On the Distribution of the Sum of n Non-Identically Distributed Uniform Random Variables

The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the characteristic function, we derive explicit formulae for the distribution of the sum of n non-identically distributed uniform random variables in both the continuous and the discrete case. The results, though involved, have a certain elegance. As examples, we derive from our general formulae some special cases which have appeared in the literature.Comment: 20 page

Consistency in statistical moments as a test for bubble cloud clustering

Frequency dependent measurements of attenuation and/or sound speed through clouds of gas bubbles in liquids are often inverted to find the bubble size distribution and the void fraction of gas. The inversions are often done using an effective medium theory as a forward model under the assumption that the bubble positions are Poisson distributed (i.e., statistically independent). Under circumstances in which single scattering does not adequately describe the pressure field, the assumption of independence in position can yield large errors when clustering is present, leading to errors in the inverted bubble size distribution. It is difficult, however, to determine the existence of clustering in bubble clouds without the use of specialized acoustic or optical imaging equipment. A method is described here in which the existence of bubble clustering can be identified by examining the consistency between the first two statistical moments of multiple frequency acoustic measurements

Thermal Analysis of As-received and Clinically Retrieved Copper-Nickel-Titanium Orthodontic Archwires

Objective: To compare as-received copper-nickel-titanium (CuNiTi) archwires to those used in patients by means of differential scanning calorimetry (DSC). Also, the thermal or phase properties of 27°C, 35°C, and 40°C CuNiTi archwires were studied to ascertain if their properties match those indicated by the manufacturer. Materials and Methods: Six wires of 27°C, 35°C, and 40°C CuNiTi were tested as-received, and six each of the 27°C and 35°C wires were examined after use in patients for an average of approximately 9 and 7 weeks, respectively. Segments of archwire were investigated by DSC over the temperature range from −100°C to 150°C at 10°C per minute. Results: There were no significant differences between as-received and clinically used 27°C and 35°C wires for all parameters (heating onset, endset, and enthalpy and cooling onset, endset, and enthalpy), except the 27°C wires exhibited a significant decrease in the heating enthalpy associated with the martensite-to-austenite transition after clinical use. The heating endsets (austenite finish temperatures) of the 27°C and 35°C wires were within 2°C of those claimed by the manufacturer, but the 40°C wires were found to be nearer to 36°C than 40°C. Conclusions: Clinical use of CuNiTi wires resulted in few differences when compared with as-received wires analyzed by DSC. Two temperature varieties of CuNiTi are reasonably within the parameters of those identified by the manufacturer

An Estimate of the Gas Transfer Rate from Oceanic Bubbles Derived from Multibeam Sonar Observations of a Ship Wake

Measurements of gas transfer rates from bubbles have been made in the laboratory, but these are difficult to extrapolate to oceanic bubbles where populations of surfactants and particulate matter that inhibit gas transfer are different. Measurements at sea are complicated by unknown bubble creation rates that make it difficult to uniquely identify and observe the evolution of individual bubble clouds. One method that eliminates these difficulties is to measure bubbles in a ship wake where bubble creation at any given location is confined to the duration of the passing ship. This method assumes that the mechanisms slowing the gas dissolution of naturally created bubbles act in a similar manner to slow the dissolution of bubbles in a ship wake. A measurement of the gas transfer rate for oceanic bubbles using this method is reported here. A high-frequency upward-looking multibeam echosounder was used to measure the spatial distribution of bubbles in the wake of a twin screw 61-m research vessel. Hydrodynamic forcing functions are extracted from the multibeam data and used in a bubble cloud evolution model in which the gas transfer rate is treated as a free parameter. The output of model runs corresponding to different gas transfer rates is compared to the time-dependent wake depth observed in the data. Results indicating agreement between the model and the data show that the gas transfer rate must be approximately 15 times less then it would be for surfactant-free bubbles in order to explain the bubble persistence in the wake

The Use of Multi-beam Sonars to Image Bubbly Ship Wakes

During the past five years, researchers at Penn State University (PSU) have used upward-looking multi-beam (MB) sonar to image the bubbly wakes of surface ships. In 2000, a 19-beam, 5° beam width, 120° sector, 250 kHz MB sonar integrated into an autonomous vehicle was used to obtain a first-of-a-kind look at the three-dimensional variability of bubbles in a large ship wake. In 2001 we acquired a Reson 8101 MB sonar, which operates at 240 kHz and features 101-1.5º beams spanning a 150º sector. In July 2002, the Reson sonar was deployed looking upward from a 1.4 m diameter buoy moored at 29.5 m depth in 550 m of water using three anchor lines. A fiber optic cable connected the sonar to a support ship 500 m away. Images of the wake of a small research vessel provided new information about the persistence of bubble clouds in the ocean. An important goal is to use the MB sonar to estimate wake bubble distributions, as has been done with single beam sonar. Here we show that multipath interference and strong, specular reflections from the sea surface adversely affect the use of MB sonars to unambiguously estimate wake bubble distributio

Electricity load profile classification using Fuzzy C-Means method

This paper presents the Fuzzy C-Means (FCM) clustering method. The FCM technique assigns a degree of membership for each data set to several clusters, thus offering the opportunity to deal with load profiles that could belong to more than one group at the same time. The FCM algorithm is based on minimising a c-means objective function to determine an optimal classification. The simulation of FCM was carried out using actual sample data from Indonesia and the results are presented. Some validity index measurements was carried out to estimate the compactness of the resulting clusters or to find the optimal number of clusters for a data set

Multimodal Representation of Space in the Posterior Parietal Cortex and its use in Planning Movements

Recent experiments are reviewed that indicate that sensory signals from many modalities, as well as efference copy signals from motor structures, converge in the posterior parietal cortex in order to code the spatial locations of goals for movement. These signals are combined using a specific gain mechanism that enables the different coordinate frames of the various input signals to be combined into common, distributed spatial representations. These distributed representations can be used to convert the sensory locations of stimuli into the appropriate motor coordinates required for making directed movements. Within these spatial representations of the posterior parietal cortex are neural activities related to higher cognitive functions, including attention. We review recent studies showing that the encoding of intentions to make movements is also among the cognitive functions of this area