Passage Problem Research Articles

Solitary intestinal myofibroma – an unusual cause of neonatal intestinal obstruction

Congenital solitary myofibroma is an exceptional tumor of newborn period and presents as solitary or multiple lesions usually confined to soft tissues. It induces intestinal obstruction or perforation, which most frequently involves the jejunum and ileum. However, jejunoileal atresia is the most frequently encountered cause of small bowel obstruction in the neonatal period. We report a new case of solitary myofibroma located in the wall of the ileum, measuring 2×3 cm2 in size, about 25 cm from the ileocecal junction, in a 17-day-old baby girl who presented with abdominal distention and bilious vomiting. Laparotomy was performed on the patient and the tumor was removed; the patient did well after surgery. Despite all the common causes of intestinal obstruction—intestinal atresia, Hirschsprung disease, anorectal anomaly, malrotation, and meconium passage problem in the neonatal period—myofibroma of the small bowel has to be considered because treatment is fairly easy and prognosis is excellent.

Interaction-induced backscattering in short quantum wires

We study interaction-induced backscattering in clean quantum wires with adiabatic contacts exposed to a voltage bias. Particle backscattering relaxes such systems to a fully equilibrated steady state only on length scales exponentially large in the ratio of bandwidth of excitations and temperature. Here we focus on shorter wires in which full equilibration is not accomplished. Signatures of relaxation then are due to backscattering of hole excitations close to the band bottom which perform a diffusive motion in momentum space while scattering from excitations at the Fermi level. This is reminiscent to the first passage problem of a Brownian particle and, regardless of the interaction strength, can be described by an inhomogeneous Fokker-Planck equation. From general solutions of the latter we calculate the hole backscattering rate for different wire lengths and discuss the resulting length dependence of interaction-induced correction to the conductance of a clean single channel quantum wire.

Stability, control and reliability of a ship crane payload motion

This paper investigates the stochastic dynamics, stability and control of a ship-based crane payload motion, as well as the first time passage type of failure. The simplified nonlinear model of the payload motion is considered, where the excitation of a suspension point is imposed due to the heaving motion of waves. The latter enters the system parametrically, leading to a Mathieu type nonlinear equation. The stability boundaries are numerically calculated, using the Lyapunov exponent approach. The control strategy, based on the feedback bang–bang control policy, is implemented to minimize the load's swinging motion. Finally, the first time passage problem is addressed employing Monte-Carlo sampling of the failure process.

Fishway Bottleneck Relief Models: a Case Study using Radio‐Tagged Pacific Lampreys

AbstractStructural or operational changes to fishways can improve fish passage efficiency, but there is often uncertainty regarding which improvements will be most effective. We developed a “bottleneck relief” model using Kaplan–Meier methods to help managers assess where remediation efforts are likely to provide the largest increases in fishway passage. The simulation model uses a matrix of observed efficiency estimates from fishway subsections and incorporates multiple passage attempts by individual tagged fish. In a case study application to test the model, we used radiotelemetry data from 2,170 adult Pacific Lampreys Entosphenus tridentatus at Bonneville Dam (Columbia River, Washington–Oregon), which features multiple fishways and low lamprey passage success (mean fishway passage efficiency ∼0.50; n = 10 years). The model was run iteratively to test potential dam passage benefits from improving efficiency in 20 individual fishway segments. The highest benefits were for improvements at top‐of‐fishway segments and at sites where passage routes converged. Benefits were lower for segments used by fewer fish, segments located downstream from serious bottlenecks, and segments with a limited scope for improvement (i.e., efficiency was already high). The model provides a flexible and objective method for assessing complex fish passage problems and informing remediation decision making.Received December 19, 2013; accepted March 11, 2014

Overview of Structural Life Assessment and Reliability, Part V: Joints and Weldments

Overview of Structural Life Assessment and Reliability, Part V: Joints and Weldments

First passage of stochastically dynamical system with fractional derivative and power-form restoring force under Gaussian excitation

First passage problem in a dynamical system with power-form restoring force and fractional derivative is studied in this paper. At first, the original system is transformed into an diffusion differential equation by way of generalized Van der Pol transformation and stochastic averaging method. After that , according to the definition of first passage, BK equation and GP equation are constructed and solved. The numerical results tell us that the reliability probabilities are decreased monotonously with respect to time. Higher order of fractional derivative can lead to higher reliability of the system. Boundary value of safe domain can affect the reliability probability greatly. The larger it is, the higher probability value is.

