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Adequacy Condition

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Yamauchi Takuya – One of the best experts on this subject based on the ideXlab platform.

  • Serre weights for $GSp_4$ over totally real fields
    , 2021
    Co-Authors: Yamauchi Takuya
    Abstract:

    We prove the existence of a potentially diagonalizable lift of a given automorphic mod $p$ Galois representation $\overline{\rho}:{\rm Gal}(\overline{F}/F)\longrightarrow {\rm GSp}_4(\overline{\mathbb{F}}_p)$ for any totally real field $F$ and any rational prime $p>2$ under the Adequacy Condition by using automorphic lifting techniques developed by Barnet-Lamb, Gee, Geraghty, and Taylor. As an application, when $p$ is split completely in $F$, we prove a variant of Serre’s weight conjecture for $\overline{\rho}$. The formulation of our Serre conjecture is done by following Toby Gee’s philosophy. Applying these results to the case when $F=\mathbb{Q}$ with a detailed study of potentially diagonalizable, crystalline lifts with some prescribed properties, we also define classical (naive) Serre’s weights. This weight would be the minimal weight among possible classical weights in some sense which occur in candidates of holomorphic Siegel Hecke eigen cusp forms of degree 2 with levels prime to $p$. The main task is to construct a potentially ordinary automorphic lift for $\overline{\rho}$ by assuming only the Adequacy Condition. The main theorems in this paper also extend many results obtained by Barnet-Lamb, Gee and Geraghty for potentially ordinary lifts and Gee and Geraghty for companion forms.Comment: 60 pages, some errors are fixed. Examples for the classical Serre weights and some description (Theorem 1.5) for companion forms are also adde

Takuya Yamauchi – One of the best experts on this subject based on the ideXlab platform.

  • Serre weights for $GSp_4$ over totally real fields
    arXiv: Number Theory, 2020
    Co-Authors: Takuya Yamauchi
    Abstract:

    We prove the existence of a potentially diagonalizable lift of a given automorphic mod $p$ Galois representation $\overline{\rho}:{\rm Gal}(\overline{F}/F)\longrightarrow {\rm GSp}_4(\overline{\mathbb{F}}_p)$ for any totally real field $F$ and any rational prime $p>2$ under Adequacy Condition by using automorphic lifting techniques developed by Barnet-Lamb, Gee, Geraghty, and Taylor. As an application, when $p$ is split completely in $F$, we prove a variant of Serre’s weight conjecture for $\overline{\rho}$. The formulation of our Serre conjecture is done by following Toby Gee’s philosophy. Applying these results to the case when $F=\mathbb{Q}$ with a detailed study of potentially diagonalizable, crystalline lifts with some prescribed properties, we also define classical (naive) Serre’s weights. This weight would be the minimal weight among possible classical weights in some sense which occur in candidates of holomorphic Siegel Hecke eigen cusp forms of degree 2 with levels prime to $p$. The main task is to construct a potentially ordinary automorphic lift for $\overline{\rho}$ by assuming only the Adequacy Condition. The main theorems in this paper also extend many results obtained by Barnet-Lamb, Gee and Geraghty for potentially ordinary lifts and Gee and Geraghty for companion forms.

Sri Dewi Sujiati – One of the best experts on this subject based on the ideXlab platform.

  • ANALISIS PERBANDINGAN KECUKUPAN MODAL ANTARA PT BANK NEGARA INDONESIA PERSERO TBK DAN PT BANK CENTRAL ASIA TBK
    , 2007
    Co-Authors: Sri Dewi Sujiati
    Abstract:

