Negative Numbers Research Articles

Reflectance confocal microscopy for margin mapping of melanoma of the lentigo maligna type: A systematic review and meta-analysis.

Melanoma of the lentigo maligna (LM) type and its invasive counterpart, lentigo maligna melanoma (LMM), occur in chronically sun-damaged skin and tend to have subclinical extension that makes presurgical margin mapping challenging. Reflectance confocal microscopy (RCM) is a non-invasive imaging modality that enables invivo visualization of the skin at the cellular level, allowing for adequate estimation of LM/LMM margins. We aimed to perform a systematic review and meta-analysis evaluating RCM's performance compared with histopathology in margin mapping of LM/LMM. We searched MEDLINE, Embase, Cochrane, and Clinicaltrials.gov for studies published until July 2023, assessing RCM diagnostic accuracy for presurgical LM/LMM margin delineation. Negative predictive value (NPV; number of true negatives confirmed by histopathology out of all negatives found on RCM) was our primary outcome. Secondary outcomes were proportion of agreement between RCM and histopathology, mean number of stages to clear lesion, sensitivity, and specificity. Of the 955 search results, nine studies (329 participants) were included. Pooled NPV for RCM detection of LM/LMM clear margins was 89.15% (95% CI 80.95-95.46; I2 = 80%). The RCM and histopathology agreement rate was 92.09% (95% CI 84.71-96.07; I2 = 57%). Mean number of stages needed to clear the lesion using RCM was 1.16 (95% CI 1.08-1.23; I2 = 0). Compared with histopathology, RCM sensitivity and specificity were 91.4% (95% CI 82.2-96.1; I2 = 0%) and 95.7% (95% CI 90.7-98; I2 = 68%), respectively. These results support that RCM has a high concordance rate with the gold standard histopathology for presurgical LM/LMM margin mapping, constituting a valuable tool for its management.

Supplemental Material for All Real Numbers Are Important: The Significance of Negative Number Understanding for Mathematics Achievement

Supplemental Material for All Real Numbers Are Important: The Significance of Negative Number Understanding for Mathematics Achievement

Axiomatization of Boolean Connexive Logics with syncategorematic negation and modalities

Abstract In the article we investigate three classes of extended Boolean Connexive Logics. Two of them are extensions of Modal and non-Modal Boolean Connexive Logics with a property of closure under an arbitrary number of negations. The remaining one is an extension of Modal Boolean Connexive Logic with a property of closure under the function of demodalization. In our work we provide a formal presentation of mentioned properties and axiom schemata that allow us to incorporate them into Hilbert-style calculi. The presented axiomatic systems are provided with proofs of soundness, completeness and decidability. The properties of closure under negation and demodalization are motivated by the syncategorematic view on the connectives of negation and modalities, which is discussed in the paper.

Experimental colitis is comorbid with social interaction deficits and anxiety-like behaviors in mice: mechanistic intuitions into neuroinflammation and Claudin 5 expression in the hippocampus.

Inflammatory bowel disease (IBD) is accompanied by psychiatric disorders, including Schizophrenic-like manifestations. Although incompletely illustrated, intestinal mucosal membrane damage and blood-brain barrier (BBB) penetrability may have significant roles in psychiatric symptoms of IBD. This study aimed to investigate role of the Claudin-5 (CLDN5) (a regulator of the permeability of BBB) and neuroinflammatory response in the comorbid behavioral disorders in experimental colitis in mice. Acetic acid was used to induce colitis in mice. 7 days after induction of colitis, behaviors including social interaction and locomotor activity as well as anxiety-like behaviors were evaluated. Then, the colon was extracted for gross and microscopic evaluations. The expression of CLDN5, TNF-α, IL1β and IL23 was measured by RT-PCR in the colon and hippocampus. Histopathologic evaluations demonstrated mucosal, submucosal, and crypt-related damages in the colon. The negative and positive number of social interactions significantly increased in the colitis group. A considerable increase in locomotor activities (horizontal and vertical components) shown in the colitis group. Mice in colitis group spent less time in the central zone in the open field apparatus. Gene expressions of TNF-α, IL1β, and IL23 increased and CLDN5 decreased in the colitis group. The barrier function of the intestine and brain would be impaired, partially at least, following colitis (as we observed decrease in CLDN5 gene expression). Furthermore, we found that beside inflammatory response in the colon, a neuro-immune response triggered in the hippocampus following colitis. These alterations probably, mediated comorbid behavioral disorders in acetic acid-induced colitis in mice.

