Exploring the Local Grammar of Evaluation: The Case of Adjectival Patterns in American and Italian Judicial Discourse

Based on a 2-million word bilingual comparable corpus of American and Italian judgments, this paper tests the applicability of a local grammar to study evaluative phraseology in judicial discourse in English and Italian. In particular, the study compares the use of two patterns: v-link + ADJ + that pattern / copula + ADJ + che and v-link + ADJ + to-infinitive pattern / copula + ADJ + verbo all’infinito in the disciplinary genre of criminal judgments delivered by the US Supreme Court and the Italian Corte Suprema di Cassazione. It is argued that these two patterns represent a viable and efficient diagnostic tool for retrieving instances of evaluative language and they represent an ideal starting point and a relevant unit of analysis for a cross-language analysis of evaluation in domainrestricted specialised discourse. Further, the findings provided shed light on important interactions occurring among major interactants involved in the judicial discourse

A divisibility result on combinatorics of generalized braids

For every finite Coxeter group $\Gamma$, each positive braids in the corresponding braid group admits a unique decomposition as a finite sequence of elements of $\Gamma$, the so-called Garside-normal form.The study of the associated adjacency matrix $Adj(\Gamma)$ allows to count the number of Garside-normal form of a given length.In this paper we prove that the characteristic polynomial of $Adj(B_n)$ divides the one of $Adj(B_{n+1})$. The key point is the use of a Hopf algebra based on signed permutations. A similar result was already known for the type $A$. We observe that this does not hold for type $D$. The other Coxeter types ($I$, $E$, $F$ and $H$) are also studied.Comment: 28 page

Biomarker analyses of clinical outcomes in patients with advanced hepatocellular carcinoma treated with Sorafenib with or without Erlotinib in the SEARCH Trial

Purpose: Sorafenib is the current standard therapy for advanced HCC, but validated biomarkers predicting clinical outcomes are lacking. This study aimed to identify biomarkers predicting prognosis and/or response to sorafenib, with or without erlotinib, in HCC patients from the phase 3 SEARCH trial. Experimental Design: 720 patients were randomized to receive oral sorafenib 400 mg BID plus erlotinib 150 mg QD or placebo. Fifteen growth factors relevant to the treatment regimen and/or to HCC were measured in baseline plasma samples. Results: Baseline plasma biomarkers were measured in 494 (69%) patients (sorafenib plus erlotinib, n=243; sorafenib plus placebo, n=251). Treatment arm–independent analyses showed that elevated HGF (HR, 1.687 [high vs low expression]; endpoint multiplicity adjusted [e-adj] P=0.0001) and elevated plasma VEGF-A (HR, 1.386; e-adj P=0..0377) were significantly associated with poor OS in multivariate analyses, and low plasma KIT (HR, 0.75 [high vs low]; P=0.0233; e-adj P=0.2793) tended to correlate with poorer OS. High plasma VEGF-C independently correlated with longer TTP (HR, 0.633; e-adj P=0.0010) and trended toward associating with improved disease control rate (univariate:OR, 2.047; P=0.030; e-adj P=0.420). In 67% of evaluable patients (339/494), a multimarker signature of HGF, VEGF-A, KIT, epigen, and VEGF-C correlated with improved median OS in multivariate analysis (HR, 0.150; P<0.00001). No biomarker predicted efficacy from erlotinib. Conclusions: Baseline plasma HGF, VEGF-A, KIT, and VEGF-C correlated with clinical outcomes in HCC patients treated with sorafenib with or without erlotinib. These biomarkers plus epigen constituted a multimarker signature for improved OS

Ideals associated to two sequences and a matrix

Let \u_{1\times n}, \X_{n\times n}, and \v_{n\times 1} be matrices of indeterminates, \Adj \X be the classical adjoint of \X, and $H(n)$ be the ideal I_1(\u\X)+I_1(\X\v)+I_1(\v\u-\Adj \X). Vasconcelos has conjectured that $H(n)$ is a perfect Gorenstein ideal of grade $2n$. In this paper, we obtain the minimal free resolution of $H(n)$; and thereby establish Vasconcelos' conjecture

Can one factor the classical adjoint of a generic matrix?

