Voluntary Activation and Variability During Maximal Dynamic Contractions with Aging

Whether reduced supraspinal activation contributes to age-related reductions in maximal torque during dynamic contractions is not known. The purpose was to determine whether there are age differences in voluntary activation and its variability when assessed with stimulation at the motor cortex and the muscle during maximal isometric, concentric, and eccentric contractions. Thirty young (23.6 ± 4.1 years) and 31 old (69.0 ± 5.2 years) adults performed maximal isometric, shortening (concentric) and lengthening (eccentric) contractions with the elbow flexor muscles. Maximal isometric contractions were performed at 90° elbow flexion and dynamic contractions at a velocity of 60°/s. Voluntary activation was assessed by superimposing an evoked contraction with transcranial magnetic stimulation (TMS) or with electrical stimulation over the muscle during maximal voluntary contractions (MVCs). Old adults had lower MVC torque during isometric (− 17.9%), concentric (− 19.7%), and eccentric (− 9.9%) contractions than young adults, with less of an age difference for eccentric contractions. Voluntary activation was similar between the three contraction types when assessed with TMS and electrical stimulation, with no age group differences. Old adults, however, were more variable in voluntary activation than young (standard deviation 0.99 ± 0.47% vs. 0.73 ± 0.43%, respectively) to both the motor cortex and muscle, and had greater coactivation of the antagonist muscles during dynamic contractions. Thus, the average voluntary activation to the motor cortex and muscle did not differ with aging; however, supraspinal activation was more variable during maximal dynamic and isometric contractions in the old adults. Lower predictability of voluntary activation may indicate subclinical changes in the central nervous system with advanced aging

Contractions of Low-Dimensional Lie Algebras

Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of requisite invariant and semi-invariant quantities are calculated for wide classes of Lie algebras including all low-dimensional Lie algebras. An algorithm that allows one to handle one-parametric contractions is presented and applied to low-dimensional Lie algebras. As a result, all one-parametric continuous contractions for the both complex and real Lie algebras of dimensions not greater than four are constructed with intensive usage of necessary criteria of contractions and with studying correspondence between real and complex cases. Levels and co-levels of low-dimensional Lie algebras are discussed in detail. Properties of multi-parametric and repeated contractions are also investigated.Comment: 47 pages, 4 figures, revised versio

Constraints on Disconnected Contributions in ππ\pi\pi Scattering

The accuracy of the lattice QCD computation of hadron-hadron scattering at low isospin depends critically on the ability to compute correlation functions with fermionic disconnected Wick contractions. This happens, for instance, in isospin $I=0$ $\pi\pi$ scattering, which receives contributions from rectangular and vacuum types of contractions among other easier calculable ones. Combining L\"{u}scher's formula and partially-quenched chiral perturbation theory, we provide precise theory predictions of the discrete energy levels extracted from specific linear combinations of lattice correlation functions corresponding to various types of contractions. Expressions are provided for extracting the unphysical low-energy constants in the partially-quenched chiral perturbation theory from the energy levels for these contractions. The predictions for the rectangular and vacuum contractions may serve as solid tests of the accuracy for existing and future lattice studies of $\pi\pi$ scattering.Comment: Version to appear in JHE

Graded contractions of bilinear invariant forms of Lie algebras

We introduce a new construction of bilinear invariant forms on Lie algebras, based on the method of graded contractions. The general method is described and the $\Bbb Z_2$-, $\Bbb Z_3$-, and $\Bbb Z_2\otimes\Bbb Z_2$-contractions are found. The results can be applied to all Lie algebras and superalgebras (finite or infinite dimensional) which admit the chosen gradings. We consider some examples: contractions of the Killing form, toroidal contractions of $su(3)$, and we briefly discuss the limit to new WZW actions.Comment: 15 page

Contractions of Degenerate Quadratic Algebras, Abstract and Geometric

Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by B\^ocher contractions of the conformal Lie algebra $\mathfrak{so}(4,\mathbb {C})$ to itself. In 2 dimensions there are two kinds of quadratic algebras, nondegenerate and degenerate. In the geometric case these correspond to 3 parameter and 1 parameter potentials, respectively. In a previous paper we classified all abstract parameter-free nondegenerate quadratic algebras in terms of canonical forms and determined which of these can be realized as quadratic algebras of 2D nondegenerate superintegrable systems on constant curvature spaces and Darboux spaces, and studied the relationship between B\^ocher contractions of these systems and abstract contractions of the free quadratic algebras. Here we carry out an analogous study of abstract parameter-free degenerate quadratic algebras and their possible geometric realizations. We show that the only free degenerate quadratic algebras that can be constructed in phase space are those that arise from superintegrability. We classify all B\^ocher contractions relating degenerate superintegrable systems and, separately, all abstract contractions relating free degenerate quadratic algebras. We point out the few exceptions where abstract contractions cannot be realized by the geometric B\^ocher contractions

