GENUS MINIMAL k-NOIDS AND SADDLE TOWERS IN

For each $k\geq 3$ , we construct a $1$ -parameter family of complete properly Alexandrov-embedded minimal surfaces in the Riemannian product space $\mathbb {H}^2\times \mathbb {R}$ with genus $1$ and k embedded ends asymptotic to vertical planes. We also obtain complete minimal surfaces with genus $1$ and $2k$ ends in the quotient of $\mathbb {H}^2\times \mathbb {R}$ by an arbitrary vertical translation. They all have dihedral symmetry with respect to k vertical planes, as well as finite total curvature $-4k\pi $ . Finally, we provide examples of complete properly Alexandrov-embedded minimal surfaces with finite total curvature with genus $1$ in quotients of $\mathbb {H}^2\times \mathbb {R}$ by the action of a hyperbolic or parabolic translation.

A Methodology for Vertical Translation Between Molecular and Organismal Level in Biological Feedback Loops

Feedback loops are among the primary network motifs in living organisms, ensuring survival via homeostatic control of key metabolites and physical properties. However, from a scientific perspective, their characterization is unsatisfactory since the usual modelling methodology is incompatible with the physiological and biochemical basis of metabolic networks. Therefore, any "vertical translation", i.e. the study of the correspondence between molecular and organismal levels of causality, is difficult and in most cases impossible. As a viable solution, we demonstrate an alternative modelling platform for biological feedback loops that is based on key biochemical principles, including mass action law, enzyme kinetics, binding of mediators to transporters and receptors, and basic pharmacological properties. Subsequently, we show how this framework can be used for translating from molecular to systems-level behaviour. Basic elements of the proposed modelling platform include Michaelis-Menten kinetics defining nonlinear dependence of the output y(t) on an input signal x(t) with the Hill-Langmuir equation y(t) = G * x(t)n / (D + x(t)n), non-competitive inhibition for linking stimulatory and inhibitory inputs with y(t) = G + x1(t) / ((D + x1(t) * (1 + x2(t) / KI)) and processing structures for distribution and elimination. Depending on the structure of the feedback loop, its equifinal (steady-state) behaviour can be solved in form of polynomials, with a quadratic equation for the simplest case with one feedback loop and a Hill exponent of 1, and higher-grade polynomials for additional feedback loops and/or integer Hill exponents > 1. As a companion to the analytical solution, a flexible class library (CyberUnits) facilitates computer simulations for studying the transitional behaviour of the feedback loop. Unlike other modelling strategies in biocybernetics and systems biology, this platform allows for straightforward translation from the statistical properties of single molecules on a "microscopic" level to the behaviour of the whole feedback loop on an organismal "macroscopic" level. An example is the Michaelis constant D, which is equivalent to (k-1 + k2) / k1, where k1, k-1 and k2 denote the rate constants for the association and dissociation of the enzyme-substrate or receptor-hormone complex, respectively. From the perspective of a single molecule the rate constants represent the probability (per unit time) that the corresponding reaction will happen in the subsequent time interval. Therefore 1/k represents the mean lifetime of the complex. Very similar considerations apply to the other described constants of the feedback loop. In summary, this modelling technique renders the translation from a molecular level to a systems perspective possible. In addition to providing new insights into the physiology of biological feedback loops, it may be a valuable tool for multiple disciplines of biomedical research, including drug design, molecular genetics and investigations on the effects of endocrine disruptors.

Necessary Conditions for Boundedness of Translation Operator in de Branges Spaces

The translation operator is bounded in the Paley–Wiener spaces and, more generally, in the Bernstein spaces. The goal of this paper is to find some necessary conditions for the boundedness of the translation operator in the de Branges spaces, of which the Paley–Wiener spaces are special cases. Indeed, if the vertical translation operator $$T_\tau $$ T τ defined on the de Branges space $${\mathcal H}(E)$$ H ( E ) is bounded, then a suitably defined measure $$d\mu (z)$$ d μ ( z ) is a Carleson measure for the associated model space $$K(\Theta )$$ K ( Θ ) . This relation allows us to state necessary conditions for the boundedness of the vertical translation $$T_\tau $$ T τ . Finally, similar results are also obtained for the horizontal translation $$T_\sigma $$ T σ .

