BatchI: Batch effect Identification in high-throughput screening data using a dynamic programming algorithm.

MOTIVATION: In contemporary biological experiments, bias, which interferes with the measurements, requires attentive processing. Important sources of bias in high-throughput biological experiments are batch effects and diverse methods towards removal of batch effects have been established. These include various normalization techniques, yet many require knowledge on the number of batches and assignment of samples to batches. Only few can deal with the problem of identification of batch effect of unknown structure. For this reason, an original batch identification algorithm through dynamical programming is introduced for omics data that may be sorted on a timescale. RESULTS: BatchI algorithm is based on partitioning a series of high-throughput experiment samples into sub-series corresponding to estimated batches. The dynamic programming method is used for splitting data with maximal dispersion between batches, while maintaining minimal within batch dispersion. The procedure has been tested on a number of available datasets with and without prior information about batch partitioning. Datasets with a priori identified batches have been split accordingly, measured with weighted average Dice Index. Batch effect correction is justified by higher intra-group correlation. In the blank datasets, identified batch divisions lead to improvement of parameters and quality of biological information, shown by literature study and Information Content. The outcome of the algorithm serves as a starting point for correction methods. It has been demonstrated that omitting the essential step of batch effect control may lead to waste of valuable potential discoveries. AVAILABILITY AND IMPLEMENTATION: The implementation is available within the BatchI R package at http://zaed.aei.polsl.pl/index.php/pl/111-software. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Application of Crowd Simulations in the Evaluation of Tracking Algorithms.

Tracking and action-recognition algorithms are currently widely used in video surveillance, monitoring urban activities and in many other areas. Their development highly relies on benchmarking scenarios, which enable reliable evaluations/improvements of their efficiencies. Presently, benchmarking methods for tracking and action-recognition algorithms rely on manual annotation of video databases, prone to human errors, limited in size and time-consuming. Here, using gained experiences, an alternative benchmarking solution is presented, which employs methods and tools obtained from the computer-game domain to create simulated video data with automatic annotations. Presented approach highly outperforms existing solutions in the size of the data and variety of annotations possible to create. With proposed system, a potential user can generate a sequence of random images involving different times of day, weather conditions, and scenes for use in tracking evaluation. In the design of the proposed tool, the concept of crowd simulation is used and developed. The system is validated by comparisons to existing methods.

Inter-population Differences in Retrogene Loss and Expression in Humans.

Gene retroposition leads to considerable genetic variation between individuals. Recent studies revealed the presence of at least 208 retroduplication variations (RDVs), a class of polymorphisms, in which a retrocopy is present or absent from individual genomes. Most of these RDVs resulted from recent retroduplications. In this study, we used the results of Phase 1 from the 1000 Genomes Project to investigate the variation in loss of ancestral (i.e. shared with other primates) retrocopies among different human populations. In addition, we examined retrocopy expression levels using RNA-Seq data derived from the Ilumina BodyMap project, as well as data from lymphoblastoid cell lines provided by the Geuvadis Consortium. We also developed a new approach to detect novel retrocopies absent from the reference human genome. We experimentally confirmed the existence of the detected retrocopies and determined their presence or absence in the human genomes of 17 different populations. Altogether, we were able to detect 193 RDVs; the majority resulted from retrocopy deletion. Most of these RDVs had not been previously reported. We experimentally confirmed the expression of 11 ancestral retrogenes that underwent deletion in certain individuals. The frequency of their deletion, with the exception of one retrogene, is very low. The expression, conservation and low rate of deletion of the remaining 10 retrocopies may suggest some functionality. Aside from the presence or absence of expressed retrocopies, we also searched for differences in retrocopy expression levels between populations, finding 9 retrogenes that undergo statistically significant differential expression.

Quality Control Procedure Based on Partitioning of NMR Time Series.

