Orthomodular-Valued Models for Quantum Set Theory

In 1981, Takeuti introduced quantum set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed linear subspaces of a Hilbert space in a manner analogous to Boolean-valued models of set theory, and showed that appropriate counterparts of the axioms of Zermelo-Fraenkel set theory with the axiom of choice (ZFC) hold in the model. In this paper, we aim at unifying Takeuti's model with Boolean-valued models by constructing models based on general complete orthomodular lattices, and generalizing the transfer principle in Boolean-valued models, which asserts that every theorem in ZFC set theory holds in the models, to a general form holding in every orthomodular-valued model. One of the central problems in this program is the well-known arbitrariness in choosing a binary operation for implication. To clarify what properties are required to obtain the generalized transfer principle, we introduce a class of binary operations extending the implication on Boolean logic, called generalized implications, including even non-polynomially definable operations. We study the properties of those operations in detail and show that all of them admit the generalized transfer principle. Moreover, we determine all the polynomially definable operations for which the generalized transfer principle holds. This result allows us to abandon the Sasaki arrow originally assumed for Takeuti's model and leads to a much more flexible approach to quantum set theory.Comment: 25 pages, v2: to appear in Rev. Symb. Logic, v3: corrected typo

NMNAT1 inhibits axon degeneration via blockade of SARM1-mediated NAD+ depletion

Overexpression of the NAD(+) biosynthetic enzyme NMNAT1 leads to preservation of injured axons. While increased NAD(+) or decreased NMN levels are thought to be critical to this process, the mechanism(s) of this axon protection remain obscure. Using steady-state and flux analysis of NAD(+) metabolites in healthy and injured mouse dorsal root ganglion axons, we find that rather than altering NAD(+) synthesis, NMNAT1 instead blocks the injury-induced, SARM1-dependent NAD(+) consumption that is central to axon degeneration. DOI: http://dx.doi.org/10.7554/eLife.19749.00

Confinement and Topological Charge in the Abelian Gauge of QCD

We study the relation between instantons and monopoles in the abelian gauge. First, we investigate the monopole in the multi-instanton solution in the continuum Yang-Mills theory using the Polyakov gauge. At a large instanton density, the monopole trajectory becomes highly complicated, which can be regarded as a signal of monopole condensation. Second, we study instantons and monopoles in the SU(2) lattice gauge theory both in the maximally abelian (MA) gauge and in the Polyakov gauge. Using the $16^3 \times 4$ lattice, we find monopole dominance for instantons in the confinement phase even at finite temperatures. A linear-type correlation is found between the total monopole-loop length and the integral of the absolute value of the topological density (the total number of instantons and anti-instantons) in the MA gauge. We conjecture that instantons enhance the monopole-loop length and promote monopole condensation.Comment: 3 pages, LaTeX, Talk presented at LATTICE96(topology

Candida albicans keratitis modified by steroid application

The paper reports on Candida albicans ocular infection modified by steroid eye drops. A 74-year-old male complained of conjunctival injection and pain in his right eye three months after pterygium and cataract surgery. After treatment with antibiotics and steroid eye drops for three days, he was referred to our hospital. Clear localized corneal endothelial plaque with injection of ciliary body was observed. No erosion of the corneal epithelium, or infiltration of stromal edema was observed, suggesting that the pathological organism derived from the intracameral region. Because ocular infection was suspected, steroid eye drops were stopped, which led immediately to typical infectious keratitis in the pathological region, with epithelial erosion, fluffy abscess, stromal infiltration, and edema. For diagnostic purposes, the plaque was surgically removed with forceps and the anterior chamber was irrigated with antibiotics. The smear and culture examination from the plaque revealed C. albicans surrounded by neutrophils. However, aqueous fluid and fibrous tissue after gonio procedure contained no mycotic organisms. Topical fluconazole, micafungin, and pimaricin with oral itraconazole (150 mg/day) were effective. Special attention is needed when prescribing steroid eye drops to treat corneal disease especially postoperatively. Diagnosing infectious keratitis is sometimes difficult because of modification by some factors, such as postoperative conditions, scarring, and drug-induced masking. Here, we report on mycotic keratitis modified by postoperative steroid administration

Instanton Calculus in R-R 3-form Background and Deformed N=2 Super Yang-Mills Theory

We study the ADHM construction of instantons in N=2 supersymmetric Yang-Mills theory deformed in constant Ramond-Ramond (R-R) 3-form field strength background in type IIB superstrings. We compare the deformed instanton effective action with the effective action of fractional D3/D(-1) branes at the orbifold singularity of C^2/Z_2 in the same R-R background. We find discrepancy between them at the second order in deformation parameters, which comes from the coupling of the translational zero modes of the D(-1)-branes to the R-R background. We improve the deformed action by adding a term with space-time dependent gauge coupling. Although the space-time action differs from the action in the omega-background, both actions lead to the same instanton equations of motion at the lowest order in gauge coupling.Comment: 27 pages, version to appear in JHE

Diagnostic Ureteroscopy for Cases Clinically Suspected of Carcinoma in Situ of the Upper Urinary Tract

　We elucidate the fate of cases clinically suspected of carcinoma in situ (Cis) of the upper tract with serial ureteroscopy. Of 143 patients who underwent ureteroscopy for suspected upper tract urothelial carcinoma (UTUC) between January 2008 and February 2016, 12 cases with consistently positive urine cytology and poorly detectable upper-tract malignancies by imaging were reviewed. In these 12 patients, 19 ureteroscopy procedures (25 renal units) were performed. Vesical random biopsy was performed before the 1st ureteroscopy to exclude malignancy of the bladder in all 12 cases. Median follow-up was 42 (13-67) months. Positive biopsy results at the 1st ureteroscopy were obtained in 3 (25%) patients and all were diagnosed wth Cis of the upper tract. Two (17%) of 9 patients who were negative or inconclusive at the 1st ureteroscopy were finally diagnosed as UTUC, but plural ureteroscopy procedures were needed for the diagnoses in both. Carcinoma of the bladder appeared in 5 (42%) patients during follow-up, despite the earlier ruling out of vesical malignancy. Four (33%) of those 5 patients never developed upper-tract urothelial carcinoma during follow-up. Caution is required before undertaking radical surgery for cases clinically suspected of Cis of the upper tract. In our experience, only 42% of such patients developed UTUC; another 33% eventually developed carcinoma of the bladder without UTUC

GDP/GTP exchange reaction-stimulating activity of Rabphilin-3A for Rab3A small GTP-binding protein

AbstractRabphilin-3A is a putative target protein for Rab3A, a small GTP-binding protein particularly implicated in neurotransmitter release. Rabphilin-3A interacts more preferentially with GTP-Rab3A than with GDP-Rab3A. Moreover, Rabphilin-3A shows a weak activity to stimulate the GTPase activity of Rab3A and a strong activity to inhibit the Rab3A GTPase-activating protein (GAP)-stimulated GTPase activity of Rab3A. Here, we show that Rabphilin-3A has another activity to stimulate the GDP/GTP exchange reaction of Rab3A. Rabphifin-3A may keep Rab3A continuously in the GTP-bound form by converting again GDP-Rab3A, which may be converted from GTP-Rab3A by Rab3A GAP, to GTP-Rab3A, until the function of Rab3A is accomplished