Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.

Tidal effects on sea water intrusion in unconfined aquifers

A variable-density groundwater model is used to analyse the effects of tidal fluctuations on sea-water intrusion in an unconfined aquifer. It is shown that the tidal activity forces the sea-water to intrude further inland and it also creates a thicker interface than would occur without tidal effects. Moreover, the configuration of the interface is radically changed when the tidal fluctuations are included. This is because of the dramatic changes in the flow pattern and velocity of the groundwater near the shoreline. For aquifer depths much larger than tidal amplitudes, the tidal fluctuation does not have much effect on how far the sea-water intrudes into the aquifer; nevertheless, a significant change in the configuration of concentration contours because of the effect of tidal fluctuations is observed. This change is more noticeable at the top of the aquifer, near the water table, than at the bottom of the aquifer, and is caused by the infiltration of salt water into the top of the aquifer at higher tidal levels. A flatter beach slope, therefore, intensifies this phenomenon. The interface configurations do not change noticeably over the course of a tidal cycle. Neglecting tidal fluctuation effects results in an inaccurate evaluation of the water table elevation at the land end of the aquifer, although no distinguishable difference is seen between the water tables near the shoreline. Where the landward boundary condition is a constant head, the effects of tidal fluctuations on sea-water intrusion are more pronounced than for cases where the landward boundary condition is a specified flux. Also it is shown that the effects of tidal fluctuations are more significant for a sloping beach than for a vertical shoreline and the salt water intrudes further inland for the sloping case. (C) 1999 Elsevier Science B.V. All rights reserved.

Errors in lamina growth of primary olfactory axons in the rat and mouse olfactory bulb

In the adult olfactory nerve pathway of rodents, each primary olfactory axon forms a terminal arbor in a single glomerulus in the olfactory bulb. During development, axons are believed to project directly to and terminate precisely within a glomerulus without any exuberant growth or mistargeting. To gain insight into mechanisms underlying this process, the trajectories of primary olfactory axons during glomerular formation were studied in the neonatal period. Histochemical staining of mouse olfactory bulb sections with the lectin Dolichos biflorus-agglutinin revealed that many olfactory axons overshoot the glomerular layer and course into the deeper laminae of the bulb in the early postnatal period. Single primary olfactory axons were anterogradely labelled either with the lipophilic carbocyanine dye, 1,1'-dioctodecyl-3,3,3',3'-tetramethylindocarbocyanine perchlorate (DiI), or with horseradish peroxidase (HRP) by localized microinjections into the nerve fiber layer of the rat olfactory bulb. Five distinct trajectories of primary olfactory axons were observed in DLI-labelled preparations at postnatal day 1.5 (P1.5). Axons either coursed directly to and terminated specifically within a glomerulus, branched before terminating in a glomerulus, bypassed glomeruli and entered the underlying external plexiform layer, passed through the glomerular layer with side branches into glomeruli, or branched into more than one glomerulus. HRP-labelled axon arbors from eight postnatal ages were reconstructed by camera lucida and were used to determine arbor length, arbor area, and arbor branch number. Whereas primary olfactory axons display errors in laminar targeting in the mammalian olfactory bulb, axon arbors typically achieve their adult morphology without exuberant growth. Many olfactory axons appear not to recognize appropriate cues to terminate within the glomerular layer during the early postnatal period. However, primary olfactory axons exhibit precise targeting in the glomerular layer after P5.5, indicating temporal differences in either the presence of guidance cues or the ability of axons to respond to these cues. (C) 1999 Wiley-Liss, Inc.

Quantum error correction for continuously detected errors

We show that quantum feedback control can be used as a quantum-error-correction process for errors induced by a weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per physical qubit, quantum feedback can act to perfectly protect a stabilizer codespace. Using the stabilizer formalism we derive an explicit scheme, involving feedback and an additional constant Hamiltonian, to protect an (n-1)-qubit logical state encoded in n physical qubits. This works for both Poisson (jump) and white-noise (diffusion) measurement processes. Universal quantum computation is also possible in this scheme. As an example, we show that detected-spontaneous emission error correction with a driving Hamiltonian can greatly reduce the amount of redundancy required to protect a state from that which has been previously postulated [e.g., Alber , Phys. Rev. Lett. 86, 4402 (2001)].

