Discrete Painlevé equations from Y-systems

We consider T-systems and Y-systems arising from cluster mutations applied to quivers that have the property of being periodic under a sequence of mutations. The corresponding nonlinear recurrences for cluster variables (coefficient-free T-systems) were described in the work of Fordy and Marsh, who completely classified all such quivers in the case of period 1, and characterized them in terms of the skew-symmetric exchange matrix B that defines the quiver. A broader notion of periodicity in general cluster algebras was introduced by Nakanishi, who also described the corresponding Y-systems, and T-systems with coefficients. A result of Fomin and Zelevinsky says that the coefficient-free T-system provides a solution of the Y-system. In this paper, we show that in general there is a discrepancy between these two systems, in the sense that the solution of the former does not correspond to the general solution of the latter. This discrepancy is removed by introducing additional non-autonomous coefficients into the T-system. In particular, we focus on the period 1 case and show that, when the exchange matrix B is degenerate, discrete Painlev\'e equations can arise from this construction

Identification of de Novo Germline Mutations in the HRPT2 Gene in Two Apparently Sporadic Cases with Challenging Parathyroid Tumor Diagnoses

The diagnosis of parathyroid carcinomas is often difficult. HRPT2 mutations have been identified in familial [hyperparathyroidism-jaw tumor (HPT-JT) syndrome] and sporadic parathyroid carcinomas, supporting that HRPT2 mutations may confer a malignant potential to parathyroid tumors. In this study, we report the clinical, histopathological, and genetic investigation of two unrelated cases, whom had apparently sporadic malignant parathyroid tumors, initially diagnosed as adenomas. In one case, the differential diagnosis was complicated by cervical seeding of parathyroid tumor cells. Genetic studies identified de novo HRPT2 germline mutations in cases 1 (c.518_521delTGTC [p.Ser174LysfsX27]) and 2 (c.226 C > T [p.Arg76X]), unveiling the hereditary HPT-JT syndrome in both patients. Furthermore, the identification of somatic mutations in the patients‟ parathyroid tumors provided evidence for complete inactivation of the HRPT2 gene, which was consistent with the tumor malignant features. The sensitivity of parafibromin immunostaining to detect HRPT2 mutations was limited. The present data suggests that patients with apparently sporadic parathyroid carcinomas, or parathyroid tumors with atypical histological features, should undergo molecular genetic testing, as it may detect germline HRPT2 mutations. Establishing the diagnosis of hereditary HPT-JT syndrome is relevant for clinical counseling and management of the carriers and their relatives

Design and Fabrication of a Prototype Automated Instant Noodle Vending Machine

The project aims to help people especially those who are working in call centres to enjoy eating noodles easily and quickly during their short breaks. The unique feature of this instant noodle vending machine is that it eliminates the use of plastic or paper cups during dispensing. Instead, cooked noodle mix is directly dispensed into the mug provided by the user. The working prototype is flexible to dispense crushed noodles, four different flavours to choose from, and hot water. The dispensing process is sequential which starts from the detection of the cup, crushed noodles dispensing, seasoning dispensing based on the desired flavour, and lastly, the water injection. The researchers were able to design and fabricate the machine based on set standards with an acceptable percent error which are within the tolerance limits. The working prototype was fabricated, and statistical results showed an acceptable range of values

The matrix realization of affine Jacobi varieties and the extended Lotka-Volterra lattice

We study completely integrable Hamiltonian systems whose monodromy matrices are related to the representatives for the set of gauge equivalence classes $\boldsymbol{\mathcal{M}}_F$ of polynomial matrices. Let $X$ be the algebraic curve given by the common characteristic equation for $\boldsymbol{\mathcal{M}}_F$. We construct the isomorphism from the set of representatives to an affine part of the Jacobi variety of $X$. This variety corresponds to the invariant manifold of the system, where the Hamiltonian flow is linearized. As the application, we discuss the algebraic completely integrability of the extended Lotka-Volterra lattice with a periodic boundary condition.Comment: Revised version, 26 page

Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry

The box-ball system is an integrable cellular automaton on one dimensional lattice. It arises from either quantum or classical integrable systems by the procedures called crystallization and ultradiscretization, respectively. The double origin of the integrability has endowed the box-ball system with a variety of aspects related to Yang-Baxter integrable models in statistical mechanics, crystal base theory in quantum groups, combinatorial Bethe ansatz, geometric crystals, classical theory of solitons, tau functions, inverse scattering method, action-angle variables and invariant tori in completely integrable systems, spectral curves, tropical geometry and so forth. In this review article, we demonstrate these integrable structures of the box-ball system and its generalizations based on the developments in the last two decades.Comment: 73 page

First narrow-band search for continuous gravitational waves from known pulsars in advanced detector data

