The average crossing number of equilateral random polygons.

In this paper, we study the average crossing number of equilateral random walks and polygons. We show that the mean average crossing number ACN of all equilateral random walks of length n is of the form . A similar result holds for equilateral random polygons. These results are confirmed by our numerical studies. Furthermore, our numerical studies indicate that when random polygons of length n are divided into individual knot types, the for each knot type can be described by a function of the form where a, b and c are constants depending on and n0 is the minimal number of segments required to form . The profiles diverge from each other, with more complex knots showing higher than less complex knots. Moreover, the profiles intersect with the ACN profile of all closed walks. These points of intersection define the equilibrium length of , i.e., the chain length at which a statistical ensemble of configurations with given knot type -upon cutting, equilibration and reclosure to a new knot type -does not show a tendency to increase or decrease . This concept of equilibrium length seems to be universal, and applies also to other length-dependent observables for random knots, such as the mean radius of gyration Rg.

Fourth order pseudo maximum likelihood methods

We extend PML theory to account for information on the conditional moments up to order four, but without assuming a parametric model, to avoid a risk of misspecification of the conditional distribution. The key statistical tool is the quartic exponential family, which allows us to generalize the PML2 and QGPML1 methods proposed in Gourieroux et al. (1984) to PML4 and QGPML2 methods, respectively. An asymptotic theory is developed. The key numerical tool that we use is the Gauss-Freud integration scheme that solves a computational problem that has previously been raised in several fields. Simulation exercises demonstrate the feasibility and robustness of the methods [Authors]

Therapeutic drug monitoring of imatinib: Bayesian and alternative methods to predict trough levels

Background: The imatinib trough plasma concentration (C(min)) correlates with clinical response in cancer patients. Therapeutic drug monitoring (TDM) of plasma C(min) is therefore suggested. In practice, however, blood sampling for TDM is often not performed at trough. The corresponding measurement is thus only remotely informative about C(min) exposure. Objectives: The objectives of this study were to improve the interpretation of randomly measured concentrations by using a Bayesian approach for the prediction of C(min), incorporating correlation between pharmacokinetic parameters, and to compare the predictive performance of this method with alternative approaches, by comparing predictions with actual measured trough levels, and with predictions obtained by a reference method, respectively. Methods: A Bayesian maximum a posteriori (MAP) estimation method accounting for correlation (MAP-ρ) between pharmacokinetic parameters was developed on the basis of a population pharmacokinetic model, which was validated on external data. Thirty-one paired random and trough levels, observed in gastrointestinal stromal tumour patients, were then used for the evaluation of the Bayesian MAP-ρ method: individual C(min) predictions, derived from single random observations, were compared with actual measured trough levels for assessment of predictive performance (accuracy and precision). The method was also compared with alternative approaches: classical Bayesian MAP estimation assuming uncorrelated pharmacokinetic parameters, linear extrapolation along the typical elimination constant of imatinib, and non-linear mixed-effects modelling (NONMEM) first-order conditional estimation (FOCE) with interaction. Predictions of all methods were finally compared with 'best-possible' predictions obtained by a reference method (NONMEM FOCE, using both random and trough observations for individual C(min) prediction). Results: The developed Bayesian MAP-ρ method accounting for correlation between pharmacokinetic parameters allowed non-biased prediction of imatinib C(min) with a precision of ±30.7%. This predictive performance was similar for the alternative methods that were applied. The range of relative prediction errors was, however, smallest for the Bayesian MAP-ρ method and largest for the linear extrapolation method. When compared with the reference method, predictive performance was comparable for all methods. The time interval between random and trough sampling did not influence the precision of Bayesian MAP-ρ predictions. Conclusion: Clinical interpretation of randomly measured imatinib plasma concentrations can be assisted by Bayesian TDM. Classical Bayesian MAP estimation can be applied even without consideration of the correlation between pharmacokinetic parameters. Individual C(min) predictions are expected to vary less through Bayesian TDM than linear extrapolation. Bayesian TDM could be developed in the future for other targeted anticancer drugs and for the prediction of other pharmacokinetic parameters that have been correlated with clinical outcomes.