The quality of the magnetic resonance spectroscopy (MRS) depends on the stability of magnetic resonance (MR) system performance and optimal hardware functioning, which ensure adequate levels of signal-to-noise ratios (SNR) as well as good spectral resolution and minimal artifacts in the spectral data. MRS quality control (QC) protocols and methodologies are based on phantom measurements that are repeated regularly. In this work, a signal partitioning algorithm based on a dynamic programming (DP) method for QC assessment of the spectral data is described. The proposed algorithm allows detection of the change points-the abrupt variations in the time series data. The proposed QC method was tested using the simulated and real phantom data. Simulated data were randomly generated time series distorted by white noise. The real data were taken from the phantom quality control studies of the MRS scanner collected for four and a half years and analyzed by LCModel software. Along with the proposed algorithm, performance of various literature methods was evaluated for the predefined number of change points based on the error values calculated by subtracting the mean values calculated for the periods between the change-points from the original data points. The time series were checked using external software, a set of external methods and the proposed tool, and the obtained results were comparable. The application of dynamic programming in the analysis of the phantom MRS data is a novel approach to QC. The obtained results confirm that the presented change-point-detection tool can be used either for independent analysis of MRS time series (or any other) or as a part of quality control.

Inertial Motion Capture Costume Design Study.

The paper describes a scalable, wearable multi-sensor system for motion capture based on inertial measurement units (IMUs). Such a unit is composed of accelerometer, gyroscope and magnetometer. The final quality of an obtained motion arises from all the individual parts of the described system. The proposed system is a sequence of the following stages: sensor data acquisition, sensor orientation estimation, system calibration, pose estimation and data visualisation. The construction of the system's architecture with the dataflow programming paradigm makes it easy to add, remove and replace the data processing steps. The modular architecture of the system allows an effortless introduction of a new sensor orientation estimation algorithms. The original contribution of the paper is the design study of the individual components used in the motion capture system. The two key steps of the system design are explored in this paper: the evaluation of sensors and algorithms for the orientation estimation. The three chosen algorithms have been implemented and investigated as part of the experiment. Due to the fact that the selection of the sensor has a significant impact on the final result, the sensor evaluation process is also explained and tested. The experimental results confirmed that the choice of sensor and orientation estimation algorithm affect the quality of the final results.

Adaptive filtering of microarray gene expression data based on Gaussian mixture decomposition.

BACKGROUND: DNA microarrays are used for discovery of genes expressed differentially between various biological conditions. In microarray experiments the number of analyzed samples is often much lower than the number of genes (probe sets) which leads to many false discoveries. Multiple testing correction methods control the number of false discoveries but decrease the sensitivity of discovering differentially expressed genes. Concerning this problem, filtering methods for improving the power of detection of differentially expressed genes were proposed in earlier papers. These techniques are two-step procedures, where in the first step some pool of non-informative genes is removed and in the second step only the pool of the retained genes is used for searching for differentially expressed genes. RESULTS: A very important parameter to choose is the proportion between the sizes of the pools of removed and retained genes. A new method, which we propose, allow to determine close to optimal threshold values for sample means and sample variances for gene filtering. The method is adaptive and based on the decomposition of the histogram of gene expression means or variances into mixture of Gaussian components. CONCLUSIONS: By performing analyses of several publicly available datasets and simulated datasets we demonstrate that our adaptive method increases sensitivity of finding differentially expressed genes compared to previous methods of filtering microarray data based on using fixed threshold values.

RuleGO: a logical rules-based tool for description of gene groups by means of Gene Ontology.

Genome-wide expression profiles obtained with the use of DNA microarray technology provide abundance of experimental data on biological and molecular processes. Such amount of data need to be further analyzed and interpreted in order to obtain biological conclusions on the basis of experimental results. The analysis requires a lot of experience and is usually time-consuming process. Thus, frequently various annotation databases are used to improve the whole process of analysis. Here, we present RuleGO--the web-based application that allows the user to describe gene groups on the basis of logical rules that include Gene Ontology (GO) terms in their premises. Presented application allows obtaining rules that reflect coappearance of GO-terms describing genes supported by the rules. The ontology level and number of coappearing GO-terms is adjusted in automatic manner. The user limits the space of possible solutions only. The RuleGO application is freely available at http://rulego.polsl.pl/.

