Optimal designs for evaluating a series of treatments

Several articles in this journal have studied optimal designs for testing a series of treatments to identify promising ones for further study. These designs formulate testing as an ongoing process until a promising treatment is identified. This formulation is considered to be more realistic but substantially increases the computational complexity. In this article, we show that these new designs, which control the error rates for a series of treatments, can be reformulated as conventional designs that control the error rates for each individual treatment. This reformulation leads to a more meaningful interpretation of the error rates and hence easier specification of the error rates in practice. The reformulation also allows us to use conventional designs from published tables or standard computer programs to design trials for a series of treatments. We illustrate these using a study in soft tissue sarcoma.

Light scattering studies on solutions of chlorinated rubber

Measurements have been made of the depolarisation factors \sigma u ,\sigma v ,\sigma h, and the intensity of scattering in the horizontal transverse direction, in the case of solutions of four different samples of chlorinated rubber in carbon tetrachloride. The size, shape and molecular weight of the micelles have been deduced by the application of the light scattering theories of Gans, Vrklajan and Katalinic and Debye. The extent to which the degradation of the rubber molecule occurs on chlorination has also been assessed.

Closed-form solutions for low-rank non-rigid reconstruction

Recovering the motion of a non-rigid body from a set of monocular images permits the analysis of dynamic scenes in uncontrolled environments. However, the extension of factorisation algorithms for rigid structure from motion to the low-rank non-rigid case has proved challenging. This stems from the comparatively hard problem of finding a linear “corrective transform” which recovers the projection and structure matrices from an ambiguous factorisation. We elucidate that this greater difficulty is due to the need to find multiple solutions to a non-trivial problem, casting a number of previous approaches as alleviating this issue by either a) introducing constraints on the basis, making the problems nonidentical, or b) incorporating heuristics to encourage a diverse set of solutions, making the problems inter-dependent. While it has previously been recognised that finding a single solution to this problem is sufficient to estimate cameras, we show that it is possible to bootstrap this partial solution to find the complete transform in closed-form. However, we acknowledge that our method minimises an algebraic error and is thus inherently sensitive to deviation from the low-rank model. We compare our closed-form solution for non-rigid structure with known cameras to the closed-form solution of Dai et al. [1], which we find to produce only coplanar reconstructions. We therefore make the recommendation that 3D reconstruction error always be measured relative to a trivial reconstruction such as a planar one.

Approximate closed-form solutions of realistic true proportional navigation guidance using the Adomian decomposition method

Approximate closed-form solutions of the non-linear relative equations of motion of an interceptor pursuing a target under the realistic true proportional navigation (RTPN) guidance law are derived using the Adomian decomposition method in this article. In the literature, no study has been reported on derivation of explicit time-series solutions in closed form of the nonlinear dynamic engagement equations under the RTPN guidance. The Adomian method provides an analytical approximation, requiring no linearization or direct integration of the non-linear terms. The complete derivation of the Adomian polynomials for the analysis of the dynamics of engagement under RTPN guidance is presented for deterministic ideal case, and non-ideal dynamics in the loop that comprises autopilot and actuator dynamics and target manoeuvre, as well as, for a stochastic case. Numerical results illustrate the applicability of the method.

A hierarchical system of learning automata that can learn die globally optimal path

Systems of learning automata have been studied by various researchers to evolve useful strategies for decision making under uncertainity. Considered in this paper are a class of hierarchical systems of learning automata where the system gets responses from its environment at each level of the hierarchy. A classification of such sequential learning tasks based on the complexity of the learning problem is presented. It is shown that none of the existing algorithms can perform in the most general type of hierarchical problem. An algorithm for learning the globally optimal path in this general setting is presented, and its convergence is established. This algorithm needs information transfer from the lower levels to the higher levels. Using the methodology of estimator algorithms, this model can be generalized to accommodate other kinds of hierarchical learning tasks.

Note on the Similarity Solutions of Unsteady Jets in Rotating Fluids

The structure of time dependent jets in rotating fluids using similarity transformations is studied theoretically for which exact solutions are discussed. Approximate solution using a modified yon Mises transformation is also explored.

Multinomial solutions of the beach equation

Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.

Deriving optimal competition in infrastructure procurement

Typically only a limited number of consortiums are able to competitively bid for Public Private Partnership (PPP) projects. Consequently, this may lead to oligopoly pricing constraints and ineffective competition, thus engendering ex ante market failure. In addressing this issue, this paper aims to determine the optimal number of bidders required to ensure a healthy level of competition is available to procure major infrastructure projects. The theories of Structure-Conduct-Performance (SCP) paradigm; Game Theory and Auction Theory and Transaction Cost Economics are reviewed and discussed and used to produce an optimal level of competition for major infrastructure procurement, that prevents market failure ex ante (lack of competition) and market failure ex post (due to asymmetric lock-in).

Optimal Parameter Trajectory Estimation in Parameterized SDEs: An Algorithmic Procedure

We consider the problem of estimating the optimal parameter trajectory over a finite time interval in a parameterized stochastic differential equation (SDE), and propose a simulation-based algorithm for this purpose. Towards this end, we consider a discretization of the SDE over finite time instants and reformulate the problem as one of finding an optimal parameter at each of these instants. A stochastic approximation algorithm based on the smoothed functional technique is adapted to this setting for finding the optimal parameter trajectory. A proof of convergence of the algorithm is presented and results of numerical experiments over two different settings are shown. The algorithm is seen to exhibit good performance. We also present extensions of our framework to the case of finding optimal parameterized feedback policies for controlled SDE and present numerical results in this scenario as well.

