or, in vector notation, Cs = Xsβ1 + Zsβ s 2 + Vs, where Cs = [Cs1, . . . , CsT ] ′ is T × 1, Xs = [xs1, . . . , xsT ] ′ is T ×k1, Zs = [zs1, . . . , zsT ]′ is T ×k2, and Vs = [vs1, . . . , vsT ]′ is T ×1. Also, let xsth be the h th element of xst so that x ′ st = [xst1, . . . , xstk1 ], and define zsth similarly. Define v̈st = vst − z′ st(Z ′ sZs)Z ′ sVs, ẍst = xst − z′ st(Z ′ sZs)Z ′ sXs, V̈s = ...

We describe an application of DNorm – a mathematically principled and high performing methodology for disease recognition and normalization, even in the presence of term variation – to clinical notes. DNorm consists of a text processing pipeline, including the BANNER named entity recognizer to locate diseases in the text, and a novel machine learning approach based on pairwise learning to rank ...

We study unusual gapped topological phases where they admit $\mathbb{Z}_N$ fractional excitations in the same manner as topologically ordered phases, yet their ground state degeneracy depends on local geometry of system. Placing such 2D lattice, composed an arbitrary connected graph and 1D line, we find that fusion rules quasiparticle are described by Laplacian number superselection sectors is ...

Let A denote the family of all analytic functions f in the unit disk D with the normalization f (0) = 0 = f ′(0)− 1. Define S = { f ∈ A : f is univalent in D}, U = { f ∈A : ∣∣ f ′(z)(z/ f (z))2−1∣∣< 1 for z ∈ D}, and P(1/2) = { f ∈A : Re( f (z)/z) > 1/2 for z ∈ D}. In this paper, we determine the radius of univalency of F(z) = z f (z)/g(z) whenever f ∈S or U , and g ∈S or P(1/2). Based on our i...

In this paper we complete the characterization of Ext(G, Z) for any torsion-free abelian group G assuming Gödel’s axiom of constructibility plus there is no weakly compact cardinal. In particular, we prove in (V = L) that, for a singular cardinal ν of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence of cardinals (νp : p ∈ Π) satisfying νp ≤ 2 , ...

We propose MoNoise: a normalization model focused on generalizability and efficiency, it aims at being easily reusable and adaptable. Normalization is the task of translating texts from a noncanonical domain to a more canonical domain, in our case: from social media data to standard language. Our proposed model is based on a modular candidate generation in which each module is responsible for a...

Let φ be an automorphism of a free group Fn of rank n, and let Mφ = Fn oφ Z be the corresponding mapping torus of φ. We study the group Out(Mφ) under certain technical conditions on φ. Moreover, in the case of rank 2, we classify the cases when this group is finite or virtually cyclic, depending on the conjugacy class of the image of φ in GL2(Z). As an application, we solve the isomorphism prob...

Due to the presence of systematic measurement biases, data normalization is an essential preprocessing step in the analysis of single-cell RNA sequencing (scRNA-seq) data. While a variety of normalization procedures are available for bulk RNA-seq, their suitability with respect to single-cell data is still largely unexplored. Furthermore, there may be multiple, competing considerations behind t...

Microarray gene expression data sets are jointly analyzed to increase statistical power. They could either be merged together or analyzed by meta-analysis. For a given ensemble of data sets, it cannot be foreseen which of these paradigms, merging or meta-analysis, works better. In this article, three joint analysis methods, Z-score normalization, ComBat and the inverse normal method (meta-analy...

Let K be a global field of char p and let Fq be the algebraic closure of Fp in K. For an elliptic curve E/K with non-constant j-invariant, the L-function L(T,E/K) is a polynomial in 1+T ·Z[T ]. For any N > 1 invertible in K and finite subgroup T ⊂ E(K) of order N , we compute the mod N reduction of L(T,E/K) and determine an upper-bound for the order of vanishing at 1/q, the so-called analytic r...