Academic literature on the topic 'P-concavity'

We study the log-concavity of a sequence of [Formula: see text]-binomial coefficients located on a ray of the [Formula: see text]-Pascal triangle for certain directions, and we establish the preserving log-concavity of linear transformations associated to [Formula: see text]-Pascal triangle.

Objectives: The mechanism of concavity-compression is known to be a key factor for glenohumeral stability in the mid-range of motion. This stabilizing effect is impaired by traumatic bone loss at the anterior glenoid rim. Currently, a critical threshold based on the defect size is used as a decisive criterion for surgical treatment. However, recent studies using finite element method (FEM)-simulations indicate that glenoid concavity is essential for an assessment of remaining glenohumeral stability. To date, there is no biomechanical investigation involving glenoid concavity in combination with defect size. In this biomechanical study we focused on the interdependence between glenoid concavity, defect size and glenohumeral stability. We hypothesized that glenohumeral stability is mainly dependent on concavity and that the initial concavity affects the loss of stability caused by bony defects at the anterior glenoid rim. Methods: A 6-degree-of-freedom industrial robot was utilized to determine the stability of 17 human cadaveric glenoids, depending on osteochondral concavity and anterior defect size. Load-and-shift tests were performed with artificial humeri equipped with a best-fit implant while joint positions and loads were captured. The Stability Ratio (SR), defined as the maximum tolerated anterior force related to a constant compression force, was determined for a compression of 50 N. In addition to a translation in 3 o’clock direction relative to a right scapula, a passive path dislocation was performed using compensatory translations to minimize superoinferior forces occurring during anterior translation. Defects were created in 2 mm steps parallel to the long axis of the glenoid until dislocation occurred self-acting and a 3D measuring arm was used for morphometric measurements as depicted in Figure 1. For statistical analysis, linear mixed-effects models were established to exploit the impacts of fixed effects (defect size and concavity gradient) as well as random effects (repeated measures and friction) on the SR. The influence of defect size on SR was analyzed for a translation in 3 o’clock by classifying the specimens into three groups of low (<25 %, n = 6), medium (25-35 %, n = 6) and high (>35 %, n = 5) initial concavity gradients. In addition, the Bony Shoulder Stability Ratio (BSSR), a characteristic based on glenoid depth and radius, was determined to evaluate its correlation with the measured SR and to find a suitable characteristic for the assessment of SR independent of defect size. Results: For a translation in 3 o’clock, the linear model resulted in an intercept of 7.13 ± 1.57 (95 % CI [4.01, 10.24]), representing the SR for zero defect size and concavity gradient. The linear coefficient for the predictor concavity gradient averaged 1.05 ± 0.05 (95 % CI [0.96, 1.14]) corresponding to a rise of SR by 1.05 % with each percentage of concavity gradient. Both coefficients were significantly different from zero with p<0.001. The defect size had only an indirect impact on SR, as the linear coefficient of 0.03 ± 0.04 (95 % CI [-0.10, 0.05]) differed insignificantly from zero (p = 0.53). The entire model featured a determination coefficient of R² = 0.98 and a mean squared error (MSE) of 4.22 %. This relationship is diagramed in Figure 2. Using the defect size as an exclusive predictor reduced R² to 0.87 and increased MSE up to 25.72 %. The passive path translation started on average in 2:16 o’clock for the intact glenoid and shifted to 3:06 o’clock with increasing defect size. Though the model indicated a significant impact of concavity gradient as well as defect size on SR (p<0.001), the influence of defect size ( 0.18 ± 0.03, 95 % CI [ 0.24, -0.11])) was significantly smaller than the effect of concavity gradient (0.97 ± 0.04, 95 % CI [0.88, 1.05]). However, the linear model for the passive path resulted in R² = 0.97 and MSE = 5.5 %. Separate linear models for the three groups of low, medium and high initial concavity gradients indicated significant differences in the slope coefficients (low: -0.55 ± 0.05 (95 % CI [ 0.65, 0.45]); medium: 0.78 ± 0.04 (95 % CI [-0.87, -0.70]); high: -1.25 ± 0.06 (95 % CI [ 1.36, -1.13])). This represented a significant impact of the initial glenoid concavity on the loss of SR per defect size. Raw data points as well as the linear approximations are shown in Figure 3. The linear model with the BSSR as a predictor for the measured SR is depicted in Figure 4 indicating a highly linear correlation with R² = 0.98 and MSE = 3.4 % for the translation in 3 o’clock. Conclusions: The SR is significantly dependent on the glenoid concavity whereas the defect size has a negligible indirect impact, provided that both predictors are included in a linear model. Due to constitutional different glenoid shapes, the loss of SR per defect size is significantly dependent on the initial concavity gradient. However, the BSSR has proven to be a reliable predictor of glenohumeral stability independent of defect size. These findings demonstrate that concavity is a crucial factor in estimating residual SR and substantiate that defect size as the only critical threshold is an inappropriate decisive criterion in the treatment of shoulder instabilities with anterior glenoid bone loss.

