Marked Point Research Articles

Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic

Abstract We prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for $GL_{n}(k)$, where $k$ is an algebraically closed field of characteristic $p> n$. Let $X$ be a smooth projective curve over $k$ with marked points, and fix a parabolic subgroup of $GL_{n}(k)$ at each marked point. We denote by $\operatorname{Bun}_{n,P}$ the moduli stack of (quasi-)parabolic vector bundles on $X$, and by $\mathcal{L}oc_{n,P}$ the moduli stack of parabolic flat connections such that the residue is nilpotent with respect to the parabolic reduction at each marked point. We construct an equivalence between the bounded derived category $D^{b}(\operatorname{QCoh}({\mathcal{L}oc_{n,P}^{0}}))$ of quasi-coherent sheaves on an open substack $\mathcal{L}oc_{n,P}^{0}\subset \mathcal{L}oc_{n,P}$, and the bounded derived category $D^{b}(\mathcal{D}^{0}_{{\operatorname{Bun}}_{n,P}}\operatorname{-mod})$ of $\mathcal{D}^{0}_{{\operatorname{Bun}}_{n,P}}$-modules, where $\mathcal{D}^{0}_{\operatorname{Bun}_{n,P}}$ is a localization of $\mathcal{D}_{\operatorname{Bun}_{n,P}}$ the sheaf of crystalline differential operators on $\operatorname{Bun}_{n,P}$. Thus, we extend the work of Bezrukavnikov–Braverman [ 8] to the tamely ramified case. We also prove a correspondence between flat connections on $X$ with regular singularities and meromorphic Higgs bundles on the Frobenius twist $X^{(1)}$ of $X$ with first-order poles.

Distributed measurement system calibration method with automatic networking mechanism

This paper presents a new method that balances accuracy and efficiency in the process of coordinate unification for distributed measurement systems. The method unifies the local coordinate systems of any two measuring units by installing a measuring point on the unit as a marker point and measuring the marker points between them in the working area, combined with the distance between the marker points. Moreover, it enables automatic networking of newly added or moved measurement units with the original measurement network, thereby further improving the efficiency of the dynamic measurements made using the system. The key factors affecting the accuracy of calibration achieved using this method were analysed via simulations. The results indicate that the accuracy of length measurement using the proposed methods is within 0.1 mm m−1 when the measurement units are distributed among the four corners of a rectangle with an area of 50 m2 or more. The experiments indicate that four measurement units calibrated using this method over an area of 35 m2 achieve an accuracy of within 0.2 mm m−1 and 0.1 mm standard deviations for length and three-dimensional coordinate measurements, respectively. Compared with traditional coordinate-unification methods, the proposed method simplifies the calibration process, improves the calibration efficiency by more than ten times, and significantly reduces the calibration time. It is universally applicable in the calibration of large-space distributed measurement systems.

Muscular Strategies for Correcting the Pelvic Position to Improve Posture-An Exploratory Study.

The correction of postural weaknesses through the better positioning of the pelvis is an important approach in sports therapy and physiotherapy. The pelvic position in the sagittal plane is largely dependent on the muscular balance of the ventral and dorsal muscle groups. The aim of this exploratory study was to examine whether healthy persons use similar muscular activation patterns to correct their pelvic position or whether there are different motor strategies. The following muscles were recorded in 41 persons using surface electromyography (EMG): M. trapezius pars ascendens, M. erector spinae pars lumbalis, M. gluteus maximus, M. biceps femoris, M. rectus abdominis, and M. obliquus externus. The participants performed 10 voluntary pelvic movements (retroversion of the pelvis). The anterior pelvic tilt was measured videographically via marker points on the anterior and posterior superior iliac spine. The EMG data were further processed and normalized to the maximum voluntary contraction. A linear regression analysis was conducted to assess the relationship between changes in the pelvic tilt and muscle activities. Subsequently, a Ward clustering analysis was applied to detect potential muscle activation patterns. The differences between the clusters and the pelvic tilt were examined using ANOVA. Cluster analysis revealed the presence of four clusters with different muscle activation patterns in which the abdominal muscles and dorsal muscle groups were differently involved. However, the gluteus maximus muscle was involved in every activation pattern. It also had the strongest correlation with the changes in pelvic tilt. Different individual muscle patterns are used by different persons to correct pelvic posture, with the gluteus maximus muscle apparently playing the most important role. This can be important for therapy, as different muscle strategies should be trained depending on the individually preferred motor patterns.

