Distance Distributions and Energy of Designs in Hamming Spaces

We obtain new combinatorial upper and lower bounds for the potential energy of designs in q-ary Hamming space. Combined with results on reducing the number of all feasible distance distributions of such designs this gives reasonable good bounds. We compute and compare our lower bounds to recently obtained universal lower bounds. Some examples in the binary case are considered.

Minimum Description Length Principle in Discriminating Marginal Distributions

2010 Mathematics Subject Classification: 94A17, 62B10, 62F03.

Régularité Lipschitzienne des Géodésiques Minimisantes pour Quelques Distributions Affines

2000 Mathematics Subject Classification: 49J15, 49J30, 53B50.

On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)

MSC 2010: 46F30, 46F10

International stock portfolio selection and performance measures recognizing higher moments of return distributions

Since the seminal works of Markowitz (1952), Sharpe (1964), and Lintner (1965), numerous studies on portfolio selection and performance measure have been based upon the mean-variance framework. However, several researchers (e.g., Arditti (1967, and 1971), Samuelson (1970), and Rubinstein (1973)) argue that the higher moments cannot be neglected unless there is reason to believe that: (i) the asset returns are normally distributed and the investor's utility function is quadratic, or (ii) the empirical evidence demonstrates that higher moments are irrelevant to the investor's decision. Based on the same argument, this dissertation investigates the impact of higher moments of return distributions on three issues concerning the 14 international stock markets.^ First, the portfolio selection with skewness is determined using: the Polynomial Goal Programming in which investor preferences for skewness can be incorporated. The empirical findings suggest that the return distributions of international stock markets are not normally distributed, and that the incorporation of skewness into an investor's portfolio decision causes a major change in the construction of his optimal portfolio. The evidence also indicates that an investor will trade expected return of the portfolio for skewness. Moreover, when short sales are allowed, investors are better off as they attain higher expected return and skewness simultaneously.^ Second, the performance of international stock markets are evaluated using two types of performance measures: (i) the two-moment performance measures of Sharpe (1966), and Treynor (1965), and (ii) the higher-moment performance measures of Prakash and Bear (1986), and Stephens and Proffitt (1991). The empirical evidence indicates that higher moments of return distributions are significant and relevant to the investor's decision. Thus, the higher moment performance measures should be more appropriate to evaluate the performances of international stock markets. The evidence also indicates that various measures provide a vastly different performance ranking of the markets, albeit in the same direction.^ Finally, the inter-temporal stability of the international stock markets is investigated using the Parhizgari and Prakash (1989) algorithm for the Sen and Puri (1968) test which accounts for non-normality of return distributions. The empirical finding indicates that there is strong evidence to support the stability in international stock market movements. However, when the Anderson test which assumes normality of return distributions is employed, the stability in the correlation structure is rejected. This suggests that the non-normality of the return distribution is an important factor that cannot be ignored in the investigation of inter-temporal stability of international stock markets. ^

Statistical analysis and optimal classification of blood cell populations using Gaussian distributions

This dissertation develops a new figure of merit to measure the similarity (or dissimilarity) of Gaussian distributions through a novel concept that relates the Fisher distance to the percentage of data overlap. The derivations are expanded to provide a generalized mathematical platform for determining an optimal separating boundary of Gaussian distributions in multiple dimensions. Real-world data used for implementation and in carrying out feasibility studies were provided by Beckman-Coulter. It is noted that although the data used is flow cytometric in nature, the mathematics are general in their derivation to include other types of data as long as their statistical behavior approximate Gaussian distributions. ^ Because this new figure of merit is heavily based on the statistical nature of the data, a new filtering technique is introduced to accommodate for the accumulation process involved with histogram data. When data is accumulated into a frequency histogram, the data is inherently smoothed in a linear fashion, since an averaging effect is taking place as the histogram is generated. This new filtering scheme addresses data that is accumulated in the uneven resolution of the channels of the frequency histogram. ^ The qualitative interpretation of flow cytometric data is currently a time consuming and imprecise method for evaluating histogram data. This method offers a broader spectrum of capabilities in the analysis of histograms, since the figure of merit derived in this dissertation integrates within its mathematics both a measure of similarity and the percentage of overlap between the distributions under analysis. ^

Tropical seagrass-associated macroalgae distributions and trends relative to water quality

