Positive Quadrant Research Articles

Distribution-free tests for independence against positive quadrant dependence: A generalization

A class of distribution-free tests based on two matched pairs is considered for testing independence against positive quadrant dependence. The class of tests proposed by Kochar and Gupta (1990) is a member of the proposed class. The performance of the proposed class is evaluated in terms of Pitman asymptotic relative efficiency for Block-Basu (1974) model and Woodworth family of distributions. The small sample performance of few members of the proposed class is also studied by finding empirical powers. Unbiasedness and consistency of the proposed class of tests have been established.

The Local Coefficient of Ergodicity of a Nonnegative Matrix

The local coefficient of ergodicity $\tau(T,Y',w)$ of a nonnegative column-allowable matrix T at a fixed positive vector Y is defined as the supremum of d(X'T,Y'T)/d(X',Y') for X not colinear to Y and d(X',Y')\leq w$ (d is the projective distance in the positive quadrant). A near-closed-form expression is given for $\tau(T,Y',w)$. If T' is scrambling (i.e., no two rows of T' are orthogonal), then for any Y>0, $w < \infty$ we have $\tau(T,Y',w)<1$. When Y is a positive left eigenvector of T and Xo>0, these results can be used to prove the convergence in direction of X'oTp to Y'. Results are illustrated with a numerical example.

Global Asymptotic Behavior of a Two-dimensional System of Difference Equations Modeling Cooperation

Dedicated to Allan Peterson on the Occasion of His 60th Birthday. We investigate the global asymptotic behavior of solutions of the system of difference equations where the parameters A and B are in (0, ∞) and the initial conditions x 0 and y 0 are arbitrary nonnegative numbers. We show that the stable manifold of this system separates the positive quadrant into the basins of attraction of two types of asymptotic behavior.

Global asymptotic behavior of a two-dimensional difference equation modelling competition

We investigate the global asymptotic behavior of solutions of the system of difference equations x n+1= x n a+cy n , y n+1= y n b+dx n , n=0,1,…, where the parameters a and b are in (0,1), c and d are arbitrary positive numbers and the initial conditions x 0 and y 0 are arbitrary nonnegative numbers. We show that the stable manifold of this system separates the positive quadrant into basins of attraction of two types of asymptotic behavior. In the case where a= b we find an explicit equation for the stable manifold.

Vanishing Ideals of Lattice Diagram Determinants

A lattice diagram is a finite set L={( p 1, q 1),…,( p n , q n )} of lattice cells in the positive quadrant. The corresponding lattice diagram determinant is Δ L ( X n ; Y n )=det ∥ x I p j y I q j ∥. The space M L is the space spanned by all partial derivatives of Δ L ( X n ; Y n ). We denote by M L 0 the Y-free component of M L . For μ a partition of n+1, we denote by μ/ ij the diagram obtained by removing the cell ( I, j) from the Ferrers diagram of μ. Using homogeneous partially symmetric polynomials, we give here a dual description of the vanishing ideal of the space M μ 0 and we give the first known description of the vanishing ideal of M μ/ ij 0.

ON A CENTRAL LIMIT THEOREM FOR A STATIONARY MULTIVARIATE LINEAR PROCESS GENERATED BY LINEARLY POSITIVE QUADRANT DEPENDENT RANDOM VECTORS

For a stationary multivariate linear process of the form Xt = 1 X j=0 AjZtij, where fZt : t = 0;§1;§2;¢¢¢g is a sequence of stationary linearly positive quadrant dependent m-dimensional random vectors with E(Zt) = O and EkZtk 2 < 1, we prove a

Positive Quadrant Dependence and Marginal Modeling in Two-Way Tables With Ordered Margins

For a collection of two-way tables, where subjects are cross-classified according to the same pair of ordinal categorical variables conditionally on the value of one or more discrete explanatory variables, we propose a general approach to likelihood inference that combines marginal modeling with fitting and testing of inequality constraints such as those implied by the assumption that one marginal distribution is stochastically larger than the other, positive dependence and stronger positive dependence. The approach is based on parameterizing bivariate conditional distributions with global logits and global log-odds ratios, and we provide a general framework for handling models defined by equality and inequality constraints on these parameters. In this way, such models as marginal homogeneity, proportional odds among row or columns margins, and Plackett distribution may be treated together with various models defined by inequality constraints on the same parameters, such as, for instance, those implied by the positive quadrant dependence. For this class of models, we define a Fisher scoring algorithm for computing maximum likelihood estimates and derive the asymptotic distribution of the likelihood ratio tests that turn out to be of the chi-bar squared type when inequalities are involved. When the main interest is on positive dependence, we derive tight bounds on the asymptotic distribution of these statistics that are independent of the marginal logits. These also may be removed by conditioning on one or both observed margins in each table, and we describe in detail how the approach may be adapted to these sampling schemes. Three applications to real datasets are discussed.