Bristle Motion, Forces, and Related Vertical Translation for a Novel Electric Toothbrush Design

This paper presents a combination of theoretical and experimental techniques applied to characterize the bristle motion, forces, and related vertical translation for a novel electric toothbrush design with a linear drive system. Results of the theoretical description, based on a single filament, were successfully compared with laboratory-based investigations: force measurements and high-speed video analysis, and tracking the toothbrush motion. This work describes the vertical translation induced in the toothbrush head, of up to 250 μm, when the toothbrush bristles are applied against a contact surface at brushing loads of approximately 1 N to 2.5 N. Using these techniques, including Fast-Fourier transform analysis, it is shown that the vertical motion of the head is composed of the driving frequency and its harmonics.

Efficient Coarse Registration of Pairwise TLS Point Clouds Using Ortho Projected Feature Images

The degree of automation and efficiency are among the most important factors that influence the availability of Terrestrial light detection and ranging (LiDAR) Scanning (TLS) registration algorithms. This paper proposes an Ortho Projected Feature Images (OPFI) based 4 Degrees of Freedom (DOF) coarse registration method, which is fully automated and with high efficiency, for TLS point clouds acquired using leveled or inclination compensated LiDAR scanners. The proposed 4DOF registration algorithm decomposes the parameter estimation into two parts: (1) the parameter estimation of horizontal translation vector and azimuth angle; and (2) the parameter estimation of the vertical translation vector. The parameter estimation of the horizontal translation vector and the azimuth angle is achieved by ortho projecting the TLS point clouds into feature images and registering the ortho projected feature images by Scale Invariant Feature Transform (SIFT) key points and descriptors. The vertical translation vector is estimated using the height difference of source points and target points in the overlapping regions after horizontally aligned. Three real TLS datasets captured by the Riegl VZ-400 and the Trimble SX10 and one simulated dataset were used to validate the proposed method. The proposed method was compared with four state-of-the-art 4DOF registration methods. The experimental results showed that: (1) the accuracy of the proposed coarse registration method ranges from 0.02 m to 0.07 m in horizontal and 0.01 m to 0.02 m in elevation, which is at centimeter-level and sufficient for fine registration; and (2) as many as 120 million points can be registered in less than 50 s, which is much faster than the compared methods.

CurviPicker: a continuum robot for pick-and-place tasks

Purpose Pick-and-place tasks are common across many industrial sectors, and many rigid-linked robots have been proposed for this application. This paper aims to alternatively present the development of a continuum robot for low-load medium-speed pick-and-place tasks. Design/methodology/approach An inversion of a previously proposed dual continuum mechanism, as a key design element, was used to realize the horizontal movements of the CurviPicker’s end effector. A flexible shaft was inserted to realize rotation and translation about a vertical axis. The design concept, kinematics, system descriptions and proof-of-concept experimental characterizations are elaborated. Findings Experimental characterizations show that the CurviPicker can achieve satisfactory accuracy after motion calibration. The CurviPicker is easy to control due to its simple kinematics, while its structural compliance makes it safe to work with, as well as less sensitive to possible target picking position errors to avoid damaging itself or the to-be-picked objects. Research limitations/implications The vertical translation of the CurviPicker is currently realized by moving the flexible shaft. Insertion of the flexible shaft introduces possible disturbances. It is desired to explore other form of variations to use structural deformation to realize the vertical translation. Practical implications The proposed CurviPicker realizes the Schöenflies motions via a simple structure. Such a robot can be used to increase robot presence and automation in small businesses for low-load medium-speed pick-and-place tasks. Originality/value To the best of the authors’ knowledge, the CurviPicker is the first continuum robot designed and constructed for pick-and-place tasks. The originality stems from the concept, kinematics, development and proof-of-concept experimental characterizations of the CurviPicker.

ON TYPICALITY OF TRANSLATION FLOWS WHICH ARE DISJOINT WITH THEIR INVERSE

In this paper we prove that the set of translation structures for which the corresponding vertical translation flows are disjoint with its inverse contains a $G_{\unicode[STIX]{x1D6FF}}$-dense subset in every non-hyperelliptic connected component of the moduli space ${\mathcal{M}}$. This is in contrast to hyperelliptic case, where for every translation structure the associated vertical flow is reversible, i.e., it is isomorphic to its inverse by an involution. To prove the main result, we study limits of the off-diagonal 3-joinings of special representations of vertical translation flows. Moreover, we construct a locally defined continuous embedding of the moduli space into the space of measure-preserving flows to obtain the $G_{\unicode[STIX]{x1D6FF}}$-condition. Moreover, as a by-product we get that in every non-hyperelliptic connected component of the moduli space there is a dense subset of translation structures whose vertical flow is reversible.