A two-dimensional, two-sided Euler inversion algorithm with computable error bounds and its financial applications

Open AccessOpen Access licenseAboutSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InEmail Go to SectionOpen AccessOpen Access license HomeStochastic SystemsVol. 4, No. 2 A Two-dimensional, Two-sided Euler Inversion Algorithm with Computable Error Bounds and its Financial ApplicationsNing Cai, Chao ShiNing Cai, Chao ShiPublished Online:23 Mar 2015https://doi.org/10.1287/12-SSY094AbstractIn this paper we propose an inversion algorithm with computable error bounds for two-dimensional, two-sided Laplace transforms. The algorithm consists of two discretization parameters and two truncation parameters. Based on the computable error bounds, we can select these parameters appropriately to achieve any desired accuracy. Hence this algorithm is particularly useful to provide benchmarks. In many cases, the error bounds decay quickly (e.g., exponentially), making the algorithm very efficient. We apply this algorithm to price exotic options such as spread options and barrier options under various asset pricing models as well as to evaluate the joint cumulative distribution functions of related state variables. The numerical examples indicate that the inversion algorithm is accurate, fast and easy to implement. Previous Back to Top Next FiguresReferencesRelatedInformationCited byA Computational Approach to First Passage Problems of Reflected Hyperexponential Jump Diffusion ProcessesNing Cai, Xuewei Yang22 June 2020 | INFORMS Journal on Computing, Vol. 33, No. 1 Volume 4, Issue 2December 2014Pages 321-603 Article Information Metrics Information Received:January 01, 2013Published Online:March 23, 2015 Copyright © 2014, The author(s)Cite asNing Cai, Chao Shi (2015) A Two-dimensional, Two-sided Euler Inversion Algorithm with Computable Error Bounds and its Financial Applications. Stochastic Systems 4(2):404-448. https://doi.org/10.1287/12-SSY094 KeywordsTwo-dimensional Laplace inversiontwo-sided Laplace transformsEuler inversioncomputable error boundsdiscretization errorstruncation errorsoption pricingexotic optionsPDF download

Ratcheted diffusion transport through crowded nanochannels

The problem of transport through nanochannels is one of the major questions in cell biology, with a wide range of applications. In this paper we discuss the process of spontaneous translocation of molecules (Brownian particles) by ratcheted diffusion: a problem relevant for protein translocation along bacterial flagella or injectosome complex, or DNA translocation by bacteriophages. We use molecular dynamics simulations and statistical theory to identify two regimes of transport: at low rate of particle injection into the channel the process is controlled by the individual diffusion towards the open end (the first passage problem), while at a higher rate of injection the crowded regime sets in. In this regime the particle density in the channel reaches a constant saturation level and the resistance force increases substantially, due to the osmotic pressure build-up. To achieve a steady-state transport, the apparatus that injects new particles into a crowded channel has to operate with an increasing power consumption, proportional to the length of the channel and the required rate of transport. The analysis of resistance force, and accordingly – the power required to inject the particles into a crowded channel to overcome its clogging, is also relevant for many microfluidics applications.