Effects of Vibrational Frequency Correlations on Two-Dimensional Infrared Spectra

The response functions needed for simulating and fitting two-dimensional infrared spectra are described including the distributions of vibrational frequency, anharmonicity, and coupling between vibrators. A simple method that does not involve explicit calculation is introduced to characterize the spectral line narrowing properties of each of the quantum paths contributing to 2D IR. It is shown that the 2D IR spectra need to be collected in both positive and negative frequency quadrants in order to optimize the information needed to evaluate these correlations. Two experimental examples of heterodyned 2D IR (acetone in ethylene glycol and acetylproline-ND2 in D2O) are described where the 2D IR spectra are obtained for both the conventional echo sequence of pulse delays and for the usually nonrephased signal. These two sets of spectra are quite different for both examples, as predicted. The latter exhibits an echo only when there is some anticorrelation between the relevant inhomogeneous distributions.

A Temporal Analysis of Earnings Surprises: Profits versus Losses

I show that median earnings surprise has shifted rightward from small negative (miss analyst estimates by a small amount) to zero (meet analyst estimates exactly) to small positive (beat analyst estimates by a small amount) during the 16 years, 1984 to 1999. I show that a rightward temporal shift in median surprise from negative to positive describes earnings, but neither profits nor losses. Median profit surprise shifts within the positive quadrant, from zero to one cent per share. Median loss surprise shifts within the negative quadrant from extreme negative (about ‐33 cents per share) to zero. I show that the median surprise for profits exceeds that for losses in every year. I document significant positive temporal trends in both meet and beat analyst estimates for both profits and losses, but I find a greater frequency of profits that either meet or beat analyst estimates in every year. I find a significant positive temporal trend in positive profits that are “a little bit of good news,” and a significant negative temporal trend in managers who report losses that are an “extreme amount of bad news.” My results are robust to the four internal validity threats I consider—namely temporal changes in: (1) analyst forecast accuracy, (2) the mix of earnings of one sign preceded by earnings of another sign four quarters ago, (3) the timeliness of the most recent analyst forecast, and (4) the I/B/E/S definition of actual earnings. I find that managers of growth firms are relatively more likely than managers of value firms to report good news profits. I show that when they do report positive profit surprises, managers of growth firms are more likely to report “a little bit of good news” in every year.

Positive Numerical Integration Methods for Chemical Kinetic Systems

Chemical kinetics conserves mass and renders nonnegative solutions; a good numerical simulation would ideally produce mass-balanced, positive concentration vectors. Many time-stepping methods are mass conservative; however, unconditional positivity restricts the order of a traditional method to one. The projection method presented in this paper ensures mass conservation and positivity. First, a numerical approximation is computed with one step of a mass-preserving traditional scheme. If there are negative components, the nearest vector in the reaction simplex is found by solving a quadratic optimization problem; this vector is shown to better approximate the true solution. A simpler version involves just one projection step and stabilizes the reaction simplex. This technique works best when the underlying time-stepping scheme favors positivity. Projected methods are more accurate than clipping and allow larger time steps for kinetic systems which are unstable outside the positive quadrant.

New generalized Farlie-Gumbel-Morgenstern distributions and concomitants of order statistics

We consider a generalization of the bivariate Farlie-Gumbel-Morgenstern (FGM) distribution by introducing additional parameters. For the generalized FGM distribution, the admissible range of the association parameter allowing positive quadrant dependence property is shown. Distributional properties of concomitants for this generalized FGM distribution are studied. Recurrence relations between moments of concomitants are presented.

Value at Risk Bounds for Portfolios of Non-Normal Returns

This paper studies Value at Risk (VaR) bounds for sums of stochastically dependent random variables, i.e. portfolios of correlated financial assets. The bounds hold under no restrictions on the dependence or on the marginal distributions of returns. An improvement of the bounds is given for positive (quadrant) dependent rvs. Both sets of bounds are computed for portfolios of 6 international indices. Backtesting confirms the usefulness of the approach, even with respect to other shortcuts, such as the normality assumption. For small portfolios, bounds are not over conservative.

