Formation Pattern Analysis of Spheroids Formed by a Droplet-Based Microfluidic System for Predicting the Aggressiveness of Tumor Cells

Examining tumor heterogeneity is essential for selecting an appropriate anticancer treatment for an individual. This study aimed to distinguish low- and high-aggressive tumor cells by analyzing the formation patterns of spheroids. The droplet-based microfluidic system was employed for the formation of each spheroid from four different subtypes of breast tumor cells. Additionally, heterotypic spheroids with T lymphocytes and cancer-associated fibroblasts (CAFs) were produced, and distinctions between low- and high-aggressive tumor cells were explored through the analysis of formation patterns using circularity, convexity, and cell distributions. In both homotypic spheroids and heterotypic spheroids with T lymphocytes, spheroids formed from low-aggressive tumor cells exhibited high circularity and convexity. On the other hand, spheroids formed from high-aggressive tumor cells had relatively low circularity and convexity. In the case of heterotypic spheroids with CAFs, circularity and convexity did not exhibit clear differences between low- and high-aggressive tumor cells, but distinct variations were observed in cell distributions. CAFs and low-aggressive tumor cells were evenly distributed, whereas the CAFs were predominantly located in the inner layer, and high-aggressive tumor cells were primarily located in the outer layer. This finding can offer valuable insights into predicting the aggressiveness of unknown tumor cells.

Positive outcome after endoscopic treatment of a symptomatic convexity arachnoid cyst in an elderly

Cerebral convexity arachnoid cysts (ACs) only represent around 10-14% of the cysts. Symptomatic ACs in the elderly are rare. We present a 66-year-old woman with headache and a focal epileptic seizure. Imaging revealed a left parietal AC. Conservative management chosen but the patient's neurological condition worsened, and an endoscopic fenestration was then performed. Postoperatively, her symptoms completely resolved and MRI image showed significant shrinkage of the AC.

Convexity Dural Arteriovenous Fistula without Cortical Venous Reflux Presenting with Pure Acute Subdural Hematoma

Hemorrhagic changes in a dural arteriovenous fistula are typically associated with cortical venous reflux and occur as intracerebral or subarachnoid hemorrhages. A convexity dural arteriovenous fistula (DAVF) usually flows directly into the cortical veins and exhibits cortical venous reflux. Herein, we report a rare case of a convexity DAVF without cortical venous reflux presenting with a pure acute subdural hematoma. A 19-year-old man complaining of headache without any history of head injury was diagnosed with a left acute subdural hematoma on magnetic resonance imaging (MRI) and referred to our hospital. The patient was conscious and exhibited no neurological signs. The MRI did not reveal any possible abnormalities leading to hemorrhage. Cerebral angiography revealed a dural arteriovenous fistula in the left parietal cranium with a feeder from the middle meningeal artery and a drainer into the main transverse sinus via a diploic vein. Part of the shunt blood flowed into the superior sagittal sinus from the meningeal vein; however, there was no reflux into the cortical vein or stasis of the cerebral vein, suggesting venous hypertension. A convexity DAVF was diagnosed as the source of bleeding, and transarterial embolization was performed. The patient recovered without any neurological deficits. In the absence of trauma, an acute subdural hematoma requires an appropriate evaluation of the vascular lesions and a treatment plan.

Impact of Stoma Baseplate Convexity on Tension and Compression Around the Stoma Site: A Finite Element Analysis

For patients living with intestinal or urinary stomas, skin barriers play an essential role in protecting the peristomal skin and preventing peristomal complications. Convex baseplates press into the peristomal skin and are suitable for retracted stomas that do not protrude, peristomal skin with creases, folds, or dips, and stomas where frequent leaking can occur with flat pouching systems. However, there is a lack of data on the magnitude and location of tension applied to the abdomen by convex baseplates. We evaluated the impact of a range of convex baseplates applied to a simulated stoma site. A comparative finite element analysis investigation was conducted to evaluate the impact of eight different convex stoma system baseplates applied to an idealised flat abdomen, representing skin, subcutaneous tissue, and musculature layers. The baseplates considered had varying convexity with depths of 3.5 mm and 7 mm and internal structural diameters between ~30 mm and ~60 mm. The convex product range provided tension in the skin (maximum principal strain) and compression through the fat layer (minimum principal strain). Large differences in the locations and magnitudes of skin tension and fat layer compression were seen between the baseplates under analysis, with both the depth and diameter of convexity influencing the strain experienced across the abdominal topography. The results generated highlight the importance of having an appropriate range of convexity products available and selecting an appropriate option for use based on the stoma type and condition of the peristomal skin.

A topological model for partial equivariance in deep learning and data analysis

In this article, we propose a topological model to encode partial equivariance in neural networks. To this end, we introduce a class of operators, called P-GENEOs, that change data expressed by measurements, respecting the action of certain sets of transformations, in a non-expansive way. If the set of transformations acting is a group, we obtain the so-called GENEOs. We then study the spaces of measurements, whose domains are subjected to the action of certain self-maps and the space of P-GENEOs between these spaces. We define pseudo-metrics on them and show some properties of the resulting spaces. In particular, we show how such spaces have convenient approximation and convexity properties.