Context:Various studies report decreased muscle activation in the concavity of the curve in patients with scoliosis. Such decreased muscle-performance capacity could lead to sustained postural deficits.Objective:To investigate whether specific asymmetrical sports therapy exercises rather than symmetrical back strengthening can increase EMG amplitudes of paraspinal muscles in the concavity of the curve.Design:Cross-sectional.Setting:Laboratory.Participants:16 patients with idiopathic scoliosis.Interventions:Patients performed 4 back-strengthening exercises (front press, lat pull-down, roman chair, bent-over barbell row) during 1 test session. Each exercise was performed in a symmetrical and asymmetrical variant and repeated 3 times.Main Outcome Measure:EMG amplitudes of the paraspinal muscles were recorded in the thoracic and lumbar apexes of the scoliotic curve during each exercise. Ratios of convex- to concave-side EMG activity were calculated.Results:Statistical analysis revealed that the asymmetrical variants of front press at the lumbar level (P = .002) and roman chair and bent-over barbell row at the thoracic level (P < .0001, .001 respectively) were superior in increasing EMG amplitudes in the concavity of the scoliotic curve.Conclusions:Specific asymmetrical exercises increase EMG amplitudes of paraspinal muscles in the concavity. If confirmed in longitudinal studies measuring improvements of postural deficits, these exercises may advance care of patients with scoliosis.

Background We tested the hypothesis that the pressure-time (P-t) curve during constant flow ventilation can be used to set a noninjurious ventilatory strategy. Methods In an isolated, nonperfused, lavaged model of acute lung injury, tidal volume and positive end-expiratory pressure were set to obtain: (1) a straight P-t curve (constant compliance, minimal stress); (2) a downward concavity in the P-t curve (increasing compliance, low volume stress); and (3) an upward concavity in the P-t curve (decreasing compliance, high volume stress). The P-t curve was fitted to: P = a. tb +c, where b describes the shape of the curve, b = 1 describes a straight P-t curve, b &lt; 1 describes a downward concavity, and b &gt; 1 describes an upward concavity. After 3 h, lungs were analyzed for histologic evidence of pulmonary damage and lavage concentration of inflammatory mediators. Ventilator-induced lung injury occurred when injury score and cytokine concentrations in the ventilated lungs were higher than those in 10 isolated lavaged rats kept statically inflated for 3 h with an airway pressure of 4 cm H2O. Results The threshold value for coefficient b that discriminated best between lungs with and without histologic and inflammatory evidence of ventilator-induced lung injury (receiver-operating characteristic curve) ranged between 0.90-1.10. For such threshold values, the sensitivity of coefficient b to identify noninjurious ventilatory strategy was 1.00. A significant relation (P &lt; 0.001) between values of coefficient b and injury score, interleukin-6, and macrophage inflammatory protein-2 was found. Conclusions The predictive power of coefficient b to predict noninjurious ventilatory strategy in a model of acute lung injury is high.