Fishway passage bottleneck identification and prioritization: a case study of Pacific lamprey at Bonneville Dam

Fishways designed for salmonids often restrict passage by non-salmonids, and effective tools are needed both to identify passage problems for nontarget species and to inform remediation planning. In this case study, we used migration histories from 2170 radio-tagged adult Pacific lamprey (Entosphenus tridentatus) to identify locations of poor passage (bottlenecks) at a large, multifishway dam. Over 10 years, 49% of tagged lamprey that entered fishways failed to pass the dam. Models accounting for repeated attempts by individual lamprey indicated successful passage strongly depended on attempted passage route. Success also varied with time of fishway entry, water temperature, and lamprey body size. Most failed passage attempts terminated in lower fishway segments, but extensive seasonal shifts in bottleneck locations were detected. Ranking metrics helped prioritize bottlenecks and identified sites where structural or operational modifications should improve lamprey passage. Our integration of spatially intensive monitoring with novel analytical techniques was critical to understanding the complex relationships among fishway features, environmental variation, and lamprey behavior. The prioritization framework can be applied to a wide range of fish passage assessments.

Peculiarities of passage of an oscillator through a potential barrier

The problem of passage of a classical oscillator through a potential barrier is solved. Nonlinear sub-barrier passage and above-barrier reflection of the oscillator with elements of energy quantization are revealed. Within the framework of the laws of classical mechanics, an explanation is proposed for the obtained regularities of motion of the oscillator. The results not only enable an extension of the region of applicability of the laws of classical mechanics, but also reveal the essence of its limitations due to the requirement of holonomic couplings in the Lagrangian and Hamiltonian formalisms.

Search times with arbitrary detection constraints

Random encounters in space are central to describing diffusion-limited reactions, animal foraging, search processes, and many other situations in nature. These encounters, however, are often constrained by the capacity of the searcher to detect and/or recognize its target. This can be due to limited binding and perception abilities of the searcher or hiding and avoiding mechanisms used by the target. Hence detection failure upon passage over the target location turns the process into an n-passage problem, with n being random. Here we provide a general description of this detection problem for arbitrary dimensions and arbitrary detection constraints. The mean detection time (MDT) for a random searcher embedded in a sea of homogeneously distributed targets is obtained as a function of the target density ρ, the size domain L, and the effective detection distance a. While the scaling with ρ and L is found to be universal and equivalent to that found for the corresponding first-passage problem, the scaling of the MDT on a depends on the specific detection mechanism considered.

Bulk-mediated Surface Diffusion on a Cylinder in the Fast Exchange Limit

In various biological systems and small scale technological applications particles transiently bind to a cylindrical surface. Upon unbinding the particles diffuse in the vicinal bulk before rebinding to the surface. Such bulk-mediated excursions give rise to an effective surface translation, for which we here derive and discuss the dynamic equations, including additional surface diffusion. We discuss the time evolution of the number of surface-bound particles, the effective surface mean squared displacement, and the surface propagator. In particular, we observe sub- and superdiffusive regimes. A plateau of the surface mean-squared displacement reflects a stalling of the surface diffusion at longer times. Finally, the corresponding first passage problem for the cylindrical geometry is analysed.

FIRST PASSAGE TIMES OF REFLECTED GENERALIZED ORNSTEIN–UHLENBECK PROCESSES

We study first passage problems of a class of reflected generalized Ornstein–Uhlenbeck processes without positive jumps. By establishing an extended Dynkin's formula associated with the process, we derive that the joint Laplace transform of the first passage time and an integral functional stopped at the time satisfies a truncated integro-differential equation. Two solvable examples are presented when the driven Lévy process is a drifted-Brownian motion and a spectrally negative stable process with index α ∈ (1, 2], respectively. Finally, we give two applications in finance.

