Piecewise Linear Term Research Articles

Influence of time-to-diagnosis on time-to-percutaneous coronary intervention for emergency department ST-elevation myocardial infarction patients: Time-to-electrocardiogram matters.

Earlier electrocardiogram (ECG) acquisition for ST-elevation myocardial infarction (STEMI) is associated with earlier percutaneous coronary intervention (PCI) and better patient outcomes. However, the exact relationship between timely ECG and timely PCI is unclear. We quantified the influence of door-to-ECG (D2E) time on ECG-to-PCI balloon (E2B) intervention in this three-year retrospective cohort study, including patients from 10 geographically diverse emergency departments (EDs) co-located with a PCI center. The study included 576 STEMI patients excluding those with a screening ECG before ED arrival or non-diagnostic initial ED ECG. We used a linear mixed-effects model to evaluate D2E's influence on E2B with piecewise linear terms for D2E times associated with time intervals designated as ED intake (0-10 min), triage (11-30min), and main ED (>30min). We adjusted for demographic and visit characteristics, past medical history, and included ED location as a random effect. The median E2B interval was longer (76vs 68 min, p<0.001) in patients with D2E>10 min than in those with timely D2E. The proportion of patients identified at the intake, triage, and main ED intervals was 65.8%, 24.9%, and 9.7%, respectively. The D2E and E2B association was statistically significant in the triage phase, where a 1-minute change in D2E was associated with a 1.24-minute change in E2B (95% confidence interval [CI]: 0.44-2.05, p=0.003). Reducing D2E is associated with a shorter E2B. Targeting D2E reduction in patients currently diagnosed during triage (11-30 min) may be the greatest opportunity to improve D2B and could enable 24.9% more ED STEMI patients to achieve timely D2E.

A new chaotic jerk system with hidden heart-shaped attractor: dynamical analysis, multistability, connecting curves and its application in image encryption

Application of chaos in modeling natural phenomena and encryption encourages researchers to design new chaotic systems with exciting features. Here a chaotic jerk oscillator with different properties is proposed. Previous studies mainly used non-polynomial and piecewise linear terms to design the attractors’ shape. In the paper, the heart-shaped attractor is designed using just polynomial terms. This system is studied by considering its bifurcation diagram, Lyapunov exponent, and basin of attraction. These tools show that the proposed system has chaotic and periodic attractors that coexist in some parameter intervals. The oscillator does not have an equilibrium and has a heart-shaped attractor. Moreover, the connecting curves of the oscillator are considered to explore other structural properties. Numerical results confirm the analytical solutions for the system’s connecting curves. The interesting dynamics of the oscillator are used in an encryption and compression application.

Assessment of the joint effects of PM2.5 and pollen on childhood asthma exacerbation in the Philadelphia metropolitan region, 2011-2016

Background and aims: Mechanistic evidence suggests synergism of PM2.5 and pollen in their effects with asthma exacerbation (AE). Nevertheless, few epidemiologic studies have investigated health impacts of their joint exposures. We conducted a time-series study for the interactions between both triggers during the pollen season (Mar 18 – Oct 30) within the Philadelphia region. Methods: PM2.5 levels were averaged from the nearest monitor values for asthmatic individuals identified through electronic health records from the Children’s Hospital of Philadelphia, and pollen concentrations from a National Allergy Bureau-certified monitor in Center City, Philadelphia. We applied quasi-Poisson regression in distributed lag non-linear model (DLNM), with both PM2.5 (natural spline, 3df) and pollen (total/oak tree, grass, total/ragweed and other) (piecewise linear terms) in addition to interaction terms, and adjusted for temperature, relative humidity, long-term/seasonal trends, day-of-week, and holidays. For each PM2.5/pollen combination, one was treated as the main exposure, the other, the effect modifier in categorical terms for strata-specific estimates. Results: We observed increased RRs for the association between same-day total tree pollen and daily AE rates (90th vs. 0) at higher PM2.5 levels, 7-day preceding the exacerbation event (low: 0.95, 95% CI: 0.79 – 1.16; medium: 1.10, 95% CI: 0.93 – 1.31; 1.05, 95% CI: 0.86-1.28). Same-day association for late-season grass pollen was stronger, when followed a high PM2.5 concentration 5-day before the event (1.05, 95% CI: 0.97-1.14), than when following low PM2.5 (1.02, 95% CI: 0.95-1.09). However, we also observed decreased RRs for association between PM2.5 and AE, at increased tree/late-season grass pollen concentrations. Conclusion: Our study provides evidence suggesting interactions for several exposure combinations; however, many had no association with AE, and others suggested antagonistic effects. With mixed evidence, continued epidemiologic studies are called in the total impact of concurrent environmental asthma triggers. Keywords: PM2.5, pollen, interaction, children, asthma exacerbation (AE)

