741 research outputs found
Uncertainty principles connected with the Mobius inversion formula
No full textWe say that two arithmetic functions and form a \emph{M\"{o}bius pair} if for all natural numbers . In that case, can be expressed in terms of by the familiar M\"{o}bius inversion formula of elementary number theory. In a previous paper, the first-named author showed that if the members and of a M\"{o}bius pair are both finitely supported, then both functions vanish identically. Here we prove two significantly stronger versions of this uncertainty principle. A corollary of our results is that in a nonzero M\"{o}bius pair, one cannot have both $\sum_{f(n) \neq 0}\frac{1}{n
Iwasawa theory for modular forms at supersingular primes
No full textLet f=\sum a_nq^n be a normalised eigen-newform of weight k\ge2 and p an odd prime which does not divide the level of f. We study a reformulation of Kato's main conjecture for f over the Zp-cyclotomic extension of Q. In particular, we generalise Kobayashi's main conjecture on p-supersingular elliptic curves over Q with a_p=0, which asserts that Pollack's p-adic L-functions generate the characteristic ideals of some \pm-Selmer groups which are cotorsion over the Iwasawa algebra \Lambda=Zp[[Zp]].
We begin by studying the p-adic Hodge theory for the p-adic representation associated to f in the case when a_p=0. It allows us to give analogous definitions of Kobayashi's \pm-Coleman maps and \pm-Selmer groups. The Coleman maps are used to show that the Pontryagin duals of these new Selmer groups are torsion over \Lambda as in the elliptic curve case. As a consequence, we formulate a main conjecture stating that Pollack's p-adic L-functions generate their characteristic ideals. Similar to Kobayashi's works, we prove one inclusion of the main conjecture using an Euler system constructed by Kato.
We then prove the other inclusion of the main conjecture for CM modular forms, generalising works of Pollack and Rubin on CM elliptic curves. As a key step of the proof, we generalise the reciprocity law of Coates-Wiles and Rubin.
Next, we study Wach modules associated to positive crystalline p-adic representations in general and generalise the construction of the Coleman maps. By applying this to modular forms with much more general a_p, we define two Coleman maps and decompose the classical p-adic L functions of f into linear combinations of two power series of bounded coefficients generalising works of Pollack (in the case a_p=0) and Sprung (when f corresponds to an elliptic curve over Q with a_p\ne0). Once again, this leads to a reformulation of Kato's main conjecture involving cotorsion Selmer groups and p-adic L-functions of bounded coefficients. One inclusion of this new main conjecture is proved in the same way as the a_p=0 case.
Finally, we explain how the \pm-Coleman maps can be extended to Lubin-Tate extensions of height 1 in place of the Zp-cyclotomic extension. This generalises works of Iovita and Pollack for elliptic curves over Q
A HOUSEHOLD PRODUCTION ANALYSIS OF FUELWOOD DEMAND IN RHODE ISLAND
No full textA model analyzing household substitution of fuelwood for other heating fuels is needed to clarify the relationship between energy prices and patterns of forest resource utilization. This paper employs the household production methodology to model fuelwood demand in Rhode Island. Data from a cross-sectional survey of 515 households are employed to test a discrete-choice model of household participation in wood-burning and a four-equation system modeling household production of heat and aesthetic benefits from fuelwood and stove capital. Control of selection bias via inclusion of an appropriate instrument allows analysis of aggregate demands. Some broad policy prescriptions applicable to the Northeast generally are presented.Resource /Energy Economics and Policy,
Wach modules and Iwasawa theory for modular forms
No full textWe define a family of Coleman maps for positive crystalline p-adic representations of the absolute Galois group of Qp using the theory of Wach modules. Let f be a normalized new eigenform and p an odd prime at which f is either good ordinary or supersingular. By applying our theory to the p-adic representation associated to f, we define Coleman maps Col_i for i = 1, 2 with values in Qp ⊗Zp Λ, where
Λ is the Iwasawa algebra of Zp× . Applying these maps to the Kato zeta elements gives a decomposition of the (generally unbounded) p-adic L-functions of f into linear combinations of two power series of bounded coefficients, generalizing works of Pollack (in the case ap = 0) and Sprung (when f corresponds to a supersingular elliptic curve). Using ideas of Kobayashi for elliptic curves which are supersingular at p, we associate to each of these power series a Λ-cotorsion Selmer group. This allows us to formulate a "main conjecture". Under some technical conditions, we prove one inclusion of the "main conjecture" and show that the reverse inclusion is equivalent to Kato’s main conjecture
Abstract 3940: Transformation by ENO1 highlights the positive relationship between HIF1A's and VEGFA's RNA expression levels, putatively by counteracting heterogeneity in glioblastomas
