Esta dissertação apresenta uma análise semântica, no paradigma da Semântica Formal, da (i) restrição de domínio no DP e da (ii) expressão kar, que veicula a ideia de totalidade, no dialeto paranaense da língua Kaingang, do tronco Macro-Jê, família Jê, falada nas regiões sul e sudeste do Brasil. Num primeiro momento, o artigo definido parece ter, no Kaingang Paranaense, uma distribuição não trivial: aplica-se primeiro a um determinante quantificacional e restringe, via essa combinação, o domínio do quantificador, tal como no Basco, Grego e Státimcets (Giannakidou 2003, Etxeberria 2005 e Etxeberria & Giannakidou 2009), línguas muito parecidas com o Kaingang no domínio nominal. Alguns dados, contudo, apontaram a análise em outra direção. Entendemos que certos padrões de comportamento semântico e sintático apresentado por kar nas sentenças, tal como sua neutralidade quanto à propriedade de distributividade e a possibilidade da conjunção de duas sequências de [NP+kar] sob um mesmo artigo definido (ao contrário do Basco, no qual a mesma estrutura é agramatical, sugerindo que os quantificadores universais em Basco criam um QP), são algumas das evidências que, no conjunto, dão suporte para a hipótese, defendida nesta dissertação, de que kar, no Kaingang Paranaense, parece ser um modificador - à la Lasersohn (1999) -, não tendo, por isso, uma força quantificacional própria. A função semântica de kar seria de controlar o quanto de desvio da verdade é pragmaticamente permissível. Como consequência desta análise, no Kaingang Paranaense o artigo definido não operaria sobre um determinante quantificacional, mas sim sobre um NP. O que aponta no sentido de que os artigos definidos ag/fag (os/as) no Kaingang Paranaense, em contextos em que eles co-ocorrem com kar, não perderiam a sua função max, i.e., de formadores de indivíduo a partir de um conjunto, para funcionar meramente como um operador preservador de tipo e restritor de domínio adjungido ao determinante quantificacional, como proposto por Giannakidou 2003, Etxeberria (2005) e Etxeberria & Giannakidou (2009) para o Basco e o Grego. Ag/fag continuariam sendo artigos definidos clássicos ocupando o núcleo de uma projeção DP e kar um modificador. Também discutimos brevemente algumas das vantagens e problemas de se tentar estender esta análise para o Basco, Grego e Státimcets. E, por último, investigamos o comportamento de kar na sentença, as possíveis leituras quando da sua interação com indefinidos, numerais, tipos de predicados e o operador distributivo introduzido via reduplicação verbal. Com base nos dados, nossa proposta é de que - em função de a leitura distributiva, na maioria dos exemplos, ser permitida pelos informantes somente quando houve reduplicação verbal - kar é neutro quanto à propriedade da distributividade e que o operador distributivo introduzido por reduplicação verbal tem escopo sobre todo o VP. / This dissertation presents, in the paradigm of formal semantics, a semantic analysis of both (i) the phenomenon of domain restriction in the DP and (ii) the expression kar, which conveys the idea of totality, in a dialect of the Kaingang language, a Brazilian language from the Macro-Jê Stock, Jê family, spoken in southern and southeastern Brazil. Although, at first, the definite article in Kaingang seems to have a non-trivial distribution: it applies first to a quantificational expression, and via such combination restricts the domain of quantifier, such as in Basque, Greek and Státimcets (Giannakidou 2003, Etxeberria 2005 and Etxeberria & Giannakidou 2009), some data pointed the analysis in another direction. Patterns of semantic and syntactic bevavior presented by kar in some sentences, such as its neutralite regarding the property of distributivity and the possibility of conjoining two [NP + kar] sequences under the same definite article (unlike Basque, which does not allow such structure, suggesting that in Basque the universal quantifier creats a QP), seem to be as a whole evidences for the hypothesis, advocated in this thesis, that the expression kar may be a modifier - à la Lasersohn (1999) - and as such would not have a quantificational force of its own. The semantic function of kar would be to control how much deviation from the truth conditions of the sentences is pragmatically allowed. As a result of this analysis, the definite articles ag/fag in Kaingang do not operate on a quantificational expression, as in Basque and Greek, but on the NP. Such fact suggests that the definite articles in Kaingang, in contexts they co-occur with kar, do not lose their max function in order to work merely as a type preserver and a domain restrictor combined with a quantificational expression, as proposed by Giannakidou 2003, Etxeberria (2005) e Etxeberria & Giannakidou (2009) for Basque and Greek. Ag/fag would still be a classical definite article occupying the head of a DP projection and kar a modifier, instead of a universal quantifier. We also discuss briefly some of the advantages and problems of trying to extend this analysis to the Basque, Greek and Státimcets languages. And lastly, we investigated the behavior of kar in the sentence, its interaction with indefinites, numerals, types of predicates and the distributive operator introduced via verbal reduplication. Based on such data, once distributive readings were permitted by the informants only via verbal reduplication, our proposal is that kar is neutral regarding the property of distributivity and that the distributive operator introduced via verbal reduplication has scope over the VP.

