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Adaptive Optical Scanning Holography (AOSH) represents a powerful technique that employs an adaptive approach to selectively omit certain lines within holograms, guided by the utilization of Normalized-Mean-Error (NME) as a predictive measure. This approach effectively diminishes scanning time and conserves the storage space required for data preservation. However, there exists alternative methods superior to NME in terms of evaluating the model's efficacy. This paper introduces two novel methods, namely Normalized-Root-Mean-Square-Error (NRMSE) and Normalized-Mean-Square-Error (NMSE), into the AOSH system, leading to the development of NRMSE-AOSH and NMSE-AOSH. These new systems aim to further minimize duration of holographic recording. Through a comparative analysis of hologram lines between the two newly proposed AOSH systems and the original AOSH, we demonstrate that both NRMSE-AOSH and NMSE-AOSH effectively reduce the number of hologram lines while maintaining the hologram's informational content. Among the three methods, our two new methods exhibit better performance compared with the original method. [ABSTRACT FROM AUTHOR]

Let R be an excellent Noetherian ring of prime characteristic. Consider an arbitrary nested pair of ideals (or more generally, a nested pair of submodules of a fixed finite module). We do not assume that their quotient has finite length. In this paper, we develop various sufficient numerical criteria for when the tight closures of these ideals (or submodules) match. For some of the criteria we only prove sufficiency, while some are shown to be equivalent to the tight closures matching. We compare the various numerical measures (in some cases demonstrating that the different measures give truly different numerical results) and explore special cases where equivalence with matching tight closure can be shown. All of our measures derive ultimately from Hilbert-Kunz multiplicity. [ABSTRACT FROM AUTHOR]

Let R be a commutative Noetherian ring. We give criteria for flatness of R-modules in terms of associated primes and torsion-freeness of certain tensor products. This allows us to develop a criterion for regularity if R has characteristic p, or more generally if it has a locally contracting endomorphism. Dualizing, we give criteria for injectivity of R-modules in terms of coassociated primes and (h-)divisibility of certain Hom-modules. Along the way, we develop tools to achieve such a dual result. These include a careful analysis of the notions of divisibility and h-divisibility (including a localization result), a theorem on coassociated primes across a Hom-module base change, and a local criterion for injectivity. [ABSTRACT FROM AUTHOR]

It is proved that when R is a local ring of positive characteristic, $${\phi\colon R{\to} R}$$ is its Frobenius endomorphism, and some non-zero finite R-module has finite flat dimension or finite injective dimension for the R-module structure induced through $${\phi}$$ , then R is regular. This broad generalization of Kunz's characterization of regularity in positive characteristic is deduced from a theorem concerning a local ring R with residue field of k of arbitrary characteristic: If $${\phi}$$ is a contracting endomorphism of R, then the Betti numbers and the Bass numbers over $${\phi}$$ of any non-zero finitely generated R-module grow at the same rate, on an exponential scale, as the Betti numbers of k over R. [ABSTRACT FROM AUTHOR]

Doxorubicin (DOX) is a widely used anti-tumor agent. The clinical application of the medication is limited by its side effect which can elicit myocardial apoptosis and cardiac dysfunction. However, the underlying mechanism by which DOX causes cardiomyocyte apoptosis is not clear. The aim of present study is to investigate the role of high-mobility group box 1 (HMGB1) in DOX-induced myocardial injury, and signal pathway involved in regulation of HMGB1 expression in cardiomyocytes with DOX. We found treatment of isolated cardiomyocytes and naive mice with the DOX resulted in an increased HMGB1 expression which was associated with increased myocardial cell apoptosis. Pharmacological (A-box) or genetic blockade (TLR4 deficiency, TLR4) of HMGB1 attenuated the DOX-induced myocardial apoptosis and cardiac dysfunction. In addition, our study showed that DOX resulted in an increment in the generation of peroxynitrite (ONOO) and an elevation in phosphorylation of c-Jun N terminal kinase (JNK). Pretreatment of myocytes with FeTPPS, a peroxynitrite decomposition catalyst, prevented DOX-induced JNK phosphorylation, HMGB1 expression, myocardial apoptosis and cardiac dysfunction. Genetic (JNK) or pharmacological (SP600125) inhibition of JNK ameliorated the DOX-induced HMGB1 expression and diminished myocardial apoptosis and cardiac dysfunction. Taken together, our results indicate that HMGB1 mediates the myocardial injury induced by DOX and ONOO/JNK is a key regulatory pathway of myocardial HMGB1 expression induced by DOX. [ABSTRACT FROM AUTHOR]