No full textAbstract
Analysis of metabolic gene expression is compromised by tumor heterogeneity. Therefore, we investigated the use of RNA expression levels from ENO1, which encodes enolase 1, to adjust for glycolytic heterogeneity within glioblastomas attributed to irregular vascularity, necrosis, surgical removal, etc. Recently, this approach revealed relationships between carbonic anhydrases and amplified oncogenes (Beckner, et al. BBA Clinical 5 (2016):1-15). Here in frozen tissue samples from 22 glioblastomas, expressions of the metabolic gene encoding hypoxia inducible factor - 1A (HIF1A) and its target, vascular endothelial growth factor A (encoded by VEGFA), were contrasted with two non-metabolic genes, i.e. those encoding platelet derived growth factor A (PDGFA) and epidermal growth factor (EGF) using RT-qPCR analysis. Genes of interest (GOI) were initially normalized with delta-delta crossing threshold methodology using housekeeping genes, ACTB and GAPDH. Then, concurrent expressions of ENO1 (ave 0.83 +/- 0.18 CI (95%), range of 0.22 - 1.97 times normal) were used to mathematically transform expressions of GOI to multiples of ENO1 to putatively correct for glycolytic variation. Expressions of PDGFA (ave 1.90 +/- 0.69 CI (95%), 0.17 - 4.01 times normal) and EGF (ave 1.25 +/- 0.57 CI (95%), 0.07 - 5.14 times normal), had correlations, r = 0.65 and 0.66, unranked (Pearson's) and ranked (Spearman's) data, respectively, among the 22 tumors. After ENO1 transformation, r = 0.68 for their unranked data & the difference in their ranges rose to 1.31-fold. Prior to ENO1 transformation, expressions of HIF1A (ave 1.33 +/- 0.28 CI (95%), 0.25 - 2.55 times normal) and VEGFA (ave 2.89 +/- 1.36 CI (95%), 0.17 - 9.94 times normal) had negative correlations, r = - 0.15 and - 0.09, unranked and ranked data, respectively. However, after transforming HIF1A and VEGFA expressions to multiples of concurrent ENO1 expression, their correlation became positive in both unranked and ranked data, with r = 0.30 for the ranked (Spearman) data. The difference in the ranges of the two metabolic genes expanded to 6.76-fold. Whereas the Wilcoxon Rank Sum of VEGFA's untransformed values, with versus without 2.02-fold elevations of HIF1A expression, was insignificant, p = 0.704, using ENO1 transformed values indicated a significant relationship, p = 0.042. Therefore, ENO1 transformation revealed the anticipated relationship between HIF1A and its target, VEGFA, at the RNA expression level that was not initially apparent in this small group of tumors. Transformation via expression levels of ENO1 compensates for glycolytic heterogeneity to reveal and highlight relationships among metabolic genes when analyzing resected tumors. Support from The Pittsburgh Foundation's Walter L. Copeland Fund for Cranial Research (D2006-0379) and the Molecular Lab, Dept. of Pathology, Univ. of Pittsburgh Medical Center.
Citation Format: Marie E. Beckner, Ian F. Pollack, Ronald L. Hamilton. Transformation by ENO1 highlights the positive relationship between HIF1A's and VEGFA's RNA expression levels, putatively by counteracting heterogeneity in glioblastomas [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2017; 2017 Apr 1-5; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2017;77(13 Suppl):Abstract nr 3940. doi:10.1158/1538-7445.AM2017-3940</jats:p
Flight Control Law Design using Hybrid Incremental Nonlinear Dynamic Inversion
No full textIncremental Nonlinear Dynamic Inversion (INDI) is a sensor-based control strategy, which has shown robustness against model uncertainties on various aerospace platforms. The sensor-based nature of the method brings attractive properties, which has made it popular in the last decade. INDI globally linearizes the system by making use of control input and state derivative feedback. Despite the enhanced robustness against parametric system uncertainties compared to traditional NDI, mitigating the effects of time lag between the control input and state derivative feedback paths represents an important challenge for INDI. Past research has shown that this can be addressed by synchronizing these feedback signals, although the method remains vulnerable to unexpected measurement delays. This paper proposes a hybrid INDI approach based on complementary filtering to further mitigate this robustness issue. The approach fuses the system model and sensor measurement to generate an estimate of the angular acceleration of the system. The estimation responds rapidly to the system input thanks to the on-board model, whereas adequate accuracy in the low-to-medium frequency range is maintained by the sensor measurement. The control law is found to retain good performance in case of model mismatches and measurement delays. To demonstrate the method, a hybrid INDI-based attitude control law is designed for a nonlinear F-16 aircraft model. The robustness properties of the resulting control system are analyzed using time-domain simulations.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Control & Simulatio
Pediatric Brain Tumors: Application of Stratification Criteria to Refine Patient Management
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