Ten Answers: Why Multiplying Two Negatives Is Positive

Why does multiplying two negative numbers result in a positive number? Here are ten diverse instructional approaches teachers can use to help students understand and explain this concept.

Advanced modelling techniques for magnetohydrodynamic Casson fluid squeezing flow via generalized fractional operators with neural network scheme

Abstract This paper aims to simulate and examine the unstable squeezed circulation of fractional-order (FO) magnetohydrodynamic (MHD) Casson fluid via a permeable medium. The Casson fluid system performs an essential role in comprehending the characteristics of non-Newtonian fluids, including toothpaste, condiments, printing substances and plasma circulation. The outcomes of this investigation are significant because previous research has not addressed the unsteady circulation of Casson fluid in a fractional nonsingular kernel and neural network-based stochastic context, considering the indicated consequences. An exceptionally dynamic ordinary differential equation is produced by using fractional calculus in combination with similarity transforms. After that, the predicted problem is addressed employing an amalgam of the Laplace transform in the Caputo-Fabrizio, modified Atangana-Baleanu-Caputo fractional derivatives operators, and the $q$-homotopy analysis transform method, accompanied by no-slip boundary requirements. The responses and oversights at various points in the FOs are scrutinized, along with previous findings, in order to ensure reliability. In terms of precision, $q$-HATM findings outperform other outcomes that are accessible in research. The focus of this research is on the influence of FOs on the velocity distribution, skin friction coefficient (SFC) and practices of relevant fluid factors. To find out how relevant fluid components affect the velocity distribution and SFC, an extensive, qualitative and visual evaluation is carried out. It was discovered through evaluation that the FO shows an analogous impact for both positive and negative squeezing numbers. Additionally, as the FO increases, SFC reduces. Analysis revealed that the FO exhibits a similar effect with regard to positive and negative compression numbers. Furthermore, SFC decreases with increasing FOs. Additionally, a highly effective stochastic method employing artificial neural networks (ANNs) and a back-propagated Levenberg-Marquardt (BPLM) procedure is generated to explore the effect of different parameter modifications on the SFC, velocity distribution, as well as various fluid factors. Multiple effectiveness measures were developed according to mean absolute deviations (MAD), erroneous Nash-Sutcliffe effectiveness (ENSE), and Theil's inequity coefficient (TIC) in order to verify the preciseness, productivity, and computing cost of the ANN-BPLM algorithms. The outlined scheme's analytical findings are verified through comparison using numerical outcomes obtained through the $q$-HATM, artificial intelligence strategies like NARX-LM, and the least squares methodology (LSM). The outcomes indicate the resilience and accuracy of the layout procedure by demonstrating that the average percentage of errors in our proposed outcomes in terms of ENSE, TIC, and MAD is nearly zero.

Refined selection of individuals for preventive cardiovascular disease treatment with a transformer-based risk model

Abstract Background Although statistical models have been commonly used to identify patients at risk of cardiovascular disease (CVD) for preventive therapy, these models tend to over-recommend therapy [1]. Moreover, in populations with pre-existing diseases, the current approach is to indiscriminately treat all individuals, as modelling in this context is currently inadequate. Aims To develop and validate a novel deep learning model, the Transformer-based Risk assessment survival model (TRisk) model, for prediction of 10-year risk of CVD in both the general population and individuals with diabetes. Methods An open cohort of 3 million adults aged 25 to 84 years free of CVD and statin use was identified using linked primary and secondary electronic health records from 291 and 98 general practices in England, which were used for TRisk model development and external validation, respectively. Comparison against two commonly recommended statistical models (QRISK3 [2] and SCORE2 [3]) and a deep learning derivation of QRISK3 was conducted. Additional analyses compared discriminatory performance in other age groups, by sex, and across categories of socioeconomic status. Similar analyses were conducted in a subgroup of 59 thousand patients with diabetes. Results TRisk demonstrated superior discrimination (C index in the general population: 0.910; 95% confidence interval [CI]: 0.906 to 0.913). TRisk’s performance was found to be less sensitive to population age range than the benchmark models and outperformed other models also in all stratified analyses. All models were overall well-calibrated. In decision curve analyses, TRisk demonstrated greater net benefit than benchmark models across the range of relevant thresholds. In impact analyses, at the widely recommended 10% risk threshold and the higher 15% threshold for the general population, TRisk reduced both the total number of patients classified at high risk (by 27% and 39% respectively) and the number of false negatives as compared with currently recommended strategies. TRisk similarly outperformed other models in patients with diabetes. Compared with the widely recommended treat-all policy approach for patients with diabetes, TRisk at a 10% risk threshold would lead to deselection of 24% of individuals with a small fraction of false negatives (0.2% of cohort). Conclusion TRisk enabled a more targeted selection of individuals at risk of CVD compared to benchmark statistical and deep learning models, in both the general population and patients with diabetes. Incorporation of TRisk into routine clinical care would allow a reduction in the number of treatment-eligible patients in general population and subgroup with diabetes by approximately one-third and one-quarter respectively while preventing at least as many events as with currently adopted approaches.Models' discrimination on both cohortsImpact analyses for both cohorts

