“Electronic nose” technology, including technical and software tools to analyze gas mixtures, is promising regarding the diagnosis of malignant neoplasms. This paper presents the research results of breath samples analysis from 59 people, including patients with a confirmed diagnosis of respiratory tract cancer. The research was carried out using a gas analytical system including a sampling device with 14 metal oxide sensors and a computer for data analysis. After digitization and preprocessing, the data were analyzed by a neural network with perceptron architecture. As a result, the accuracy of determining oncological disease was 81.85%, the sensitivity was 90.73%, and the specificity was 61.39%.
The paper proposes the kernel probability density function approach to estimate the distribution of measurements on a part which is measured in a coordinate measuring machine (CMM). The study is based on the experimental data derived from internal cylinder measurements. The distribution free model suggested by Wilks was used as a reference for the selection of the sample size. Three cross sections of a cylinder were measured regarding to this reference. The work defines the minimum required sample size for obtaining at least 0.95 proportion of radius variation for particular studied cylindrical part with 95% confidence level.
Novel non-invasive methods for the diagnosis of malignancies should be effective for early diagnosis, reproducible, inexpensive, and independent from the human factor. Our aim was to establish the applicability of the non-invasive method, based on the analysis of air exhaled by patients who are at different stages of oropharyngeal, larynx and lung cancer. The diagnostic device includes semiconductor sensors capable of measuring the concentrations of gas components in exhaled air, with the high sensitivity of 1 ppm. The neural network uses signals from these sensors to perform classification and identify cancer patients. Prior to the diagnostic procedure of the non-invasive method, we clarified the extent and stage of the tumor according to current international standards and recommendations for the diagnosis of malignancies. The statistical dataset for neural network training and method validation included samples from 121 patients with the most common tumor localizations (lungs, oropharyngeal region and larynx). The largest number of cases (21 patients) were lung cancer, while the number of patients with oropharyngeal or laryngeal cancer varied from 1 to 9, depending on tumor localization (oropharyngeal, tongue, oral cavity, larynx and mucosa of the lower jaw). In the case of lung cancer, the parameters of the diagnostic device are determined as follows: sensitivity—95.24%, specificity—76.19%. For oropharyngeal cancer and laryngeal cancer, these parameters were 67.74% and 87.1%, respectively. This non-invasive method could lead to relevant medicinal findings and provide an opportunity for clinical utility and patient benefit upon early diagnosis of malignancies.
In this paper, we study a wide range of variants for computing the (discrete and continuous) Fréchet distance between uncertain curves. An uncertain curve is a sequence of
uncertainty regions,
where each region is a disk, a line segment, or a set of points. A
realisation
of a curve is a polyline connecting one point from each region. Given an uncertain curve and a second (certain or uncertain) curve, we seek to compute the lower and upper bound Fréchet distance, which are the minimum and maximum Fréchet distance for any realisations of the curves.
We prove that both problems are NP-hard for the Fréchet distance in several uncertainty models, and that the upper bound problem remains hard for the discrete Fréchet distance. In contrast, the lower bound (discrete [5] and continuous) Fréchet distance can be computed in polynomial time in some models. Furthermore, we show that computing the expected (discrete and continuous) Fréchet distance is #P-hard in some models.
On the positive side, we present a FPTAS in constant dimension for the lower bound problem when
Δ
/
δ
is polynomially bounded, where
δ
is the Fréchet distance and
Δ
bounds the diameter of the regions. We also show a near-linear-time 3-approximation for the decision problem on roughly
δ
-separated convex regions. Finally, we study the setting with Sakoe–Chiba time bands, where we restrict the alignment between the curves, and give polynomial-time algorithms for the upper bound and expected discrete and continuous Fréchet distance for uncertainty modelled as point sets.
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