Mutations and short geodesics in hyperbolic 3-manifolds

In this paper, we explicitly construct large classes of incommensurable hyperbolic knot complements with the same volume and the same initial (complex) length spectrum. Furthermore, we show that these knot complements are the only knot complements in their respective commensurabiltiy classes by analyzing their cusp shapes. The knot complements in each class differ by a topological cut-and-paste operation known as mutation. Ruberman has shown that mutations of hyperelliptic surfaces inside hyperbolic 3-manifolds preserve volume. Here, we provide geometric and topological conditions under which such mutations also preserve the initial (complex) length spectrum. This work requires us to analyze when least area surfaces could intersect short geodesics in a hyperbolic 3-manifold.Comment: This is the final (accepted) version of this pape

Dynamical Systems; Proceedings of an IIASA Workshop, Sopron, Hungary, September 9-13, 1985

The investigation of special topics in systems dynamics -- uncertain dynamic processes, viability theory, nonlinear dynamics in models for biomathematics, inverse problems in control systems theory -- has become a major issue at the System and Decision Sciences Research Program of IIASA. The above topics actually reflect two different perspectives in the investigation of dynamic processes. The first, motivated by control theory, is concerned with the properties of dynamic systems that are stable under variations in the systems' parameters. This allows us to specify classes of dynamic systems for which it is possible to construct and control a whole "tube" of trajectories assigned to a system with uncertain parameters and to resolve some inverse problems of control theory within numerically stable solution schemes. The second perspective is to investigate generic properties of dynamic systems that are due to nonlinearity (as bifurcations theory, chaotic behavior, stability properties, and related problems in the qualitative theory of differential systems). Special stress is given to the applications of nonlinear dynamic systems theory to biomathematics and ecology. The proceedings of a workshop on the "Mathematics of Dynamic Processes", dealing with these topics is presented in this volume

Karakteritega suhestumine ja digikogukondlik praktika: “Halvale teele” multidistsiplinaarne uurimus