Echocaridographic assessment of pulmonary hypertension: improving the probability

Abstract Introduction Pulmonary hypertension (PH) is a cardio-pulmonary disorder characterised by raised pulmonary artery pressure (mPAP >20mmHg) leading to right ventricular failure, and death if left untreated. Transthoracic echocardiography (TTE) assessment of PH uses a probability-based approach, combining peak tricuspid regurgitant velocity with other supporting signs. We evaluated the latest ESC TTE PH guidelines in a real-world UK dataset and identified markers that may improve the sensitivity of the existing algorithm. Method Retrospective analysis of 447 patients referred for initial PH assessment. This was a select population of patients who underwent both TTE and right heart catheter (RHC) (mean time to RHC = 40±30 days). In addition to current TTE PH probability markers we analysed right ventricular free wall strain (RVFWS). Measurements were made by a single operator using Tomtec Arena 2020. Crosstabulation, ROC curve analysis and T-tests were used to compare variables between PH and no PH. Results Mean sample age was 64±15 yrs (61% female). 6.9% (n=4) of the no PH group had pulmonary mid-systolic notching, which may be due to pseudo-notching attributable to incomplete Doppler envelope. Sensitivity and specificity of current ESC TTE probability guidelines were 83%, and 65% respectively (95% C.I.). However, within the low probability group (i.e. those felt to be less likely to have PH) 62% (n=63) had confirmed PH at RHC (mPAP = 28±9). The addition of RVFWS as an additional marker to the existing supporting signs of PH (Table 1) resulted in an improvement of the sensitivity of the algorithm to 92% with a mild reduction in specificity (63%). The number of false negatives were reduced by 51%. Of these, the majority were in the low TTE probability group (n = 32). Conclusions Using current PH TTE probability algorithms classifies a significant proportion of those with PH as having a low TTE PH probability. The addition of RVFWS improves the sensitivity of the existing algorithm to 92% and reduces false negatives by 51%.

The conception of negative numbers: A study of Kṛṣṇa Daivajña’s Bījapallava

The conception of negative numbers: A study of Kṛṣṇa Daivajña’s Bījapallava

120 GOPS Photonic tensor core in thin-film lithium niobate for inference and in situ training

Photonics offers a transformative approach to artificial intelligence (AI) and neuromorphic computing by enabling low-latency, high-speed, and energy-efficient computations. However, conventional photonic tensor cores face significant challenges in constructing large-scale photonic neuromorphic networks. Here, we propose a fully integrated photonic tensor core, consisting of only two thin-film lithium niobate (TFLN) modulators, a III-V laser, and a charge-integration photoreceiver. Despite its simple architecture, it is capable of implementing an entire layer of a neural network with a computational speed of 120 GOPS, while also allowing flexible adjustment of the number of inputs (fan-in) and outputs (fan-out). Our tensor core supports rapid in-situ training with a weight update speed of 60 GHz. Furthermore, it successfully classifies (supervised learning) and clusters (unsupervised learning) 112 × 112-pixel images through in-situ training. To enable in-situ training for clustering AI tasks, we offer a solution for performing multiplications between two negative numbers.