Sex Differences in Fatigability of Dynamic Contractions

Women are usually less fatigable than men during single-limb isometric contractions, primarily because of sex-related differences in contractile mechanisms. It is less clear whether these sex differences in muscle fatigue occur for dynamic fatiguing tasks. This review highlights new findings that the sex difference in fatigability for dynamic shortening contractions with a single limb is dependent on the contraction velocity and the muscle group involved. Recent studies demonstrate that women are less fatigable than men for a dynamic task as follows: (i) the elbow-flexor muscles at slow- but not high-velocity contractions; and (ii) the knee-extensor muscles when muscle fatigue was quantified as a reduction in the maximal voluntary isometric contraction force after the dynamic fatiguing task. Contractile mechanisms are responsible for the sex difference in muscle fatigue of the dynamic contractions, with no evidence for a sex difference in the reduction in voluntary activation (i.e. central fatigue). Thus, these findings indicate that the sex difference in muscle fatigue of dynamic contractions is task specific. These data also challenge the assumption that men and women respond in a similar manner to training and rehabilitation that involve fatiguing contractions to overload the neuromuscular system. There is, however, a tremendous opportunity for conducting high-impact studies to gain insight into those factors that define the sex-based differences in muscle fatigue during dynamic tasks. Such studies can define the boundaries to human performance in both men and women during athletic endeavours, ergonomic tasks and rehabilitation

Pain Relief in Older Adults Following Static Contractions is not Task-Dependent

Pain complaints increase with age. Exercise is frequently utilized for pain relief but the optimal exercise prescription to relieve pain is not clear. Following static contractions, young adults experience the greatest pain relief with low intensity, long duration contractions. The pain response to static contractions in older adults however is unknown. PURPOSE : To compare pain reports in healthy older adults before and after static contractions of varying intensity and duration. METHODS: Pain perception was assessed in 23 healthy older adults (11 men, 12 women; 72.0 ± 6.3 yrs) using a pressure pain device consisting of a 10 N force applied to the right index finger through a Lucite edge (8 x 1.5mm) for two minutes. Subjects pushed a timing device when they first felt pain (i.e., pain threshold) and rated their pain intensity every 20 seconds using a 0-10 numerical rating scale. Pain threshold and pain ratings were measured before and immediately after static contractions of the left elbow flexors at the following three doses: 1) three brief maximal voluntary contractions (MVC); 2) 25% MVC sustained for 2 minutes; and 3) 25% MVC sustained until task failure. Experimental sessions were randomized and separated by one week. RESULTS : Time to task failure for the 25% MVC contraction was 11.8 ± 5.1 minutes. A reduction in pain was found following all three tasks with no difference between tasks (trial x task effect: p \u3e 0.05), despite the duration of the 2 minute low-intensity contraction being ~17% of the contraction held to task failure. Pain thresholds for all doses increased 20% from 51 ± 33 to 61 ± 37 seconds and pain ratings averaged over the six time points decreased 20% from 3.3 ± 2.8 to 2.6 ± 2.5 following static contractions (trial effect: p \u3c 0.001 and p \u3c 0.001, respectively). CONCLUSION : Low and high intensity static contractions of both long and short duration produce similar levels of pain reduction in older adults. These preliminary data suggest that several different types of static contractions can induce significant pain relief in older adults. Age-related changes in the pain response to static contractions must be taken into account when prescribing static exercise for the management of pain

Strong contraction of the representations of the three dimensional Lie algebras

For any Inonu-Wigner contraction of a three dimensional Lie algebra we construct the corresponding contractions of representations. Our method is quite canonical in the sense that in all cases we deal with realizations of the representations on some spaces of functions; we contract the differential operators on those spaces along with the representation spaces themselves by taking certain pointwise limit of functions. We call such contractions strong contractions. We show that this pointwise limit gives rise to a direct limit space. Many of these contractions are new and in other examples we give a different proof