K1,3K_{1,3}-covering red and blue points in the plane

We say that a finite set of red and blue points in the plane in general position can be $K_{1,3}$-covered if the set can be partitioned into subsets of size $4$, with $3$ points of one color and $1$ point of the other color, in such a way that, if at each subset the fourth point is connected by straight-line segments to the same-colored points, then the resulting set of all segments has no crossings. We consider the following problem: Given a set $R$ of $r$ red points and a set $B$ of $b$ blue points in the plane in general position, how many points of $R\cup B$ can be $K_{1,3}$-covered? and we prove the following results: (1) If $r=3g+h$ and $b=3h+g$, for some non-negative integers $g$ and $h$, then there are point sets $R\cup B$, like $\{1,3\}$-equitable sets (i.e., $r=3b$ or $b=3r$) and linearly separable sets, that can be $K_{1,3}$-covered. (2) If $r=3g+h$, $b=3h+g$ and the points in $R\cup B$ are in convex position, then at least $r+b-4$ points can be $K_{1,3}$-covered, and this bound is tight. (3) There are arbitrarily large point sets $R\cup B$ in general position, with $r=b+1$, such that at most $r+b-5$ points can be $K_{1,3}$-covered. (4) If $b\le r\le 3b$, then at least $\frac{8}{9}(r+b-8)$ points of $R\cup B$ can be $K_{1,3}$-covered. For $r>3b$, there are too many red points and at least $r-3b$ of them will remain uncovered in any $K_{1,3}$-covering. Furthermore, in all the cases we provide efficient algorithms to compute the corresponding coverings.Comment: 29 pages, 10 figures, 1 tabl

K1,3-covering red and blue points in the plane

We say that a finite set of red and blue points in the plane in general position can be K1, 3-covered if the set can be partitioned into subsets of size 4, with 3 points of one color and 1 point of the other color, in such a way that, if at each subset the fourth point is connected by straight-line segments to the same-colored points, then the resulting set of all segments has no crossings. We consider the following problem: Given a set R of r red points and a set B of b blue points in the plane in general position, how many points of R ¿ B can be K1, 3-covered? and we prove the following results: (1) If r = 3g + h and b = 3h + g, for some non-negative integers g and h, then there are point sets R ¿ B, like {1, 3}-equitable sets (i.e., r = 3b or b = 3r) and linearly separable sets, that can be K1, 3-covered. (2) If r = 3g + h, b = 3h + g and the points in R ¿ B are in convex position, then at least r + b - 4 points can be K1, 3-covered, and this bound is tight. (3) There are arbitrarily large point sets R ¿ B in general position, with r = b + 1, such that at most r + b - 5 points can be K1, 3-covered. (4) If b = r = 3b, then at least 9 8 (r + b- 8) points of R ¿ B can be K1, 3-covered. For r > 3b, there are too many red points and at least r - 3b of them will remain uncovered in any K1, 3-covering. Furthermore, in all the cases we provide efficient algorithms to compute the corresponding coverings

Reduction of motion effects in myocardial arterial spin labeling

Purpose To evaluate the accuracy and reproducibility of myocardial blood flow measurements obtained under different breathing strategies and motion correction techniques with arterial spin labeling. Methods A prospective cardiac arterial spin labeling study was performed in 12 volunteers at 3 Tesla. Perfusion images were acquired twice under breath-hold, synchronized-breathing, and free-breathing. Motion detection based on the temporal intensity variation of a myocardial voxel, as well as image registration based on pairwise and groupwise approaches, were applied and evaluated in synthetic and in vivo data. A region of interest was drawn over the mean perfusion-weighted image for quantification. Original breath-hold datasets, analyzed with individual regions of interest for each perfusion-weighted image, were considered as reference values. Results Perfusion measurements in the reference breath-hold datasets were in line with those reported in literature. In original datasets, prior to motion correction, myocardial blood flow quantification was significantly overestimated due to contamination of the myocardial perfusion with the high intensity signal of blood pool. These effects were minimized with motion detection or registration. Synthetic data showed that accuracy of the perfusion measurements was higher with the use of registration, in particular after the pairwise approach, which probed to be more robust to motion. Conclusion Satisfactory results were obtained for the free-breathing strategy after pairwise registration, with higher accuracy and robustness (in synthetic datasets) and higher intrasession reproducibility together with lower myocardial blood flow variability across subjects (in in vivo datasets). Breath-hold and synchronized-breathing after motion correction provided similar results, but these breathing strategies can be difficult to perform by patients

