Extremal Functions Research Articles

The Effects of Whole-Body Vibration Therapy in Weight-Bearing and Non-Weight-Bearing Positions for Upper and Lower Extremities on Balance and Function in Cerebral Palsy Children: A Randomized Controlled Trial.

Background and objective Cerebral palsy (CP) is one of the most prevalent neurological conditions affecting children; it is characterized by poor motor control, restricted range of motion (ROM), and poor balance. While whole-body vibration therapy (WBVT) has been used to treat these symptoms, its efficacy in different configurations remains unexplored. Hence,this study aimed to determine and compare the effects of WBVT applied to either the upper extremities, lower extremities, or both upper and lower extremities in weight-bearing and non-weight-bearing positions on ROM (shoulders, elbows, wrists, hips, knees, and ankle joints), balance, and function in children with spastic hemiplegic CP. Methods This randomized clinical trial involved 60 hemiplegic spastic CP children aged5-15 years. After randomization, all the participants were divided into sixgroups of equal size based on the WBVT application for upper extremities, lower extremities, or both in weight-bearing or non-weight-bearing positions. The therapy was applied three times per week for four consecutive weeks. The outcome measures were ROM, hand grip strength, balance quantification score using My Fitness Trainer (MFT) 2.0, and timed up and go (TUG) scores. Results While all the groups were homogenous before treatment, after treatment, it was observed that all the ranges improved significantly in all groups. The same was observed for hand grip strength, balance score, and TUG test scores (p<0.05).The post-hoc analysis revealed that the weight-bearing position for the upper and lower extremities combined showed the highest level of improvement. Conclusions Based on our findings, WBVT in weight-bearing positions produces more significant results than in non-weight-bearing positions. We also observed that when WBVT is applied to the upper extremities, it can improve the function of the lower extremities and vice versa.

Discovery of Stable Surfaces with Extreme Work Functions by High‐Throughput Density Functional Theory and Machine Learning (Adv. Funct. Mater. 19/2024)

Discovery of Stable Surfaces with Extreme Work Functions by High‐Throughput Density Functional Theory and Machine Learning (Adv. Funct. Mater. 19/2024)

Inclusive Physical Education of Students with Disabilities Due to War Injuries: Restoration of the Functions of the Lower Extremities

Background. The relevance of the study is because the institutions of higher education are now tasked with creating all the conditions for the recovery of body functions lost as a result of injuries of students with disabilities, which additionally actualizes the stated problem in connection with the long-term hostilities on the territory of Ukraine. Objectives. The purpose of the article is to reveal the effectiveness of the developed program of inclusive PE on the recovery of lost functions due to injuries of the lower limbs in students with disabilities. Materials and methods. To solve the tasks, a complex of scientific intelligence methods was used at the empirical and theoretical level: literature analysis, observation, testing, experiment, and methods of mathematical statistics. The test program consisted of the star excursion balance, weight–bearing lunge test, and the single leg stance test. 24 male students with disabilities in the first year of study at a higher education institution took part in the experiment. Results. According to the qualitative assessment of the obtained results, it can be stated that after the end of the experiment, there is a general tendency to increase the results of the test tasks. A significant improvement of the indicators was found in all the investigated parameters without exception: as a positive trend in the range of 15% is observed. The results of the static and dynamic tests performed with support on the injured leg were significantly lower than with support on the uninjured leg (p &lt;0.05). Conclusions. The results of the final testing allow us to ascertain the effectiveness of the implemented program. Statistically reliable positive dynamics of the set of investigated indicators proved that the implementation of the developed inclusive PE program for students with disabilities due to injuries of the lower extremities ensures the effectiveness of recovery due to functional injuries.

Some properties of subclass of multivalent functions associated with a generalized differential operator

In this paper, the new subclass Sb,λ,δ,pn(α)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {S}^n_{b,\\lambda ,\\delta ,p} ({\\alpha })$$\\end{document} of a linear differential operator’s Nλ,δ,pnf(ζ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}_{\\lambda ,\\delta ,p}^{n}f(\\zeta )$$\\end{document} associated with multivalent analytical function has been introduced. Further, the coefficient inequalities, extreme points for the extremal function, sharpness of the growth and distortion bounds, partial sums, starlikeness, and convexity of the subclass is investigated.

