outputs of tca is studied explicitly without recourse to asymptotics as done by benzecri les cahiers de l analyse des donnees 4 413 16 1979 a reweighting of the heavyweight column is proposed which can also be applied to ca a real data set is analyzed

or forum an algorithmic approach to linear regression linear regression models are traditionally built through trial and error to balance many competing goals such as predictive power interpretability significance robustness to error in data and sparsity among others this problem lends itself naturally to a mixed integer quadratic optimization miqo approach but has not been modeled this way because of the belief in the statistics community that miqo is intractable for large scale problems however in the last 25 years 1991 2015 algorithmic advances in integer optimization combined with hardware improvements have resulted in an astonishing 450 billion factor speedup in solving mixed integer optimization problems we present an miqo based approach for designing high quality linear regression models that explicitly addresses various competing objectives and demonstrate the effectiveness of our approach on both real and synthetic data sets

an interior point algorithm for minimum sum of squares clustering an exact algorithm is proposed for minimum sum of squares nonhierarchical clustering i e for partitioning a given set of points from a euclidean m space into a given number of clusters in order to minimize the sum of squared distances from all points to the centroid of the cluster to which they belong this problem is expressed as a constrained hyperbolic program in 0 1 variables the resolution method combines an interior point algorithm i e a weighted analytic center column generation method with branch and bound the auxiliary problem of determining the entering column i e the oracle is an unconstrained hyperbolic program in 0 1 variables with a quadratic numerator and linear denominator it is solved through a sequence of unconstrained quadratic programs in 0 1 variables to accelerate resolution variable neighborhood search heuristics are used both to get a good initial solution and to solve quickly the auxiliary problem as long as global optimality is not reached estimated bounds for the dual variables are deduced from the heuristic solution and used in the resolution process as a trust region proved minimum sum of squares partitions are determined for the first time for several fairly large data sets from the literature including fisher s 150 iris