Uniform Maps Research Articles

Parallel transmit hybrid pulse design for controlled on-resonance magnetization transfer in R1 mapping at 7T.

This work proposes a "hybrid" RF pulse design method for parallel transmit (pTx) systems to simultaneously control flip angle and root-mean-squared ( ). These pulses are generally only designed for flip angle, however, this can lead to uncontrolled , which then leads to variable magnetization transfer (MT) effects. We demonstrate the hybrid design approach for quantitative imaging where both flip angle and are important. A dual cost function optimization is performed containing the normalized mean squared errors of the flip angle and distributions weighted by a parameter . Simulations were conducted to study the behavior of both properties when simultaneously optimizing them. In vivo experiments on a 7T MRI system with an 8-channel pTx head coil were carried out to study the effect of the hybrid design approach on variable flip angle (= 1/T1) mapping. Simulations showed that both flip angle and can be homogenized simultaneously without detriment to either when compared to an individual optimization. By homogenizing flip angle and , maps were more uniform (coefficient of variation 6.6% vs. 13.0%) compared to those acquired with pulses that only homogenized flip angle. The proposed hybrid design homogenizes on-resonance MT effects while homogenizing the flip angle distribution, with only a small detriment in the latter compared to a pulse that just homogenizes flip angle. This improved mapping by controlling incidental MT effects, yielding more uniform maps.

Impact of the superimposition reference area on intraoral scanning accuracy in a partially dentate maxilla

Statement of problemThe alignment of 3-dimensional (3D) files involves selecting a reference area before performing a local best fit alignment during the digital scan superimposition and is essential for comparing digital scans. Scan alignment relies on both reference area location and the alignment algorithm. However, a consensus on the impact of different reference areas on intraoral scanning accuracy is lacking. PurposeThe purpose of this in vitro study was to assess the impact of 3 superimposition reference areas on the accuracy of 3 intraoral scanners for a partially dentate maxilla. Material and methodsA Kennedy class II resin cast was scanned using 3 intraoral scanners (Primescan, TRIOS 3, and Emerald) outputting 30 digital scans (10 per scanner). Test scans from intraoral scanners were subsequently compared with a reference digital standard tessellation language file generated by a laboratory scanner with validated accuracy. The files were superimposed using best fit alignment for each intraoral scanner using 3 different superimposition reference areas (whole region of interest, palate, and all teeth). Accuracy was assessed by using a 3D analysis program (Geomagic Control X; 3D systems) for each scanner at 4 preselected areas. Test and reference scan differences were depicted on color maps and quantified via root mean square deviations. Differences were analyzed using regression analysis with the post hoc student t test and Bonferroni correction (α=.05). ResultsThe TRIOS 3 and Emerald produced positive deviations in the palatal color maps, whereas Primescan produced more uniform color maps, regardless of the superimposition strategy used. Primescan exhibited the best accuracy (trueness and precision) in both palatal and bounded edentulous areas, regardless of the superimposition reference area. The TRIOS 3 recorded the highest distal extension trueness (ranging from 42.9±7.7 µm to 65 ±19.5 µm), and Primescan achieved the highest precision (ranging from 28.5 ±9.8 µm to 48.9 ±16.9 µm), regardless of the superimposition area. Emerald demonstrated the highest teeth trueness (ranging from 31.6 ±6.8 µm to 69.6 ±11.5 µm), while Primescan produced the highest precision (ranging from 17.9 ±6.1 µm to 30.7 ±9.2 µm), regardless of the reference area used. ConclusionsThe chosen reference area for best fit alignment significantly influenced digital scan accuracy (P<.001). Primescan displayed the highest palatal and bounded edentulous area accuracy, with TRIOS 3 recording the highest distal extension trueness. Emerald recorded the highest teeth trueness and Primescan recorded the highest distal extension and tooth precision. All conclusions were independent of the superimposition strategy used.