Working with Convex Responses: Antifragility from Finance to Oncology

We extend techniques and learnings about the stochastic properties of nonlinear responses from finance to medicine, particularly oncology, where it can inform dosing and intervention. We define antifragility. We propose uses of risk analysis for medical problems, through the properties of nonlinear responses (convex or concave). We (1) link the convexity/concavity of the dose-response function to the statistical properties of the results; (2) define "antifragility" as a mathematical property for local beneficial convex responses and the generalization of "fragility" as its opposite, locally concave in the tails of the statistical distribution; (3) propose mathematically tractable relations between dosage, severity of conditions, and iatrogenics. In short, we propose a framework to integrate the necessary consequences of nonlinearities in evidence-based oncology and more general clinical risk management.

Anisotropic Hardening of TRIP780 Steel Sheet: Experiments and Analytical Modeling

By combining experimental and theoretical models, this research investigates the anisotropic hardening behaviors of TRIP780 steel. The specimens of TRIP780 steel were subjected to uniaxial tensile and bulging tests under different loading conditions to obtain hardening data. The experimental results show that the strength and plastic deformation of TRIP780 steel vary with the loading directions, which indicates that TRIP780 steel has anisotropy characteristics. In this paper, the dichotomous method is used to ensure the convexity of the Chen-coupled quadratic and non-quadratic (CQN) function. Comparing the predictions of the hardening behavior of the TRIP780 steel sheet by the Yld2000-2d, Stoughton-Yoon'2009 and Chen-CQN functions, the results show that the Chen-CQN function exhibits the advantages of simple numerical implementation and a more realistic prediction of yield stress compared to the former two, respectively. Comparing the prediction of Chen-CQN function with the experimental hardening data, the results show that the deviation between the experimental data and the experimental response given by the function is always within 3%, and this function maintains an accurate prediction under different stress states, indicating that the Chen-CQN yield function has accuracy and flexibility for the characterization of the yield surface of TRIP780 steel.

The Outline of Seed Silhouettes: A Morphological Approach to Silene (Caryophyllaceae)

Seed morphology is an important source of information for plant taxonomy. Nevertheless, the characters under study are diverse, and a simple, unified method is lacking in the literature. A new method for the classification of seeds of the genus Silene based on optical images and image analysis has recently been described on the basis of morphological measurements of the lateral seed views. According to the outline of their silhouettes, seeds from 52 species (49 of Silene and three related species) were classified in three groups: smooth, rugose and echinate, revealing remarkable differences between these groups. This methodology has been applied here to 51 new species, making a total of 100 species of Silene analyzed so far. According to our data, a new group was described, termed papillose. The results showed morphological differences between the four mentioned seed groups, with reduced values of circularity for dorsal and lateral seed views in the papillose and echinate groups and reduced values of solidity in the papillose seeds. The method was applied to the analysis of individual as well as to average seed silhouettes and some of the differences between groups were maintained in both cases.

Modelling brain tissue elasticity with the Ogden model and an alternative family of constitutive models†

The Ogden model is often considered as a standard model in the literature for application to the deformation of brain tissue. Here, we show that, in some of those applications, the use of the Ogden model leads to the non-convexity of the strain-energy function and mis-prediction of the correct concavity of the experimental stress-stretch curves over a range of the deformation domain. By contrast, we propose a family of models which provides a favourable fit to the considered datasets while remaining free from the highlighted shortcomings of the Ogden model. While, as we discuss, those shortcomings might be due to the artefacts of the testing protocols, the proposed family of models proves impervious to such artefacts. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

Life history adaptations to fluctuating environments: Combined effects of demographic buffering and lability

Demographic buffering and lability have been identified as adaptive strategies to optimise fitness in a fluctuating environment. These are not mutually exclusive, however, we lack efficient methods to measure their relative importance for a given life history. Here, we decompose the stochastic growth rate (fitness) into components arising from nonlinear responses and variance-covariance of demographic parameters to an environmental driver, which allows studying joint effects of buffering and lability. We apply this decomposition for 154 animal matrix population models under different scenarios to explore how these main fitness components vary across life histories. Faster-living species appear more responsive to environmental fluctuations, either positively or negatively. They have the highest potential for strong adaptive demographic lability, while demographic buffering is a main strategy in slow-living species. Our decomposition provides a comprehensive framework to study how organisms adapt to variability through buffering and lability, and to predict species responses to climate change.

An Extended Primal-Dual Algorithm Framework for Nonconvex Problems: Application to Image Reconstruction in Spectral CT

Using the convexity of each component of the forward operator, we propose an extended primal-dual algorithm framework for solving a kind of nonconvex and probably nonsmooth optimization problems in spectral CT image reconstruction. Following the proposed algorithm framework, we present six different iterative schemes or algorithms, and then establish the relationship to some existing algorithms. Under appropriate conditions, we prove the convergence of these schemes for the general case. Moreover, when the proposed schemes are applied to solving a specific problem in spectral CT image reconstruction, namely, total variation regularized nonlinear least-squares problem with nonnegative constraint, we also prove the particular convergence for these schemes by using some special properties. The numerical experiments with densely and sparsely data demonstrate the convergence and accuracy of the proposed algorithm framework in terms of visual inspection of images of realistic anatomic complexity and quantitative analysis with metrics structural similarity, peak signal-to-noise ratio, mean square error and maximum pixel difference. We analyze the computational complexity of these schemes, and discuss the extended applications of this algorithm framework in other nonlinear imaging problems.