Tropical coastal marine ecosystems including mangroves, seagrass beds and coral reef communities are undergoing intense degradation in response to natural and human disturbances, therefore, understanding the causes and mechanisms present challenges for scientist and managers. In order to protect our marine resources, determining the effects of nutrient loads on these coastal systems has become a key management goal. Data from monitoring programs were used to detect trends of macroalgae abundances and develop correlations with nutrient availability, as well as forecast potential responses of the communities monitored. Using eight years of data (1996–2003) from complementary but independent monitoring programs in seagrass beds and water quality of the Florida Keys National Marine Sanctuary (FKNMS), we: (1) described the distribution and abundance of macroalgae groups; (2) analyzed the status and spatiotemporal trends of macroalgae groups; and (3) explored the connection between water quality and the macroalgae distribution in the FKNMS. In the seagrass beds of the FKNMS calcareous green algae were the dominant macroalgae group followed by the red group; brown and calcareous red algae were present but in lower abundance. Spatiotemporal patterns of the macroalgae groups were analyzed with a non-linear regression model of the abundance data. For the period of record, all macroalgae groups increased in abundance (Abi) at most sites, with calcareous green algae increasing the most. Calcareous green algae and red algae exhibited seasonal pattern with peak abundances (Φi) mainly in summer for calcareous green and mainly in winter for red. Macroalgae Abi and long-term trend (mi) were correlated in a distinctive way with water quality parameters. Both the Abi and mi of calcareous green algae had positive correlations with NO3−, NO2−, total nitrogen (TN) and total organic carbon (TOC). Red algae Abi had a positive correlation with NO2−, TN, total phosphorus and TOC, and the mi in red algae was positively correlated with N:P. In contrast brown and calcareous red algae Abi had negative correlations with N:P. These results suggest that calcareous green algae and red algae are responding mainly to increases in N availability, a process that is happening in inshore sites. A combination of spatially variable factors such as local current patterns, nutrient sources, and habitat characteristics result in a complex array of the macroalgae community in the seagrass beds of the FKNMS.

Spatial and temporal distributions of epiphytic diatoms growing on Thalassia testudinum Banks ex König: relationships to water quality

The spatial and temporal distributions of the epiphytic diatom flora on Thalassia testudinum was described within the Florida Bay estuary and at one Atlantic site east of the Florida Keys over a 1-year period. Species of the genus Mastogloia dominated the epiphytic diatom flora (82 out of 332 total species). Nonmetric Multidimensional Scaling (NMDS) and Analysis of Similarity (ANOSIM) revealed four distinct spatial assemblages and two temporal assemblages. Eastern and western Florida Bay assemblages were identified within the estuary. The eastern diatom assemblage was characterized by high relative abundances of Brachysira aponina and Nitzschia liebetruthii, while the western assemblage was characterized by the abundance of Reimerothrix floridensis, particularly during summer. Two diverse and distinct marine assemblages, one located in the Gulf of Mexico along the western edge of Florida Bay and the other behind the Florida reef tract in the Atlantic Ocean, were also identified. Analysis of the spatial distribution of diatoms and water quality characteristics within Florida Bay suggest that these assemblages may be structured by salinity and nutrient availability, particularly P. The Gulf of Mexico and the western Florida Bay assemblages were associated with higher water column salinities and TP concentrations and lower DIN concentrations and TN:TP ratios relative to the eastern Florida Bay assemblage. The temporal variation in diatom assemblages was associated with water temperature, though temporal indicator species were few relative to the number of spatial indicators.

Forecasting Responses of Seagrass Distributions to Changing Water Quality Using Monitoring Data

Extensive data sets on water quality and seagrass distributions in Florida Bay have been assembled under complementary, but independent, monitoring programs. This paper presents the landscape-scale results from these monitoring programs and outlines a method for exploring the relationships between two such data sets. Seagrass species occurrence and abundance data were used to define eight benthic habitat classes from 677 sampling locations in Florida Bay. Water quality data from 28 monitoring stations spread across the Bay were used to construct a discriminant function model that assigned a probability of a given benthic habitat class occurring for a given combination of water quality variables. Mean salinity, salinity variability, the amount of light reaching the benthos, sediment depth, and mean nutrient concentrations were important predictor variables in the discriminant function model. Using a cross-validated classification scheme, this discriminant function identified the most likely benthic habitat type as the actual habitat type in most cases. The model predicted that the distribution of benthic habitat types in Florida Bay would likely change if water quality and water delivery were changed by human engineering of freshwater discharge from the Everglades. Specifically, an increase in the seasonal delivery of freshwater to Florida Bay should cause an expansion of seagrass beds dominated by Ruppia maritima and Halodule wrightii at the expense of the Thalassia testudinum-dominated community that now occurs in northeast Florida Bay. These statistical techniques should prove useful for predicting landscape-scale changes in community composition in diverse systems where communities are in quasi-equilibrium with environmental drivers.