Multi-Echo Complex Quantitative Susceptibility Mapping and Quantitative Blood Oxygen Level-Dependent Magnitude (mcQSM + qBOLD or mcQQ) for Oxygen Extraction Fraction (OEF) Mapping.

Oxygen extraction fraction (OEF), the fraction of oxygen that tissue extracts from blood, is an essential biomarker used to directly assess tissue viability and function in neurologic disorders. In ischemic stroke, for example, increased OEF can indicate the presence of penumbra-tissue with low perfusion yet intact cellular integrity-making it a primary therapeutic target. However, practical OEF mapping methods are not currently available in clinical settings, owing to the impractical data acquisitions in positron emission tomography (PET) and the limitations of existing MRI techniques. Recently, a novel MRI-based OEF mapping technique, termed QQ, was proposed. It shows high potential for clinical use by utilizing a routine sequence and removing the need for impractical multiple gas inhalations. However, QQ relies on the assumptions of Gaussian noise in susceptibility and multi-echo gradient echo (mGRE) magnitude signals for OEF estimation. This assumption is unreliable in low signal-to-noise ratio (SNR) regions like disease-related lesions, risking inaccurate OEF estimation and potentially impacting clinical decisions. Addressing this, our study presents a novel multi-echo complex QQ (mcQQ) that models realistic Gaussian noise in mGRE complex signals. We implemented mcQQ using a deep learning framework (mcQQ-NET) and compared it with the existing QQ-NET in simulations, ischemic stroke patients, and healthy subjects, using identical training and testing datasets and schemes. In simulations, mcQQ-NET provided more accurate OEF than QQ-NET. In the subacute stroke patients, mcQQ-NET showed a lower average OEF ratio in lesions relative to unaffected contralateral normal tissue than QQ-NET. In the healthy subjects, mcQQ-NET provided uniform OEF maps, similar to QQ-NET, but without unrealistically high OEF outliers in areas of low SNR, such as SNR ≤ 15 (dB). Therefore, mcQQ-NET improves OEF accuracy by more accurately reflecting realistic Gaussian noise in complex mGRE signals. Its enhanced sensitivity to OEF abnormalities, based on more realistic biophysics modeling, suggests that mcQQ-NET has potential for investigating tissue variability in neurologic disorders.

Nonuniform sliding-window reconstruction for accelerated dual contrast agent quantification with MR fingerprinting

ObjectiveMR fingerprinting (MRF) can enable preclinical studies of cell tracking by quantifying multiple contrast agents simultaneously, but faster scan times are required for in vivo applications. Sliding window (SW)-MRF is one option for accelerating MRF, but standard implementations are not sufficient to preserve the accuracy of T2*, which is critical for tracking iron-labelled cells in vivo.PurposeTo develop a SW approach to MRF which preserves the T2* accuracy required for accelerated concentration mapping of iron-labelled cells on single-channel preclinical systems.MethodsA nonuniform SW was applied to the MRF sequence and dictionary. Segments of the sequence most sensitive to T2* were subject to a shorter window length, preserving the T2* sensitivity. Phantoms containing iron-labelled CD8+ T cells and gadolinium were used to compare 24× undersampled uniform and nonuniform SW-MRF parameter maps. Dual concentration maps were generated for both uniform and nonuniform MRF and compared.ResultsLin’s concordance correlation coefficient, compared to gold standard parameter values, was much greater for nonuniform SW-MRF than for uniform SW-MRF. A Wilcoxon signed-rank test showed no significant difference between nonuniform SW-MRF and gold standards. Nonuniform SW-MRF outperformed the uniform SW-MRF concentration maps for all parameters, providing a balance between T2* sensitivity of short window lengths, and SNR of longer window lengths.ConclusionsNonuniform SW-MRF improves the accuracy of matching compared to uniform SW-MRF, allowing higher accelerated concentration mapping for preclinical systems.