Use of a Convex Pouching System in the Postoperative Period: A National Consensus

Convex pouching systems have been available for ostomy patients for decades; however, controversy remains over the use of convexity in the postoperative period. A group of 10 nurses and physicians with expertise caring for patients with an ostomy completed a scoping review identifying research-based evidence and gaps in our knowledge of the safety and effectiveness related to the use of a convex pouching system following ostomy surgery. Results of this scoping review demonstrated the need for a structured consensus to define best practices when selecting a pouching system that provides a secure and reliable seal around the stoma, avoids undermining and leakage of effluent from the pouching system, and contributes to optimal health-related quality of life for patients following ostomy surgery. The expert panel reached consensus on 8 statements for the use of convex products immediately after surgery and throughout the first 6 months after stoma creation, as well as describing goals in choosing the best pouching system for the patient with an ostomy.

Survey Results on Use of a Convex Pouching System in the Postoperative Period

PURPOSE

The purpose of this study was to validate time frames for postoperative care following stoma surgery and to determine participants' current practice with convex pouching systems during the postoperative period.

DESIGN

A Cross-sectional survey.

SUBJECTS AND SETTING

The sample comprised 332 ostomy care specialists practicing in the United States. Most (n = 220; 66%) had more than 10 years' experience caring for patients with ostomies, 82% (n = 272) were certified WOC or ostomy care nurses (CWOCN and COCN), and 7% (n = 23) were board-certified colorectal surgeons.

METHODS

A 23-item online questionnaire was created for purposes of the study. Items in the questionnaire queried professional background and experience caring for patients with an ostomy. A single item was used to identify postoperative care periods following ostomy surgery. Additional items queried current practice patterns related to use of convex pouching systems and the timing of their use. Data were collected from January 18 to February 8, 2021.

RESULTS

Most respondents (n = 270; 90%) agreed with the following postoperative periods after ostomy surgery: immediate postoperative period (days 0-8); postoperative period (days 9-30); and transition phase (days 31-180). Most respondents (n = 274; 95%) indicated they would use a convex pouching system when clinically appropriate during the first 30 days following ostomy surgery and 79% (n = 228) indicated using a convex pouching system regardless of when the surgery was performed. Less than 1% (n = 2) indicated never using convexity within the first 30 days following stoma surgery, and only 3% (n = 8) indicated avoidance of convexity pouching systems in the immediate postoperative period.

CONCLUSIONS

Findings indicate that use of convexity during the postoperative period is prevalent to provide a secure seal and predictable wear time.

Characteristics of Convex Skin Barriers and Clinical Application: Results of an International Consensus Panel

Regulatory bodies do not set parameters for measuring certain ostomy product characteristics. As a result, each manufacturer has a different way of measuring specific convex skin barrier characteristics that may create confusion among clinicians when selecting a product. In order to alleviate this confusion and encourage consistency in reporting product characteristics, an international meeting of clinicians with expertise in the care of persons living with an ostomy was convened. The goal of the meeting was to define and establish consistency in convex skin barrier characteristics and their clinical application of the product based on these characteristics. Twelve nurse panelists from 11 countries reviewed, discussed, and reached consensus on a group of proposed statements designed to provide standard definitions of convex skin barrier characteristics and clinically relevant application. The group reached consensus on 5 characteristics of convex skin barriers: depth, compressibility, flexibility, slope, and tension location. These statements provide a basis for quantifying the most clinically relevant characteristics of convex skin barriers and a framework for their application in clinical practice.

Severe intracranial atherosclerotic disease presenting as symptomatic isolated convexity subarachnoid haemorrhage

Isolated convexity cortical subarachnoid haemorrhage (cSAH) is a rare form of non-traumatic subarachnoid haemorrhage localised to one or few cortical sulci of the brain without involving the adjacent brain parenchyma or spreading to sylvian fissure, interhemispheric fissure, basal cisterns and ventricles. cSAH has multiple aetiologies described in medical literature. Intracranial high-grade stenosis is rarely presented as cSAH, especially in young adult patients. Patients presenting with cSAH warrant appropriate diagnostic work up to identify and treat the underlying aetiology.

PARTITIONING SIGNAL CLASSES USING TRANSPORT TRANSFORMS FOR DATA ANALYSIS AND MACHINE LEARNING

A relatively new set of transport-based transforms (CDT, R-CDT, LOT) have shown their strength and great potential in various image and data processing tasks such as parametric signal estimation, classification, cancer detection among many others. It is hence worthwhile to elucidate some of the mathematical properties that explain the successes of these transforms when they are used as tools in data analysis, signal processing or data classification. In particular, we give conditions under which classes of signals that are created by algebraic generative models are transformed into convex sets by the transport transforms. Such convexification of the classes simplify the classification and other data analysis and processing problems when viewed in the transform domain. More specifically, we study the extent and limitation of the convexification ability of these transforms under an algebraic generative modeling framework. We hope that this paper will serve as an introduction to these transforms and will encourage mathematicians and other researchers to further explore the theoretical underpinnings and algorithmic tools that will help understand the successes of these transforms and lay the groundwork for further successful applications.

