A finitely presented infinite simple group of homeomorphisms of the circle

We construct a finitely presented, infinite, simple group that acts by homeomorphisms on the circle, but does not admit a non-trivial action by $C^1$-diffeomorphisms on the circle. The group emerges as a group of piecewise projective homeomorphisms of $S^1=\mathbf{R}\cup \{\infty\}$. However, we show that it does not admit a non-trivial action by piecewise linear homeomorphisms of the circle. Another interesting and new feature of this example is that it produces a non amenable orbit equivalence relation with respect to the Lebesgue measure.Comment: 30 pages (Some typos have been corrected and some proofs have been streamlined.

A finitely presented group of piecewise projective homeomorphisms

In this article we will describe a finitely presented subgroup of Monod's group of piecewise projective homeomorphisms of R. This in particular provides a new example of a finitely presented group which is nonamenable and yet does not contain a nonabelian free subgroup. It is in fact the first such example which is torsion free. We will also develop a means for representing the elements of the group by labeled tree diagrams in a manner which closely parallels Richard Thompson's group F.Comment: Formerly "A geometric solution to the von Neumann-Day problem for finitely presented groups". Section added on tree diagrams. Minor revisions elsewher

Commutators in groups of piecewise projective homeomorphisms

In 2012 Monod introduced examples of groups of piecewise projective homeomorphisms which are not amenable and which do not contain free subgroups, and later Lodha and Moore introduced examples of finitely presented groups with the same property. In this article we examine the normal subgroup structure of these groups. Two important cases of our results are the groups $H$ and $G_0$. We show that the group $H$ of piecewise projective homeomorphisms of $\mathbb{R}$ has the property that $H"$ is simple and that every proper quotient of $H$ is metabelian. We establish simplicity of the commutator subgroup of the group $G_0$, which admits a presentation with $3$ generators and $9$ relations. Further we show that every proper quotient of $G_0$ is abelian. It follows that the normal subgroups of these groups are in bijective correspondence with those of the abelian (or metabelian) quotient

Charge trap layer enabled positive tunable Vfb_{fb} in β\beta-Ga2_{2}O3_{3} gate stacks for enhancement mode transistors

$\beta$-Ga$_{2}$O$_{3}$ based enhancement mode transistor designs are critical for the realization of low loss, high efficiency next generation power devices with rudimentary driving circuits. A novel approach towards attaining a high positive flat band voltage (V$_{fb}$) of 10.6 V in $\beta$-Ga$_{2}$O$_{3}$ metal-oxide-semiconductor capacitors (MOSCAPs), with the ability to fine tune it between 3.5 V to 10.6 V, using a polycrystalline AlN charge trap layer has been demonstrated. This can enable enhancement mode operation over a wide doping range. Excellent V$_{fb}$ retention of ${\sim}$97% for 10$^{4}$ s at 55 $^{\circ}$C was exhibited by the gate stacks after charge trapping, hence reducing the requirement of frequent charge injection cycles. In addition, low gate leakage current density (J$_{g}$) for high negative gate voltages (V$_{g}$${\sim}$-60 V) indicates the potential of this gate stack to enable superior breakdown characteristics in enhancement mode transistors.Comment: Single file (Manuscript and Supplementary material combined) of 19 pages. Total 5 and 4 figures in manuscript and supplementary material, respectivel

Motor Output Variability Impairs Driving Ability in Older Adults

Background: The functional declines with aging relate to deficits in motor control and strength. In this study, we determine whether older adults exhibit impaired driving as a consequence of declines in motor control or strength. Methods: Young and older adults performed the following tasks: (i) maximum voluntary contractions of ankle dorsiflexion and plantarflexion; (ii) sinusoidal tracking with isolated ankle dorsiflexion; and (iii) a reactive driving task that required responding to unexpected brake lights of the car ahead. We quantified motor control with ankle force variability, gas position variability, and brake force variability. We quantified reactive driving performance with a combination of gas pedal error, premotor and motor response times, and brake pedal error. Results: Reactive driving performance was ~30% more impaired (t = 3.38; p \u3c .01) in older adults compared with young adults. Older adults exhibited greater motor output variability during both isolated ankle dorsiflexion contractions (t = 2.76; p \u3c .05) and reactive driving (gas pedal variability: t = 1.87; p \u3c .03; brake pedal variability: t = 4.55; p \u3c .01). Deficits in reactive driving were strongly correlated to greater motor output variability (R 2 = .48; p \u3c .01) but not strength (p \u3e .05). Conclusions: This study provides novel evidence that age-related declines in motor control but not strength impair reactive driving. These findings have implications on rehabilitation and suggest that interventions should focus on improving motor control to enhance driving-related function in older adults

Motor Output Variability Impairs Driving Ability in Older Adults: Reply to Stinchcombe, Dickerson, Weaver, and Bedard

Driving is a complex skill, as indicated by Stinchcombe and colleagues in their letter. It requires the integration of sensory inputs, cognitive processing, and motor execution. Although our title is broad, we clearly indicate that our findings only address a single component of driving, namely reactive driving. We also indicate that these findings are based on a simulated task and recommend that future studies should examine the contribution of motor output variability to on-road driving performance (see Considerations in the Discussion section). Thus, we share the consideration of Stinchcombe and colleagues that the current results only address a small portion of the driving complexity