Basic Survey Scheduling for the Wide Field Survey Telescope (WFST)

Aiming at improving the survey efficiency of the Wide Field Survey Telescope, we have developed a basic scheduling strategy that takes into account the telescope characteristics, observing conditions, and weather conditions at the Lenghu site. The sky area is divided into rectangular regions, referred to as “tiles,” with a size of 2.°577 × 2.°634 slightly smaller than the focal area of the mosaic CCDs. These tiles are continuously filled in annulars parallel to the equator. The brightness of the sky background, which varies with the moon phase and distance from the moon, plays a significant role in determining the accessible survey fields. Approximately 50 connected tiles are grouped into one block for observation. To optimize the survey schedule, we perform simulations by taking into account the length of exposures, data readout, telescope slewing, and all relevant observing conditions. We utilize the Greedy Algorithm for scheduling optimization. Additionally, we propose a dedicated dithering pattern to cover the gaps between CCDs and the four corners of the mosaic CCD array, which are located outside of the 3° field of view. This dithering pattern helps to achieve relatively uniform exposure maps for the final survey outputs.

Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity

We set the foundation for a series of works aimed at proving strong relations between uniform random planar maps and Liouville quantum gravity (LQG). Our method relies on a bijective encoding of site-percolated planar triangulations by certain 2D lattice paths. Our bijection parallels in the discrete setting the mating-of-trees framework of LQG and Schramm-Loewner evolutions (SLE) introduced by Duplantier, Miller, and Sheffield. Combining these two correspondences allows us to relate uniform site-percolated triangulations to 8 / 3 \sqrt {8/3} -LQG and SLE 6 _6 . In particular, we establish the convergence of several functionals of the percolation model to continuous random objects defined in terms of 8 / 3 \sqrt {8/3} -LQG and SLE 6 _6 . For instance, we show that the exploration tree of the percolation converges to a branching SLE 6 _6 , and that the collection of percolation cycles converges to the conformal loop ensemble CLE 6 _6 . We also prove convergence of counting measure on the pivotal points of the percolation. Our results play an essential role in several other works, including a program for showing convergence of the conformal structure of uniform triangulations and works which study the behavior of random walk on the uniform infinite planar triangulation.

Integrative data system for monitoring biota and natural habitats in the Israeli Eastern Mediterranean marine environment.

An integrative data system for monitoring the biota of the Mediterranean waters of Israel as well as selected records from adjacent Levantine basin regions is presented here, aimed at providing data and research tools for long-term bio-geographic and ecological studies and more important, providing background data for assisting governmental regulators to establish educated habitat-oriented environmental policy. The system relies on the geographic information system (GIS) online map-based platform and contains at present the following components: biotic database of ~ 170,000 recorded sampling events; uniform habitat maps of 63 benthic habitats and 2 pelagic ones, constructed using relevant bathymetric features and biotic community compositions; bathymetric hill-shade map; depth contours; raster depth grid and human interference map. Other informative auxiliary maps are planned to be added (e.g., map of potential pockmark sites, detailed maps of tiny carbonate crust nolls and more). A number of 883 cited documents were listed by us for potential extraction of sampling efforts, most of them areavailable to us as PDFs andare available also to the users, excluding copyright-protected ones. Forty-three major projects were depicted in addition to a variety of small studies (e.g., university theses). Thirty-five sampling devices were documented and described, and 3187 species-level identifications were already recorded. In addition, the system provides access to description of sampling devices and pictures of species and seascapes. New data is continuously deposited to the system and the system is flexible, allowing future addition of new types of information. The system site is accessible through the link: https://experience.arcgis.com/experience/40e86605ff4d4e5096ed2c901fec2a2f .

