Relation between fundamental estimation limit and stability in linear quantum systems with imperfect measurement

From the noncommutative nature of quantum mechanics, estimation of canonical observables $\hat{q}$ and $\hat{p}$ is essentially restricted in its performance by the Heisenberg uncertainty relation, \mean{\Delta \hat{q}^2}\mean{\Delta \hat{p}^2}\geq \hbar^2/4. This fundamental lower-bound may become bigger when taking the structure and quality of a specific measurement apparatus into account. In this paper, we consider a particle subjected to a linear dynamics that is continuously monitored with efficiency $\eta\in(0,1]$. It is then clarified that the above Heisenberg uncertainty relation is replaced by \mean{\Delta \hat{q}^2}\mean{\Delta \hat{p}^2}\geq \hbar^2/4\eta if the monitored system is unstable, while there exists a stable quantum system for which the Heisenberg limit is reached.Comment: 4 page

On Proving Soundness of the Computationally Equivalent Transformation for Normal Conditional Term Rewriting Systems by Using Unravelings

In this paper, we show that the SR transformation, a computationally equivalent transformation proposed by Serbanuta and Rosu, is sound for weakly left-linear normal conditional term rewriting systems (CTRS). Here, soundness for a CTRS means that reduction of the transformed unconditional term rewriting system (TRS) creates no undesired reduction for the CTRS. We first show that every reduction sequence of the transformed TRS starting with a term corresponding to the one considered on the CTRS is simulated by the reduction of the TRS obtained by the simultaneous unraveling. Then, we use the fact that the unraveling is sound for weakly left-linear normal CTRSs

Cellular density‐dependent increases in HIF‐1α compete with c‐Myc to down‐regulate human EP4 receptor promoter activity through Sp‐1‐binding region

The up‐regulated expression of E‐type prostanoid (EP) 4 receptors has been implicated in carcinogenesis; however, the expression of EP4 receptors has also been reported to be weaker in tumor tissues than in normal tissues. Indeed, EP4 receptors have been suggested to play a role in the maintenance of colorectal homeostasis. This study aimed to examine the underlying mechanisms/reasons for why inconsistent findings have been reported regarding EP4 receptor expression levels in homeostasis and carcinogenesis by focusing on cellular densities. Thus, the human colon cancer HCA‐7 cells, which retain some functional features of normal epithelia, and luciferase reporter genes containing wild‐type or mutated EP4 receptor promoters were used for elucidating the cellular density‐dependent mechanisms about the regulation of EP4 receptor expression. In silico analysis was also utilized for confirming the relevance of the findings with respect to colon cancer development. We here demonstrated that the expression of EP4 receptors was up‐regulated by c‐Myc by binding to Sp‐1 under low cellular density conditions, but was down‐regulated under high cellular density conditions via the increase in the expression levels of HIF‐1α protein, which may pull out c‐Myc and Sp‐1 from DNA‐binding. The tightly regulated EP4 receptor expression mechanism may be a critical system for maintaining homeostasis in normal colorectal epithelial cells. Therefore, once the system is altered, possibly due to the transient overexpression of EP4 receptors, it may result in aberrant cellular proliferation and transformation to cancerous phenotypes. However, at the point, EP4 receptors themselves and their mediated homeostasis would be no longer required

Microstructural Analysis of Superconducting Joint Fabricated Using CJMB Between Gd123-coated Conductors

A superconducting joint between two Gd123-coated conductors was successfully formed using crystal growth in the bulk (CJMB). An intermediate Yb123 layer was used at the junction, and was melted to form a joint by heat treatment at a temperature below the melting point of the RE123 (such as Gd123) in the coated conductor. This liquid-phase bonding results in high tensile strength, which has exceeded 100 MPa in previous studies. Nevertheless, the joint principle has not been sufficiently clarified. In this study, we performed microstructural analysis of the joint using X-ray diffraction and scanning electron microscopy combined with energy-dispersive X-ray spectroscopy to form a clearer understanding of the joint formation mechanism in order to achieve a high critical current in the junction

Coupling between infraslow activities and high-frequency oscillations precedes seizure onset

Hashimoto H., Khoo H.M., Yanagisawa T., et al. Coupling between infraslow activities and high-frequency oscillations precedes seizure onset. Epilepsia Open 5, 501 (2020); https://doi.org/10.1002/epi4.12425.Infraslow activities and high-frequency oscillations (HFOs) are observed in seizure-onset zones. However, the relation between them remains unclear. In this study, we investigated phase-amplitude coupling between infraslow phase (0.016-1 Hz) and HFOs' amplitude of focal impaired awareness seizures followed by focal to bilateral tonic-clonic seizures, in a 28-year-old right-handed man with a dysembryoplastic neuroepithelial tumor. We recorded five habitual seizures. After the time of seizure onset, a significant increase in the power of HFOs was observed, and the power was significantly coupled with θ (4-8 Hz) phase. In contrast, coupling of infraslow activities and HFOs surged a few minutes before the seizure-onset time, and ictal HFOs discharged after that. Collectively, our results show that coupling of infraslow activities and HFOs precedes the seizure-onset time. We infer that such coupling may be a potential biomarker for seizure prediction

Phase-amplitude coupling between infraslow and high-frequency activities well discriminates between the preictal and interictal states

Hashimoto H., Khoo H.M., Yanagisawa T., et al. Phase-amplitude coupling between infraslow and high-frequency activities well discriminates between the preictal and interictal states. Scientific Reports 11, 17405 (2021); https://doi.org/10.1038/s41598-021-96479-1.Infraslow activity (ISA) and high-frequency activity (HFA) are key biomarkers for studying epileptic seizures. We aimed to elucidate the relationship between ISA and HFA around seizure onset. We enrolled seven patients with drug-resistant focal epilepsy who underwent intracranial electrode placement. We comparatively analyzed the ISA, HFA, and ISA-HFA phase-amplitude coupling (PAC) in the seizure onset zone (SOZ) or non-SOZ (nSOZ) in the interictal, preictal, and ictal states. We recorded 15 seizures. HFA and ISA were larger in the ictal states than in the interictal or preictal state. During seizures, the HFA and ISA of the SOZ were larger and occurred earlier than those of nSOZ. In the preictal state, the ISA-HFA PAC of the SOZ was larger than that of the interictal state, and it began increasing at approximately 87 s before the seizure onset. The receiver-operating characteristic curve revealed that the ISA-HFA PAC of the SOZ showed the highest discrimination performance in the preictal and interictal states, with an area under the curve of 0.926. This study demonstrated the novel insight that ISA-HFA PAC increases before the onset of seizures. Our findings indicate that ISA-HFA PAC could be a useful biomarker for discriminating between the preictal and interictal states