A Study on Agreement in PICO Span Annotations

In evidence-based medicine, relevance of medical literature is determined by predefined relevance conditions. The conditions are defined based on PICO elements, namely, Patient, Intervention, Comparator, and Outcome. Hence, PICO annotations in medical literature are essential for automatic relevant document filtering. However, defining boundaries of text spans for PICO elements is not straightforward. In this paper, we study the agreement of PICO annotations made by multiple human annotators, including both experts and non-experts. Agreements are estimated by a standard span agreement (i.e., matching both labels and boundaries of text spans), and two types of relaxed span agreement (i.e., matching labels without guaranteeing matching boundaries of spans). Based on the analysis, we report two observations: (i) Boundaries of PICO span annotations by individual human annotators are very diverse. (ii) Despite the disagreement in span boundaries, general areas of the span annotations are broadly agreed by annotators. Our results suggest that applying a standard agreement alone may undermine the agreement of PICO spans, and adopting both a standard and a relaxed agreements is more suitable for PICO span evaluation.Comment: Accepted in SIGIR 2019 (Short paper

Constructing Linear-Sized Spectral Sparsification in Almost-Linear Time

We present the first almost-linear time algorithm for constructing linear-sized spectral sparsification for graphs. This improves all previous constructions of linear-sized spectral sparsification, which requires $\Omega(n^2)$ time. A key ingredient in our algorithm is a novel combination of two techniques used in literature for constructing spectral sparsification: Random sampling by effective resistance, and adaptive constructions based on barrier functions.Comment: 22 pages. A preliminary version of this paper is to appear in proceedings of the 56th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2015

Dynamics of continued fractions and distribution of modular symbols

We formulate a thermodynamical approach to the study of distribution of modular symbols, motivated by the work of Baladi-Vall\'ee. We introduce the modular partitions of continued fractions and observe that the statistics for modular symbols follow from the behavior of modular partitions. We prove the limit Gaussian distribution and residual equidistribution for modular partitions as a vector-valued random variable on the set of rationals whose denominators are up to a fixed positive integer by studying the spectral properties of transfer operator associated to the underlying dynamics. The approach leads to a few applications. We show an average version of conjectures of Mazur-Rubin on statistics for the period integrals of an elliptic newform. We further observe that the equidistribution of mod $p$ values of modular symbols leads to mod $p$ non-vanishing results for special modular $L$-values twisted by a Dirichlet character.Comment: 42 page

An SDP-Based Algorithm for Linear-Sized Spectral Sparsification

For any undirected and weighted graph $G=(V,E,w)$ with $n$ vertices and $m$ edges, we call a sparse subgraph $H$ of $G$, with proper reweighting of the edges, a $(1+\varepsilon)$-spectral sparsifier if $$(1-\varepsilon)x^{\intercal}L_Gx\leq x^{\intercal} L_{H} x\leq (1+\varepsilon) x^{\intercal} L_Gx$$ holds for any $x\in\mathbb{R}^n$, where $L_G$ and $L_{H}$ are the respective Laplacian matrices of $G$ and $H$. Noticing that $\Omega(m)$ time is needed for any algorithm to construct a spectral sparsifier and a spectral sparsifier of $G$ requires $\Omega(n)$ edges, a natural question is to investigate, for any constant $\varepsilon$, if a $(1+\varepsilon)$-spectral sparsifier of $G$ with $O(n)$ edges can be constructed in $\tilde{O}(m)$ time, where the $\tilde{O}$ notation suppresses polylogarithmic factors. All previous constructions on spectral sparsification require either super-linear number of edges or $m^{1+\Omega(1)}$ time. In this work we answer this question affirmatively by presenting an algorithm that, for any undirected graph $G$ and $\varepsilon>0$, outputs a $(1+\varepsilon)$-spectral sparsifier of $G$ with $O(n/\varepsilon^2)$ edges in $\tilde{O}(m/\varepsilon^{O(1)})$ time. Our algorithm is based on three novel techniques: (1) a new potential function which is much easier to compute yet has similar guarantees as the potential functions used in previous references; (2) an efficient reduction from a two-sided spectral sparsifier to a one-sided spectral sparsifier; (3) constructing a one-sided spectral sparsifier by a semi-definite program.Comment: To appear at STOC'1

Cold ions of ionospheric origin observed at the dayside magnetopause and their effects on magnetic reconnection

Thesis (Ph.D.) University of Alaska Fairbanks, 2015Magnetic reconnection at the dayside magnetopause is one of the most important mechanisms that efficiently transfers solar wind particles, momentum, and energy into the magnetosphere. Magnetic reconnection at the magnetopause is usually asymmetric since the plasma and magnetic field properties are quite different in the magnetosphere and the magnetosheath. Cold dense plasma, originating either directly from the ionosphere or from the plasmasphere, has often been observed at the adjacent magnetopause. These cold plasmas may affect reconnection since they modify the plasma properties on the magnetospheric side significantly. This dissertation presents case and statistical studies of the characteristics of the cold ions observed at the dayside magnetopause by using Cluster spacecraft datasets. The plasmaspheric plumes have been distinguished from the ionospheric outows using ion pitch angle distributions. The ionospheric outows feature unidirectional or bidirectional field-aligned pitch angle distributions, whereas the plasmaspheric plumes are characterized by 90° pitch angle distributions. The occurrence rates of the plasmaspheric plumes and ionospheric outows and their dependence on the solar wind/Interplanetary Magnetic Field (IMF) conditions have been investigated. It is found that the occurrence rate of plasmaspheric plume or ionospheric plasma strongly depends on the solar wind/IMF conditions. In particular, plasmaspheric plumes tend to occur during southward IMF while ionospheric outows tends to occur during northward IMF. The occurrence rate of the plasmaspheric plumes is significantly higher on the duskside than that on the dawnside, indicating that the plasmaspheric plumes may lead to a dawn-dusk asymmetry of dayside reconnection. Furthermore, this dissertation investigates the behavior of the cold dense plasma of ionospheric origin during magnetic reconnection at the dayside magnetopause. The motion of cold plasmaspheric ions entering the reconnection region differs from that of warmer magnetosheath and magnetospheric ions. In contrast to the warmer ions, which are probably accelerated by reconnection near the subsolar magnetopause, the colder ions are simply entrained by E x B drift at high latitudes on the recently reconnected magnetic field lines. This indicates that plasmaspheric ions can sometimes play a very limited role in magnetic reconnection process. Finally, this dissertation examines a controlling factor that leads to the asymmetric reconnection geometry at the magnetopause. It is demonstrated that the separatrix and ow boundary angles are greater on the magnetosheath side than on the magnetospheric side of the magnetopause, probably due to the stronger density asymmetry rather than magnetic field asymmetry at this boundary