A quantum probabilistic approach to Hecke algebras for p\mathfrak{p}-adic PGL2{\rm PGL}_2

The subject of the present paper is an application of quantum probability to $p$-adic objects. We give a quantum-probabilistic interpretation of the spherical Hecke algebra for ${\rm PGL}_2(F)$, where $F$ is a $p$-adic field. As a byproduct, we obtain a new proof of the Fourier inversion formula for ${\rm PGL}_2(F)$

The limit theorem with respect to the matrices on non-backtracking paths of a graph

We give a limit theorem with respect to the matrices related to non-backtracking paths of a regular graph. The limit obtained closely resembles the $k$th moments of the arcsine law. Furthermore, we obtain the asymptotics of the averages of the $p^m$th Fourier coefficients of the cusp forms related to the Ramanujan graphs defined by A. Lubotzky, R. Phillips and P. Sarnak

Lattice sums of II-Bessel functions, theta functions, linear codes and heat equations

We extend a certain type of identities on sums of $I$-Bessel functions on lattices, previously given by G. Chinta, J. Jorgenson, A Karlsson and M. Neuhauser. Moreover we prove that, with continuum limit, the transformation formulas of theta functions such as the Dedekind eta function can be given by $I$-Bessel lattice sum identities with characters. We consider analogues of theta functions of lattices coming from linear codes and show that sums of $I$-Bessel functions defined by linear codes can be expressed by complete weight enumerators. We also prove that $I$-Bessel lattice sums appear as solutions of heat equations on general lattices. As a further application, we obtain an explicit solution of the heat equation on $\mathbb{Z}^n$ whose initial condition is given by a linear code

Gender difference in the relationships between vision and hearing impairments and negative well-being.

OBJECTIVES: To evaluate the association of hearing impairment, vision impairment and their combination (dual sensory impairment) with negative well-being such as depression, subjective poor health and the reduced functional ability in community-dwelling older adults, and to determine whether any association varies by gender. METHODS: Between 2005 and 2006, we objectively examined vision and hearing impairment (using best-corrected visual acuity and pure-tone audiometric test) in 843 people aged 65 years and older (351 males, 492 females) in a rural Japanese town. Through a home visit interview survey using a structured questionnaire, we also collected information on depression (the five-item Geriatric Depression Scale), subjective poor health, and reduced functional activity (the Tokyo Metropolitan Institute of Gerontology's Index of Competence). RESULTS: We observed gender differences in the association between sensory impairment and depression. Multiple logistic regression analysis revealed that hearing impairment in males (adjusted odds ratio: 2.22, 95% confidence interval; 1.07-4.61) and vision impairment in females (1.91, 1.14-3.21) were related to depression. Vision impairment and dual sensory impairment were also associated with subjective poor health and reduced functional activity in both sexes. CONCLUSIONS: Sensory impairment is significantly associated with negative well-being in older persons, and its association with depression may differ between males and females

Kampo, a Traditional Japanese Medicine, for the Body, Mind, and Soul

Traditional Japanese (Kampo) medicine is widely used to treat numerous conditions. Kampo medicine includes herbal formulas, acupuncture, moxibustion, and massage. After the Great East Japan Earthquake (GEJE), Kampo medicine was used to treat the imbalances in the body, mind, and soul in severely affected areas. The effects of the Kampo medicine saikokeishikankyoto (SKK) for the treatment of post-traumatic stress disorder (PTSD) have been proven in our clinical study. In this chapter, we have summarized both our reports from the Kampo medical clinics that were set up after the GEJE disaster and our findings of the clinical study on PTSD treatment in disaster survivors

Interdisciplinary therapy for severe periodontitis with Angle Class II Division 1 malocclusion : A case report with 7-year follow-up

Background: Previous studies have suggested that occlusal discrepancy is a risk factor contributing to periodontal disease. 1-3 Occlusal discrepancy could increase the risk of infrabony defects. This is a case of a patient with severe periodontitis who exhibited many infrabony defects in the molar region due to malocclusion-induced trauma. Here, we report the 7-year prognosis of the patient after periodontal regenerative and comprehensive orthodontic therapies for functional recovery with implant prosthodontics. Case Description: A 54-year-old female presented with the chief complaint of masticatory disturbance. In the molar region, significant tooth mobility, deep periodontal pockets, and infrabony defects were observed. She had excessive overjet, resulting in collapse of anterior guidance. Malocclusion was considered to be an exacerbating factor of the infrabony defects. After initial periodontal therapy, we performed periodontal regenerative therapy in the mandibular molar regions. We carefully placed implants in a position in the maxillary molar region that would ensure an appropriate anterior dental relationship after orthodontic treatment. Comprehensive orthodontic treatment was subsequently performed using implants as anchoring units. Then, definitive surgery was performed on the mandibular molars before placing the final prosthesis. A favorable periodontal condition and a stable occlusion have been maintained for the 7-year post-treatment period. Practical Implications: Comprehensive and interdisciplinary treatment enables stable occlusion and establishment of periodontal tissue and peri-implant tissues with high cleansability, even in patients with severe periodontitis and malocclusion. In the present case, a favorable long-term treatment outcome can be expected

Serum levels of retinol and other antioxidants for hearing impairment among Japanese older adults.

BACKGROUND: The objective of this study was to assess the relation between serum levels of retinol and other antioxidants and hearing impairment in Japanese older adults. METHODS: This is a community-based cross-sectional study comprising 762 residents aged 65 years or older in Kurabuchi, Gumma, Japan. We measured serum retinol and other antioxidants (alpha- and gamma-tocopherols, and carotenoids including beta-cryptoxanthin, alpha- and beta-carotenes, lycopene, and lutein plus zeaxanthin) by high-performance liquid chromatography and divided each measurement into quartiles. Hearing impairment was defined as a failure to hear a 30-dB hearing level (HL) signal at 1 kHz and a 40-dB HL signal at 4 kHz in the better ear in pure-tone audiometric tests. The odds ratios (OR) for hearing impairment were calculated for each of the upper three quartiles of retinol and other antioxidant levels relative to the lowest quartile. RESULTS: Crude analysis showed that serum levels of retinol and provitamin A carotenoids (beta-cryptoxanthin, and alpha- and beta-carotenes) were inversely related to the prevalence of hearing impairment. The multiadjusted ORs (95% confidence intervals) for the highest quartile of retinol and the provitamin A family (combinations of provitamin A carotenoids) compared with the lowest were 0.51 (0.26-1.00) and 0.53 (0.27-1.02), respectively. A dose-response relationship was observed for retinol (p = .03) and provitamin A (p = .09). CONCLUSION: Increased serum levels of retinol and provitamin A carotenoids were clearly associated with a decreased prevalence of hearing impairment