Neste trabalho apresentamos uma demonstração detalhada para um conhecido teorema de I. J. Schoenberg que caracteriza certas funções positivas definidas em esferas. Analisamos ainda um critério para a obtenção de positividade definida de uma função a partir de condições de suavidade e convexidade dela, em uma tentativa de ratificar alguns resultados da literatura conhecidos como critérios de Pólya. / In this work we present a proof for a famous theorem of Schoenberg on positive definite functions on spheres. We analyze some results that deduce positive definiteness from diferentiability and convexity assumption on the function, an attempt to ratify some Pólya type conjectures found in the literature.

Let $\Omega\subset\mathbb{R}^n$ be an open and connected subset of $\mathbb{R}^n$. We say that a function $F\colon \Omega-\Omega\to\mathbb{C}$, where $\Omega-\Omega=\{x-y\colon x,y\in\Omega\}$, is positive definite if for any $x_1,\ldots,x_m\in\Omega$ and any $c_1,\ldots,c_m\in \mathbb{C}$ we have that $\sum_{j,k=1}^m F(x_j-x_k)c_j\overline{c_k}\geq 0$. Let $F\colon\Omega-\Omega\to\mathbb{C}$ be a continuous positive definite function. We give necessary and sufficient conditions for $F$ to have an extension to a continuous and positive definite function defined on the entire Euclidean space $\mathbb{R}^n$. The conditions are formulated in terms of strong commutativity of some certain selfadjoint operators defined on a Hilbert space associated to our positive definite function.

We present bounds on various quantities of interest regarding the central trajectory of a semi-definite program (SDP), where the bounds are functions of Renegar's condition number C(d) and other naturally-occurring quantities such as the dimensions n and m. The condition number C(d) is defined in terms of the data instance d = (A, b, C) for SDP; it is the inverse of a relative measure of the distance of the data instance to the set of ill-posed data instances, that is, data instances for which arbitrary perturbations would make the corresponding SDP either feasible or infeasible. We provide upper and lower bounds on the solutions along the central trajectory, and upper bounds on changes in solutions and objective function values along the central trajectory when the data instance is perturbed and/or when the path parameter defining the central trajectory is changed. Based on these bounds, we prove that the solutions along the central trajectory grow at most linearly and at a rate proportional to the inverse of the distance to ill-posedness, and grow at least linearly and at a rate proportional to the inverse of C(d)2 , as the trajectory approaches an optimal solution to the SDP. Furthermore, the change in solutions and in objective function values along the central trajectory is at most linear in the size of the changes in the data. All such bounds involve polynomial functions of C(d), the size of the data, the distance to ill-posedness of the data, and the dimensions n and m of the SDP.

