Functional Limit Research Articles

The Susceptibility of the Aortic Root: Porcine Aortic Rupture Testing Under Cardiopulmonary Bypass

An earlier study on the functional limits of the aneurysmal aortic root determined that a pig root is susceptible to failure at high aortic pressures levels. This study established a pig rupture model using cardiopulmonary bypass to determine the most susceptible region of the aortic root under the highest pressures achievable using continuous flow, and what changes occur in these regions on macroscopic and histological levels. This information may help guide clinical management of aortic root and ascending aorta pathology.

YOLO V5 for Vehicle Plate Detection in DKI Jakarta

The odd-even rule on vehicle number plates in DKI Jakarta aims to reduce congestion that occurs in DKI Jakarta. The application of these regulations is constrained by the limitations of the manual supervision function by officers. This problem can be overcome by implementing intelligence in the form of detecting number plate objects with the YOLO v5 algorithm and the character extraction process with Optical Character Recognition technology using Tesseract OCR. Object detection technology will detect objects in the form of vehicle plates. The OCR method can extract the characters on the number plate, the extraction results can be processed into parameter categorization so that the program can distinguish between vehicles that violate the rules and do not violate the rules automatically and more effectively and minimize errors. Based on this research, the average percentage of objects detected in each video is 92.38%, and the average confidence value obtained in object detection is between 75.55%. The success rate of the character extraction process on number plates is 95.45%, and the average proportion according to the detected number plate category is 97.2%. The implementation of the YOLO Algorithm has succeeded in detecting license plates with odd and even categories on videos that can provide signs and save violations of vehicles that violate the odd and even rules.

Spherical Induced Ensembles with Symplectic Symmetry

We consider the complex eigenvalues of the induced spherical Ginibre ensemble with symplectic symmetry and establish the local universality of these point processes along the real axis. We derive scaling limits of all correlation functions at regular points both in the strong and weak non-unitary regimes as well as at the origin having spectral singularity. A key ingredient of our proof is a derivation of a differential equation satisfied by the correlation kernels of the associated Pfaffian point processes, thereby allowing us to perform asymptotic analysis.

Determining Key Parameters with Data-Assisted Analysis of Conditionally Automated Driving

In conditionally automated driving, a vehicle issues a take-over request when it reaches the functional limits of self-driving, and the driver must take control. The key driving parameters affecting the quality of the take-over (TO) process have yet to be determined and are the motivation for our work. To determine these parameters, we used a dataset of 41 driving and non-driving parameters from a previous user study with 216 TOs while performing a non-driving-related task on a handheld device in a driving simulator. Eight take-over quality aspects, grouped into pre-TO predictors (attention), during-TO predictors (reaction time, solution suitability), and safety performance (off-road drive, braking, lateral acceleration, time to collision, success), were modeled using multiple linear regression, support vector machines, M5’, 1R, logistic regression, and J48. We interpreted the best-suited models by highlighting the most influential parameters that affect the overall quality of a TO. The results show that these are primarily maximal acceleration (88.6% accurate prediction of collisions) and the TOR-to-first-brake interval. Gradual braking, neither too hard nor too soft, as fast as possible seems to be the strategy that maximizes the overall TO quality. The position of the handheld device and the way it was held prior to TO did not affect TO quality. However, handling the device during TO did affect driver attention when shorter attention times were observed and drivers held their mobile phones in only one hand. In the future, automatic gradual braking maneuvers could be considered instead of immediate full TOs.