Mathematical Evaluation of Deep Learning Architecture with Feature Fusion for Cervical Cancer Detection Classification

Cervical cancer is still one of the main reasons women die around the world, which shows how important it is to have accurate and quick ways to diagnose the disease. This study looks into how to improve the accuracy of finding cervical cancer using a deep learning-based classification system that combines features. In this mixed classic feature extraction methods, like Histogram of Oriented Gradients (HOG) and Scale-Invariant Feature Transform (SIFT), with deep learning architectures, like Graph Convolutional Networks (GCNs) and Capsule Networks. Each of these added its own benefits to the fusion model. Both HOG and SIFT are good at capturing important texture and structure features, even when the image conditions change. GCNs are used to learn relationship data between picture areas. This helps get a better sense of how things fit together in space, which is very important for medical imaging. Capsule Networks, on the other hand, let you understand the subtleties of hierarchical patterns in pictures of cervical cells. They do this by looking at spatial hierarchies and rotational changes that are very important for finding cancer. Our suggested fusion model combines these multi-level features, taking advantage of how the best features of deep learning and standard learning methods work together. Validation on standard cervical cancer image datasets showed that this fusion approach was much more accurate and precise at classifying than individual methods. Quantitative testing showed that the fusion model had higher sensitivity and specificity, which shows that it can reduce the number of fake negatives and positives, which is very important in clinical diagnosis. Our results show that the feature fusion model not only gives us a strong and accurate way to classify cervical cancer, but it also lays the groundwork for more uses in other complicated areas of medical imaging.

Machine Learning Models for the Spatial Prediction of Gully Erosion Susceptibility in the Piraí Drainage Basin, Paraíba Do Sul Middle Valley, Southeast Brazil

Soil erosion is a global issue—with gully erosion recognized as one of the most important forms of land degradation. The purpose of this study is to compare and contrast the outcomes of four machine learning models, Classification and Regression (CART), eXtreme Gradient Boosting (XGBoost), Random Forest (RF), and Support Vector Machine (SVM), used for mapping susceptibility to soil gully erosion. The controlling factors of gully erosion in the Piraí Drainage Basin, Paraíba do Sul Middle Valley were analysed by image interpretation in Google Earth and gully erosion samples (n = 159) were used for modelling and spatial prediction. The XGBoost and RF models achieved identical results for the area under the receiver operating characteristic curve (AUROC = 88.50%), followed by the SVM and CART models, respectively (AUROC = 86.17%; AUROC = 85.11%). In all models analysed, the importance of the main controlling factors predominated among Lineaments, Land Use and Cover, Slope, Elevation and Rainfall, highlighting the need to understand the landscape. The XGBoost model, considering a smaller number of false negatives in spatial prediction, was considered the most appropriate, compared to the Random Forest model. It is noteworthy that the XGBoost model made it possible to validate the hypothesis of the study area, for susceptibility to gully erosion and identifying that 9.47% of the Piraí Drainage Basin is susceptible to gully erosion. Furthermore, replicable methodologies are evidenced by their rapid applicability at different scales.

Current legal activities come to the complexity of the term "electronic commerce": international and national level

The article provides a comprehensive study of various approaches to defining the term «electronic commerce» in the context of modern legal, economic and technological challenges. The analysis begins with an overview of scholarly perspectives on e-commerce, which range from narrow interpretations that focus on basic online sales contracts to broader concepts that encompass all aspects of electronic interaction between business entities, including logistics, marketing, financial operations and international transactions. The term «e-commerce» is clearly distinguished from related concepts, such as «e-commerce», «e-business», which mostly focuses on the sale of goods and services. The article also explores the positive aspects of e-commerce, such as increasing the efficiency of business processes, reducing transaction costs, access to global markets, increased convenience for consumers, etc. At the same time, a number of negatives have been identified, including the risk of personal data theft, payment fraud, and other types of cybercrime. The normative regulation of electronic commerce at the level of international law and in Ukraine is separately analyzed. The main legislative acts and their impact on the development of e-commerce are highlighted. On the basis of the conducted research, three key criteria for a clear definition of e-commerce are formulated, including legal relations arising through electronic means, interaction of entities through the Internet, and multi-level business processes, namely: basic e-commerce, integrated e-commerce and global e-commerce. As a result, a proper understanding of e-commerce as a form of business activity is proposed, which involves the implementation of commercial transactions using information and telecommunication means, covering a wide range of processes, including the conclusion and execution of contracts for the sale of goods and services, payment processing, logistics, marketing and advertising , as well as management of currency and customs operations during international transactions, which allows to increase business efficiency and reduce costs due to process automation, optimization of resource management, rapid exchange of information, reduction of transaction costs and simplification of communication between market participants.

