Higher rank numerical ranges of normal matrices

The higher rank numerical range is closely connected to the construction of quantum error correction code for a noisy quantum channel. It is known that if a normal matrix $A \in M_n$ has eigenvalues $a_1, \..., a_n$, then its higher rank numerical range $\Lambda_k(A)$ is the intersection of convex polygons with vertices $a_{j_1}, \..., a_{j_{n-k+1}}$, where $1 \le j_1 < \... < j_{n-k+1} \le n$. In this paper, it is shown that the higher rank numerical range of a normal matrix with $m$ distinct eigenvalues can be written as the intersection of no more than $\max\{m,4\}$ closed half planes. In addition, given a convex polygon ${\mathcal P}$ a construction is given for a normal matrix $A \in M_n$ with minimum $n$ such that $\Lambda_k(A) = {\mathcal P}$. In particular, if ${\mathcal P}$ has $p$ vertices, with $p \ge 3$, there is a normal matrix $A \in M_n$ with $n \le \max\left\{p+k-1, 2k+2 \right\}$ such that $\Lambda_k(A) = {\mathcal P}$.Comment: 12 pages, 9 figures, to appear in SIAM Journal on Matrix Analysis and Application

The Bouncing Jet: A Newtonian Liquid Rebounding off a Free Surface

We find that a liquid jet can bounce off a bath of the same liquid if the bath is moving horizontally with respect to the jet. Previous observations of jets rebounding off a bath (e.g. Kaye effect) have been reported only for non-Newtonian fluids, while we observe bouncing jets in a variety of Newtonian fluids, including mineral oil poured by hand. A thin layer of air separates the bouncing jet from the bath, and the relative motion replenishes the film of air. Jets with one or two bounces are stable for a range of viscosity, jet flow rate and velocity, and bath velocity. The bouncing phenomenon exhibits hysteresis and multiple steady states.Comment: 9 pages, 7 figures. submitted to Physical Review

Mapping radiation dose distribution on the Fractional Anisotropy Map: application in the assessment of treatment-induced white matter injury

published_or_final_versio

Discrepant FA reduction between the frontal and parietal lobes of post irradiation medulloblastoma survivors: preliminary findings of regional susceptibility?

In this study of 16 medulloblastoma survivors and corresponding age-matched control subjects, we tested the hypothesis that fractional anisotropy (FA) in the frontal lobe is more severely reduced than the parietal lobe after whole brain irradiation. Quantitative measurement of regional mean FA was performed using automatically generated masks. We found significant FA reduction in the frontal lobe, but not parietal lobe, in the medulloblastoma survivors compared to controls. Although more severe FA reduction in the frontal lobe was found, this difference did not achieve statistical significance. However, a trend of regional susceptibility of the frontal lobe to radiation was suggested.published_or_final_versio

Observation of femto-joule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities

We observe experimentally optical bistability enhanced through Fano interferences in high-Q localized silicon photonic crystal resonances (Q ~ 30,000 and modal volume ~ 0.98 cubic wavelengths). This phenomenon is analyzed through nonlinear coupled-mode formalism, including the interplay of chi(3) effects such as two-photon absorption and related free-carrier dynamics, and optical Kerr as well as thermal effects and linear losses. Our experimental and theoretical results demonstrate for the first time Fano-resonance based bistable states with switching thresholds of 185 micro-Watt and 4.5 fJ internally stored cavity energy (~ 540 fJ consumed energy) in silicon for scalable optical buffering and logic

Intraneural Hemangioma: Case Report of a Rare Tibial Nerve Lesion.

