Extremal Functions Research Articles

The Hypermetabolic Response to Burns and its Treatment: A Literature Review

Abstract: Major burn injuries provoke a profound stress response marked by extreme hypermetabolism and impaired immune function. The physiological alterations to glucose, protein and lipid metabolism can be detected even years after the inciting burns injury and when untreated can lead to profound wasting, fatty liver, and even death. Therapeutic strategies which target these physiological disturbances are of paramount importance. Treating burn injuries begins with active cooling, to minimize loss of heat and water, and nutrition, to counteract the extensive catabolism. Providers should follow the strict guidelines published to ensure caloric requirements are met in adult and pediatric patients, with supplementation as indicated. Several pharmacotherapies have proven beneficial in helping to counteract and reverse these physiological changes by lowering insulin resistance, slowing catabolism, and minimizing loss of lean body mass. The most promising drugs include anabolic agents such as insulin, recombinant human growth hormone (rhGH), insulin-like growth factor 1 (IGF-1), metformin, beta-blockers, oxandrolone, and fenofibrate. Surgery is a necessary adjunct, either in the acute phase to debride compromised soft tissue and prevent compartment syndromes, but also in the chronic setting to release contractures and fibrotic strictures which may impair function. This narrative literature review provides a synopsis of our understanding of the hypermetabolic response to burn injury and discusses the different treatment options aiming to control postburn hypermetabolism and ultimately improve patient outcomes.

Prediction of hospitalization time and independence level with functional outcomes for patients with acute stroke: a retrospective study

ABSTRACT Objectives The objective of this study was to develop predictive models for estimating the length of stay (LOS) with standardized clinical outcome measures (Functional Independence Measure, Trunk Impairment Scale, Postural Assessment Scale for Stroke Patients, Fugl Meyer Assessment Scale, and Functional Ambulation Category) during acute care setting. Methods One hundred sixty-nine patients were included in the retrospective study. Predictors chosen for the LOS included scores of functional outcome measures at admission. We used Spearman’s rank correlation coefficients to calculate correlations among clinical outcome measures and LOS, stepwise multiple regression analysis to develop a predictive model, and receiver operating characteristics curve to analyze the predictive value of explanatory factors obtained from the previous model for discharge Functional Independence Measure score. Results The predictive equation explained 81% of the variance in LOS. The most important predictors were trunk impairment, motor function of the upper extremity, walking ability, and independence level at admission. The receiver operating characteristic curve was obtained with a cut-off score of 13 points for the Trunk Impairment Scale, 47 points for Fugl Meyer Assessment-Upper Extremity, and 2 points for Functional Ambulation Category, demonstrating the highest percentage of the accurately predicted ability of independence level at discharge. Discussion The models presented in this study could help clinicians and researchers to predict the LOS and discharge independence level of clinical outcomes for patients with acute stroke enrolled in an acute care setting.

The eigenvalues and eigenfunctions of the non-linear equation associated to second order Sobolev embeddings

We consider the non-linear eigenvalue equations characterizing Lp into Lq Sobolev embeddings of second order for Navier boundary conditions at both ends of a line segment. We give a complete description of the s-numbers and the extremal functions in the general case (p,q)∈(1,∞)2. Among other results, we show that these can be expressed in terms of those of related first order embeddings, if and only if 1p+1q=1. Our findings shed new light on the surprising nature of higher order Sobolev spaces in the Banach space setting.

A Characterization of Edge-Ordered Graphs with Almost Linear Extremal Functions

The systematic study of Turán-type extremal problems for edge-ordered graphs was initiated by Gerbner et al. (Turán problems for Edge-ordered graphs, 2021). They conjectured that the extremal functions of edge-ordered forests of order chromatic number 2 are n^{1+o(1)}. Here we resolve this conjecture proving the stronger upper bound of n2^{O(sqrt{log n})}. This represents a gap in the family of possible extremal functions as other forbidden edge-ordered graphs have extremal functions Omega (n^c) for some c>1. However, our result is probably not the last word: here we conjecture that the even stronger upper bound of nlog ^{O(1)}n also holds for the same set of extremal functions.

The Clinical Variables Predicting the Acquisition of Independent Ambulation in the Acute Phase of Stroke: A Retrospective Study.

