The theory of runs with application to drought predictions

The primary interest was in predicting the distribution runs in a sequence of Bernoulli trials. Difference equation techniques were used to express the number of runs of a given length k in n trials under three assumptions (1) no runs of length greater than k, (2) no runs of length less than k, (3) no other assumptions about the length of runs. Generating functions were utilized to obtain the distributions of the future number of runs, future number of minimum run lengths and future number of the maximum run lengths unconditional on the number of successes and failures in the Bernoulli sequence. When applying the model to Texas hydrology data, the model provided an adequate fit for the data in eight of the ten regions. Suggested health applications of this approach to run theory are provided. ^

(Table 1) Bulk and grain density, porosity, and p- and s-wave velocity characteristics of ODP Hole 163-990A sediments

Seismic velocities in rocks are influenced by the properties of the solid, the pore fluid, and the pore space. Cracks dramatically affect seismic velocities in rocks; their influence on the effective elastic moduli of rocks depends on their shape and concentration. Thin cracks (or fractures) substantially lower the moduli of a rock relative to the effect of spherical voids (or vesicles), and lower moduli are reflected by lower P- and S-wave velocities. The objective of this research is to determine the types and concentrations of cracks and their influence on the seismic properties of subaerially erupted basalts drilled from Hole 990A on the Southeast Greenland margin during Ocean Drilling Program Leg 163. Ellipsoidal cracks are used to model the voids in the rocks. The elastic moduli of the solid (grains) are also free parameters in the inverse modeling procedure. The apparent grain moduli reflect a weighted average of the moduli of the constituent minerals (e.g., plagioclase, augite, and clay minerals). The results indicate that (1) there is a strong relationship between P-wave velocity and porosity, suggesting a similarity of pore shape distributions, (2) the distribution of crack types within the massive, central region of aa flows from Hole 990A is independent of total porosity, (3) thin cracks are the first to be effectively sealed by alteration products, and (4) grain densities (an alteration index) and apparent grain moduli of the basalt samples are directly related.

Theory of a Flowchart Approach to Industrial Cluster Policy

A flowchart approach to industrial cluster policy emphasizes the importance ofthe ordering of policy measures. The flow of policy implementation is to establish an industrial zone, to invite an anchor company, and to promote its related companies to invest in the industrial zone. This article delineated "a flowchart approach to industrial cluster policy" by proposing sufficient conditions for forming industrial clusters typical in the manufacturing industry in Asia to enhance regional economic growth. The typical industrial cluster policy was theorized by defining an industrial zone as "quasi-public goods", and it was shown that the policy enhances economic growth under a production function of "increasing returns to scale" of an anchor company. Critical amounts of the production of "scale economies" that are used by the related companies to decide whether or not to invest in clusters were also shown.

A Mathematical Representation of "Excitement" in Games: A Contribution to the Theory of Game Systems

Researchers have long believed the concept of "excitement" in games to be subjective and difficult to measure. This paper presents the development of a mathematically computable index that measures the concept from the viewpoint of an audience and from that of a player. One of the key aspects of the index is the differential of the probability of "winning" before and after one specific "play" in a given game. The index makes a large contribution to the study of games and enables researchers to compare and analyze the “excitement” of various games. It may be applied in many fields, especially the area of welfare economics, and applications may range from those related to allocative efficiency to axioms of justice and equity.

Technical Challenges in the Construction of Gothic Vaults: The Gothic Theory of Structural Design

The construction of a Gothic vault implied the solution of several technical challenges. The literature on Gothic vault construction is quite large and its growth continues steadily. The main challenge of any structure is that, during and after construction, it must be "safe", that is, it must not collapse. Indeed, it must be amply safe, able to support different loads for long periods of time. Masonry architecture has shown its structural safety for centuries or millennia. The Pantheon of Rome stands today after almost 2,000 years without having needed any structural reinforcement (of course, the survival of any building implies continuous maintenance) . Hagia Sophia in Istanbul, finished in the 6th century AD, has withstood not only the dead loads but also many severe earthquakes . Finally, the Gothic cathedrals, with their appearance of weakness, are• more than a half millennium old. The question arises of what the source of this amazing strength is and how the illiterate master masons were able to design such daring and safe structures . This question is usually evaded in manuals of Gothic architecture. This is quite surprising, the structure being a fundamental part of Gothic buildings. The present article aims to give such an explanation, which has been studied in detail elsewhere. In the first part, the Gothic design methods "V ill be discussed. In the second part, the validity of these methods wi11 be verified within the frame of the modern theory of masonry structures . References have been reduced to a minimum to make the text simpler and more direct.