Calculation Method of Loose Pressure in Surrounding Rock Mass

With the implementation of the regional coordinated development strategy, traffic flow has grown explosively. The construction of a larger tunnel section becomes an effective way to solve the highway network’s insufficient transport capability problem. Currently, there is little research on the factors influencing and methods of calculating the loose pressure in the surrounding rock mass for highway tunnels with super-large cross-sections. Based on the Bifurcation Tunnel, which is one of the sign projects in the past five years, this paper discusses the influencing factors for the range of loose zone in deeply buried tunnels using a combination of a numerical analysis and an orthogonal test. The weight of influencing factors is calculated via an efficiency evaluation method. This paper establishes a limit analysis model of the loose pressure in the surrounding rock mass under a non-linear failure criterion based on the fitted boundary function and upper bound limit analysis method and deduces the correlations of the loose pressure. The distribution law of the loose pressure, obtained via the limit analysis method, is consistent with the pressure-monitoring results, verifying the correctness of the proposed calculation method. This study can provide a calculation basis for the design of a supporting structure and the selection of similar super-section tunnel projects.

Queuing models with Mittag-Leffler inter-event times

We study three non-equivalent queueing models in continuous time that each generalise the classical M/M/1 queue in a different way. Inter-event times in all models are Mittag-Leffler distributed, which is a heavy tail distribution with no moments. For each of the models we answer the question of the queue being at zero infinitely often (the ‘recurrence’ regime) or not (the transient regime). Aside from this question, the different analytical properties of each models allow us to answer a number of questions such as existence and description of equilibrium distributions, mixing times, asymptotic behaviour of return probabilities and moments and functional limit theorems.

Free boundary dimers: random walk representation and scaling limit

We study the dimer model on subgraphs of the square lattice in which vertices on a prescribed part of the boundary (the free boundary) are possibly unmatched. Each such unmatched vertex is called a monomer and contributes a fixed multiplicative weight z>0 to the total weight of the configuration. A bijection described by Giuliani et al. (J Stat Phys 163(2):211–238, 2016) relates this model to a standard dimer model but on a non-bipartite graph. The Kasteleyn matrix of this dimer model describes a walk with transition weights that are negative along the free boundary. Yet under certain assumptions, which are in particular satisfied in the infinite volume limit in the upper half-plane, we prove an effective, true random walk representation for the inverse Kasteleyn matrix. In this case we further show that, independently of the value of z>0, the scaling limit of the centered height function is the Gaussian free field with Neumann (or free) boundary conditions. It is the first example of a discrete model where such boundary conditions arise in the continuum scaling limit.

Functional Convergence of Berry’s Nodal Lengths: Approximate Tightness and Total Disorder

We consider Berry’s random planar wave model (J Phys A 10(12):2083–2092, 1977), and prove spatial functional limit theorems—in the high-energy limit—for discretized and truncated versions of the random field obtained by restricting its nodal length to rectangular domains. Our analysis is crucially based on a detailed study of the projection of nodal lengths onto the so-called second Wiener chaos, whose high-energy fluctuations are given by a Gaussian total disorder field indexed by polygonal curves. Such an exact characterization is then combined with moment estimates for suprema of stationary Gaussian random fields, and with a tightness criterion by Davydov and Zitikis (Ann Inst Stat Math 60(2):345–365, 2008).

Some limitations of the Fraser-Suzuki function for fitting thermokinetic curves

Mathematical deconvolution (MD) can offer a simple way to solve independent multistep kinetics. However, there are always doubts about the cases in which it loses efficiency.This work analyzes the adjustability of the Fraser-Suzuki function (FSF) for processes with F0, D1, and Pn models. Curves dα/dt vs t for were simulated and fitted using the FSF for each case. Their kinetic parameters were determined and compared with the real ones. Furthermore, an example of deconvolution was analyzed. The results show that the FSF fit does not lead to satisfactory results when applied to dα/dt vs t curves that show sharp peaks and sudden decays.This work is not intended to discourage MD use since it has led to correct parameters in many investigations. However, the aim is to show examples of limitations so that the analyst can choose other appropriate approaches. Therefore, MD should always be used with caution and judgment.

Random normal matrices in the almost-circular regime

We study random normal matrix models whose eigenvalues tend to be distributed within a narrow “band” around the unit circle of width proportional to 1∕n, where n is the size of matrices. For general radially symmetric potentials with various boundary conditions, we derive the scaling limits of the correlation functions, some of which appear in the previous literature notably in the context of almost-Hermitian random matrices. We also obtain that fluctuations of the maximal and minimal modulus of the ensembles follow the Gumbel or exponential law depending on the boundary conditions.

