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PubMed2004

Granulometric analysis of spots in DNA microarray images.

As the topological properties of each spot in DNA microarray images may vary from one another, we employed granulometries to understand the shape-size content contributed due to a significant intensity value within a spot. Analysis was performed on the microarray image that consisted of 240 spots by using concepts from mathematical morphology. In order to find out indices for each spot and to further classify them, we adopted morphological multiscale openings, which provided microarrays at multiple scales. Successive opened microarrays were subtracted to identify the protrusions that were smaller than the size of structuring element. Spot-wise details, in terms of probability of these observed protrusions, were computed by placing a regularly spaced grid on microarray such that each spot was centered in each grid. Based on the probability of size distribution functions of these protrusions isolated at each level, we estimated the mean size and texture index for each spot. With these characteristics, we classified the spots in a microarray image into bright and dull categories through pattern spectrum and shape-size complexity measures. These segregated spots can be compared with those of hybridization levels.

Computational Biology↗
PubMed2003

The formation of rhythmic categories and metric priming.

Two experiments on categorical rhythm perception are reported, the object of which was to investigate how listeners perceive discrete rhythmic categories while listening to rhythms performed on a continuous time scale. This is studied by considering the space of all temporal patterns (all possible rhythms made up of three intervals) and how they, in perception, are partitioned into categories, ie where the boundaries of these categories are located. This process of categorisation is formalised as the mapping from the continuous space of a series of time intervals to a discrete, symbolic domain of integer-ratio sequences. The methodological framework uses concepts from mathematics and psychology (eg convexity and entropy) that allow precise characterisations of the empirical results. In the first experiment, twenty-nine participants performed an identification task with 66 rhythmic stimuli (a systematic sampling of the performance space). The results show that listeners do not just perceive the time intervals between onsets of sounds as placed in a homogeneous continuum. Instead, they can reliably identify rhythmic categories, as a chronotopic time clumping map reveals. In a second experiment, the effect of metric priming was studied by presenting the same stimuli but preceded with a duple or triple metre subdivision. It is shown that presenting patterns in the context of a metre has a large effect on rhythmic categorisation: the presence of a specific musical metre primes the perception of specific rhythmic patterns.

Auditory Perception↗
PubMed2002

Protein unfolding: rigidity lost.

We relate the unfolding of a protein to its loss of structural stability or rigidity. Rigidity and flexibility are well defined concepts in mathematics and physics, with a body of theorems and algorithms that have been applied successfully to materials, allowing the constraints in a network to be related to its deformability. Here we simulate the weakening or dilution of the noncovalent bonds during protein unfolding, and identify the emergence of flexible regions as unfolding proceeds. The transition state is determined from the inflection point in the change in the number of independent bond-rotational degrees of freedom (floppy modes) of the protein as its mean atomic coordination decreases. The first derivative of the fraction of floppy modes as a function of mean coordination is similar to the fraction-folded curve for a protein as a function of denaturant concentration or temperature. The second derivative, a specific heat-like quantity, shows a peak around a mean coordination of = 2.41 for the 26 diverse proteins we have studied. As the protein denatures, it loses rigidity at the transition state, proceeds to a state where just the initial folding core remains stable, then becomes entirely denatured or flexible. This universal behavior for proteins of diverse architecture, including monomers and oligomers, is analogous to the rigid to floppy phase transition in network glasses. This approach provides a unifying view of the phase transitions of proteins and glasses, and identifies the mean coordination as the relevant structural variable, or reaction coordinate, along the unfolding pathway.

Databases, Protein↗
PubMed1995

Algebraic decomposition of the TU wave morphology patterns.