Dural-based Cavernous Malformation at the Temporal Convexity Presenting with Hemorrhage in a Pregnant Woman: Case Report

Intracranial cavernous malformations (CMs) are benign vascular malformations that arise mostly within the brain parenchyma, but occasionally from the dura mater. Here, we report an extremely rare case of a 29-year-old pregnant woman presenting with hemorrhage in a dural-based CM at the temporal convexity. She presented with headache at 38 weeks of pregnancy. Imaging showed a hemorrhagic mass lesion in the left temporal lobe. Consciousness was clear, with no apparent neurological symptoms or headache. Her baby was delivered by emergency Caesarean section. Magnetic resonance (MR) imaging revealed an enhanced lesion around the hematoma and flow void appearances. Cerebral angiography confirmed the left middle meningeal artery feeding the lesion with apparent contrast medium pooling. Surgical removal of the lesion as a single block was performed. Histological examinations were consistent with CM. The lesion was located outside the brain and attached to the dura mater of the convexity, so the final diagnosis was dural-based CM. The patient was discharged home with her baby without any neurological deficits, and no recurrence has been seen for 2 years. Dural-based CM at the temporal convexity was detected, presenting as headache induced by hemorrhage during pregnancy. The relationship between bleeding of the lesion and pregnancy remains unclear, but female hormones and vascular growth factors during pregnancy can induce morphological changes and angiogenesis in CMs.

Postoperative diffusion-weighted imaging and neurological outcome after convexity meningioma resection

OBJECTIVE

Convexity meningiomas are commonly managed with resection. Motor outcomes and predictors of new deficits after surgery are poorly studied. The objective of this study was to determine whether postoperative diffusion-weighted imaging (DWI) was associated with neurological deficits after convexity meningioma resection and to identify the risk factors for postoperative DWI restriction.

METHODS

A retrospective review of patients who had undergone convexity meningioma resection from 2014 to 2018 was performed. Univariate and multivariate logistic regressions were performed to identify variables associated with postoperative neurological deficits and a DWI signal. The amount of postoperative DWI signal was measured and was correlated with low apparent diffusion coefficient maps to confirm ischemic injury.

RESULTS

The authors identified 122 patients who had undergone a total of 125 operations for convexity meningiomas. The median age at surgery was 57 years, and 70% of the patients were female. The median follow-up was 26 months. The WHO grade was I in 62% of cases, II in 36%, and III in 2%. The most common preoperative deficits were seizures (24%), extremity weakness/paralysis (16%), cognitive/language/memory impairment (16%), and focal neurological deficit (16%). Following resection, 89% of cases had no residual deficit. Postoperative DWI showed punctate or no diffusion restriction in 78% of cases and restriction > 1 cm in 22% of cases. An immediate postoperative neurological deficit was present in 14 patients (11%), but only 8 patients (7%) had a deficit at 3 months postoperatively. Univariate analysis identified DWI signal > 1 cm (p < 0.0001), tumor diameter (p < 0.0001), preoperative motor deficit (p = 0.0043), older age (p = 0.0113), and preoperative embolization (p = 0.0171) as risk factors for an immediate postoperative deficit, whereas DWI signal > 1 cm (p < 0.0001), tumor size (p < 0.0001), and older age (p = 0.0181) were risk factors for deficits lasting more than 3 months postoperatively. Multivariate analysis revealed a DWI signal > 1 cm to be the only significant risk factor for deficits at 3 months postoperatively (OR 32.42, 95% CI 3.3-320.1, p = 0.0002). Further, estimated blood loss (OR 1.4 per 100 ml increase, 95% CI 1.1-1.7, p < 0.0001), older age (OR 1.1 per year older, 95% CI 1.0-1.1, p = 0.0009), middle third location in the sagittal plane (OR 16.9, 95% CI 1.3-216.9, p = 0.0026), and preoperative peritumoral edema (OR 4.6, 95% CI 1.2-17.7, p = 0.0249) were significantly associated with a postoperative DWI signal > 1 cm.

CONCLUSIONS

A DWI signal > 1 cm is significantly associated with postoperative neurological deficits, both immediate and long-lasting. Greater estimated blood loss, older age, tumor location over the motor strip, and preoperative peritumoral edema increase the risk of having a postoperative DWI signal > 1 cm, reflective of perilesional ischemia. Most immediate postoperative deficits will improve over time. These data are valuable when preoperatively communicating with patients about the risks of surgery and when postoperatively discussing prognosis after a deficit occurs.

Copula modeling of receiver operating characteristic and predictiveness curves

Receiver operating characteristic (ROC) and predictiveness curves are graphical tools to study the discriminative and predictive power of a continuous-valued marker in a binary outcome. In this paper, a copula-based construction of the joint density of the marker and the outcome is developed for plotting and analyzing both curves. The methodology only requires a copula function, the marginal distribution of the marker, and the prevalence rate for the model to be characterized. The adoption of the Gaussian copula and the customization of the margin for the marker are proposed for such characterization. The computation of both curves is numerically more feasible than methods that attempt to obtain one curve in terms of the other. Estimation is carried out using maximum likelihood and resampling-based methods. Randomized quantile residuals from each conditional distribution are employed for both assessing the adequacy of the model and identifying outliers. The performance of the estimators of both curves and their underlying quantities is evaluated in simulation studies that assume different dependence structures and sample sizes. The methods are illustrated with an analysis of the level of progesterone receptor gene expression for the diagnosis and prediction of estrogen receptor-positive breast cancer.

Strongly Convex Divergences

We consider a sub-class of the f-divergences satisfying a stronger convexity property, which we refer to as strongly convex, or κ-convex divergences. We derive new and old relationships, based on convexity arguments, between popular f-divergences.

