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Temporal nutrition analysis associates dietary regularity and quality with gut microbiome diversity: insights from the Food & You digital cohort. [PDF]
Nat CommunSingh R +6 more
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Compositionality and systematicity emerge from iterated learning in deep linear networks. [PDF]
Proc Natl Acad Sci U S AJarvis D, Klein R, Rosman B, Saxe AM.
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Estimation of the Modulus of Hölder Metric Regularity
Functional Analysis and Its Applications, 2022Исследуется модуль метрической регулярности по Гeльдеру. Вводятся понятия обобщенного множества Кларка порядка $p$ и обобщенной производной по графику, с помощью которых оценивается модуль метрической регулярности по Гeльдеру. В качестве следствия основного результата получена верхняя оценка этого модуля верхним пределом внутренней нормы обратного ...
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Tikhonov regularization of metrically regular inclusions
Positivity, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gaydu, Michaël, Geoffroy, Michel H.
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Metrically Regular Square of Metrically Regular Bigraphs
1992Summary: The paper deals with the spectra of powers of metrically regular graphs. A necessary condition for \(G\) to have the square \(G^ 2\) metrically regular is found and the problem of the construction such graphs \(G\) is solved for metrically regular bipartite graphs with 4 and 5 distinct eigenvalues (these eigenvalues can have various ...
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Metrically Regular Differential Generalized Equations
SIAM Journal on Control and Optimization, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Radek Cibulka +3 more
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Regular Quotients of Metric Spaces
Canadian Mathematical Bulletin, 1975In this note we consider the class of topological spaces whose every Hausdorff quotient is regular (or equivalently, normal). Sufficient conditions in order that a space belongs to this class have appeared in papers by Morita [3], and more recently by MacDonald and Willard [2]. In both cases, the authors impose conditions implying paracompactness.
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On Perturbation Stability of Metric Regularity
Set-Valued Analysis, 2001Let \(F: X\to Y\), where \(X\) is a complete metric space and \(Y\) is a Banach space, be a closed set-valued map and let \(V(x):= \{y\in Y\mid d(y,F(x))\leq R\}\), where \(R\in[0,\infty)\), for \(x\in X\) (i.e. \(F\subset V\)). Suppose that \(F\) covers on \(V\) with constant not smaller than \(a> 0\), i.e., for any \(t> 0\) and \(x\in X\), \(V(x)\cap
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On theN *-metric completion of regular rings
Archiv der Mathematik, 1986In this paper we prove that if R is a regular \(N^*\)-torsion free ring and S is its \(N^*\)-completion, then S is unit-regular, \(K_ 0\)(S) is unperforated and even archimedean and there is an affine homeomorphism between P(R) and P(S). We apply this result in order to prove that if R satisfies central separability then S can be seen as the ring of ...
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