In principle, the T wave results from the differences in durations of action potentials (AP) of different ventricular regions. Based on this concept, a mathematical model has been developed that represents the TU wave morphology as a summation of four AP-like functions: TU = S1 - S2 + L1 - L2. The sigmoidal shape of AP-like curves is produced by Hill's equation V(t) = a . tn/(bn + tn). Each of the decomposition functions is characterized by two parameters: the amplitude at the beginning of QRS (Amax), and the duration at 5% of Amax (D95). The set of four decomposition functions leads to eight parameters that provide detailed characteristics of the TU wave morphology. The model was validated using 170 TU wave complexes recorded digitally in leads V2-V6 from 22 normal subjects and 12 patients with abnormal TU wave morphologies (negative, biphasic, and notched T waves). The electrocardiographic signals were sampled at 100 Hz and a best-fit procedure was used to obtain the decomposition. In all cases the coefficients of correlation between original TU patterns and their mathematical models were > or = 0.99. The mean absolute difference between the observed and modeled values of the TU patterns was similar in cases with normal and abnormal TU wave morphologies (4.65 +/- 0.41 microV vs 5.19 +/- 0.48 microV respectively) demonstrating that the model is capable of describing and categorizing various TU patterns by a set of eight numerical parameters.

Cardiomyopathy, Hypertrophic↗
PubMedDate not supplied

Unsupervised neural learning on lie group.

The present paper aims at introducing the concepts and mathematical details of unsupervised neural learning with orthonormality constrains. The neural structures considered are single non-linear layers and the learnable parameters are organized in matrices, as usual, which gives the parameters spaces the geometrical structure of the Euclidean manifold. The constraint of orthonormality for the connection-matrices further restricts the parameters spaces to differential manifolds such as the orthogonal group, the compact Stiefel manifold and its extensions. For these reasons, the instruments for characterizing and studying the behavior of learning equations for these particular networks are provided by the differential geometry of Lie groups. In particular, two sub-classes of the general Lie-group learning theories are studied in detail, dealing with first-order (gradient-based) and second-order (non-gradient-based) learning. Although the considered class of learning theories is very general, in the present paper special attention is paid to unsupervised learning paradigms.

Algorithms↗
PubMedDate not supplied

Distributed heterogeneous inspecting system and its middleware-based solution.

There are many cases when an organization needs to monitor the data and operations of its supervised departments, especially those departments which are not owned by this organization and are managed by their own information systems. Distributed Heterogeneous Inspecting System (DHIS) is the system an organization uses to monitor its supervised departments by inspecting their information systems. In DHIS, the inspected systems are generally distributed, heterogeneous, and constructed by different companies. DHIS has three key processes-abstracting core data sets and core operation sets, collecting these sets, and inspecting these collected sets. In this paper, we present the concept and mathematical definition of DHIS, a metadata method for solving the interoperability, a security strategy for data transferring, and a middleware-based solution of DHIS. We also describe an example of the inspecting system at WENZHOU custom.

Computer Communication Networks↗
PubMed2005

Sample homogeneity and coefficient alpha: comment on MJI and Alkhateeb's reliability generalization study and a theoretical clarification.

Reliability generalization studies are increasingly frequently reported in the literature, including Mji and Alkhateeb's 2005 study of the Conceptions of Mathematics Questionnaire. The present article comments on an issue of reliability generalization as used in that study and clarifies a theoretical point regarding the meaning of coefficient alpha and what data features tend to influence it as a measure of score reliability.

Generalization, Psychological↗
PubMed1990

[General conceptions of pharmacokinetics: physiological and mathematical approaches].

Intensity and duration of drug effects depend upon both their pharmacodynamic and pharmacokinetic properties. The former characterize the potential intrinsic activity of the molecule and are dependent upon its ability to modulate, stimulate or inhibit a biological system. The latter control the amount and time during which the drug is present at the site of action. During the last few years, pharmacokinetics have developed in two directions: first, the recognition of the physiological mechanisms responsible for the drug disposition; second, the quantitative analysis of the fate of the drug concentrations using mathematical models. These models have become more and more sophisticated, and now include a physiological approach.

Absorption↗
PubMed1990

Entropy as an algorithm for the statistical description of DNA cytometric data obtained by image analysis microscopy.

In an effort to obtain an additional statistical descriptor of DNA histograms we analysed a concept from mathematical information theory, called entropy, which describes the information content of histograms irrespective of parametric or non-parametric distributions. For this study, 32 fine-needle biopsies were analysed. It seems that the entropy of the DNA histogram is an extremely useful descriptor for the separation of distributions obtained from malignant tumours when compared with non-malignant lesions or normal controls.