The present thesis offers a thorough examination of Modern Greek distributive determiner (o) kathe (every, each, any) nominal phrases and accounts for the different readings of these expressions. Kathe NPs exhibit a universal distributive every reading (definite use), a Free Choice any (indefinite use) and a kind interpretation. O kathe NPs exhibit a universal distributive each reading (familiar and definite use), a Free Choice any and an Indiscriminative Free Choice just any reading (indefinite uses). In line with previous proposals for every, I suggest that kathe determiners do not lexicalize a universal operator. Following Szabolcsi (2010) on every NPs, I argue that (o) kathe NPs are (inherently) indefinite expressions (in the sense of Heim 1982) that make part of a quantificational concord. A distributive operator binds the element variables of their NP set; a clause-typing operator in the left periphery, a Definiteness, a Generic or a Modal Operator binds the context set variables of the NP, rendering a universal, a kind or an FC reading to the expression, accordingly. The presence of different sentential operators under C determines the readings that arise. I argue that binding by these operators corresponds to two Agree operations in syntax: One is between the Distributive operator in C and Q on the DP as well as with Aspect on the vP. The other one is between the sentential operator and the relevant feature on Q but also on TP/ vP. The quantificational chains formed are argued to be, to some extent, similar to that of wh- chains. In Chapter 1, I present the essential syntactic and semantic background, as well as an outline of my proposal to the riddle of every and (o)kathe NPs interpretational variability. In Chapter 2, I discuss and analyze the syntax of Determiner Phrases and Quantifier Phrases and in particular the syntactic structure of Greek kathe, o kathe, oli i NPs, as well as that of English every, each, all and all the NPs. In Chapter 3 I investigate the different readings the kathe and o kathe NPs give rise to and the semantics behind that, as well as previous approaches on the issue. In Chapter 4, I explain the interpretational variability of the expression in hand as a result of the binding of the NPs’ context set variables by different Operators (a Definiteness, a Generic or a Modal Operator) and Operation Agree. In Chapter 5, I discuss how the theory proposed for Greek kathe, o kathe and English every, each NPs could explain relevant phenomena of quantificational variability in Chinese and Japanese, as well as Greek Polarity phenomena. In Chapter 6, I conclude the discussion. / Η παρούσα διατριβή προσφέρει μια αναλυτική εξέταση των επιμεριστικών δεικτών κάθε και ο κάθε της Νέας Ελληνικής και των Ονοματικών Φράσεών τους, όπως επίσης και μία εξήγηση για τις ποικίλες διαφορετικές ερμηνείες των εκφράσεων αυτών, αλλά και των αντιστοίχων της Αγγλικής. Οι Ονοματικές Φράσεις (ΟΦ) με το κάθε (κάθε ΟΦ) στην οριστική τους χρήση παρουσιάζουν μία ερμηνεία καθολικής ποσοτικής δείξης, όπως επίσης μία ερμηνεία ελεύθερης επιλογής, αόριστης χρήσης, και μία ερμηνεία είδους. Οι Ονοματικές Φράσεις με το ο κάθε (ο κάθε ΟΦ) παρουσιάζουν μία ερμηνεία καθολικής ποσοτικής δείξης ως οριστική και οικεία χρήση, μία ερμηνεία ελεύθερης επιλογής και μία υποτιμητικής ελεύθερης επιλογής ως αόριστες χρήσεις. Σε συμφωνία με προηγούμενες αναλύσεις για τον αντίστοιχο προσδιοριστή της Αγγλικής, προτείνω ότι τα κάθε και ο κάθε δεν λεξικοποιούν τον καθολικό ποσοτικό τελεστή της λογικής. Αντίθετα, ισχυρίζομαι ότι οι Ονοματικές Φράσεις με τα κάθε και ο κάθε είναι κατά βάση αόριστες εκφράσεις, οι οποίες συμμετέχουν σε διαφορετικές ποσοδεικτικές αλυσίδες εκφράσεων κάθε φορά. Ένας επιμεριστικός τελεστής στην αριστερή περιφέρεια δεσμεύει την στοιχειώδη μεταβλητή του συνόλου της ΟΦ. Ένας οριστικός, ένας γενικός ή ένας τροπικός τελεστής, επίσης στην αριστερή περιφέρεια, δεσμεύει τη μεταβλητή περικειμένου, δίνοντας αντίστοιχα τις ερμηνείες της καθολικής ποσοτικής δείξης, του είδους και της ελεύθερης επιλογής. Η παρουσία διαφορετικών προτασιακών τελεστών, λοιπόν, καθορίζει την ανάδυση των διαφορετικών ερμηνειών. Επίσης, ισχυρίζομαι ότι η όλη διαδικασία της δέσμευσης αντιστοιχεί σε λειτουργίες Συμφωνείν στη σύνταξη. Οι ποσοδεικτικές αλυσίδες που σχηματίζονται είναι σε κάποιο βαθμό όμοιες με αυτές των ερωτηματικών προτάσεων. Στο Κεφάλαιο 1 παραθέτω το απαραίτητο συντακτικό και σημασιολογικό υπόβαθρο, όπως επίσης και μια προεπισκόπηση της πρότασής μου. Στο Κεφάλαιο 2 παρουσιάζεται μια συντακτική ανάλυση των εκφράσεων αυτών και των αντιστοίχων αγγλικών. Το Κεφάλαιο 3 διερευνά την σημασιολογία και τις διαφορετικές ερμηνείες. Στο Κεφάλαιο 4 προσφέρω την θεωρητική μου ανάλυση, ενώ στο Κεφάλαιο 5 παρατίθεται μία σύγκριση με ανάλογα φαινόμενα στην Κινεζική και την Ιαπωνική, όπως επίσης και με εκφράσεις πολικότητας της Νέας Ελληνικής. Στο Κεφάλαιο 6 συνοψίζονται τα συμπεράσματα της έρευνας.