Nonlinear vibratory energy exchanges in a meta-cell

Meta-materials are utilized for bringing passive attenuation solution especially in the acoustics and vibration domains. Generally speaking, they are composed of an array or a chain of meta-cells. Here the vibratory energy exchanges between particles of a nonlinear meta-cell are studied. The meta-cell is composed of an outer mass which houses an inner mass with a compound nonlinear restoring forcing term. It is globally non-smooth, containing pure cubic and piece-wise linear terms, which constitutes a new type of nonlinearity for such mass-in-mass cells. The complexified form of system equations is treated by the multiple time scale method to find out its fast and slow dynamics, leading to determination of the slow invariant manifold as well as the singular and equilibrium points of the system. The compound nonlinear restoring forcing function of the inner mass makes the global geometry of the slow invariant manifold to be different from those of systems with pure cubic nonlinearities, for example, including four singular lines and two distinct unstable zones. Amplitude dependency of the frequency of such a nonlinear system in the conservative form is represented by the backbone curves. Furthermore, detected equilibrium points for different external forcing amplitudes are represented by three-dimensional frequency response curves. Finally, analytical predictions are confronted with numerical results obtained by direct time integration of the system equations. An application of such system can be the passive control of main systems via embedding another nonlinear oscillator inside it. Moreover, such system can also be extended in the form of an array to create meta-materials.

A Bayesian Multi-Outcome Analysis of Fine Particulate Matter and Cardiorespiratory Hospitalizations.

Short-term fine particulate matter (PM2.5) exposure is positively associated with acute cardiovascular and respiratory events. Understanding whether this association varies across specific cardiovascular and respiratory conditions has important biologic, clinical, and public health implications. We conducted a time-stratified case-crossover study of hospitalizations from 2000 through 2014 among United States Medicare beneficiaries aged 65+. The outcomes were hospitalizations with any of 57 cardiovascular and 32 respiratory discharge diagnoses. We estimated associations with two-day moving average PM2.5 as a piecewise linear term with a knot at PM2.5 = 25 g/m3. We used Multi-Outcome Regression with Tree-structured Shrinkage (MOReTreeS) to identify de novo groups of related diseases such that PM2.5 associations are: (1) similar within outcome groups; but (2) different between outcome groups. We adjusted for temperature, humidity, and individual-level characteristics. We introduce an R package, moretrees. Our dataset included 16,007,293 cardiovascular and 8,690,837 respiratory hospitalizations. Of 57 cardiovascular diseases, 51 were grouped and positively associated with PM2.5. We observed a stronger positive association for heart failure, which formed a separate group. We observed negative associations for groups containing the outcomes other aneurysm and intracranial hemorrhage. Of 32 respiratory outcomes, 31 were grouped and were positively associated with PM2.5. Influenza formed a separate group with a negative association. We used a new statistical approach, MOReTreeS, to uncover variation in the association between short-term PM2.5 exposure and hospitalizations for cardiovascular and respiratory causes controlling for patient characteristics, time trends, and environmental confounders.

Associations between Heat Index and Child Emergency and Hospital Visits in New York City

BACKGROUND AND AIM: Emerging literature has documented heat-related impacts on child health, yet few studies have evaluated the effects of heat among children of different age groups or compared emergency department (ED) with hospitalization risks, which may serve to indicate morbidity severity. We examine the differing associations between maximum heat index (a metric that combines maximum temperature and relative humidity) and risk of ED visits and hospitalizations among children by age group. METHODS: We used New York Statewide Planning and Research Cooperative System (SPARCS) data on children aged 0-18 years admitted to EDs (n = 2,252,550) and hospitals (n = 228,006) during the warm months (May-September) from 2005 to 2011. Using a time-stratified, case-crossover design, we estimated the risk of ED visits and hospitalizations associated with daily heat index for children of all ages and by age group. Heat index was modeled using distributed lag functions accumulated over lag 0 to 5 days using a linear term for ED visits and a piecewise linear term above the threshold of 90F for hospitalization. RESULTS:The average maximum heat index over the study period was 84.4F (range 48F-135F). Heat index conferred an increased risk of ED visits for children of all age groups, with the strongest effect observed among children 0-4, followed by those 13-18 and 5-12 years. For hospitalizations, an elevated risk was observed when heat index exceeded a threshold of 90F, and the effect was found only among adolescents 13-18 years. CONCLUSIONS:Heat impacts on child morbidity differ between ED visits and hospitalizations and by age groups. Young children, as well as older children and adolescents, are sensitive to heat effects. Our findings underscore the importance of focusing on children and adolescents in targeting heat illness prevention and emergency response activities, especially as global temperatures continue to rise. KEYWORDS: Temperature, Children and adolescents, Emergency department, Hospitalization, New York City