Algorithms↗
PubMed1982

Chemotherapy strategies to improve the control of Hodgkin's disease: the Richard and Hinda Rosenthal Foundation Award Lecture.

The paper reviews new chemotherapy strategies for intermediate and advanced stages of Hodgkin's disease as well as the implications of recent biological concepts and mathematical models which appear useful in the interpretation and design of new treatments. The development and the application of the Adriamycin-bleomycin-vinblastine-dacarbazine (ABVD) combination was based on critical reevaluation of benefits and limits of the mechlorethamine-vincristine-procarbazine-prednisone (MOPP) combination. The attempts to develop non-cross-resistant regimens, such as ABVD, arose intuitively at first from the desire to improve salvage treatment in MOPP-refractory patients; more recently, a theoretical framework for this approach has been proposed by Goldie and Coldman (Cancer Treat. Rep., 63: 1727-1733, 1979). The 5-year results achieved with different forms of salvage chemotherapy and with the cyclic delivery of non-cross-resistant combinations (MOPP and ABVD) can be explained largely by the assumption that drug-resistant mutants represent a major limiting factor in the cure of Hodgkin's disease, as well as of other neoplasms, by chemotherapy. The initial results from a prospective randomized trial indicate that the administration as front-line therapy of non-cross-resistant regimens is a logical and powerful strategic approach and therefore that it may constitute an important avenue of clinical research. Recent observations also emphasized the problem of the quality of life, since the administration of multidrug combinations not including alkylating agents and/or procarbazine appears to be associated with a decreased incidence of carcinogenesis and sterility. The departure from the standard practice of utilizing a single multidrug regimen for chemotherapy of Hodgkin's disease should be supported by sound research and controlled studies built on drug combinations of known efficacy and toxicity.

Antineoplastic Agents↗
PubMed1984

Automatic detection of microaneurysms in diabetic fluorescein angiography.

A computerized method for the detection of microaneurysms (MA) in fluorescein angiograms is proposed, using the concepts of mathematical morphology. The MA which are almost circular particles, are extracted from the image by performing different "top-hat transformations". Some particles, however, may then be detected inside the nonhomogeneous vessels, and it is necessary to be able to extract the vasculary net. The MA which present fuzzy boundaries (due to the leakage of fluorescein) are the most difficult to extract. The algorithm has been tested on 25 angiograms, with 1 045 MA analysed. A comparison between the automatic counting procedure and three manual methods of counting has been made to prove the robustness of the proposed method.

Aneurysm↗
PubMed1983

[Protein synthesis following experimental injuries in the pig as disease model. Comparison of infusion solutions with various amino acid patterns].

This study compares the effect of two amino acid solutions on protein metabolism after injury by measuring nitrogen balance, 15N-elimination, total body protein synthesis and utilisation of administered nitrogen in an experimental study using pigs. Protein synthesis and nitrogen utilisation were determined using a 15N-tracer technique with recourse to mathematical model concepts. The non-surgical control animals had a lower urinary nitrogen excretion, a more favourable nitrogen balance, a higher 15N-retention, greater total body protein synthesis and utilisation of the infused amino acids during infusion of an amino acid solution with a standard amino acid pattern (A) than the operated animals (solution B). Comparison of the post-operative data shows that if solution A is compared with solution B whose amino acid content takes account of changes in plasma amino acid metabolism following trauma, solution B yields the better results in respect of 15N-retention as well as total body protein synthesis and nitrogen utilisation.

Amino Acids↗
PubMed1981

Three-pool analysis for quality control: a method for daily differentiation of analytic error from random variability.

Using the Z statistic we have devised a novel, mathematically simple concept for daily quality control of laboratory procedures. The method allows rapid identification and differentiation of systematic errors from random variability on a daily basis, increases confidence in the accuracy of reported results, reduces the number of repeat analyses, and allows the analyst to detect a deteriorating quality control pool. Using three controls instead of one or two increases the chance of detecting out-of-control situations and uses simplified statistical calculations summarized on a single graphic wall chart to monitor the daily accuracy and precision of analytic procedures. The method is adaptable to any type of specimen quantitatively analyzed and can be used in large or small laboratories with light or heavy workloads. This paper reflects what happens in a small laboratory with only one run each day, but, the system has been tested in a large community hospital with a heavy workload and multiple runs each day. Although this procedure is presented for the clinical laboratory, the method would be equally useful in industry.

