Running into Fatigue: The Effects of Footwear on Kinematics, Kinetics, and Energetics.

Recent studies identified a redistribution of positive mechanical work from distal to proximal joints during prolonged runs, which might partly explain the reduced running economy observed with running-induced fatigue. Higher mechanical demand of plantar flexor muscle-tendon-units, e.g., through minimal footwear, can lead to an earlier onset of fatigue, which might affect the redistribution of lower extremity joint work during prolonged runs. Therefore, the purpose of this study was to examine the effects of a racing-flat and cushioned running shoe on the joint-specific contributions to lower extremity joint work during a prolonged fatiguing run. On different days, eighteen runners performed two 10-km runs with near-maximal effort in a racing-flat and a cushioned shoe on an instrumented treadmill synchronized with a motion-capture-system. Joint kinetics and kinematics were calculated at 13 pre-determined distances throughout the run. The effects of shoes, distance, and their interaction were analyzed using a two-factor repeated-measures ANOVA. For both shoes, we found a redistribution of positive joint work from ankle (-6%) to knee (+3%) and hip (+3%) throughout the entire run. Negative ankle joint work was higher (p<0.01) with the racing-flat compared to the cushioned shoe. Initial differences in foot-strike patterns between shoes disappeared after 2 km of running distance. Irrespective of the shoe design, alterations in the running mechanics occurred in the first 2 km of the run, which might be attributed to the existence of a habituation rather than fatigue effect. While we did not find a difference between shoes in the fatigue-related redistribution of joint work from distal to more proximal joints, more systematical studies are needed to explore the effects of specific footwear design features. [Abstract copyright: Copyright © 2020 American College of Sports Medicine.

On the Hierarchy of Block Deterministic Languages

A regular language is $k$-lookahead deterministic (resp. $k$-block deterministic) if it is specified by a $k$-lookahead deterministic (resp. $k$-block deterministic) regular expression. These two subclasses of regular languages have been respectively introduced by Han and Wood ($k$-lookahead determinism) and by Giammarresi et al. ($k$-block determinism) as a possible extension of one-unambiguous languages defined and characterized by Br\"uggemann-Klein and Wood. In this paper, we study the hierarchy and the inclusion links of these families. We first show that each $k$-block deterministic language is the alphabetic image of some one-unambiguous language. Moreover, we show that the conversion from a minimal DFA of a $k$-block deterministic regular language to a $k$-block deterministic automaton not only requires state elimination, and that the proof given by Han and Wood of a proper hierarchy in $k$-block deterministic languages based on this result is erroneous. Despite these results, we show by giving a parameterized family that there is a proper hierarchy in $k$-block deterministic regular languages. We also prove that there is a proper hierarchy in $k$-lookahead deterministic regular languages by studying particular properties of unary regular expressions. Finally, using our valid results, we confirm that the family of $k$-block deterministic regular languages is strictly included into the one of $k$-lookahead deterministic regular languages by showing that any $k$-block deterministic unary language is one-unambiguous

The impact of phenotypic heterogeneity of tumour cells on treatment and relapse dynamics

Intratumour heterogeneity is increasingly recognized as a frequent problem for cancer treatment as it allows for the evolution of resistance against treatment. While cancer genotyping becomes more and more established and allows to determine the genetic heterogeneity, less is known about the phenotypic heterogeneity among cancer cells. We investigate how phenotypic differences can impact the efficiency of therapy options that select on this diversity, compared to therapy options that are independent of the phenotype. We employ the ecological concept of trait distributions and characterize the cancer cell population as a collection of subpopulations that differ in their growth rate. We show in a deterministic model that growth rate-dependent treatment types alter the trait distribution of the cell population, resulting in a delayed relapse compared to a growth rate-independent treatment. Whether the cancer cell population goes extinct or relapse occurs is determined by stochastic dynamics, which we investigate using a stochastic model. Again, we find that relapse is delayed for the growth rate-dependent treatment type, albeit an increased relapse probability, suggesting that slowly growing subpopulations are shielded from extinction. Sequential application of growth rate-dependent and growth rate-independent treatment types can largely increase treatment efficiency and delay relapse. Interestingly, even longer intervals between decisions to change the treatment type may achieve close-to-optimal efficiencies and relapse times. Monitoring patients at regular check-ups may thus provide the temporally resolved guidance to tailor treatments to the changing cancer cell trait distribution and allow clinicians to cope with this dynamic heterogeneity.Author summary The individual cells within a cancer cell population are not all equal. The heterogeneity among them can strongly affect disease progression and treatment success. Recent diagnostic advances allow measuring how the characteristics of this heterogeneity change over time. To match these advances, we developed deterministic and stochastic trait-based models that capture important characteristics of the intratumour heterogeneity and allow to evaluate different treatment types that either do or do not interact with this heterogeneity. We focus on growth rate as the decisive characteristic of the intratumour heterogeneity. We find that by shifting the trait distribution of the cancer cell population, the growth rate-dependent treatment delays an eventual relapse compared to the growth rate-independent treatment. As a downside, however, we observe a refuge effect where slower-growing subpopulations are less affected by the growth rate-dependent treatment, which may decrease the likelihood of successful therapy. We find that navigating along this trade-off may be achieved by sequentially combining both treatment types, which agrees qualitatively with current clinical practice. Interestingly, even rather large intervals between treatment changes allow for close-to-optimal treatment results, which again hints towards a practical applicability.Competing Interest StatementMB performed contract research for Affimed, Amgen and Regeneron, served on the advisory board of Amgen and Incyte, and in the speaker bureau of Amgen, Janssen, Pfizer and Roche

Coherent magnetization precession in ferromagnetic (Ga,Mn)As induced by picosecond acoustic pulses

We show that the magnetization of a thin ferromagnetic (Ga,Mn)As layer can be modulated by picosecond acoustic pulses. In this approach a picosecond strain pulse injected into the structure induces a tilt of the magnetization vector M, followed by the precession of M around its equilibrium orientation. This effect can be understood in terms of changes in magneto-crystalline anisotropy induced by the pulse. A model where only one anisotropy constant is affected by the strain pulse provides a good description of the observed time-dependent response.Comment: 13 pages, 3 figure

Modulation of a surface plasmon-polariton resonance by sub-terahertz diffracted coherent phonons

Coherent sub-THz phonons incident on a gold grating that is deposited on a dielectric substrate undergo diffraction and thereby induce an alteration of the surface plasmon-polariton resonance. This results in efficient high-frequency modulation (up to 110 GHz) of the structure's reflectivity for visible light in the vicinity of the plasmon-polariton resonance. High modulation efficiency is achieved by designing a periodic nanostructure which provides both plasmon-polariton and phonon resonances. Our theoretical analysis shows that the dynamical alteration of the plasmon-polariton resonance is governed by modulation of the slit widths within the grating at the frequencies of higher-order phonon resonances.Comment: 5 pages, 4 figure