Fair lending needs explainable models for responsible recommendation

The financial services industry has unique explainability and fairness challenges arising from compliance and ethical considerations in credit decisioning. These challenges complicate the use of model machine learning and artificial intelligence methods in business decision processes.Comment: 4 pages, position paper accepted for FATREC 2018 conference at ACM RecSy

Constructing Financial Sentimental Factors in Chinese Market Using Natural Language Processing

In this paper, we design an integrated algorithm to evaluate the sentiment of Chinese market. Firstly, with the help of the web browser automation, we crawl a lot of news and comments from several influential financial websites automatically. Secondly, we use techniques of Natural Language Processing(NLP) under Chinese context, including tokenization, Word2vec word embedding and semantic database WordNet, to compute Senti-scores of these news and comments, and then construct the sentimental factor. Here, we build a finance-specific sentimental lexicon so that the sentimental factor can reflect the sentiment of financial market but not the general sentiments as happiness, sadness, etc. Thirdly, we also implement an adjustment of the standard sentimental factor. Our experimental performance shows that there is a significant correlation between our standard sentimental factor and the Chinese market, and the adjusted factor is even more informative, having a stronger correlation with the Chinese market. Therefore, our sentimental factors can be important references when making investment decisions. Especially during the Chinese market crash in 2015, the Pearson correlation coefficient of adjusted sentimental factor with SSE is 0.5844, which suggests that our model can provide a solid guidance, especially in the special period when the market is influenced greatly by public sentiment

Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain

Inverse imaging problems are inherently under-determined, and hence it is important to employ appropriate image priors for regularization. One recent popular prior---the graph Laplacian regularizer---assumes that the target pixel patch is smooth with respect to an appropriately chosen graph. However, the mechanisms and implications of imposing the graph Laplacian regularizer on the original inverse problem are not well understood. To address this problem, in this paper we interpret neighborhood graphs of pixel patches as discrete counterparts of Riemannian manifolds and perform analysis in the continuous domain, providing insights into several fundamental aspects of graph Laplacian regularization for image denoising. Specifically, we first show the convergence of the graph Laplacian regularizer to a continuous-domain functional, integrating a norm measured in a locally adaptive metric space. Focusing on image denoising, we derive an optimal metric space assuming non-local self-similarity of pixel patches, leading to an optimal graph Laplacian regularizer for denoising in the discrete domain. We then interpret graph Laplacian regularization as an anisotropic diffusion scheme to explain its behavior during iterations, e.g., its tendency to promote piecewise smooth signals under certain settings. To verify our analysis, an iterative image denoising algorithm is developed. Experimental results show that our algorithm performs competitively with state-of-the-art denoising methods such as BM3D for natural images, and outperforms them significantly for piecewise smooth images.Comment: More discussions and results are provide

Numerical Evidence of Small Coherent Subsystems at Low Temperatures in Light Harvesting Complex II

The extent of exciton coherence in protein-pigment complexes has significant implications for the initial light harvesting step in photosynthetic organisms. In this work we model the main antenna protein of photosystem II, namely light harvesting complex II (LHC-II), with a single-exciton Hamiltonian with sites coupled via dipole-dipole interaction, with linear coupling to a dissipative phonon bath. With appropriate parameters, Monte Carlo path integral (MCPI) results of the exciton coherence length from 1 K to 500 K show that at thermodynamic equilibrium, an exciton in LHC-II is localized mostly on 2 single chlorophyll pigment sites, with persistent short-range coherence over the A2-B2 pair, A3-B3 pair and B1-B5-B6 triplet. Quasi-adiabatic path integral (QUAPI) calculations of the subsystems mentioned above show a smooth, incoherent relaxation towards thermodynamic equilibrium. The results obtained imply that with the exception of small coherent subsystems at cryogenic temperatures, excitons in LHC-II are more localized than in the analogous light harvesting complex II (LH-II) of the purple bacterium Rs. molischianum, which may be expected from the lower symmetry of the former.Comment: 28 pages, 5 figures, summary of JC's BSc thesi

Regionally proximal relation and null systems

In this paper, it is shown that if a dynamical system is null and distal, then it is equicontinuous. It turns out that a null system with closed proximal relation is mean equicontinuous. As a direct application, it follows that a null dynamical system with dense minimal points is also mean equicontinuous. Meanwhile, a distal system with trivial $\text{Ind}_{fip}$-pairs, and a non-trivial regionally proximal relation of order $\infty$ is constructed.Comment: arXiv admin note: text overlap with arXiv:1312.7663 by other author

Size-extensive polarizabilities with intermolecular charge transfer in a fluctuating-charge model

