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We rely on a total of 23 (cluster size, 8 structural, and 14 connectivity) descriptors to investigate structural patterns and connectivity motifs associated with water cluster aggregation. In addition to the cluster size n (number of molecules), the 8 structural descriptors can be further categorized into (i) one-body (intramolecular): covalent OH bond length (rOH) and HOH bond angle (θHOH), (ii) two-body: OO distance (rOO), OHO angle (θOHO), and HOOX dihedral angle (ϕHOOX), where X lies on the bisector of the HOH angle, (iii) three-body: OOO angle (θOOO), and (iv) many-body: modified tetrahedral order parameter (q) to account for two-, three-, four-, five-coordinated molecules (qm, m = 2, 3, 4, 5) and radius of gyration (Rg). The 14 connectivity descriptors are all many-body in nature and consist of the AD, AAD, ADD, AADD, AAAD, AAADD adjacencies [number of hydrogen bonds accepted (A) and donated (D) by each water molecule], Wiener index, Average Shortest Path Length, hydrogen bond saturation (% HB), and number of non-short-circuited three-membered cycles, four-membered cycles, five-membered cycles, six-membered cycles, and seven-membered cycles. We mined a previously reported database of 4 948 959 water cluster minima for (H2O)n, n = 3–25 to analyze the evolution and correlation of these descriptors for the clusters within 5 kcal/mol of the putative minima. It was found that rOH and % HB correlated strongly with cluster size n, which was identified as the strongest predictor of energetic stability. Marked changes in the adjacencies and cycle count were observed, lending insight into changes in the hydrogen bond network upon aggregation. A Principal Component Analysis (PCA) was employed to identify descriptor dependencies and group clusters into specific structural patterns across different cluster sizes. The results of this study inform our understanding of how water clusters evolve in size and what appropriate descriptors of their structural and connectivity patterns are with respect to system size, stability, and similarity. The approach described in this study is general and can be easily extended to other hydrogen-bonded systems. [ABSTRACT FROM AUTHOR]

This review aimed to assess the effect of repetitive transcranial magnetic stimulation (rTMS) in improving post-stroke unilateral spatial neglect (USN) using a meta-analysis. Further, we aimed to identify any association between rTMS parameters, patient demographics, and treatment effect sizes using subgroup analyses and meta-regression. A literature search was conducted through four databases from inception to March 6, 2024, to retrieve all relevant controlled trials investigating the effects of rTMS on symptoms of USN in post-stroke patients. Overall, rTMS significantly improved post-stroke USN, as measured by the line bisection test (Hedges' g = – 1.301, p < 0.0001), the cancelation test (Hedge's g = – 1.512, p < 0.0001), and the Catherine Bergego Scale (Hedges'g = – 0.770, p < 0.0001), compared to sham stimulation. Subgroup analysis found that generally larger effect sizes following excitatory rTMS across several outcome measures, indicating that excitatory rTMS on the ipsilesional hemisphere may be more effective than inhibitory rTMS on the contralesional hemisphere in ameliorating neglect symptoms. Meta-regression analysis of the line bisection test showed a significant difference in the chronicity of stroke patients, suggesting that rTMS may be more effective for USN in patients at the acute stage (within 3 months since stroke) than in those at the post-acute stage (p = 0.035). In conclusion, rTMS appears to be effective in promoting recovery from post-stroke USN. Excitatory protocols and early intervention may enhance recovery outcomes for neglect behaviors in post-stroke survivors. [ABSTRACT FROM AUTHOR]

This article explores the importance of calibration in prediction models when applied to new populations. It compares different calibration approaches and introduces Elkan's general updating approach (GUA), which accounts for differences in base rates between populations without re-estimation. The article explains how calibrated probability can be expressed as a function of base rates, which are estimated using proportions of subjects with a certain outcome in training and calibration data. The text discusses two approaches for estimating base probability in a training data set: Elkan's GUA calculates the average of the target variable, while Baker's GUA suggests using the average of the conditional probability. Both approaches assume that the only difference between populations is the change in base rate and require a calibration data set. A simulation study comparing different calibration methods for machine learning models found that beta calibration performed the best, while isotonic calibration and IVAP calibration were similar. Elkan calibration and Baker calibration also showed similar performance. The article provides detailed information on the simulation scenarios and the performance of each calibration method. [Extracted from the article]

How stress affects functional hemispheric asymmetries is relevant because stress represents a risk factor for the development of mental disorders and various mental disorders are associated with atypical lateralization. Using three lateralization tasks, we investigated whether functional hemispheric asymmetries in the form of hemispheric dominance for language (verbal dichotic listening task), emotion processing (emotional dichotic listening task), and visuo-spatial attention (line bisection task) were affected by acute stress in healthy adults. One hundred twenty right-handed men and women performed these lateralization tasks in randomized order after exposure to a mild online stressor (i.e., an online variant of the Trier Social Stress Test (TSST), TSST-OL) and a non-stressful online control task (friendly TSST-OL, fTSST-OL) in a within-subjects design. Importantly, the verbal and the emotional dichotic listening tasks were presented online whereas the line bisection task was completed in paper–pencil form. During these tasks, we found the expected hemispheric asymmetries, indicating that online versions of both the verbal and the emotional dichotic listening task can be used to measure functional hemispheric asymmetries in language and emotion processing remotely. Even though subjective and physiological markers confirmed the success of the online stress manipulation, replicating previous studies, we found no stress-induced effect on functional hemispheric asymmetries. Thus, in healthy participants, functional hemispheric asymmetries do not seem to change flexibly in response to acute stress. [ABSTRACT FROM AUTHOR]