A novel simulation paradigm utilising MRI-derived phosphene maps for cortical prosthetic vision

Objective. We developed a realistic simulation paradigm for cortical prosthetic vision and investigated whether we can improve visual performance using a novel clustering algorithm. Approach. Cortical visual prostheses have been developed to restore sight by stimulating the visual cortex. To investigate the visual experience, previous studies have used uniform phosphene maps, which may not accurately capture generated phosphene map distributions of implant recipients. The current simulation paradigm was based on the Human Connectome Project retinotopy dataset and the placement of implants on the cortices from magnetic resonance imaging scans. Five unique retinotopic maps were derived using this method. To improve performance on these retinotopic maps, we enabled head scanning and a density-based clustering algorithm was then used to relocate centroids of visual stimuli. The impact of these improvements on visual detection performance was tested. Using spatially evenly distributed maps as a control, we recruited ten subjects and evaluated their performance across five sessions on the Berkeley Rudimentary Visual Acuity test and the object recognition task. Main results. Performance on control maps is significantly better than on retinotopic maps in both tasks. Both head scanning and the clustering algorithm showed the potential of improving visual ability across multiple sessions in the object recognition task. Significance. The current paradigm is the first that simulates the experience of cortical prosthetic vision based on brain scans and implant placement, which captures the spatial distribution of phosphenes more realistically. Utilisation of evenly distributed maps may overestimate the performance that visual prosthetics can restore. This simulation paradigm could be used in clinical practice when making plans for where best to implant cortical visual prostheses.

Towards risk-targeted seismic hazard models for Europe

Standards and Codes of Practice for designing new constructions and for assessing and strengthening existing ones are usually based on uniform hazard maps, where different Limit States (LSs) are associated with different hazard-exceedance probabilities. This approach yields non-homogeneous LS-exceedance probabilities across a territory, thus failing to achieve the goal of uniform risk throughout a territory. Such lack of uniformity stems from estimating the probability of failure using capacity and demand models. If the capacity of new constructions—or the capacity increase of strengthened existing constructions—are designed based on a prescribed hazard-exceedance probability, then the seismic risk depends on both the structure (depending on the design philosophy and corresponding design objectives), through the capacity model, and the location, through the hazard model. The aim of this study is threefold. First, it provides a seismic probability assessment formulation and a risk-targeted intensity measure based on a linear model in log–log coordinates of the hazard, under the assumption of log-normal capacity and demand. The proposed framework introduces a factor that multiplies the code hazard-based demand to account either for intentional (from design) over-capacity or for undesired (e.g., in existing constructions) under-capacity. Second, this paper shows an application to peak ground accelerations in Europe considering parameters taken from Standards and Codes of Practice. The developed framework is used to determine the risk-target levels of peak ground acceleration used for design in Europe, for both new and existing constructions. Third, the obtained target risk levels are used to determine a risk-based intensity modification factor and a risk-based mean return period modification factor, which can be readily implemented in current Standards to achieve risk-targeted design actions, with equal LS-exceedance probability across the territory. The framework is independent of the chosen hazard-based intensity measure, be it the commonly used peak ground acceleration or any other measure. The results highlight that in large areas of Europe the design peak ground acceleration should be increased to achieve the proposed seismic risk target and that this is particularly significant for existing constructions, given their larger uncertainties and typical low capacity with respect to the code hazard-based demand.

Real-time, acquisition parameter-free voxel-wise patient-specific Monte Carlo dose reconstruction in whole-body CT scanning using deep neural networks