A Polynomial Chaos Expansion Based Reliability Method for Linear Random Structures

Within the framework of mechanical engineering, reliability assessment is usually involved in the procedure of finite element analysis (FEA) combined with Monte Carlo simulation (MCS). Unfortunately, such approaches require high computational effort. To improve efficiency, we propose a polynomial chaos expansion (PCE) based MCS method for linear random structures, in which the time consuming repeated FEA is avoided in manner of approximating the random response by PCE. However, applications of PCE are always restricted for the first passage problem due to the curse of high dimensionality. To overcome this, we use the convolution form to compute the dynamic response, in which PCE is raised to approximate the modal properties so that the dimension of uncertainties is reduced since only structural random parameters are considered. Four examples are studied to show the effectiveness and relevancy of the proposed method.

A first passage problem for a bivariate diffusion process: Numerical solution with an application to neuroscience when the process is Gauss–Markov

We consider a bivariate Gauss–Markov process and we study the first passage time of one component through a constant boundary. We prove that its probability density function is the unique solution of a new integral equation and we propose a numerical algorithm for its solution. Convergence properties of this algorithm are discussed and the method is applied to the study of the integrated Brownian motion and to the integrated Ornstein–Uhlenbeck process. Finally a model of neuroscience interest is discussed.

A barrier to upstream migration in the fish passage of Itaipu Dam (Canal da Piracema), Paraná River basin

The majority of the fish passages built in the Neotropical region are characterised by low efficiency and high selectivity; in many cases, the benefits to fish populations are uncertain. Studies conducted in the Canal da Piracema at Itaipu dam on the Parana River indicate that the system component designated as the Discharge channel in the Bela Vista River (herein named Canal de deságue no rio Bela Vista or CABV), a 200 m long technical section, was the main barrier to the upstream migration. The aim of this study was to evaluate the degree of restriction imposed by the CABV on upstream movements of Prochilodus lineatus and Leporinus elongatus, Characiformes. Fish were tagged with passive integrated transponders (PIT tags) and released both downstream and upstream of this critical section. Individuals of both species released downstream of the CABV took much more time to reach the upper end of the system (43.6 days vs. 15.9 days), and passed in much lower proportions (18% vs. 60.8%) than those tagged upstream of this component. Although more work is needed to differentiate between fishway effects and natural variation in migratory motivation, the results clearly demonstrate passage problems at the CABV.

Derivation of response spectrum compatible non-stationary stochastic processes relying on Monte Carlo-based peak factor estimation

In this paper a novel approach is proposed to address the problem of deriving non-stationary stochastic processes which are compatible in the mean sense with a given (target) response (uniform hazard) spectrum (UHS) as commonly desired in the aseismic structural design regulated by contemporary codes of practice. The appealing feature of the approach is that it is non-iterative and “one-step”. This is accomplished by solving a standard over-determined minimization problem in conjunction with appropriate median peak factors. These factors are determined by a plethora of reported new Monte Carlo studies which on their own possess considerable stochastic dynamics merit. In the proposed approach, generation and treatment of samples of the processes individually on a deterministic basis is not required as is the case with the various “two-step” approaches found in the literature addressing the herein considered task. The applicability and usefulness of the approach is demonstrated by furnishing extensive numerical data associated with the elastic design UHS of the current European (EC8) and the Chinese (GB 50011) aseismic code provisions. Purposely, simple and thus attractive from a practical viewpoint, uniformly modulated processes assuming either the Kanai-Tajimi (K-T) or the Clough-Penzien (C-P) spectral form are employed. The Monte Carlo studies yield damping and duration dependent median peak factor spectra, given in a polynomial form, associated with the first passage problem for UHS compatible K-T and C-P uniformly modulated stochastic processes. Hopefully, the herein derived stochastic processes and median peak factor spectra can be used to facilitate the aseismic design of structures regulated by contemporary code provisions in a Monte Carlo simulation-based or stochastic dynamics-based context of analysis.