A bilateral whitish lesion on the mucosa of the cheek

An 8-year-old girl with no medical history presented with a bilateral whitish lesion on the mucosa of the cheek, evident since early childhood. There was no relevant family history, and her parents had not presented similar lesions. They reported a progressive growth of the lesion in the last months, for which she had been evaluated by maxillofacial surgery, the lesion being oriented as a frictional keratosis. However, the use of occlusal splint was not associated with any improvement. She was otherwise asymptomatic. Physical examination revealed a bilateral, whitish, well-demarcated cheek mucosal plaque, which partially coincided with the dental occlusion line. The lesion did not detach with scratching (Figure 1). No other alterations were observed in the oral cavity or in the systematic physical examination

Multiparametric renal magnetic resonance imaging: A reproducibility study in renal allografts with stable function

Monitoring renal allograft function after transplantation is key for the early detection of allograft impairment, which in turn can contribute to preventing the loss of the allograft. Multiparametric renal MRI (mpMRI) is a promising noninvasive technique to assess and characterize renal physiopathology; however, few studies have employed mpMRI in renal allografts with stable function (maintained function over a long time period). The purposes of the current study were to evaluate the reproducibility of mpMRI in transplant patients and to characterize normal values of the measured parameters, and to estimate the labeling efficiency of Pseudo-Continuous Arterial Spin Labeling (PCASL) in the infrarenal aorta using numerical simulations considering experimental measurements of aortic blood flow profiles. The subjects were 20 transplant patients with stable kidney function, maintained over 1 year. The MRI protocol consisted of PCASL, intravoxel incoherent motion, and T1 inversion recovery. Phase contrast was used to measure aortic blood flow. Renal blood flow (RBF), diffusion coefficient (D), pseudo-diffusion coefficient (D*), flowing fraction ( f ), and T1 maps were calculated and mean values were measured in the cortex and medulla. The labeling efficiency of PCASL was estimated from simulation of Bloch equations. Reproducibility was assessed with the within-subject coefficient of variation, intraclass correlation coefficient, and Bland-Altman analysis. Correlations were evaluated using the Pearson correlation coefficient. The significance level was p less than 0.05. Cortical reproducibility was very good for T1, D, and RBF, moderate for f , and low for D*, while medullary reproducibility was good for T1 and D. Significant correlations in the cortex between RBF and f (r = 0.66), RBF and eGFR (r = 0.64), and D* and eGFR (r = -0.57) were found. Normal values of the measured parameters employing the mpMRI protocol in kidney transplant patients with stable function were characterized and the results showed good reproducibility of the techniques

Successful working memory processes and cerebellum in an elderly sample: A neuropsychological and fMRI study

Background Imaging studies help to understand the evolution of key cognitive processes related to aging, such as working memory (WM). This study aimed to test three hypotheses in older adults. First, that the brain activation pattern associated to WM processes in elderly during successful low load tasks is located in posterior sensory and associative areas; second, that the prefrontal and parietal cortex and basal ganglia should be more active during high-demand tasks; third, that cerebellar activations are related to high-demand cognitive tasks and have a specific lateralization depending on the condition. Methods We used a neuropsychological assessment with functional magnetic resonance imaging and a core N-back paradigm design that was maintained across the combination of four conditions of stimuli and two memory loads in a sample of twenty elderly subjects. Results During low-loads, activations were located in the visual ventral network. In high loads, there was an involvement of the basal ganglia and cerebellum in addition to the frontal and parietal cortices. Moreover, we detected an executive control role of the cerebellum in a relatively symmetric fronto-parietal network. Nevertheless, this network showed a predominantly left lateralization in parietal regions associated presumably with an overuse of verbal storage strategies. The differential activations between conditions were stimuli-dependent and were located in sensory areas. Conclusion Successful WM processes in the elderly population are accompanied by an activation pattern that involves cerebellar regions working together with a fronto-parietal network

Sex-related differences of fatty acid-binding protein 4 and leptin levels in atrial fibrillation

Aims: Adiposity plays a key role in the pathogenesis of atrial fibrillation (AF). Our aim was to study the sex differences in adipokines levels according to AF burden. Methods and results: Two independent cohorts of patients were studied: (i) consecutive patients with AF undergoing catheter ablation (n = 217) and (ii) a control group (n = 105). (i) Adipokines, oxidative stress, indirect autonomic markers, and leucocytes mRNA levels were analysed; (ii) correlation between biomarkers was explored with heatmaps and Kendall correlation coefficients; and (iii) logistic regression and random forest model were used to determine predictors of AF recurrence after ablation. Our results showed that: (i) fatty acid-binding protein 4 (FABP4) and leptin levels were higher in women than in men in both cohorts (P < 0.01). In women, FABP4 levels were higher on AF cohort (20 ± 14 control, 29 ± 18 paroxysmal AF and 31 ± 17 ng/mL persistent AF; P < 0.01). In men, leptin levels were lower on AF cohort (22 ± 15 control, 13 ± 16 paroxysmal AF and 13 ± 11 ng/mL persistent AF; P < 0.01). (ii) In female with paroxysmal AF, there was a lower acetylcholinesterase and higher carbonic anhydrase levels with respect to men (P < 0.05). (iii) Adipokines have an important role on discriminate AF recurrence after ablation. In persistent AF, FABP4 was the best predictor of recurrence after ablation (1.067, 95% confidence interval 1-1.14; P = 0.046). Conclusion: The major finding of the present study is the sex-based differences of FABP4 and leptin levels according to AF burden. These adipokines are associated with oxidative stress, inflammatory and autonomic indirect markers, indicating that they may play a role in AF perpetuation.This study was supported by projects (PI16/01282 and PI18/01584) integrated in the Plan Estatal de I+D+I 2016–2019 and cofounded by ISCIII-Subdirección General de Evaluación y Fomento de la Investigación del Fondo Europeo de Desarrollo Regional (FEDER). J.N.L.-C. and M.R.-M. were a recipient of a Sociedade Galega de Cardioloxía (SOGACAR) research grant. D.d.G.-C. was a recipient of a Juan de la Cierva-Incorporación grant from the Ministry of Science Innovation and Universities (IJCI-2016-29393). CIBER Cardiovascular (CB16/11/00403 to V.Ll.-C. and D.d.G.-C.) is a project from Carlos III Health Institute.Peer reviewe