Hemispheric asymmetry is a fundamental principle in the functional architecture of the brain. It plays an important role in attention research where right hemisphere dominance is core to many attention theories. Lesion studies seem to confirm such hemispheric dominance with patients being more likely to develop left hemineglect after right hemispheric stroke than vice versa. However, the underlying concept of hemispheric dominance is still not entirely clear. Brain stimulation studies using transcranial magnetic stimulation (TMS) might be able to illuminate this concept. To examine the putative hemispheric asymmetry in spatial attention, we conducted a meta-analysis of studies applying inhibitory TMS protocols to the left or right posterior parietal cortices (PPC), assessing effects on attention biases with the landmark and line bisection task. A total of 18 studies including 222 participants from 1994 to February 2022 were identified. The analysis revealed a significant shift of the perceived midpoint towards the ipsilateral hemifield after right PPC suppression (Cohen's d = 0.52), but no significant effect after left PPC suppression (Cohen's d = 0.26), suggesting a hemispheric asymmetry even though the subgroup difference does not reach significance (p =.06). A complementary Bayesian meta-analysis revealed a high probability of at least a medium effect size after right PPC disruption versus a low probability after left PPC disruption. This is the first quantitative meta-analysis supporting right hemisphere-specific TMS-induced spatial attention deficits, mimicking hemineglect in healthy participants. We discuss the result in the light of prominent attention theories, ultimately concluding how difficult it remains to differentiate between these theories based on attentional bias scores alone. [ABSTRACT FROM AUTHOR]

The solar eclipse of 2017 August 21 was observed with the Potsdam Echelle Polarimetric and Spectroscopic Instrument (PEPSI) on the Large Binocular Telescope (LBT), which is located at Mt. Graham International Observatory (MGIO), Arizona, USA. At this location, a partial eclipse was observed with maximum obscuration of about 61.6%. The 11-millimeter-aperture, binocular Solar Disk-Integrated (SDI) telescope, located on the kitchen balcony of the LBT building, feeds sunlight to PEPSI, which has recorded a total of 116 Sun-as-a-star spectra in the wavelength range of 5300 – 6300 Å, with a spectral resolution R ≈ 250 , 000 and signal-to-noise ratio of about 733:1. The temporal evolution of the Fraunhofer Na i D doublet at λ 5890/5896 Å is analyzed using contrast profiles that illustrate subtle changes in the spectral line, not obvious in the intensity profiles. Line bisectors are used to study the height-dependent signature of convective motions. Sun-as-a-star spectra illustrate the radial atmospheric stratification and are affected by limb darkening, solar differential rotation, convective motions, and magnetic activity. During a partial solar eclipse, the contribution of these features is modified by the passage of the Moon, resulting in a transit spectral signature. These observations are compared with synthetic Na i D spectra generated by the Spectropolarimetic NLTE Analytically Powered Inversion (SNAPI) code, based on state-of-the-art Bifrost atmospheric parameters, applied to a geometrically accurate model of the solar eclipse. The model is in qualitative agreement with the observations. However, the discrepancies indicate that models need to be improved, where high-resolution eclipse spectroscopy can serve as a benchmark. [ABSTRACT FROM AUTHOR]

The causal and statistical hypotheses diverge in determining whether the lateralization of language function in one cerebral hemisphere entails the lateralization of visuospatial function in the opposite hemisphere. Additionally, it remains unclear if the atypical segregation of these functions could influence cognitive performance. This study addresses these questions by examining the hemispheric lateralization of visuospatial attention during a line bisection judgement (landmark) task in three groups of healthy non-right-handed individuals with different language production segregations: left (typical), ambilateral (atypical), and right (atypical). Consistent with the causal hypothesis, results indicate that the groups with left and right language lateralization primarily utilize the opposite hemisphere for visuospatial attention. The ambilateral group, however, displays a pattern compatible with an independent segregation, supporting the statistical hypothesis. Behavioral analyses reveal that atypical lateralization of visuospatial attention (non-right) can lead to either better or worse performance during the landmark task, depending on the specific pattern. Bilateral organization is associated with reduced overall accuracy, whereas the left segregation results in improved performance during the most challenging trials. These findings suggest the existence of diverse pathways to lateralization, akin to either the causal or statistical hypothesis, which can result in cognitive advantages or disadvantages. [ABSTRACT FROM AUTHOR]