Penerapan Model Log-Logistik Proporsional Hazard Untuk Menentukan Faktor yang Mempengaruhi Kondisi Financial Distress

&lt;p class="AbstractEnglish"&gt;Every company is likely to experience an up or down phase in its financial performance. A decline in financial performance is a condition of financial distress. Financial distress is an event of a continuous decline in a company's financial performance over a certain period of time. The variables in this research are the response variable in the form of the time of company experiences financial distress, while the covariates are the solvency ratio, liquidity ratio, growth ratio, profitability ratio, company size and activity ratio. The aim and objective of the research is to obtain the property and significance of covariates when a company experiences financial distress. How to determine covariates that are significant to financial distress. The model used is a log-logistic proportional hazard regression model. The log-logistic model is a regression model in the form of a maximum extreme function with right asymptotics and non-negative random variables, while the Cox proportional hazards model is a survival model with the independent variables being time and covariates, between time and covariates being independent. The results of this research are that companies in the infrastructure, utilities and transportation sectors experience financial distress, influenced by solvency ratios, liquidity ratios and profitability ratios. The solvency ratio and profitability ratio have a positive effect, while the liquidity ratio has a negative effect on the timing of financial distress. The contribution of these factors to companies experiencing financial distress is 1.1% (for liquidity ratio), 3.4% (for solvency ratio), and 95.5% (for profitability ratio).&lt;/p&gt;&lt;p class="AbstractEnglish"&gt;&lt;strong&gt;Keywords: &lt;/strong&gt;financial distress; log-logistic; portional hazard; profitability ratio&lt;/p&gt;

THE USE OF A TRAINING 3D-MODEL IN THE TREATMENT OF A PATIENT WITH A PATHOLOGICAL FRACTURE OF THE PROXIMAL PART OF THE FEMUR (CASE FROM PRACTICE)

Prostate cancer is the second most common cause of malignancy in men, with bone metastases being a significant source of morbidity and mortality in advanced cases. Objective. To give a clinical example of a patient with a pathological transtrochanteric fracture of the right femur with displacement of fragments, the presence of metastasis at the fracture site, to emphasize the importance of 3D-training before surgery. Methods. A clinical example with a significant impairment of the function of the right lower extremity against the background of a significant pain syndrome is given. The diagnosis was established: pathological transtrochanteric fracture of the right femur with displacement of fragments, the presence of metastasis at the fracture site. Pre-surgical training was carried out using a 3D-model and total endoprosthetics of the right hip joint with a revision individual implant of the cement fixation type was carried out. The patient fully recovered the function of the right lower limb and hip joint, the pain syndrome was eliminated, and sleep normalized. The use of a 3D-model for preoperative training of surgeons made it possible to rationally limit traumatization of healthy tissues during tumor removal, prevent possible complications and optimize the time of surgical intervention and thus minimize blood loss. Conclusions. The use of a training 3D-model before surgery followed by prosthetics with a special oncological endoprosthesis provided satisfactory functional results and restoration of the patient's quality of life in the given clinical case. The use of a 3D-model is the key to careful preparation for surgical intervention, taking into account the individual anatomical features of the pathological process and adjacent tissues, which allows you to significantly optimize the terms of the operation and reduce blood loss, and also provides valuable experience for further surgical practice.

Effects of Transcutaneous Electrical Nerve Stimulation with Taping on Wrist Spasticity, Strength, and Upper Extremity Function in Patients with Stroke: A Randomized Control Trial.