Disertacijoje tyrinėjama apibrėžtumo raiška dviejose tipologiniu požiūriu skirtingose kalbose — lietuvių kalboje, kuri yra neartikelinė ir turi mažai sugramatintą apibrėžtumo raišką, ir danų kalboje, turinčioje išplėtotą apibrėžtumo rodiklių sistemą. Disertacijos tikslas yra palyginti lietuvių kalbos apibrėžtumo rodiklius — apibrėžiamuosius būdvardžius ir gramatėjančius demonstratyvus (artroidus) — su artikelinių kalbų (danų, anglų ir kt.) apibrėžtumo rodikliais. Disertacijoje naudojamasi kontrastyvinės analizės metodu, Hjelmslevo komutacijos testu ir semantinio žemėlapio metodu. Šalia kontrastyvinės pasirinkta ir tipologinė perspektyva siekiant nustatyti universalius apibrėžtumo rodiklių vartosenos tipus, taip pat įvertinti lietuvių bei danų kalbų apibrėžtumo raišką tipologiniame kontekste. Sudaryti lietuvių kalbos apibrėžiamųjų būdvardžių ir danų kalbos apibrėžtumo rodiklių semantiniai žemėlapiai padeda išryškinti apibrėžtumo raiškos šiose kalbose panašumus bei skirtumus. Disertacijoje teigiama, kad įvardžiuotinės būdvardžio formos įvardinė morfema –jis, –ji lietuvių kalboje pagrįstai gali būti laikoma formaliu daiktavardinės frazės apibrėžtumo rodikliu, nes ši morfema visais atvejais žymi daiktavardinės frazės apibrėžtumą, kuris gali būti tiek individo referencijos, tiek tipo (taksonominės) referencijos lygmens. Besiformuojančiu apibrėžtumo rodikliu lietuvių kalboje gali būti laikomi gramatėjantys demonstratyvai (artroidai) tas, ta. / The dissertation investigates definiteness marking in two typologically diverse languages — Lithuanian which is an articleless language and has a partially grammaticalized marking of definiteness and Danish which has a fully developed system of definiteness markers. The aim of the thesis is to compare Lithuanian definiteness markers — definite adjectival forms and emergent articles — to definiteness markers of article languages (Danish, English, etc.). The following methods of analysis were applied in the dissertation: contrastive analysis, L. Hjelmslev’s commutation test and semantic map method. Besides the contrastive perspective, the dissertation also has a typological perspective with the aim of determining the universal usage types of definiteness markers and considering definiteness marking in Lithuanian and Danish in a typological context. The Semantic Map of Lithuanian Definite Adjectivals and the Semantic Map of Definiteness Markers in Danish, which were drawn in the thesis, help to highlight the similarities and differences of definiteness marking in Lithuanian and Danish. In the dissertation, it is argued that the pronominal morpheme –jis, –ji contained in the definite adjectival form can be regarded as a formal marker of definiteness in Lithuanian since in all cases this morpheme marks the definiteness of a noun phrase, whether it is definiteness on the level of individual reference or definiteness on the level of type (taxonomic) reference. The demonstrative tas... [to full text]