Fluctuating-charge models have been used to model polarization effects in molecular mechanics methods. However, they overestimate polarizabilities in large systems. Previous attempts to remedy this have been at the expense of forbidding intermolecular charge-transfer. Here, we investigate this lack of size-extensivity and show that the neglect of terms arising from charge conservation is partly responsible; these terms are also vital for maintaining the correct translational symmetries of the dipole moment and polarizability that classical electrostatic theory requires. Also, QTPIE demonstrates linear-scaling polarizabilities when coupling the external electric field in a manner that treats its potential as a perturbation of the atomic electronegativities. Thus for the first time, we have a fluctuating-charge model that predicts size-extensive dipole polarizabilities, yet allows intermolecular charge-transfer.Comment: 16 pages, 4 figure

A unified theoretical framework for fluctuating-charge models in atom-space and in bond-space

Our previously introduced QTPIE (charge transfer with polarization current equilibration) model (J. Chen and T. J. Martinez, Chem. Phys. Lett. 438, 315 (2007)) is a fluctuating-charge model with correct asymptotic behavior. Unlike most other fluctuating-charge models, QTPIE is formulated in terms of charge-transfer variables and pairwise electronegativities, not atomic charge variables and electronegativities. The pairwise character of the electronegativities in QTPIE avoids spurious charge transfer when bonds are broken. However, the increased number of variables leads to considerable computational expense and a rank-deficient set of working equations, which is numerically inconvenient. Here, we show that QTPIE can be exactly reformulated in terms of atomic charge variables, leading to a considerable reduction in computational complexity. The transformation between atomic and bond variables is generally applicable to arbitrary fluctuating charge models, and uncovers an underlying topological framework that can be used to understand the relation between fluctuating-charge models and the classical theory of electrical circuits.Comment: 36 pages, 7 figures; submitted to J. Chem. Phy

Hopf algebras arising from dg manifolds

Let $(\mathcal{M}, Q)$ be a dg manifold. The space of vector fields with shifted degrees $(\mathcal{X}(\mathcal{M})[-1], L_Q)$ is a Lie algebra object in the homology category $\mathrm{H}((C^{\infty}_{\mathcal{M}},Q)\mathrm{-}\mathbf{mod})$ of dg modules over $(\mathcal{M},Q)$, the Atiyah class $\alpha_{\mathcal{M}}$ being its Lie bracket. The triple $(\mathcal{X}(\mathcal{M})[-1], L_Q; \alpha_{\mathcal{M}})$ is also a Lie algebra object in the Gabriel-Zisman homotopy category $\Pi((C^{\infty}_{\mathcal{M}},Q)\mathrm{-}\mathbf{mod})$. In this paper, we describe the universal enveloping algebra of $(\mathcal{X}(\mathcal{M})[-1], L_Q; \alpha_{\mathcal{M}})$ and prove that it is a Hopf algebra object in $\Pi((C^{\infty}_{\mathcal{M}},Q)\mathrm{-}\mathbf{mod})$. As an application, we study Fedosov dg Lie algebroids and recover a result of Sti\'enon, Xu, and the second author on the Hopf algebra arising from a Lie pair.Comment: 37 pages, revised according to referees' comment

Multiparameter estimation via an ensemble of spinor atoms

Multiparameter estimation, which aims to simultaneously determine multiple parameters in the same measurement procedure, attracts extensive interests in measurement science and technologies. Here, we propose a multimode many-body quantum interferometry for simultaneously estimating linear and quadratic Zeeman coefficients via an ensemble of spinor atoms. Different from the scheme with individual atoms, by using an $N$-atom multimode GHZ state, the measurement precisions of the two parameters can simultaneously attain the Heisenberg limit, and they respectively depend on the hyperfine spin number $F$ in the form of $\Delta p \propto 1/(FN)$ and $\Delta q \propto 1/(F^2N)$. Moreover, the simultaneous estimation can provide better precision than the individual estimation. Further, by taking a three-mode interferometry with Bose condensed spin-1 atoms for an example, we show how to perform the simultaneous estimation of $p$ and $q$. Our scheme provides a novel paradigm for implementing multiparameter estimation with multimode quantum correlated states.Comment: 11 pages, 10 figure

Direct computation of stresses in linear elasticity

We present a new finite element method based on the formulation introduced by Philippe G.~Ciarlet and Patrick Ciarlet, Jr. in [{\em Math. Models Methods Appl. Sci., 15 (2005), pp. 259--571}], which approximates strain tensor directly. We also show the convergence rate of strain tensor is optimal. This work is a non-trivial generalization of its two dimensional analogue in [{\em Math. Models Methods Appl. Sci., 19 (2009), pp. 1043--1064}