AbstractThe paper contains a study of weighted exponential inequalities for differentially subordinate martingales, under the assumption that the underlying weight satisfies Muckenhoupt’s condition $$A_{\infty }$$ A ∞ . The proof exploits certain functions enjoying appropriate size conditions and concavity. The martingales are adapted, uniformly integrable, and càdlàg - we do not assume any path-continuity restrictions. Because of this generality, we need to handle jump parts of processes which forces us to construct a Bellman function satisfying a stronger condition than local concavity. As a corollary, we will establish some new weighted $$L^p$$ L p estimates for differential subordinates of bounded martingales.

A simple, self-contained proof is presented for the concavity of the map (A, B) ↦ Tr Ap K† B1-p K. The author makes no claim to originality; this paper gives Lieb's original argument in its simplest, rather than its most general, form. A sketch of the chain of implications from this result to concavity of A ↦ Tr eK+ log A is then presented. An independent elementary proof is given for the joint convexity of the map [Formula: see text], which plays a key role in entropy inequalities.

Many people are concerned about the stock market in 2022 as it faces several threats, from rising inflation rates to geopolitical events. The S&P 500 Index has already dropped about 10% from the peak in early January 2022 until the end of February 2022. This paper aims at updating the crisis indicator to predict when the market may experience a significant drawdown, which we developed in Crisis Risk Prediction with Concavity from Polymodel (2022). This indicator uses regime switching and Polymodel theory to calculate the market concavity. We found that concavity had not increased in the past 6 months. We conclude that at present, the market does not bear inherent dynamic instability. This does not exclude a possible collapse which would be due to external events unrelated to financial markets.

Background. To preliminary explore the correlations among corneal biomechanical parameters, stiffness, and thickness in patients with ocular hypertension (OHT) before and after treatment with topical antiglaucoma medications. Methods. This was a retrospective study that included 35 eyes with newly diagnosed OHT. Axial length (AL), apical corneal thickness, and minimum corneal thickness were measured using Pentacam. The lengths, velocities, and times of the first and second corneal applanations (A1L, A1V, A1T, A2L, A2V, and A2T, respectively); the highest concavity radius; highest concavity peak distance (PDHC); highest concavity deformation amplitude (DAHC); highest concavity time (HCT); pachymetry (PACH); stress-strain index (SSI); stiffness parameter-A1 (SP-A1); deformation amplitude ratio (DA ratio); integrated radius (IR); Ambrosio’s relational thickness horizontal (ARTh); corneal biomechanical index; noncorrected intraocular pressure (IOPnct); and biomechanically corrected IOP (bIOP) values were measured using the corneal visualization Scheimpflug technology (Corvis ST/CST). Results. After 5 weeks of treatment, Goldman applanation tonometer-IOP, IOPnct, bIOP, PACH, A1T, A2V, SSI, SP-A1, and ARTh decreased, but A1V, A2T, PDHC, DAHC, DA ratio, and IR increased significantly (all p < 0.05 ). SP-A1 and A1T were positively associated with premedication IOP and IOP changes, whereas A1V, A2T, PDHC, and IR were negatively associated (all p < 0.05 ). DAHC and DA ratio had significantly negative correlations with IOP variations. PDHC was found to be positively correlated with AL ( p < 0.05 ). A positive relationship was noted between SP-A1 and HCT before medication ( p < 0.05 ). Conclusions. SP-A1 was significantly and consistently associated with IOP. HCT might be correlated with SP-A1. SP-A1 and CST parameters could serve as potential biomarkers for evaluating OHT treatment efficacy.