Abstract: Recent reviews on prism adaptation training (PAT) for visuospatial neglect concluded that it is ineffective. In our view, this conclusion goes too far. In this contribution, we discuss the limitations present in these reviews: the inclusion of right-sided neglect patients; failure to differentiate between patients with and without parietal lesions; ignoring results of line bisection or other tests. We argue that another aspect may play a role in the effectiveness of PAT: the extension of the task-work space. We show that using a workspace of more than 10° toward the contralesional side seems to improve the effectiveness of PAT. PAT still offers an important approach to treating neglect patients, and future studies should consider the extension of the workspace. [ABSTRACT FROM AUTHOR]

Background: To capture the distortion of exploratory activity typical of patients with spatial neglect, traditional diagnostic methods and new virtual reality applications use confined workspaces that limit patients' exploration behavior to a predefined area. Our aim was to overcome these limitations and enable the recording of patients' biased activity in real, unconfined space. Methods: We developed the Free Exploration Test (FET) based on augmented reality technology. Using a live stream via the back camera on a tablet, patients search for a (non-existent) virtual target in their environment, while their exploration movements are recorded for 30 s. We tested 20 neglect patients and 20 healthy participants and compared the performance of the FET with traditional neglect tests. Results: In contrast to controls, neglect patients exhibited a significant rightward bias in exploratory movements. The FET had a high discriminative power (area under the curve = 0.89) and correlated positively with traditional tests of spatial neglect (Letter Cancellation, Bells Test, Copying Task, Line Bisection). An optimal cut-off point of the averaged bias of exploratory activity was at 9.0° on the right; it distinguished neglect patients from controls with 85% sensitivity. Discussion: FET offers time-efficient (execution time: ∼3 min), easy-to-apply, and gamified assessment of free exploratory activity. It supplements traditional neglect tests, providing unrestricted recording of exploration in the real, unconfined space surrounding the patient. [ABSTRACT FROM AUTHOR]

The emphasis on traditional hand-drawn compass and straight-edge geometrical constructions has been reduced in the core narrative of most current curricula. In response to this trend, this paper presents a virtual toolkit for producing precision geometrical figures within the popular note-taking app, NotabilityTM. These graphical procedures employ the app’s stylus-based input and shape tools (for lines, circles, and squares) to offer a modern take on classical geometrical construction. These procedures are adaptations of familiar textbook methods, necessary because the app’s circle-drawing tool behaves differently from a standard compass. Beyond the familiar canon of elementary Euclidean constructions, such as angle bisectors and perpendiculars, these tools are also used to sketch examples of sangaku diagrams from original 19th-century Japanese temple geometry problems. That such precision figures can be created within a popular tablet app is a rallying call to geometers; the art and craft of traditional manual constructions need not go extinct and can continue to be nurtured in this age of digital paper. [ABSTRACT FROM AUTHOR]

Assessment of cognitive impairments is a vital part of clinical practice. Cancellation (visual search) and line bisection are commonly used tasks to assess visuospatial attention. Despite the fact visuospatial attention is engaged in both near (within reach) and far-space (out of reach), most studies have been conducted in near-space alone. Moreover, despite their use in clinical practice, it is unclear whether cancellation and bisection tasks are related. Here, we investigated the impact of aging on cancellation and line bisection performance in far-space in a large healthy sample. We provide preliminary age-graded norms for assessing visuospatial attention in far-space calculated from a sample of 179 healthy adults, between the ages of 18–94 (mean age = 49.29). Cancellation and line bisection were presented on a large screen in far-space and completed using a wireless remote. Aging was accompanied by longer task duration for both tasks, slower search speed and poorer quality of search. However, there was no significant effect of aging on line bisection error. There was a significant correlation between the two tasks in that longer task duration in line bisection was associated with slower search speed and poorer quality of search. Overall, participants presented a leftward bias during cancellation and line bisection akin to pseudoneglect. Moreover, we found that irrespective of age, search speed was faster in males than females. We offer novel evidence that performance on cancellation and line bisection tasks are related to one another in far-space, but are also sensitive to age-related decline, and even sex differences. [ABSTRACT FROM AUTHOR]

The celebrated Steiner-Lehmus theorem states that if the internal bisectors of two angles of a triangle are equal then the corresponding sides have equal lengths. That is to say if P is the incentre of Δ ABC and if BP and CP meet the sides AC and AB at B ′ and C ′, respectively, then An elegant proof of this theorem appeared in [1] and is reproduced in [2]. [ABSTRACT FROM AUTHOR]