Calculation of correction factors for ionization chamber measurements with small fields in low-density media.

The quantity of interest for high-energy photon beam therapy recommended by most dosimetric protocols is the absorbed dose to water. Thus, ionization chambers are calibrated in absorbed dose to water, which is the same quantity as what is calculated by most treatment planning systems (TPS). However, when measurements are performed in a low-density medium, the presence of the ionization chamber generates a perturbation at the level of the secondary particle range. Therefore, the measured quantity is close to the absorbed dose to a volume of water equivalent to the chamber volume. This quantity is not equivalent to the dose calculated by a TPS, which is the absorbed dose to an infinitesimally small volume of water. This phenomenon can lead to an overestimation of the absorbed dose measured with an ionization chamber of up to 40% in extreme cases. In this paper, we propose a method to calculate correction factors based on the Monte Carlo simulations. These correction factors are obtained by the ratio of the absorbed dose to water in a low-density medium □D(w,Q,V1)(low) averaged over a scoring volume V₁ for a geometry where V₁ is filled with the low-density medium and the absorbed dose to water □D(w,QV2)(low) averaged over a volume V₂ for a geometry where V₂ is filled with water. In the Monte Carlo simulations, □D(w,QV2)(low) is obtained by replacing the volume of the ionization chamber by an equivalent volume of water, according to the definition of the absorbed dose to water. The method is validated in two different configurations which allowed us to study the behavior of this correction factor as a function of depth in phantom, photon beam energy, phantom density and field size.

Pacemakers and magnetic resonance imaging: Current status and survey in Switzerland.

Electromagnetic fields arising from magnetic resonance imaging (MRI) can cause various clinically relevant functional disturbances in patients with cardiac pacemakers. Consequently, an implanted pacemaker is generally considered a contraindication for an MRI scan. With approximately 60 million MRI scans performed worldwide per year, MRI may be indicated for an estimated majority of pacemaker patients during the lifetime of their pacemakers. The availability of MR conditional pacemakers with CE labelling is of particular advantage since they allow the safe use of pacemakers in MRI. In this article the current state of knowledge on pacemakers and MR imaging is discussed. We present the results of a survey conducted among Swiss radiologists to assess current practice in patients with pacemakers.

Dissociation of allocentric and egocentric orientation: Effect on hippocampal place cells and place navigation

Navigation by means of cognitive maps appears to require the hippocampus; hippocampal place cells (PCs) appear to store spatial memories because their discharge is confined to cell-specific places called firing fields (FFs). Experiments with rats manipulated idiothetic and landmark-related information to understand the relationship between PC activity and spatial rotation. Rotating a circular arena in the caused a discrepancy between these cuse. This discrepancy caused most FFs to disappear in both the arena and room reference frames. However, FFs persisted in the rotating arena frame when the discrepancy was reduced by darkness or by a card in the arena. The discrepancy was increased by "field clamping" the rat in a room-defined FF location by rotations that countered its locomotion. Most FFs disspared and reappeared an hour or more after the clamp. Place-avoidance experiments showed that navigation uses independent idiothetic and exteroceptive memories. Rats learned to avoid the unmarked footshock region within a circular arena. When acquired on the stable arena in the light, the location of the punishment was learned by using both room and idiothetic cues; extinction in the dark transferred to the following session in the light. If, however, extinction occured during rotation, only the arena-frame avoidance was extinguished in darkness; the room-defined location was avoided when the light were turned back on. Idiothetic memory of room-defined avoidance was not formed during rotation in light; regardless of rotation with a randomly dispersed pellet. The resulting behaviour alternated between random pellet searching and target-directed navigation, making it possible to examine PC correlates of these two classes of spatial behaviour. The independence of idiothetic and exteroceptive spatial memories and the disruption of PC firing during rotation suggest that PCs may not be necessary for spatial cognition; this idea can be tested by recording during place-avoidance and preference tasks.