Nonrigid Motion Compensation of Free Breathing Acquired Myocardial Perfusion Data

In this work, we present a novel method to compensate the movement in images acquired during free breathing using first-pass gadolinium enhanced, myocardial perfusion magnetic resonance imaging (MRI). First, we use independent component analysis (ICA) to identify the optimal number of independent components (ICs) that separate the breathing motion from the intensity change induced by the contrast agent. Then, synthetic images are created by recombining the ICs, but other then in previously published work (Milles et al. 2008), we omit the component related to motion, and therefore, the resulting reference image series is free of motion. Motion compensation is then achieved by using a multi-pass non-rigid image registration scheme. We tested our method on 15 distinct image series (5 patients) consisting of 58 images each and we validated our method by comparing manually tracked intensity profiles of the myocardial sections to automatically generated ones before and after registration. The average correlation to the manually obtained curves before registration 0:89 0:11 was increased to 0:98 0:02

Hydrodynamic stability theory of double ablation front structures in inertial confinement fusion.

The aim of inertial confinement fusion is the production of energy by the fusion of thermonuclear fuel (deuterium-tritium) enclosed in a spherical target due to its implosion. In the direct-drive approach, the energy needed to spark fusion reactions is delivered by the irradiation of laser beams that leads to the ablation of the outer shell of the target (the so-called ablator). As a reaction to this ablation process, the target is accelerated inwards, and, provided that this implosion is sufficiently strong a symmetric, the requirements of temperature and pressure in the center of the target are achieved leading to the ignition of the target (fusion). One of the obstacles capable to prevent appropriate target implosions takes place in the ablation region where any perturbation can grow even causing the ablator shell break, due to the ablative Rayleigh-Taylor instability. The ablative Rayleigh-Taylor instability has been extensively studied throughout the last 40 years in the case where the density/temperature profiles in the ablation region present a single front (the ablation front). Single ablation fronts appear when the ablator material has a low atomic number (deuterium/tritium ice, plastic). In this case, the main mechanism of energy transport from the laser energy absorption region (low density plasma) to the ablation region is the electron thermal conduction. However, recently, the use of materials with a moderate atomic number (silica, doped plastic) as ablators, with the aim of reducing the target pre-heating caused by suprathermal electrons generated by the laser-plasma interaction, has demonstrated an ablation region composed of two ablation fronts. This fact appears due to increasing importance of radiative effects in the energy transport. The linear theory describing the Rayleigh-Taylor instability for single ablation fronts cannot be applied for the stability analysis of double ablation front structures. Therefore, the aim of this thesis is to develop, for the first time, a linear stability theory for this type of hydrodynamic structures.

An approach to automatic learning assessment based on the computational theory of perceptions

E-learning systems output a huge quantity of data on a learning process. However, it takes a lot of specialist human resources to manually process these data and generate an assessment report. Additionally, for formative assessment, the report should state the attainment level of the learning goals defined by the instructor. This paper describes the use of the granular linguistic model of a phenomenon (GLMP) to model the assessment of the learning process and implement the automated generation of an assessment report. GLMP is based on fuzzy logic and the computational theory of perceptions. This technique is useful for implementing complex assessment criteria using inference systems based on linguistic rules. Apart from the grade, the model also generates a detailed natural language progress report on the achieved proficiency level, based exclusively on the objective data gathered from correct and incorrect responses. This is illustrated by applying the model to the assessment of Dijkstra’s algorithm learning using a visual simulation-based graph algorithm learning environment, called GRAPHs

Automatic motion compensation of free breathing acquired myocardial perfusion data by using independent component analysis

Images acquired during free breathing using first-pass gadolinium-enhanced myocardial perfusion magnetic resonance imaging (MRI) exhibit a quasiperiodic motion pattern that needs to be compensated for if a further automatic analysis of the perfusion is to be executed. In this work, we present a method to compensate this movement by combining independent component analysis (ICA) and image registration: First, we use ICA and a time?frequency analysis to identify the motion and separate it from the intensity change induced by the contrast agent. Then, synthetic reference images are created by recombining all the independent components but the one related to the motion. Therefore, the resulting image series does not exhibit motion and its images have intensities similar to those of their original counterparts. Motion compensation is then achieved by using a multi-pass image registration procedure. We tested our method on 39 image series acquired from 13 patients, covering the basal, mid and apical areas of the left heart ventricle and consisting of 58 perfusion images each. We validated our method by comparing manually tracked intensity profiles of the myocardial sections to automatically generated ones before and after registration of 13 patient data sets (39 distinct slices). We compared linear, non-linear, and combined ICA based registration approaches and previously published motion compensation schemes. Considering run-time and accuracy, a two-step ICA based motion compensation scheme that first optimizes a translation and then for non-linear transformation performed best and achieves registration of the whole series in 32 ± 12 s on a recent workstation. The proposed scheme improves the Pearsons correlation coefficient between manually and automatically obtained time?intensity curves from .84 ± .19 before registration to .96 ± .06 after registration