The balanced superelliptic mapping class groups are generated by three elements

Abstract The balanced superelliptic mapping class group is the normalizer of the transformation group of the balanced superelliptic covering in the mapping class group of the total surface. We prove that the balanced superelliptic mapping class groups with either one marked point, one boundary component, or no marked points and boundary are generated by three elements. To prove this, we also show that its liftable mapping class groups are also generated by three elements. These generating sets are minimal except for several cases of closed surfaces.

Automatic 3D cell segmentation of fruit parenchyma tissue from X-ray micro CT images using deep learning

BackgroundHigh quality 3D information of the microscopic plant tissue morphology—the spatial organization of cells and intercellular spaces in tissues—helps in understanding physiological processes in a wide variety of plants and tissues. X-ray micro-CT is a valuable tool that is becoming increasingly available in plant research to obtain 3D microstructural information of the intercellular pore space and individual pore sizes and shapes of tissues. However, individual cell morphology is difficult to retrieve from micro-CT as cells cannot be segmented properly due to negligible density differences at cell-to-cell interfaces. To address this, deep learning-based models were trained and tested to segment individual cells using X-ray micro-CT images of parenchyma tissue samples from apple and pear fruit with different cell and porosity characteristics.ResultsThe best segmentation model achieved an Aggregated Jaccard Index (AJI) of 0.86 and 0.73 for apple and pear tissue, respectively, which is an improvement over the current benchmark method that achieved AJIs of 0.73 and 0.67. Furthermore, the neural network was able to detect other plant tissue structures such as vascular bundles and stone cell clusters (brachysclereids), of which the latter were shown to strongly influence the spatial organization of pear cells. Based on the AJIs, apple tissue was found to be easier to segment, as the porosity and specific surface area of the pore space are higher and lower, respectively, compared to pear tissue. Moreover, samples with lower pore network connectivity, proved very difficult to segment.ConclusionsThe proposed method can be used to automatically quantify 3D cell morphology of plant tissue from micro-CT instead of opting for laborious manual annotations or less accurate segmentation approaches. In case fruit tissue porosity or pore network connectivity is too low or the specific surface area of the pore space too high, native X-ray micro-CT is unable to provide proper marker points of cell outlines, and one should rely on more elaborate contrast-enhancing scan protocols.

Nesting statistics in the $O(n)$ loop model on random maps of arbitrary topologies

We pursue the analysis of nesting statistics in the O(n) loop model on random maps, initiated for maps with the topology of disks and cylinders by Borot, Bouttier and Duplantier (2016), here for arbitrary topologies. For this purpose, we rely on the topological recursion results by Borot, Eynard and Orantin (2011, 2015) for the enumeration of maps in the O(n) model. We characterize the generating series of maps of genus \mathsf{g} with k boundaries and k' marked points which realize a fixed nesting graph. These generating series are amenable to explicit computations in the loop model with bending energy on triangulations, and we characterize their behavior at criticality in the dense and in the dilute phase.

EWSeg: a fast segmentation algorithm for images based on edge linking and watershed constraints

In this paper, we propose a two-stage algorithm, named watershed-constrained image segmentation, for exploring complete edge-closed regions from edges. In the first stage, the input image is pre-processed and the image gradient information is obtained using a gradient operator. Anchors are then obtained from the gradient information. Finally, initial edges are obtained by intelligently connecting the anchors. In the second stage, a marker-based watershed algorithm is adopted to obtain marker points from the gradient information obtained in the first stage. A Gaussian filtered image is then used as the input image to obtain a watershed hyper-segmented edge map. Finally, complete edge-closed regions are obtained by combining the initial edges and the hyper-segmented edge map and searching for weak edges. The image segmentation results are then obtained from the edge-closed regions, demonstrating the excellent performance of our proposed algorithm on various images and videos.

Effect of Tooth Mobility on the Accuracy of Conventional Impressions: A Pilot Study.

