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  1. Book ; Online: Improving the Lower Bound for the Union-closed Sets Conjecture via Conditionally IID Coupling

    Liu, Jingbo

    2023  

    Abstract: Recently, Gilmer proved the first constant lower bound for the union-closed sets conjecture via an information-theoretic argument. The heart of the argument is an entropic inequality involving the OR function of two i.i.d.\ binary vectors, and the best ... ...

    Abstract Recently, Gilmer proved the first constant lower bound for the union-closed sets conjecture via an information-theoretic argument. The heart of the argument is an entropic inequality involving the OR function of two i.i.d.\ binary vectors, and the best constant obtainable through the i.i.d.\ coupling is $\frac{3-\sqrt{5}}{2}\approx0.38197$. Sawin demonstrated that the bound can be strictly improved by considering a convex combination of the i.i.d.\ coupling and the max-entropy coupling, and the best constant obtainable through this approach is around 0.38234, as evaluated by Yu and Cambie. In this work we show analytically that the bound can be further strictly improved by considering another class of coupling under which the two binary sequences are i.i.d.\ conditioned on an auxiliary random variable. We also provide a new class of bounds in terms of finite-dimensional optimization. For a basic instance from this class, analysis assisted with numerically solved 9-dimensional optimization suggests that the optimizer assumes a certain structure. Under numerically verified hypotheses, the lower bound for the union-closed sets conjecture can be improved to approximately 0.38271, a number that can be defined as the solution to an analytic equation.
    Keywords Computer Science - Information Theory ; Mathematics - Combinatorics
    Subject code 511
    Publishing date 2023-06-14
    Publishing country us
    Document type Book ; Online
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  2. Book ; Online: From Soft-Minoration to Information-Constrained Optimal Transport and Spiked Tensor Models

    Liu, Jingbo

    2023  

    Abstract: Let $P_Z$ be a given distribution on $\mathbb{R}^n$. For any $y\in\mathbb{R}^n$, we may interpret $\rho(y):=\ln\mathbb{E}[e^{\left ... }]$ as a soft-max of $\left ... $. We explore lower bounds on $\mathbb{E}[\rho(Y)]$ in terms of the minimum ...

    Abstract Let $P_Z$ be a given distribution on $\mathbb{R}^n$. For any $y\in\mathbb{R}^n$, we may interpret $\rho(y):=\ln\mathbb{E}[e^{\left<y,Z\right>}]$ as a soft-max of $\left<y,Z\right>$. We explore lower bounds on $\mathbb{E}[\rho(Y)]$ in terms of the minimum mutual information $I(Z,\bar{Z})$ over $P_{Z\bar{Z}}$ which is a coupling of $P_Z$ and itself such that $Z-\bar{Z}$ is bounded in a certain sense. This may be viewed as a soft version of Sudakov's minoration, which lower bounds the expected supremum of a stochastic process in terms of the packing number. Our method is based on convex geometry (thrifty approximation of convex bodies), and works for general non-Gaussian $Y$. When $Y$ is Gaussian and $\bar{Z}$ converges to $Z$, this recovers a recent inequality of Bai-Wu-Ozgur on information-constrained optimal transport, previously established using Gaussian-specific techniques. We also use soft-minoration to obtain asymptotically (in tensor order) tight bounds on the free energy in the Sherrington-Kirkpatrick model with spins uniformly distributed on a type class, implying asymptotically tight bounds for the type~II error exponent in spiked tensor detection.

    Comment: ISIT 2023
    Keywords Computer Science - Information Theory
    Subject code 519
    Publishing date 2023-05-14
    Publishing country us
    Document type Book ; Online
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  3. Book ; Online: An algorithm for $g$-invariant on unary Hermitian lattices over imaginary quadratic fields

    Liu, Jingbo

    2023  

    Abstract: Let $E=\mathbb{Q}\big(\sqrt{-d}\big)$ be an imaginary quadratic field for a square-free positive integer $d$, and let $\mathcal{O}$ be its ring of integers. For each positive integer $m$, let $I_m$ be the free Hermitian lattice over $\mathcal{O}$ with an ...

    Abstract Let $E=\mathbb{Q}\big(\sqrt{-d}\big)$ be an imaginary quadratic field for a square-free positive integer $d$, and let $\mathcal{O}$ be its ring of integers. For each positive integer $m$, let $I_m$ be the free Hermitian lattice over $\mathcal{O}$ with an orthonormal basis, let $\mathfrak{S}_d(1)$ be the set consisting of all positive definite integral unary Hermitian lattices over $\mathcal{O}$ that can be represented by some $I_m$, and let $g_d(1)$ be the least positive integer such that all Hermitian lattices in $\mathfrak{S}_d(1)$ can be uniformly represented by $I_{g_d(1)}$. The main results of this work provide an algorithm to calculate the explicit form of $\mathfrak{S}_d(1)$ and the exact value of $g_d(1)$ for every imaginary quadratic field $E$, which can be viewed as a natural extension of the Pythagoras number in the lattice setting.

