The Stinespring theorem is reformulated in terms of conditional expectations in a von Neumann algebra. A generalisation for map-valued measures is obtained.
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How to select a structuring element for a given task is one of the most frequently asked questions in morphology. Present work tries to give a solution for a restricted class of problems, namely shape classification. In this work an algorithm that extracts distinctive structure of each of a given set of objects is proposed. The proposed algorithm is based on a new approach for computing distance transform.
We inductively describe an embedding of a complete ternary tree Tₕ of height h into a hypercube Q of dimension at most ⎡(1.6)h⎤+1 with load 1, dilation 2, node congestion 2 and edge congestion 2. This is an improvement over the known embedding of Tₕ into Q. And it is very close to a conjectured embedding of Havel [3] which states that there exists an embedding of Tₕ into its optimal hypercube with load 1 and dilation 2. The optimal hypercube has dimension ⎡(log₂3)h⎤ ( = ⎡(1.585)h⎤) or ⎡(log₂3)h⎤+1.
Dysphagia concerns 10–89% patients after total laryngectomy; to a greater extent it regards patients receiving complementary radiotherapy. The disease mechanism is associated with anatomical changes after surgery (typeof surgery) or complications of adjuvant therapy (xerostomia, neuropathy, swelling of tissue, etc.). The above changes lead to: decreased mobility of the lateral walls of the pharynx and tongue retraction, the occurrence of tounge pumping movements, decreased swallowing reflex, weakening of the upper esophageal sphincter opening, contraction of the cricopharyngeal muscle, tissue fibrosis, formation of pharyngeal pseudodiverticulum, etc. As a result: regurgitation of food through the nose and oral cavity, food sticking in middle and lower pharynx, prolongation of bolus transit time. Upon the formation of tracheoesophageal fistula, there may be aspiration of gastric contents. The above changes considerably reduce patients’ quality of life after surgery. The diagnostic protocol includes: medical interview (questionnaires such as EAT 10, SSQ, MDADI, DHI can be helpful), clinical swallowing assessment and instrumental examinations: primarily videofluoroscopy but also endoscopic evaluation of swallowing. Selected cases also require high frequency manometry. The treatment options include: surgical methods (e.g. balloon dilatation of the upper esophageal sphincter, cricopharyngeal myotomy, pharyngeal plexus neurectomy, removal of the pharyngeal pseudodiverticulum), pharmacological treatment or conservative methods (e.g. botulinum toxin injection of the upper esophageal sphincter, speech therapy, nutritional treatment) and supportive methods such as consultation with a psychologist, physiotherapist, clinical dietitian). The selection of a specific treatment method should be preceded by a diagnostic process in which the mechanism of functional disorders related to voice formation and swallowing will be established.
A mathematical background of solid particle shape projective description method was established in the paper. A particle was assumed to be the compact and connected subset of .R3space. The definition of contoured dilation coat was introduced. The contoured dilation function of particle projective image was defined. Properties of the function mentioned were described. A numerical form of functional characteristics for some real particle shapes was derived.
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Mathematical morphology is a geometric approach in image processing and analysis with a strong mathematical flavor. Originally, it was developed as a powerful tool for shape analysis in binary and, later, grey-scale images. But it was soon recognized that the underlying ideas could be extended naturally to a much wider class of mathematical objects, namely complete lattices. This paper presents, in a bird's eye view, the foundations of mathematical morphology, or more precisely, the theory of morphological operators on complete lattices.
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