Use of high-resolution geophysical data to characterize heterogeneous aquifers: influence of data integration method on hydrological predictions

The integration of geophysical data into the subsurface characterization problem has been shown in many cases to significantly improve hydrological knowledge by providing information at spatial scales and locations that is unattainable using conventional hydrological measurement techniques. The investigation of exactly how much benefit can be brought by geophysical data in terms of its effect on hydrological predictions, however, has received considerably less attention in the literature. Here, we examine the potential hydrological benefits brought by a recently introduced simulated annealing (SA) conditional stochastic simulation method designed for the assimilation of diverse hydrogeophysical data sets. We consider the specific case of integrating crosshole ground-penetrating radar (GPR) and borehole porosity log data to characterize the porosity distribution in saturated heterogeneous aquifers. In many cases, porosity is linked to hydraulic conductivity and thus to flow and transport behavior. To perform our evaluation, we first generate a number of synthetic porosity fields exhibiting varying degrees of spatial continuity and structural complexity. Next, we simulate the collection of crosshole GPR data between several boreholes in these fields, and the collection of porosity log data at the borehole locations. The inverted GPR data, together with the porosity logs, are then used to reconstruct the porosity field using the SA-based method, along with a number of other more elementary approaches. Assuming that the grid-cell-scale relationship between porosity and hydraulic conductivity is unique and known, the porosity realizations are then used in groundwater flow and contaminant transport simulations to assess the benefits and limitations of the different approaches.

Conditional deletion of ferritin h in mice reduces B and T lymphocyte populations.

The immune system and iron availability are intimately linked as appropriate iron supply is needed for cell proliferation, while excess iron, as observed in hemochromatosis, may reduce subsets of lymphocytes. We have tested the effects of a ferritin H gene deletion on lymphocytes. Mx-Cre mediated conditional deletion of ferritin H in bone marrow reduced the number of mature B cells and peripheral T cells in all lymphoid organs. FACS analysis showed an increase in the labile iron pool, enhanced reactive oxygen species formation and mitochondrial depolarization. The findings were confirmed by a B-cell specific deletion using Fth(lox/lox) ; CD19-Cre mice. Mature B cells were strongly under-represented in bone marrow and spleen of the deleted mice, whereas pre-B and immature B cells were not affected. Bone marrow B cells showed increased proliferation as judged by the number of cells in S and G2/M phase as well as BrdU incorporation. Upon in vitro culture with B-cell activating factor of the tumor necrosis factor family (BAFF), ferritin H-deleted spleen B cells showed lower survival rates than wild type cells. This was partially reversed with iron-chelator deferiprone. The loss of T cells was also confirmed by a T cell-specific deletion in Fth(lox/lox) ;CD4-Cre mice. Our data show that ferritin H is required for B and T cell survival by actively reducing the labile iron pool. They further suggest that natural B and T cell maturation is influenced by intracellular iron levels and possibly deregulated in iron excess or deprivation.