ObjectiveWe propose a deep learning-guided approach to generate voxel-based absorbed dose maps from whole-body CT acquisitions.MethodsThe voxel-wise dose maps corresponding to each source position/angle were calculated using Monte Carlo (MC) simulations considering patient- and scanner-specific characteristics (SP_MC). The dose distribution in a uniform cylinder was computed through MC calculations (SP_uniform). The density map and SP_uniform dose maps were fed into a residual deep neural network (DNN) to predict SP_MC through an image regression task. The whole-body dose maps reconstructed by the DNN and MC were compared in the 11 test cases scanned with two tube voltages through transfer learning with/without tube current modulation (TCM). The voxel-wise and organ-wise dose evaluations, such as mean error (ME, mGy), mean absolute error (MAE, mGy), relative error (RE, %), and relative absolute error (RAE, %), were performed.ResultsThe model performance for the 120 kVp and TCM test set in terms of ME, MAE, RE, and RAE voxel-wise parameters was − 0.0302 ± 0.0244 mGy, 0.0854 ± 0.0279 mGy, − 1.13 ± 1.41%, and 7.17 ± 0.44%, respectively. The organ-wise errors for 120 kVp and TCM scenario averaged over all segmented organs in terms of ME, MAE, RE, and RAE were − 0.144 ± 0.342 mGy, and 0.23 ± 0.28 mGy, − 1.11 ± 2.90%, 2.34 ± 2.03%, respectively.ConclusionOur proposed deep learning model is able to generate voxel-level dose maps from a whole-body CT scan with reasonable accuracy suitable for organ-level absorbed dose estimation.Clinical relevance statementWe proposed a novel method for voxel dose map calculation using deep neural networks. This work is clinically relevant since accurate dose calculation for patients can be carried out within acceptable computational time compared to lengthy Monte Carlo calculations.Key Points• We proposed a deep neural network approach as an alternative to Monte Carlo dose calculation.• Our proposed deep learning model is able to generate voxel-level dose maps from a whole-body CT scan with reasonable accuracy, suitable for organ-level dose estimation.• By generating a dose distribution from a single source position, our model can generate accurate and personalized dose maps for a wide range of acquisition parameters.

No impact of attenuation and scatter correction on the interpretation of dopamine transporter SPECT in patients with clinically uncertain parkinsonian syndrome

PurposeThe benefit from attenuation and scatter correction (ASC) of dopamine transporter (DAT)-SPECT for the detection of nigrostriatal degeneration in clinical routine is still a matter of debate. The current study evaluated the impact of ASC on visual interpretation and semi-quantitative analysis of DAT-SPECT in a large patient sample.MethodsOne thousand seven hundred forty consecutive DAT-SPECT with 123I-FP-CIT from clinical routine were included retrospectively. SPECT images were reconstructed iteratively without and with ASC. Attenuation correction was based on uniform attenuation maps, scatter correction on simulation. All SPECT images were categorized with respect to the presence versus the absence of Parkinson-typical reduction of striatal 123I-FP-CIT uptake by three independent readers. Image reading was performed twice to assess intra-reader variability. The specific 123I-FP-CIT binding ratio (SBR) was used for automatic categorization, separately with and without ASC.ResultsThe mean proportion of cases with discrepant categorization by the same reader between the two reading sessions was practically the same without and with ASC, about 2.2%. The proportion of DAT-SPECT with discrepant categorization without versus with ASC by the same reader was 1.66% ± 0.50% (1.09–1.95%), not exceeding the benchmark of 2.2% from intra-reader variability. This also applied to automatic categorization of the DAT-SPECT images based on the putamen SBR (1.78% discrepant cases between without versus with ASC).ConclusionGiven the large sample size, the current findings provide strong evidence against a relevant impact of ASC with uniform attenuation and simulation-based scatter correction on the clinical utility of DAT-SPECT to detect nigrostriatal degeneration in patients with clinically uncertain parkinsonian syndrome.

The uniform homotopy category

This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the respective Lipschitz and uniform settings. Cubical sets and uniform spaces admit the additional compatible structures of categories of (co)fibrant objects. A categorical equivalence between classical homotopy categories of cubical sets and spaces lifts to a full and faithful embedding from an associated Lipschitz homotopy category of cubical sets into an associated uniform homotopy category of uniform spaces. Bounded cubical cohomology generalizes to a representable theory on the Lipschitz homotopy category. Bounded singular cohomology on path-connected spaces generalizes to a representable theory on the uniform homotopy category. Along the way, this paper develops a cubical analogue of Kan's Ex∞ functor and proves a cubical approximation theorem for uniform maps.

