{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T23:28:03Z","timestamp":1698190083208},"reference-count":26,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2005,6,3]],"date-time":"2005-06-03T00:00:00Z","timestamp":1117756800000},"content-version":"vor","delay-in-days":4933,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Am. J. Med. Genet."],"published-print":{"date-parts":[[1991,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We explore the pursuit in a plane of a target moving at constant slow speed in a straight line. Two models of the pursuit are given. In the continuous case, the pursuer is moving at constant speed and is subject to proportionate angular homeostasis with correction constant <jats:italic>b<\/jats:italic>. In the discrete version movement occurs at a constant speed in a sequence of straight line segments of constant length (called the step size, <jats:italic>s<\/jats:italic>) the end of the segments being called the vertices. The pattern considered is not the absolute position of the pursuer, but its distance and orientation relative to the target. Both the transients and the asymptotic orbit are addressed. A key quantity is <jats:italic>r<\/jats:italic>, the speed of the target expressed as a fraction of that of the pursuer. If the speed of the pursuer is defined as unity, <jats:italic>r<\/jats:italic> is also the ratio of the speeds. There exists a critical speed fraction, <jats:italic>R<\/jats:italic>(<jats:italic>b, s<\/jats:italic>), a function of <jats:italic>b<\/jats:italic> and <jats:italic>s<\/jats:italic>, that defines what the term <jats:italic>slow<\/jats:italic> designates. <jats:italic>R<\/jats:italic>(<jats:italic>b<\/jats:italic>,<jats:italic>s<\/jats:italic>), which has to be found numerically, has the following property. For <jats:italic>r<\/jats:italic> &lt; <jats:italic>R<\/jats:italic>(<jats:italic>b, s<\/jats:italic>), the asymptotic path is a simple closed curve. In the discrete case the vertices converge to a simple closed curve. The larger <jats:italic>r<\/jats:italic>, the more the path (or in the discrete analogue its set of vertices) departs from a circle, and the more eccentric the target is with respect to it. Interest centers on two issues. First we address the transient patterns of the path, notably whether or not the sense of any particular path (clockwise or counterclockwise) is the same throughout, or changes at some stage. These studies have a bearing on ontogenetic lateralization of the viscera; its relationship to the classification of dextrocardia is addressed. Second, we considor the asymptotic form of the path and its relationship to the parameters. The critical values of R (<jats:italic>b, s<\/jats:italic>) are extensively explored.<\/jats:p>","DOI":"10.1002\/ajmg.1320410319","type":"journal-article","created":{"date-parts":[[2005,6,12]],"date-time":"2005-06-12T03:47:06Z","timestamp":1118548026000},"page":"362-370","source":"Crossref","is-referenced-by-count":3,"title":["Angular homeostasis VIII. Pursuit of a slowly moving target in a plane: Relevance to lateralization in cardiovascular ontogeny"],"prefix":"10.1002","volume":"41","author":[{"given":"Edmond A.","family":"Murphy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sonia","family":"Rhee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Reed E.","family":"Pyeritz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kenneth R.","family":"Berger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2005,6,3]]},"reference":[{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/ajmg.1320160107"},{"key":"e_1_2_1_3_1","unstructured":"BergerKR: Unpublished studies."},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00489654"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.1931.0002"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/ajmg.1320260411"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.86.13.5035"},{"key":"e_1_2_1_8_1","first-page":"323","volume-title":"Studies in Developmental Neurobiology. 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