Construction and analysis of a new conditional ferritin H knockout mouse strain/

Résumé Le fer joue un rôle important dans la plupart des fonctions biologiques mais sa présence excessive provoque la production de molécules réactives d'oxygène (ROS) qui peuvent contribuer à diverses maladies. La protéine de stockage du fer, la ferritine H, capte l'excès en fer et le stocke sous forme non-toxique, ce qui empêche des dommages potentiels. La délétion de la ferritine H dans des souris knock-out a été essayée antérieurement, mais ces souris mouraient au stade précoce du développement embryonnaire. Pour étudier l'importance du fer, et en particulier son stockage dans la ferritine, et pour pouvoir mieux comprendre les fonctions de la ferritine H, nous avons créé un modèle de souris knock-out conditionnelles de la ferritine H, selon le système classique de Cre-LoxP. Le premier exon et la région du promoteur du gène de la ferritine H ont été entourés de sites loxP. La mortalité embryonnaire provoquée par la délétion constitutive du gène de la ferritine H a été confirmée en croisant nos souris avec des souris exprimant nestin-Cre1. En croisant nos souris avec des souris transgéniques Mx-Cre, nous avons observé que l'induction de Cre par injection de polyI-polyC provoque la délétion presque complète de la ferritine H dans le foie (> 99%) et la rate (> 88%). Ces tissus ont également perdu une grande partie de leur réserve de fer. Cette observation apporte pour la première fois la preuve in vivo que la ferritine H est indispensable pour le stockage du fer, que les fonctions de la ferritine H et de la ferritine L ne sont pas équivalentes, et que la ferritine L ne peut pas assumer seule la fonction de stockage du fer. Dans le foie des souris knock-out, l'expression de l'ARN messager de l'hepcidine a été induite après 10 jours. En même temps, l'expression de l'ARN messager des gènes codant pour des protéines de l'absorption de fer (DMT1, ferroportin, Dcytb1 et hephaestin) a été réprimée mais dans le duodénum seulement. L'expression d'hepcidine est inversément corrélée avec celle des gènes liés à l'absorption de fer. Cette observation corrobore des études antérieures. Mais, en plus, elle montre également que cette répression se produit seulement dans l'intestin. Nous pouvons ainsi tirer la conclusion suivante : ou bien l'hepcidine a un récepteur spécifique dans le duodénum ou bien les gènes liés à l'absorption de fer dans le duodénum ont un facteur spécifique de transcription sensible à l'hepcidine. Aucune répression de DMT1 et de ferroportin n'a été observée dans les macrophages de la rate après l'induction d'hepcidine. La délétion de ferritine H a entraîné une augmentation du taux de mortalité des cellules hépatiques, ainsi que des altérations dans l'architecture normale du tissu de la rate. Vu par l'immunohistologie, le nombre de lymphocytes B et T était réduit dans la rate, tendant à démontrer que la ferritine H et l'homéostase du fer jouent un rôle dans l'immunité. En conclusion, le modèle de souris knock-out conditionnelles de la ferritine H nous fournit un outil précieux pour l'étude in vivo du rôle joué par la ferritine dans l'homéostase du fer, dans les dommages créés par les ROS, ainsi que dans l'apoptose et l'immunité. Summary Iron plays an important role in most biological functions. However, excess of iron results in production of reactive oxygen species (ROS) which could substantially contribute to pathology of various diseases. Ferritin H scavenges excess of iron and stores it in non-toxic form and potentially prevents the damage. Fenitin H targeting in mice has been attempted before, however, straight knockout was lethal in early embryonic stage. To study the role of iron and its storage protein ferritin and to further elucidate ferritin H functions, we aimed at creating a conditional ferritin H knockout mouse model by classical Cre-LoxP system. First exon along with promoter region of the ferritin H gene was foxed. Embryonic lethality of the constitutive ferritin H deletion was confirmed by crossing the foxed mice with mice expressing nestin Cre-1 as transgene. Almost complete deletion was observed in liver (> 99%) and spleen (>88%) upon induction of Cre by injecting polyI-polyC in Fth Lox/Lox; MxCre mice. These tissues also lost substantial fraction of their iron stores. This provides first in vivo evidence that ferritin H is required for iron storage, ferritin H and L functions are not redundant and that ferritin L cannot perform iron storage function alone. Hepcidin mRNA expression was induced after 10 days in the livers of deleted mice and, simultaneously, mRNA expression of iron absorption related genes (DMT 1, ferroportin, Dcytb1 and hephaestin) was repressed in duodenum only. Hepcidin expression is inversely correlated with that of duodenal iron absorption related genes. This is in agreement with previous studies. However, we also show that this repression happens only in intestine. This leads to the conclusion that either hepcidin has a specific receptor in duodenum or the iron absorption related genes have duodenum specific transcription factor that is responsive to hepcidin. No repression of DMT1 and ferroportin was observed in spleen macrophages upon hepcidin induction. Ferritin H deletion showed increased cell death in liver and disruption of normal architecture of spleen. B lymphocytes were reduced in spleen on immunohistology which point towards a role of ferritin H and iron homeostasis in immunity. In conclusion, ferritin H conditional knockout mouse model provides us with an invaluable tool to study the in vivo role of ferritin H in iron homeostasis, ROS mediated damage, apoptosis and immunity.

