Polynomial Growth Harmonic Functions on Finitely Generated Abelian Groups

In the present paper, we develop geometric analytic techniques on Cayley graphs of finitely generated abelian groups to study the polynomial growth harmonic functions. We develop a geometric analytic proof of the classical Heilbronn theorem and the recent Nayar theorem on polynomial growth harmonic functions on lattices \mathds{Z}^n that does not use a representation formula for harmonic functions. We also calculate the precise dimension of the space of polynomial growth harmonic functions on finitely generated abelian groups. While the Cayley graph not only depends on the abelian group, but also on the choice of a generating set, we find that this dimension depends only on the group itself.Comment: 15 pages, to appear in Ann. Global Anal. Geo

Deep ocean mineral supplementation enhances the cerebral hemodynamic response during exercise and decreases inflammation postexercise in men at two age levels.

Background: Previous studies have consistently shown that oral supplementation of deep ocean minerals (DOM) improves vascular function in animals and enhances muscle power output in exercising humans. Purpose: To examine the effects of DOM supplementation on the cerebral hemodynamic response during physical exertion in young and middle-aged men. Design: Double-blind placebo-controlled crossover studies were conducted in young (N = 12, aged 21.2 ± 0.4 years) and middle-aged men (N = 9, aged 46.8 ± 1.4 years). The counter-balanced trials of DOM and Placebo were separated by a 2-week washout period. DOM and Placebo were orally supplemented in drinks before, during, and after cycling exercise. DOM comprises desalinated minerals and trace elements from seawater collected ~618 m below the earth's surface. Methods: Cerebral hemodynamic response (tissue hemoglobin) was measured during cycling at 75% VO2max using near infrared spectroscopy (NIRS). Results: Cycling time to exhaustion at 75% VO2max and the associated plasma lactate response were similar between the Placebo and DOM trials for both age groups. In contrast, DOM significantly elevated cerebral hemoglobin levels in young men and, to a greater extent, in middle-aged men compared with Placebo. An increased neutrophil to lymphocyte ratio (NLR) was observed in middle-aged men, 2 h after exhaustive cycling, but was attenuated by DOM. Conclusion: Our data suggest that minerals and trace elements from deep oceans possess great promise in developing supplements to increase the cerebral hemodynamic response against a physical challenge and during post-exercise recovery for middle-aged men.This work was supported by Pacific Deep Ocean Biotech (Taipei,Taiwan) and University of Taipei (Taipei, Taiwan). The funding sponsors had no role in the design of the study; in the of the manuscript, and in the decision to publish the results. We declare that the results of the study are presented clearly, honestly, and without fabrication, falsification, or inappropriate data manipulation

Humans have already increased the risk of major disruptions to Pacific rainfall

© The Author(s) 2017.Intermittent disruptions to rainfall patterns and intensity over the Pacific Ocean lasting up to ∼ 1 year have major impacts on severe weather, agricultural production, ecosystems, and disease within the Pacific, and in many countries beyond. The frequency with which major disruptions to Pacific rainfall occur has been projected to increase over the 21st century, in response to global warming caused by large 21st century greenhouse gas emissions. Here we use the latest generation of climate models to show that humans may have contributed to the major disruption that occurred in the real world during the late 20th century. We demonstrate that although marked and sustained reductions in 21st century anthropogenic greenhouse gas emissions can greatly moderate the likelihood of major disruption, elevated risk of occurrence appears locked in now, and for at least the remainder of the 21st century

A Fully Tunable Single-Walled Carbon Nanotube Diode

We demonstrate a fully tunable diode structure utilizing a fully suspended single-walled carbon nanotube (SWNT). The diode's turn-on voltage under forward bias can be continuously tuned up to 4.3 V by controlling gate voltages, which is ~6 times the nanotube bandgap energy. Furthermore, the same device design can be configured into a backward diode by tuning the band-to-band tunneling current with gate voltages. A nanotube backward diode is demonstrated for the first time with nonlinearity exceeding the ideal diode. These results suggest that a tunable nanotube diode can be a unique building block for developing next generation programmable nanoelectronic logic and integrated circuits.Comment: 14 pages, 4 figure

Chiral Baryon Fields in the QCD Sum Rule

We study the structure of local baryon fields using the method of QCD sum rule. We only consider the single baryon fields and calculate their operator product expansions. We find that the octet baryon fields belonging to the chiral representations [(3,3*)+(3*,3)] and [(8,1)+(1,8)] and the decuplet baryon fields belonging to the chiral representations [(3,6)+(6,3)] lead to the baryon masses which are consistent with the experimental data of ground baryon masses. We also calculate their decay constants, check our normalizations for baryon fields in PRD81:054002(2010) and find that they are well-defined.Comment: 12 pages, 6 figure, 1 table, accepted by EPJ

