Graphlet and Orbit Computation on Heterogeneous Graphs

Many applications, ranging from natural to social sciences, rely on graphlet analysis for the intuitive and meaningful characterization of networks employing micro-level structures as building blocks. However, it has not been thoroughly explored in heterogeneous graphs, which comprise various types of nodes and edges. Finding graphlets and orbits for heterogeneous graphs is difficult because of the heterogeneity and abundance of semantic information. We consider heterogeneous graphs, which can be treated as colored graphs. By applying the canonical label technique, we determine the graph isomorphism problem with multiple states on nodes and edges. With minimal parameters, we build all non-isomorphic graphs and associated orbits. We provide a Python package that can be used to generate orbits for colored directed graphs and determine the frequency of orbit occurrence. Finally, we provide four examples to illustrate the use of the Python package.Comment: 13 pages, 7 figure

Hybrid High-order Functional Connectivity Networks Using Resting-state Functional MRI for Mild Cognitive Impairment Diagnosis

Conventional functional connectivity (FC), referred to as low-order FC, estimates temporal correlation of the resting-state functional magnetic resonance imaging (rs-fMRI) time series between any pair of brain regions, simply ignoring the potentially high-level relationship among these brain regions. A high-order FC based on "correlation's correlation" has emerged as a new approach for abnormality detection of brain disease. However, separate construction of the low- and high-order FC networks overlooks information exchange between the two FC levels. Such a higher-level relationship could be more important for brain diseases study. In this paper, we propose a novel framework, namely "hybrid high-order FC networks" by exploiting the higher-level dynamic interaction among brain regions for early mild cognitive impairment (eMCI) diagnosis. For each sliding window-based rs-fMRI sub-series, we construct a whole-brain associated high-order network, by estimating the correlations between the topographical information of the high-order FC sub-network from one brain region and that of the low-order FC sub-network from another brain region. With multi-kernel learning, complementary features from multiple time-varying FC networks constructed at different levels are fused for eMCI classification. Compared with other state-of-the-art methods, the proposed framework achieves superior diagnosis accuracy, and hence could be promising for understanding pathological changes of brain connectome

Metastatic Gallbladder Cancer Presenting as a Gingival Tumor and Deep Neck Infection

Gallbladder cancer has an extremely poor prognosis because it is often diagnosed at an advanced stage. We describe a 63-year-old woman who was treated 4 years previously for gallbladder cancer, with laparoscopic cholecystectomy and secondary hepatectomy after presenting with acute cholecystitis and gallbladder rupture. At her second presentation, she had a left lower gingival tumor and deep neck infection. Incision and drainage and tumor biopsies were performed, and pathology at both sites revealed adenocarcinoma. Positron emission tomography revealed other tumors in the left breast and left lower lung field, which were both proven to be adenocarcinoma by biopsy. The patient's presentation with a metastatic oral tumor was rare. Although the incidence is very low, physicians should consider the possibility of metastatic cancer in a patient with a history of cancer, who presents with new oral tumor or deep neck infection

CoxPhLb: An R Package for Analyzing Length Biased Data under Cox Model

Data subject to length-biased sampling are frequently encountered in various applications including prevalent cohort studies and are considered as a special case of left-truncated data under the stationarity assumption. Many semiparametric regression methods have been proposed for lengthbiased data to model the association between covariates and the survival outcome of interest. In this paper, we present a brief review of the statistical methodologies established for the analysis of length-biased data under the Cox model, which is the most commonly adopted semiparametric model, and introduce an R package CoxPhLb that implements these methods. Specifically, the package includes features such as fitting the Cox model to explore covariate effects on survival times and checking the proportional hazards model assumptions and the stationarity assumption. We illustrate usage of the package with a simulated data example and a real dataset, the Channing House data, which are publicly available

Derived pp-adic heights and the leading coefficient of the Bertolini--Darmon--Prasanna pp-adic LL-function

Let $E/\mathbf{Q}$ be an elliptic curve and let $p$ be an odd prime of good reduction for $E$. Let $K$ be an imaginary quadratic field satisfying the classical Heegner hypothesis and in which $p$ splits. In a previous work, Agboola--Castella formulated an analogue of the Birch--Swinnerton-Dyer conjecture for the $p$-adic $L$-function $L_{\mathfrak{p}}^{\rm BDP}$ of Bertolini--Darmon--Prasanna attached to $E/K$, assuming the prime $p$ to be ordinary for $E$. The goal of this paper is two-fold: (1) We formulate a $p$-adic BSD conjecture for $L_{\mathfrak{p}}^{\rm BDP}$ for all odd primes $p$ of good reduction. (2) For an algebraic analogue $F_{\overline{\mathfrak{p}}}^{\rm BDP}$ of $L_{\mathfrak{p}}^{\rm BDP}$, we show that the ``leading coefficient'' part of our conjecture holds, and that the ``order of vanishing'' part follows from the expected ``maximal non-degeneracy'' of an anticyclotomic $p$-adic height. In particular, when the Iwasawa--Greenberg Main Conjecture $(F_{\overline{\mathfrak{p}}}^{\rm BDP})=(L_{\mathfrak{p}}^{\rm BDP})$ is known, our results determine the leading coefficient of $L_{\mathfrak{p}}^{\rm BDP}$ at $T=0$ up to a $p$-adic unit. Moreover, by adapting the approach of Burungale--Castella--Kim in the $p$-ordinary case, we prove the main conjecture for supersingular primes $p$ under mild hypotheses.Comment: 34 page

The Nematic Energy Scale and the Missing Electron Pocket in FeSe

Superconductivity emerges in proximity to a nematic phase in most iron-based superconductors. It is therefore important to understand the impact of nematicity on the electronic structure. Orbital assignment and tracking across the nematic phase transition prove to be challenging due to the multiband nature of iron-based superconductors and twinning effects. Here, we report a detailed study of the electronic structure of fully detwinned FeSe across the nematic phase transition using angle-resolved photoemission spectroscopy. We clearly observe a nematicity-driven band reconstruction involving dxz, dyz, and dxy orbitals. The nematic energy scale between dxz and dyz bands reaches a maximum of 50 meV at the Brillouin zone corner. We are also able to track the dxz electron pocket across the nematic transition and explain its absence in the nematic state. Our comprehensive data of the electronic structure provide an accurate basis for theoretical models of the superconducting pairing in FeSe