Objective: Six months after the onset of stroke, over 60% of patients experience upper limb dysfunction, with spasticity being a major contributor alongside muscle weakness. This study investigated the effect of transcutaneous electrical nerve stimulation (TENS) with taping on wrist spasticity, strength, and upper extremity function in patients with stroke. Methods: In total, 40 patients with stroke were included and randomly divided into two groups: the TENS + taping (n = 20, age 52.4 ± 9.3 (range: 39 to 70)) and TENS (n = 20, age 53.5 ± 10.8 (range: 39 to 74)) groups. All subjects performed 30 sessions of task-related training, which included 10 min of postural control training and 20 min of task performance. Additionally, all subjects received TENS on the spastic muscle belly for 30 min before task-related training. In the TENS + taping group, taping was additionally applied to the forearm and wrist but not in the TENS group. The Modified Ashworth Scale was used to measure spasticity, and a handheld dynamometer was used to measure muscle strength. The Fugl-Meyer Assessment of Upper Extremity was used to evaluate the functional ability of the upper extremity. Results: In the TENS + taping group, spasticity and upper extremity function were significantly improved as compared to those in the TENS group (p < 0.05). However, no significant difference in muscle strength was observed between the two groups (p > 0.05). Conclusions: This study demonstrated that the combination of TENS and taping for spasticity and function of the upper extremity was more effective in relieving the spasticity than TENS alone. Therefore, we suggest this combination as an additional treatment for spasticity and function of the upper extremity.

Effects of Perfetti's Method on Cognition, Dexterity and Sensory Motor Function of the Upper Extremity in Stroke Patients: A Randomized Controlled Tria

Background: A stroke is the sudden loss of neural function caused by an interruption of blood flow to the brain. It causes symptoms such as paresis, hypoesthesia, cognitive impairment, and spasticity. Objective(s): To compare the effects of Perfetti's Method versus routine physical therapy on the upper extremities' cognition, dexterity, and sensorimotor function in stroke patients. Methodology: In this study, 74 stroke participants were enrolled and randomized into two groups by the Goldfish Bowl Procedure, with 37 patients in each group. Group A was treated with routine physical therapy, and Group B was treated with Perfetti's Method and routine physical therapy. The measurements of both groups were recorded at the beginning of the study and after the 12th post-treatment week. Sensorimotor function was measured with the Fugal-Meyer Assessment Upper Extremity (FMA-UE), dexterity was measured with the Box and Block Test (BBT), and level of cognition was measured with the Mini-Mental State Exam (MMSE) in both groups at the beginning of the study and after the end of training (12th post-treatment weak). Results: According to this study, 74 participants had a mean age of 53.21±12.02; males were 45(60.8%), and females were 29(40.2%). The mean Body Mass Index was 23.23±3.47. The right side was affected by 32(43.2%), and Left Side was affected by 42(56.8%). Sensorimotor Function mean was Pre-treatment 66.70±26.88 and posttreatment 110.09±11.91. The level of cognition mean was pre-treatment 22.62±3.30 and post-treatment 29.31±1.47. Dexterity means Pre-treatment was 8.18±11.64 and posttreatment was 84.48±15.03. P-Value was 0.00, which was &lt;0.005, which means that there was a significant difference between the mean value of pre-treatment and post-treatment Sensorimotor function, Level of Cognition, and Dexterity. There was a significant difference between the mean values of Groups A and B in sensorimotor function, level of cognition, and dexterity, as the P-values were 0.027, 0.04, and 0.02, respectively. Conclusion: Perfetti's Method, combined with routine physical therapy, resulted in significantly improved cognition levels, dexterity and sensory motor function in the upper extremity of stroke patients compared to those receiving only routine physical therapy.

Discovery of Stable Surfaces with Extreme Work Functions by High‐Throughput Density Functional Theory and Machine Learning