Optimization of testing protocols to screen for COVID-19: a multi-objective model.

In this paper we develop a new multi-objective simulated annealing (MOSA) algorithm to generate optimal testing protocols for infectious diseases, using the COVID-19 pandemic as our context. A SEIR (susceptible-exposed-infected-recovered) epidemiological model is embedded as the computational platform for our MOSA algorithm to optimize testing protocols for screening across three joint objectives: minimum cost of test materials, minimum total infections over the testing horizon, and minimum number of false negatives over the horizon. We demonstrate the application of this optimization tool to recommend screening protocols for K-12 school districts in the U.S.State of North Carolina. Our approach is scalable by population coverage and can be employed at the level of individual school districts or regional collections of districts, individual schools or collections of schools across a district, business sites, or nursing homes, among other congregate settings where individuals may be screened prior to gaining entry to the site. The algorithm can be solved two ways, generating either independent optimal protocols across individual testing locations, or a common protocol covering all locations in the collection of testing sites. Our findings can be used to inform policy decisions to guide the development of effective testing strategies for controlling the spread of COVID-19 or other pandemic diseases in a wide range of congregate settings across various geographic regions.

A NOVEL CONCEPT: THE PRODUCT OF TWO NEGATIVELY DIRECTED NUMBERS IS A NEGATIVELY DIRECTED NUMBER THOUGH THE NEGATIVE OF A NEGATIVE NUMBER IS A POSITIVE NUMBER

In this paper, the author proved that the product of two negatively directed numbers is a negatively directed number. This article is the outcome of previously published (2021-2024) ten (10) articles of this author. It is true that the negative of a negative number is a positive number. It has been done by applying the inversion process to a negative number. The process of inversion does not satisfy the basic concept of multiplication. Multiplication is defined as the adding of a number concerning another number repeatedly. So, the process of inversion does not comply with the fundamental concept of multiplication. According to the Theory of Dynamics of Numbers there exist three types of numbers: (1) Neutral or discrete numbers (2) Positively directed numbers (3) Negatively directed numbers. In general, we use four types of operators: addition (+), subtraction (-), multiplication (x), and division (÷) in mathematical calculations. Besides these, we use the negative sign (-) as an inversion operator. The positive sign (+) and negative sign (-) also represent the direction of neutral or discrete numbers. In this paper, the author introduced Fermat's Last Theorem: xn + yn = zn for n = 2 in Bhattacharyya's Theorem to prove that the product of two negatively directed numbers is a negatively directed number using the concept of the Theory of Dynamics of Numbers. In this paper, the author framed new laws of multiplication and inversion. Also, the author has given a comparative study between the conventional method of multiplication and the present concept of multiplication citing some practical examples. The author has become successful in finding the root of a quadratic equation in real numbers even if the discriminant, b2 – 4ac < 0 without using the concept of the imaginary number and also in determining the radius of a circle even if g2 + f2 < c, in real number without using the concept of complex numbers. With one example the author proved that this theorem is applicable in ‘Calculus’ also.

Stability Analysis and Optimal Control for Spreading Typhoid Fever Model with Direct and Indirect Transmissions

This article discusses a model of spreading typhoid fever with direct and indirect transmissions. There are five compartments included in the model, namely susceptible individuals, infected individuals, chronic carrier individuals, recovered individuals, and salmonella typhi bacteria in the environment. As an effort to control and minimize the numbers of infected individuals and chronic carrier individuals, we introduce simultaneously campaign for the susceptible individuals and treatment for the infected individuals and for chronic carrier individuals. The resulting model is a system of non-linear differential equations and quite challenging to analysis globally. Existence of both disease-free equilibrium point and endemic equilibrium point are analysed analytically. Stability of the equilibrium point is analysed locally by determining the eigenvalues of the associated Jacobian matrix, Routh-Hurwitz stability criteria, and basic reproduction number () via next generation matrix. The minimum Pontryagin principle and Hamiltonian equation are referred to minimize the numbers of infected and chronic carrier individuals. Simulation is carried out using suitable values of parameters. We found that the eigenvalues for endemic equilibrium point are all negative real numbers and . Optimal paths for state and constate variables are plotted using fourth order forward-backward Runge-Kutta method. In case there are no campaign and treatments, we found and endemic occurs. When campaign and treatments are included together in the model, we found optimal paths for all compartments that minimize the number of infected and chronic carrier individuals. Giving campaign and treatments increase significantly the susceptible and recovered individuals. At the same time, it reduces significantly the infected, chronic carrier individuals, and salmonella typhi bacteria in the environment. Involving campaign and treatment in the model of spreading typhoid fever can be considered as an effective strategy to minimize the numbers of infected and chronic carrier individuals.