Laboratories↗
PubMed1995

Nuclear texture in poorly differentiated small round cell tumors. Image analysis study of fine needle aspiration material.

Gradient analysis and pattern spectrum decomposition based on mathematical morphology concepts were used to explore nuclear texture patterns in a pool of 108 cells obtained by fine needle aspiration of five undifferentiated small round cell tumors of childhood, including one case each of Wilms' tumor, neuroblastoma, lymphoblastic lymphoma, Ewing's sarcoma and rhabdomyosarcoma. The aim of the study was to determine the presumptive value of nuclear pattern to correctly allocate each isolated cell to each of the five patients. The cells were examples of five histogenetically different tumors, all undifferentiated and with a close microscopic resemblance to one another. High gradient structures (heterochromatin-euchromatin and nuclear membrane edges) were estimated by a difference-of-boxes filter, and pattern spectrum decomposition was obtained by successive openings and closings performed on the input gray tone image. One important feature of these procedures was that no prior selection by thresholding of the structures to be studied was required, thus obviating subjective bias. Percentages of correctly allocated cells by canonical analysis ranged from 70.0% (rhabdomyosarcoma) to 92.9% (Ewing's sarcoma). Although the five cases could be distinguished using seven texture variables, this does not imply generalization of the results for the differential diagnosis of these tumors. Nonetheless, the possibility that undifferentiated small round cells present distinctive nuclear patterns when studied by sensitive image analysis techniques is suggested by our results.

Biopsy, Needle↗
PubMed1994

Image analysis of hemosiderin-laden macrophages in bronchoalveolar lavage fluid.

The aim of this study was to assess quantitatively the relationship between the number of iron-laden macrophages, extent of hemosiderin content and amount of dark-stained hemosiderin clumps in bronchoalveolar lavage (BAL) fluids. The series included specimens from 20 subjects whose BAL had yielded iron-laden macrophages. Six had developed hemoptysis 3-15 days prior to BAL. Quantitative studies were performed on smears stained by the ferrocyanide reaction, using true color image analysis for image segmentation. A top-hat function based on mathematical morphologic concepts was used for extraction of dark clumps of hemosiderin. The results demonstrated the presence of iron-laden macrophages three days after hemoptysis. There was a moderate correlation between the percentage of macrophages and amount of hemosiderin content, but the extent of dark-stained clumps did not increase in parallel to the increase in hemosiderin content and probably represented an advanced stage in the phagocytic processing of hemosiderin formed from engulfed red blood cells. The main difference between subjects with and without previous hemoptysis was higher values for dark clumps of hemosiderin in the former.

Adult↗
PubMed1993

Fine needle aspiration diagnosis of renal oncocytoma. A mathematical morphologic approach.

Differentiation between renal oncocytomas and well-differentiated oxyphilic cell renal carcinomas from fine needle aspiration cytology smears may present considerable difficulties. To better define diagnostic criteria, we used high-resolution architectural characteristics of nucleus and cytoplasm based on mathematical morphologic concepts. Particulate structural elements were selected for their size and optical density by the so-called top-hat function. Spatial density, size distribution and a function of distance between particles were computed. We quantitated cellular samples from fine needle aspirates obtained from 10 renal oncocytomas and 5 well-differentiated oxyphilic cell renal carcinomas. In two of the former, cytologic diagnosis was doubtful. Subsequent removal of the tumor and its histologic examination established the final diagnosis in all cases. Stepwise discriminant analysis correctly classified all cases as oncocytomas or renal carcinomas, although the results need to be considered with caution due to the necessarily limited number of observations. Multivariate graphic representation by star glyphs clearly depicted the differences between oncocytoma and oxyphilic cell renal carcinomas and the abnormal characteristics of two oncocytoma cases misclassified initially.

Adenoma↗