Unruptured internal carotid-posterior communicating artery aneurysm splitting the oculomotor nerve: A case report and literature review

Background: Although it is well known that internal carotid-posterior communicating artery (ICA-PcomA) aneurysms compress the oculomotor nerve and cause nerve palsy, cases of ICA-PcomA aneurysms splitting the oculomotor nerve are extremely rare. Case Description: We present the rare case of an asymptomatic, growing, left-sided ICA-PcomA aneurysm that was confirmed to split the oculomotor nerve. We report the clinical course and discuss the underlying mechanism. The oculomotor nerve, which is an aggregate of multiple fibers, exhibits age-related loss of compactness in the arrangement of its nerve fibers. Conclusion: We speculate that injury to the nerve fibers by aneurysmal compression was avoided because of the rare phenomenon of splitting of the oculomotor nerve.

A new analytical approach to consistency and overfitting in regularized empirical risk minimization

This work considers the problem of binary classification: given training data x1, . . ., xn from a certain population, together with associated labels y1,. . ., yn ∈ {0,1}, determine the best label for an element x not among the training data. More specifically, this work considers a variant of the regularized empirical risk functional which is defined intrinsically to the observed data and does not depend on the underlying population. Tools from modern analysis are used to obtain a concise proof of asymptotic consistency as regularization parameters are taken to zero at rates related to the size of the sample. These analytical tools give a new framework for understanding overfitting and underfitting, and rigorously connect the notion of overfitting with a loss of compactness.

On the loss of compactness in the vectorial heteroclinic connection problem

We give an alternative proof of the theorem of Alikakos and Fusco concerning existence of heteroclinic solutions U : ℝ → ℝN to the systemHere a± are local minima of a potential W ∈ C2(ℝN) with W(a±) = 0. This system arises in the theory of phase transitions. Our method is variational but differs from the original artificial constraint method of Alikakos and Fusco and establishes existence by analysing the loss of compactness in minimizing sequences of the action in the appropriate functional space. Our assumptions are slightly different from those considered previously and also imply a priori estimates for the solution.

Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent

We consider nonlinear Choquard equation [Formula: see text] where N ≥ 3, V ∈ L∞(ℝN) is an external potential and Iα(x) is the Riesz potential of order α ∈ (0, N). The power [Formula: see text] in the nonlocal part of the equation is critical with respect to the Hardy–Littlewood–Sobolev inequality. As a consequence, in the associated minimization problem a loss of compactness may occur. We prove that if [Formula: see text] then the equation has a nontrivial solution. We also discuss some necessary conditions for the existence of a solution. Our considerations are based on a concentration compactness argument and a nonlocal version of Brezis–Lieb lemma.

Structural evolution of massive early-type galaxies

We use a large sample of cosmological re-simulations of individual massive galaxies to investigate the origin of the strong increase in sizes and weak decrease of the stellar velocity dispersions since z = 2. At the end of a rapid early phase of star-formation, where stars are created from infalling cold gas, our simulated galaxies are all compact with projected half-mass radii of ≲ 1 kpc and central line-of-sight velocity dispersions of ≈ 262 km s−1. At lower redshifts (z < 2) those galaxies grow predominantly by the accretion of smaller stellar systems and evolve towards the observed local mass-size and mass-velocity dispersion relations. This loss of compactness is accompanied with an increase of central dark matter fractions. We find that the structural evolution of massive galaxies can be explained by frequent minor stellar mergers, which is the dominant mode of accretion for our simulated galaxies.

Descriptive and Quantitative Study of Ultrastructural Changes in the Apical Meristem of Mustard in Transition to Flowering

Transition to flowering was induced in the shoot apical meristem of Sinapis alba (mustard), a long-day species, by subjecting vegetative plants to a single 22-h long day. The ultrastructural changes occurring in the meristematic cells during the complete morphogenetic switch were quantitatively investigated using both the planimetric and the point-counting stereological methods. The 2 methods yield very similar results and are thus equally appropriate for the study. The cell, nucleus, and dispersed chromatin sizes are greater in meristems of plants induced to flower (evoked meristems) than in meristems of control vegetative plants. A first size maximum is reached at 26 h after the start of the inductive long day and a second at 54 h. These 2 maxima occur just prior to 2 mitotic waves culminating respectively at 26-30 and 62 h. Neither the condensed chromatin size nor the number of chromocentre profiles per nucleus section change. Consequently the dispersed chromatin: condensed chromatin ratio increases in evoked meristems. This change is discussed in relation to current views on the differential genetic activity of the 2 kinds of chromatin. There is a late but large increase in size of the nucleolus. Dramatic changes in texture are associated with the enlargement of this organelle. These changes are the disappearance of the segregation of fibrillar and granular components and a loss of compactness due to marked vacuolation. All these changes in size and structure are interpreted as indicating a late increase in nucleolar synthesis of ribosomes in the evoked meristems.