Improving Effectiveness by Reducing Overconfidence in Large Catalogue Sequential Recommendation with gBCE loss

A large catalogue size is one of the central challenges in training recommendation models: a large number of items makes them memory and computationally inefficient to compute scores for all items during training, forcing these models to deploy negative sampling. However, negative sampling increases the proportion of positive interactions in the training data, and therefore, models trained with negative sampling tend to overestimate the probabilities of positive interactions – a phenomenon we call overconfidence . While the absolute values of the predicted scores/probabilities are not important for the ranking of retrieved recommendations, overconfident models may fail to estimate nuanced differences in the top-ranked items, resulting in degraded performance. In this paper, we show that overconfidence explains why the popular SASRec model underperforms when compared to BERT4Rec. This is contrary to the BERT4Rec authors’ explanation that the difference in performance is due to the bi-directional attention mechanism. To mitigate overconfidence, we propose a novel Generalised Binary Cross-Entropy Loss function (gBCE) and theoretically prove that it can mitigate overconfidence. We further propose the gSASRec model, an improvement over SASRec that deploys an increased number of negatives and the gBCE loss. Through detailed experiments on three datasets, we show that gSASRec does not exhibit the overconfidence problem. As a result, gSASRec can outperform BERT4Rec (e.g. +9.47% NDCG on the MovieLens-1M dataset), while requiring less training time (e.g. -73% training time on MovieLens-1M). Moreover, in contrast to BERT4Rec, gSASRec is suitable for large datasets that contain more than 1 million items. Finally, we show how addressing overconfidence can improve model calibration – the ability of a model to predict actual interaction probabilities accurately. By applying gBCE to the SASRec model on MovieLens-1M dataset, we reduce the models’ expected calibration error by 98.9% (from 0.966 to 0.01).

Long-term Outcomes of Bilateral Lateral Rectus Recession Using a Modified Normogram for Targeting Small Overcorrection in Intermittent Exotropia.

To evaluate the surgical outcomes of a modified normogram for bilateral lateral rectus recession in the surgical management of intermittent exotropia, with a focus on achieving small overcorrection. A retrospective medical chart review of 242 patients who underwent surgery for intermittent exotropia between October 2014 and June 2020 was performed. Our modified normogram reducing amount of recession targeted for small postoperative overcorrection within 5 prism diopters (PD). Patients were observed for at least 3 years. Esodeviation was denoted by negative numbers and positive values indicated exodeviation. A satisfactory outcome was defined as if distant angle of deviation ranged between ≤10 PD of exotropia and ≤5 PD of esotropia. Recurrence was defined as an exodeviation of >10 PD at distance. Overcorrection was defined as an esodeviation of >5 PD at distance. The mean preoperative deviation angles were 29.32 ± 3.92 PD at distance and 29.88 ± 4.41 PD at near. At postoperative day 1, the mean deviation angles at distance and near were -6.22 ± 1.44 and -6.22 ± 1.49 PD, respectively. Overcorrection within 6 PD of esodeviation was seen in 168 patients (69.42%), undercorrection with exophoria was noted in 11 patients (4.55%), and overcorrection by more than 6 PD of esodeviation was seen in 63 patients (26.03%) at postoperative day 1. The long-term success rate at postoperative 3 years was 77.27% (187 of 242), with a recurrence rate of 19.83% (48 of 242) and an overcorrection rate of 2.89% (7 of 242). A positive correlation between the angle of deviation at postoperative day 1 and 3 years was observed (r = 0.22, p = 0.001). The final success rate at the final examination after a mean follow-up of 38.60 ± 7.99 months was 83.06%. Our modified normogram for bilateral lateral rectus recession in intermittent exotropia surgery resulted in successful surgical outcomes with small overcorrection, reducing the risk of consecutive esotropia due to excessive overcorrection.