Predictive factors associated with independent ambulation post-stroke are less commonly reported for patients during the acute phase of stroke. This study aimed to identify the clinical variables predicting ambulation independence in the acute phase of stroke and test the superiority of their prediction accuracy. Sixty-nine patients, hospitalized in the acute phase for an initial unilateral, supratentorial stroke lesion, were divided into independent (n = 24) and dependent ambulation (n = 45) groups, with functional ambulation category scores of 4-5 and ≤ 3, respectively. They were evaluated upon admission using the modified Rankin scale (mRS), Stroke Impairment Assessment Set (SIAS) concerning the motor function of the lower extremities, Ability for Basic Movement Scale modified version 2 (ABMS2), and Functional Independence Measure (FIM). The scores of the four measures were significantly different between the groups. A univariate logistic regression analysis identified these variables as prognostic factors for independent ambulation. A receiver operating characteristic curve analysis identified the cutoff values (area under the curve) for the mRS, SIAS, FIM, and ABMS2 as 3 (0.74), 12 (0.73), 55 (0.85), and 23 (0.84), respectively. In summary, the FIM and ABMS2 may be more accurate in predicting ambulation independence in patients with stroke during the acute phase.

Sharp Coefficient Bounds for a Subclass of Bounded Turning Functions with a Cardioid Domain

In the present paper, we give a new simple proof on the sharp bounds of coefficient functionals related to the Carathéodory functions and make a correction on the extremal functions. The result is further used to investigate some initial coefficient bounds on a subclass of bounded turning functions R℘ associated with a cardioid domain. For functions in this class, we calculate the bounds of the Fekete–Szegö-type inequality and the second- and third-order Hankel determinants. All the results are proved to be sharp.

Effects of non-immersive virtual reality intervention on children with spastic cerebral palsy: a meta-analysis and systematic review.

This review aimed to assess the effectiveness of non-immersive virtual reality intervention compared to traditional rehabilitation in improving the functions of the upper and lower extremities, balance, and social participation among children with spastic cerebral palsy. We used librarian-designed searches of 10 databases to identify research articles on randomized controlled trials that assessed the effectiveness of non-immersive virtual reality in intervening spastic cerebral palsy patients up to 4/15/2023. Independent evaluation was conducted by two trained investigators using the evaluation criteria of RCT quality indicated in the Cochrane Manual of Assessment 'risk- of- bias tool.' The PEDro scale was used to evaluate the method and quality of the literature. 21 research articles involving 779 patients with spastic cerebral palsy were included. Significant differences between the non-immersive virtual reality rehabilitation and traditional rehabilitation groups were observed in all indicators, except for the Jebsen-Taylor Hand Function Test. Non-immersive virtual reality intervention is effective in improving the function of the lower extremity, balance, and social participation in children with spastic cerebral palsy, but its effect on upper limb function is still controversial.

On the Realization of Exact Upper Bounds of the Best Approximations on the Classes H1,1 by Favard Sums

In this paper, we find the sets of all extremal functions for approximations of the Hölder classes of H1 2π-periodic functions of one variable by the Favard sums, which coincide with the set of all extremal functions realizing the exact upper bounds of the best approximations of this class by trigonometric polynomials. In addition, we obtain the sets of all of extremal functions for approximations of the class H1 by linear methods of summation of Fourier series. Furthermore, we receive the set of all extremal functions for the class H1 in the Korneichuk–Stechkin lemma and its analogue, the Stepanets lemma, for the Hölder class H1,1 functions of two variables being 2π-periodic in each variable.

Effects of Mind-Body Exercises for Osteoporosis in Older Adults: A Systematic Review and Meta-analysis of Randomized Controlled Trials.

Osteoporosis is a major cause of fractures and even life-threatening fractures in the elderly. Mind-body exercise is a beneficial intervention to improve flexibility, control body balance and reduce pain. We aimed to evaluate the effects of physical and mental exercise on osteoporosis in the elderly. Randomized controlled trials (RCTs) focusing on mind-body exercises for osteoporosis were included. Web of Science, PubMed, Science Direct, Medline, Cochrane Library, China National Knowledge Infrastructure (CNKI), and Wanfang were searched from inception to January 2023. Outcomes included bone mineral density (BMD), bone mineral content (BMC), body balance (BB), pain, indicators of bone metabolism (BMI), lower extremity function, fearing level, and quality of life (QOL). The quality of study reporting was rated by 2 reviewers independently, and Review Manager software (version 5.3) was used for meta-analysis. Thirty-nine trials with 2325 participants were included. The pooled results showed that mind-body exercises have encouraging effect on elderly people with osteoporosis, especially in aspects of BMD, BMC, QOL, improving the function of lower extremity, reducing pain and fearing level. While, dance and eight-section brocade could not improve the quality of life,or dance and eight-section brocade have no effect on BMD. Mind-body exercises may have potential efficacy for osteoporosis in the elderly. However, due to the poor methodological quality of the included trials, more clinical trials with precise methodological design and rigorous reporting are needed.

