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  1. Buch ; 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.
    Schlagwörter Computer Science - Information Theory ; Mathematics - Combinatorics
    Thema/Rubrik (Code) 511
    Erscheinungsdatum 2023-06-14
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    Dokumenttyp Buch ; Online
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  2. Buch ; 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
    Schlagwörter Computer Science - Information Theory
    Thema/Rubrik (Code) 519
    Erscheinungsdatum 2023-05-14
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    Dokumenttyp Buch ; Online
    Datenquelle BASE - Bielefeld Academic Search Engine (Lebenswissenschaftliche Auswahl)

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  3. Buch ; 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
    Schlagwörter Mathematics - Number Theory ; Computer Science - Data Structures and Algorithms ; Primary 11E39. Secondary 11Y16 ; 11Y40
    Thema/Rubrik (Code) 512
    Erscheinungsdatum 2023-09-27
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  4. Buch ; 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.
    Schlagwörter Computer Science - Information Theory ; 94A05
    Thema/Rubrik (Code) 519
    Erscheinungsdatum 2022-08-31
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  5. Buch ; 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
    Schlagwörter Computer Science - Information Theory ; Mathematics - Statistics Theory
    Thema/Rubrik (Code) 519
    Erscheinungsdatum 2021-07-01
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    Dokumenttyp Buch ; Online
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  6. Buch ; Online: Minoration via Mixed Volumes and Cover's Problem for General Channels

    Liu, Jingbo

    2020  

    Abstract: We propose a method for establishing lower bounds on the supremum of processes in terms of packing numbers by means of mixed-volume inequalities (the Alexandrov-Fenchel inequality). A simple and general bound in terms of packing numbers under the convex ... ...

    Abstract We propose a method for establishing lower bounds on the supremum of processes in terms of packing numbers by means of mixed-volume inequalities (the Alexandrov-Fenchel inequality). A simple and general bound in terms of packing numbers under the convex distance is derived, from which some known bounds on the Gaussian processes and the Rademacher processes can be recovered when the convex set is taken to be the ball or the hypercube. However, the main thrust for our study of this approach is to handle non-i.i.d.\ (noncanonical) processes (correspondingly, the convex set is not a product set). As an application, we give a complete solution to an open problem of Thomas Cover in 1987 about the capacity of a relay channel in the general discrete memoryless setting.

    Comment: some minor typos corrected
    Schlagwörter Computer Science - Information Theory ; Mathematics - Probability ; Mathematics - Statistics Theory
    Erscheinungsdatum 2020-12-28
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  7. Artikel: 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  , Seite(n) 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,
    Sprache Englisch
    Erscheinungsdatum 2022-09-26
    Erscheinungsland Canada
    Dokumenttyp Journal Article
    ISSN 0748-321X
    ISSN 0748-321X
    DOI 10.3138/jvme-2022-0036
    Datenquelle MEDical Literature Analysis and Retrieval System OnLINE

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  8. Artikel ; 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  Band 273, Seite(n) 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-Begriff(e) Humans ; Antioxidants/pharmacology ; Proto-Oncogene Proteins c-akt ; Nickel/toxicity ; AMP-Activated Protein Kinases/metabolism ; TOR Serine-Threonine Kinases/metabolism ; Apoptosis ; Autophagy
    Chemische Substanzen 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)
    Sprache Englisch
    Erscheinungsdatum 2024-03-01
    Erscheinungsland Netherlands
    Dokumenttyp 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
    Datenquelle MEDical Literature Analysis and Retrieval System OnLINE

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  9. Artikel: 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  Band 13, Heft 3

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

    Abstract Puerarin is an isoflavone extracted from
    Sprache Englisch
    Erscheinungsdatum 2024-02-27
    Erscheinungsland Switzerland
    Dokumenttyp Journal Article
    ZDB-ID 2704216-9
    ISSN 2076-3921
    ISSN 2076-3921
    DOI 10.3390/antiox13030290
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  10. Artikel ; Online: Nickel induces mitochondrial damage in renal cells in vitro and in vivo through its effects on mitochondrial biogenesis, fusion, and fission.

    Yin, Heng / Li, Xinglai / Wang, Chengbi / Li, Xiaocong / Liu, Jingbo

    Chemico-biological interactions

    2024  Band 394, Seite(n) 110975

    Abstract: Nickel (Ni) and its compounds are common, widely distributed components of hazardous waste in the chemical industry. Excessive exposure to Ni can cause kidney damage in humans and animals. We investigated the impact of Ni on renal mitochondria using in ... ...

    Abstract Nickel (Ni) and its compounds are common, widely distributed components of hazardous waste in the chemical industry. Excessive exposure to Ni can cause kidney damage in humans and animals. We investigated the impact of Ni on renal mitochondria using in vivo and in vitro models of Ni nephrotoxicity, and explored the Ni nephrotoxic mechanism. We showed that nickel chloride (NiCl
    Mesh-Begriff(e) Nickel/toxicity ; Animals ; Mitochondria/drug effects ; Mitochondria/metabolism ; Mitochondrial Dynamics/drug effects ; Mice ; Kidney/drug effects ; Kidney/metabolism ; Kidney/pathology ; Reactive Oxygen Species/metabolism ; Membrane Potential, Mitochondrial/drug effects ; Organelle Biogenesis ; Male ; Mitochondrial Proteins/metabolism ; Mitochondrial Proteins/genetics ; Peroxisome Proliferator-Activated Receptor Gamma Coactivator 1-alpha/metabolism ; Peroxisome Proliferator-Activated Receptor Gamma Coactivator 1-alpha/genetics ; Mice, Inbred C57BL ; Transcription Factors/metabolism ; Transcription Factors/genetics ; Cell Line
    Chemische Substanzen Nickel (7OV03QG267) ; Reactive Oxygen Species ; Mitochondrial Proteins ; nickel chloride (696BNE976J) ; Peroxisome Proliferator-Activated Receptor Gamma Coactivator 1-alpha ; Transcription Factors ; Ppargc1a protein, mouse
    Sprache Englisch
    Erscheinungsdatum 2024-03-27
    Erscheinungsland Ireland
    Dokumenttyp Journal Article
    ZDB-ID 218799-1
    ISSN 1872-7786 ; 0009-2797
    ISSN (online) 1872-7786
    ISSN 0009-2797
    DOI 10.1016/j.cbi.2024.110975
    Datenquelle MEDical Literature Analysis and Retrieval System OnLINE

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