    Comment: arXiv admin note: text overlap with arXiv:2111.10825
    Keywords Mathematics - Number Theory ; Computer Science - Data Structures and Algorithms ; Primary 11E39. Secondary 11Y16 ; 11Y40
    Subject code 512
    Publishing date 2023-09-27
    Publishing country us
    Document type Book ; Online
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  4. Book ; Online: Stability of the Gaussian Stationary Point in the Han-Kobayashi Region for Z-Interference Channels

    Liu, Jingbo

    2022  

    Abstract: The Gaussian stationary point in an inequality motivated by the Z-interference channel was recently conjectured by Costa, Nair, Ng, and Wang to be the global optimizer, which, if true, would imply the optimality of the Han-Kobayashi region for the ... ...

    Abstract The Gaussian stationary point in an inequality motivated by the Z-interference channel was recently conjectured by Costa, Nair, Ng, and Wang to be the global optimizer, which, if true, would imply the optimality of the Han-Kobayashi region for the Gaussian Z-interference channel. This conjecture was known to be true for some parameter regimes, but the validity for all parameters, although suggested by Gaussian tensorization, was previously open. In this paper we construct several counterexamples showing that this conjecture may fail in certain regimes: A simple construction without Hermite polynomial perturbation is proposed, where distributions far from Gaussian are analytically shown to be better than the Gaussian stationary point. As alternatives, we consider perturbation along geodesics under either the $L^2$ or Wasserstein-2 metric, showing that the Gaussian stationary point is unstable in a certain regime. Similarity to stability of the Levy-Cramer theorem is discussed. The stability phase transition point admits a simple characterization in terms of the maximum eigenvalue of the Gaussian maximizer. Similar to the Holley-Stroock principle, we can show that in the stable regime the Gaussian stationary point is optimal in a neighborhood under the $L^{\infty}$-norm with respect to the Gaussian measure. For protocols with constant power control, our counterexamples imply Gaussian suboptimality for the Han-Kobayashi region. Allowing variable power control, we show that the Gaussian optimizers for the Han-Kobayashi region always lie in the stable regime. We propose an amended conjecture, whose validity would imply Gaussian optimality of the Han-Kobayashi bound in a certain regime.
    Keywords Computer Science - Information Theory ; 94A05
    Subject code 519
    Publishing date 2022-08-31
    Publishing country us
    Document type Book ; Online
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  5. Book ; Online: A Few Interactions Improve Distributed Nonparametric Estimation, Optimally

    Liu, Jingbo

    2021  

    Abstract: Consider the problem of nonparametric estimation of an unknown $\beta$-H\"older smooth density $p_{XY}$ at a given point, where $X$ and $Y$ are both $d$ dimensional. An infinite sequence of i.i.d.\ samples $(X_i,Y_i)$ are generated according to this ... ...

    Abstract Consider the problem of nonparametric estimation of an unknown $\beta$-H\"older smooth density $p_{XY}$ at a given point, where $X$ and $Y$ are both $d$ dimensional. An infinite sequence of i.i.d.\ samples $(X_i,Y_i)$ are generated according to this distribution, and two terminals observe $(X_i)$ and $(Y_i)$, respectively. They are allowed to exchange $k$ bits either in oneway or interactively in order for Bob to estimate the unknown density. We show that the minimax mean square risk is order $\left(\frac{k}{\log k} \right)^{-\frac{2\beta}{d+2\beta}}$ for one-way protocols and $k^{-\frac{2\beta}{d+2\beta}}$ for interactive protocols. The logarithmic improvement is nonexistent in the parametric counterparts, and therefore can be regarded as a consequence of nonparametric nature of the problem. Moreover, a few rounds of interactions achieve the interactive minimax rate: the number of rounds can grow as slowly as the super-logarithm (i.e., inverse tetration) of $k$. The proof of the upper bound is based on a novel multi-round scheme for estimating the joint distribution of a pair of biased Bernoulli variables, and the lower bound is built on a sharp estimate of a symmetric strong data processing constant for biased Bernoulli variables.

    Comment: To appear on IEEE Trans. Inf. Theory
    Keywords Computer Science - Information Theory ; Mathematics - Statistics Theory
    Subject code 519
    Publishing date 2021-07-01
    Publishing country us
    Document type Book ; Online
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  6. Article: Incorporating MOOC and COVID-19-Related Scientific Papers into Veterinary Microbiology Teaching to Enhance Students' Learning Performance and Professional Recognition.

    Zhang, Hongna / Liu, Jingbo

    Journal of veterinary medical education

    2022  , Page(s) e20220036

    Abstract: The COVID-19 pandemic has exerted a huge adverse influence on global teaching activities and students' psychological status. Veterinary microbiology is mainly concerned with bacterial and viral diseases, including coronavirus diseases. An innovative ... ...