To study the influence of tooth mobility on the accuracy of conventional impressions. In total, 10 patients with mobile anterior teeth and 10 healthy patients were treated with conventional impressions and intraoral digital impressions. The digital impression group was recorded as standard data, the mobile teeth group was recorded as the experimental group, and the healthy anterior teeth group was recorded as the control group. We imported digital impression and irreversible hydrocolloid impression files into Geomagic Wrap and marked reference points to execute N-point alignment, then we recorded the coordinates. Paired-samples t test was used to analyze whether the point coordinates of mobile teeth were statistically significant (a = .05). One-way ANOVA was used to analyze whether there was a relationship between coordinate differences and tooth mobility in the distal, coronal, and buccal directions (a = .05). In the buccal and coronal directions, the difference was statistically significant between the conventional and digital impression groups. In the buccal direction, the accuracy differences of I-degree and II-degree mobile teeth were 0.149 mm and 0.401 mm, respectively. In the coronal direction, the differences were 0.128 mm and 0.233 mm, respectively. Meanwhile, ANOVA analysis showed that there was a relationship between point coordinate difference and tooth mobility in the buccal and coronal directions. Conventional impressions can influence the accuracy of mobile tooth impressions. Therefore, digital impressions should be adopted for mobile teeth impressions.

Radiographic grid for locating foreign bodies in maxillofacial emergency trauma

ObjectivesThe accurate localization of the foreign bodies (FBs) is essential. This work presents a new noninvasive technique for subcutaneous metallic FBs under a radiographic grid, a system that simplifies the localization of facial FBs removal using a grid with embedded reference points.MethodsThis work designed a retrospective study to evaluate the effect of a radiographic grid on FBs removal surgery. All patients who met the inclusion criteria and attended the Hospital of Stomatology of China Medical University from January 2022 to June 2023 were enrolled and randomly divided into grid and non-grid groups. The assessment of facial swelling, the primary indicator, was conducted on days 2 and 7 post-surgery. The variables were analyzed using the Student t test and a repeated-measures general linear model.ResultsThe study sample consisted of 20 patients, with 14 males (70%) and 6 females (30%), who had an average age of 30.30 ± 5.38. The average time of operation was 1.85 ± 0.66 h (range 0.7 to 3.2). In the present cases in this report, of the 20 patients’ FBs, 14 were metal, 5 were glass, and 1 was residual root. And the FBs were surgically removed with no postoperative complications. Through comparison, it was found that the degree of swelling on day 2 postoperatively was significantly different between the grid group and the non-grid group (P < 0.05).ConclusionsThis study demonstrates that a radiographic grid with mark points is a more efficient approach compared with traditional methods for FBs removal, and this surgical method is more accurate, fast and noninvasive.

Dick pics and the shifty meanings of porn

ABSTRACT Dick pics are ubiquitous objects in social media shared for the purposes of harassment, flirtation, suggestion, amusement, and titillation alike. Starting with the question of how dick pics are, or are not classifiable as porn, this article opens up lines of inquiry on the possibilities and limitations of porn as a genre marker, content classifier, and reference point in and for understanding sexual content distributed through networked means. In the contemporary moment when sexual content continues to multiply online even as most social media platforms vigilantly moderate and remove it, scholarly vocabularies risk either lagging behind or posing normative categorisation on the things published and shared, from dick pics to webcam shows and OnlyFans content. This article calls for contextual care in how the notion of porn becomes applied to networked sexual media, the shapes of continue to morph, as well as in how dick pics are made sense of as communication devices and cultural symbols.

A new method for selecting and evaluating the hyperelastic model of tread rubber material under rolling contact condition

The selection and evaluation of the hyperelastic model of tread rubber material were of great value and significance to the clarification and application of the mechanical properties of tread rubber material. In this article, a non-contact tread rubber material rolling test bench was established. The improved digital image correlation method was used to calculate the strain rate distribution of the marked point under different test conditions. Combined with the stress distribution of the marked point, the rolling dynamic stress-strain characteristics of tread rubber material were obtained. Based on rubber material models under different tensile test modes, the parameter inversion identification of the hyperelastic model was completed, and the influence of the tensile test mode on the parameter inversion of the tread rubber hyperelastic model was revealed. A new method for selecting and evaluating the hyperelastic model of tread rubber material under rolling contact conditions was proposed. The selection criterion for the hyperelastic model of tread rubber material was developed under different rolling conditions. The experimental and analytical results show that the nonlinear degree of the constitutive relation of the hyperelastic model decreased with the increase in rolling speed. Compared with hyperelastic models under different tensile modes, the fitting error of the Yeoh model was less than 3%, and the overall fitting error of the Yeoh model was less than 2%. Therefore, the Yeoh model had better stability and accuracy and was more suitable for describing the rolling mechanical properties of tread rubber under rolling contact conditions.

