On the Reduced Testing of a Primitive Element in Zn×{\mathbb Z}_n^\times

The primitive roots in ${\mathbb Z}_n^\times$ are defined and exist iff $n = 2, 4, p^{\alpha}, 2p^{\alpha}$. Knuth gave the definition of the primitive roots in ${\mathbb Z}_{p^\alpha}^\times$, and showed the necessary and sufficient condition for testing a primitive root in ${\mathbb Z}_{p^\alpha}^\times$. In this paper we define the primitive elements in ${\mathbb Z}_n^\times$, which is a generalization of primitive roots, as elements that take the maximum multiplicative order.And we give two theorems for the reduced testing of a primitive element in ${\mathbb Z}_n^\times$ for any composite $n$. It is shown that the two theorems, using a technique of a lemma, for testing a primitive element allow us an effective reduction in testing processes and in computing time cost as a consequence.The primitive roots in ${\mathbb Z}_n^\times$ are defined and exist iff $n = 2, 4, p^{\alpha}, 2p^{\alpha}$. Knuth gave the definition of the primitive roots in ${\mathbb Z}_{p^\alpha}^\times$, and showed the necessary and sufficient condition for testing a primitive root in ${\mathbb Z}_{p^\alpha}^\times$. In this paper we define the primitive elements in ${\mathbb Z}_n^\times$, which is a generalization of primitive roots, as elements that take the maximum multiplicative order.And we give two theorems for the reduced testing of a primitive element in ${\mathbb Z}_n^\times$ for any composite $n$. It is shown that the two theorems, using a technique of a lemma, for testing a primitive element allow us an effective reduction in testing processes and in computing time cost as a consequence

A Rat Model Examining Behavioral and Neurochemical Effects of Passive Exposure to Aggression on Observers

Previous studies have consistently reported that passive exposure to aggression is a risk of aggressive inclinations for a human witness. However, it is unclear whether a witness\u27 aggressiveness is semi-permanently socialized or temporarily primed. Furthermore, a neurochemical mechanism of passive exposure to aggression also remains unaddressed in clinical literature. The present research used a rat model to clarify the behavioral and neurochemical effects of passive exposure to aggression. First, rats were screened for their aggressiveness after they were acutely or chronically exposed to aggression or non-aggression. It was found that observer rats chronically exposed to aggression exhibited more aggression than those exposed to non-aggression and even those exposed to aggression only acutely. This behavioral difference was maintained over 16 days. Next, radioimmunoassay and autoradiography were used to test the levels of serum testosterone and corticosterone, as well as the densities of dopamine D2 receptors and 5-HT1B receptors, among observer rats chronically exposed to aggression or non-aggression. No differences in the hormonal levels were detected between the groups of exposure to aggression and non-aggression, whereas observer rats chronically exposed to aggression showed lower densities of dopamine D2 receptors and higher densities of 5-HT1B receptors, compared with controls. These suggest that chronic passive exposure to aggression inclined observer rats to be aggressive in the long run, which may be mediated by low densities of dopamine D2 receptors and high densities of 5-HT1B receptors

Unique secretory dynamics of tissue plasminogen activator and its modulation by plasminogen activator inhibitor-1 in vascular endothelial cells

We analyzed the secretory dynamics of tissue plasminogen activator (tPA) in EA.hy926 cells, an established vascular endothelial cell (VEC) line producing GFP-tagged tPA, using total internal reflection fluorescence (TIR-F) microscopy. tPA-GFP was detected in small granules in EA.hy926 cells, the distribution of which was indistinguishable from intrinsically expressed tPA. Its secretory dynamics were unique, with prolonged (>5min.) retention of the tPA-GFP on the cell surface, appearing as fluorescent spots in two-thirds of the exocytosis events. The rapid disappearance (mostly by 250ms) of a domain-deletion mutant of tPA-GFP possessing only the signal peptide and catalytic domain indicates that the amino-terminal heavy chain of tPA-GFP is essential for binding to the membrane surface. The addition of PAI-1 dose-dependently facilitated the dissociation of membrane-retained tPA and increased the amounts of tPA-PAI-1 high molecular weight complexes in the medium. Accordingly, suppression of PAI-1 synthesis in EA.hy926 cells by siRNA prolonged the dissociation of tPA-GFP, whereas a catalytically inactive mutant of tPA-GFP not forming complexes with PAI-1 remained on the membrane even after PAI-1 treatment. Our results provide new insights into the relationship between exocytosed, membrane-retained tPA and PAI-1, which would modulate cell surface-associated fibrinolytic potential