AbstractThe work function is the key surface property that determines the energy required to extract an electron from the surface of a material. This property is crucial for thermionic energy conversion, band alignment in heterostructures, and electron emission devices. This work presents a high‐throughput workflow using density functional theory (DFT) to calculate the work function and cleavage energy of 33,631 slabs (58,332 work functions) that are created from 3,716 bulk materials. The number of calculated surface properties surpasses the previously largest database by a factor of ≈27. Several surfaces with an ultra‐low (&lt;2 eV) and ultra‐high (&gt;7 eV) work function are identified. Specifically, the (100)‐Ba‐O surface of BaMoO3 and the (001)‐F surface of Ag2F have record‐low (1.25 eV) and record‐high (9.06 eV) steady‐state work functions. Based on this database a physics‐based approach to featurize surfaces is utilized to predict the work function. The random forest model achieves a test mean absolute error (MAE) of 0.09 eV, comparable to the accuracy of DFT. This surrogate model enables rapid predictions of the work function (≈ 105 faster than DFT) across a vast chemical space and facilitates the discovery of material surfaces with extreme work functions for energy conversion and electronic device applications.

Sharp affine weighted L 2 Sobolev inequalities on the upper half space

Abstract We establish some sharp affine weighted L 2 Sobolev inequalities on the upper half space, which involves a divergent operator with degeneracy on the boundary. Moreover, for some certain exponents cases, we also characterize the extremal functions and best constants. Our approach only relies on the L 2 structure of gradient norm, affine invariance and a class of weighted L 2 Sobolev inequality on the upper half space. This is a simple approach which does not depend on the geometric structure of Euclidean space such as Brunn–Minkowski theory on convex geometry.

Anisotropic Moser–Trudinger-Type Inequality with Logarithmic Weight

Our main purpose in this paper is to study the anisotropic Moser–Trudinger-type inequalities with logarithmic weight ωβ(x)=[−lnFo(x)|(n−1)β. This can be seen as a generation result of the isotropic Moser–Trudinger inequality with logarithmic weight. Furthermore, we obtain the existence of extremal function when β is small. Finally, we give Lions’ concentration-compactness principle, which is the improvement of the anisotropic Moser–Trudinger-type inequality.

The role of direct capital cash transfers towards poverty and extreme poverty alleviation - an omega risk process

Trapping refers to the event when a household falls into the area of poverty. Households that live or fall into the area of poverty are said to be in a poverty trap, where a poverty trap is a state of poverty from which it is difficult to escape without external help. Similarly, extreme poverty is considered as the most severe type of poverty, in which households experience severe deprivation of basic human needs. In this article, we consider an Omega risk process with deterministic growth and a multiplicative jump (collapse) structure to model the capital of a household. It is assumed that, when a household's capital level is above a certain capital barrier level that determines a household's eligibility for a capital cash transfer programme, its capital grows exponentially. As soon as its capital falls below the capital barrier level, the capital dynamics incorporate external support in the form of direct transfers (capital cash transfers) provided by donors or governments. Otherwise, once trapped, the capital grows only due to the capital cash transfers. Under this model, we first derive closed-form expressions for the trapping probability and then do the same for the probability of extreme poverty, which only depends on the current value of the capital given by some extreme poverty rate function. Numerical examples illustrate the role of capital cash transfers on poverty and extreme poverty dynamics.

Automatic rehabilitation assessment method of upper limb motor function based on posture and distribution force.

The clinical rehabilitation assessment methods for hemiplegic upper limb motor function are often subjective, time-consuming, and non-uniform. This study proposes an automatic rehabilitation assessment method for upper limb motor function based on posture and distributed force measurements. Azure Kinect combined with MediaPipe was used to detect upper limb and hand movements, and the array distributed flexible thin film pressure sensor was employed to measure the distributed force of hand. This allowed for the automated measurement of 30 items within the Fugl-Meyer scale. Feature information was extracted separately from the affected and healthy sides, the feature ratios or deviation were then fed into a single/multiple fuzzy logic assessment model to determine the assessment score of each item. Finally, the total score of the hemiplegic upper limb motor function assessment was derived. Experiments were performed to evaluate the motor function of the subjects' upper extremities. Bland-Altman plots of physician and system scores showed good agreement. The results of the automated assessment system were highly correlated with the clinical Fugl-Meyer total score (r = 0.99, p < 0.001). The experimental results state that this system can automatically assess the motor function of the affected upper limb by measuring the posture and force distribution.