Functional limit theorems for random walks perturbed by positive alpha-stable jumps

Let ξ1, ξ2,… be i.i.d. random variables of zero mean and finite variance and η1, η2,… positive i.i.d. random variables whose distribution belongs to the domain of attraction of an α-stable distribution, α∈(0,1). The two collections are assumed independent. We consider a Markov chain with jumps of two types. If the present position of the Markov chain is positive, then the jump ξk occurs; if the present position of the Markov chain is nonpositive, then the jump ηk occurs. We prove functional limit theorems for this and two closely related Markov chains under Donsker’s scaling. The weak limit is a nonnegative process (X(t))t≥0 satisfying a stochastic equation dX(t)=dW(t)+dUα(LX(0)(t)), where W is a Brownian motion, Uα is an α-stable subordinator which is independent of W, and LX(0) is a local time of X at 0. Also, we explain that X is a Feller Brownian motion with a ‘jump-type’ exit from 0.

Free Cooling for Saving Energy: Technical Market Analysis of Dry, Wet, and Hybrid Cooling Based on Manufacturer Data

In light of energy and climate targets, free cooling unlocks a major resource-saving potential compared to refrigeration. To fill the knowledge gap in quantifying this saving potential, we aim to specify the physical and technical limits of cooling tower applications and provide comprehensive data on electricity and water consumption. For this purpose, we distinguish six types of package-type cooling towers: dry, closed wet, open wet, and three types of hybrid systems; defining one generalized system for all types enables comparability. Subsequently, we collect data from 6730 system models of 27 manufacturers, using technical information from data sheets and additional material. The analysis reveals, for example, specific ranges of electricity demand from 0.01 to 0.06 kWel/kWth and highlights influencing factors, including type and operating point. Refrigeration systems would consume approximately ten times more electricity per cooling capacity. Furthermore, the evaluation demonstrates the functional limits, for example, the minimum cooling temperatures. Minimum outlet temperatures using evaporative cooling are up to 16 K lower than for dry cooling. The collected data have crucial implications for designing and optimizing cooling systems, including potential analysis of free cooling and efficiency assessment of cooling towers in operation.

Functional Reference Limits: Describing Physiological Relationships and Determination of Physiological Limits for Enhanced Interpretation of Laboratory Results.

Functional reference limits describe key changes in the physiological relationship between a pair of physiologically related components. Statistically, this can be represented by a significant change in the curvature of a mathematical function or curve (e.g., an observed plateau). The point at which the statistical relationship changes significantly is the point of curvature inflection and can be mathematically modeled from the relationship between the interrelated biomarkers. Conceptually, they reside between reference intervals, which describe the statistical boundaries of a single biomarker within the reference population, and clinical decision limits that are often linked to the risk of morbidity or mortality and set as thresholds. Functional reference limits provide important physiological and pathophysiological insights that can aid laboratory result interpretation. Laboratory professionals are in a unique position to harness data from laboratory information systems to derive clinically relevant values. Increasing research on and reporting of functional reference limits in the literature will enhance their contribution to laboratory medicine and widen the evidence base used in clinical decision limits, which are currently almost exclusively contributed to by clinical trials. Their inclusion in laboratory reports will enhance the intellectual value of laboratory professionals in clinical care beyond the statistical boundaries of a healthy reference population and pave the way to them being considered in shaping clinical decision limits. This review provides an overview of the concepts related to functional reference limits, clinical examples of their use, and the impetus to include them in laboratory reports.