Electronic Channels of Distributions: Challenges and Solutions for Hotel Operators

This paper addresses the issues of hotel operators identifying effective means of allocating rooms through various electronic channels of distribution. Relying upon the theory of coercive isomorphism, a think tank was constructed to identify and define electronic channels of distribution currently being utilized in the hotel industry. Through two full-day focus groups consisting of key hotel electives and industry practitioners, distribution channels wen identified as were challenges and solutions associated with each

Experimental deuteron momentum distributions with reduced final state interactions

This dissertation presents a study of the D( e, e′p)n reaction carried out at the Thomas Jefferson National Accelerator Facility (Jefferson Lab) for a set of fixed values of four-momentum transfer Q 2 = 2.1 and 0.8 (GeV/c)2 and for missing momenta pm ranging from pm = 0.03 to pm = 0.65 GeV/c. The analysis resulted in the determination of absolute D(e,e′ p)n cross sections as a function of the recoiling neutron momentum and it's scattering angle with respect to the momentum transfer [vector] q. The angular distribution was compared to various modern theoretical predictions that also included final state interactions. The data confirmed the theoretical prediction of a strong anisotropy of final state interaction contributions at Q2 of 2.1 (GeV/c)2 while at the lower Q2 value, the anisotropy was much less pronounced. At Q2 of 0.8 (GeV/c)2, theories show a large disagreement with the experimental results. The experimental momentum distribution of the bound proton inside the deuteron has been determined for the first time at a set of fixed neutron recoil angles. The momentum distribution is directly related to the ground state wave function of the deuteron in momentum space. The high momentum part of this wave function plays a crucial role in understanding the short-range part of the nucleon-nucleon force. At Q2 = 2.1 (GeV/c)2, the momentum distribution determined at small neutron recoil angles is much less affected by FSI compared to a recoil angle of 75°. In contrast, at Q2 = 0.8 (GeV/c)2 there seems to be no region with reduced FSI for larger missing momenta. Besides the statistical errors, systematic errors of about 5–6 % were included in the final results in order to account for normalization uncertainties and uncertainties in the determi- nation of kinematic veriables. The measurements were carried out using an electron beam energy of 2.8 and 4.7 GeV with beam currents between 10 to 100 &mgr; A. The scattered electrons and the ejected protons originated from a 15cm long liquid deuterium target, and were detected in conicidence with the two high resolution spectrometers of Hall A at Jefferson Lab.^

Association between mean residual life (MRL) and failure rate functions for continuous and discrete lifetime distributions

The purpose of this study was to correct some mistakes in the literature and derive a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. It was also desired to find the conditions under which the discrete failure rate function has an upside-down bathtub shape if corresponding MRL function has a bathtub shape. The study showed that if discrete MRL has a bathtub shape, then under some conditions the corresponding failure rate function has an upside-down bathtub shape. Also the study corrected some mistakes in proofs of Tang, Lu and Chew (1999) and established a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. Similarly, some mistakes in Gupta and Gupta (2000) are corrected, with the ensuing results being expanded and proved thoroughly to establish the relationship between the crossing points of the failure rate and associated MRL functions. The new results derived in this study will be useful to model various lifetime data that occur in environmental studies, medical research, electronics engineering, and in many other areas of science and technology.