Let k be a field, n a positive integer, X a generic nxn matrix over k (i.e., a matrix (x_{ij}) of n^2 independent indeterminates over the polynomial ring k[x_{ij}]), and adj(X) its classical adjoint. It is shown that if char k=0 and n is odd, then adj(X) is not the product of two noninvertible nxn matrices over k[x_{ij}]. If n is even and >2, a restricted class of nontrivial factorizations occur. The nonzero-characteristic case remains open. The operation adj on matrices arises from the (n-1)st exterior power functor on modules; the same question can be posed for matrix operations arising from other functors.Comment: Revised version contains answer to "even n" question left open in original version. (Answer due to Buchweitz & Leuschke; simple proof in this note.) Copy at http://math.berkeley.edu/~gbergman/papers will always have latest version; revisions sent to arXiv only for major change

Data types

A Mathematical interpretation is given to the notion of a data type. The main novelty is in the generality of the mathematical treatment which allows procedural data types and circularly defined data types. What is meant by data type is pretty close to what any computer scientist would understand by this term or by data structure, type, mode, cluster, class. The mathematical treatment is the conjunction of the ideas of D. Scott on the solution of domain equations (Scott (71), (72) and (76)) and the initiality property noticed by the ADJ group (ADJ (75), ADJ (77)). The present work adds operations to the data types proposed by Scott and generalizes the data types of ADJ to procedural types and arbitrary circular type definitions. The advantages of a mathematical interpretation of data types are those of mathematical semantics in general : throwing light on some ill-understood constructs in high-level programming languages, easing the task of writing correct programs and making possible proofs of correctness for programs or implementations"

Volume independence in large Nc QCD-like gauge theories

Volume independence in large \Nc gauge theories may be viewed as a generalized orbifold equivalence. The reduction to zero volume (or Eguchi-Kawai reduction) is a special case of this equivalence. So is temperature independence in confining phases. In pure Yang-Mills theory, the failure of volume independence for sufficiently small volumes (at weak coupling) due to spontaneous breaking of center symmetry, together with its validity above a critical size, nicely illustrate the symmetry realization conditions which are both necessary and sufficient for large \Nc orbifold equivalence. The existence of a minimal size below which volume independence fails also applies to Yang-Mills theory with antisymmetric representation fermions [QCD(AS)]. However, in Yang-Mills theory with adjoint representation fermions [QCD(Adj)], endowed with periodic boundary conditions, volume independence remains valid down to arbitrarily small size. In sufficiently large volumes, QCD(Adj) and QCD(AS) have a large \Nc ``orientifold'' equivalence, provided charge conjugation symmetry is unbroken in the latter theory. Therefore, via a combined orbifold-orientifold mapping, a well-defined large \Nc equivalence exists between QCD(AS) in large, or infinite, volume and QCD(Adj) in arbitrarily small volume. Since asymptotically free gauge theories, such as QCD(Adj), are much easier to study (analytically or numerically) in small volume, this equivalence should allow greater understanding of large \Nc QCD in infinite volume.Comment: 32 pages, 4 figure

Nonperturbative equation of state of quark-gluon plasma. Applications

The vacuum-driven nonperturbative factors $L_i$ for quark and gluon Green's functions are shown to define the nonperturbative dynamics of QGP in the leading approximation. EoS obtained recently in the framework of this approach is compared in detail with known lattice data for $\mu=0$ including $P/T^4$, $\epsilon/T^4$, $\frac{\epsilon-3P}{T^4}$. The basic role in the dynamics at T\la 3T_c is played by the factors $L_i$ which are approximately equal to the modulus of Polyakov line for quark $L_{fund}$ and gluon $L_{adj}$. The properties of $L_i$ are derived from field correlators and compared to lattice data, in particular the Casimir scaling property $L_{adj} =(L_{fund})^{\frac{C_2(adj)}{C_2(fund)}}$ follows in the Gaussian approximation valid for small vacuum correlation lengths. Resulting curves for $P/T^4$, $\epsilon/T^4$, $\frac{\epsilon-3P}{T^4}$ are in a reasonable agreement with lattice data, the remaining difference points out to an effective attraction among QGP constituents.Comment: 20 pages, 6 figure