Non-random Case Research Articles

A Comparative Study on Shoulder Rotational Strength, Range of Motion and Proprioception between the Throwing Athletes and Non-athletic Persons

The repetitive micro traumatic stresses placed on the athletes shoulder joint complex during the throwing motion challenge the surrounding tissues. The purpose of this study was to compare shoulder rotational strength, range of motion and proprioception between the throwing athletes and non-athletic persons. Fifteen throwing athletes and 15 non-athletes participated in a nonrandom case - control study. Strength of shoulder rotational movements was tested with a hand held dynamometer. The ranges of internal and external rotation of shoulder were measured by a standard goniometer. The ability of subjects to replicate the target position and kinesthetic sense was examined on the subjects' right shoulder by using a continuous passive motion device. Independent and paired t tests were used to statistically analyze between and within group differences. No significant difference was detected on the range of internal rotation between throwing athletes and non-athletic candidates (P=0.3). The range of external rotation was significantly more in athletic subjects (P=0.03). The results also showed that throwing athletes demonstrated a significantly higher isometric strength of shoulder external and internal rotation than the non-athletic group (P<0.05). However, the comparison of the internal and external rotation strength of dominant side in each group showed that throwing athletes showed a significant lower isometric strength of shoulder external rotation than internal rotation (P<0.001). It was also demonstrated higher joint position acuity in the throwing athletes than non athlete subjects (P=0.01). The repetitive nature of overhead throwing and the high forces that it causes result in adaptive changes of the dominant extremity. Throwing can lead to mobility, strength and neural adaptation.

The mixed-spins 1/2 and 3/2 Blume—Capel model with a random crystal field

The random crystal field (RCF) effects are investigated on the phase diagrams of the mixed-spins 1/2 and 3/2 Blume-Capel (BC) model on the Bethe lattice. The bimodal random crystal field is assumed and the recursion relations are employed for the solution of the model. The system gives only the second-order phase transitions for all values of the crystal fields in the non-random bimodal distribution for given probability. The randomness does not change the order of the phase transitions for higher crystal field values, i.e., it is always second-order, but it may introduce first-order phase transitions at lower negative crystal field values for the probability in the range about 0.20 and 0.45, which is only the second-order for the non-random case in this range. Thus our work claims that randomness may be used to induce first-order phase transitions at lower negative crystal field values at lower probabilities.

A Central Limit Theorem for Time-Dependent Dynamical Systems

The work by Ott et al. (Math. Res. Lett. 16:463–475, 2009) established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled Birkhoff-like partial sums of appropriate test functions. A substantial part of the problem is to ensure that the variances of the partial sums tend to infinity (cf. the zero-cohomology condition in the autonomous case). In fact, the present paper is the first one where non-random examples are also found, which are not small perturbations of a given map. Our approach uses martingale approximation technique in the form of Sethuraman and Varadhan (Electron. J. Probab. 10:121–1235, 2005).

Asymptotic evolution of quantum walks with random coin

We study the asymptotic position distribution of general quantum walks on a lattice, including walks with a random coin, which is chosen from step to step by a general Markov chain. In the unitary (i.e., nonrandom) case, we allow any unitary operator which commutes with translations and couples only sites at a finite distance from each other. For example, a single step of the walk could be composed of any finite succession of different shift and coin operations in the usual sense, with any lattice dimension and coin dimension. We find ballistic scaling and establish a direct method for computing the asymptotic distribution of position divided by time, namely as the distribution of the discrete time analog of the group velocity. In the random case, we let a Markov chain (control process) pick in each step one of finitely many unitary walks, in the sense described above. In ballistic order, we find a nonrandom drift which depends only on the mean of the control process and not on the initial state. In diffusive scaling, the limiting distribution is asymptotically Gaussian, with a covariance matrix (diffusion matrix) depending on momentum. The diffusion matrix depends not only on the mean but also on the transition rates of the control process. In the nonrandom limit, i.e., when the coins chosen are all very close or the transition rates of the control process are small, leading to long intervals of ballistic evolution, the diffusion matrix diverges. Our method is based on spatial Fourier transforms, and the first and second order perturbation theory of the eigenvalue 1 of the transition operator for each value of the momentum.

