On cobordisms between knots, braid index, and the Upsilon-invariant

We use Ozsv\'ath, Stipsicz, and Szab\'o's Upsilon-invariant to provide bounds on cobordisms between knots that `contain full-twists'. In particular, we recover and generalize a classical consequence of the Morton-Franks-Williams inequality for knots: positive braids that contain a positive full-twist realize the braid index of their closure. We also establish that quasi-positive braids that are sufficiently twisted realize the minimal braid index among all knots that are concordant to their closure. Finally, we provide inductive formulas for the Upsilon invariant of torus knots and compare it to the Levine-Tristram signature profile.Comment: 25 pages, 3 figures, comments welcome! Second version: Typos fixed, implementation of recommendations. Accepted for publication by Mathematische Annale

Dexterity, workspace and performance analysis of the conceptual design of a novel three-legged, redundant, lightweight, compliant, serial-parallel robot

In this article, the mechanical design and analysis of a novel three-legged, agile robot with passively compliant 4-degrees-of-freedom legs, comprising a hybrid topology of serial, planar and spherical parallel structures, is presented. The design aims to combine the established principle of the Spring Loaded Inverted Pendulum model for energy efficient locomotion with the accuracy and strength of parallel mechanisms for manipulation tasks. The study involves several kinematics and Jacobian based analyses that specifically evaluate the application of a non-overconstrained spherical parallel manipulator as a robot hip joint, decoupling impact forces and actuation torques, suitable for the requirements of legged locomotion. The dexterity is investigated with respect to joint limits and workspace boundary contours, showing that the mechanism stays well conditioned and allows for a sufficient range of motion. Based on the functional redundancy of the constrained serial-parallel architecture it is furthermore revealed that the robot allows for the exploitation of optimal leg postures, resulting in the possible optimization of actuator load distribution and accuracy improvements. Consequently, the workspace of the robot torso as additional end-effector is investigated for the possible application of object manipulation tasks. Results reveal the existence of a sufficient volume applicable for spatial motion of the torso in the statically stable tripodal posture. In addition, a critical load estimation is derived, which yields a posture dependent performance index that evaluates the risks of overload situations for the individual actuators

Topological analysis of a novel compact omnidirectional three-legged robot with parallel hip structures regarding locomotion capability and load distribution

In this study, a novel design for a compact, lightweight, agile, omnidirectional three-legged robot involving legs with four degrees of freedom, utilizing an spherical parallel mechanism with an additional non-redundant central support joint for the robot hip structure is proposed. The general design and conceptual ideas for the robot are presented, targeting a close match of the well-known SLIP-model. CAD models, 3d-printed prototypes, and proof-of-concept multi-body simulations are shown, investigating the feasibility to employ a geometrically dense spherical parallel manipulator with completely spherically shaped shell-type parts for the highly force-loaded application in the legged robot hip mechanism. Furthermore, in this study, an analytic expression is derived, yielding the calculation of stress forces acting inside the linkage structures, by directly constructing the manipulator hip Jacobian inside the force domain

Mechanical design and analysis of a novel three-legged, compact, lightweight, omnidirectional, serial–parallel robot with compliant agile legs

In this work, the concept and mechanical design of a novel compact, lightweight, omnidirectional three-legged robot, featuring a hybrid serial–parallel topology including leg compliance is proposed. The proposal focusses deeply on the design aspects of the mechanical realisation of the robot based on its 3D-CAD assembly, while also discussing the results of multi-body simulations, exploring the characteristic properties of the mechanical system, regarding the locomotion feasibility of the robot model. Finally, a real-world prototype depicting a single robot leg is presented, which was built by highly leaning into a composite design, combining complex 3D-printed parts with stiff aluminium and polycarbonate parts, allowing for a mechanically dense and slim construction. Eventually, experiments on the prototype leg are demonstrated, showing the mechanical model operating in the real world

Environmental forcing of ambient noise in the Nansen and Amundsen Basins of the Arctic Ocean