Correlation dimension and entropy in the assessment of sex differences based on human gait data.

Introduction: It is proved that there are differences between gait performed by females and males, which appear in movements of selected body parts. Despite numerous state-of-the-art studies related to the discriminative analysis of motion capture data, the question of whether measures of signal complexity and uncertainty can extract valuable features for the problem of sex distinction still remains open. It is the subject of the paper. Methods: Correlation dimension, as well as approximate and sample entropies, are selected to describe motion data. In the numerical experiments, the collected dataset with 884 samples of 25 females and 30 males was used. The measurements took place in the Human Motion Laboratory (HML), equipped with a highly precise motion capture system. Two variants of data representation were investigated-time series that contain joint rotations of taken skeleton model as well as positions of the markers attached to the human body. Finally, a comparative analysis between the populations of females and males using descriptive statistics, non-parametric estimation, and statistical hypotheses verification was carried out. Results: There are statistically significant sex differences extracted by the taken measures. In general, the movements of lower limbs result in greater values of correlation dimension and entropies for females, while selected upper body parts play a similar role for males. The dissimilarities are mainly observed in hip, ankle, shoulder, and head movements. Discussion: Correlation dimension and entropy measures provide robust and explainable features of motion capture data with a valuable description of the human locomotion system. Thus, beyond the importance of discovered differences between females and males, their interpretation and understanding are also known.

BWtrs: A tool for searching for tandem repeats in DNA sequences based on the Burrows-Wheeler transform.

Genomes of organisms contain a variety of repeated structures of various length and type, interspersed or tandem. Tandem repeats play important role in molecular biology as they are related to genetic backgrounds of inherited diseases, and also they can serve as markers for DNA mapping and DNA fingerprinting. Improving the efficiency of algorithms for searching for tandem repeats in DNA sequences can lead to many useful applications in the area of genomics. We introduce a very efficient, web-based tool for large scale searching for exact tandem repeats in genomes, based on the use of the Burrows-Wheeler Transform. The service is a remarkably efficient and powerful application that allows analyzing complete genomes without any restrictions. The Burrows-Wheeler Tandem Repeat Searcher (BWtrs) is an on-line application that searches for the exact occurrences of tandem repetitions in DNA sequences. The BWtrs service is freely available at: http://bioinfo.polsl.pl/BWtrs. We present examples of the use of our web application and we compare results of our computations with the results obtained by using other existing tools for searches for exact tandem repeats.

The mutation profile of differentiated thyroid cancer coexisting with undifferentiated anaplastic cancer resembles that of anaplastic thyroid cancer but not that of archetypal differentiated thyroid cancer.

Differentiated thyroid cancer (DTC) has one of the lowest cancer mutational burdens, while anaplastic thyroid cancer (ATC) has a much higher mutation frequency. A fraction of ATC has an associated differentiated component, which suggests the coevolution of both cancers. Here, we aimed to compare mutation frequency in coexisting ATC and DTC diagnosed concurrently in the same thyroid gland (3 cases) as well as in archetypal DTC and ATC alone (5 cases each). Single-nucleotide variations (SNV) and copy number variations (CNV) were analyzed in each case based on the next-generation sequencing data. We found a similar extent of mutational events, both SNV and CNV, in undifferentiated and differentiated components of thyroid cancers coexisting in one patient. The magnitude of these mutations was comparable to the level of mutations observed in ATC alone; yet, it was much higher than in archetypal DTC. This suggested that, despite histopathological features of differentiated tumors, molecular characteristics of such cancers coexisting with ATC and archetypal DTC could be significantly different. Pairwise comparison of mutational profiles of coexisting cancers enabled assumption on the possible evolution of both components, which appeared distinct in 3 analyzed cases. This included independent development of ATC and DTC diagnosed concurrently in two lobes of the same thyroid, as well as the development of anaplastic and differentiated cancer from the common ancestor that putatively gained a key driver mutation (BRAFV600E or KRASQ61R), which was followed either by early or late molecular separation of both cancers.