Efficacy of Dashmool Vasti as an adjuvant therapy with the standard of care (modern + physiotherapy) in the rehabilitation of stroke as compared to standard of care – a clinical trial protocol

Background Stroke is ischemia and neurological dysfunction caused by acute brain circulation loss. It causes acute localized neurological abnormalities such as weakness, sensory deficit, or language issues that require long-term treatment. These deficiencies harm the patient and their family psychologically, socially, and economically. Thus, combination treatment can rapidly rehabilitate such patients. Detoxification methods like Ayurvedic medicated enema help stroke pathophysiology. Physical modalities in physiotherapy have been shown to facilitate normal movement and function on the stroke patient’s affected side, increasing independence with everyday duties. A stroke patient may benefit from Dashmoola Niruha Basti, Function Electrical Stimulation (FES), and Motor Relearning Programme (MRP). Aim &amp; Objectives This study compares the adjuvant role of Dashmoola Basti with MRP and FES in stroke recovery. The main goals of this study are to assess and compare the adjuvant role of Dashmoola Basti with standard control over sensorimotor function of lower extremities, static and dynamic balance in stroke patients; gait parameters; resistance experienced during passive range of motion; quality of life of patients; Barthel Index; Modified Ashworth Scale; and Fuglmeyer assessment, Single Limb Stance Test, Functional Reach Test. Methods A total of 40 patients will be enrolled and divided randomly into two equal groups. In Group A (control), standard treatment (modern + physiotherapy) will be prescribed for one month. In Group B (interventional group), Dashmoola Basti will be added to the aforementioned standard treatment for one month. Expected results Improvement in Fuglmeyer assessment, Single Limb Stance Test, Functional Reach Test, quality of Life of Patients, Barthel Index, Modified Ashworth scale, and National Institute of Health (NIH) stroke-scale-score will be observed and recorded. Conclusions Results and conclusions will be derived according to the data collected in case record form and assessment sheets filled at baseline and follow-up visits. Trial registration CTRI/2021/10/037445 dated 21.10.2021.

Stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds

We study the qualitative stability of two classes of Sobolev inequalities on Riemannian manifolds. In the case of positive Ricci curvature, we prove that an almost extremal function for the sharp Sobolev inequality is close to an extremal function of the round sphere. In the setting of non-negative Ricci curvature and Euclidean volume growth, we show an analogous result in comparison with the extremal functions in the Euclidean Sobolev inequality. As an application, we deduce a stability result for minimizing Yamabe metrics. The arguments rely on a generalized Lions' concentration compactness on varying spaces and on rigidity results of Sobolev inequalities on singular spaces.

The Schwarzian norm estimates for Janowski convex functions

AbstractFor $-1\leq B \lt A\leq 1$, let $\mathcal{C}(A,B)$ denote the class of normalized Janowski convex functions defined in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z| \lt 1\}$ that satisfy the subordination relation $1+zf''(z)/f'(z)\prec (1+Az)/(1+Bz)$. In the present article, we determine the sharp estimate of the Schwarzian norm for functions in the class $\mathcal{C}(A,B)$. The Dieudonné’s lemma which gives the exact region of variability for derivatives at a point of bounded functions, plays the key role in this study, and we also use this lemma to construct the extremal functions for the sharpness by a new method.

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.

Efficacy of motor relearning programme on rehabilitation of upper extremity function in stroke patients

Background: The most debilitating condition for stroke patients, impacting their quality of life, is motor impairment in the upper extremities. This study aimed to evaluate the impact of the Motor Relearning Programme (MRP) on enhancing stroke patient’s upper limb motor function. Methods: A systematic review using trial studies from an online journal database published from 2013 to 2023. The participants of this study are stroke patients. The utilization of the MRP is compared with an alternative intervention, with the study aiming to assess the motor function of the upper extremities as its primary outcome. The quality of the trial was assessed using the JBI checklist Results: Eight studies, encompassing 279 stroke patients aged 35 to 70, were incorporated. These trials compared the MRP with various interventions, including mirror therapy, Constraint-Induced Movement Therapy (CIMT), bobath, progressive resisted exercise, thermal stimulation, and bilateral task-related training. The interventions spanned an average duration of 3-8 weeks, with sessions occurring 3-6 times per week and lasting between 30 and 120 minutes each. According to the Joanna Briggs Institute (JBI) assessment, all studies achieved a good quality rating, with total points ranging from 9-12. Notably, six studies demonstrated a significant improvement in upper extremity motor function with MRP, while one showed no significant difference. In contrast, one study indicated that CIMT demonstrated more effective results. Conclusion: MRP significantly improves upper extremity function in stroke patients.

