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)

An alternating boundary integral based method for a Cauchy problem for the Laplace equation in a quadrant

We study the Cauchy problem for the Laplace equation in a quadrant (quarter-plane) containing a bounded inclusion. Given the values of the solution and its derivative on the edges of the quadrant the solution is reconstructed on the boundary of the inclusion. This is achieved using an alternating iterative method where at each iteration step mixed boundary value problems are being solved. A numerical method is also proposed and investigated for the direct mixed problems reducing these to integral equations over the inclusion. Numerical examples verify the efficiency of the proposed scheme.

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)

Pseudoperiodic "Living" and/or controlled cationic ring-opening copolymerization of oxetane with tetrahydropyran:microstructure of polymers vs kinetics of chain growth

The "living" and/or controlled cationic ring-opening bulk copolymerization of oxetane (Ox) with tetrahydropyran (THP) (cyclic ether with no homopolymerizability) at 35°C was examined using ethoxymethyl-1 -oxoniacyclohexane hexafluoroantimonate (EMOA) and (BF3 · CH3OH)THP as fast and slow initiator, respectively, yielding living and nonliving polymers with pseudoperiodic sequences (i.e., each pentamethylene oxide fragment inserted into the polymer is flanked by two trimethylene oxide fragments). Good control over number-average molecular weight (Mn up to 150000 g mol-1) with molecular weight distribution (MWD ∼ 1.4-1, 5) broader than predicted by the Poison distribution (MWDs > 1 +1/DPn) was attained using EMOA as initiating system, i.e., C 2H5OCH2Cl with 1.1 equiv of AgSbF6 as a stable catalyst and 1.1 equiv of 2,6-di-tert-butylpyridine used as a non-nucleophilic proton trap. With (BF3 · CH 3OH)THP, a drift of the linear dependence M n(GPC) vs Mn(theory) to lower molecular weight was observed together with the production of cyclic oligomers, ∼3-5% of the Ox consumed in THP against ∼30% in dichloromethane. Structural and kinetics studies highlighted a mechanism of chains growth where the rate of mutual conversion between "strain ACE species" (chain terminated by a tertiary 1-oxoniacyclobutane ion, Al) and "strain-free ACE species" (chain terminated by a tertiary 1-oxoniacyclohexane ion, Tl) depends on the rate at which Ox converts the stable species T1 (kind of "dormant" species) into a living "propagating" center A1 (i.e., k aapp[Ox]). The role of the THP solvent associated with the suspension of irreversible and reversible transfer reactions to polymer, when the polymerization is initiated with EMOA, was predicted by our kinetic considerations. The activation -deactivation pseudoequilibrium coefficient (Qt) was then calculated in a pure theoretical basis. From the measured apparent rate constant of Ox (kOxapp) and THP (kTHPapp = ka(endo)app) consumption, Qt and reactivity ratio (kp/kd, k a(endo)/ka(exo), and ks/ka(endo) were calculated, which then allow the determination of the transition rate constant of elementary step reactions that governs the increase of Mu with conversion. © 2009 American Chemical Society.

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.