PSOAS SHEATH INJECTION AND PELVIC STABILISATION IN BACK PAIN. LONG TERM OUTCOMES

Methods: Anonymous patient questionnaires with reply paid addressed envelopes and separate reply paid consent slip were sent to 134 patients confirmed to have had a psoas sheath injection over six months previously by data base search and then manual confirmation of records. Pain was rated using a 10 point VAS for pain pre procedure and at time of reply. Area of main and secondary pain was recorded. Results: Average length of time in pain was 43 months. At average 14 month follow up: 72% of patients with primary low back pain were good or excellent 69% of patients with primary groin were good or excellent 72% of patients with upper AND lower leg pain were good or excellent The worst responding group were those with lateral hip pain, which is in keeping with labral tears of the hip. 10% of patients were worse on VAS of pain. Those with an excellent response had the following distribution of pain: Main area of pain: LBP 58%, Groin 23%, Upper leg 8% Discussion: Psoas dysfunction is defined as: Low back & or groin pain Tight & tender psoas muscle belly. L23 & L34 facet joint dysfunction. Groin pain in “thomas test” position Positive hip quadrant ± abdominal discomfort The commonest cause is pelvic instability. Others are: Psoas dysfunction and insufficiency syndrome Hip labral tears True back pathology Gross pelvic instability Tumours Conclusion: Psoas sheath injection followed by transversus abdominus retraining appears to have a place in the treatment of back and groin pain. More work needs to be done on identifying those in the good and excellent groups.

A central limit theorem for stationary linear processes generated by linearly positively quadrant-dependent process

A central limit theorem is obtained for a stationary linear process of the form X t =∑ j=0 ∞ a j ε t− j , where { ε t } is a strictly stationary sequence of linearly positive quadrant dependent random variables with Eε t=0, E|ε t| s<∞ for some s>2, and ∑ t= n+1 ∞ Eε 1 ε t =O( n − ρ ) for some ρ>0 and ∑ j=0 ∞| a j |<∞.

Polynomial Time Approximation Scheme for Symmetric Rectilinear Steiner Arborescence Problem

The Symmetric Rectilinear Steiner Arborescence (SRStA) problem is defined as follows: given a set of terminals in the positive quadrant of the plane, connect them using horizontal and vertical lines such that each terminal can be reached from the origin via a y-monotone path and the total length of all the line segments is the minimum possible. Finding an SRStA has applications in VLSI design, in data structures used in some optimization algorithms and in dynamic server problems. In this paper, we provide a polynomial time approximation scheme for the SRStA problem, improving the previous best approximation ratio of 3 for this problem.

Stabilization of the Extended Nonholonomic Double Integrator Via Logic-Based Hybrid Control

This paper derives a hybrid control law for an extended nonholonomic double integrator (ENDI) that captures the dynamics of a wheeled robot subject to force and torque inputs. A simple logic-based hybrid controller is proposed which yields global stability and convergence of the closed-loop system to an arbitrarily small neighborhood of the origin. This is achieved by mapping the state-space into a two dimensional closed positive quadrant space and dividing it into three overlapping regions where, for each region, a feedback law is conveniently designed. Convergence and stability of the closed-loop hybrid system are analyzed theoretically. An application is made to the control of a wheeled mobile robot of the unicycle-type. Simulation results are presented that illustrate the performance of the hybrid control law.

Multiple Left Regular Representations Generated by Alternants

Let p1>…>pn⩾0, and Δp=det‖xpji‖ni, j=1. Let Mp be the linear span of the partial derivatives of Δp. Then Mp is a graded Sn-module. We prove that it is the direct sum of graded left regular representations of Sn. Specifically, set λj=pj−(n−j), and let Ξλ(t) be the Hilbert polynomial of the span of all skew Schur functions sλ/μ as μ varies in λ. Then the graded Frobenius characteristic of Mp is Ξλ(t)H1n(x; q, t), a multiple of a Macdonald polynomial. Corresponding results are also given for the span of partial derivatives of an alternant over any complex reflection group. Let (i, j) denote the lattice cell in the i+1st row and j+1st column of the positive quadrant of the plane. If L is a diagram with lattice cells (p1, q1), …, (pn, qn), we set ΔL=det‖xpjiyqji‖ni, j=1, and let ML be the linear span of the partial derivatives of ΔL. The bihomogeneity of ΔL and its alternating nature under the diagonal action of Sn gives ML the structure of a bigraded Sn-module. We give a family of examples and some general conjectures about the bivariate Frobenius characteristic of ML for two dimensional diagrams.

