Internal Languages of Finitely Complete (∞,1)(\infty, 1)-categories

We prove that the homotopy theory of Joyal's tribes is equivalent to that of fibration categories. As a consequence, we deduce a variant of the conjecture asserting that Martin-L\"of Type Theory with dependent sums and intensional identity types is the internal language of $(\infty, 1)$-categories with finite limits.Comment: 41 pages, minor revision

Correlation coefficients between AHA and MA2 with joint specific parameters during hand-to-mouth.

<p>Correlation coefficients between AHA and MA2 with joint specific parameters during hand-to-mouth.</p

Clinical assessment and three-dimensional movement analysis: An integrated approach for upper limb evaluation in children with unilateral cerebral palsy

<div><p>Introduction</p><p>The clinical application of upper limb (UL) three-dimensional movement analysis (3DMA) in children with unilateral cerebral palsy (uCP) remains challenging, despite its benefits compared to conventional clinical scales. Moreover, knowledge on UL movement pathology and how this relates to clinical parameters remains scarce. Therefore, we investigated UL kinematics across different manual ability classification system (MACS) levels and explored the relation between clinical and kinematic parameters in children with uCP.</p><p>Patients and methods</p><p>Fifty children (MACS: I = 15, II = 26, III = 9) underwent an UL evaluation of sensorimotor impairments (grip force, muscle strength, muscle tone, two-point discrimination, stereognosis), bimanual performance (Assisting Hand Assessment, AHA), unimanual capacity (Melbourne Assessment 2, MA2) and UL-3DMA during hand-to-head, hand-to-mouth and reach-to-grasp tasks. Global parameters (Arm Profile Score (APS), duration, (timing of) maximum velocity, trajectory straightness) and joint specific parameters (angles at task endpoint, ROM and Arm Variable Scores (AVS)) were extracted. The APS and AVS refer respectively to the total amount of movement pathology and movement deviations of wrist, elbow, shoulder, scapula and trunk.</p><p>Results</p><p>Longer movement durations and increased APS were found with higher MACS-levels (p<0.001). Increased APS was also associated with more severe sensorimotor impairments (r = -0.30-(-0.73)) and with lower AHA and MA2-scores (r = -0.50-(-0.86)). For the joint specific parameters, stronger movement deviations distally were significantly associated with increased muscle weakness (r = -0.32-(-0.74)) and muscle tone (r = 0.33-(-0.61)); proximal movement deviations correlated only with muscle weakness (r = -0.35–0.59). Regression analysis exposed grip force as the most important predictor for the variability in APS (p<0.002).</p><p>Conclusion</p><p>We found increased movement pathology with increasing MACS-levels and demonstrated the adverse impact of especially muscle weakness. The lower correlations suggest that 3DMA provides additional information regarding UL motor function, particularly for the proximal joints. Integrating both methods seems clinically meaningful to obtain a comprehensive representation of all aspects of a child’s UL functioning.</p></div

Statistical comparison of spatiotemporal parameters between MACS I, II and III for all tasks.

<p>2A, movement duration; 2B, timing of maximum velocity; 2C, maximum velocity; 2D, trajectory straightness; HTH, hand-to-head; HTM, hand-to-mouth; RGV, reach-to-grasp vertically; MACS, Manual Ability Classification System; Holm-Bonferroni sequential significance levels * p<0.0167; ** p<0.025; *** p<0.05.</p

Correlation coefficients between AHA and MA2 with joint specific parameters during reach-to-grasp.

<p>Correlation coefficients between AHA and MA2 with joint specific parameters during reach-to-grasp.</p

Statistical comparison of the joint specific parameters (Me, IQR) between MACS I, II and III during reach-to-grasp.

<p>Statistical comparison of the joint specific parameters (Me, IQR) between MACS I, II and III during reach-to-grasp.</p

Correlation coefficients between sensorimotor impairments and joint specific parameters during reach-to-grasp.

<p>Correlation coefficients between sensorimotor impairments and joint specific parameters during reach-to-grasp.</p

Statistical comparison of the Arm Profile Score between MACS I, II and III for all tasks.

<p>HTH, hand-to-head; HTM, hand-to-mouth; RGV, reach-to-grasp vertically, MACS; Manual Ability Classification System; Holm-Bonferroni sequential significance levels * p<0.0167; ** p<0.025; *** p<0.05.</p

Correlation coefficients between sensorimotor impairments and global kinematic parameters.

<p>Correlation coefficients between sensorimotor impairments and global kinematic parameters.</p

Correlation coefficients between AHA and MA2 with global kinematic parameters.

<p>Correlation coefficients between AHA and MA2 with global kinematic parameters.</p