Background: In recent years, there has been considerable interest in prosthetic alignment techniques for total knee arthroplasty (TKA), particularly in the so-called kinematic alignment, which aims to restore the knee's native alignment. However, implementing this technique requires specialized instruments and procedural steps that can be laborious. This study introduces the bisector of the trochlear groove as a reliable landmark for performing the distal femoral cut while maintaining parallelism with the native femoral joint line. Methods: Three orthopedic specialists assessed 110 X-ray images of full-leg, weight-bearing lower limbs obtained from healthy individuals between January 2021 and December 2022. The bisector of the trochlear groove was identified on the X-ray images, and the angle between this bisector and the femoral joint line was measured. The consistency of these measurements across repeated assessments and different examiners was evaluated. Results: The bisector of the trochlear groove was found to be perpendicular to the femoral joint line, with a mean angle of 89.4°. The inter-rater reliability was 68% within ±1.3° from the mean, while the intra-rater reliability was 82% within ±1.5° from the mean. Conclusions: These results suggest that by performing a femoral cut perpendicular to the bisector of the trochlear groove, surgeons can inherently restore the femoral joint line of the native knee in patients where the native joint line is no longer identifiable due to the effect of osteoarthritis. This method may offer a viable and straightforward alternative to the standard surgical technique currently practiced for kinematic alignment in TKA. [ABSTRACT FROM AUTHOR]

The spinal accessory nerve, considered part of the eleventh cranial nerve, provides motor innervation to sternocleidomastoid and trapezius. A comprehensive literature review and two cadaveric dissections were undertaken. The spinal accessory nerve originates from the spinal accessory nucleus. Its rootlets unite and ascend between the denticulate ligament and dorsal spinal rootlets. Thereafter, it can anastomose with spinal roots, such as the McKenzie branch, and/or cranial roots. The spinal accessory nerve courses intracranially via foramen magnum and exits via jugular foramen, within which it usually lies anteriorly. Extracranially, it usually crosses anterior to the internal jugular vein and lies lateral to internal jugular vein deep to posterior belly of digastric. The spinal accessory nerve innervates sternocleidomastoid, receives numerous contributions in the posterior triangle and terminates within trapezius. Its posterior triangle course approximates a perpendicular bisection of the mastoid-mandibular angle line. The spinal accessory nerve contains sensory nociceptive fibres. Its cranial nerve classification is debated due to occasional non-fusion with the cranial root. Surgeons should familiarize themselves with the variable course of the spinal accessory nerve to minimize risk of injury. Patients with spinal accessory nerve injuries might require specialist pain management. [ABSTRACT FROM AUTHOR]

A canal surface is the envelope of spheres with centers traversing a spatial curve called spine curve. The spheres contact the envelope along so-called characteristics, which are circles in general. If a canal surface contains two lines, then the spine curve is located on the bisector of these lines which in the case of skew lines is an orthogonal hyperbolic paraboloid. There are trivial cases of canal surfaces with infinitely many lines, the right cylinders, the right cones, and the one-sheeted hyperboloids of revolution. The only nontrivial case of a canal surface through four straight lines, that are not the limits of characteristics, is related to a Plücker conoid. The four given lines must be concyclic generators, i.e., they intersect each tangent plane of the conoid in four points lying on a circle. We are going to analyse and visualize this particular canal surface. [ABSTRACT FROM AUTHOR]

Geometry is a science with very wide applications in life. Everything around us is geometric shapes. Solving geometry problems helps us solve many real-life problems. In geometry there are many complex problems. But if a solution is found, many difficult problems will be solved quickly and easily. This article presents the auriliary projection method to solve many problems in geometry. The following data can be determined. [ABSTRACT FROM AUTHOR]

Background: This study investigated whether music training led to better length estimation and/or rightward bias by comparing the performance of musicians (pianists) and non-musicians on performance of line sections and line extensions. Methods: One hundred and sixteen participants, among them 62 musicians and 54 non-musicians, participated in the present study, completed line section and line extension task under three conditions: 1/2, 1/3 and 2/3. Results: The mixed repeated measures ANOVA analysis revealed a significant group × condition interaction, that the musicians were more accurate than non-musicians in all the line section tasks and showed no obvious pseudoneglect, while their overall performance on the line extension tasks was comparable to the non-musicians, and only performed more accurately in the 1/2 line extension condition. Conclusion: These findings indicated that there was a dissociation between the effects of music training on line section and line extension. This dissociation does not support the view that music training has a general beneficial effect on line estimation, and provides insight into a potentially important limit on the effects of music training on spatial cognition. [ABSTRACT FROM AUTHOR]

Each cerebellar hemisphere projects to the contralateral cerebral hemisphere. Previous research suggests a lateralization of cognitive functions in the cerebellum that mirrors the cerebral cortex, with attention/visuospatial functions represented in the left cerebellar hemisphere, and language functions in the right cerebellar hemisphere. Although there is good evidence supporting the role of the right cerebellum with language functions, the evidence supporting the notion that attention and visuospatial functions are left lateralized is less clear. Given that spatial neglect is one of the most common disorders arising from right cortical damage, we reasoned that damage to the left cerebellum would result in increased spatial neglect-like symptoms, without necessarily leading to an official diagnosis of spatial neglect. To examine this disconnection hypothesis, we analyzed neglect screening data (line bisection, cancellation, figure copying) from 20 patients with isolated unilateral cerebellar stroke. Results indicated that left cerebellar patients (n = 9) missed significantly more targets on the left side of cancellation tasks compared to a normative sample. No significant effects were observed for right cerebellar patients (n = 11). A lesion overlap analysis indicated that Crus II (78% overlap), and lobules VII and IX (66% overlap) were the regions most commonly damaged in left cerebellar patients. Our results are consistent with the notion that the left cerebellum may be important for attention and visuospatial functions. Given the poor prognosis typically associated with neglect, we suggest that screening for neglect symptoms, and visuospatial deficits more generally, may be important for tailoring rehabilitative efforts to help maximize recovery in cerebellar patients. [ABSTRACT FROM AUTHOR]