The neural substrate and functional integration of uncertainty in decision making: an information theory approach

Decision making can be regarded as the outcome of cognitive processes leading to the selection of a course of action among several alternatives. Borrowing a central measurement from information theory, Shannon entropy, we quantified the uncertainties produced by decisions of participants within an economic decision task under different configurations of reward probability and time. These descriptors were used to obtain blood oxygen level-dependent (BOLD) signal correlates of uncertainty and two clusters codifying the Shannon entropy of task configurations were identified: a large cluster including parts of the right middle cingulate cortex (MCC) and left and right pre-supplementary motor areas (pre-SMA) and a small cluster at the left anterior thalamus. Subsequent functional connectivity analyses using the psycho-physiological interactions model identified areas involved in the functional integration of uncertainty. Results indicate that clusters mostly located at frontal and temporal cortices experienced an increased connectivity with the right MCC and left and right pre-SMA as the uncertainty was higher. Furthermore, pre-SMA was also functionally connected to a rich set of areas, most of them associative areas located at occipital and parietal lobes. This study provides a map of the human brain segregation and integration (i.e., neural substrate and functional connectivity respectively) of the uncertainty associated to an economic decision making paradigm

Consensus-based technical recommendations for clinical translation of renal ASL MRI

OBJECTIVES: This study aimed at developing technical recommendations for the acquisition, processing and analysis of renal ASL data in the human kidney at 1.5 T and 3 T field strengths that can promote standardization of renal perfusion measurements and facilitate the comparability of results across scanners and in multi-centre clinical studies. METHODS: An international panel of 23 renal ASL experts followed a modified Delphi process, including on-line surveys and two in-person meetings, to formulate a series of consensus statements regarding patient preparation, hardware, acquisition protocol, analysis steps and data reporting. RESULTS: Fifty-nine statements achieved consensus, while agreement could not be reached on two statements related to patient preparation. As a default protocol, the panel recommends pseudo-continuous (PCASL) or flow-sensitive alternating inversion recovery (FAIR) labelling with a single-slice spin-echo EPI readout with background suppression and a simple but robust quantification model. DISCUSSION: This approach is considered robust and reproducible and can provide renal perfusion images of adequate quality and SNR for most applications. If extended kidney coverage is desirable, a 2D multislice readout is recommended. These recommendations are based on current available evidence and expert opinion. Nonetheless they are expected to be updated as more data become available, since the renal ASL literature is rapidly expanding

Technical recommendations for clinical translation of renal MRI: a consensus project of the Cooperation in Science and Technology Action PARENCHIMA

PURPOSE: The potential of renal MRI biomarkers has been increasingly recognised, but clinical translation requires more standardisation. The PARENCHIMA consensus project aims to develop and apply a process for generating technical recommendations on renal MRI. METHODS: A task force was formed in July 2018 focused on five methods. A draft process for attaining consensus was distributed publicly for consultation and finalised at an open meeting (Prague, October 2018). Four expert panels completed surveys between October 2018 and March 2019, discussed results and refined the surveys at a face-to-face meeting (Aarhus, March 2019) and completed a second round (May 2019). RESULTS: A seven-stage process was defined: (1) formation of expert panels; (2) definition of the context of use; (3) literature review; (4) collection and comparison of MRI protocols; (5) consensus generation by an approximate Delphi method; (6) reporting of results in vendor-neutral and vendor-specific terms; (7) ongoing review and updating. Application of the process resulted in 166 consensus statements. CONCLUSION: The process generated meaningful technical recommendations across very different MRI methods, while allowing for improvement and refinement as open issues are resolved. The results are likely to be widely supported by the renal MRI community and thereby promote more harmonisation