A closed-form solution to the inverse problem in interpolation by a Bézier-spline curve

A geometric construction of a Bézier curve is presented by a unifiable way from the mentioned literature with some modification. A closed-form solution to the inverse problem in cubic Bézier-spline interpolation will be obtained. Calculations in the given examples are performed by a Maple procedure using this solution

The Kalman-Levy filter

The Kalman filter combines forecasts and new observations to obtain an estimation which is optimal in the sense of a minimum average quadratic error. The Kalman filter has two main restrictions: (i) the dynamical system is assumed linear and (ii) forecasting errors and observational noises are taken Gaussian. Here, we offer an important generalization to the case where errors and noises have heavy tail distributions such as power laws and L\'evy laws. The main tool needed to solve this ``Kalman-L\'evy'' filter is the ``tail-covariance'' matrix which generalizes the covariance matrix in the case where it is mathematically ill-defined (i.e. for power law tail exponents $\mu \leq 2$). We present the general solution and discuss its properties on pedagogical examples. The standard Kalman-Gaussian filter is recovered for the case $\mu = 2$. The optimal Kalman-L\'evy filter is found to deviate substantially fro the standard Kalman-Gaussian filter as $\mu$ deviates from 2. As $\mu$ decreases, novel observations are assimilated with less and less weight as a small exponent $\mu$ implies large errors with significant probabilities. In terms of implementation, the price-to-pay associated with the presence of heavy tail noise distributions is that the standard linear formalism valid for the Gaussian case is transformed into a nonlinear matrice equation for the Kalman-L\'evy filter. Direct numerical experiments in the univariate case confirms our theoretical predictions.Comment: 41 pages, 9 figures, correction of errors in the general multivariate cas

Proceedings of the OMS COVID-19 Response Conference

The coronavirus disease 2019 (COVID-19) pandemic has affected the world in unprecedented ways. It is clear that this pandemic, unlike any public health challenge in recent memory, has the potential to fundamentally alter the delivery of many healthcare services, including the practice of oral and maxillofacial surgery. In response to this global health crisis, the Oral and Maxillofacial Surgery (OMS) COVID-19 Response Conference was held virtually on April 9, 2020, organized by oral and maxillofacial surgeons (OMSs) and administrators from multiple institutions to provide a forum for OMSs to discuss how COVID-19 has affected the specialty. As evidence-based information on COVID-19 continues to emerge, the present report serves as a method to disseminate the current opinions and management strategies from a variety of experts in OMS. © 202

B2 0902+34: A Collapsing Protogiant Elliptical Galaxy at z=3.4

We have used the visible integral-field replicable unit spectrograph prototype (VIRUS-P), a new integral field spectrograph, to study the spatially and spectrally resolved Lyman-alpha emission line structure in the radio galaxy B2 0902+34 at z=3.4. We observe a halo of Lyman-alpha emission with a velocity dispersion of 250 km/s extending to a radius of 50 kpc. A second feature is revealed in a spatially resolved region where the line profile shows blueshifted structure. This may be viewed as either HI absorption at -450 km/s or secondary emission at -900 km/s from the primary peak. Our new data, in combination with the 21 cm absorption, suggest two important and unexplained discrepancies. First, nowhere in the line profiles of the Lyman-alpha halo is the 21 cm absorber population evident. Second, the 21 cm absorption redshift is higher than the Lyman-alpha emission redshift. In an effort to explain these two traits, we have undertaken the first three dimensional Monte Carlo simulations of resonant scattering in radio galaxies. Though simple, the model produces the features in the Lyman-alpha data and predicts the 21 cm properties. To reach agreement between this model and the data, global infall of the HI is strictly necessary. The amount of gas necessary to match the model and data is surprisingly high, >= 10E12 solar masses, an order of magnitude larger than the stellar mass. The collapsing structure and large gas mass lead us to interpret B2 0902+34 as a protogiant elliptical galaxy.Comment: 30 pages, 8 figures, 4 tables, accepted in Ap