Mass spectrometry-based analysis of therapy-related changes in serum proteome patterns of patients with early-stage breast cancer.

BACKGROUND: The proteomics approach termed proteome pattern analysis has been shown previously to have potential in the detection and classification of breast cancer. Here we aimed to identify changes in serum proteome patterns related to therapy of breast cancer patients. METHODS: Blood samples were collected before the start of therapy, after the surgical resection of tumors and one year after the end of therapy in a group of 70 patients diagnosed at early stages of the disease. Patients were treated with surgery either independently (26) or in combination with neoadjuvant chemotherapy (5) or adjuvant radio/chemotherapy (39). The low-molecular-weight fraction of serum proteome was examined using MALDI-ToF mass spectrometry, and then changes in intensities of peptide ions registered in a mass range between 2,000 and 14,000 Da were identified and correlated with clinical data. RESULTS: We found that surgical resection of tumors did not have an immediate effect on the mass profiles of the serum proteome. On the other hand, significant long-term effects were observed in serum proteome patterns one year after the end of basic treatment (we found that about 20 peptides exhibited significant changes in their abundances). Moreover, the significant differences were found primarily in the subgroup of patients treated with adjuvant therapy, but not in the subgroup subjected only to surgery. This suggests that the observed changes reflect overall responses of the patients to the toxic effects of adjuvant radio/chemotherapy. In line with this hypothesis we detected two serum peptides (registered m/z values 2,184 and 5,403 Da) whose changes correlated significantly with the type of treatment employed (their abundances decreased after adjuvant therapy, but increased in patients treated only with surgery). On the other hand, no significant correlation was found between changes in the abundance of any spectral component or clinical features of patients, including staging and grading of tumors. CONCLUSIONS: The study establishes a high potential of MALDI-ToF-based analyses for the detection of dynamic changes in the serum proteome related to therapy of breast cancer patients, which revealed the potential applicability of serum proteome patterns analyses in monitoring the toxicity of therapy.

GaMRed-Adaptive Filtering of High-Throughput Biological Data.

Data filtering based on removing non-informative features, with unchanged signal between compared experimental conditions, can significantly increase sensitivity of methods used to detect differentially expressed genes or other molecular components measured in high-throughput biological experiments. Criteria for data filtering can be stated on the basis of averages or variances of signal levels across samples. The crucial parts of feature filtering are selection of filter type and cut-off threshold, which are specific to the particular dataset. In this paper, we present an algorithm and a stand-alone application, GaMRed, for adaptive filtering insignificant features in high-throughput data, based on Gaussian mixture decomposition. We have tested the performance of our algorithm using datasets from three different high-throughput biological experiments. We estimated the number of differentially expressed features after applying multiple testing correction and performed functional analysis of obtained features using Gene Ontology terms. Also, we checked if the control of false discovery rate and family-wise error rate after applying feature filtering remains at appropriate level. GaMRed is fast, automatic, and does not require expert knowledge in parameter tuning. The algorithm increases sensitivity of methods used to find differentially expressed features and biological validity of the findings. The program can be downloaded from: http://zaed.aei.polsl.pl/index.php/pl/oprogramowanie-zaed.

Application of high field magnetic resonance microimaging in polymer gel dosimetry.