Large expanders in high genus unicellular maps

We study large uniform random maps with one face whose genus grows linearly with the number of edges. They can be seen as a model of discrete hyperbolic geometry. In the past, several of these hyperbolic geometric features have been discovered, such as their local limit or their logarithmic diameter. In this work, we show that with high probability such a map contains a very large induced subgraph that is an expander.Mathematics Subject Classifications: 05C10, 05C48, 60C05, 60D05Keywords: Combinatorial maps, high genus, expander graphs

Effect of iterations and time of flight on normal distributions of 82Rb PET relative perfusion and myocardial blood flow

BackgroundAs clinical use of myocardial blood flow (MBF) increases, dynamic series are becoming part of the typical workflow. The methods and parameters used to reconstruct these series require investigation to ensure accurate quantification. MethodsFifty-nine rest/stress dynamic 82Rb PET studies, acquired on a Biograph mCT, from a combination of normal volunteers and low-likelihood patients were reconstructed with and without time of flight (TOF) for varying iterations and processed to obtain relative perfusion and MBF polar maps. Regional values from mean polar maps were fit to a linear mixed-effect model to quantify convergence and select the optimal number of iterations. ResultsTOF reconstructions converged faster and yielded more uniform relative perfusion polar maps. However, the stress MBF distribution for TOF reconstructions was more heterogeneous, with a higher-intensity septal wall. This phenomenon requires further investigation, with right ventricle blood pool spillover possibly having an effect. Optimal reconstructions were defined as 5-iteration non-TOF (24-subset) reconstructions and 3-iteration TOF (21-subset) reconstructions. ConclusionOptimal cardiac reconstructions were identified for non-TOF and TOF reconstructions of dynamic series. TOF reconstruction presents as the more accurate method, given the more uniform relative perfusion distribution.

The mesoscopic geometry of sparse random maps

We investigate the structure of large uniform random maps with $n$ edges, $\mathrm{f}_n$ faces, and with genus $\mathrm{g}_n$ in the so-called sparse case, where the ratio between the number vertices and edges tends to $1$. We focus on two regimes: the planar case $(\mathrm{f}_n, 2\mathrm{g}_n) = (\mathrm{s}_n, 0)$ and the unicellular case with moderate genus $(\mathrm{f}_n, 2 \mathrm{g}_n) = (1, \mathrm{s}_n-1)$, both when $1 \ll \mathrm{s}_n \ll n$. Albeit different at first sight, these two models can be treated in a unified way using a probabilistic version of the classical core-kernel decomposition. In particular, we show that the number of edges of the core of such maps, obtained by iteratively removing degree $1$ vertices, is concentrated around $\sqrt{n \mathrm{s}_{n}}$. Further, their kernel, obtained by contracting the vertices of the core with degree $2$, is such that the sum of the degree of its vertices exceeds that of a trivalent map by a term of order $\sqrt{\mathrm{s}_{n}^{3}/n}$; in particular they are trivalent with high probability when $\mathrm{s}_{n} \ll n^{1/3}$. This enables us to identify a mesoscopic scale $\sqrt{n/\mathrm{s}_n}$ at which the scaling limits of these random maps can be seen as the local limit of their kernels, which is the dual of the UIPT in the planar case and the infinite three-regular tree in the unicellular case, where each edge is replaced by an independent (biased) Brownian tree with two marked points.

Recurrence of the uniform infinite half-plane map via duality of resistances

We study the simple random walk on the Uniform Infinite Half-Plane Map, which is the local limit of critical Boltzmann planar maps with a large and simple boundary. We prove that the simple random walk is recurrent, and that the resistance between the root and the boundary of the hull of radius r is at least of order logr. This resistance bound is expected to be sharp, and is better than those following from previous proofs of recurrence for nonbounded-degree planar maps models. Our main tools are the self-duality of uniform planar maps, a classical lemma about duality of resistances and some peeling estimates. The proof shares some ideas with Russo–Seymour–Welsh theory in percolation.