Potential Mechanisms and Functions of Intermittent Neural Synchronization

Neural synchronization is believed to play an important role in different brain functions. Synchrony in cortical and subcortical circuits is frequently variable in time and not perfect. Few long intervals of desynchronized dynamics may be functionally different from many short desynchronized intervals although the average synchrony may be the same. Recent analysis of imperfect synchrony in different neural systems reported one common feature: neural oscillations may go out of synchrony frequently, but primarily for a short time interval. This study explores potential mechanisms and functional advantages of this short desynchronizations dynamics using computational neuroscience techniques. We show that short desynchronizations are exhibited in coupled neurons if their delayed rectifier potassium current has relatively large values of the voltage-dependent activation time-constant. The delayed activation of potassium current is associated with generation of quickly-rising action potential. This “spikiness� is a very general property of neurons. This may explain why very different neural systems exhibit short desynchronization dynamics. We also show how the distribution of desynchronization durations may be independent of the synchronization strength. Finally, we show that short desynchronization dynamics requires weaker synaptic input to reach a pre-set synchrony level. Thus, this dynamics allows for efficient regulation of synchrony and may promote efficient formation of synchronous neural assemblies

DEA efficiency of German savings banks: evidence from a goal-oriented perspective

We provide one of very few Data Envelopment Analysis efficiency studies of the German savings banks, thereby contributing evidence on the credit of their business model. This model distinguishes itself by the ultimate purposes to ensure public access to financial services and to support regional economies. To capture the respective goal set of the German savings banks, we propose a framework incorporating rationality concepts of decision making to derive appropriate performance criteria. On this basis, the 2006–2011 analysis reveals the active role of the savings banks in stabilizing the German economy during the financial crisis 2008–2009. The results also suggest that the banks are more efficient in fulfilling their public mandate than in generating profit. Furthermore, a stable scale efficiency pattern is observed, particularly showing that larger banks are experiencing notable decreasing returns to scale

A Prospective Study to Assess In Vivo Optical Coherence Tomography Imaging for Early Detection of Chemotherapy-induced Oral Mucositis

Background and Objective Oral mucositis (OM) is a common and severe complication of many cancer therapies. Currently, prediction and early detection are not possible and objective monitoring remains problematic. Goal of this prospective study is to assess non-invasive imaging using optical coherence tomography (OCT) for early detection and evaluation of chemotherapy-induced OM in 48 patients, 12 of whom developed clinical mucositis. Study Design/Materials and Methods In 48 patients receiving neoadjuvant chemotherapy for primary breast cancer, oral mucosal health was assessed clinically, and imaged using non-invasive OCT. Images were evaluated for mucositis using an imaging-based scoring system ranging from 0 to 6. Conventional clinical assessment using the OM assessment scale (OMAS) was used as the gold standard. Patients were evaluated on Days 0-11 after commencement of chemotherapy. OCT images were visually scored by three blinded investigators. Results The following events were identified from OCT images (1) change in epithelial thickness and subepithelial tissue integrity (beginning on Day 2), (2) loss of surface keratinized layer continuity (beginning on Day 4), (3) loss of epithelial integrity (beginning on Day 4). Imaging data gave higher scores compared to clinical scores early in treatment, suggesting that the imaging-based diagnostic scoring was more sensitive to early mucositic change than the clinical scoring system. Once mucositis was established, imaging and clinical scores converged. Conclusion Using OCT imaging and a novel scoring system, earlier, more sensitive detection of mucositis was possible than using OMAS. Specific imaging-based changes were a consistent predictor of clinical mucositis. Lasers Surg. Med. 45: 22-27, 2013. © 2013 Wiley Periodicals, Inc. Copyright © 2013 Wiley Periodicals, Inc

Inhomogeneously doped two-leg ladder systems

A chemical potential difference between the legs of a two-leg ladder is found to be harmful for Cooper pairing. The instability of superconductivity in such systems is analyzed by compairing results of various analytical and numerical methods. Within a strong coupling approach for the t-J model, supplemented by exact numerical diagonalization, hole binding is found unstable beyond a finite, critical chemical potential difference. The spinon-holon mean field theory for the t-J model shows a clear reduction of the the BCS gaps upon increasing the chemical potential difference leading to a breakdown of superconductivity. Based on a renormalization group approach and Abelian bosonization, the doping dependent phase diagram for the weakly interacting Hubbard model with different chemical potentials was determined.Comment: Revtex4, 11 pages, 7 figure