PURPOSE: The purpose of this work was to examine the suitability of VIPARnd polymer gel-9.4 T magnetic resonance microimaging system for high spatial resolution dose distribution measurements. METHODS: The VIPARnd samples (3 cm in outside diameter and 12 cm in height) were exposed to ionizing radiation by using a linear accelerator (Varian TrueBeam, USA; 6 MV x-ray beam). In the calibration stage, nine gel dosimeter vials were irradiated in a water phantom homogenously to the doses from 1.5 to 30 Gy in order to obtain R2-dose relation. In the verification stage, two gel dosimeter vials were irradiated in the half beam penumbra area of 10 × 10 cm radiation field using the amount of monitor units appropriate to deliver 20 Gy at the field center. The gels were imaged on a vertical 9.4 T magnetic resonance (MR) microimaging scanner using single slice and multislice (9 slices) multiecho (90 × 7 ms) sequences at the spatial resolutions of 0.2-0.4 × 0.2-0.4 × 3 mm3 and 0.2-0.4 × 0.2-0.4 × 1 mm3 respectively. The gels were subjected to microimaging during the period of two weeks after irradiation. The reference data consisted of the dose profiles measured using the diode dosimetry, radiochromic film, ionization chamber, and the water phantom system. RESULTS: The VIPARnd -9.4 T MR microimaging system was characterized by the dose sensitivity of 0.067 ± 0.002 Gy-1  s-1 at day 3 after irradiation. The dose resolution at 10 Gy (at P = 95%) was equal to 0.42 Gy at day 3 after irradiation using a single slice sequence (0.2 × 0.2 × 3 mm3 ) and 2.0 Gy at day 4 after irradiation using a multislice sequence (0.2 × 0.2 × 1 mm3 ) for one signal acquisition (measurement time: 15 min). These values were improved by ~1.4-fold when using four signal acquisitions in the single slice sequence, and by ~2.78-fold for 12 signal acquisitions in the multislice sequence. Furthermore, decreasing the in-plane resolution from 0.2 × 0.2 mm2 to 0.4 × 0.4 mm2 resulted in a dose resolution of 0.3 Gy and 1 Gy at 10 Gy (at P = 95%) for one signal acquisition in the single slice and multislice sequences respectively (measurement time: 7.5 min). As reveals from the gamma index analysis the dose distributions measured at days 3-4 postirradiation using both VIPARnd verification phantoms agree with the data obtained using a silicon diode, assuming 1 mm/5% criterion. A good interphantom reproducibility of the polymer gel dosimetry was proved by monitoring of two phantoms up to 10 days after irradiation. However, the agreement between the dose distributions measured using the diode and polymer gel started to get worse from day 5 after irradiation. CONCLUSION: The VIPARnd -9.4T MR microimaging system allows to obtain dose resolution of 0.42 Gy at 10 Gy (at P = 95%) for a spatial resolution of 0.2 × 0.2 × 3 mm3 (acquisition time: 15 min). Further studies are required to improve a temporal stability of the gel-derived dose distribution.

MicroRNA Profile of Exosomes and Parental Cells is Differently Affected by Ionizing Radiation.

Exosomes are key mediators of cell-to-cell communication involved in different aspects of the response to ionizing radiation. The functional role of exosomes depends on their molecular cargo, including protein and miRNA content. In this work, we compared the miRNA profile of cells exposed to a high-dose of radiation and the exosomes released by those cells. FaDu cells (derived from human head and neck cancer) were exposed to 2 and 8 Gy doses, exosomes were purified from culture media at 36 h postirradiation using a combination of differential centrifugation, ultrafiltration and precipitation, then microRNA was analyzed using the RNA-seq approach. There were 439 miRNA species quantified, and significant differences in their relative abundance were observed between the cells and exosomes; several low-abundance miRNAs were over-represented while high-abundance miRNA were under-represented in exosomes. There were a few miRNA species markedly affected in irradiated cells and in exosomes released by these cells. However, markedly different radiation-induced effects were observed in both miRNA sets, which could be exemplified by miR-3168 significantly downregulated in cells and upregulated in exosomes. On the other hand, both 2 and 8 Gy radiation doses induced similar effects. Radiation-affected miRNA species present in exosomes are linked to genes involved in the DNA damage and cytokine-mediated response, which may suggest their hypothetical role in the exosome-mediated radiation-induced bystander effect reported elsewhere.