In some patients with unilateral spatial neglect, symptoms reflect impaired lateralized spatial attention and representation (perceptual bias) whereas in others the inability to respond to stimuli located in contralesional space (response bias). Here, we investigated whether prismatic adaptation (PA) and visual scanning training (VST) differentially affect perceptual and response bias and whether rehabilitation outcome depends on the type of bias underlying symptoms. Two groups of neglect patients in the subacute phase were evaluated before, immediately after, and two weeks following 10 days of PA (n = 9) or VST (n = 9). Standard neuropsychological tests (i.e., Behavioural Inattentional Test, Diller cancellation test, and Line Bisection test) were administered to assess neglect symptoms, while the Landmark task was used to disentangle perceptual and response biases. Performance on the Landmark task revealed that PA was more effective in improving the perceptual bias, while VST mainly modulated the response bias. Neuropsychological tests performance suggested that VST is better suited to modulate neglect in patients with response bias, while PA may be effective in patients with both types of bias. These findings may offer novel insights into the efficacy of PA and VST in the rehabilitation of perceptual and response biases in patients with neglect. [ABSTRACT FROM AUTHOR]

The golden ratio, also known as Phi (ϕ ≈ 1.618034), attracted the interest of mathematicians, artists, and intellectuals for many centuries, probably from when it was discovered in human anthropometry. Even in recent times, researchers found the presence of the golden ratio in Renaissance paintings and aesthetic preferences. The reasons behind the fascination with the golden ratio remain unclear, but it has been suggested that stimuli containing this proportion are often perceived as beautiful. However, evidence is conflicting, and the literature struggles to establish the existence of individual preferences for the golden ratio. To gain new insights into the nature of these preferences, one hundred participants completed an implicit association task, with either golden ratio or random stimuli presented with positive or negative words. Participants initially categorized the stimuli based on their assigned categories. Then, we assessed their explicit preferences by asking them to rate the stimuli in terms of pleasantness and by completing a line bisection task and the Ultimatum Game. The results revealed the typical effects observed in implicit association tasks, with improved response times and accuracy when golden ratio stimuli were associated with positive word categories. In contrast, explicit ratings yielded mixed results. We discuss our findings in relation to previous studies that have explored this issue, highlighting the ongoing debate surrounding preferences for the golden ratio. [ABSTRACT FROM AUTHOR]

If we talk about the centre of a triangle, what might we be referring to? Any triangle has many different points that could regarded as its centre; in fact, Encyclopedia of Triangle Centres lists over 70 000 possibilities. Three of the most famous centres, that every triangle will possess (although they may coincide), are the incentre (where the three angle bisectors meet), the centroid (where the three medians meet) and the orthocentre (where the three altitudes meet). Proofs that these centres are well-defined and exist for every triangle are simple and satisfying, good examples of reasoning (if we are teachers) for our students. Proving the three altitudes of a triangle share a point using the scalar product of vectors is a wonderful demonstration of the power of this idea. [ABSTRACT FROM AUTHOR]

In this study, we tested the theory of angles that was proposed almost a century ago by the tennis player Henri Cochet. This theory proposes that expert tennis players should position themselves on the bisector of the angle of the opponent's possibilities in order to optimize shot return, suggesting a geometric occupation of the court relative to the opponent's affordances; namely what he/she is capable of doing. We tested this hypothesis by analysing player and ball positioning data from professional tennis matches recorded with a Hawk-Eye system. We compared this hypothesis with two alternative computational and probabilistic hypotheses which would consist in positioning oneself on the average or the median of the shots usually played from a given location. The results show that expert tennis players apply the principles of the theory of angles and thus confirm Henri Cochet's intuition. That is, for lateral court positioning, a geometric strategy is deemed optimal by expert players. It also appears that the more experienced the players are, the more precise their application of this strategy becomes. [ABSTRACT FROM AUTHOR]

We determine the range of values for the length of an area bisector or a perimeter bisector in a triangle. In particular, we determine all such bisectors of extreme length. Our work highlights a few remarkable properties of the area and perimeter bisectors perpendicular to the angle bisectors. [ABSTRACT FROM AUTHOR]