Multivariate discriminant analysis for branching classification of colonic tubular adenoma glands

BACKGROUND

Many morphologic findings of histology can be translated into mathematically computerized data, and identifying important parameters is primarily pathologists' task as users. Shape-specific parameters based on computational geometry properties of glands can be used in the field of pathology. We evaluated the diagnostic utility of three shape-specific parameters: the chord intersection ratio, convexity ratio, and maximum concave area ratio for branching classification of glands.

METHODS

Seven cases of tubular adenoma were studied. After image analysis, segmented neoplastic glands were classified into nonbranching, mild branching, and moderate branching. Using image analysis formulae for the three shape-specific parameters, we compared the values of the parameters with the branching classification results for colonic tubular adenoma.

RESULTS

Multivariate discriminant analysis was used to classify the branching groups. Classification accuracies of nonbranching, mild branching, and moderate branching group based on the three shape-specific parameters were 98, 94, and 95%, respectively. More branching growth exhibited a higher chord intersection ratio and maximum concave area ratio but lower convexity ratio. We found a statistically significant difference in chord intersection ratio, maximum concave area ratio, and convexity ratio between mild, moderate, and nonbranching groups. Among the three features, the chord intersection ratio was the most significant parameter.

CONCLUSIONS

Shape-based parameters of chord intersection ratio, convexity ratio, and maximum concave area ratio are valid assessment parameters for irregular branching structures. For the understanding of spatial relationships of histology, the holistic geometric approach using shape-based parameters can be useful.

Relationship between tumor location, size, and WHO grade in meningioma

OBJECTIVE Prior studies have investigated preoperative risk factors for meningioma; however, no association has been shown between meningioma tumor size and tumor grade. The objective of this study was to investigate the relationship between tumor size and grade in a large single-center study of patients undergoing meningioma resection. METHODS A retrospective chart review of patients undergoing meningioma resection at the University of California, San Francisco, between 1985 and 2015 was performed. Patients with incomplete information, spinal meningiomas, multiple meningiomas, or WHO grade III meningiomas were excluded. The largest tumor dimension was used as a surrogate for tumor size. Univariate and multivariate logistic regression models were used to investigate the relationship between tumor grade and tumor size. A recursive partitioning analysis was performed to identify groups at higher risk for atypical (WHO grade II) meningioma. RESULTS Of the 1113 patients identified, 905 (81%) had a WHO grade I tumor and in 208 (19%) the tumors were WHO grade II. The median largest tumor dimension was 3.6 cm (range 0.2-13 cm). Tumors were distributed as follows: skull base (n = 573, 51%), convexity/falx/parasagittal (n = 431, 39%), and other (n = 109, 10%). On univariate regression, larger tumor size (p < 0.001), convexity/falx/parasagittal location (p < 0.001), and male sex (p < 0.001) were significant predictors of WHO grade II pathology. After controlling for interactions, multivariate regression found male sex (OR 1.74, 95% CI 1.25-2.43), size 3-6 cm (OR 1.69, 95% CI 1.08-2.66), size > 6 cm (OR 3.01, 95% CI 1.53-5.94), and convexity/falx/parasagittal location (OR 1.83, 95% CI 1.19-2.82) to be significantly associated with WHO grade II. Recursive partitioning analysis identified male patients with tumors > 3 cm as a high-risk group (32%) for WHO grade II meningioma. CONCLUSIONS Larger tumor size is associated with a greater likelihood of a meningioma being WHO grade II, independent of tumor location and male sex, which are known risk factors.

Robust Least-SquareLocalization Based on Relative Angular Matrix in Wireless Sensor Networks

Accurate position information plays an important role in wireless sensor networks (WSN), and cooperative positioning based on cooperation among agents is a promising methodology of providing such information. Conventional cooperative positioning algorithms, such as least squares (LS), rely on approximate position estimates obtained from prior measurements. This paper explores the fundamental mechanism underlying the least squares algorithm’s sensitivity to the initial position selection and approaches to dealing with such sensitivity. This topic plays an essential role in cooperative positioning, as it determines whether a cooperative positioning algorithm can be implemented ubiquitously. In particular, a sufficient and unnecessary condition for the least squares cost function to be convex is found and proven. We then propose a robust algorithm for wireless sensor network positioning that transforms the cost function into a globally convex function by detecting the null space of the relative angle matrix when all the targets are located inside the convex polygon formed by its neighboring nodes. Furthermore, we advance one step further and improve the algorithm to apply it in both the time of arrival (TOA) and angle of arrival/time of arrival (AOA/TOA) scenarios. Finally, the performance of the proposed approach is quantified via simulations, and the results show that the proposed method has a high positioning accuracy and is robust in both line-of-sight (LOS) and non-line-of-sight (NLOS) positioning environments.

Surgical outcomes after reoperation for recurrent non-skull base meningiomas

OBJECTIVE

Recurrent meningiomas are primarily managed with radiation therapy or repeat resection. Surgical morbidity after reoperation for recurrent meningiomas is poorly understood. Thus, the objective of this study was to report surgical outcomes after reoperation for recurrent non-skull base meningiomas.

METHODS

A retrospective review of patients was performed. Inclusion criteria were patients with recurrent meningioma who had prior resection and supratentorial non-skull base location. Univariate and multivariate logistic regression and recursive partitioning analysis were used to identify risk factors for surgical complications.