Polymyalgia rheumatica-Achallenge in geriatrics : Interdisciplinary presentation of diagnostics and treatment

Polymyalgia rheumatica is the second most frequent inflammatory rheumatic disease in people aged over 50years, after rheumatoid arthritis. It is characterized by pain and morning stiffness in the region of the shoulders, hip girdle and neck. It can be associated with giant cell arteritis (CGA). Treatment with glucocorticoids is indispensable. The duration of treatment varies and often exceeds 1year. The additive administration of methotrexate is an option for saving glucocorticoids. The biologicals tocilizumab or secukinumab are very promising alternatives. The course of treatment should be closely monitored for inflammation parameters, glucocorticoid side effects, pain, visual acuity, depression, activities of daily living and especially related to functions of the upper extremities. The geriatric assessment plays an important role in the management of this condition.

Harnessing Instability Mechanisms in Airfoil Flow for Data-Driven Forecasting of Extreme Events

For certain Reynolds numbers, airfoils are subject to sporadic high-amplitude fluctuations in the aerodynamic forces. These extreme excursions may be seen as prototypical of the kind of unsteady and intermittent dynamics relevant to the flow around airfoils and wings in a variety of real-world applications. Here we investigate the instability mechanisms at the heart of these extreme events, and how they may be harnessed for efficient data-driven forecasting. Through a wavelet and spectral analysis of the pressure and vorticity, we find that the extreme events arise due to the instability of a specific frequency component distinct from the vortex shedding mode. During these events, this extreme event frequency draws energy from the energetically dominant vortex shedding flow and undergoes an abrupt transfer of energy from small to large scales. We propose a preprocessing algorithm to extract this extreme event frequency from the surface pressure data, which in conjunction with an extreme event-tailored loss function, allows us to avoid the commonly used long short-term memory architecture in favor of a simple feed-forward network—a significant reduction in cost over the previous state-of-the-art. Our model requires only three pressure sensors, and it is robust to their location—showing promise for the use of our model in dynamically varying applications. Finally, we show that relying solely on the statistics of the pressure and drag data for optimal sensor placement fails to improve model prediction over uniform or random sensor placement.

Monotone extremal functions and the weighted Hilbert’s inequality

In this note we find optimal one-sided majorants of exponential type for the signum function subject to certain monotonicity conditions. As an application, we use these special functions to obtain a simple Fourier analysis proof of the (non-sharp) weighted Hilbert– Montgomery–Vaughan inequality.

Large N analytical functional bootstrap. Part I. 1D CFTs and total positivity

We initiate the analytical functional bootstrap study of conformal field theories with large N limits. In this first paper we particularly focus on the 1D O(N) vector bootstrap. We obtain a remarkably simple bootstrap equation from the O(N) vector crossing equations in the large N limit. The numerical conformal bootstrap bound is saturated by the generalized free field theories, while its extremal functional actions do not converge to any non-vanishing limit. We study the analytical extremal functionals of this crossing equation, for which the total positivity of the SL(2, ℝ) conformal block plays a critical role. We prove the SL(2, ℝ) conformal block is totally positive in the limits with large ∆ or small 1 − z and show that the total positivity is violated below a critical value {Delta }_{textrm{TP}}^{ast } ≈ 0.32315626. The SL(2, ℝ) conformal block forms a surprisingly sophisticated mathematical structure, which for instance can violate total positivity at the order 10−5654 for a normal value ∆ = 0.1627! We construct a series of analytical functionals {αM} which satisfy the bootstrap positive conditions up to a range ∆ ⩽ ΛM. The functionals {αM} have a trivial large M limit. However, due to total positivity, they can approach the large M limit in a way consistent with the bootstrap positive conditions for arbitrarily high ΛM. Moreover, in the region ∆ ⩽ ΛM, the analytical functional actions are consistent with the numerical bootstrap results, therefore it clarifies the positive structure in the crossing equation analytically. Our result provides a concrete example to illustrate how the analytical properties of the conformal block lead to nontrivial bootstrap bounds. We expect this work paves the way for large N analytical functional bootstrap in higher dimensions.