Fos ensembles encode and shape stable spatial maps in the hippocampus

In the hippocampus, spatial maps are formed by place cells while contextual memories are thought to be encoded as engrams1–6. Engrams are typically identified by expression of the immediate early gene Fos, but little is known about the neural activity patterns that drive, and are shaped by, Fos expression in behaving animals7–10. Thus, it is unclear whether Fos-expressing hippocampal neurons also encode spatial maps and whether Fos expression correlates with and affects specific features of the place code11. Here we measured the activity of CA1 neurons with calcium imaging while monitoring Fos induction in mice performing a hippocampus-dependent spatial learning task in virtual reality. We find that neurons with high Fos induction form ensembles of cells with highly correlated activity, exhibit reliable place fields that evenly tile the environment and have more stable tuning across days than nearby non-Fos-induced cells. Comparing neighbouring cells with and without Fos function using a sparse genetic loss-of-function approach, we find that neurons with disrupted Fos function have less reliable activity, decreased spatial selectivity and lower across-day stability. Our results demonstrate that Fos-induced cells contribute to hippocampal place codes by encoding accurate, stable and spatially uniform maps and that Fos itself has a causal role in shaping these place codes. Fos ensembles may therefore link two key aspects of hippocampal function: engrams for contextual memories and place codes that underlie cognitive maps.

Pullback functors for reduced and unreduced $$L^{q,p}$$-cohomology

In this paper we study the reduced and unreduced $L^{q,p}$-cohomology groups of manifolds of bounded geometry and their behavior under uniform maps. A \textit{uniform map} is a uniformly continuous map such that the diameter of the preimage is bounded in terms of the diameter of the subset. In general, the pullback map along a uniformly proper lipschitz map doesn't induce a morphism in, reduced or not, $L^{q,p}$-cohomology. Then, our goal is to introduce some contravariant functors between the category of manifolds of bounded geometry and uniform maps and the category of complex vector spaces and linear maps. As consequence we obtain that the, reduced or not, $L^{q,p}$-cohomology is a uniform homotopy invariant. Moreover these functors coincide with the pullback, when the pullback does induce a map between the reduced and unreduced $L^{q,p}$-cohomologies.

Local limits of bipartite maps with prescribed face degrees in high genus

We study the local limits of uniform high genus bipartite maps with prescribed face degrees. We prove the convergence toward a family of infinite maps of the plane, the q-IBPMs, which exhibit both a spatial Markov property and a hyperbolic behaviour. Therefore, we observe a similar local behaviour for a wide class of models of random high genus maps which can be seen as a result of universality. Our results cover all the regimes where the expected degree of the root face remains finite in the limit. This follows a work by the same authors on high genus triangulations.

A flow-diffusion model of oxygen transport for quantitative mapping of cerebral metabolic rate of oxygen (CMRO2) with single gas calibrated fMRI

One promising approach for mapping CMRO2 is dual-calibrated functional MRI (dc-fMRI). This method exploits the Fick Principle to combine estimates of CBF from ASL, and OEF derived from BOLD-ASL measurements during arterial O2 and CO2 modulations. Multiple gas modulations are required to decouple OEF and deoxyhemoglobin-sensitive blood volume. We propose an alternative single gas calibrated fMRI framework, integrating a model of oxygen transport, that links blood volume and CBF to OEF and creates a mapping between the maximum BOLD signal, CBF and OEF (and CMRO2). Simulations demonstrated the method’s viability within physiological ranges of mitochondrial oxygen pressure, PmO2, and mean capillary transit time. A dc-fMRI experiment, performed on 20 healthy subjects using O2 and CO2 challenges, was used to validate the approach. The validation conveyed expected estimates of model parameters (e.g., low PmO2), with spatially uniform OEF maps (grey matter, GM, OEF spatial standard deviation ≈ 0.13). GM OEF estimates obtained with hypercapnia calibrated fMRI correlated with dc-fMRI (r = 0.65, p = 2·10−3). For 12 subjects, OEF measured with dc-fMRI and the single gas calibration method were correlated with whole-brain OEF derived from phase measures in the superior sagittal sinus (r = 0.58, p = 0.048; r = 0.64, p = 0.025 respectively). Simplified calibrated fMRI using hypercapnia holds promise for clinical application.