In recent years, alignment-free methods have been widely applied in comparing genome sequences, as these methods compute efficiently and provide desirable phylogenetic analysis results. These methods have been successfully combined with hierarchical clustering methods for finding phylogenetic trees. However, it may not be suitable to apply these alignment-free methods directly to existing statistical classification methods, because an appropriate statistical classification theory for integrating with the alignment-free representation methods is still lacking. In this article, we propose a discriminant analysis method which uses the discrete wavelet packet transform to classify whole genome sequences. The proposed alignment-free representation statistics of features follow a joint normal distribution asymptotically. The data analysis results indicate that the proposed method provides satisfactory classification results in real time.

Background: Identification of functional elements of a genome often requires dividing a sequence of measurements along a genome into segments where adjacent segments have different properties, such as different mean values. This problem is often called the segmentation problem in the field of genomics, and the change-point problem in other scientific disciplines. Despite dozens of algorithms developed to address this problem in genomics research, methods with improved accuracy and speed are still needed to effectively tackle both existing and emerging genomic and epigenomic segmentation problems. Results: We designed an efficient algorithm, called iSeg, for segmentation of genomic and epigenomic profiles. iSeg first utilizes dynamic programming to identify candidate segments and test for significance. It then uses a novel data structure based on two coupled balanced binary trees to detect overlapping significant segments and update them simultaneously during searching and refinement stages. Refinement and merging of significant segments are performed at the end to generate the final set of segments. By using an objective function based on the p -values of the segments, the algorithm can serve as a general computational framework to be combined with different assumptions on the distributions of the data. As a general segmentation method, it can segment different types of genomic and epigenomic data, such as DNA copy number variation, nucleosome occupancy, nuclease sensitivity, and differential nuclease sensitivity data. Using simple t-tests to compute p -values across multiple datasets of different types, we evaluate iSeg using both simulated and experimental datasets and show that it performs satisfactorily when compared with some other popular methods, which often employ more sophisticated statistical models. Implemented in C++, iSeg is also very computationally efficient, well suited for large numbers of input profiles and data with very long sequences. Conclusions: We have developed an effective and efficient general-purpose segmentation tool for sequential data and illustrated its use in segmentation of genomic and epigenomic profiles.

Mathematical formulations and proofs for a wavelet based statistic employed in functional data analysis is elaborately discussed in this report. The propositions and derivations discussed here apply to a wavelet based statistic with hard thresholding. The proposed analytic distribution is made feasible only due to the assumption of normality. Since the statistic is developed for applications in high dimensional data analysis, the assumption holds true in most practical situations. In the future, the work here could be extended to address data that are non-Gaussian. Aside from establishing a rigorous mathematical foundation for the distribution of the statistic, the report also explores a few approximations for the proposed statistic.

Aquifer storage and recovery (ASR) wells along northern Lake Okeechobee, Florida, have been proposed as part of the Comprehensive Everglades Restoration Plan. However, researchers have linked elevated concentrations of As, Hg and transition metals in groundwater because of ASR in carbonate rocks. This study presents portable X-ray fluorescence (pXRF) analyses of four continuous cores (C38S, C59, L63N, and L63S) recovered from the Floridan Aquifer System north of Lake Okeechobee, Florida. A total of 5078 pXRF measurements were collected at approximately 30.5 cm along the four cores. Measurements along the cores included the Intermediate Confining Unit, Upper Floridan Aquifer (UFA), Avon Park Permeable Zones (APPZ), and portions of the Lower Floridan Aquifer (LFA). Emphasis was placed on the concentrations of mercury (Hg), arsenic (As), molybdenum (Mo), chromium (Cr), and nickel (Ni), which have been identified as elements of concern during ASR operations. Major-element trends in the cores often reflect lithologic changes in the Floridan Aquifer System. This includes decreases in Ca and Sr and increases in Mg associated with dolomitization in the Avon Park Formation. Trace-metal concentrations vary systematically within hydrostratigraphic units. Mercury commonly exhibits elevated concentrations near the base of the UFA, whereas Mo is often enriched near the top of the UFA. Elevated concentrations of Hg, As, Mo, Ni, and other trace metals frequently occur at hydrostratigraphic boundaries, formation contacts, clay-rich intervals, and especially within organic-rich layers. Organic layers contained metal concentrations several times greater than surrounding carbonate rocks and hosted the highest measured concentrations of Hg, As, and Mo in the cores. The paucity of organic layers and generally lower metal concentrations in the UFA suggest it may represent a favorable zone for ASR storage. In contrast, the APPZ and LFA contain numerous metal-enriched organic layers which may increase the potential for trace metal mobilization during ASR operations. These results suggest pXRF characterization provides an effective tool for geochemical characterization of storage zones and evaluating water-quality risks potentially associated with ASR development.