An intraneural hemangioma is a rare, benign mesodermal lesion. We present a case of a three-year-old female with the inability to straighten her right knee and fullness over the right popliteal fossa for one year. Magnetic resonance imaging (MRI) demonstrated a T2 hyperintense lesion of the popliteal fossa, within the tibial nerve. The patient underwent an uncomplicated right knee excisional biopsy, which confirmed the diagnosis of an intraneural hemangioma. Although rare, an intraneural hemangioma should be considered in the differential diagnosis of a soft tissue lesion located in the expected course of a peripheral nerve

Measurement of Thermal-Energy Charge-Transfer Rate Coefficient of Mo6+ and Argon

The charge-transfer rate coefficient of Mo6+ and argon has been measured at mean ion energies of 8.8 and 1.4 eV using a laser-ablation ion source and an ion trap. The rate coefficient deduced from these measurements is 1.02(0.10)×10-10 cm3 s-1 and appears to be independent of the mean ion energy at this energy range. However, the measured value is an order of magnitude smaller than the Langevin rate coefficient

Nonet Symmetry and Two-Body Decays of Charmed Mesons

The decay of charmed mesons into pseudoscalar (P) and vector (V) mesons is studied in the context of nonet symmetry. We have found that it is badly broken in the PP channels and in the P sector of the PV channels as expected from the non-ideal mixing of the \eta and the \eta'. In the VV channels, it is also found that nonet symmetry does not describe the data well. We have found that this discrepancy cannot be attributed entirely to SU(3) breaking at the usual level of 20--30%. At least one, or both, of nonet and SU(3) symmetry must be very badly broken. The possibility of resolving the problem in the future is also discussed.Comment: 9 pages, UTAPHY-HEP-

Pancreatic cysts suspected to be branch duct intraductal papillary mucinous neoplasm without concerning features have low risk for development of pancreatic cancer.

BackgroundThe risk of developing pancreatic cancer is uncertain in patients with clinically suspected branch duct intraductal papillary mucinous neoplasm (BD-IPMN) based on the "high-risk stigmata" or "worrisome features" criteria proposed in the 2012 international consensus guidelines ("Fukuoka criteria").MethodsRetrospective case series involving patients referred for endoscopic ultrasound (EUS) of indeterminate pancreatic cysts with clinical and EUS features consistent with BD-IPMN. Rates of pancreatic cancer occurring at any location in the pancreas were compared between groups of patients with one or more Fukuoka criteria ("Highest-Risk Group", HRG) and those without these criteria ("Lowest-Risk Group", LRG).ResultsAfter exclusions, 661 patients comprised the final cohort (250 HRG and 411 LRG patients), 62% female with an average age of 67 years and 4 years of follow up. Pancreatic cancer, primarily adenocarcinoma, occurred in 60 patients (59 HRG, 1 LRG). Prevalent cancers diagnosed during EUS, immediate surgery, or first year of follow up were found in 48/661 (7.3%) of cohort and exclusively in HRG (33/77, 42.3%). Using Kaplan-Meier method, the cumulative incidence of cancer at 7 years was 28% in HRG and 1.2% in LRG patients (P&lt;0.001).ConclusionsThis study supports using Fukuoka criteria to stratify the immediate and long-term risks of pancreatic cancer in presumptive BD-IPMN. The risk of pancreatic cancer was highest during the first year and occurred exclusively in those with "high-risk stigmata" or "worrisome features" criteria. After the first year all BD-IPMN continued to have a low but persistent cancer risk

Low frequency noise statistics for the breakdown characterization of ultra-thin gate oxides

We have investigated the statistics of low frequency noise in the tunneling current of ultrathin oxides (2.5nm-4nm) in metal oxide semiconductor capacitors as a function of the applied voltage stress. The statistical analysis includes (i) non-Gaussianity (nG), which is a measure of the degree of temporal correlation in the noise, and (ii) ratio of integrated noise power to the DC leakage current (R). The occurrence of high peaks in nG indicates the appearance of new percolation paths, and the subsequent conduction through these paths is indicated by R. Our results show that the nG and R characteristics are generic for the oxides of different thickness and growth quality and have the potential, in conjunction with leakage itself, of being used as a prognosticator of oxide reliability.Comment: 4 page