Rogramming the Atoms & Compounds and the Unification of Physics and Chemistry

One of the most important concepts in Geometry is, distance, which is the Quanta in geometry, while in Material-Geometry the composition of Opposite, the Material-Point which is the Quanta in Chemistry and Physics. As in Algebra Zero ,0, is the Master-key number for all Positive and Negative numbers and this because their sum and multiplication become zero, and the same on any coordinate-System where ± axes pass from zero, The Rolling of Positive ⊕, constituent on the Negative ⊝, constituent, creates the Neutral Material Point Which Equilibrium. Angular-Momentum is identical with Spin and consists the First-Discrete-Energy-Monad which occupies, Discrete Value and Direction, in contradiction to the Point which is Nothing, Dimensionless and without any Direction. Quaternion [(+) ↻↺ (-)] ≡ Box which carries the Principal stress σ between A (+), B (-) which σ, as Centripetal-acceleration is the minimum Energy becoming from the in-storage AB acceleration and is equal to the Gravity g. Because of the two different motions, Revolving and Periodic, acceleration of the Gravity g ≡ ± σ exists as the First Energy-Box- ,while in the Second is followed the Local-Extreme-case this acceleration of Gravity g ≡ ± σ, is altered Locally by changing the Principal-stress σ with a Local-uniform-Pressure → ≡ g k = g. [ Force/Area] = G, i.e. The minimum Local - Energy acceleration is the known, Universal Gravitational-constant G = g k = g = σ, for Macrocosm and Microcosm, Obeying Newton`s Laws of motion. It was proved that, Constant G, is the mechanism for the First-kick-Start on the Granular-Energy-monad, g, which Acts in the lightest and less-mass Particle and which is the Hydrogen. The Electron-Nutation-Energy due to g, effect is the minimum frequency ≡ = 2 ,8398447. , and which so exists in all Atoms. This Energy in Hydrogen-Cave as E-M, Conductor ≡ The Pin of Atom-Plug Into their Sockets, which are the Orbit – Bracket – Hooks ≡ The Hands of Atoms, i.e. → The Atoms Plug with their Pins into the other Atoms-Drains = Holes, and so are Bonded. This is the Resonance frequency between all Atoms, and because Hydrogen is Common to all Atoms, so Bond to Molecules and Crystals, and all other Compounds in this Cosmos.

Reliability of a Photo-Based Modified Foot Posture Index (MFPI) in Quantifying Severity of Foot Deformity in Children With Cerebral Palsy.

Children with cerebral palsy (CP) have high rates of foot deformity. Accurate assessment of foot morphology is crucial for therapeutic planning and outcome evaluation. This study aims to evaluate the reliability of a novel photo-based Modified Foot Posture Index (MFPI) in the evaluation of foot deformity in children with CP. Thirteen orthopaedic surgeons with neuromuscular clinical focus from 12 institutions evaluated standardized standing foot photographs of 20 children with CP, scoring foot morphology using the MFPI. Raters scored the standardized photographs based on five standard parameters. Two parameters assessed the hindfoot: curvature above and below the malleoli and calcaneal inversion/eversion. Three parameters assessed the midfoot and forefoot: talonavicular congruence, medial arch height, and forefoot abduction/adduction. Summary MFPI scores range from -10 to +10, where positive numbers connote planovalgus, whereas negative numbers connote a tendency toward cavovarus. Intra- and interrater reliability were calculated using a 2-way mixed model of the intraclass correlation coefficient (ICC) set to absolute agreement. Feet spanned the spectrum of potential pathology assessable by the MFPI, including no deformity, mild, moderate, and severe planovalgus or cavovarus deformities. All scored variables showed high intrarater reliability with ICCs from 0.891 to 1. ICCs for interrater reliability ranged from 0.965 to 0.984. Hindfoot total score had an ICC of 0.979, with a 95% CI, 0.968-0.988 (P<0.001). The forefoot total score had an ICC of 0.984 (95% CI, 0.976-0.991, P<0.001). Mean total score by the MFPI was 3.67 with an ICC of 0.982 (95% CI, 0.972-0.990, P<0.001). The photo-based MFPI demonstrates high intra- and interrater reliability in assessing foot deformities in children with CP. Its noninvasive nature and ease of use make it a promising tool for both clinical and research settings. MFPI should be considered as part of standard outcomes scores in studies regarding the treatment of CP-associated foot deformities. Level V.