Stability conditions for line bundles on nodal curves

Abstract We introduce the abstract notion of a smoothable fine compactified Jacobian of a nodal curve, and of a family of nodal curves whose general element is smooth. Then we introduce the combinatorial notion of a stability assignment for line bundles and their degenerations. We prove that smoothable fine compactified Jacobians are in bijection with these stability assignments. We then turn our attention to fine compactified universal Jacobians – that is, fine compactified Jacobians for the moduli space $\overline {\mathcal {M}}_g$ of stable curves (without marked points). We prove that every fine compactified universal Jacobian is isomorphic to the one first constructed by Caporaso, Pandharipande and Simpson in the nineties. In particular, without marked points, there exists no fine compactified universal Jacobian unless $\gcd (d+1-g, 2g-2)=1$ .

Test-retest reliability and agreement of remote home-based functional capacity self-administered assessments in community-dwelling, socially isolated older adults.

To determine the test-retest reliability and agreement of home-based functional capacity self-administered assessments in socially isolated older adults. Fourteen community-dwelling older adults (eight females, 67.9 ± 7.7 years) volunteered for this study. Before testing, participants were screened online for eligibility and received instructional videos explaining test set-up and execution. Participants underwent the 30-second sit-to-standing test, gait speed tests at the usual pace, and timed-up-and-go tests administered 4 weeks apart. For the 30-second sit-to-standing protocol, participants were instructed to repeatedly sit and stand from a chair (with a height of ∼ 43 cm and without armrests) for 30 s, with the number of repetitions recorded. In the gait speed test protocol, participants were instructed to walk at their usual and comfortable pace, with the time taken recorded (seconds). In the timed-up-and-go, participants stood up from a chair, walked as fast as possible for 3 m, circled a marked point, and returned to the chair to sit down, completing the test, with the score recorded (seconds). A trained researcher conducted the scoring virtually via synchronous video. 30-second sit-to-standing, gait speed test, and timed-up-and-go showed excellent mean coefficient of variation values (2.0-4.9), small standard error of measurement (0.08-1.27), excellent intraclass coefficient (0.97-0.99), very strong correlations (0.97-0.99) and good agreement between the two days of testing. Self-administered functional capacity tests performed by older adults at home were reliable with good agreement. Healthcare professionals and older adults should take advantage of simple remote self-administered assessments performed at home to evaluate older adults' health status.

Decoding a Cognitive Performance State from Behavioral Data in the Presence of Auditory Stimuli.

Cognitive performance state is an unobserved state that refers to the overall performance of cognitive functions. Deriving an informative observation vector as well as the adaptive model and decoder would be essential in decoding the hidden performance. We decode the performance from behavioral observation data using the Bayesian state-space approach. Forming an observation from the paired binary response with the associated continuous reaction time may lead to an overestimation of the performance, especially when an incorrect response is accompanied by a fast reaction time. We apply the marked point process (MPP) framework such that the performance decoder takes the correct/incorrect responses and the reaction time associated with correct responses as an observation. We compare the MPP-based performance with two other decoders in which the pairs of binary and continuous signals are taken as the observation; one decoder considers an autoregressive (AR) model for the performance state, and the other one employs an autoregressive-autoregressive conditional heteroskedasticity (AR-ARCH) model which incorporates the time-varying and adaptive innovation term within the model. To evaluate decoders, we use the simulated data and the n-back experimental data in the presence of multiple music sessions. The Bayesian state-space approach is a promising way to decode the performance state. With respect to individual perspective, the estimated MPP-based and ARCH-based performance states outperform the AR-based estimation. Based on the aggregated data analysis, the ARCH-based performance decoder outperforms the other decoders. Performance decoders can be employed in educational settings and smart workplaces to monitor one's performance and contribute to developing a feedback controller in closed-loop architecture to improve cognitive performance.

Золотое сечение в римском эпосе (на материале «Фиваиды» Стация)

Golden section poetic phenomena studies comprise a wide range of topics, starting from basic prosodic elements to the work’s entire composition structure. The primary purpose of this paper is to establish the connection between the golden section and the literary composition and form and to analyze it on the material of the episode of aristeia and katabasis of Amphiaraus in Statius’ “Thebaid” (VII, 690–823). The following objectives are included: to define and measure the segments of the golden section; to determine the marking points dividing the segments which, as a rule, contain salient features — literary devices, hero’s speech, poet’s apostrophe etc.; to identify the functions and role of the golden section in the episode’s composition. The methodology uses general scientific methods such as philological textual analysis and mathematical tools. The supportive research is grounded on parallel comparison of episodic structure, framed by visual techniques and segment dividing points. It is observed that proportional segmentation is achieved by typical epic techniques such as epitaph or catalogue of victims serving the closing part of the narrative. As for the simile’s structural functions, they mark the poetic period by opening and, more frequently, ending it and highlight the culmination moments functioning similar to the hero’s speeches. The overall examination concludes that the golden section in “Thebaid” manifests itself with striking precision in relation to separate parts and to the whole poem as well. Similarly, it applies to corresponding stages of emotional tension and moments of culmination and the correlating literary devices and techniques. The utilization of the golden section provides the symmetrical composition and the triadic structure of the episode, demonstrating the poetic skillfulness of Statius and mastery of attracting the reader’s attention to the most significant points.