Relationship between a history of disabled throwing shoulder/elbow and the ability to perform the deep squat test among youth baseball players

AimThe deep squat test (DST) is a screening test to assess the function of the lower extremity and the flexibility of ankle dorsiflexion. Previous study reported that approximately 70% of players with disabled throwing shoulder and/or elbows were unable to perform DST. The aim of this study was to reveal the relationship between performance of DST and history of disabled throwing shoulder/elbow. MethodsA total of 1,439 youth baseball players (10.9 years; range 6–16 years), who participated in pre-season medical examination were included in the study. Players who experienced shoulder or elbow pain of the throwing side during or after playing baseball in the past were defined as players with a history of disabled throwing shoulder/elbow. The DST was evaluated by having the players perform a full squat with while having their arms crossed in front of their chest and their feet apart without lifting the heel off the floor or falling backwards. The relationship between a history of disabled throwing shoulder/elbow and the ability to perform DST was analyzed. ResultsAmong the study participants, 499 (34.7%) had a history of disabled throwing shoulder/elbow, and 532 players (37.0%) were unable to perform DST. Of the players with disabled throwing shoulder/elbow history, 227 players (45.5%) were unable to perform DST, as were 305 players out of 940 players (32.5%) without a disability; this difference was statistically significant (P < 0.001). ConclusionInability to perform DST may be related to the previous incidence of disabled throwing shoulder/elbow.

Proximal forearm nerve branching patterns: an anatomical study and its clinical significance.

The aim of this study was to add to the understanding of nerve branching patterns in the proximal forearm and consider optimal nerve transfer options to address the various injuries that affect the function of the upper extremity. Eleven upper-extremity cadaveric specimens were dissected to expose the radial, median, and ulnar nerves in the proximal forearm. The site of origin of nerve branches from the major nerves was assessed, with measurements made in reference to the lateral epicondyle for the radial nerve branches and the medial epicondyle for the median and ulnar nerve branches. The distances to where these branches entered their respective muscles (muscle entry point) were assessed using the same landmarks. To plan a transfer, the length of the nerve branches was then calculated as the difference from the apparent origin from the main nerve trunk to the location where the nerve entered the muscle. Importantly, the nerve branch origin was established as the location of obvious separation from the main nerve trunk without additional fascicular dissection from the major nerve trunk. The number of branches was determined, and the diameter for each branch was measured using a Vernier caliper. The radial nerve branch to the extensor carpi radialis brevis (ECRB) muscle had an average length of 50.7 mm and average diameter of 1.6 mm. The mean medial and lateral lengths of the radial branches to the supinator muscle were found to be 22.2 mm (diameter 1.4 mm) and 15.3 mm (diameter 1.3 mm), respectively. The anterior interosseous nerve (AIN) branch of the median nerve was found 67.8 mm distal to the medial epicondyle with a diameter of 2.3 mm. The flexor carpi ulnaris (FCU) muscle innervation from the ulnar nerve was provided by 3 or 4 branches in most specimens. The second and third of these branches were the longest, with means of 30.5 mm (diameter 1.4 mm) and 30.7 mm (diameter 1.3 mm), respectively. While there is variability of the nerve branching pattern in the proximal forearm between specimens, the authors provide evidence of commonalities (branching patterns and distances) that can facilitate planning for upper-extremity nerve reconstructions. Importantly, all measurements are provided with reference to easily identified bony landmarks and to their muscle entry points to aid operative decision-making. These data complement the growing practice of nerve transfers in the upper extremity for a variety of pathologies.

Impact of Cerebral Microbleeds on Gait, Balance, and Upper Extremities Function in Cerebral Small Vessel Disease.

White matter hyperintensites (WMHs) , lacunes and brain atrophy have been demonstrated to be positively related to gait disorder. However, cerebral microbleeds (CMBs) as a manifestation of cerebral small vessel disease (CSVD) is still under-investigated. Therefore, correlations between CMBs and upper extremity, gait and balance performance were investigated in this study. A cross-sectional study of middle-aged to older adults was conducted. CSVD burden was measured with magnetic resonance imaging (MRI) and the location and number of CMBs were analysed. Gait and balance functions were evaluated using a four meter walkway, Tinetti, Timed-Up-and-Go (TUG) and Short Physical Performance Battery (SPPB) tests. Upper extremity function was measured by 10 repeated pronation-supination time, 10 repeated finger tapping time, and 10 repeated opening and closings of the hands. A total of 224 participants were included in this study, with a mean age of 60.6 ± 10.5 years. The prevalence of CMB was 34.8% and most was lobar. Multiple linear regression analysis showed that CMB was associated with lower gait velocity, wider stride width, longer TUG test time, and poor performance on Tinetti and SPPB tests independently of other coexisting CSVD markers and risk factors. These relationships appeared to be explained by CMBs in the frontal, temporal, basal ganglia and infratentorial regions. The motor function of upper extremity also had independent correlations with CMBs especially in frontal, parietal, and temporal areas, and in the basal ganglia. CMBs were found to be associated with both gait, balance and upper extremity disturbances. The presence of CMB seems to be another major driving force for CSVD on lower and upper extremity impairment in healthy elderly subjects.