RESULTS

The authors identified 67 patients who underwent 111 reoperations for recurrent supratentorial non-skull base meningiomas. The median age was 53 years, 49% were female, and the median follow-up was 9.8 years. The most common presenting symptoms were headache, weakness, and seizure. The WHO grade after the last reoperation was grade I in 22% of cases, grade II in 51%, and grade III in 27%. The tumor grade increased at reoperation in 22% of cases. Tumors were located on the convexity (52%), parasagittal (33%), falx (31%), and multifocal (19%) locations. Tumors involved the middle third of the sagittal plane in 52% of cases. In the 111 reoperations, 48 complications occurred in 32 patients (48%). There were 26 (54%) complications requiring surgical intervention. There was no perioperative mortality. Complications included neurological deficits (14% total, 8% permanent), wound dehiscence/infection (14%), and CSF leak/pseudomeningocele/hydrocephalus (9%). Tumors that involved the middle third of the sagittal plane (OR 6.97, 95% CI 1.5-32.0, p = 0.006) and presentation with cognitive changes (OR 20.7, 95% CI 2.3-182.7, p = 0.001) were significantly associated with complication occurrence on multivariate analysis. The median survival after the first reoperation was 11.5 years, and the 2-, 5-, and 10-year Kaplan-Meier survival rates were 91.0%, 68.8%, and 50.0%, respectively.

CONCLUSIONS

Reoperation for recurrent supratentorial non-skull base meningioma is associated with a high rate of complications. Patients with cognitive changes and tumors that overlap the middle third of the sagittal plane are at increased risk of complications. Nevertheless, excellent long-term survival can be achieved without perioperative mortality.

Penalized likelihood and multiple testing

The classical multiple testing model remains an important practical area of statistics with new approaches still being developed. In this paper we develop a new multiple testing procedure inspired by a method sometimes used in a problem with a different focus. Namely, the inference after model selection problem. We note that solutions to that problem are often accomplished by making use of a penalized likelihood function. A classic example is the Bayesian information criterion (BIC) method. In this paper we construct a generalized BIC method and evaluate its properties as a multiple testing procedure. The procedure is applicable to a wide variety of statistical models including regression, contrasts, treatment versus control, change point, and others. Numerical work indicates that, in particular, for sparse models the new generalized BIC would be preferred over existing multiple testing procedures.

Convexity of the moment map image for torus actions on bm -symplectic manifolds

We prove a convexity theorem for the image of the moment map of a Hamiltonian torus action on a b^m -symplectic manifold.This article is part of the theme issue 'Finite dimensional integrable systems: new trends and methods'.

From Actions to Effects: Three Constraints on Event Mappings

Events can be modeled through a geometric approach, representing event structures in terms of spaces and mappings between spaces. At least two spaces are needed to describe an event, an action space and a result space. In this article, we invoke general mathematical structures in order to develop this geometric perspective. We focus on three cognitive processes that are crucially involved in events: causal thinking, control of action and learning by generalization. These cognitive processes are supported by three corresponding mathematical properties: monotonicity (that we relate to qualitative causal thinking and allows extrapolation); continuity (that plays a key role in our activities of action control); and convexity (that facilitates generalization and the categorization of events, and enables interpolation). We define how such properties constrain events representations and relate them to thinking about events. We discuss the relevance of the three constraints for event segmentation and explore the implications of such constraints for semantics. We conclude by a discussion that relates our approach to other accounts of events.

A Method for the Analysis of AP Foot Convexity: Insights into Smooth Muscle Biophysics

Action potential (AP) profiles vary based on the cell type, with cells of the same type typically producing APs with similar shapes. But in certain syncytial tissues, such as the smooth muscle of the urinary bladder wall, even a single cell is known to exhibit APs with diverse profiles. The origin of this diversity is not currently understood, but is often attributed to factors such as syncytial interactions and the spatial distribution of parasympathetic nerve terminals. Thus, the profile of an action potential is determined by the inherent properties of the cell and influenced by its biophysical environment. The analysis of an AP profile, therefore, holds potential for constructing a biophysical picture of the cellular environment. An important feature of any AP is its depolarization to threshold, termed the AP foot, which holds information about the origin of the AP. Currently, there exists no established technique for the quantification of the AP foot. In this study, we explore several possible approaches for this quantification, namely, exponential fitting, evaluation of the radius of curvature, triangulation altitude, and various area based methods. We have also proposed a modified area-based approach (C_X,Y) which quantifies foot convexity as the area between the AP foot and a predefined line. We assess the robustness of the individual approaches over a wide variety of signals, mimicking AP diversity. The proposed (C_X,Y) method is demonstrated to be superior to the other approaches, and we demonstrate its application on experimentally recorded AP profiles. The study reveals how the quantification of the AP foot could be related to the nature of the underlying synaptic activity and help shed light on biophysical features such as the density of innervation, proximity of varicosities, size of the syncytium, or the strength of intercellular coupling within the syncytium. The work presented here is directed toward exploring these aspects, with further potential toward clinical electrodiagnostics by providing a better understanding of whole-organ biophysics.

Monotonicity, convexity, and inequalities for the generalized elliptic integrals

We provide the monotonicity and convexity properties and sharp bounds for the generalized elliptic integrals [Formula: see text] and [Formula: see text] depending on a parameter [Formula: see text], which contains an earlier result in the particular case [Formula: see text].

