Learning Discriminative Bayesian Networks from High-dimensional Continuous Neuroimaging Data

Due to its causal semantics, Bayesian networks (BN) have been widely employed to discover the underlying data relationship in exploratory studies, such as brain research. Despite its success in modeling the probability distribution of variables, BN is naturally a generative model, which is not necessarily discriminative. This may cause the ignorance of subtle but critical network changes that are of investigation values across populations. In this paper, we propose to improve the discriminative power of BN models for continuous variables from two different perspectives. This brings two general discriminative learning frameworks for Gaussian Bayesian networks (GBN). In the first framework, we employ Fisher kernel to bridge the generative models of GBN and the discriminative classifiers of SVMs, and convert the GBN parameter learning to Fisher kernel learning via minimizing a generalization error bound of SVMs. In the second framework, we employ the max-margin criterion and build it directly upon GBN models to explicitly optimize the classification performance of the GBNs. The advantages and disadvantages of the two frameworks are discussed and experimentally compared. Both of them demonstrate strong power in learning discriminative parameters of GBNs for neuroimaging based brain network analysis, as well as maintaining reasonable representation capacity. The contributions of this paper also include a new Directed Acyclic Graph (DAG) constraint with theoretical guarantee to ensure the graph validity of GBN.Comment: 16 pages and 5 figures for the article (excluding appendix

On minor-closed classes of matroids with exponential growth rate

Let \cM be a minor-closed class of matroids that does not contain arbitrarily long lines. The growth rate function, h:\bN\rightarrow \bN of \cM is given by h(n) = \max(|M|\, : \, M\in \cM, simple, rank-$n$). The Growth Rate Theorem shows that there is an integer $c$ such that either: $h(n)\le c\, n$, or ${n+1 \choose 2} \le h(n)\le c\, n^2$, or there is a prime-power $q$ such that $\frac{q^n-1}{q-1} \le h(n) \le c\, q^n$; this separates classes into those of linear density, quadratic density, and base-$q$ exponential density. For classes of base-$q$ exponential density that contain no $(q^2+1)$-point line, we prove that $h(n) =\frac{q^n-1}{q-1}$ for all sufficiently large $n$. We also prove that, for classes of base-$q$ exponential density that contain no $(q^2+q+1)$-point line, there exists k\in\bN such that $h(n) = \frac{q^{n+k}-1}{q-1} - q\frac{q^{2k}-1}{q^2-1}$ for all sufficiently large $n$

A Multi-Epoch Study of the Radio Continuum Emission of Orion Source I: Constraints on the Disk Evolution of a Massive YSO and the Dynamical History of Orion BN/KL

We present new 7mm continuum observations of Orion BN/KL with the VLA. We resolve the emission from the protostar radio Source I and BN at several epochs. Source I is highly elongated NW-SE, and remarkably stable in flux density, position angle, and overall morphology over nearly a decade. This favors the extended emission component arising from an ionized disk rather than a jet. We have measured the proper motions of Source I and BN for the first time at 43 GHz. We confirm that both sources are moving at high speed (12 and 26 km/s, respectively) approximately in opposite directions, as previously inferred from measurements at lower frequencies. We discuss dynamical scenarios that can explain the large motions of both BN and Source I and the presence of disks around both. Our new measurements support the hypothesis that a close (~50 AU) dynamical interaction occurred around 500 years ago between Source I and BN as proposed by Gomez et al. From the dynamics of encounter we argue that Source I today is likely to be a binary with a total mass on the order of 20 Msun, and that it probably existed as a softer binary before the close encounter. This enables preservation of the original accretion disk, though truncated to its present radius of ~50 AU. N-body numerical simulations show that the dynamical interaction between a binary of 20 Msun total mass (I) and a single star of 10 Msun mass (BN) may lead to the ejection of both and binary hardening. The gravitational energy released in the process would be large enough to power the wide-angle flow traced by H2 and CO emission in the BN/KL nebula. Assuming the proposed dynamical history is correct, the smaller mass for Source I recently estimated from SiO maser dynamics (>7 Msun) by Matthews et al., suggests that non-gravitational forces (e.g. magnetic) must play an important role in the circumstellar gas dynamics.Comment: 17 pages, 7 figures, 4 tables, accepted by Ap

Computing Optical Properties of Ultra-thin Crystals

An overview is given of recent advances in experimental and theoretical understanding of optical properties of ultra-thin crystal structures (graphene, phosphorene, silicene, MoS2, MoSe2 , WS2 , WSe2 , h-AlN, h-BN, fluorographene, graphane). Ultra-thin crystals are atomically-thick layered crystals that have unique properties which differ from their 3D counterpart. Because of the difficulties in the synthesis of few-atom-thick crystal structures, which are thought to be the main building blocks of future nanotechnology, reliable theoretical predictions of their electronic, vibrational and optical properties are of great importance. Recent studies revealed the reliable predictive power of existing theoretical approaches based on density functional theory (DFT)

Liu Bie Ju Centre for Mathematical Sciences Linear Difference Equations with Transition Points

Two linearly independent asymptotic solutions are constructed for the second-order linear difference equation yn+1(x) − (Anx + Bn)yn(x)+yn−1(x) =0, where An and Bn have power series expansions of the form α