    The research at PT Bank Negara Indonesia Persero Tbk and PT Bank Central Asia Tbk used case study, titled “Comparison Analysis of Capital Adequacy between PT Bank Negara Indonesia Persero Tbk and PT Bank Central Asia Tbk. This research aimed to find out the capital Adequacy Condition at PT Bank Negara Indonesia Persero Tbk and PT Bank Central Asia Tbk year 2004 to 2006 and to compare CAR at PT Bank Negara Indonesia Persero Tbk and PT Bank Central Asia Tbk year 2004 to 2006, also stated which bank have better capital Condition. Data used was secondary data. Data was owed from three-monthly report of PT Bank Negara Indonesia Persero Tbk and PT Bank Central Asia Tbk by documentation method. Analysis tool to determine Capital Adequacy was Capital Adequacy Ratio (CAR). The result from PT Bank Negara Indonesia Persero Tbk and PT Bank Central Asia Tbk year 2004 to 2006 showed that capital Adequacy at both bank were enough, since Capital Adequacy Ratio (CAR) both bank were above minimum limit stated, that was 8%. PT Bank Negara Indonesia Persero Tbk CAR year 2004 per March was 19,13%, per June was 19,88%, per September was 18,48%, and December was 17,13%. CAR PT Bank Negara Indonesia Persero Tbk year 2005 per March was 18,42%, per June was 15,98%, per September was 15,52%, per December was 15,99%. PT Bank Negara Indonesia Persero Tbk CAR year 2006 per March was 190,45%, per June was 19,04%, per September was 16,95%, per December was 15,30% PT Bank Central Asia Tbk CAR year 2004 per March was 30,53%, per June was 28,65%, per September was 25,84%, per December was 23,95%. PT Bank Central Asia Tbk CAR year 2005 per March was 26,64%, per June was 25,14%, per September was 22,21%, per December was 21,53% PT Bank Central Asia Tbk CAR year 2006 per March was 25,11%, per June was 23,70%, per September 23,86%, per December was 22,09%. From both bank, capital Adequacy of PT Bank Central Asia Tbk was better than capital Adequacy of PT Bank Negara Indonesia Persero Tbk, from three monthlies period.

Arnold G. Kluge – One of the best experts on this subject based on the ideXlab platform.

  • Clade support measures and their Adequacy
    Cladistics, 2008
    Co-Authors: Taran Grant, Arnold G. Kluge
    Abstract:

    In addition to hypothesis optimality, the evaluation of clade (group, edge, split, node) support is an important aspect of phylogenetic analysis. Here we clarify the logical relationship between support and optimality and formulate Adequacy Conditions for support measures. Support, S, and optimality, O, are both empirical knowledge claims about the strength of hypotheses, h1, h2, … hn, in relation to evidence, e, given background knowledge, b. Whereas optimality refers to the absolute strength of hypotheses, support refers to the relative strength of hypotheses. Consequently, support and optimality are logically related such that they vary in direct proportion to each other, S(h | e,b) � O(h | e,b). Furthermore, in order for a support measure to be objective it must quantify support as a function of explanatory power. For example, Goodman–Bremer support and ratio of explanatory power (REP) support satisfy the Adequacy requirement S(h | e,b) � O(h | e,b) and calculate support as a function of explanatory power. As such, these are adequate measures of objective support. The equivalent measures for statistical optimality criteria are the likelihood ratio (or log-likelihood difference) and likelihood difference support measures for maximum likelihood and the posterior probability ratio and posterior probability difference support measures for Bayesian inference. These statistical support measures satisfy the Adequacy requirement S(h | e,b) � O(h | e,b) and to that extent are internally consistent; however, they do not quantify support as a function of explanatory power and therefore are not measures of objective support. Neither the relative fit difference (RFD; relative GB support) nor any of the parsimony (bootstrap and jackknife character resampling) or statistical [bootstrap character resampling, Markov chain Monte Carlo (MCMC) clade frequencies] support measures based on clade frequencies satisfy the Adequacy Condition S(h | e,b) � O(h | e,b) or calculate support as a function of explanatory power. As such, they are not adequate support measures.

David Pereplyotchik – One of the best experts on this subject based on the ideXlab platform.

  • language acquisition and the explanatory Adequacy Condition
    , 2017
    Co-Authors: David Pereplyotchik
    Abstract:

    I examine John Collins’ reconstruction of the cognitive revolution in linguistics, showing that one of the main arguments for cognitivism is simply not compelling. While there is a convincing case for aiming to achieve “explanatory Adequacy” in linguistics, over and above mere observational and descriptive Adequacy, this aim need not be underwritten by a cognitivist conception of language. A unified theory of all human languages is desirable whether or not cognitivism is correct. Next, I point out that, although cognitivism entails that grammars are psychologically real, the reverse entailment does not hold; a grammar can be psychologically real even if the objects of the formal syntactician’s concern are public, conventional E-languages. Chomsky’s view entails that psycholinguists should seek a relatively transparent relation between the syntacticians’ grammar and the “knowledge-base” that constitutes competence—a “natural” grammar-parser combination. Progress toward this goal has been slow, in part because syntacticians are not as concerned with psycholinguistic data as a cognitivist would expect them to be. In the mainstream syntax literature, psychological reality is a distant, dimly understood, and rarely invoked desideratum. Nevertheless, a parsing model that makes direct use of independently plausible syntactic principles is the simplest and strongest theoretical option.