Internal mammary node irradiation neither decreases distant metastases nor improves survival in stage I and II breast cancer

Purpose: To compare outcome for ipsilateral breast tumor recurrence (IBTR), or regional node recurrence, initial and subsequent distant metastases, and overall and cause-specific survival in women treated with conservative surgery and radiation based on whether or not radiation was targeted to the internal mammary nodes (IMN). Methods and Materials: From 1979–1994, 1383 women with Stage I–II breast cancer underwent wide excision, axillary node dissection with ≥10 nodes removed, and radiation. Median follow-up was 6 years; median age was 55 years. A total of 114 women had radiation targeted to the IMN with deep tangents and 1269 did not. Women who received IMN treatment were more often axillary node–positive (40% vs. 25%, p = 0.002), had central or inner quadrant tumors (61% vs. 40%, p = 0.001), and had T2 tumors (47% vs. 31%, p = 0.001). All axillary node–positive women received adjuvant chemotherapy and/or tamoxifen. For axillary node–negative women, 13% of the IMN treatment group received adjuvant systemic therapy compared to 37% of the no treatment group ( p = 0.001). Radiation was directed to the breast only in 97% of the axillary node–negative women who had IMN treatment and 99% of the no IMN treatment group. For axillary node–positive women, 98% of the IMN-treated group had radiation to the breast and supraclavicular nodes ± a posterior axillary field compared to 77% of the no IMN treatment group ( p = 0.001). There were no significant differences between the two groups for median age, menopausal status, histology, final surgical margin, estrogen and progesterone receptor status, or the number of positive nodes. Results: There were no significant differences in the 5- and 10-year cumulative incidence of an IBTR, regional node recurrence, initial or total distant metastases for the two groups. Similarly 5- and 10-year actuarial overall and cause-specific survival were not significantly different. However, subset analysis revealed a statistically significant increase in initial (29% vs. 15% at 10 yr, p = 0.002) and total (30% vs. 17% at 10 yr, p = 0.01) distant metastases and a significant decrease in cause-specific survival (76% vs. 89% at 10 yr, p = 0.02) for postmenopausal women who received IMN treatment. These findings could not be attributed to differences in the use of systemic therapy or the number of positive nodes. Axillary node–positive patients did not experience a significant decrease in initial (36% vs. 22% at 10 yr, p = 0.21) or total distant metastases (37% vs. 28% at 10 yr, p = 0.62) or a significant improvement in cause-specific survival (72% vs. 76% at 10 yr, p = 0.76) with IMN treatment regardless of whether the tumor was lateral or medial/central in location. IMN treatment was not associated with an increase in non–breast cancer deaths during this period of observation. Conclusions: This retrospective series was unable to identify a significant benefit for IMN irradiation in terms of distant metastases or cause-specific survival for the entire patient population, and in particular, for patients with positive axillary nodes and medially located lesions. The results of the proposed or ongoing prospective randomized trials will further address this controversial issue.

The role of the Mg 2+ cation in ATPsynthase studied by electron paramagnetic resonance using VO 2+ and Mn 2+ paramagnetic probes

The electron paramagnetic resonance (EPR), electron spin echo envelope modulation (ESEEM) and hyperfine sublevel correlation (HYSCORE) spectra of Mg 2+-depleted chloroplast F1-ATPase substituted with stoichiometric VO 2+ are reported. The ESEEM and HYSCORE spectra of the complex are dominated by the hyperfine and quadrupole interactions between the VO 2+ paramagnet and two different nitrogen ligands with isotropic hyperfine couplings | A 1|=4.11 MHz and | A 2|=6.46 MHz and nuclear quadrupole couplings e 2q Q 1≈3.89–4.49 MHz and e 2q Q 2≈1.91–2.20 MHz, respectively. Aminoacid functional groups compatible with these magnetic couplings include a histidine imidazole, the ε-NH 2 of a lysine residue, and the guanidinium group of an arginine. Consistent with this interpretation, very characteristic correlations are detected in the HYSCORE spectra between the 14N Δ M I=2 transitions in the negative quadrant, and also between some of the Δ M I=1 transitions in the positive quadrant. The interaction of the substrate and product ADP and ATP nucleotides with the enzyme has been studied in protein complexes where Mg 2+ is substituted for Mn 2+. Stoichiometric complexes of Mn·ADP and Mn·ATP with the whole enzyme show distinct and specific hyperfine couplings with the 31P atoms of the bonding phosphates in the HYSCORE (ADP, A( 31P β)=5.20 MHz; ATP, A( 31P β)=4.60 MHz and A( 31P γ)=5.90 MHz) demonstrating the role of the enzyme active site in positioning the di- or triphosphate chain of the nucleotide for efficient catalysis. When the complexes are formed with the isolated α or β subunits of the enzyme, the HYSCORE spectra are substantially modified, suggesting that in these cases the nucleotide binding site is only partially structured.

Nonlinear Matrix Iterative Processes and Generalized Coefficients of Ergodicity

A nonlinear matrix iterative process is a linear dynamical system for which there is a nonlinear feedback of the current vector on the entries of the matrix. Stability conditions for an asymptotically exponential solution are studied for such a process in the positive quadrant of $\mathbb{R}^{n}.$ The results hinge on a generalization of the coefficient of ergodicity of a nonnegative matrix.