Relaxation of alternating iterative algorithms for the Cauchy problem associated with the modified Helmholtz equation

We propose two algorithms involving the relaxation of either the given Dirichlet data or the prescribed Neumann data on the over-specified boundary, in the case of the alternating iterative algorithm of ` 12 ` 12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Kozlov91 applied to Cauchy problems for the modified Helmholtz equation. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed methods.

A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity

We propose two algorithms involving the relaxation of either the given Dirichlet data (boundary displacements) or the prescribed Neumann data (boundary tractions) on the over-specified boundary in the case of the alternating iterative algorithm of Kozlov et al. [16] applied to Cauchy problems in linear elasticity. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed method.

An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.

An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions

We consider a Cauchy problem for the Laplace equation in a two-dimensional semi-infinite region with a bounded inclusion, i.e. the region is the intersection between a half-plane and the exterior of a bounded closed curve contained in the half-plane. The Cauchy data are given on the unbounded part of the boundary of the region and the aim is to construct the solution on the boundary of the inclusion. In 1989, Kozlov and Maz'ya [10] proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems in bounded domains. We extend their approach to our setting and in each iteration step mixed boundary value problems for the Laplace equation in the semi-infinite region are solved. Well-posedness of these mixed problems are investigated and convergence of the alternating procedure is examined. For the numerical implementation an efficient boundary integral equation method is proposed, based on the indirect variant of the boundary integral equation approach. The mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing the feasibility of the proposed method.

An alternating potential based approach for a Cauchy problem for the Laplace equation in a planar domain with a cut

We consider a Cauchy problem for the Laplace equation in a bounded region containing a cut, where the region is formed by removing a sufficiently smooth arc (the cut) from a bounded simply connected domain D. The aim is to reconstruct the solution on the cut from the values of the solution and its normal derivative on the boundary of the domain D. We propose an alternating iterative method which involves solving direct mixed problems for the Laplace operator in the same region. These mixed problems have either a Dirichlet or a Neumann boundary condition imposed on the cut and are solved by a potential approach. Each of these mixed problems is reduced to a system of integral equations of the first kind with logarithmic and hypersingular kernels and at most a square root singularity in the densities at the endpoints of the cut. The full discretization of the direct problems is realized by a trigonometric quadrature method which has super-algebraic convergence. The numerical examples presented illustrate the feasibility of the proposed method.

An alternating method for the stationary Stokes system

An alternating procedure for solving a Cauchy problem for the stationary Stokes system is presented. A convergence proof of this procedure and numerical results are included.

Build-up of auditory stream segregation induced by tone sequences of constant or alternating frequency and the resetting effects of single deviants

A sequence of constant-frequency tones can promote streaming in a subsequent sequence of alternating-frequency tones, but why this effect occurs is not fully understood and its time course has not been investigated. Experiment 1 used a 2.0-s-long constant-frequency inducer (10 repetitions of a low-frequency pure tone) to promote segregation in a subsequent, 1.2-s test sequence of alternating low- and high-frequency tones. Replacing the final inducer tone with silence substantially reduced reported test-sequence segregation. This reduction did not occur when either the 4th or 7th inducer was replaced with silence. This suggests that a change at the induction/test-sequence boundary actively resets build-up, rather than less segregation occurring simply because fewer inducer tones were presented. Furthermore, Experiment 2 found that a constant-frequency inducer produced its maximum segregation-promoting effect after only three tones—this contrasts with the more gradual build-up typically observed for alternating-frequency sequences. Experiment 3 required listeners to judge continuously the grouping of 20-s test sequences. Constant-frequency inducers were considerably more effective at promoting segregation than alternating ones; this difference persisted for ~10 s. In addition, resetting arising from a single deviant (longer tone) was associated only with constant-frequency inducers. Overall, the results suggest that constant-frequency inducers promote segregation by capturing one subset of test-sequence tones into an ongoing, preestablished stream, and that a deviant tone may reduce segregation by disrupting this capture. These findings offer new insight into the dynamics of stream segregation, and have implications for the neural basis of streaming and the role of attention in stream formation. (PsycINFO Database Record (c) 2013 APA, all rights reserved)

Models of Alternating Renewal Process at Discrete Time

We study a class of models used with success in the modelling of climatological sequences. These models are based on the notion of renewal. At first, we examine the probabilistic aspects of these models to afterwards study the estimation of their parameters and their asymptotical properties, in particular the consistence and the normality. We will discuss for applications, two particular classes of alternating renewal processes at discrete time. The first class is defined by laws of sojourn time that are translated negative binomial laws and the second class, suggested by Green is deduced from alternating renewal process in continuous time with sojourn time laws which are exponential laws with parameters α^0 and α^1 respectively.