Theorem on the Structure of the Fractionally Linear Functional Extremal Function

The paper proves a theorem about the structure of the distribution function on which the extremum of the fractionally linear functional is reached in the presence of an uncountable number of linear constraints. The problem of finding an extremal distribution function arises when determining the optimal control strategy in a class of Markov homogeneous randomized control strategies. The structure of extremal functions is described by a finite number of parameters; hence, the problem is greatly simplified since it is reduced to the search for an extremum of some function.

An Extreme-Adaptive Time Series Prediction Model Based on Probability-Enhanced LSTM Neural Networks

Forecasting time series with extreme events has been a challenging and prevalent research topic, especially when the time series data are affected by complicated uncertain factors, such as is the case in hydrologic prediction. Diverse traditional and deep learning models have been applied to discover the nonlinear relationships and recognize the complex patterns in these types of data. However, existing methods usually ignore the negative influence of imbalanced data, or severe events, on model training. Moreover, methods are usually evaluated on a small number of generally well-behaved time series, which does not show their ability to generalize. To tackle these issues, we propose a novel probability-enhanced neural network model, called NEC+, which concurrently learns extreme and normal prediction functions and a way to choose among them via selective back propagation. We evaluate the proposed model on the difficult 3-day ahead hourly water level prediction task applied to 9 reservoirs in California. Experimental results demonstrate that the proposed model significantly outperforms state-of-the-art baselines and exhibits superior generalization ability on data with diverse distributions.

A semi-supervised network-based tissue-aware contrast enhancement method for CT images

To propose a tissue- aware contrast enhancement network (T- ACEnet) for CT image enhancement and validate its accuracy in CT image organ segmentation tasks. The original CT images were mapped to generate low dynamic grayscale images with lung and soft tissue window contrasts, and the supervised sub-network learned to recognize the optimal window width and level setting of the lung and abdominal soft tissues via the lung mask. The self-supervised sub-network then used the extreme value suppression loss function to preserve more organ edge structure information. The images generated by the T-ACEnet were fed into the segmentation network to segment multiple abdominal organs. The images obtained by T-ACEnet were capable of providing more window setting information in a single image, which allowed the physicians to conduct preliminary screening of the lesions. Compared with the suboptimal methods, T-ACE images achieved improvements by 0.51, 0.26, 0.10, and 14.14 in SSIM, QABF, VIFF, and PSNR metrics, respectively, with a reduced MSE by an order of magnitude. When T-ACE images were used as input for segmentation networks, the organ segmentation accuracy could be effectively improved without changing the model as compared with the original CT images. All the 5 segmentation quantitative indices were improved, with the maximum improvement of 4.16%. The T-ACEnet can perceptually improve the contrast of organ tissues and provide more comprehensive and continuous diagnostic information, and the T-ACE images generated using this method can significantly improve the performance of organ segmentation tasks.

Vertical jump performance and the relationship with sprint speed at 20 m and 50 m in professional soccer players.

Background: Jumping and sprinting are essential skills for several sports, especially for soccer, since they allow to determine neuromuscular function and maximum power of the lower extremities in athletes. This study aimed to establish the relationship between vertical jump performance and sprint speed at 20 m and 50 m in professional soccer players. Methods: This study took place from June 2020 to November 2021 with participants from the U20 category of the Colombian professional team Fortaleza CEIF, and the U18 category of the Brazilian professional team Boston City. The vertical jump was assessed with the countermovement jump (CMJ), squat jump (SJ), and rebound jump (RJ) variants using the WheelerJump jump sensor while the sprint was measured using the Winlaborat horizontal encoder. Results: 200 participants from the selected teams were included in this study. Almost perfect correlations (p &lt; 0,05 – r: 0.97) and excellent coefficients of determination (R2: 0.95 – 0.93) were observed between the reactive force index with the mean height of the different jump protocols and the 50-meter sprint speed, indicating that the higher the altitude and/or the higher the reactive force index, the higher the 50-meter sprint speed. The same behavior was found with the 20-meter race, but the correlation levels (p &lt;0,05, r: 0.63-0.62) and the determination coefficients were lower (0.40). Conclusions: The results of this study suggest that, in professional soccer players, long sprint performance like 50 m is strongly correlated and could be accuracy explained by the average height reached in SJ, CMJ, and RJ and by the ability to perform repeated jumps using short contact times, thus increasing the ground reaction forces, which translates into a similar behavior during successive contacts of the player's feet against the ground during the race.