Background: Unilateral spatial neglect (USN) is a commonly occurring neurocognitive disability after a stroke. The neglect may affect the motor recovery of the upper and lower limbs and functional performances. Mirror therapy, a simple and economical approach has the potential to reduce the USN and related impairments. Aim: The primary objective of this study is to determine the effectiveness of task-based and magnified mirror therapy on the USN and on the motor recovery of the post-stroke subjects. The secondary objective is to investigate the effectiveness of the intervention on the function and disability of the subjects. Methods: In this randomized controlled, assessor-blinded trial, 86 post-stroke subjects will be recruited from the neuro-rehabilitation laboratory of a rehabilitation institute, located in northern India. The participants,aged20 to 80 years, with 1 to 36 months of stroke onset, hemiparesis, and the USN, will be considered eligible for the study. In addition to the conventional rehabilitation, the experimental group(n = 43) will receive 40 sessions (8 weeks) of Task-based and MAGnified Mirror Therapy for Unilateral Spatial Neglect (T-MAGUSN). The control group (n = 43) will undergo a dose-matched conventional program only. The participants will be assessed at baseline, post-intervention and 4-week follow-up using primary (Line Bisection Test, Letter Cancellation Test, and Fugl-Myer Assessment) and secondary (Catherine Bergego Scale, Berg Balance Scale, Functional Ambulation Classification, Modified Rankin Scale) outcome measures. Discussion: This proposed study will lead to the development of a novel rehabilitation protocol for the management of USN, aiming to enhance motor and functional recovery. The investigation will consider both the upper and lower limbs for the intervention, reducing the impact of cognitive disability in stroke. Trial registration: Clinical Trial Registry of India (CTRI) as CTRI/2023/05/053184 (www.ctri.nic.in/Clinicaltrials/pmaindet2.php?trialid=74659). [ABSTRACT FROM AUTHOR]

Alertness, or one's general readiness to respond to stimulation, has previously been shown to affect spatial attention. However, most of this previous research focused on speeded, laboratory-based reaction tasks, as opposed to the classical line bisection task typically used to diagnose deficits of spatial attention in clinical settings. McIntosh et al. (Cogn Brain Res 25:833–850, 2005) provide a form of line bisection task which they argue can more sensitively assess spatial attention. Ninety-eight participants were presented with this line bisection task, once with and once without spatial cues, and both before and after a 50-min vigilance task that aimed to decrease alertness. A single participant was excluded due to potentially inconsistent behaviour in the task, leaving 97 participants for the full analyses. While participants were, on a group level, less alert after the 50-min vigilance task, they showed none of the hypothesised effects of reduced alertness on spatial attention in the line bisection task, regardless of with or without spatial cues. Yet, they did show the proposed effect of decreased alertness leading to a lower level of general attention. This suggests that alertness has no effect on spatial attention, as measured by a line bisection task, in neurotypical participants. We thus conclude that, in neurotypical participants, the effect of alertness on spatial attention can be examined more sensitively with tasks requiring a speeded response compared to unspeeded tasks. [ABSTRACT FROM AUTHOR]

The document titled "Problems and Solutions" is an article from the American Mathematical Monthly that provides a list of proposed problems and solutions for mathematicians to submit. The problems cover various topics in mathematics and include instructions for submission. The article also includes solutions to specific problems, such as a field homomorphism and angle bisectors meeting opposite sides of a triangle. It further discusses mathematical equations, identities, and problems related to chair loading, ski lift patterns, tile elimination, and properties of points inside triangles. The solutions to these problems are provided by different mathematicians from various countries. [Extracted from the article]

The article explores the relationship between Euclidean geometry and calculus, speculating on what would have happened if calculus had been developed before geometry. It discusses the application of Apollonius's theorem and Stewart's theorem in geometry, as well as the work of Heron of Alexandria. The text also discusses the law of cosines and Newton's assumption about the length of the angle bisector. It explores the generalization of the Pythagorean theorem in three dimensions and discusses a method called de Gua's theorem for deriving classical theorems in Euclidean geometry. The text acknowledges the contributions of others in developing this method. [Extracted from the article]

The accuracy of passive localization is impacted by the position of the receiving stations. In practical applications, signal reception is frequently influenced by the emission angle of the target signal, which makes it a challenge to ensure localization accuracy. We present an optimal placement method for TDOA localization with constraints on the signal angle. Firstly, we establish a localization error model based on polar coordinates, which reveals that the localization error is solely dependent on the angular relationships between the target and receiving stations. We determine the optimal locations of the stations without constraints. We then introduce a novel approach where the quarter-angle and one-fifth angle within the emitted beam angle are employed as critical values to determine station placement. Given the constraint of the angle, we use the critical values to evaluate the angular relationship between the station and the target, determining if the station should be positioned on the boundary or on the angle bisector to achieve optimal placement method. Finally, we validate our proposed method through simulations, demonstrating its ability to minimize errors in various scenarios. The method proposed provides an effective solution to the challenge of target localization with constraints on the received signal beam angle. [ABSTRACT FROM AUTHOR]

This article, published in Mathematical Notes, discusses the absolute convergence of Fourier series of functions of two variables in the space C1, ¿. The authors explore the conditions that ensure the absolute convergence of the series and define the space A, which consists of functions for which the series converges. They also discuss the classical results of Bochner and Weinger, who extended the Bernstein theorems to functions of two variables. The authors refine Weinger's result using probabilistic considerations and provide a theorem that demonstrates the existence of a function in the space C1, ¿ that is not included in A. The article also mentions the sufficient conditions on the modulus of continuity ¿(¿) that ensure the embedding C1, ¿ ¿ A. The work was financially supported by the Russian Science Foundation. [Extracted from the article]