    Abstract The COVID-19 pandemic has exerted a huge adverse influence on global teaching activities and students' psychological status. Veterinary microbiology is mainly concerned with bacterial and viral diseases, including coronavirus diseases. An innovative online-to-offline teaching approach for this course was established to stimulate students' learning initiative and mitigate their anxiety about COVID-19. A well-established massive open online course (MOOC) was first adopted as preview material before class, followed by in-person teaching. Additionally, COVID-19-related scientific papers were also used as pre-class reading material in veterinary microbiology and were further explained in class. The effect of this innovative teaching mode was systematically evaluated by final examination scores and questionnaires. The average score (81.75) and excellence score rating (> 85 scores, 37.3%) resulting from this blended teaching mode were not statistically higher than those of the online-only (79.19,
    Language English
    Publishing date 2022-09-26
    Publishing country Canada
    Document type Journal Article
    ISSN 0748-321X
    ISSN 0748-321X
    DOI 10.3138/jvme-2022-0036
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  7. Article ; Online: The mechanism of nickel-induced autophagy and its role in nephrotoxicity.

    Yin, Heng / Wang, Chengbi / Guo, Hongrui / Li, Xiaocong / Liu, Jingbo

    Ecotoxicology and environmental safety

    2024  Volume 273, Page(s) 116150

    Abstract: Nickel (Ni), an environmental health hazard, is nephrotoxic to humans, but the exact mechanism is unknown. This study aims to identify whether nephrotoxicity is associated with autophagy. Here, nickel chloride ( ... ...

    Abstract Nickel (Ni), an environmental health hazard, is nephrotoxic to humans, but the exact mechanism is unknown. This study aims to identify whether nephrotoxicity is associated with autophagy. Here, nickel chloride (NiCl
    MeSH term(s) Humans ; Antioxidants/pharmacology ; Proto-Oncogene Proteins c-akt ; Nickel/toxicity ; AMP-Activated Protein Kinases/metabolism ; TOR Serine-Threonine Kinases/metabolism ; Apoptosis ; Autophagy
    Chemical Substances Antioxidants ; Proto-Oncogene Proteins c-akt (EC 2.7.11.1) ; Nickel (7OV03QG267) ; AMP-Activated Protein Kinases (EC 2.7.11.31) ; TOR Serine-Threonine Kinases (EC 2.7.11.1)
    Language English
    Publishing date 2024-03-01
    Publishing country Netherlands
    Document type Journal Article
    ZDB-ID 436536-7
    ISSN 1090-2414 ; 0147-6513
    ISSN (online) 1090-2414
    ISSN 0147-6513
    DOI 10.1016/j.ecoenv.2024.116150
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  8. Article ; Online: Nickel induces epithelial-mesenchymal transition in pulmonary fibrosis in mice via activation of the oxidative stress-mediated TGF-β1/Smad signaling pathway.

    Cao, Shanchuan / Yin, Heng / Li, Xinglai / Zeng, Xin / Liu, Jingbo

    Environmental toxicology

    2024  

    Abstract: Nickel (Ni) is recognized as a carcinogenic metal, and its widespread use has led to severe environmental and health problems. Although the lung is among the main organs affected by Ni, the precise mechanisms behind this effect remain poorly understood. ... ...

    Abstract Nickel (Ni) is recognized as a carcinogenic metal, and its widespread use has led to severe environmental and health problems. Although the lung is among the main organs affected by Ni, the precise mechanisms behind this effect remain poorly understood. This study aimed to elucidate the physiological mechanisms underlying Ni-induced pulmonary fibrosis (PF), using various techniques including histopathological detection, biochemical analysis, immunohistochemistry, western blotting, and quantitative real-time PCR. Mice were treated with nickel chloride (NiCl
    Language English
    Publishing date 2024-03-15
    Publishing country United States
    Document type Journal Article
    ZDB-ID 1463449-1
    ISSN 1522-7278 ; 1520-4081
    ISSN (online) 1522-7278
    ISSN 1520-4081
    DOI 10.1002/tox.24229
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  9. Article: Dietary Puerarin Supplementation Improves Immune Response and Antioxidant Capacity of Sows.

    Cao, Shanchuan / Li, Xinglai / Yin, Heng / Wang, Juan / Liu, Jingbo

    Antioxidants (Basel, Switzerland)

    2024  Volume 13, Issue 3

    Abstract: Puerarin is an isoflavone extracted ... ...

    Abstract Puerarin is an isoflavone extracted from
    Language English
    Publishing date 2024-02-27
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2704216-9
    ISSN 2076-3921
    ISSN 2076-3921
    DOI 10.3390/antiox13030290
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  10. Article ; Online: Corrigendum to "Potential antihypertensive mechanism of egg white-derived peptide QIGLF revealed by proteomic analysis" [Int. J. Biol. Macromol. Volume 218, 1 October 2022, pages 439-446].

    Zhou, Mingjie / Zhao, Wenzhu / Xue, Wenjun / Liu, Jingbo / Yu, Zhipeng

    International journal of biological macromolecules

    2024  Volume 265, Issue Pt 1, Page(s) 130925

    Language English
    Publishing date 2024-03-19
    Publishing country Netherlands
    Document type Published Erratum
    ZDB-ID 282732-3
    ISSN 1879-0003 ; 0141-8130
    ISSN (online) 1879-0003
    ISSN 0141-8130
    DOI 10.1016/j.ijbiomac.2024.130925
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