Mass spectrometry-based serum proteome pattern analysis in molecular diagnostics of early stage breast cancer.

BACKGROUND: Mass spectrometric analysis of the blood proteome is an emerging method of clinical proteomics. The approach exploiting multi-protein/peptide sets (fingerprints) detected by mass spectrometry that reflect overall features of a specimen's proteome, termed proteome pattern analysis, have been already shown in several studies to have applicability in cancer diagnostics. We aimed to identify serum proteome patterns specific for early stage breast cancer patients using MALDI-ToF mass spectrometry. METHODS: Blood samples were collected before the start of therapy in a group of 92 patients diagnosed at stages I and II of the disease, and in a group of age-matched healthy controls (104 women). Serum specimens were purified and the low-molecular-weight proteome fraction was examined using MALDI-ToF mass spectrometry after removal of albumin and other high-molecular-weight serum proteins. Protein ions registered in a mass range between 2,000 and 10,000 Da were analyzed using a new bioinformatic tool created in our group, which included modeling spectra as a sum of Gaussian bell-shaped curves. RESULTS: We have identified features of serum proteome patterns that were significantly different between blood samples of healthy individuals and early stage breast cancer patients. The classifier built of three spectral components that differentiated controls and cancer patients had 83% sensitivity and 85% specificity. Spectral components (i.e., protein ions) that were the most frequent in such classifiers had approximate m/z values of 2303, 2866 and 3579 Da (a biomarker built from these three components showed 88% sensitivity and 78% specificity). Of note, we did not find a significant correlation between features of serum proteome patterns and established prognostic or predictive factors like tumor size, nodal involvement, histopathological grade, estrogen and progesterone receptor expression. In addition, we observed a significantly (p = 0.0003) increased level of osteopontin in blood of the group of cancer patients studied (however, the plasma level of osteopontin classified cancer samples with 88% sensitivity but only 28% specificity). CONCLUSION: MALDI-ToF spectrometry of serum has an obvious potential to differentiate samples between early breast cancer patients and healthy controls. Importantly, a classifier built on MS-based serum proteome patterns outperforms available protein biomarkers analyzed in blood by immunoassays.

Does social-economical transformation influence the incidence of type 1 diabetes mellitus? A Polish example.

BACKGROUND: The dramatic increase in the incidence of diabetes mellitus type 1 (DMT1) in all countries of Central and Eastern Europe seems to be correlated with the rapid transformations of the political, economical, and social conditions. The aim of this study was to analyze the increase of DMT1 incidence vs. changes of parameters describing economical conditions, medical care standards, and level of hygiene. MATERIALS AND METHODS: The study was based on the Upper Silesia, Poland, prospective register of DMT1 cases, a part of the EURODIAB program. The analyzed parameters were number of salmonellosis, taeniasis, diarrhea, and diarrhea in children aged 0 - 2 yr, alimentary toxicosis, neonatal mortality rate, average male and female life expectancy, gross domestic product (GDP), and accessibility to the water supply and sewage lines. RESULTS: The dynamics of incidence increase has been very high: from 4.71/100 000 (1989) to 15.20/100 000 (2002); average increase per year is 7.52%. The statistically significant positive associations between DMT1 incidence and average male and female life expectancy, GDP, and accessibility of the water supply and sewage systems as well as the negative association for both neonatal mortality rate and nursery attendance were observed. No significant correlation was found between DMT1 and incidence rates of chosen diseases. CONCLUSIONS: Currently, Poland and its part, Upper Silesia, belong to regions with high DMT1 incidence in children. The change from low to high incidence of DMT1 over the past 14 yr corresponded to profound social and economical transformations. Our observations confirm the importance of environmental factors in the aetiopathogenesis of DMT1. The state of hygiene and the state of the health of the society influence its susceptibility to DMT1.