MCMC-based estimation methods for continuous longitudinal data with non-random (non)-monotone missingness

The analysis of incomplete longitudinal data requires joint modeling of the longitudinal outcomes (observed and unobserved) and the response indicators. When non-response does not depend on the unobserved outcomes, within a likelihood framework, the missingness is said to be ignorable, obviating the need to formally model the process that drives it. For the non-ignorable or non-random case, estimation is less straightforward, because one must work with the observed data likelihood, which involves integration over the missing values, thereby giving rise to computational complexity, especially for high-dimensional missingness. The stochastic EM algorithm is a variation of the expectation–maximization (EM) algorithm and is particularly useful in cases where the E (expectation) step is intractable. Under the stochastic EM algorithm, the E-step is replaced by an S-step, in which the missing data are simulated from an appropriate conditional distribution. The method is appealing due to its computational simplicity. The SEM algorithm is used to fit non-random models for continuous longitudinal data with monotone or non-monotone missingness, using simulated, as well as case study, data. Resulting SEM estimates are compared with their direct likelihood counterparts wherever possible.

On the Mixing Time of the 2D Stochastic Ising Model with “Plus” Boundary Conditions at Low Temperature

We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature β and random boundary conditions τ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to + (equal to −). For β large enough we show that for any \({\varepsilon >0 }\) there exists \({c=c(\beta,\varepsilon)}\) such that the corresponding mixing time T mix satisfies \({{\rm lim}_{L\to\infty}\,{\bf P}\left(T_{\rm mix}\ge {\rm exp}({cL^\varepsilon})\right) =0}\). In the non-random case τ ≡ + (or τ ≡ −), this implies that \({T_{\rm mix}\le {\rm exp}({cL^\varepsilon})}\). The same bound holds when the boundary conditions are all + on three sides and all − on the remaining one. The result, although still very far from the expected Lifshitz behavior T mix = O(L 2), considerably improves upon the previous known estimates of the form \({T_{\rm mix}\le {\rm exp}({c L^{\frac 12 + \varepsilon}})}\). The techniques are based on induction over length scales, combined with a judicious use of the so-called “censoring inequality” of Y. Peres and P. Winkler, which in a sense allows us to guide the dynamics to its equilibrium measure.

RANDOM COINCIDENCE POINTS AND RANDOM FIXED POINTS OF MULTIFUNCTIONS IN METRIC SPACES

In this paper, we present some new random coincidence point and random fixed point theorems for multifunctions in separable complete metric spaces, which improve some existing results in the literature (even some results in the non-random case).

Effects of disorder on a lattice Ginzburg-Landau model ofd-wave superconductors and superfluids

We study the effects of quenched disorder on the two-dimensional $d$-wave superconductors (SCs) at zero temperature by Monte Carlo simulations. The model is defined on the three-dimensional (3D) lattice and the SC pair field is put on each spatial link as motivated in the resonating-valence-bond theory of the high-${T}_{c}$ SCs. For the nonrandom case, the model exhibits a second-order phase transition to a SC state as density of charge carriers is increased. It belongs to the universality class different from that of the 3D $XY$ model. Quenched disorders (impurities) are introduced both in the hopping amplitude and the plaquette term of pair fields. Then the second-order transition disappears at a critical concentration of quenched disorder, ${p}_{c}\ensuremath{\simeq}15%$. Implication of the results to cold atomic systems in optical lattices is also discussed.

RANDOM COINCIDENCE POINTS AND RANDOM FIXED POINTS OF MULTIFUNCTIONS IN METRIC SPACES

In this paper, we present some new random coincidence point and random fixed point theorems for multifunctions in separable complete metric spaces, which improve some existing results in the literature (even some results in the non-random case).

Decays in quantum hierarchical models

We study the dynamics of a simple model for quantum decay, where a single state is coupled to a set of discrete states, the pseudocontinuum, each coupled to a real continuum of states. We find that for constant matrix elements between the single state and the pseudocontinuum the decay occurs via one state in a certain region of the parameters, involving the Dicke and quantum Zeno effects. When the matrix elements are random, several cases are identified. For a pseudocontinuum with small bandwidth there are weakly damped oscillations in the probability to be in the initial single state. For intermediate bandwidth one finds mesoscopic fluctuations in the probability with amplitude inversely proportional to the square root of the volume of the pseudocontinuum space. They last for a long time compared to the nonrandom case.