Proposing and Dynamical Analysis of a Hyperjerk Piecewise Linear Chaotic System with Offset Boostable Variable and Hidden Attractors

Designing chaotic systems with different properties helps to increase our knowledge about real-world chaotic systems. In this article, a piecewise linear (PWL) term is employed to modify a simple chaotic system and obtain a new chaotic model. The proposed model does not have any equilibrium for different values of the control parameters. Therefore, its attractor is hidden. It is shown that the PWL term causes an offset boostable variable. This feature provides more flexibility and controllability in the designed system. Numerical analyses show that periodic and chaotic attractors coexist in some fixed values of the parameters, indicating multistability. Also, the feasibility of the system is approved by designing field programmable gate arrays (FPGA).

Locally Active Memristor with Three Coexisting Pinched Hysteresis Loops and Its Emulator Circuit

Locally active memristors with multiple coexisting pinched hysteresis loops have attracted the attention of researchers. However, the currently reported multiple coexisting pinched hysteresis loops memristors are obtained by adding additional piecewise-linear terms into the original Chua corsage memristor. This paper proposes a novel locally active memristor by introducing a polynomial characteristic function into the state equation. The novel memristor has three coexisting pinched hysteresis loops, large relative range of active region and simple emulator circuit. The characteristics of the novel memristor such as power-off plot, coexisting pinched hysteresis loops and DC [Formula: see text]–[Formula: see text] plot are studied. The memristor is used in a Chua chaotic system to investigate the effects of locally active characteristic on the chaotic oscillation system. Furthermore, the memristor emulator and chaotic system are designed and implemented by commercial circuit elements. The hardware experiments are consistent with numerical simulations.

An Approximate Analytic Solution to a Non-Linear ODE for Air Jet Velocity Decay through Tree Crops Using Piecewise Linear Emulations and Rectangle Functions

The velocity of air that crosses the canopy of tree crops when using orchard sprayers is a variable that affects pesticide dispersion in the environment. Therefore, having an equation to describe air velocity decay through the canopy is of interest. It was necessary to start from a more general non-linear ordinary differential equation (ODE) obtained from the momentum theorem. After approximating the non-linearity with some piecewise linear terms, analytic solutions were found. Subsequently, to obtain a single equation for velocity decay, a combination of these solutions was proposed by using rectangle functions formed through the hyperbolic tangent function. This single equation was assessed in comparison to the experimental value obtained on a vineyard row by measuring the air velocity at exit of canopy. The results have shown good correspondence, with a mean relative error of 6.6%; moreover, there was no significant difference. To simplify, a combination of only two linearized solutions was also proposed. Again, there was no significant difference between the experimental value and the predicted one, but the mean relative error between the two equations was 3.6%.

Efficient response determination of a M-D-O-F gear model subject to combined periodic and stochastic excitations

The nonlinear response of a multi-degree-of-freedom (M-D-O-F) gear model subject to combined periodic and stochastic excitations is investigated by an efficient linearization scheme, accounting for the time-variant stiffness, and the backlash feature involved in the model. The steady-state response of the model is expressed as the sum of a periodic (deterministic) part, and of a zero-mean stochastic part. Further, the piecewise linear term accounting for the teeth backlash in the gear model is approximated by a 5-th order polynomial expression. Harmonic balance and statistical linearization schemes are used to derive a set of coupled nonlinear algebraic equations involving the amplitudes of the periodic part, and the statistical moments of the stochastic part of the solution. These equations can be solved iteratively by any of the apropos standard numerical algorithms. Examples of a two-stage gear system under combined excitations with wide-band spectrum stochastic excitation, and narrow-band spectrum stochastic excitation are considered. The derived numerical results demonstrate the reliability and efficiency of the proposed scheme by juxtaposition with data from pertinent Monte Carlo simulations.