Application of Bayesian networks for inferring cause-effect relations from gene expression profiles of cancer versus normal cells.

The paper is devoted to two questions: whether distinction of causes versus effects of neoplasia leaves a signature in the cancer versus normal gene expression profiles and whether roles of genes, "causes" or "effects", can be inferred from repeated measurements of gene expressions. We model joint probability distributions of logarithms of gene expressions with the use of Bayesian networks (BN). Fitting our models to real data confirms that our BN models have the ability to explain some aspects of observational evidence from DNA microarray experiments. Effects of neoplastic transformation are well seen among genes with the highest power to differentiate between normal and cancer cells. Likelihoods of BNs depend on the biological role of selected genes, defined by Gene Ontology. Also predictions of our BN models are coherent with the set of putative causes and effects constructed based on our data set of papillary thyroid cancer.

Comprehensive Analysis of MILE Gene Expression Data Set Advances Discovery of Leukaemia Type and Subtype Biomarkers.

Large collections of data in studies on cancer such as leukaemia provoke the necessity of applying tailored analysis algorithms to ensure supreme information extraction. In this work, a custom-fit pipeline is demonstrated for thorough investigation of the voluminous MILE gene expression data set. Three analyses are accomplished, each for gaining a deeper understanding of the processes underlying leukaemia types and subtypes. First, the main disease groups are tested for differential expression against the healthy control as in a standard case-control study. Here, the basic knowledge on molecular mechanisms is confirmed quantitatively and by literature references. Second, pairwise comparison testing is performed for juxtaposing the main leukaemia types among each other. In this case by means of the Dice coefficient similarity measure the general relations are pointed out. Moreover, lists of candidate main leukaemia group biomarkers are proposed. Finally, with this approach being successful, the third analysis provides insight into all of the studied subtypes, followed by the emergence of four leukaemia subtype biomarkers. In addition, the class enhanced DEG signature obtained on the basis of novel pipeline processing leads to significantly better classification power of multi-class data classifiers. The developed methodology consisting of batch effect adjustment, adaptive noise and feature filtration coupled with adequate statistical testing and biomarker definition proves to be an effective approach towards knowledge discovery in high-throughput molecular biology experiments.

Coalescence computations for large samples drawn from populations of time-varying sizes.

We present new results concerning probability distributions of times in the coalescence tree and expected allele frequencies for coalescent with large sample size. The obtained results are based on computational methodologies, which involve combining coalescence time scale changes with techniques of integral transformations and using analytical formulae for infinite products. We show applications of the proposed methodologies for computing probability distributions of times in the coalescence tree and their limits, for evaluation of accuracy of approximate expressions for times in the coalescence tree and expected allele frequencies, and for analysis of large human mitochondrial DNA dataset.

Signal Partitioning Algorithm for Highly Efficient Gaussian Mixture Modeling in Mass Spectrometry.

Mixture - modeling of mass spectra is an approach with many potential applications including peak detection and quantification, smoothing, de-noising, feature extraction and spectral signal compression. However, existing algorithms do not allow for automated analyses of whole spectra. Therefore, despite highlighting potential advantages of mixture modeling of mass spectra of peptide/protein mixtures and some preliminary results presented in several papers, the mixture modeling approach was so far not developed to the stage enabling systematic comparisons with existing software packages for proteomic mass spectra analyses. In this paper we present an efficient algorithm for Gaussian mixture modeling of proteomic mass spectra of different types (e.g., MALDI-ToF profiling, MALDI-IMS). The main idea is automated partitioning of protein mass spectral signal into fragments. The obtained fragments are separately decomposed into Gaussian mixture models. The parameters of the mixture models of fragments are then aggregated to form the mixture model of the whole spectrum. We compare the elaborated algorithm to existing algorithms for peak detection and we demonstrate improvements of peak detection efficiency obtained by using Gaussian mixture modeling. We also show applications of the elaborated algorithm to real proteomic datasets of low and high resolution.