Strong Euler well-composedness

In this paper, we define a new flavour of well-composedness, called strong Euler well-composedness. In the general setting of regular cell complexes, a regular cell complex of dimension n is strongly Euler well-composed if the Euler characteristic of the link of each boundary cell is 1, which is the Euler characteristic of an $$(n-1)$$ ( n - 1 ) -dimensional ball. Working in the particular setting of cubical complexes canonically associated with $$n$$ n D pictures, we formally prove in this paper that strong Euler well-composedness implies digital well-composedness in any dimension $$n\ge 2$$ n ≥ 2 and that the converse is not true when $$n\ge 4$$ n ≥ 4 .

Spatial and temporal patterns of wound periderm development in Cryptomeria japonica bark

Limited investigations have been carried out on the physiological and growth responses of bark to wounding, even though wound periderms play crucial roles in tree defenses. To understand the mechanisms of wound periderm formation, we studied the growth responses and structural changes of wounded bark of three Cryptomeria japonica individuals. We observed the developmental time frame and morphology of wound periderms around mechanically induced wounds in summer. The wound responses included discoloration, lignification, and suberization in tissues present at the time of wounding, followed by wound periderm formation and secondary metabolite deposition. The trees had developed wound periderms approximately 4 weeks after wounding. The wound periderms were within 3 mm in the axial directions and within 1 mm in the lateral directions from the wound surfaces. The distinct patterns of wound periderm formation in the axial and lateral regions resulted from the arrangement and anatomical features of the cells adjacent to the wounds. The wound phellem cells were tangentially narrower and axially shorter in the side and upper/lower regions, respectively, of the wounds. Therefore, the cell division frequencies in the planes parallel to the wound surface may be greater than those in the other directions. Wound reactions in bark might initially be triggered by microenvironmental changes, such as the spread of desiccation, which depends directly on the morphology of phloem cell complexes.

Tactile sensitivity in the rat: a correlation between receptor structure and function

Single cutaneous fibers were recorded in the median nerve of the deeply anesthetized rat and the receptor morphology in the forelimb glabrous skin was analyzed to establish a probable correlation between receptor anatomy and physiology. Receptor complexes in the glabrous skin of the rat forelimb were stained immunologically with antibodies NF-200 and PGP-9.5, confirming the presence of Meissner corpuscles and Merkel complexes within the dermal papilla similar to other mammals including primates. Both the Meissner corpuscles and Merkel cell complexes were sparse and located in the pyramidal-shaped palmer pads and the apex of the digit extremities. They were almost totally absent elsewhere in the glabrous skin. No Ruffini receptors or Pacinian corpuscles were found in our samples. A total of 92 cutaneous fibers were retained long enough for analysis. Thirty-five (38%) were characterized as rapidly adapting fibers (RA) and 57 (62%) were slowly adapting afferents (SA). Despite the very limited number of receptors at the tip of the digit, RA receptors outnumbered SA fibers 3.2/1.0. In contrast, SA fibers on the thenar pad outnumbered RA receptors by a ratio of 3–1. Despite the very limited number of low threshold mechanoreceptors in the glabrous skin of the rat forelimb, the prevalence of SA afferents in the palm and more frequent occurrence of RA afferents in the digit extremity suggest differences in functionality both for locomotion and object manipulation.

A Geometric and Combinatorial Exploration of Hochschild Lattices

Hochschild lattices are specific intervals in the dexter meet-semilattices recently introduced by Chapoton. A natural geometric realization of these lattices leads to some cell complexes introduced by Saneblidze, called the Hochschild polytopes. We obtain several geometrical properties of the Hochschild lattices, namely we give cubic realizations, establish that these lattices are EL-shellable, and show that they are constructible by interval doubling. We also prove several combinatorial properties as the enumeration of their $k$-chains and compute their degree polynomials.

Adiponectin-expressing Treg facilitate T lymphocyte development in thymic nurse cell complexes

Adiponectin is a well-known insulin sensitizer and anti-inflammatory molecule, possessing therapeutic potentials in cardiovascular, metabolic and cancer diseases. Results of the present study demonstrate that adiponectin is expressed in a population of regulatory T-cells (Treg) resided within the thymic nurse cell (TNC) complexes. Adoptive transfer of adiponectin-expressing Treg precursors effectively attenuated obesity, improved glucose and insulin tolerance, prevented fatty liver injuries in wild-type mice fed a high-fat diet, and significantly inhibited breast cancer development in MMTV-PyVT transgenic mice. Within the TNC complexes, locally produced adiponectin bound to and regulated the expression as well as the distribution of CD100, a transmembrane lymphocyte semaphorin, in turn modulating the lymphoepithelial interactions to facilitate T-cell development and maturation. In summary, adiponectin plays an important role in the selection and development of T lymphocytes within the TNC complexes. Adiponectin-expressing Treg represent a promising candidate for adoptive cell immunotherapy against obesity-related metabolic and cancer diseases.

Hydrogen Sulfide as a Factor of Neuroprotection during the Constitutive and Reparative Neurogenesis in Fish Brain

The H2S-producing systems were studied in trout telencephalon, tectum, and cerebellum at 1 week after eye injury. The results of ELISA analysis have shown a 1.7-fold increase in the CBS expression at 1 week post-injury, as compared to the intact trout. In the ventricular and subventricular regions of trout telencephalon, CBS+ cells, as well as neuroepithelial and glial types, were detected. As a result of injury, the number of CBS+ neuroepithelial cells in the pallial and subpallial periventricular regions of the telencephalon increases. In the tectum, a traumatic damage leads to an increase in the CBS expression in radial glia with a simultaneous decrease in the number of CBS immunopositive neuroepithelial cells detected in intact animals. In the cerebellum, we revealed neuroglial interrelations, in which H2S is probably released from the astrocyte-like cells with subsequent activation of the neuronal NMDA receptors. The organization of the H2S-producing cell complexes suggests that the amount of glutamate produced in the trout cerebellum and its reuptake is controlled with the involvement of astrocyte-like cells, reducing its excitotoxicity. We believe that the increase in the number of H2S-producing cells constitutes a response to oxidative stress, and the overproduction of H2S neutralizes the reactive oxygen species.

Min-Max Theory for Cell Complexes

In the study of smooth functions on manifolds, min-max theory provides a mechanism for identifying critical values of a function. We introduce a discretized version of this theory associated to a discrete Morse function on a (regular) cell complex. As applications we prove a discrete version of the mountain pass lemma and give an alternate proof of a discrete Lusternik–Schnirelmann theorem.