Phase relations between Al2O3---Cr2O3 and FeAl2O4---FeCr2O4 solid solutions at 1823 K

Tie-lines between the corundum and spinel solid solutions have been determined experimentally at 1823 K. Next, activities of FeCr2O4 and FeAl2O4 in the spinel solid solution were determined by combining the tie-line data with literature values for the activities of Cr2O3 and Al2O3 in the corundum phase. Activities and the Gibbs energy of mixing for the spinel solid solution were also obtained from a model based on cation distribution between nonequivalent crystallographic sites in the oxide lattice. The difference between the Gibbs energy of mixing obtained experimentally and from the model has been attributed to a strain enthalpy term which is relatively unchanged in magnitude from the reported at 1373 K. The integral enthalpy of mixing obtained from experimental data at 1373 and 1823 K using the second law is compared with the model result.

Pitch discrimination in optimal and suboptimal acoustic environments: electroencephalographic, magnetoencephalographic, and behavioral evidence

Pitch discrimination is a fundamental property of the human auditory system. Our understanding of pitch-discrimination mechanisms is important from both theoretical and clinical perspectives. The discrimination of spectrally complex sounds is crucial in the processing of music and speech. Current methods of cognitive neuroscience can track the brain processes underlying sound processing either with precise temporal (EEG and MEG) or spatial resolution (PET and fMRI). A combination of different techniques is therefore required in contemporary auditory research. One of the problems in comparing the EEG/MEG and fMRI methods, however, is the fMRI acoustic noise. In the present thesis, EEG and MEG in combination with behavioral techniques were used, first, to define the ERP correlates of automatic pitch discrimination across a wide frequency range in adults and neonates and, second, they were used to determine the effect of recorded acoustic fMRI noise on those adult ERP and ERF correlates during passive and active pitch discrimination. Pure tones and complex 3-harmonic sounds served as stimuli in the oddball and matching-to-sample paradigms. The results suggest that pitch discrimination in adults, as reflected by MMN latency, is most accurate in the 1000-2000 Hz frequency range, and that pitch discrimination is facilitated further by adding harmonics to the fundamental frequency. Newborn infants are able to discriminate a 20% frequency change in the 250-4000 Hz frequency range, whereas the discrimination of a 5% frequency change was unconfirmed. Furthermore, the effect of the fMRI gradient noise on the automatic processing of pitch change was more prominent for tones with frequencies exceeding 500 Hz, overlapping with the spectral maximum of the noise. When the fundamental frequency of the tones was lower than the spectral maximum of the noise, fMRI noise had no effect on MMN and P3a, whereas the noise delayed and suppressed N1 and exogenous N2. Noise also suppressed the N1 amplitude in a matching-to-sample working memory task. However, the task-related difference observed in the N1 component, suggesting a functional dissociation between the processing of spatial and non-spatial auditory information, was partially preserved in the noise condition. Noise hampered feature coding mechanisms more than it hampered the mechanisms of change detection, involuntary attention, and the segregation of the spatial and non-spatial domains of working-memory. The data presented in the thesis can be used to develop clinical ERP-based frequency-discrimination protocols and combined EEG and fMRI experimental paradigms.

On exact solutions of the unsteady navierstokes equationsâ the vortex with instantaneous curvilinear axis

The unsteady pseudo plane motions have been investigated in which each point of the parallel planes is subjected to non-torsional oscillations in their own plane and at any given instant the streamlines are concentric circles. Exact solutions are obtained and the form of the curve , the locus of the centers of these concentric circles, is discussed. The existence of three infinite sets of exact solutions, for the flow in the geometry of an orthogonal rheometer in which the above non-torsional oscillations are superposed on the disks, is established. Three cases arise according to whether is greater than, equal to or less than , where is angular velocity of the basic rotation and is the frequency of the superposed oscillations. For a symmetric solution of the flow these solutions reduce to a single unique solution. The nature of the curve is illustrated graphically by considering an example of the flow between coaxial rotating disks.

A class of exact solutions for the flow of a micropolar fluid

The flow of a micropolar fluid in an orthogonal rheometer is considered. It is shown that an infinite number of exact solutions characterizing asymmetric motions are possible. The expressions for pressure in the fluid, the components of the forces and couples acting on the plates are obtained. The effect of microrotation on the flow is brought out by considering numerical results for the case of coaxially rotating disks.

Bi-criteria single machine scheduling problem with a learning effect: Aneja-Nair method to obtain the set of optimal sequences

In this paper, we consider the bi-criteria single machine scheduling problem of n jobs with a learning effect. The two objectives considered are the total completion time (TC) and total absolute differences in completion times (TADC). The objective is to find a sequence that performs well with respect to both the objectives: the total completion time and the total absolute differences in completion times. In an earlier study, a method of solving bi-criteria transportation problem is presented. In this paper, we use the methodology of solvin bi-criteria transportation problem, to our bi-criteria single machine scheduling problem with a learning effect, and obtain the set of optimal sequences,. Numerical examples are presented for illustrating the applicability and ease of understanding.

Dipole ordering in dilute solutions of ferroelectrics in antiferroelectric materials

The coefficients of thermal expansion reported by Worlton et al. [6] in the case of zircon are given in Table II along with the present data. Although Oql > or• in both cases, the anisotropy is more marked in the case of DyV04. From Table II, it is clear that the coefficient of volume expansion (,6) is almost the same for both compounds.