Morphological criteria for diagnosis of primary hyperparathyroidism

The work performed on the operating material. A morphological study of the parathyroid glands removed in 128 patients with hyperparathyroidism was performed. For the histological study pieces of the parathyroid gland were taken. The pieces were fixed in 10 % buffered formalin for 10 days, then washed in running water, passed through a processor and embedded in paraffin. From paraffin blocks, sections of 5–6 µm were prepared. Sections were stained with hematoxylin and eosin, pikrofuksin according to Van Gieson, toluidine blue, according to Mallory, used CHIC-reaction. The results of the study showed that primary hypothyroidism is more common in women (82 %) aged 41–50 years (42.2 %). The size of the parathyroid glands ranged from 0.3 to 8.2 cm. Adenomas were found in 51.6 % of patients, hyperplasia in 43.0 %, cancer in 5.4 % of them. In primary hyperplasia, there is an increase in all parathyroid glands, upper pair or lower pair. Upper pairs are increased more. Histological examination indicates lobular structure of the gland, lobular hyperplasia, diffuse proliferation of the main, acidophilic and transitional forms of parathyrocytes, monomorphic structure, reduction or absence of stromal fat, the presence of a large number of vessels. Hyperplasia of the main cells was detected in 67 % of patients, hyperplasia of acidophilic cells in 28 %, hyperplasia of light cells in 3 %, mixed hyperplasia in 2 % of them.

A Screw Approach to the Approximation of the Local Geometry of the Configuration Space and of the Set of Configurations of Certain Rank of Lower Pair Linkages

A motion of a mechanism is a curve in its configuration space (c-space). Singularities of the c-space are kinematic singularities of the mechanism. Any mobility analysis of a particular mechanism amounts to investigating the c-space geometry at a given configuration. A higher-order analysis is necessary to determine the finite mobility. To this end, past research leads to approaches using higher-order time derivatives of loop closure constraints assuming (implicitly) that all possible motions are smooth. This continuity assumption limits the generality of these methods. In this paper, an approach to the higher-order local mobility analysis of lower pair multiloop linkages is presented. This is based on a higher-order Taylor series expansion of the geometric constraint mapping, for which a recursive algebraic expression in terms of joint screws is presented. An exhaustive local analysis includes analysis of the set of constraint singularities (configurations where the constraint Jacobian has certain corank). A local approximation of the set of configurations with certain rank is presented, along with an explicit expression for the differentials of Jacobian minors in terms of instantaneous joint screws. The c-space and the set of points of certain corank are therewith locally approximated by an algebraic variety determined algebraically from the mechanism's screw system. The results are shown for a simple planar 4-bar linkage, which exhibits a bifurcation singularity and for a planar three-loop linkage exhibiting a cusp in c-space. The latter cannot be treated by the higher-order local analysis methods proposed in the literature.

Kinematic topology and constraints of multi-loop linkages

SUMMARYModeling the instantaneous kinematics of lower pair linkages using joint screws and the finite kinematics with Lie group concepts is well established on a solid theoretical foundation. This allows for modeling the forward kinematics of mechanisms as well the loop closure constraints of kinematic loops. Yet there is no established approach to the modeling of complex mechanisms possessing multiple kinematic loops. For such mechanisms, it is crucial to incorporate the kinematic topology within the modeling in a consistent and systematic way. To this end, in this paper a kinematic model graph is introduced that gives rise to an ordering of the joints within a mechanism and thus allows to systematically apply established kinematics formulations. It naturally gives rise to topologically independent loops and thus to loop closure constraints. Geometric constraints as well as velocity and acceleration constraints are formulated in terms of joint screws. An extension to higher order loop constraints is presented. It is briefly discussed how the topology representation can be used to amend structural mobility criteria.

Group Size as a Trade Off Between Fertility and Predation Risk: Implications for Social Evolution

Cluster analysis reveals a fractal pattern in the sizes of baboon groups, with peaks at ∼20, ∼40, ∼80 and ∼160. Although all baboon species individually exhibit this pattern, the two largest are mainly characteristic of the hamadryas and gelada. We suggest that these constitute three pairs of linear oscillators (20/40, 40/80 and 80/160), where in each case the higher value is set by limits on female fertility and the lower by predation risk. The lower pair of oscillators form an ESS in woodland baboons, with choice of oscillator being determined by local predation risk. Female fertility rates would naturally prevent baboons from achieving the highest oscillator with any regularity; nonetheless, hamadryas and gelada have been able to break through this fertility ‘glass ceiling’ and we suggest that they have been able to do so by using substructuring (based partly on using males as ‘hired guns’). This seems to have allowed them to increase group size significantly so as to occupy higher predation risk habitats (thereby creating the upper oscillator).

Higher-Order Local Analysis of Kinematic Singularities of Lower Pair Linkages

Kinematic singularities of linkages are configurations where the differential mobility changes. Constraint singularities are critical points of the constraint mapping defining the loop closure constraints. Configuration space (c-space) singularities are points where the c-space ceases to be a smooth manifold. These singularity types are not identical. C-space singularities are reflected by the c-space geometry. Identifying kinematic singularities amounts to locally analyze the set of critical points. The local geometry of the set of critical points is best approximated by its tangent cone (an algebraic variety). The latter is defined in this paper in a form that allows for its computational determination using the Jacobian minors. An explicit closed form expression for the derivatives of the minors is presented in terms of Lie brackets of joint screws. A computational method is proposed to determine a polynomial system defining the tangent cone. This finally allows for identifying c-space and kinematic singularities.

Computational Local Mobility Analysis of Mechanisms With Higher Kinematic Pairs

The finite mobility of a mechanism is reflected by its configuration space (c-space), and the mobility analysis aims at determining this c-space. Crucial for the computational mobility analysis is an adequate formulation of the constraints. For lower pair linkages an analytic formulation is the product-of-exponential (POE) formula in terms of the screw systems of the lower pair joints. In other words, the screw coordinates of a lower pair joint serve as canonical coordinates on the corresponding motion subgroup. For such linkages, a computational approach to the local mobility analysis has been reported recently. The approach is applicable to general multi-loop linkages. Higher pairs do not generate motion subgroups so that their motion cannot be expressed in terms of screw coordinates. Hence their kinematics cannot be expressed in terms of a POE, and there is no efficient and generally applicable computational method for the mobility analysis. In this paper a formulation of higher-order constraints for mechanisms with higher pair joints is proposed making use of the result for lower pair linkages. The method is applicable to mechanisms where each fundamental loop comprises no more than one higher pair, which covers the majority of mechanisms. Based on this, a computational algorithm is introduced that allows mobility determination. As for lower pair linkages, this algorithm only requires simple algebraic operations.

Configuration Workspaces of Series-Parallel Mechanisms

The workspace of a mechanism is the set of positions and orientations that is reachable by its end effector. Workspaces have numerous applications, including motion planning, mechanism design, and manufacturing process planning, but their representation and computation is challenging due to high dimensionality and geometric/topological complexity. We propose a new formulation of the workspace computation problem for a large class of mechanisms represented by series-parallel constraint graphs. A wide variety of allowable constraints include all lower pair, some higher pair, and non-collision constraints. We show that the workspace of such mechanisms may be computed by a constraint propagation algorithm. After the space of all rigid body motions is discretized, these operations can be efficiently implemented using the Fast Fourier Transform and a depth first search. In contrast to algebraic formulations, the proposed method assures that all configurations in the computed workspace not only satisfy pairwise constraints but can be reached without breaking and reassembling the mechanism.