Correlation and prediction the activity coefficients and solubility of amino acids and simple peptide in aqueous solution using the modified local composition model

In this work, the modified Wilson model was used to obtain the activity coefficients of amino acids and simple peptides in non-electrolyte aqueous solutions. The Wilson model was modified using the new local mole fraction proposed by Zhao et al. and non-random case for the reference state. The binary interaction parameters (BIP) of the modified Wilson model for amino acid–water pairs were obtained using the experimental data of the activity coefficients for amino acids available in the literature. The modified Wilson model was also used to correlate the solubility of amino acids in water and the values of Δ h/ R, Δ s/ R, and Δ g/ R of the solutions studied were reported. The results obtained showed that the modified Wilson model can accurately correlate the activity coefficients as well as the solubility of amino acids and simple peptides in aqueous solutions. Also the modified Wilson model was coupled with the Pazuki–Rohani model to correlate the mean ionic activity coefficients of electrolytes in aqueous amino acid solutions. The results showed that the proposed model can accurately correlate the activity coefficients of the electrolytes in aqueous amino acid solution.

The Global Sunyaev-Zel'dovich Effect of the Cluster Population and Its Detectability in Cosmic Microwave Background Maps

Clusters of galaxies can distort the cosmological signal in the cosmic microwave background (CMB) temperature fluctuations maps through the Sunyaev-Zel'dovich (SZ) effect. The analysis of this effect, which depends on the properties of the cluster population and its spatial distribution, could therefore be used to constrain the cluster mass function and its evolution. We present the global SZ effect expected for a cluster population extending to z = 0.2, z = 0.5, and z = 0.8, for random and nonrandom spatial distributions. The local population (up to z = 0.2) was built according to current results and in agreement with the XBACs data for the high-mass fraction of the cluster mass distribution. The resulting signal from the global SZ effect is well under the noise level of the Wilkinson Microwave Anisotropy Probe (WMAP) data for both distributions. The extension of the population to higher redshifts was done keeping the same mass distribution (without evolution). For the Poissonian distribution only at multipoles l ≥ 300 in the z = 0.8 case, the effects are over the noise level of the WMAP data. However, for the more realistic, nonrandom distribution case that signal would be detectable in the WMAP maps for multipoles higher than l = 100 at z = 0.5 and for nearly all multipoles at z = 0.8, in clear conflict with the data. The analysis of high-quality CMB data, as those expected from the Planck mission, will allow us to determine the contribution from the cluster population and to determine the evolution of clusters even at low redshift.

Using geographic information systems and spatial and space-time scan statistics for a population-based risk analysis of the 2002 equine West Nile epidemic in six contiguous regions of Texas

BackgroundIn 2002, West Nile virus (WNV) first appeared in Texas. Surveillance data were retrospectively examined to explore the temporal and spatial characteristics of the Texas equine WNV epidemic in 2002. Using Geographic Information Systems (GIS) and the Spatial and Space-Time Scan (SaTScan) statistics, we analyzed 1421 of the reported equine WNV cases from six contiguous state Health Service Regions (HSRs), comprising 158 counties, in western, northern, central and eastern Texas.ResultsTwo primary epidemic peaks occurred in Epidemiological (Epi) week 35 (August 25 to 31) and Epi week 42 (October 13 to 19) of 2002 in the western and eastern part of the study area, respectively. The SaTScan statistics detected nine non-random spatio-temporal equine case aggregations (mini-outbreaks) and five unique high-risk areas imbedded within the overall epidemic.ConclusionThe 2002 Texas equine WNV epidemic occurred in a bi-modal pattern. Some "local hot spots" of the WNV epidemic developed in Texas. The use of GIS and SaTScan can be valuable tools in analyzing on-going surveillance data to identify high-risk areas and shifts in disease clustering within a large geographic area. Such techniques should become increasingly useful and important in future epidemics, as decisions must be made to effectively allocate limited resources.

Condensation in a Disordered Infinite-Range Hopping Bose–Hubbard Model

We study Bose-Einstein Condensation (BEC) in the Infinite-Range Hopping Bose-Hubbard model for repulsive on-site particle interaction in presence of ergodic random one-site potentials with different distributions. We show that the model is exactly soluble even if the on-site interaction is random. But in contrast to the non-random case, we observe here new phenomena: instead of enhancement of BEC for perfect bosons, for constant on-site repulsion and discrete distributions of the single-site potential there is suppression of BEC at some fractional densities. We show that this suppression appears with increasing disorder. On the other hand, the BEC suppression at integer densities may disappear, if disorder increases. For a continuous distribution we prove that the BEC critical temperature decreases for small on-site repulsion while the BEC is suppressed at integer values of density for large repulsion. Again, the threshold for this repulsion gets higher, when disorder increases.