Despite mounting evidence pointing to the contrary, classical neurosurgery presumes many cerebral regions are non-eloquent, and therefore, their excision is possible and safe. This is the case of the precuneus and posterior cingulate, two interacting hubs engaged during various cognitive functions, including reflective self-awareness; visuospatial and sensorimotor processing; and processing social cues. This inseparable duo ensures the cortico-subcortical connectivity that underlies these processes. An adult presenting a right precuneal low-grade glioma invading the posterior cingulum underwent awake craniotomy with direct electrical stimulation (DES). A supramaximal resection was achieved after locating the superior longitudinal fasciculus II. During surgery, we found sites of positive stimulation for line bisection and mentalizing tests that enabled the identification of surgical corridors and boundaries for lesion resection. When post-processing the intraoperative recordings, we further identified areas that positively responded to DES during the trail-making and mentalizing tests. In addition, a clear worsening of the patient's self-assessment ability was observed throughout the surgery. An awake cognitive neurosurgery approach allowed supramaximal resection by reaching the cortico-subcortical functional limits. The mapping of complex functions such as social cognition and self-awareness is key to preserving patients' postoperative cognitive health by maximizing the ability to resect the lesion and surrounding areas. [ABSTRACT FROM AUTHOR]

Background and purpose: This study was undertaken to assess the most sensitive combination of tests to detect peripersonal unilateral neglect (UN) after stroke. Methods: The present study is a secondary analysis of a previously reported multicentric study of 203 individuals with right hemisphere damage (RHD), mainly subacute stroke, 11 weeks postonset on average, and 307 healthy controls. A battery of seven tests, providing 19 age‐ and education‐adjusted z‐scores, were given: the bells test, line bisection, figure copying, clock drawing, overlapping figures test, and reading and writing. Statistical analyses used a logistic regression and a receiver operating characteristic (ROC) curve after adjustment on demographic variables. Results: A combination of four z‐scores based on the following three tests provided good discrimination of patients with RHD from matched healthy controls: the starting point and the difference between the number of omissions on left and right sides from the bells test, rightward deviation in bisection of long lines (20 cm), and left‐sided omissions in a reading task. The area under the ROC curve was 0.865 (95% confidence interval = 0.83–0.901), with sensitivity = 0.68, specificity = 0.95, accuracy = 0.85, positive predictive value = 0.90, and negative predictive value = 0.82. Conclusions: The most sensitive and parsimonious combination of tests to detect UN after stroke relies on four scores from three simple tests (bells test, line bisection, and reading). Future study is warranted to assess its ability to account for the functional difficulties of UN in daily life in the patient's actual environment. [ABSTRACT FROM AUTHOR]

A new multidimensional Model II regression based on bisector point of view (BRM-II) is introduced for multivariate problems that may contain measurement error. The suggested method is constructed depending on using the bisector of the minor angle between two hyperplanes identified by linear regression. The performance of the proposed method are examined by simulations up to ten variables for different sample sizes and distribution types in terms of the Mean Square Error. Moreover, the BRM-II is applied to two real problems with two and three variables, and compared with the existing methods. The results indicate that the BRM-II is easy applicable and offers relatively better accuracy. The relevant method can be easily coded in any programming language provides convenience in its application. Thus, the proposed method provide powerful tool for prediction of relevant real life problems. [ABSTRACT FROM AUTHOR]

We use about 430 CCD spectra obtained in 1998–2001 and in 2007 to study temporal radial velocity variations of the ion, He  i , and H β lines in the spectrum of the α Cyg. We found that these variations are caused by pulsation-type motions. In case of the ion and He  i lines, fluctuations occur in the fundamental radial mode with the period of about 12.5 ± 1.0 d and the amplitude of 5.0 ± 0.5 km s−1. The oscillation lasts about ∼34 ± 1 d. In the case of the H β line the radial velocity variability was studied separately for the blue and red halves of the line profile. Such a methodical approach allowed to discover three characteristic cases of radial velocity variability for the blue and red halves of the H β line profile. In 1999 and 2001, the period P and amplitude A variability parameters are the same for the blue and red halves, and hence for the line bisector too. In 1998, P and A are the same for the blue and red halves of the profile, however, there is a phase shift between the fluctuations of their radial velocity by 0.6 P. In 2000, P and A are different for the two halves of the line profile. Relative to the center of the star's mass, the average expansion rate for the atmospheric layers, where the H β line is formed, is about −10.0 km s−1. It varies over time with a semi-amplitude of around ±3.3 km s−1. [ABSTRACT FROM AUTHOR]