Simplest hyperchaotic system with only one piecewise linear term

The objective of this Letter is to report the development of the simplest hyperchaotic system in comparison with all existing simplest hyperchaotic systems. The proposed system does not contain any non-linear (product, quadratic or cubic) term and has a total of eight terms including the only one piecewise linear term. The circuit of the proposed simplest hyperchaotic system is implemented in hardware with fewer components and without using a multiplier. To the best of the authors’ knowledge, such simplest hyperchaotic system is not reported in the literature.

Lunar cycle in homicides: a population-based time series study in Finland

ObjectiveTo test whether homicides in Finland vary according to moon phases.DesignA time series study.SettingFinland.Participants6808 homicides committed in 1961–2014.OutcomeDaily numbers of homicides.MethodThe daily numbers of homicides were related to eight moon...

Numerical simulation of the soft contact dynamics of an impacting bilinear oscillator

Systems constituted by moving components that make intermittent contacts with each other can be modelled by a system of ordinary differential equations containing piecewise linear terms. We consider a soft impact bilinear oscillator for which we obtain bifurcation diagrams, Lyapunov coefficients, return maps and phase portraits of the response. Besides Lyapunov coefficients diagrams, bifurcation diagrams are represented in terms of both non-dimensional time instants of contact (when the mass impacts the obstacle) and of portions of contact duration (the percentage-time interval when the material point is inside the obstacle) vs. non-dimensional external force frequency (or amplitude). The second kind of diagrams is needed because the contact duration (or the complementary flight time duration) are quantities that can easily be measured in an experiment aiming at confirming the validity of the present model. Lyapunov coefficients are evaluated converting the piecewise linear system of ordinary differential equations into a map, the so-called impact map, where time and velocity corresponding to a given impact are evaluated as functions of time and velocity corresponding to the previous impact. Thus, the usual methods related to this last map are used. The trajectories are represented in terms of return maps (all points in the time-velocity plane involved in the impact events) and phase portraits (the trajectory-itself in the displacement-velocity plane). In the bifurcation diagrams, transition between different responses is evidenced and a perfect correlation between chaotic (periodic) attractors and positive (negative) values of the maximum Lyapunov coefficient is found.

Reduced-complexity algorithms for near-optimal decoding of turbo TCM codes

A reduced-complexity modified decoding algorithm for turbo trellis-coded modulation (TTCM) is proposed and evaluated in terms of complexity and bit error rate (BER) performance in an additive white Gaussian noise channel. The algorithm uses an optimal approximation of the Jacobian logarithm, used in the so-called Log-MAP decoding, by means of the max operation and three piecewise-linear terms. Further computational complexity savings are obtained by applying this approximation only to the two largest values within the decoding step. To improve performance, the algorithms are also investigated using a scaling factor for the extrinsic information. Computer-simulated BER performance evaluation results and complexity comparisons are reported showing the near-optimal performance as well as noticeable implementation advantages of the proposed algorithms with respect to the Log-MAP decoding.

Efficient Nonlinear Vibration Analysis of the Forced Response of Rotating Cracked Blades

The efficient nonlinear vibration analysis of a rotating elastic structure with a crack is examined. In particular, the solution of the forced vibration response of a cracked turbine engine blade is investigated. Starting with a finite element model of the cracked system, the Craig–Bampton method of component mode synthesis is used to generate a reduced-order model that retains the nodes of the crack surfaces as physical degrees of freedom. The nonlinearity due to the intermittent contact of the crack surfaces, which is caused by the opening and closing of the crack during each vibration cycle, is modeled with a piecewise linear term in the equations of motion. Then, the efficient solution procedure for solving the resulting nonlinear equations of motion is presented. The approach employed in this study is a multiharmonic hybrid frequency∕time-domain technique, which is an extension of the traditional harmonic balance method. First, a simple beam model is used to perform a numerical validation by comparing the results of the new method to those from transient finite element analysis (FEA) with contact elements. It is found that the new method retains good accuracy relative to FEA while reducing the computational costs by several orders of magnitude. Second, a representative blade model is used to examine the effects of crack length and rotation speed on the resonant frequency response. Several issues related to the rotation are investigated, including geometry changes of the crack, shifts in resonant frequencies, and the existence of multiple solutions. For the cases considered, it is found that the nonlinear vibration response exhibits the jump phenomenon only when rotation is included in the model.