Kuidas suhestab vaataja end narratiivse karakteriga? Kirjandusteadus, folkloristika, narratoloogia, psühholoogia, ja meediauuringud laiemaltki on antud seoses rakendanud käsitlusi samastumisest, empatiseerimisest ja (väljamõeldud maailma) sukeldumisest. Kuna väljamõeldud inimesed, kas kirja- või pildisõnas, polevat rohkemat autori(te) ettekujutuse viljast, siis püüdvat vaataja/lugejagi neis kas ära tunda iseend või siis teisalduda jälgitavasse situatsiooni, end vaadeldava tegelaskujuga samastades. Kui karakteriga suhestumise analüüsis lähtuda aga igapäevasuhtlustasandist, näib olevat ebapiisav eelistada üksnes taaskujutavat ja sissepoole pööratud vaadet inimteadvusele, kuna ideedel inimesest kui „sotsiaalsest olevusest“ ja tähenduse „sotsiaalsest karakterist“ (Võgotskii) on oht jääda tahaplaanile ja „karakteriga suhestumine“ taandub omamoodi sisedialoogiks: vaataja mõistab teist inimest iseenda põhjal kohandatud mudeli kaudu. Ehkki teatud olukordades on see vajalik mõistmis- ja tähendustamisstrateegia, ei saa eirata, et suhestumine kui selline on ometi suunatud. Haaratud ollakse kellestki, „sukeldutakse“ maailma, mida keegi omas-maailmas-iseseisvalt-eksisteerivana asustab. Käesoleva doktoriväitekirja avapeatükk sünteesib väga mitmekesist teaduskirjandust ja töötab välja kohase teoreetilise mõisteraamistiku, mis käsitleb suhestumist teleseriaali tegelaskujudega argiteadvuslikust sotsiaalsest kogemusest lähtuvalt. Keskne on siin käsitlus pärisustamisest: kogukondliku arutelu kontekstis lihtsalt lähenetaksegi tegelaskujudele kui päris inimestele. Narratiivsest tegelaskujust saab persoon. Internetiarutelud opereerivad kolmandas isikus (mina/tema) ja narratiiv-ajalooliselt (väljamõeldud süžee kui narratiivse persooni elu lugu). Individuaalsed kommentaaritekstid on siinjuures mõistetavad kui narrtseptid, s.o. narratiivse teis(t)e-taju tähendusloomelised saadused. Narrtseptid toovad esile narratiivsetele persoonidele suunatud tõlgenduste kogukondlikult jagatud, mitmehäälset mõõdet. Väitekirja teine peatükk tutvustatab originaalmõistet majakas. Majakal on internetikommunikatsiooni analüüsis struktureeriv roll. “Heites valgust“ kommunikatsiooni erinevatele külgedele, majakas kas liigendab narrtseptiivseid looilmu (retseptiivne, „populaarne“ dimensioon) või komponeerib neid reaalajaliselt avalduvateks ’lahtiste otstega’ diskursuseilmadeks (analüütilis-metodoloogiline, „akadeemiline“ dimensioon). Siinkohal pakubki antud peatükk ühtlasi ka kriitilisi kohandusi juba käibelolevatele mõistetele võimalike maailmade ja narratiiviteooriast ning diskursuseanalüüsist, s.o., looilm, kavatsemis-ilm, tekstiloojate-ilm ja diskursuse-ilm. Doktoriväitekirja kolmas peatükk keskendub ameerika teleseriaali “Halvale teele“ (Breaking Bad) internetikommentaaride illustratiivsele lähianalüüsile. Eelkirjeldatud teoreetilisel mõisteaparatuuril on analüüsis keskne roll.How does the viewer engage herself with narrative characters? Literary theory, folkloristics, narratology, psychology, and media studies more widely have generally found guidance in the treatments of identification, empathy, and immersion. For if fictional people, be it by the written or audiovisual depiction, are nothing but the fruits of authors’ imagination, then the viewer or the reader similarly attempts to recognize herself in, immerse herself into the world of, and identify herself with the observed character. While analyzing character engagement from the perspective of everyday communication, however, the exclusively representational and inward approach to the human mind can prove an inadequate preference. For the respective ideas of human as a „social being“ and the „social character of meaning“ (Vygotsky) hazard to become backgrounded due to „character engagement“ becoming proportionate to a kind of inner dialogue: viewer makes sense of the other through the model she has adapted about herself. Although it can be, at times, a necessary strategy for comprehension and sense-making, one cannot disregard the engagement being—even toward “fictional” people—always directed. You are absorbed by someone, you become “immersed” in a world that is inhabitated by someone autonomously-existing-with-their-world. In synthesizing diverse literature, Chapter One of the present dissertation develops appropriate theoretical framework that approaches engagement with the characters of television serials from the stance of common sense social experience. Of focal significance here is the notion of realitization: in the context of communal discussion, characters just are approached as if real people. Accordingly, a narrative character becomes a person. For Internet discussions operate in third person (me/her) and historio-narratively (“fictive” plot as narrative person’s life story). Individual commentary texts become hereby considered as narrcepts; that is, they are the sense-making products of the narrative perception of the other (narrative+precept). Through narrcepts, the distributed and polyphonic dimension of the construals directed toward narrative persons becomes acknowledged. Chapter Two of the dissertation introduces a succeeding original notion: beacon. Beacon enacts a structuring role in the analysis of online communication. Beacon „throws light“ onto the different aspects of Internet discourse, decomposing narrceptive storyworlds (reciprocal, „popular“ dimension) and composing the latter into „open ended“ discourse worlds emerging in real time (analytical-methodological, „academical“ dimension). Consequently, critical adaptations of current terminology in possible worlds theory, narrative theory, and discourse analysis are presented; that is, storyworld, intend-world, text makers’ world and discourse world. Chapter three of the dissertation concentrates on the illustrative close analysis of the online commentaries with regard to the American television serial Breaking Bad. The previously established theoretical apparatus serves a central role in the analysis