The Rates of Convergence for Functional Limit Theorems with Stable Subordinators and for CTRW Approximations to Fractional Evolutions

From the initial development of probability theory to the present days, the convergence of various discrete processes to simpler continuous distributions remains at the heart of stochastic analysis. Many efforts have been devoted to functional central limit theorems (also referred to as the invariance principle), dealing with the convergence of random walks to Brownian motion. Though quite a lot of work has been conducted on the rates of convergence of the weighted sums of independent and identically distributed random variables to stable laws, the present paper is the first to supply the rates of convergence in the functional limit theorem for stable subordinators. On the other hand, there is a lot of activity on the convergence of CTRWs (continuous time random walks) to processes with memory (subordinated Markov process) described by fractional PDEs. Our second main result is the first one yielding rates of convergence in such a setting. Since CTRW approximations may be used for numeric solutions of fractional equations, we obtain, as a direct consequence of our results, the estimates for error terms in such numeric schemes.

Infinite ergodicity in generalized geometric Brownian motions with nonlinear drift.

Geometric Brownian motion is an exemplary stochastic processes obeying multiplicative noise, with widespread applications in several fields, e.g., in finance, in physics, and biology. The definition of the process depends crucially on the interpretation of the stochastic integrals which involves the discretization parameter α with 0≤α≤1, giving rise to the well-known special cases α=0 (Itô), α=1/2 (Fisk-Stratonovich), and α=1 (Hänggi-Klimontovich or anti-Itô). In this paper we study the asymptotic limits of the probability distribution functions of geometric Brownian motion and some related generalizations. We establish the conditions for the existence of normalizable asymptotic distributions depending on the discretization parameter α. Using the infinite ergodicity approach, recently applied to stochastic processes with multiplicative noise by E. Barkai and collaborators, we show how meaningful asymptotic results can be formulated in a transparent way.

4D flat-space scattering amplitude/CFT3 correlator correspondence revisited

In this paper, we make connection between CFT3 three point correlation function of conserved currents and 4D three point amplitude of general spin massless gauge field explicit. We do so by taking flat space limit of momentum space CFT correlation function and show how they reproduce flat space amplitudes. We then point out a mismatch between number of independent structures in 3D CFT correlator of conserved currents and 4D flat space covariant vertex of massless higher spin fields. This is in contrast with general expectation that counting of 3d CFT correlator and 4d flat space amplitude should match. This mismatch is even more pronounced in spinor helicity variables.We also point out an interesting relation between parity even and parity odd flat space amplitude in momentum space. This observation helps us to construct a new momentum space CFT structure which accounts for the mismatch. However we should mention that this extra CFT structure can't be constructed out of conserved currents and hence counting mismatch between CFT correlation of conserved currents and flat space amplitude of massless gauge field persists. Story in spinor helicity variable is more complicated and is discussed in detail. We further comment on the connection of CFT correlation function in spinor helicity variables to AdS amplitudes in spinor helicity variables and light cone variables.

Convergence rates in the functional CLT for [formula omitted]-mixing triangular arrays

We obtain convergence rates (in the Levi–Prokhorove metric) in the functional central limit theorem (CLT) for partial sums Sn=∑j=1nξj,n of triangular arrays {ξ1,n,ξ2,n,…,ξn,n} satisfying some mixing and moment conditions (which are not necessarily uniform in n). For certain classes of additive functionals of triangular arrays of contracting Markov chains (in the sense of Dobrushin) we obtain rates which are close to the best rates obtained for independent random variables. In addition, we obtain close to optimal rates in the usual CLT and a moderate deviations principle and some Rosenthal type inequalities. We will also discuss applications to some classes of local statistics (e.g. covariance estimators), as well as expanding non-stationary dynamical systems, which can be reduced to non-uniformly mixing triangular arrays by an approximation argument. The main novelty here is that our results are obtained without any assumptions about the growth rate of the variance of Sn. The result are obtained using a certain type of block decomposition, which, in a sense, reduces the problem to the case when the variance of Sn is “not negligible” in comparison with the (new) number of summands.