La tesi è dedicata allo studio delle cosiddette disuguaglianze di Borell-Brascamp-Lieb, note in letteratura come forme funzionali della disuguaglianza di Brunn-Minkowski. L'intento della tesi è duplice: da una parte si prefigge come manuale dettagliato delle disuguaglianze di Borell-Brascamp-Lieb, affrontando varie estensioni e proprietà più o meno note in letteratura; in secondo luogo si concentra sulla questione della stabilità di tali disuguaglianze, citando i risultati più significativi ed esibendo i contributi originali ottenuti, tratti dagli articoli: 1) A. Rossi, P. Salani, Stability for Borell-Brascamp-Lieb inequalities, Geometric Aspects of Functional Analysis - Israel Seminar (GAFA) 2014-2016 (B. Klartag and E. Milman Eds), Springer Lecture Notes in Mathematics 2169 (2017); 2) A. Rossi, P. Salani, Stability for a strengthened one-dimensional Borell-Brascamp-Lieb inequality, Applicable Analysis (2018). All the Borell-Brascamp-Lieb inequalities can be read as the functional counterparts of the celebrated Brunn-Minkowski inequality, and they have been widely studied in the last decades. The thesis focuses on two main targets. The first is to produce a complete and detailed overview on the results (old and new) on the Borell-Brascamp-Lieb inequalities, the second is to investigate some open questions on the quantitative version of such inequalities. The thesis is divided in 7 chapters. The first five contain the overview on the state of the art, classical and alternative proofs of both Borell-Brascamp-Lieb and Brunn-Minkowski inequalities, theequality cases and some stability results. Chapter 6 and Chapter 7 are devoted to describe the original contributions of the author in the field. Precisely in Chapter 6 a strengthened version of the one dimensional Borell-Brascamp-Liebinequality is proved, while in Chapter 7 the goal is to prove a general quantitative versions of the Borell-Brascamp-Lieb inequalities without concavity assumptions on the involved function. The original results are contained in the following two papers: • A. Rossi, P. Salani, Stability for Borell-Brascamp-Lieb inequalities, Geometric Aspects of Functional Analysis - Israel Seminar (GAFA) 2014-2016 (B. Klartag - E. Milman Eds), Springer Lecture Notes in Mathematics 2169 (2017); • A. Rossi, P. Salani, Stability for a strengthened one-dimensional Borell-Brascamp- Lieb inequality, Applicable Analysis (2018).

This study correlates the stress intensity factors (Kii, Kpaii), the order of the stress singularity p-1, and the practical bonding strength of ceramic to metal joints with arbitrary interface geometry. First, in order to describe the stress behavior of TiB2 to Ni joints bonded at 1173K, the stress singularity factors (Kii, Kpaii, p-1) were theoretically derived for wedge angles of φ1:30°&lt;φ1&lt;150°. Secondly, the dependences of the singularity factors on the wedge angle φ1 were compared with experimental results using the same wedge angles on TiB2 to Ni joints with interface convexity or concavity produced by Electric Discharge Machining (EDM). In order to obtain the highest strength joints, the optimum interface shape is determined using the relationship between the singularity factors.

The aim of this study is to analyze the phenomena of heat transfer enhancement between two periodic sinusoidal walls for a single gas flow. The experimental set-up is characterized by a few geometrical parameters: amplitude of wall waviness (A); channel height (H); fin wavy-channel width (ω); fin period (l) and total wavy length (L). Combination of these ones is reduced to: the wall aspect ratio γ, the cross-section aspect ratio α and the channel spacing ratio ε. The Reynolds number defined on the hydraulic diameter and the bulk velocity is greater than 4000. A constant heat flux is maintained on the second lateral wall. For Re = 5700, we observe an entrance region from the first to the fourth period; beyond, the velocity profiles are autosimilar. A shear layer is generated just downstream of the crest and develops in its wake up to the concavity area. Thermal experimental approach is performed by local measurements of convective heat transfer coefficient along the walls, within the viscous sublayer. The heat transfer profile presents an increasing from the crest of 15%, and the maximum is located at the first quarter of the period, close to the separated point. Beyond, the value of heat transfer decreases of 50% and the minimum is located close to the reattachment point. Then the heat transfer increases up to the next crest. The same phenomenon is observed in the next periods of the channel. To explain theses results, we calculate the turbulence terms obtained from the classical equations of fluid mechanics. The turbulence production (P) presents a maximum in the core of the shear layer, where the Reynolds constraints and the heat transfer are maxima. A good correlation is obtained between turbulence production and heat transfer. The flow pattern (mean, fluctuating and turbulence terms) are performed with PIV technique in order to analyze the vortices that develop in the shear layer, based on 1000 pairs of images.