A Finite Element for Piezoelectric Multilayered Plates: Combined Higher-order and Piecewise Linear C0 Formulation

A finite element is presented for the static and dynamic analysis of smart multilayered plates. A fourth-order expansion is combined with a piecewise linear term to describe the distribution of the in-plane displacements through the thickness. The out-of-plane displacement is assumed constant through the thickness. Both free edges and interlaminar continuity conditions are satisfied, thus reducing the number of elastic unknowns to nine whatever be the number of layers. To this aim, two redundant unknowns describing the two derivatives of the out-of-plane displacement with respect to the in-plane coordinates are introduced and related to the out-of-plane displacement by the use of penalty functions. A quadratic distribution of the electric potential is used inside each piezoelectric layer to completely account for the piezoelectric coupling effects.

Piecewise linear emulation of propagating fronts as a method for determining their speeds.

We use piecewise linear terms to emulate the polynomial nonlinear terms in a typical reaction-diffusion equation, replacing it thus with a set of simple linear inhomogeneous differential equations. The resulting analytic solution constitutes an excellent approximation to the exact propagating front, as is explicitly shown in the case of cubic and quintic nonlinearities, yielding also the correct value for the physically selected speed of the observable front. Such a piecewise linear emulation can be used for any nonlinearity, giving therefore a very reliable and accurate method for determining the selected speed of fronts invading unstable states, especially pushed fronts.

Piecewise linear emulator of the nonlinear Schrödinger equation and the resulting analytic solutions for Bose-Einstein condensates

We emulate the cubic term Psi(3) in the nonlinear Schrödinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a delta function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Psi(3) one. In particular, it can be used for the nonlinear Schrödinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions.

“LORENZ ATTRACTOR” FROM DIFFERENTIAL EQUATIONS WITH PIECEWISE-LINEAR TERMS

In this paper we present a simple piecewise-linear circuit which exhibits a chaotic attractor similar to that observed from the Lorenz equation. Whereas the nonlinearities in the Lorenz equation consists of two product terms between two state variables, the nonlinearities in our circuit consists of two piecewise-linear terms.

GENERALIZATIONS OF THE CHUA EQUATIONS

In this paper we present two generalizations of the equations governing Chua’s circuit. In order to obtain the first generalization we simplify Chua’s equations by replacing the piecewise-linear term with a signum function. The resulting simplified system produces a double scroll similar to the one observed experimentally in Chua’s circuit. What is significant about this simplified system is that it can be reduced to what we shall call a two-dimensional single scroll, and from the two-dimensional single scroll we are able to derive a one-dimensional map. This entire derivation is carried out analytically, in contrast to the one-dimensional map analysis that has been carried out for the Lorenz equations which is based on axioms. After we have carried out our analysis for this simplified version of Chua’s equations, we use these equations as a guide to the construction of the first generalization to be presented in this paper. We call this a type-I generalization of Chua’s equations. The generalization consists in using a two-dimensional autonomous flow as a component in a three-dimensional autonomous flow in such a way that the resulting equations will have double scroll attractors similar to those observed experimentally in Chua’s circuit. The value of this generalization is that: (1) it provides a building block approach to the construction of chaotic circuits from simpler two-dimensional components which are not chaotic by themselves. In so doing it provides an insight into how chaotic systems can be built up from simple nonchaotic parts; (2) it illustrates a precise relationship between three-dimensional flows and one-dimensional maps. Of particular significance in this regard is a recent paper of Misiurewicz [1993], which analytically connects the two-dimensional single scroll to the class of unimodal maps, thus providing a framework within which a theory linking unimodal maps to three-dimensional flows may be possible. The second generalization is suggested by considering three-dimensional flows whose only nonlinearities are sigmoid, sgn, or piecewise-linear functions. Clearly, such flows are a generalization of the Chua equations. We call these equations type-II generalization Chua equations. The significance of this direction of investigation is that attractors similar to the Lorenz and Rössler attractors can be produced from type-II generalized Chua equations in a building block approach using only piecewise-linear vector fields. As a result we have a method of producing the Lorenz and Rössler dynamics in a circuit without the use of multipliers. This suggests that the type-II generalized Chua equations are in some sense fundamental in that the dynamics of the three most important autonomous three-dimensional differential equations producing chaos are seen as variations of a single class of equations whose nonlinearities are generalizations of the Chua diode.