Mean Reflected BSDE Driven by a Marked Point Process and Application in Insurance Risk Management

This paper aims to solve a super-hedging problem along with insurance re-payment under running risk management constraints. The initial endowment for the super-hedging problem is characterized by a class of mean reflected backward stochastic differential equation driven by a marked point process (MPP) and a Brownian motion. By Lipschitz assumptions on the generators and proper integrability on the terminal value, we give the well-posedness of this kind of BSDEs by combining a representation theorem with the fixed point argument.

Exponential growth BSDE driven by a marked point process

Exponential growth BSDE driven by a marked point process

Bird‐flower colour on islands supports the bee‐avoidance hypothesis

Abstract Many insular plant species inhabiting different archipelagos worldwide present typical ornithophilous floral traits (e.g. copious nectar, red‐orange colours), but most of them are visited by insectivorous/granivorous birds and lizards, which act as generalist pollinators. Oceanic islands promote these ecological interactions mainly due to the scarcity of arthropods. Our goal is to understand how these generalist interactions contribute to the shift of floral traits from entomophily (mainland) to ornithophily or saurophily (island), where specialist nectar‐feeding birds have not inhabited. We used the well‐known pollination interactions occurring in the Canary Islands to evaluate two proposed ecological hypotheses, bee‐avoidance or bird‐attraction, explaining evolutionary transitions of floral traits. Specifically, we studied the flower colour conspicuousness of bird‐pollinated Canarian species visited by birds and lizards with their closest relatives from the mainland mainly visited by bees. We analysed the chromatic contrast of flower colours using visual models of bees, birds and lizards and the achromatic contrast in visual models of bees. We also compared reflectance spectra marker points of flowers with available spectral discrimination sensitivities of bees and birds. Using a phylogenetically corrected framework of independent plant lineages, our results revealed that bird‐pollinated Canarian species showed lower chromatic contrast according to bees and lizard visual models than their mainland relatives, but similar chromatic contrast for bird vision. In addition, reflectance spectra marker points of the Canarian species were displaced to the longest wavelengths, far from the wavelengths of maximum discrimination of bees, but close to birds. We conclude that the avoidance of bees would be a primary ecological strategy explaining the evolutionary transitions of flower colours from melittophily to ornithophily. The lower conspicuousness of bird‐pollinated Canarian flowers in lizards is perhaps a side effect of the bee‐avoidance strategy rather than an independent evolutionary strategy. Together, these findings provide insights into how vertebrate generalist pollinators can also lead to divergence of floral traits in insular habitats, but also in other arthropod‐poor habitats. Read the free Plain Language Summary for this article on the Journal blog.

THE CERESA CLASS: TROPICAL, TOPOLOGICAL AND ALGEBRAIC

Abstract The Ceresa cycle is an algebraic cycle attached to a smooth algebraic curve with a marked point, which is trivial when the curve is hyperelliptic with a marked Weierstrass point. The image of the Ceresa cycle under a certain cycle class map provides a class in étale cohomology called the Ceresa class. Describing the Ceresa class explicitly for nonhyperelliptic curves is in general not easy. We present a ‘combinatorialization’ of this problem, explaining how to define a Ceresa class for a tropical algebraic curve and also for a topological surface endowed with a multiset of commuting Dehn twists (where it is related to the Morita cocycle on the mapping class group). We explain how these are related to the Ceresa class of a smooth algebraic curve over $\mathbb {C}(\!(t)\!)$ and show that the Ceresa class in each of these settings is torsion.

On Computing Medians of Marked Point Process Data Under Edit Distance

In this paper, we consider the problem of computing a median of marked point process data under an edit distance. We formulate this problem as a binary linear program, and propose to solve it to optimality by software. We show results of numerical experiments to demonstrate the effectiveness of the proposed method and its application in earthquake prediction.