Slow passage through multiple bifurcation points

The slow passage problem, the slow variation of a control parameter, is explored in a model problem that posses several co-existing equilibria (fixed points, limit cycles and 2-tori), and these are either created or destroyed or change their stability as control parameters are varied through Hopf, Neimark-Sacker and torus break-up bifurcations. The slow passage through the Hopf bifurcation behaves as determined in previous studies (the delay in the observation of oscillations depends only on how far from critical the ramped parameter is at the start of the ramp--a memory effect), and that through the Neimark-Sacker bifurcation also behaves similarly. We show that the range of the ramped parameter over which a Hopf oscillation can be observed (limited by the subsequent onset of torus oscillations from the Neimark-Sacker bifurcation) is twice that predicted from a static-parameter bifurcation analysis, and this is a memory-less result independent of the initial value of the ramped parameter. These delay and memory effects are independent of the ramp rate, for small enough ramp rates. The slow passage through the torus break-up bifurcation is qualitatively different. It does not depend on the initial value of the ramped parameter, but instead is found to depend, on average, on the square-root of the ramp rate. This is typical of transient behavior. We show that this transient behavior is due to the stable and unstable manifolds of the saddle limit cycles forming a very narrow escape tunnel for trajectories originating near the unstable 2-torus no matter how slow a ramp speed is used. The type of bifurcation sequence in the model problem studied (Hopf, Neimark-Sacker, torus break-up) is typical of those for the transition to spatio-temporal chaos in hydrodynamic problems, and in those physical problems the transition can occur over a very small range of the control parameter, and so the inevitable slow drift of the parameter in an experiment may lead to observations where the slow passage results reported here need to be taken into account.

Meromorphic Lévy processes and their fluctuation identities

The last couple of years has seen a remarkable number of new, explicit examples of the Wiener–Hopf factorization for Lévy processes where previously there had been very few. We mention, in particular, the many cases of spectrally negative Lévy processes in [Sixth Seminar on Stochastic Analysis, Random Fields and Applications (2011) 119–146, Electron. J. Probab. 13 (2008) 1672–1701], hyper-exponential and generalized hyper-exponential Lévy processes [Quant. Finance 10 (2010) 629–644], Lamperti-stable processes in [J. Appl. Probab. 43 (2006) 967–983, Probab. Math. Statist. 30 (2010) 1–28, Stochastic Process. Appl. 119 (2009) 980–1000, Bull. Sci. Math. 133 (2009) 355–382], Hypergeometric processes in [Ann. Appl. Probab. 20 (2010) 522–564, Ann. Appl. Probab. 21 (2011) 2171–2190, Bernoulli 17 (2011) 34–59], β-processes in [Ann. Appl. Probab. 20 (2010) 1801–1830] and θ-processes in [J. Appl. Probab. 47 (2010) 1023–1033]. In this paper we introduce a new family of Lévy processes, which we call Meromorphic Lévy processes, or just M-processes for short, which overlaps with many of the aforementioned classes. A key feature of the M-class is the identification of their Wiener–Hopf factors as rational functions of infinite degree written in terms of poles and roots of the Laplace exponent, all of which are real numbers. The specific structure of the M-class Wiener–Hopf factorization enables us to explicitly handle a comprehensive suite of fluctuation identities that concern first passage problems for finite and infinite intervals for both the process itself as well as the resulting process when it is reflected in its infimum. Such identities are of fundamental interest given their repeated occurrence in various fields of applied probability such as mathematical finance, insurance risk theory and queuing theory.

First passage times of reflected Ornstein–Uhlenbeck processes with two-sided jumps

In this paper we consider the first passage problem for reflected jump-type Ornstein---Uhlenbeck processes with two-reflecting barriers. We calculate the explicit joint Laplace transform of the first passage time and the corresponding undershoot when the jumps follow a two-sided mixed exponential law. The method of contour integrals proposed by Jacobsen and Jensen (in Stoch. Process. Appl. 117: 1330---1356, 2007) is applied to obtain the explicit joint Laplace transform. Finally, a comparison concerning Laplace transforms between the reflected case and non-reflected case is presented by taking smooth-pasting conditions at reflecting barriers into account.