Power tapping function in near infra-red region based on 45° tilted fiber gratings

We report an efficient power tapping device working in near infra-red (800 nm) wavelength region based on UV-in- scribed 45° tilted fiber grating (45°-TFG) structure. Five 45°-TFGs were UV-inscribed in hydrogenated PS750 fiber using a custom-designed phase mask with different grating lengths of 3 mm, 5 mm, 9 mm, 12 mm and 15 mm, showing polarization dependent losses (PDLs) of 1 dB, 3 dB, 7 dB, 10 dB and 13 dB, respectively. The power side-tapping efficiency is clearly depending on the grating strength. It has been identified that the power tapping efficiency increases with the grating strength and deceases along the grating length. The side-tapped power profile has also been examined in azimuthal direction, showing a near-Gaussian distribution. These experimental results clearly demonstrated that 45°- TFGs may be used as in-fiber power tapping devices for applications requiring in-line signal monitoring.

Build-up of auditory stream segregation induced by tone sequences of constant or alternating frequency and the resetting effects of single deviants

Three experiments investigated the dynamics of auditory stream segregation. Experiment 1 used a 2.0-s constant-frequency inducer (10 repetitions of a low-frequency pure tone) to promote segregation in a subsequent, 1.2-s test sequence of alternating low- and high-frequency tones. Replacing the final inducer tone with silence reduced reported test-sequence segregation substantially. This reduction did not occur when either the 4th or 7th inducer was replaced with silence. This suggests that a change at the induction/test-sequence boundary actively resets buildup, rather than less segregation occurring simply because fewer inducer tones were presented. Furthermore, Experiment 2 found that a constant-frequency inducer produced its maximum segregation-promoting effect after only 3 tone cycles - this contrasts with the more gradual build-up typically observed for alternating sequences. Experiment 3 required listeners to judge continuously the grouping of 20-s test sequences. Constant-frequency inducers were considerably more effective at promoting segregation than alternating ones; this difference persisted for ∼10 s. In addition, resetting arising from a single deviant (longer tone) was associated only with constant-frequency inducers. Overall, the results suggest that constant-frequency inducers promote segregation by capturing one subset of test-sequence tones into an on-going, pre-established stream and that a deviant tone may reduce segregation by disrupting this capture. © 2013 Acoustical Society of America.

Limiting Distributions for Lifetimes in Alternating Renewal Processes

2000 Mathematics Subject Classification: 60K05

Pub crawling at scale:tapping untappd to explore social drinking

There has been a recent surge of research looking at the reporting of food consumption on social media. The topic of alcohol consumption, however, remains poorly investigated. Social media has the potential to shed light on a topic that, traditionally, is difficult to collect fine-grained information on. One social app stands out in this regard: Untappd is an app that allows users to ‘check-in’ their consumption of beers. It operates in a similar fashion to other location-based applications, but is specifically tailored to the collection of information on beer consumption. In this paper, we explore beer consumption through the lens of social media. We crawled Untappd in real time over a period of 112 days, across 40 cities in the United States and Europe. Using this data, we shed light on the drinking habits of over 369k users. We focus on per-user and per-city characterisation, highlighting key behavioural trends.

Types and amplitudes of touch as reinforcing stimuli in operant conditioning of infant behavior

The reinforcing effects of diverse tactile stimuli were examined in this study. The study had two purposes. First, this study expanded on the Pelaez-Nogueras, Field, Gewirtz, Cigales, Gonzalez, Sanchez and Clasky (1997) finding that stroking increases infants' gaze duration, and smiling and vocalization frequencies more than tickling/poking. Instead of presenting poking and tickling as a single stimulus combination, this study separated poking and tickling in order to measure the effects of each component separately. Further, the effects of poking, tickling/tapping and stroking intensity (i.e., tactile pressure) were compared by having both mild and intense conditions. Second, this study compared the reinforcing efficacy of mother-delivered tactile stimulation to that of infant-originated tactile exploration. Twelve infants from 2- to 5-months of age participated in this study. The experiment was conducted using a repeated measures A-B-A-C-A-D reversal design. The A phases signified baselines and reversals. The B, C, and D phases consisted of alternating treatments (either mild stroking vs. mild poking vs. mild tickling/tapping, intense stroking vs. intense poking vs. intense tickling/tapping, or mother-delivered tactile stimulation vs. infant-originated tactile exploration). Three experimental hypotheses were assessed: (1) infant leg kick rate would be greater when it produced stroking or tickling/tapping (presumptive positive reinforcers), than when it produced poking (a possible punisher), regardless of tactile pressure; (2) infant leg kick rate would be greater when it produced a more intense level of stroking or tickling/tapping and lower when it produced intense poking compared to mild poking; (3) infant leg-kick rate would be greater for mother-delivered tactile stimulation than for infant-originated tactile exploration. Visual inspection and inferential statistical methods were used to analyze the results. The data supported the first two hypotheses. Mixed support emerged for the third hypothesis. This study made several important contributions to the field of psychology. First, this was the first study to quantify the pressure of tactile stimulation, via a pressure meter developed by the researcher. Additionally, the results of this study yielded valuable information about the effects of different modalities of touch. ^