Method for the unique identification of hyperelastic material properties using full-field measures. Application to the passive myocardium material response

Quantitative measurement of the material properties (eg, stiffness) of biological tissues is poised to become a powerful diagnostic tool. There are currently several methods in the literature to estimating material stiffness, and we extend this work by formulating a framework that leads to uniquely identified material properties. We design an approach to work with full-field displacement data-ie, we assume the displacement field due to the applied forces is known both on the boundaries and also within the interior of the body of interest-and seek stiffness parameters that lead to balanced internal and external forces in a model. For in vivo applications, the displacement data can be acquired clinically using magnetic resonance imaging while the forces may be computed from pressure measurements, eg, through catheterization. We outline a set of conditions under which the least-square force error objective function is convex, yielding uniquely identified material properties. An important component of our framework is a new numerical strategy to formulate polyconvex material energy laws that are linear in the material properties and provide one optimal description of the available experimental data. An outcome of our approach is the analysis of the reliability of the identified material properties, even for material laws that do not admit unique property identification. Lastly, we evaluate our approach using passive myocardium experimental data at the material point and show its application to identifying myocardial stiffness with an in silico experiment modeling the passive filling of the left ventricle.

Use of Convexity in Ostomy Care: Results of an International Consensus Meeting

Ostomy skin barriers that incorporate a convexity feature have been available in the marketplace for decades, but limited resources are available to guide clinicians in selection and use of convex products. Given the widespread use of convexity, and the need to provide practical guidelines for appropriate use of pouching systems with convex features, an international consensus panel was convened to provide consensus-based guidance for this aspect of ostomy practice. Panelists were provided with a summary of relevant literature in advance of the meeting; these articles were used to generate and reach consensus on 26 statements during a 1-day meeting. Consensus was achieved when 80% of panelists agreed on a statement using an anonymous electronic response system. The 26 statements provide guidance for convex product characteristics, patient assessment, convexity use, and outcomes.

Stable Gene Regulatory Network Modeling From Steady-State Data

Gene regulatory networks represent an abstract mapping of gene regulations in living cells. They aim to capture dependencies among molecular entities such as transcription factors, proteins and metabolites. In most applications, the regulatory network structure is unknown, and has to be reverse engineered from experimental data consisting of expression levels of the genes usually measured as messenger RNA concentrations in microarray experiments. Steady-state gene expression data are obtained from measurements of the variations in expression activity following the application of small perturbations to equilibrium states in genetic perturbation experiments. In this paper, the least absolute shrinkage and selection operator-vector autoregressive (LASSO-VAR) originally proposed for the analysis of economic time series data is adapted to include a stability constraint for the recovery of a sparse and stable regulatory network that describes data obtained from noisy perturbation experiments. The approach is applied to real experimental data obtained for the SOS pathway in Escherichia coli and the cell cycle pathway for yeast Saccharomyces cerevisiae. Significant features of this method are the ability to recover networks without inputting prior knowledge of the network topology, and the ability to be efficiently applied to large scale networks due to the convex nature of the method.

Distinguishing clinical and radiological features of non-traumatic convexal subarachnoid hemorrhage

BACKGROUND AND PURPOSE

The full spectrum of causes of convexal subarachnoid hemorrhage (cSAH) requires further investigation. Therefore, our objective was to describe the spectrum of clinical and imaging features of patients with non-traumatic cSAH.

METHODS

A retrospective observational study of consecutive patients with non-traumatic cSAH was performed at a tertiary referral center. The underlying cause of cSAH was characterized and clinical and imaging features that predict a specific etiology were identified. The frequency of future cSAH or intracerebral hemorrhage (ICH) was determined.

RESULTS

In all, 88 patients [median age 64 years (range 25-85)] with non-traumatic cSAH were identified. The most common causes were reversible cerebral vasoconstriction syndrome (RCVS) (26, 29.5%), cerebral amyloid angiopathy (CAA) (23, 26.1%), indeterminate (14, 15.9%) and endocarditis (9, 10.2%). CAA patients commonly presented at an older age than RCVS patients (75 years versus 51 years, P < 0.0001). Thirteen patients (14.7%) had recurrent cSAH, and 12 patients (13.6%) had a subsequent ICH. However, the risk was high amongst those with CAA compared to those caused by RCVS, with recurrent cSAH in 39.1% and subsequent lobar ICH in 43.5% of CAA cases.

CONCLUSIONS

Our study demonstrates the clinical diversity of cSAH. Older age, sensorimotor dysfunction and stereotyped spells suggest CAA as the underlying cause. Younger age and thunderclap headache predict RCVS. Yet, various other causes also need to be considered in the differential diagnosis.

On convex least squares estimation when the truth is linear

We prove that the convex least squares estimator (LSE) attains a n^-1/2 pointwise rate of convergence in any region where the truth is linear. In addition, the asymptotic distribution can be characterized by a modified invelope process. Analogous results hold when one uses the derivative of the convex LSE to perform derivative estimation. These asymptotic results facilitate a new consistent testing procedure on the linearity against a convex alternative. Moreover, we show that the convex LSE adapts to the optimal rate at the boundary points of the region where the truth is linear, up to a log-log factor. These conclusions are valid in the context of both density estimation and regression function estimation.

Convexity dural cavernous haemangioma mimicking meningioma: A case report

Dural cavernous haemangiomas are rare, and they do not display a classical ring of haemosiderin on MRI as parenchymal cavernous haemangiomas. Sometimes, they are misinterpreted as meningiomas with a dural tail sign. In this short report, a 37-year-old woman was diagnosed with a convexity cavernous haemangioma, and the tumour was totally resected.

