B\"acklund Transformations of MKdV and Painlev\'e Equations

For $N\ge 3$ there are $S_N$ and $D_N$ actions on the space of solutions of the first nontrivial equation in the $SL(N) MKdV hierarchy, generalizing the two$Z_2$ actions on the space of solutions of the standard MKdV equation. These actions survive scaling reduction, and give rise to transformation groups for certain (systems of) ODEs, including the second, fourth and fifth Painlev\'e equations.Comment: 8 pages, plain te

Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation

The connection between the method of comparison equations (generalized WKB method) and the Ermakov-Pinney equation is established. A perturbative scheme of solution of the generalized Ermakov-Pinney equation is developed and is applied to the construction of perturbative series for second-order differential equations with and without turning points.Comment: The collective of the authors is enlarged and the calculations in Sec. 3 are correcte

Dressing chain for the acoustic spectral problem

The iterations are studied of the Darboux transformation for the generalized Schroedinger operator. The applications to the Dym and Camassa-Holm equations are considered.Comment: 16 pages, 6 eps figure

Generalised chiral QED2 : Anomaly and Exotic Statistics

We study the influence of the anomaly on the physical quantum picture of the generalized chiral Schwinger model defined on the circle. We show that the anomaly i) results in the background linearly rising electric field and ii) makes the spectrum of the physical Hamiltonian nonrelativistic without a massive boson. The physical matter fields acquire exotic statistics . We construct explicitly the algebra of the Poincare generators and show that it differs from the Poincare one. We exhibit the role of the vacuum Berry phase in the failure of the Poincare algebra to close. We prove that, in spite of the background electric field, such phenomenon as the total screening of external charges characteristic for the standard Schwinger model takes place in the generalized chiral Schwinger model, too.Comment: LATEX file, 36 pp., to appear in Phys.Rev.

Assimilating Seizure Dynamics

Observability of a dynamical system requires an understanding of its state—the collective values of its variables. However, existing techniques are too limited to measure all but a small fraction of the physical variables and parameters of neuronal networks. We constructed models of the biophysical properties of neuronal membrane, synaptic, and microenvironment dynamics, and incorporated them into a model-based predictor-controller framework from modern control theory. We demonstrate that it is now possible to meaningfully estimate the dynamics of small neuronal networks using as few as a single measured variable. Specifically, we assimilate noisy membrane potential measurements from individual hippocampal neurons to reconstruct the dynamics of networks of these cells, their extracellular microenvironment, and the activities of different neuronal types during seizures. We use reconstruction to account for unmeasured parts of the neuronal system, relating micro-domain metabolic processes to cellular excitability, and validate the reconstruction of cellular dynamical interactions against actual measurements. Data assimilation, the fusing of measurement with computational models, has significant potential to improve the way we observe and understand brain dynamics

Quantum Tunneling in the Wigner Representation

Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various initial state preparations and local potential barriers. It is manifestly causal and includes time-lag effects and quantum spreading. Specific features of quantum dynamics which disappear in the standard semi-classical approximation are revealed. The propagator may be applied to calculation of the final momentum and coordinate distributions, for particles transmitted through or reflected from the potential barrier, as well as for elucidating the tunneling time problem.Comment: 18 pages, LATEX, no figure

Sporadic renal cell carcinoma in young and elderly patients: are there different clinicopathological features and disease specific survival rates?

BACKGROUND: Sporadic renal cell carcinoma (RCC) is rare in young adults. In the present retrospective study we reviewed clinicopathological features and disease specific survival rates in young patients (≤45 years) with RCC and compared them to old patients (≥75 years) with RCC. METHODS: Between 1992 and 2005 a total of 1042 patients were treated for RCC at our institution. We found 70 patients 45 years or younger (YP) and 150 patients 75 years or older (OP) at time of diagnosis. There were no differences in therapeutical approaches between both groups. Clinical and biologic parameters at diagnosis were compared and subjected to uni- and multivariate analysis to study cancer specific survival and progression rate. Mean postoperative follow-up in both groups was 50.1 months. RESULTS: Mean age was 39 years in YP and 80 years in OP, respectively. YP demonstrated significantly lower stage (pT1-pT2 N0 M0, p = 0.03), lower tumor grade (p = 0.01) and higher male-to-female ratio (p < 0.001). The rate of lymph node metastases or distant metastatic disease at presentation did not differ significantly between both groups. In multivariate analysis young age was independently associated with a higher 5-year cancer specific survival (95.2% vs. 72.3%, p = 0.009) and a lower 5-year progression rate (11.3% vs. 42.5%, p = 0.002). CONCLUSION: Sporadic RCC in young patients have lower tumor stages and grades and a better outcome compared to elderly. Age≤45 years was an independent prognostic factor for survival and progression

