The physical 3d $\mathcal N = 2$ theory $T\[Y]$ was previously used to predict the existence of some $3$-manifold invariants $\widehat{Z}{a}(q)$ that take form power series with integer coefficients, converging in unit disk. Their radial limits at roots unity should recover Witten–Reshetikhin–Turaev invariants. In this paper we discuss how, for complements knots $S^3$, analogue be a two-variabl...

The sentential theory of propositional attitudes is very attractive to AI workers, but it is difficult to use such a theory to assign semantics to English sentences about attitudes. The problem is that a compositional semantics cannot easily build the logical forms that the theory requires. We present a new notation for a sentential theory, and a unification grammar that builds logical forms in...

The aim of this paper is to describe a technique for identifying the sources of several types of syntactic ambiguity in Arabic Sentences with a single parse only. Normally, any sentence with two or more structural representations is said to be syntactically ambiguous. However, Arabic sentences with only one structural representation may be ambiguous. Our technique for identifying Syntactic Ambi...

This paper proposes a generation method for feature-structured)ased unification grammars. As comlx~red with fixed ~rity term notation, feature structure notation is more tlexible for representing knowledge needed to generate idiom~ttic structures as well as genem~l constructions. The method enables feature strncture retrieval via nmltiple indices. The indexing mechanism, when used with a semant...

The paper presents an algorithm, written in PROLOG, for processing English sentences which contain either Gapping, Right Node Raising (RNR) or Reduced Conjunction (RC). The DCG (Definite Clause Grammar) formalism (Pereira & Warren 80) is adopted. The algorithm is highly efficient and capable of processing a full range of coordinate constructions containing any number of coordinate conjunctions ...

In this paper we prove some characterizations of the matrix orthogonal polynomials whose derivatives are also orthogonal, which generalize other known ones in the scalar case. In particular, we prove that the corresponding orthogonality matrix functional is characterized by a Pearson-type equation with two matrix polynomials of degree not greater than 2 and 1. The proofs are given for a general...

This paper presents the new concept of second-order cone approximations for convex conic programming. Given any open convex cone K, a logarithmically homogeneous self-concordant barrier for K and any positive real number r ≤ 1, we associate, with each direction x ∈ K, a second-order cone K̂r(x) containing K. We show that K is the intersection of the second-order cones K̂r(x), as x ranges through ...

We present numerical methods for computing the Schatten p-norm of positive semi-definite matrices. Our motivation stems from uncertainty quantification and optimal experimental design inverse problems, where defines a measure uncertainty. Computing high-dimensional matrices is computationally expensive. propose matrix-free method to estimate using Monte Carlo estimator derive convergence result...

Nyström method has been successfully used to improve the computational efficiency of kernel ridge regression (KRR). Recently, theoretical analysis of Nyström KRR, including generalization bound and convergence rate, has been established based on reproducing kernel Hilbert space (RKHS) associated with the symmetric positive semi-definite kernel. However, in real world applications, RKHS is not a...