33 resultados para Birkhoff and Von Neumann ergodic theorems


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Study of nanomechanical response of iron carbides is important because presence of iron carbides greatly influences the performance and longevity of steel components. This work contributes to the literature by exploring nanoindentation of nanocrystalline Fe3C and tetrahedral-Fe4C using molecular dynamics simulation. The chemical interactions of iron and carbon were described through an analytical bond order inter-atomic potential (ABOP) energy function. The indentations were performed at an indentation speed of 50 m/sec and a repeat trial was performed at 5 m/sec. Load-displacement (P-h) curve for both these carbides showed residual indentation depth and maximum indentation depth (hf/hmax) ratio to be higher than 0.7 i.e. a circumstance where Oliver and Pharr method was not appropriate to be applied to evaluate the material properties. Alternate evaluation revealed Fe3C to be much harder than Fe4C. Gibbs free energy of formation and radial distribution function, coupled with state of the average local temperature and von Mises stresses indicate the formation of a new phase of iron-carbide. Formation of this newer phase was found to be due to deviatoric strain rather than the high temperature induced in the substrate during nanoindentation

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Abstract A classic physiologic response to hypoxia in humans is the up-regulation of the ERYTHROPOIETIN (EPO) gene, which is the central regulator of red blood cell mass. The EPO gene, in turn, is activated by hypoxia inducible factor (HIF). HIF is a transcription factor consisting of an alpha subunit (HIF-alpha) and a beta subunit (HIF-beta). Under normoxic conditions, prolyl hydroxylase domain protein (PHD, also known as HIF prolyl hydroxylase and egg laying-defective nine protein) site specifically hydroxylates HIF-alpha in a conserved LXXLAP motif (where underlining indicates the hydroxylacceptor proline). This provides a recognition motif for the von Hippel Lindau protein, a component of an E3 ubiquitin ligase complex that targets hydroxylated HIF-alpha for degradation. Under hypoxic conditions, this inherently oxygen-dependent modification is arrested, thereby stabilizing HIF-alpha and allowing it to activate the EPO gene. We previously identified and characterized an erythrocytosis-associated HIF2A mutation, G537W. More recently, we reported two additional erythrocytosis-associated HIF2A mutations, G537R and M535V. Here, we describe the functional characterization of these two mutants as well as a third novel erythrocytosis-associated mutation, P534L. These mutations affect residues C-terminal to the LXXLAP motif. We find that all result in impaired degradation and thus aberrant stabilization of HIF-2alpha. However, each exhibits a distinct profile with respect to their effects on PHD2 binding and von Hippel Lindau interaction. These findings reinforce the importance of HIF-2alpha in human EPO regulation, demonstrate heterogeneity of functional defects arising from these mutations, and point to a critical role for residues C-terminal to the LXXLAP motif in HIF-alpha.

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Inherited disorders of renal structure and function are relatively common causes of end-stage renal disease requiring renal replacement therapy. A family history of haematuria, urinary tract infection or renal failure can alert the clinician to the possible diagnosis of underlying renal genetic abnormalities. In practice, the commonest inherited renal disorder is autosomal dominant polycystic kidney disease (ADPKD), characterized by multiple kidney cysts associated with hypertension and renal failure. Insights into the cell biology of ADPKD are informing new therapeutic approaches to limit cyst growth and prevent progressive renal failure. Non-visible haematuria is a clinical finding that presents a diagnostic challenge because it has so many possible causes. Mutations in the genes encoding collagen proteins within the glomerular basement membrane (GBM) can disrupt its normal barrier function. Thin basement membrane nephropathy, caused by GBM collagen gene mutations, is a relatively common cause of familial haematuria that normally has a good long-term prognosis. Alport syndrome is a rare and genetically heterogeneous condition leading to renal failure in men inheriting the X-linked gene defect. Single-gene defects may cause diverse renal tubular disorders, such as predisposition to renal calculi, diabetes insipidus, renal tubular acidosis or hypertension with associated electrolyte imbalance. Gene mutations responsible for familial renal cancer syndromes, such as tuberous sclerosis complex and von Hippel–Lindau disease, have also been identified

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In this paper, the impact of interference from multiple licensed transceivers on cognitive underlay single carrier systems is examined. Specifically, the situation is considered in which the secondary network is limited by three key parameters: 1) maximum transmit power at the secondary transmitter, 2) peak interference power at the primary receivers, and 3) interference power from the primary transmitters. For this cognitive underlay single carrier system, the signal-to-interference ratio (SIR) of the secondary network is obtained for transmission over frequency selective fading channels. Based on this, a new closedform expression for the cumulative distribution function of the SIR is evaluated, from which the outage probability and the ergodic capacity are derived. Further insights are established by analyzing the asymptotic outage probability and the asymptotic ergodic capacity in the high transmission power regime. In particular, it is corroborated that the asymptotic outage diversity gain is equal to the multipath gain of the frequency selective channel in the secondary network. The asymptotic ergodic capacity also gives new insight into the additional power cost for different network parameters while maintaining a specified target ergodic capacity. Illustrative numerical examples are presented to validate the outage probability and ergodic capacity under different interference power profiles.

