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Background/Objectives: Baseball pitching injuries associated with fatigue-induced mechanisms may be attributed to change in lower-body power. In this study, a stretch-resistant belt (theorized to increase intra-abdominal pressure) was studied to determine if it influenced countermovement jump (CMJ) power pre- and post-pitching. Methods: Thirteen college athletes participated in three separate, randomized pitching sessions of forty pitches to evaluate the CMJ performance impacts owed to wearing a team-issued baseball belt versus a belt that was configured with the intent to raise intra-abdominal pressure (IAP). The three belt conditions were; (1) the team-issued belt, standard belt (SB), (2) the IAP-configured belt worn at regular length (RIAP), and the IAP-configured belt fastened two inches with the tightest cinch (2IN). Maximum jump heights were measured on a Jumpmat and captured with hands on hips. Data was integrated to compute jump power and the eccentric utilization ratio, being the ratio of a full stretch CMJ to a static CMJ biased to concentric power. Static CMJ testing had pitchers hold the bottom position for 5 s before takeoff. Repeated measures ANOVA with a post hoc Bonferroni correction determined significant differences; subject-specific interactions were identified. Results: Most athletes maintained or improved performance post-pitching with the RIAP with less variability in coordinating stretch-shortening responses. On a group level, RIAP had greater post-pitching CMJ height and power versus 2IN (p < 0.03) and had less CMJ power loss compared to SB and 2IN belt conditions (p < 0.02). IAP was not directly measured, yet this exploratory study provides preliminary evidence that a 5 mm, theoretical IAP design, via a stretch-resistant belt can influence pre- and post-pitching lower-body neuromuscular performance in collegiate pitchers. Conclusions: The RIAP condition showed less performance decline inferring fatigue resistance, preserved max CMJ height, and lessened post-pitch CMJ power loss. Maximal cinching tended to compromise post-pitch lower-body power and inferred the need to individualize the stretch-resistant belt, designed to increase intra-abdominal pressure, for performance and injury protection benefits.
This article was published open access under a CC BY-NC-ND licence: https://creativecommons.org/licenses/by-nc-nd/4.0/ .
Bifurcation Potential Fields (VB fields) provide a compact, field-theoretic representation of stability margins across parameter space in nonlinear dynamical systems, capturing a key geometric component of resilience. Defined as scalar fields over bifurcation geometry, VB fields synthesize phase-space structure with the number and stability of equilibria under parametric change. We apply this framework to a progression of canonical (normal-form) and mechanistic (physical and ecological) models, demonstrating how stability margins can be quantified and compared across systems with differing bifurcation organization. Across these systems, we identify stability-margin discontinuities: discrete changes in distance to collapse arising from bifurcation-induced transitions in the equilibrium that defines the stability boundary. We further highlight conceptual axes along which VB fields vary, including stability architecture, dimensionality (1D vs. 2D), symmetry, phase-space folding, and structural realism. These axes shape the location of collapse thresholds, the geometry of collapse pathways and the interpretation of collapse risk. This approach generalizes across canonical and mechanistic one-and two-dimensional model classes, offering a unified geometric framework for quantifying vulnerability to both state-space perturbations and parameter drift.
Because the history of historiography is obviously too complex to be dealt with comprehensively, this paper is in the form of an essay. It discusses several aspects of the evolution of historiography in the 18th through the 20th centuries, organized around three principal questions concerning history/historiography posed by Karl R. Popper’s 1967 article “A Pluralist Approach to the Philosophy of History.” These questions are “What is the meaning of history?” “What is the use or value of history?” and “What is the method of history?” The work of Lord Acton plays a key role in responding to these questions which is elaborated here. The final part of the essay looks at the19th and 20th schism in historiography and its impact on the study of historical study.