An equivalent algorithm for simulating thermal effects of magma intrusion problems in porous rocks

An equivalent algorithm is proposed to simulate thermal effects of the magma intrusion in geological systems, which are composed of porous rocks. Based on the physical and mathematical equivalence, the original magma solidification problem with a moving boundary between the rock and intruded magma is transformed into a new problem without the moving boundary but with a physically equivalent heat source. From the analysis of an ideal solidification model, the physically equivalent heat source has been determined in this paper. The major advantage in using the proposed equivalent algorithm is that the fixed finite element mesh with a variable integration time step can be employed to simulate the thermal effect of the intruded magma solidification using the conventional finite element method. The related numerical results have demonstrated the correctness and usefulness of the proposed equivalent algorithm for simulating the thermal effect of the intruded magma solidification in geological systems. (C) 2003 Elsevier B.V. All rights reserved.

Standard errors of fitted component means of normal mixtures

In this paper use consider the problem of providing standard errors of the component means in normal mixture models fitted to univariate or multivariate data by maximum likelihood via the EM algorithm. Two methods of estimation of the standard errors are considered: the standard information-based method and the computationally-intensive bootstrap method. They are compared empirically by their application to three real data sets and by a small-scale Monte Carlo experiment.

Transcriptional Errors in Human Immunodeficiency Virus Type 1 Generate Targets for T-Cell Responses

We measured T-cell responses to human immunodeficiency virus type 1 (HIV-1) cryptic epitopes encoded by regions of the viral genome not normally translated into viral proteins. T-cell responses to cryptic epitopes and to regions normally spliced out of the HIV-1 viral proteins Rev and Tat were detected in HIV-1-infected subjects.

A uniform white-noise model for fixed-point roundoff errors in digital systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.

Pseudo-randomness of round-off errors in discretized linear maps on the plane

We analyze the sequences of round-off errors of the orbits of a discretized planar rotation, from a probabilistic angle. It was shown [Bosio & Vivaldi, 2000] that for a dense set of parameters, the discretized map can be embedded into an expanding p-adic dynamical system, which serves as a source of deterministic randomness. For each parameter value, these systems can generate infinitely many distinct pseudo-random sequences over a finite alphabet, whose average period is conjectured to grow exponentially with the bit-length of the initial condition (the seed). We study some properties of these symbolic sequences, deriving a central limit theorem for the deviations between round-off and exact orbits, and obtain bounds concerning repetitions of words. We also explore some asymptotic problems computationally, verifying, among other things, that the occurrence of words of a given length is consistent with that of an abstract Bernoulli sequence.

Handling random errors and biases in methods used for short-term dietary assessment

Epidemiological studies have shown the effect of diet on the incidence of chronic diseases; however, proper planning, designing, and statistical modeling are necessary to obtain precise and accurate food consumption data. Evaluation methods used for short-term assessment of food consumption of a population, such as tracking of food intake over 24h or food diaries, can be affected by random errors or biases inherent to the method. Statistical modeling is used to handle random errors, whereas proper designing and sampling are essential for controlling biases. The present study aimed to analyze potential biases and random errors and determine how they affect the results. We also aimed to identify ways to prevent them and/or to use statistical approaches in epidemiological studies involving dietary assessments.

Intrusion of Lamprophyre dyke and related deformation effects in the host rock salt: A case study from the Loulé Diapir, Portugal

A rock salt-lamprophyre dyke contact zone (sub-vertical, NE-SW strike) was investigated for its petrographic, mechanic and physical properties by means of anisotropy of magnetic susceptibility CAMS) and rock magnetic properties, coupled with quantitative microstructural analysis and thermal mathematical modelling. The quantitative microstructural analysis of halite texture and solid inclusions revealed good spatial correlation with AMS and halite fabrics. The fabrics of both lamprophyre and rock salt record the magmatic intrusion, "plastic" flow and regional deformation (characterized by a NW-SE trending steep foliation). AMS and microstructural analysis revealed two deformation fabrics in the rock salt: (1) the deformation fabrics in rock salt on the NW side of the dyke are associated with high temperature and high fluid activity attributed to the dyke emplacement; (2) On the opposite side of the dyke, the emplacement-related fabric is reworked by localized tectonic deformation. The paleomagnetic results suggest significant rotation of the whole dyke, probably during the diapir ascent and/or the regional Tertiary to Quaternary deformation. (C) 2014 Elsevier B.V. All rights reserved.

How human schematization and systematic errors take effect on sketch map formalizations

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies