... of CAC and the covariance on scalar regression model with the positive-definiteness constraints. Section  3 presents the proposed estimation approach and the ADMM algorithm. Section  4 shows the convergence of the proposed algorithm. Section  5 establishes the convergence rates and theoretical...

... with label information from an additional label space. To tackle the new formulations numerically, we consider the bi-convex relaxation of the multi-marginal GW problem, which is tight in the balanced case if the cost function is conditionally negative definite. The relaxed model can be solved...

... and with . is called the ICM. Note that and exist uniquely and that is nonsingular ( Kim and Zimmerman, 2012 ). We now consider the covariance matrix of . By taking the covariance on both sides of Equation 2 , we obtain the following result: (3) Corollary in 3 is positive-definite if and only...

... in an illustrative spirit, examples being taken from conventional and non-parametric multivariate analysis and from exploratory analysis. multivariate analysis positive-definiteness invariance properties non-parametric multivariate statistics spatial models projection pursuit REFERENCES Anderson , T. W...

...Huoyuan Duan; Roger C. E. Tan; Suh-Yuh Yang; Cheng-Shu You Proposition 2.2 Assume that Assumption 2.1 holds. The finite element solution solver is symmetric, positive definite with respect to both and : The new LS method is then highly attractive for the case where...

...-temporal pollution dataset from California and demonstrate that our cross-covariance performs better than other competing models. Asymmetry Linear model of coregionalization Nonseparability Positive definiteness Space and time Stationarity Biometrika (2010), 97,1,pp. 15–30...

... #1; = DLL#2; D for a covariance matrix where D is a diagonal matrix with entries proportional to the square roots of the diagonal entries of #1; and L is a unit lower-triangular matrix solely determining its correlation matrix. This total separation of variance and correlation is definitely a major advantage...

... languages Kenesei I R M Vago and A Fenyvesi Rebrus P Siptár P and M Törkenczy Vago R M verbal paradigms consonantal morphemes English Latin Bulgarian Bybee J markedness constraints paradigm uniformity Hungarian verbal paradigm definiteness neutralization anti-harmony lexical allomorphy...

... this conflict gives rise to different kinds of compromises in the association of personal pronouns with definiteness, gender, number, modifiers, and complements in different languages. As mentioned earlier, languages generally do not allow modifiers to occur with personal pronouns, apparently...

... in the case of definiteness and indefiniteness as well. In most languages, noun phrases involve pragmatic identification, whereas proforms involve semantic identification. The notion of opaque context is relevant for semantic identification only, and not for pragmatic identification. The former is restricted...

... of this suffix, on nouns derived from verbs and adjectives, on personal names derived from adjectives, and, in Germanic, the weak adjective declension, hitherto associated with definiteness. Instead, the notional feature ‘identification’ is assigned to the whole class of Indo-European /n/-formatives. The weak...

...Demonstratives are involved in cyclical changes by becoming articles and later class or Case markers. This involves the grammaticalization of deictic features. For instance, the Old English masculine demonstrative pronoun se develops into the definite article...

.... The Freeze/Kayne approach predicts that definiteness effects in have sentences should match up with those in existential sentences. It also predicts that have sentences should show signs that their subject has raised from below, and that they should pass tests for unaccusativity...

... Uralic languages have cases, but the size of case inventories varies greatly. In some languages, the so-called grammatical cases are used to express not only grammatical roles such as Agent, Patient, or Recipient, but also definiteness or boundedness, the Finnic partitive vs accusative variation being...

... agreement aorist attributive agent voice causative classifier clitic compound complementizer conjunction copula converb dative declarative definite demonstrative determiner differential object marking discourse particle durative emphatic ergative existential feminine FACT FAM FOC FUT GEN HAB HON INF IMP...

...Table 5.1. Proportions and counts for RCE and non‐RCE tokens with respect to definiteness and predicate type Definiteness Predicate type % of RCE tokens % of Non‐RCE tokens % of RCE tokens % of Non‐RCE tokens Definite 19 (n = 10) 61...

... such solutions: supervaluation theory, degree theories, and the use of a ‘definiteness’ operator. It also explores whether vagueness is trivial or substantial, and discusses the importance of a little-recognised fact about vagueness: that there may be no clear borderline cases of the application of a vague...

... and number, and sometimes agree with the object. Generally, the trigger of object agreement is argued to be related to definiteness. It is argued that while both syntactic and semantic properties are relevant for determining object agreement, the syntactic structure of the object is the main factor: objects...

...The chapter presents and analyzes the DP-cycle and its structural consequences within the Hungarian noun phrase. The marking of definiteness is generally discussed in order to show how the emergence of the definite article and its functional spreading reshaped the nominal left periphery...

...This paper challenges some widespread assumptions about the role of the modal axiom S4 in theories of vagueness. In the context of vagueness, S4 usually appears as the principle ‘If it’s clear (determinate, definite) that A, then it’s clear that it’s clear that A’, or, formally, CA→CCA. We argue...