Patients with left unilateral spatial neglect (USN) typically place the subjective midpoint to the right of the objective centre when bisecting a horizontal line. This pathological phenomenon may be explained as a result of greater dependence on the right endpoint in the external reference frame (Koyama et al., Brain Cogn, 35, 1997, 271; McIntosh et al., Cogn Brain Res, 25, 2005, 833). Ishiai et al. (Brain, 112, 1989, 1485) reported that once patients with USN fixated on a certain point on the right part of the presented line, they persisted with this point and marked the subjective midpoint there without leftward searches. Ishiai et al.'s interpretation was that the patients saw a totalised line representation that extended equidistantly to the right and left sides, based on the information of the attended rightward extent from the subjective midpoint. Accordingly, we used virtual reality goggles (VRG) and devised a mirror‐image viewing (MV) condition that showed a full‐field view based on the right visual field information to test whether healthy participants would thereby show neglect‐like bisection performance. The participants were 30 healthy adults (22–37 years old; 15 women and 15 men). In this condition, 96.7% (29/30) of participants were judged to exhibit USN‐like performance of line bisection, indicating the effectiveness of MV condition to simulate USN. The novelty of the present study lies in the use of a task‐specific intervention of neglect‐like visuospatial processing during line bisection without attempting to modify the direction of spatial attention. This approach may contribute to the understanding of the pathological visuospatial processing of USN. [ABSTRACT FROM AUTHOR]

Pseudoneglect, that is the tendency to pay more attention to the left side of space, is typically assessed with paper-and-pencil tasks, particularly line bisection. In the present study, we used an everyday task with more complex stimuli. Subjects' task was to look for pre-specified objects in images of real-world scenes. In half of the scenes, the search object was located on the left side of the image (L-target); in the other half of the scenes, the target was on the right side (R-target). To control for left–right differences in the composition of the scenes, half of the scenes were mirrored horizontally. Eye-movement recordings were used to track the course of pseudoneglect on a millisecond timescale. Subjects' initial eye movements were biased to the left of the scene, but less so for R-targets than for L-targets, indicating that pseudoneglect was modulated by task demands and scene guidance. We further analyzed how horizontal gaze positions changed over time. When the data for L- and R-targets were pooled, the leftward bias lasted, on average, until the first second of the search process came to an end. Even for right-side targets, the gaze data showed an early left-bias, which was compensated by adjustments in the direction and amplitude of later saccades. Importantly, we found that pseudoneglect affected search efficiency by leading to less efficient scan paths and consequently longer search times for R-targets compared with L-targets. It may therefore be prudent to take spatial asymmetries into account when studying visual search in scenes. [ABSTRACT FROM AUTHOR]

Medial malleolar osteotomy has been widely performed for posteromedial osteochondral lesions of the talus (OLT) to expose the lesion. In osteochondral fragment fixation, bioabsorbable pins should be inserted as perpendicular as possible to obtain the rigid fixation. However, the exposure of the lesion may depend on the osteotomy angle, which affects the pin insertion angles. This study aimed to analyze the relationship between pin insertion and osteotomy angles in the medial malleolar osteotomy. Twenty-four ankles of 23 patients were included. The malleolar bisector angle which was calculated from radiographs and actual osteotomy angles were measured on radiographs, and the pin insertion and osteotomy angles were measured using MRI. The intersection angle was defined by the tangential line of the tibial plafond and medial malleolar articular facet, and the bisector of this angle was defined as the malleolar bisector angle. The relationship between pin insertion and osteotomy angles was analyzed. There was no significant difference between the actual osteotomy (55.7° ± 6.6°) and malleolar bisector angles (57.4° ± 4.3°) on the radiograph. There was a significant correlation between pin insertion and osteotomy angles (rs = 0.601). The pin insertion angle (54.3° ± 5.9°) in the lower actual osteotomy angle than the malleolar bisector angle was smaller than those in the higher actual osteotomy angle (63.4° ± 8.2°). This study showed the osteotomy angle affected pin insertion angle. The osteotomy angle should not be smaller than the malleolar bisector angle at medial malleolar osteotomy to insert pins as perpendicular as possible for fixation of posteromedial OLTs. [ABSTRACT FROM AUTHOR]

Pseudoneglect, the tendency to display a leftward perceptual bias, is consistently observed in line bisection tasks. Some studies have shown that pseudoneglect is sensitive to emotions. This emotion-related modulation is likely related to valence-dependent hemispheric lateralization, although the results do not converge. A possible explanation for these inconsistencies could be individual differences in emotional tone. Considering that negative and positive emotions produce different basic activations of the two hemispheres, emotional characteristics of the subjects, such as trait anxiety, could in fact modulate the pseudoneglect phenomenon. To verify this, high- and low-anxiety participants were asked to centrally bisect horizontal lines delimited by neutral or emotional (happy and sad) faces. In line with previous studies, results here showed a decrease in the leftward bisection error in the presence of happy faces, indicating a greater involvement of the left hemisphere in processing positive emotional stimuli. In addition, trait anxiety influenced the magnitude of the visual bias. High-anxiety subjects, compared to low-anxiety subjects, showed a general bias in visual attention toward the left space as a function of emotional valence. Results are discussed within the framework of valence-dependent hemispheric specialization and the relative degree of activation. In sum, our data highlight the relevance of considering emotional individual differences in studying the pseudoneglect phenomenon. [ABSTRACT FROM AUTHOR]