Theory of a probe in a strong magnetic field

An asymptotic analysis of the Langmuir-probe problem in a quiescent, fully ionized plasma in a strong magnetic field is performed, for electron cyclotron radius and Debye length much smaller than probe radius, and this not larger than either ion cyclotron radius or mean free path. It is found that the electric potential, which is not confined to a sheath, controls the diffusion far from the probe; inside the magnetic tube bounded by the probe cross section the potential overshoots to a large value before decaying to its value in the body of the plasma. The electron current is independent of the shape of the body along the field and increases with ion temperature; due to the overshoot in the potential, (1) the current at negative voltages does not vary exponentially, (2) its magnitude is strongly reduced by the field, and (3) the usual sharp knee at space potential, disappears. In the regions of the C-V diagram studied the ion current is negligible or unaffected by the field. Some numerical results are presented.The theory, which fails beyond certain positive voltage, fields useful results for weak fields, too.

Control motion approach of a lower limb orthosis to reduce energy consumption

By analysing the dynamic principles of the human gait, an economic gait‐control analysis is performed, and passive elements are included to increase the energy efficiency in the motion control of active orthoses. Traditional orthoses use position patterns from the clinical gait analyses (CGAs) of healthy people, which are then de‐normalized and adjusted to each user. These orthoses maintain a very rigid gait, and their energy cosT is very high, reducing the autonomy of the user. First, to take advantage of the inherent dynamics of the legs, a state machine pattern with different gains in eachstate is applied to reduce the actuator energy consumption. Next, different passive elements, such as springs and brakes in the joints, are analysed to further reduce energy consumption. After an off‐line parameter optimization and a heuristic improvement with genetic algorithms, a reduction in energy consumption of 16.8% is obtained by applying a state machine control pattern, and a reduction of 18.9% is obtained by using passive elements. Finally, by combining both strategies, a more natural gait is obtained, and energy consumption is reduced by 24.6%compared with a pure CGA pattern.

The theory of electrostatic probes in strong magnetic fields : Thesis submitted to the Faculty of The Graduate School of the University of Colorado for the Degree Doctor of Philosophy Department of Aerospace Engineering Science

A theory is developed of an electrostatic probe in a fully-ionized plasma in the presence of a strong magnetic field. The ratio of electron Larmor radius to probe transverse dimension is assumed to be small. Poisson's equation, together with kinetic equations for ions and electrons are considered. An asymptotic perturbation method of multiple scales is used by considering the characteristic lengths appearing in the problem. The leading behavior of the solution is found. The results obtained appear to apply to weaker fields also, agreeing with the solutions known in the limit of no magnetic field. The range of potentials for wich results are presented is limited. The basic effects produced by the field are a depletion of the plasma near the probe and a non-monotonic potential surrounding the probe. The ion saturation current is not changed but changes appear in both the floating potential Vf and the slope of the current-voltage diagram at Vf. The transition region extends beyond the space potential Vs,at wich point the current is largely reduced. The diagram does not have an exponential form in this region as commonly assumed. There exists saturation in electron collection. The extent to which the plasma is disturbed is determined. A cylindrical probe has no solution because of a logarithmic singularity at infinity. Extensions of the theory are considered.

Theory of a Probe in a Strong Magnetic Field. AT(30-1)-1238-MATT 599

A kinetic approach is used to develop a theory of electrostatic probes in a fully ionized plasma in the presence of a magnetic field. A consistent asymptotic expansion is obtained assuming that the electron Larmor radius is small compared to the radius of the probe. The order of magnitude of neglected terms is given. It is found that the electric potential within the tube of force defined by the cross section of the probe decays non-mono tonic ally from the probe; this bump disappears at a certain probe voltage and the theory is valid up to this voltage. The transition region, which extends beyond plasma potential, is not exponential. The possible saturation of the electron current is discussed. Restricted numerical results are given; they seem to be useful for weaker magnetic fields down to the zero-field limit. Extensions of the theory a r e considered.