The lemon illusion: seeing curvature where there is none

Curvature is a highly informative visual cue for shape perception and object recognition. We introduce a novel illusion—the Lemon Illusion—in which subtle illusory curvature is perceived along contour regions that are devoid of physical curvature. We offer several perceptual demonstrations and observations that lead us to conclude that the Lemon Illusion is an instance of a more general illusory curvature phenomenon, one in which the presence of contour curvature discontinuities lead to the erroneous extension of perceived curvature. We propose that this erroneous extension of perceived curvature results from the interaction of neural mechanisms that operate on spatially local contour curvature signals with higher-tier mechanisms that serve to establish more global representations of object shape. Our observations suggest that the Lemon Illusion stems from discontinuous curvature transitions between rectilinear and curved contour segments. However, the presence of curvature discontinuities is not sufficient to produce the Lemon Illusion, and the minimal conditions necessary to elicit this subtle and insidious illusion are difficult to pin down.

Geometrical illusions are not always where you think they are: a review of some classical and less classical illusions, and ways to describe them

Geometrical illusions are known through a small core of classical illusions that were discovered in the second half of the nineteenth century. Most experimental studies and most theoretical discussions revolve around this core of illusions, as though all other illusions were obvious variants of these. Yet, many illusions, mostly described by German authors at the same time or at the beginning of the twentieth century have been forgotten and are awaiting their rehabilitation. Recently, several new illusions were discovered, mainly by Italian authors, and they do not seem to take place into any current classification. Among the principles that are invoked to explain the illusions, there are principles relating to the metric aspects (contrast, assimilation, shrinkage, expansion, attraction of parallels) principles relating to orientations (regression to right angles, orthogonal expansion) or, more recently, to gestalt effects. Here, metric effects are discussed within a measurement framework, in which the geometric illusions are the outcome of a measurement process. There would be a main "convexity" bias in the measures: the measured value m(x) of an extant x would grow more than proportionally with x. This convexity principle, completed by a principle of compromise for conflicting measures can replace, for a large number of patterns, both the assimilation and the contrast effects. We know from evolutionary theory that the most pertinent classification criteria may not be the most salient ones (e.g., a dolphin is not a fish). In order to obtain an objective classification of illusions, I initiated with Kevin O'Regan systematic work on "orientation profiles" (describing how the strength of an illusion varies with its orientation in the plane). We showed first that the Zöllner illusion already exists at the level of single stacks, and that it does not amount to a rotation of the stacks. Later work suggested that it is best described by an "orthogonal expansion"-an expansion of the stacks applied orthogonally to the oblique segments of the stacks, generating an apparent rotation effect. We showed that the Poggendorff illusion was mainly a misangulation effect. We explained the hierarchy of the illusion magnitudes found among variants of the Poggendorff illusion by the existence of control devices that counteract the loss of parallelism or the loss of collinearity produced by the biased measurements. I then studied the trapezium illusion. The oblique sides, but not the bases, were essential to the trapezium illusion, suggesting the existence of a common component between the trapezium and the Zöllner illusion. Unexpectedly, the trapeziums sometimes appeared as twisted surfaces in 3d. It also appeared impossible, using a nulling procedure, to make all corresponding sides of two trapeziums simultaneously equal. The square-diamond illusion is usually presented with one apex of the diamond pointing toward the square. I found that when the figures were displayed more symmetrically, the illusion was significantly reduced. Furthermore, it is surpassed, for all subjects, by an illusion that goes in the opposite direction, in which the diagonal of a small diamond is underestimated with respect to the side of a larger square. In general, the experimental work generated many unexpected results. Each illusory stimulus was compared to a number of control variants, and often, I measured larger distortions in a variant than in the standard stimulus. In the Discussion, I will stress what I think are the main ordering principle in the metric and the orientation domains for illusory patterns. The convexity bias principle and the orthogonal expansion principles help to establish unsuspected links between apparently unrelated stimuli, and reduce their apparently extreme heterogeneity. However, a number of illusions (e.g., those of the twisted cord family, or the Poggendorff illusions) remain unpredicted by the above principles. Finally, I will develop the idea that the brain is constructing several representations, and the one that is commonly used for the purpose of shape perception generates distortions inasmuch as it must satisfy a number of conflicting constraints, such as the constraint of producing a stable shape despite the changing perspectives produced by eye movements.

Rearrangement, convection, convexity and entropy

The concepts of convexity and entropy play a crucial role in the mathematical theory of hyperbolic systems of conservation laws. We show that they also play an important role in the mathematical analysis of convection theory, through the mathematical concept of rearrangement.

Entropy and convexity for nonlinear partial differential equations

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.

A LASSO FOR HIERARCHICAL INTERACTIONS

We add a set of convex constraints to the lasso to produce sparse interaction models that honor the hierarchy restriction that an interaction only be included in a model if one or both variables are marginally important. We give a precise characterization of the effect of this hierarchy constraint, prove that hierarchy holds with probability one and derive an unbiased estimate for the degrees of freedom of our estimator. A bound on this estimate reveals the amount of fitting "saved" by the hierarchy constraint. We distinguish between parameter sparsity-the number of nonzero coefficients-and practical sparsity-the number of raw variables one must measure to make a new prediction. Hierarchy focuses on the latter, which is more closely tied to important data collection concerns such as cost, time and effort. We develop an algorithm, available in the R package hierNet, and perform an empirical study of our method.