Bilateral sequential nonarteritic anterior ischemic optic neuropathy: a comparison of visual outcomes in fellow eyes using quantitative analysis of goldmann visual fields.

OBJECTIVE To better define the concordance of visual loss in patients with nonarteritic anterior ischemic optic neuropathy (NAION). METHODS The medical records of 86 patients with bilateral sequential NAION were reviewed retrospectively, and visual function was assessed using visual acuity, Goldmann visual fields, color vision, and relative afferent papillary defect. A quantitative total visual field score and score per quadrant were analyzed for each eye using the numerical Goldmann visual field scoring method. RESULTS Outcome measures were visual acuity, visual field, color vision, and relative afferent papillary defect. A statistically significant correlation was found between fellow eyes for multiple parameters, including logMAR visual acuity (P = .01), global visual field (P < .001), superior visual field (P < .001), and inferior visual field (P < .001). The mean deviation of total (P < .001) and pattern (P < .001) deviation analyses was significantly less between fellow eyes than between first and second eyes of different patients. CONCLUSIONS Visual function between fellow eyes showed a fair to moderate correlation that was statistically significant. The pattern of vision loss was also more similar in fellow eyes than between eyes of different patients. These results may help allow better prediction of visual outcome for the second eye in patients with NAION.

The average inter-crossing number of equilateral random walks and polygons

In this paper, we study the average inter-crossing number between two random walks and two random polygons in the three-dimensional space. The random walks and polygons in this paper are the so-called equilateral random walks and polygons in which each segment of the walk or polygon is of unit length. We show that the mean average inter-crossing number ICN between two equilateral random walks of the same length n is approximately linear in terms of n and we were able to determine the prefactor of the linear term, which is a = (3 In 2)/(8) approximate to 0.2599. In the case of two random polygons of length n, the mean average inter-crossing number ICN is also linear, but the prefactor of the linear term is different from that of the random walks. These approximations apply when the starting points of the random walks and polygons are of a distance p apart and p is small compared to n. We propose a fitting model that would capture the theoretical asymptotic behaviour of the mean average ICN for large values of p. Our simulation result shows that the model in fact works very well for the entire range of p. We also study the mean ICN between two equilateral random walks and polygons of different lengths. An interesting result is that even if one random walk (polygon) has a fixed length, the mean average ICN between the two random walks (polygons) would still approach infinity if the length of the other random walk (polygon) approached infinity. The data provided by our simulations match our theoretical predictions very well.

Subknots in ideal knots, random knots, and knotted proteins.

We introduce disk matrices which encode the knotting of all subchains in circular knot configurations. The disk matrices allow us to dissect circular knots into their subknots, i.e. knot types formed by subchains of the global knot. The identification of subknots is based on the study of linear chains in which a knot type is associated to the chain by means of a spatially robust closure protocol. We characterize the sets of observed subknot types in global knots taking energy-minimized shapes such as KnotPlot configurations and ideal geometric configurations. We compare the sets of observed subknots to knot types obtained by changing crossings in the classical prime knot diagrams. Building upon this analysis, we study the sets of subknots in random configurations of corresponding knot types. In many of the knot types we analyzed, the sets of subknots from the ideal geometric configurations are found in each of the hundreds of random configurations of the same global knot type. We also compare the sets of subknots observed in open protein knots with the subknots observed in the ideal configurations of the corresponding knot type. This comparison enables us to explain the specific dispositions of subknots in the analyzed protein knots.