Generalized Tangential Sphere Bound on the MLDecoding Error Probability of Linear Binary Block Codes in AWGN Interference

The error probability of maximum-likelihood (ML) soft-decision decoded binary block codes rarely accepts nice closed forms. In addition, for long codes, ML decoding becomes prohibitively complex. Nevertheless, bounds on the performance of ML decoded systems provide insight into the effect of system parameters on the overall system performance as well as a measure of goodness of the suboptimum decoding methods used in practice. Using the so-called Gallager's first bounding technique (involving a so-called Gallager region) and within the framework of tangential sphere bound (TSB) of Poltyrev, we develop a general bound referred to as the generalized TSB (GTSB). The Gallager region is chosen to be a general hyper-surface of revolution (HSR) which is optimized to tighten the bound. The search for the optimal Gallager region is a classical problem dating back to Gallager's thesis in the early 1960s. For the random coding case, Gallager provided the optimal solution in a closed form while for the nonrandom case the problem has been an active area of research in information theory for many years. We prove that for a sphere code, the optimal HSR within the proposed GTSB is a hyper-cone. This will climax to the TSB of Poltyrev, one of the tightest bounds ever developed for binary block codes, and therefore terminates the search for a better Gallager region in the groundwork of the GTSB.

Reactive particles in random flows.

We study the dynamics of chemically or biologically active particles advected by open flows of chaotic time dependence, which can be modeled by a random time dependence of the parameters on a stroboscopic map. We develop a general theory for reactions in such random flows, and derive the reaction equation for this case. We show that there is a singular enhancement of the reaction in random flows, and this enhancement is increased as compared to the nonrandom case. We verify our theory in a model flow generated by four point vortices moving chaotically.

Effect of external Gaussian random field on phonon spectrum of linear atomic chains

We present the theoretical study of the effect of external random field characterized by a Gaussian probability distribution function on the continuous phonon spectrum of one-dimensional (1D) chain, based on the Jacobian matrix method. The cumulative effect of the random field and simple isotopic defect is studied analytically and numerically. The Gaussian random field removes a square-root divergence appearing in the phonon spectrum of ideal 1D chain. The impurity phonon DOS shows strong dependence on the variance and the mean of the random field and exhibits very different behavior from the non-random case: the continuous spectrum is expanded and the δ-peak, describing discrete impurity vibrations in the non-random chain with the impurity, falls into a continuous zone.

A random fixed point iteration for three random operators on uniformly convex Banach spaces

In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The results is also an extension of a known theorem in the corresponding non-random case.

A common unique fixed point theorem for two random operators in Hilbert spaces

We construct a sequence of measurable functions and consider its convergence to the unique common random fixed point of two random operators defined on a nonempty closed subset of a separable Hilbert space. The corresponding result in the nonrandom case is also obtained.

Effects of cloud overlap on radiative feedbacks

The column radiative model (CRM) of the National Center for Atmospheric Research Community Climate Model has been used to test feedbacks associated with changes in monthly mean cloudiness for atmospheres with two different prescriptions of how clouds overlap in the vertical. The first specification is the default CRM random overlap assumption. The second, called the nonrandom case, uses an estimate of the observed overlap based upon an analysis of satellite- and surface-based observations. The results are presented primarily in terms of the changes in top-of-the-atmosphere net cloud radiative forcing resulting from a 25% increase in total cloud water and separate 16.5% increases in low, middle and high cloud layer amounts and differences that occurred during the 1987 El Nino/Southern Oscillation (ENSO) event. Overall, the random model is about 20% more sensitive to 16.5% increases in low clouds than the nonrandom model, but the nonrandom model is about twice as sensitive to increases in middle cloud. Differences in sensitivity for changes in high cloud amount and total cloud water are relatively small. In the areas near the large sea surface temperature anomalies the 1987 ENSO related departures in the nonrandom model are 0.5–2 Wm−2 greater than for the random model. Thus, this analysis strongly suggests that accurate specification of overlap in climate models is critical to the calculation of the appropriate radiative feedbacks and sensitivities of models to external forcing such as increased carbon dioxide or sulfate aerosols.