The dissertation investigates definiteness marking in two typologically diverse languages — Lithuanian which is an articleless language and has a partially grammaticalized marking of definiteness and Danish which has a fully developed system of definiteness markers. The aim of the thesis is to compare Lithuanian definiteness markers — definite adjectival forms and emergent articles — to definiteness markers of article languages (Danish, English, etc.). The following methods of analysis were applied in the dissertation: contrastive analysis, L. Hjelmslev’s commutation test and semantic map method. Besides the contrastive perspective, the dissertation also has a typological perspective with the aim of determining the universal usage types of definiteness markers and considering definiteness marking in Lithuanian and Danish in a typological context. The Semantic Map of Lithuanian Definite Adjectivals and the Semantic Map of Definiteness Markers in Danish, which were drawn in the thesis, help to highlight the similarities and differences of definiteness marking in Lithuanian and Danish. In the dissertation, it is argued that the pronominal morpheme –jis, –ji contained in the definite adjectival form can be regarded as a formal marker of definiteness in Lithuanian since in all cases this morpheme marks the definiteness of a noun phrase, whether it is definiteness on the level of individual reference or definiteness on the level of type (taxonomic) reference. The demonstrative tas... [to full text] / Disertacijoje tyrinėjama apibrėžtumo raiška dviejose tipologiniu požiūriu skirtingose kalbose — lietuvių kalboje, kuri yra neartikelinė ir turi mažai sugramatintą apibrėžtumo raišką, ir danų kalboje, turinčioje išplėtotą apibrėžtumo rodiklių sistemą. Disertacijos tikslas yra palyginti lietuvių kalbos apibrėžtumo rodiklius — apibrėžiamuosius būdvardžius ir gramatėjančius demonstratyvus (artroidus) — su artikelinių kalbų (danų, anglų ir kt.) apibrėžtumo rodikliais. Disertacijoje naudojamasi kontrastyvinės analizės metodu, Hjelmslevo komutacijos testu ir semantinio žemėlapio metodu. Šalia kontrastyvinės pasirinkta ir tipologinė perspektyva siekiant nustatyti universalius apibrėžtumo rodiklių vartosenos tipus, taip pat įvertinti lietuvių bei danų kalbų apibrėžtumo raišką tipologiniame kontekste. Sudaryti lietuvių kalbos apibrėžiamųjų būdvardžių ir danų kalbos apibrėžtumo rodiklių semantiniai žemėlapiai padeda išryškinti apibrėžtumo raiškos šiose kalbose panašumus bei skirtumus. Disertacijoje teigiama, kad įvardžiuotinės būdvardžio formos įvardinė morfema –jis, –ji lietuvių kalboje pagrįstai gali būti laikoma formaliu daiktavardinės frazės apibrėžtumo rodikliu, nes ši morfema visais atvejais žymi daiktavardinės frazės apibrėžtumą, kuris gali būti tiek individo referencijos, tiek tipo (taksonominės) referencijos lygmens. Besiformuojančiu apibrėžtumo rodikliu lietuvių kalboje gali būti laikomi gramatėjantys demonstratyvai (artroidai) tas, ta.

Zugl.: Zürich, Techn. Hochsch., Diss., 2009

Universiẗat, Diss., 1991--Saarbrücken.

This dissertation proposes new optimization algorithms targeting protein-protein docking which is an important class of problems in computational structural biology. The ultimate goal of docking methods is to predict the 3-dimensional structure of a stable protein-protein complex. We study two specific problems encountered in predictive docking of proteins. The first problem is Side-Chain Positioning (SCP), a central component of homology modeling and computational protein docking methods. We formulate SCP as a Maximum Weighted Independent Set (MWIS) problem on an appropriately constructed graph. Our formulation also considers the significant special structure of proteins that SCP exhibits for docking. We develop an approximate algorithm that solves a relaxation of MWIS and employ randomized estimation heuristics to obtain high-quality feasible solutions to the problem. The algorithm is fully distributed and can be implemented on multi-processor architectures. Our computational results on a benchmark set of protein complexes show that the accuracy of our approximate MWIS-based algorithm predictions is comparable with the results achieved by a state-of-the-art method that finds an exact solution to SCP. The second problem we target in this work is protein docking refinement. We propose two different methods to solve the refinement problem. The first approach is based on a Monte Carlo-Minimization (MCM) search to optimize rigid-body and side-chain conformations for binding. In particular, we study the impact of optimally positioning the side-chains in the interface region between two proteins in the process of binding. We report computational results showing that incorporating side-chain flexibility in docking provides substantial improvement in the quality of docked predictions compared to the rigid-body approaches. Further, we demonstrate that the inclusion of unbound side-chain conformers in the side-chain search introduces significant improvement in the performance of the docking refinement protocols. In the second approach, we propose a novel stochastic optimization algorithm based on Subspace Semi-Definite programming-based Underestimation (SSDU), which aims to solve protein docking and protein structure prediction. SSDU is based on underestimating the binding energy function in a permissive subspace of the space of rigid-body motions. We apply Principal Component Analysis (PCA) to determine the permissive subspace and reduce the dimensionality of the conformational search space. We consider the general class of convex polynomial underestimators, and formulate the problem of finding such underestimators as a Semi-Definite Programming (SDP) problem. Using these underestimators, we perform a biased sampling in the vicinity of the conformational regions where the energy function is at its global minimum. Moreover, we develop an exploration procedure based on density-based clustering to detect the near-native regions even when there are many local minima residing far from each other. We also incorporate a Model Selection procedure into SSDU to pick a predictive conformation. Testing our algorithm over a benchmark of protein complexes indicates that SSDU substantially improves the quality of docking refinement compared with existing methods.