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Radio-frequency (RF) impairments in the transceiver hardware of communication systems (e.g., phase noise (PN), high power amplifier (HPA) nonlinearities, or in-phase/quadrature-phase (I/Q) imbalance) can severely degrade the performance of traditional multiple-input multiple-output (MIMO) systems. Although calibration algorithms can partially compensate these impairments, the remaining distortion still has substantial impact. Despite this, most prior works have not analyzed this type of distortion. In this paper, we investigate the impact of residual transceiver hardware impairments on the MIMO system performance. In particular, we consider a transceiver impairment model, which has been experimentally validated, and derive analytical ergodic capacity expressions for both exact and high signal-to-noise ratios (SNRs). We demonstrate that the capacity saturates in the high-SNR regime, thereby creating a finite capacity ceiling. We also present a linear approximation for the ergodic capacity in the low-SNR regime, and show that impairments have only a second-order impact on the capacity. Furthermore, we analyze the effect of transceiver impairments on large-scale MIMO systems; interestingly, we prove that if one increases the number of antennas at one side only, the capacity behaves similar to the finite-dimensional case. On the contrary, if the number of antennas on both sides increases with a fixed ratio, the capacity ceiling vanishes; thus, impairments cause only a bounded offset in the capacity compared to the ideal transceiver hardware case.

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We define the Schur multipliers of a separable von Neumann algebra M with Cartan masa A, generalising the classical Schur multipliers of B(` 2 ). We characterise these as the normal A-bimodule maps on M. If M contains a direct summand isomorphic to the hyper- finite II1 factor, then we show that the Schur multipliers arising from the extended Haagerup tensor product A ⊗eh A are strictly contained in the algebra of all Schur multipliers.

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We say that the Peano theorem holds for a topological vector space $E$ if, for any continuous mapping $f : {\Bbb R}\times E \to E$ and any $(t(0), x(0))$ is an element of ${\Bbb R}\times E$, the Cauchy problem $\dot x(t) = f(t,x(t))$, $x(t(0)) = x(0)$, has a solution in some neighborhood of $t(0)$. We say that the weak version of Peano theorem holds for $E$ if, for any continuous map $f : {\Bbb R}\times E \to E$, the equation $\dot x(t) = f (t, x(t))$ has a solution on some interval. We construct an example (answering a question posed by S. G. Lobanov) of a Hausdorff locally convex topological vector space E for which the weak version of Peano theorem holds and the Peano theorem fails to hold. We also construct a Hausdorff locally convex topological vector space E for which the Peano theorem holds and any barrel in E is neither compact nor sequentially compact.

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The hypoxia-inducible factors (HIFs; isoforms HIF-1 alpha, HIF-2 alpha, HIF-3 alpha) mediate many responses to hypoxia. Their regulation is principally by oxygen-dependent degradation, which is initiated by hydroxylation of specific proline residues followed by binding of von Hippel-Lindau (VHL) protein. Chuvash polycythemia is a disorder with elevated HIF. It arises through germline homozygosity for hypomorphic VHL alleles and has a phenotype of hematological, cardiopulmonary, and metabolic abnormalities. This study explores the phenotype of two other HIF pathway diseases: classic VHL disease and HIF-2 alpha gain-of-function mutation. No cardiopulmonary abnormalities were detected in classic VHL disease. HIF-2 alpha gain-of-function mutations were associated with pulmonary hypertension, increased cardiac output, increased heart rate, and increased pulmonary ventilation relative to metabolism. Comparison of the HIF-2 alpha gain-of-function responses with data from studies of Chuvash polycythemia suggested that other aspects of the Chuvash phenotype were diminished or absent. In classic VHL disease, patients are germline heterozygous for mutations in VHL, and the present results suggest that a single wild-type allele for VHL is sufficient to maintain normal cardiopulmonary function. The HIF-2 alpha gain-of-function phenotype may be more limited than the Chuvash phenotype either because HIF-1 alpha is not elevated in the former condition, or because other HIF-independent functions of VHL are perturbed in Chuvash polycythemia.-Formenti, F., Beer, P. A., Croft, Q. P. P., Dorrington, K. L., Gale, D. P., Lappin, T. R. J., Lucas, G. S., Maher, E. R., Maxwell, P. H., McMullin, M. F., O'Connor, D. F., Percy, M. J., Pugh, C. W., Ratcliffe, P. J., Smith, T. G., Talbot, N. P., Robbins, P. A. Cardiopulmonary function in two human disorders of the hypoxia-inducible factor (HIF) pathway: von Hippel-Lindau disease and HIF-2 alpha gain-of-function mutation. FASEB J. 25, 2001-2011 (2011). www.fasebj.org