Toward a model-based predictive controller design in brain-computer interfaces

A first step in designing a robust and optimal model-based predictive controller (MPC) for brain-computer interface (BCI) applications is presented in this article. An MPC has the potential to achieve improved BCI performance compared to the performance achieved by current ad hoc, nonmodel-based filter applications. The parameters in designing the controller were extracted as model-based features from motor imagery task-related human scalp electroencephalography. Although the parameters can be generated from any model-linear or non-linear, we here adopted a simple autoregressive model that has well-established applications in BCI task discriminations. It was shown that the parameters generated for the controller design can as well be used for motor imagery task discriminations with performance (with 8-23% task discrimination errors) comparable to the discrimination performance of the commonly used features such as frequency specific band powers and the AR model parameters directly used. An optimal MPC has significant implications for high performance BCI applications.Grants K25NS061001 (MK) and K02MH01493 (SJS) from the National Institute of Neurological Disorders And Stroke (NINDS) and the National Institute of Mental Health (NIMH), the Portuguese Foundation for Science and Technology (FCT) Grant SFRH/BD/21529/2005 (NSD), the Pennsylvania Department of Community and Economic Development Keystone Innovation Zone Program Fund (SJS), and the Pennsylvania Department of Health using Tobacco Settlement Fund (SJS)

Patient- and system-related barriers for the earlier diagnosis of colorectal cancer

<p>Abstract</p> <p>Background</p> <p>A cohort of colorectal cancer (CRC) patients represents an opportunity to study missed opportunities for earlier diagnosis. Primary objective: To study the epidemiology of diagnostic delays and failures to offer/complete CRC screening. Secondary objective: To identify system- and patient-related factors that may contribute to diagnostic delays or failures to offer/complete CRC screening.</p> <p>Methods</p> <p>Setting: Rural Veterans Administration (VA) Healthcare system. Participants: CRC cases diagnosed within the VA between 1/1/2000 and 3/1/2007. Data sources: progress notes, orders, and pathology, laboratory, and imaging results obtained between 1/1/1995 and 12/31/2007. Completed CRC screening was defined as a fecal occult blood test or flexible sigmoidoscopy (both within five years), or colonoscopy (within 10 years); delayed diagnosis was defined as a gap of more than six months between an abnormal test result and evidence of clinician response. A summary abstract of the antecedent clinical care for each patient was created by a certified gastroenterologist (GI), who jointly reviewed and coded the abstracts with a general internist (TW).</p> <p>Results</p> <p>The study population consisted of 150 CRC cases that met the inclusion criteria. The mean age was 69.04 (range 35-91); 99 (66%) were diagnosed due to symptoms; 61 cases (46%) had delays associated with system factors; of them, 57 (38% of the total) had delayed responses to abnormal findings. Fifteen of the cases (10%) had prompt symptom evaluations but received no CRC screening; no patient factors were identified as potentially contributing to the failure to screen/offer to screen. In total, 97 (65%) of the cases had missed opportunities for early diagnosis and 57 (38%) had patient factors that likely contributed to the diagnostic delay or apparent failure to screen/offer to screen.</p> <p>Conclusion</p> <p>Missed opportunities for earlier CRC diagnosis were frequent. Additional studies of clinical data management, focusing on following up abnormal findings, and offering/completing CRC screening, are needed.</p

Phenomenology of the Lense-Thirring effect in the Solar System

Recent years have seen increasing efforts to directly measure some aspects of the general relativistic gravitomagnetic interaction in several astronomical scenarios in the solar system. After briefly overviewing the concept of gravitomagnetism from a theoretical point of view, we review the performed or proposed attempts to detect the Lense-Thirring effect affecting the orbital motions of natural and artificial bodies in the gravitational fields of the Sun, Earth, Mars and Jupiter. In particular, we will focus on the evaluation of the impact of several sources of systematic uncertainties of dynamical origin to realistically elucidate the present and future perspectives in directly measuring such an elusive relativistic effect.Comment: LaTex, 51 pages, 14 figures, 22 tables. Invited review, to appear in Astrophysics and Space Science (ApSS). Some uncited references in the text now correctly quoted. One reference added. A footnote adde