Polycythemia vera as a presentation of renal angiomyolipoma: a case report

<p>Abstract</p> <p>Introduction</p> <p>Angiomyolipoma is a common benign renal tumor composed of thick-walled blood vessels, smooth muscle, and adipose tissue. It may be found incidentally during workup for suspected renal disease. Although angiomyolipoma may present as a palpable, tender renal mass with flank pain and gross or microscopic hematuria, many patients are asymptomatic. Erythrocytosis is an unusual presentation, and malignant transformation may be suspected. This report describes a rare case of a woman diagnosed with renal angiomyolipoma and polycythemia vera. The report discusses the differential diagnosis using erythropoietin, erythropoietin-receptor and Janus kinase 2.</p> <p>Case presentation</p> <p>A 79-year-old Chinese woman was diagnosed with erythrocytosis according to World Health Organization criteria. An upper left renal pole angiomyolipoma was successfully ablated after multiple phlebotomy treatments. Red cell count immediately returned to normal, but gradually increased after 4 months. Polycythemia vera was finally diagnosed by positive mutation of Janus kinase 2 and negative erythropoietin protein expression. Her clinical symptoms improved with regular phlebotomy and hydroxyurea treatment.</p> <p>Conclusion</p> <p>Concurrent occurence of angiomyolipoma and polycythemia vera is rare. Polycythemia vera can be easily missed. Polycythemia vera can be confirmed with high specificity and sensitivity by the acquired somatic mutation. Surgical intervention for this renal tumor should be avoided unless malignancy or renal cell carcinoma is suspected or to prevent spontaneous rupture of larger tumors.</p

Baryon Tri-local Interpolating Fields

We systematically investigate tri-local (non-local) three-quark baryon fields with U_L(2)*U_R(2) chiral symmetry, according to their Lorentz and isospin (flavor) group representations. We note that they can also be called as "nucleon wave functions" due to this full non-locality. We study their chiral transformation properties and find all the possible chiral multiplets consisting J=1/2 and J=3/2 baryon fields. We find that the axial coupling constant |g_A| = 5/3 is only for nucleon fields belonging to the chiral representation (1/2,1)+(1,1/2) which contains both nucleon fields and Delta fields. Moreover, all the nucleon fields belonging to this representation have |g_A| = 5/3.Comment: 8 pages, 3 tables, accepted by EPJ

Toll-like receptor signaling adapter proteins govern spread of neuropathic pain and recovery following nerve injury in male mice.

BackgroundSpinal Toll-like receptors (TLRs) and signaling intermediaries have been implicated in persistent pain states. We examined the roles of two major TLR signaling pathways and selected TLRs in a mononeuropathic allodynia.MethodsL5 spinal nerve ligation (SNL) was performed in wild type (WT, C57BL/6) male and female mice and in male Tlr2-/-Tlr3-/-, Tlr4-/-, Tlr5-/-, Myd88-/-, Triflps2, Myd88/Triflps2, Tnf-/-, and Ifnar1-/- mice. We also examined L5 ligation in Tlr4-/- female mice. We examined tactile allodynia using von Frey hairs. Iba-1 (microglia) and GFAP (astrocytes) were assessed in spinal cords by immunostaining. Tactile thresholds were analyzed by 1- and 2-way ANOVA and the Bonferroni post hoc test was used.ResultsIn WT male and female mice, SNL lesions resulted in a persistent and robust ipsilateral, tactile allodynia. In males with TLR2, 3, 4, or 5 deficiencies, tactile allodynia was significantly, but incompletely, reversed (approximately 50%) as compared to WT. This effect was not seen in female Tlr4-/- mice. Increases in ipsilateral lumbar Iba-1 and GFAP were seen in mutant and WT mice. Mice deficient in MyD88, or MyD88 and TRIF, showed an approximately 50% reduction in withdrawal thresholds and reduced ipsilateral Iba-1. In contrast, TRIF and interferon receptor null mice developed a profound ipsilateral and contralateral tactile allodynia. In lumbar sections of the spinal cords, we observed a greater increase in Iba-1 immunoreactivity in the TRIF-signaling deficient mice as compared to WT, but no significant increase in GFAP. Removing MyD88 abrogated the contralateral allodynia in the TRIF signaling-deficient mice. Conversely, IFNβ, released downstream to TRIF signaling, administered intrathecally, temporarily reversed the tactile allodynia.ConclusionsThese observations suggest a critical role for the MyD88 pathway in initiating neuropathic pain, but a distinct role for the TRIF pathway and interferon in regulating neuropathic pain phenotypes in male mice