Spinning neutron stars asymmetric with respect to their rotation axis are potential sources of continuous gravitational waves for ground-based interferometric detectors. In the case of known pulsars a fully coherent search, based on matched filtering, which uses the position and rotational parameters obtained from electromagnetic observations, can be carried out. Matched filtering maximizes the signalto- noise (SNR) ratio, but a large sensitivity loss is expected in case of even a very small mismatch between the assumed and the true signal parameters. For this reason, narrow-band analysis methods have been developed, allowing a fully coherent search for gravitational waves from known pulsars over a fraction of a hertz and several spin-down values. In this paper we describe a narrow-band search of 11 pulsars using data from Advanced LIGO’s first observing run. Although we have found several initial outliers, further studies show no significant evidence for the presence of a gravitational wave signal. Finally, we have placed upper limits on the signal strain amplitude lower than the spin-down limit for 5 of the 11 targets over the bands searched; in the case of J1813-1749 the spin-down limit has been beaten for the first time. For an additional 3 targets, the median upper limit across the search bands is below the spin-down limit. This is the most sensitive narrow-band search for continuous gravitational waves carried out so far

Xenon and Sevoflurane Provide Analgesia during Labor and Fetal Brain Protection in a Perinatal Rat Model of Hypoxia-Ischemia

It is not possible to identify all pregnancies at risk of neonatal hypoxic-ischemic encephalopathy (HIE). Many women use some form of analgesia during childbirth and some anesthetic agents have been shown to be neuroprotective when used as analgesics at subanesthetic concentrations. In this study we sought to understand the effects of two anesthetic agents with presumptive analgesic activity and known preconditioning-neuroprotective properties (sevoflurane or xenon), in reducing hypoxia-induced brain damage in a model of intrauterine perinatal asphyxia. The analgesic and neuroprotective effects at subanesthetic levels of sevoflurane (0.35%) or xenon (35%) were tested in a rat model of intrauterine perinatal asphyxia. Analgesic effects were measured by assessing maternal behavior and spinal cord dorsal horn neuronal activation using c-Fos. In separate experiments, intrauterine fetal asphyxia was induced four hours after gas exposure; on post-insult day 3 apoptotic cell death was measured by caspase-3 immunostaining in hippocampal neurons and correlated with the number of viable neurons on postnatal day (PND) 7. A separate cohort of pups was nurtured by a surrogate mother for 50 days when cognitive testing with Morris water maze was performed. Both anesthetic agents provided analgesia as reflected by a reduction in the number of stretching movements and decreased c-Fos expression in the dorsal horn of the spinal cord. Both agents also reduced the number of caspase-3 positive (apoptotic) neurons and increased cell viability in the hippocampus at PND7. These acute histological changes were mirrored by improved cognitive function measured remotely after birth on PND 50 compared to control group. Subanesthetic doses of sevoflurane or xenon provided both analgesia and neuroprotection in this model of intrauterine perinatal asphyxia. These data suggest that anesthetic agents with neuroprotective properties may be effective in preventing HIE and should be tested in clinical trials in the future

Thermally Induced Nano-Structural and Optical Changes of nc-Si:H Deposited by Hot-Wire CVD

We report on the thermally induced changes of the nano-structural and optical properties of hydrogenated nanocrystalline silicon in the temperature range 200–700 °C. The as-deposited sample has a high crystalline volume fraction of 53% with an average crystallite size of ~3.9 nm, where 66% of the total hydrogen is bonded as ≡Si–H monohydrides on the nano-crystallite surface. A growth in the native crystallite size and crystalline volume fraction occurs at annealing temperatures ≥400 °C, where hydrogen is initially removed from the crystallite grain boundaries followed by its removal from the amorphous network. The nucleation of smaller nano-crystallites at higher temperatures accounts for the enhanced porous structure and the increase in the optical band gap and average gap

The NASA Airborne Tropical TRopopause EXperiment (ATTREX): High-Altitude Aircraft Measurements in the Tropical Western Pacific

The February through March 2014 deployment of the NASA Airborne Tropical TRopopause EXperiment (ATTREX) provided unique in situ measurements in the western Pacific Tropical Tropopause Layer (TTL). Six flights were conducted from Guam with the long-range, high-altitude, unmanned Global Hawk aircraft. The ATTREX Global Hawk payload provided measurements of water vapor, meteorological conditions, cloud properties, tracer and chemical radical concentrations, and radiative fluxes. The campaign was partially coincident with the CONTRAST and CAST airborne campaigns based in Guam using lower-altitude aircraft (see companion articles in this issue). The ATTREX dataset is being used for investigations of TTL cloud, transport, dynamical, and chemical processes as well as for evaluation and improvement of global-model representations of TTL processes. The ATTREX data is openly available at https:espoarchive.nasa.gov