Age models, accumulation rates, and grain size distributions of sediment cores from the northern subtropical Atlantic

The terrigenous sediment proportion of the deep sea sediments from off Northwest Africa has been studied in order to distinguish between the aeolian and the fluvial sediment supply. The present and fossil Saharan dust trajectories were recognized from the distribution patterns of the aeolian sediment. The following timeslices have been investigated: Present, 6,000, 12,000 and 18,000 y. B. P. Furthermore, the quantity of dust deposited off the Saharan coast has been estimated. For this purpose, 80 surface sediment samples and 34 sediment cores have been analysed. The stratigraphy of the cores has been achieved from oxygen isotopic curves, 14C-dating, foraminiferal transfer temperatures, and carbonate contents. Silt sized biogenic opal generally accounts for less than 2 % of the total insoluble sediment proportion. Only under productive upwelling waters and off river mouths, the opal proportion exceeds 2 % significantly. The modern terrigenous sediment from off the Saharan coast is generally characterized by intensely stained quartz grains. They indicate an origin from southern Saharan and Sahelian laterites, and a zonal aeolian transport in midtropospheric levels, between 1.5 an 5.5 km, by 'Harmattan' Winds. The dust particles follow large outbreaks of Saharan air across the African coast between 15° and 21° N. Their trajectories are centered at about 18° N and continue further into a clockwise gyre situated south of the Canary Islands. This course is indicated by a sickle-shaped tongue of coarser grain sizes in the deep-sea sediment. Such loess-sized terrigenous particles only settle within a zone extending to 700 km offshore. Fine silt and clay sized particles, with grain sizes smaller than 10- 15 µm, drift still further west and can be traced up to more than 4,000 km distance from their source areas. Additional terrigenous silt which is poor in stained quartz occurs within a narrow zone off the western Sahara between 20° and 27° N only. It depicts the present dust supply by the trade winds close to the surface. The dust load originates from the northwestern Sahara, the Atlas Mountains and coastal areas, which contain a particularly low amount of stained quartz. The distribution pattern of these pale quartz sediments reveals a SSW-dispersal of dust being consistent with the present trade wind direction from the NNE. In comparison to the sediments from off the Sahara and the deeper subtropical Atlantic, the sediments off river mouths, in particular off the Senegal river, are characterized by an additional input of fine grained terrigenous particles (< 6 µm). This is due to fluvial suspension load. The fluvial discharge leads to a relative excess of fine grained particles and is observed in a correlation diagram of the modal grain sizes of terrigenous silt with the proportion of fine fraction (< 6 µm). The aeolian sediment contribution by the Harmattan Winds strongly decreased during the Climatic Optimum at 6,000 y. B. P. The dust discharge of the trade winds is hardly detectable in the deep-sea sediments. This probably indicates a weakened atmospheric circulation. In contrast, the fluvial sediment supply reached a maximum, and can be traced to beyond Cape Blanc. Thus, the Saharan climate was more humid at 6,000 y B. P. A latitudinal shift of the Harmattan driven dust outbreaks cannot be observed. Also during the Glacial, 18,000 y. B. P., Harmattan dust transport crossed the African coast at latitudes of 15°-20° N. Its sediment load increased intensively, and markedly coarser grains spread further into the Atlantic Ocean. An expanded zone of pale-quart sediments indicates an enhanced dust supply by the trade winds blowing from the NE. No synglacial fluvial sediment contribution can be recognized between 12° and 30° N. This indicates a dry glacial climate and a strengthened stmospheric circulation over the Sahelian and Saharan region. The climatic transition pahes, at 12, 000 y. B. P., between the last Glacial and the Intergalcial, which is compareable to the Alerod in Europe, is characterized by an intermediate supply of terrigenous particles. The Harmattan dust transport wa weaker than during the Glacial. The northeasterly trade winds were still intensive. River supply reached a first postglacial maximum seaward of the Senegal river mouth. This indicates increasing humidity over the southern Sahara and a weaker atmospheric circulation as compared to the glacial. The accumulation rates of the terrigenous silt proportion (> 6 µm) decrcase exponentially with increasing distance from the Saharan coast. Those of the terrigenous fine fraction (< 6 µm) follow the same trend and show almost similar gradients. Accordingly, also the terrigenous fine fraction is believed to result predominantly from aeolian transport. In the Atlantic deep-sea sediments, the annual terrigenous sediment accumulation has fluctuated, from about 60 million tons p. a. during the Late Glacial (13,500-18,000 y. B. P, aeolian supply only) to about 33 million tons p. a. during the Holocene Climatic Optimum (6,000-9,000 y. B. P, mainly fluvial supply), when the river supply has reached a maximum, and to about 45 million tons p. a. during the last 4,000 years B. P. (fluvial supply only south of 18° N).