Counting Popular Matchings in House Allocation Problems

We study the problem of counting the number of popular matchings in a given instance. A popular matching instance consists of agents A and houses H, where each agent ranks a subset of houses according to their preferences. A matching is an assignment of agents to houses. A matching M is more popular than matching M' if the number of agents that prefer M to M' is more than the number of people that prefer M' to M. A matching M is called popular if there exists no matching more popular than M. McDermid and Irving gave a poly-time algorithm for counting the number of popular matchings when the preference lists are strictly ordered. We first consider the case of ties in preference lists. Nasre proved that the problem of counting the number of popular matching is #P-hard when there are ties. We give an FPRAS for this problem. We then consider the popular matching problem where preference lists are strictly ordered but each house has a capacity associated with it. We give a switching graph characterization of popular matchings in this case. Such characterizations were studied earlier for the case of strictly ordered preference lists (McDermid and Irving) and for preference lists with ties (Nasre). We use our characterization to prove that counting popular matchings in capacitated case is #P-hard

Irving, Thomas M. - 1945 (typescript)

https://dh.howard.edu/humwa_corres/1073/thumbnail.jp

Christian Democratic Parties of Western Europe (Book Review)

Reviewed Title: The Christian Democratic Parties of Western Europe, by Ronald E. M. Irving. London: The Royal Institute of International Affairs and George Allen & Unwin, 1979. 338 pages

Vol. 11, No. 3

Contents: Some Observations on Teacher Dismissal Proceedings for Incompetence Under Section 24A, by Irving M. Friedman Recent Developments Further References, compiled by Margaret A. Chaplanhttps://scholarship.kentlaw.iit.edu/iperr/1021/thumbnail.jp

Approximation algorithms for hard variants of the stable marriage and hospitals/residents problems

When ties and incomplete preference lists are permitted in the Stable Marriage and Hospitals/Residents problems, stable matchings can have different sizes. The problem of finding a maximum cardinality stable matching in this context is known to be NP-hard, even under very severe restrictions on the number, size and position of ties. In this paper, we describe polynomial-time 5/3-approximation algorithms for variants of these problems in which ties are on one side only and at the end of the preference lists. The particular variant is motivated by important applications in large scale centralised matching schemes

Fluorescent probes of the orientation of myosin regulatory light chains in relaxed, rigor, and contracting muscle.

The orientation of the light-chain region of myosin heads in relaxed, rigor, and isometrically contracting fibers from rabbit psoas muscle was studied by fluorescence polarization. Cysteine 108 of chicken gizzard myosin regulatory light chain (cgRLC) was covalently modified with iodoacetamidotetramethylrhodamine (iodo-ATR). Native RLC of single glycerinated muscle fibers was exchanged for labeled cgRLC in a low [Mg2+] rigor solution at 30 degrees C. Troponin and troponin C removed in this procedure were replaced. RLC exchange had little effect on active force production. X-ray diffraction showed normal structure in rigor after RLC exchange, but loss of axial and helical order in relaxation. In isolated myofibrils labeled cgRLC was confined to the regions of the sarcomere containing myosin heads. The ATR dipoles showed a preference for orientations perpendicular to the fiber axis, combined with limited nanosecond rotational motion, in all conditions studied. The perpendicular orientation preference was more marked in rigor than in either relaxation or active contraction. Stretching relaxed fibers to sarcomere length 4 microns to eliminate overlap between actin- and myosin-containing filaments had little effect on the orientation preference. There was no change in orientation preference when fibers were put into rigor at sarcomere length 4.0 microns. Qualitatively similar results were obtained with ATR-labeled rabbit skeletal RLC

February 29, 1944

Know Your Officers introduces LT Roy Simmons, Base Ordnance Officer; we also get to know S/SGT Irving Meltzer; and we witness a bayonet battle between M/SGT Matthew Skypek [or Skypeck; it is shown with both spellings] and SGT. Duane Hazle.https://digicom.bpl.lib.me.us/dowfieldobserver/1034/thumbnail.jp