Modified Chinese disabilities of arm, shoulder and hand tool: Validity and reliability for upper extremity injuries

DesignClinimetric evaluation study. IntroductionThe Chinese Disabilities of the Arm, Shoulder, and Hand (DASH) questionnaire has necessitated the development of a revised version to the specific needs of individuals with upper extremity injuries with the progress of times and lifestyle changes. Purpose of the studyThis research aimed to evaluate the reliability and validity of Modified Chinese Disability of Arm, Shoulder and Hand (MC-DASH) questionnaire in individuals with upper extremity injuries. MethodsOne hundred and one individuals with upper extremity injuries (UEI) were recruited. The function of upper extremity was measured using the electronic version of MC-DASH, and compared against the Chinese Disability of Arm, Shoulder and Hand. The MC-DASH was reassessed within three days in all individuals. We investigated the internal consistency, test-retest reliability, content validity, criterion validity, and construct validity of MC-DASH. ResultsThe internal consistency was deemed sufficient, as indicated by a Cronbach's alpha of 0.986 and an intraclass correlation coefficient of 0.957. Moreover, the mean total scores of MC-DASH on the first-test and retest were 37.86 and 38.19, respectively (ICC: 0.957, 95 %CI: 0.937–0.971, p < 0.001). Furthermore, the MC-DASH version exhibited satisfactory content validity evidenced by its strong correlation (R= 0.903, p < 0.001) with the Chinese DASH. Three major influencing factors were identified from 37 items. The cumulative variance contribution rate of the MC-DASH questionnaire was 75.76 %, confirming its construct validity. ConclusionThe Modified Chinese Disability of Arm, Shoulder and Hand questionnaire has been shown to be a valid, reliable, and practical tool for use in patients with upper extremity injuries.

A System for Collecting and Evaluating Load Information about Bioelectric Signals of the Muscular Apparatus of the Foot of a Person with Cerebral Palsy

The purpose of the research is to develop a system of biomechanical investigation of the volume of movement in the foot and ankle joint for the diagnosis of patients with cerebral palsy in assessing the quality of rehabilitation measures. The process of creating a computer diagnostic system for patients with impaired motor functions of the lower extremities, which is equipped with special bio-measuring devices provided with specialized algorithms for processing the information obtained, is investigated due to the need for scientific research aimed at developing methods and tools for a comprehensive assessment of the results of physical rehabilitation using biomedical indicators.Methods of kinematic analysis of movements in the ankle joint were used, dynamic and static analyses of the forces of the supporting reactions of the foot of the lower extremities were carried out.Results. A motion detection system based on an electronic goniometer implemented on the basis of a B10K resistive potentiometer has been developed. The determination of the absolute rotation angles of the links of the diagnostic system was carried out using the MMA7361 acceleration sensor, which contains three micromachine capacitors mounted on one silicon plate. In the course of research, changing the capacitances of micromachine capacitors makes it possible to fix the recorded value in each direction. Signals passing through low-frequency filters and temperature compensation cascades are sent to the corresponding outputs X, Y and Z. The obtained angulograms allow us to evaluate the gait of the studied patient in two classes ‒ normal and in the presence of pathology.Conclusion. A system for the formation and evaluation of bioelectric signals obtained using the muscular apparatus of the foot of patients with cerebral palsy, assembled on the platform of the Arduino UNO control board and a generalpurpose personal computer, has been developed. The developed system makes it possible to register bioelectric signals with their subsequent processing using a personal computer and making diagnostic decisions.