The AREA 1992 experiment inserted three ANmmT buoys on separate ice floes about 600 ka north of Franz Josof Land. The buoys drifted in unison for most of the experimnt and provided 12-19 months of hourly ambient noise data between 5 and 4000 Hz while obtaining limited weather data. The drift pattern was neatly divided into five legs of nearly uniform ice velocities in response to major changes in the wind field. The annual median spectra of each buoy were nearly identical at or above 200 Nz but diverged below 200 Hz. The largest differences were recorded between the two closest buoys. The annual spectra wer 10 d4 greater than the long term ]urasian Basin median spectra at all frequencies. The annual median spectra was 6-7 dB greater than th,, CZAR= 1988/89 median spectra below 100 HN but was quieter than CZARIX above 100 Hz. Persistent extreme noise levels above the 95" or below the 5 eS percentiles were rare. Sustained 95• percentile noise levels were caused by the ice field convergence resulting from storms passing near the buoy cluster. Sustained noise levels near the 5"t percentile occurred during periods of slow, steady winds. Temporal coherency of the year-long record ranged from 12-23 hours at all frequencies, comparable to other reported data. Significant energy was found at synoptic periods of 16-148 hours and near the tidal/inertial 12 hour period at all three buoys, implying the smem forcing mechanisms were important in spite of buoy separations up to 300 ka. Spatial coherency between the buoys showed the highest correlation between the closest buoy pair. Differences in correlation coefficients mere mller at higher frequencies due to the increased iportance of local effects at higher frequencies. ce speed was the beat environmental correlate with ambient noise from 5-10 Hz, wind speed was best from 32-100 Hz, and wind stress was best above 100 Hz. Three periods of extreme noise levels (two loud, one quiet), each lasting for several days, were investigated in detail to establish the role of wind forcing on ambient noise generation. Periods of loud noise were associated with periods of high wind/ice speed coupled with rapid changes in direction, i.e., loud noise levels are the result of large ice convergence and shearing moment. Quiet periods occur when the buoy drift speed is slow. One of the loud noise events showed that periods of ice convergence on nearby land will increase the noise level, even during times of moderate wind speeds.http://archive.org/details/environmentalfor1094542980U.S. Navy (USN) authorApproved for public release; distribution is unlimited

Dendritic and axonal targeting patterns of a genetically-specified class of retinal ganglion cells that participate in image-forming circuits.

BackgroundThere are numerous functional types of retinal ganglion cells (RGCs), each participating in circuits that encode a specific aspect of the visual scene. This functional specificity is derived from distinct RGC morphologies and selective synapse formation with other retinal cell types; yet, how these properties are established during development remains unclear. Islet2 (Isl2) is a LIM-homeodomain transcription factor expressed in the developing retina, including approximately 40% of all RGCs, and has previously been implicated in the subtype specification of spinal motor neurons. Based on this, we hypothesized that Isl2+ RGCs represent a related subset that share a common function.ResultsWe morphologically and molecularly characterized Isl2+ RGCs using a transgenic mouse line that expresses GFP in the cell bodies, dendrites and axons of Isl2+ cells (Isl2-GFP). Isl2-GFP RGCs have distinct morphologies and dendritic stratification patterns within the inner plexiform layer and project to selective visual nuclei. Targeted filling of individual cells reveals that the majority of Isl2-GFP RGCs have dendrites that are monostratified in layer S3 of the IPL, suggesting they are not ON-OFF direction-selective ganglion cells. Molecular analysis shows that most alpha-RGCs, indicated by expression of SMI-32, are also Isl2-GFP RGCs. Isl2-GFP RGCs project to most retino-recipient nuclei during early development, but specifically innervate the dorsal lateral geniculate nucleus and superior colliculus (SC) at eye opening. Finally, we show that the segregation of Isl2+ and Isl2- RGC axons in the SC leads to the segregation of functional RGC types.ConclusionsTaken together, these data suggest that Isl2+ RGCs comprise a distinct class and support a role for Isl2 as an important component of a transcription factor code specifying functional visual circuits. Furthermore, this study describes a novel genetically-labeled mouse line that will be a valuable resource in future investigations of the molecular mechanisms of visual circuit formation