Dispersive liquid-liquid microextraction/HPLC techniques for determination of oxytetracycline and doxycycline residues in beef samples: method developments and statistical analysis

A rapid, cost-effective and environment-friendly sample pre-treatment method involving dispersive liquid-liquid microextraction (DLLME) and high-performance liquid chromatography (HPLC) was developed and applied for the extraction of oxytetracycline and doxycycline residues in beef samples (liver, kidney and muscle). Several influencing factors associated with the extraction and separation of these antibiotics residues, such as sample size, type and volume of disperser and extraction solvents, centrifugation speed and time, were optimized using Plackett-Burman design and central composite design, while insignificant factors were fixed at values determined using univariate analysis. Figures of merit of the analytical methodology including the limit of detection (LOD), the limit of quantification (LOQ), accuracy (in terms of average recoveries), precision and calibration functions were established according to the European Union commission decision 2002/657/EC. Linearity, in the range of 5–500 µg/kg, was obtained with regression coefficients ranging from 0.9983 – 0.9999. Inter-day repeatability, intra-day precision, LODs and LOQs obtained were 3.81 – 14.90%, 3.80 – 8.70%, 4.21 – 4.69 µg/kg and 14.02 – 15.65 µg/kg respectively. Samples with detectable drug residues have oxytetracycline being the most commonly detected. The developed method was successfully established and the concentration levels of drug residues detected were lower than the European Union set maximum residue level (MRL).

The body of evidence of late-life depression: the complex relationship between depressive symptoms, movement, dyspnea and cognition

ABSTRACT Background Physical symptoms play an important role in late-life depression and may contribute to residual symptomatology after antidepressant treatment. In this exploratory study, we examined the role of specific bodily dimensions including movement, respiratory functions, fear of falling, cognition, and physical weakness in older people with depression. Methods Clinically stable older patients with major depression within a Psychiatric Consultation-Liaison program for Primary Care underwent comprehensive assessment of depressive symptoms, instrumental movement analysis, dyspnea, weakness, activity limitations, cognitive function, and fear of falling. Network analysis was performed to explore the unique adjusted associations between clinical dimensions. Results Sadness was associated with worse turning and walking ability and movement transitions from walking to sitting, as well as with worse general cognitive abilities. Sadness was also connected with dyspnea, while neurovegetative depressive burden was connected with activity limitations. Discussion Limitations of motor and cognitive function, dyspnea, and weakness may contribute to the persistence of residual symptoms of late-life depression.

Abundances of CNO elements in z ∼ 0.3–0.4 Lyman continuum leaking galaxies

ABSTRACT We present observations with the Space Telescope Imaging Spectrograph onboard the Hubble Space Telescope (HST) of 11 Lyman continuum (LyC) leaking galaxies at redshifts, z, in the range 0.29–0.43, with oxygen abundances 12+log(O/H) = 7.64–8.16, stellar masses M⋆ ∼ 107.8–109.8 M⊙, and O32 = [O iii] λ5007/[O ii] λ3727 of ∼ 5–20 aiming to detect the C iii] λ1908 emission line. We combine these observations with the optical Sloan Digital Sky Survey (SDSS) spectra for the determination of carbon, nitrogen, and oxygen abundances. Our sample was supplemented by 31 galaxies from the literature, for which carbon, nitrogen, and oxygen abundances can be derived from the HST and SDSS spectra. These additional galaxies, however, do not have LyC observations. We find that log(C/O) for the entire sample at 12+log(O/H) < 8.1 does not depend on metallicity, with a small dispersion of ∼0.13 dex around the average value of ∼−0.75 dex. On the other hand, the log(N/O) in galaxies at z > 0.1, including LyC leakers, is systematically higher compared to the rest of the sample with lower metallicity. We find that log(C/O) slightly decreases with increasing M⋆ from ∼ −0.65 at M⋆ = 106 M⊙ to ∼ −0.80 at M⋆ = 109–1010 M⊙, whereas log(N/O) is considerably enhanced at M⋆ > 108 M⊙. The origin of these trends remains basically unknown. A possible solution would be to assume that the upper mass limit of the stellar initial mass function in more massive galaxies is higher. This would result in a higher production of oxygen and a larger fraction of massive stars with stellar wind polluting the interstellar medium with nitrogen.