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Suppose for clarification that we adopt time as that fourth dimension. Consider how the figure could be constructed in xyzt-space. The accompanying illustration (“Time evolution…”) shows one useful evolution of the figure. At t = 0 the wall sprouts from a bud somewhere near the “intersection” point. After the figure has grown for a while, the earliest section of the wall begins to recede, disappearing like the Cheshire Cat but leaving its ever-expanding smile behind. By the time the growth front gets to where the bud had been, there is nothing there to intersect and the growth completes without piercing existing structure. The 4-figure as defined cannot exist in 3-space but is easily understood in 4-space. [ 4 ]

More formally, the Klein bottle is the quotient space described as the square [0,1] × [0,1] with sides identified by the relations (0, y) ~ (1, y) for 0 ≤ y ≤ 1 and (x, 0) ~ (1 − x, 1) for 0 ≤ x ≤ 1.

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The new era of cooperative education in india!

“Tribhuvan” Sahkari University, through its innovative HUB-and-SPOKE model, will ensure nationwide reach and accessibility by integrating sectoral schools and leveraging strategic partnerships to build a robust Pan-India ecosystem of technical and skill development institutions.

Follow the link to join the programme ➡️

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They found that increased Hh signaling is a hallmark of human meibomian gland carcinoma, a rare and aggressive cancer of the eyelid. Furthermore, the team discovered that aged glands show decreased Hh signaling and decreased epidermal growth factor receptor (EGFR) signaling, as well as impaired innervation and a loss of collagen in niche fibroblasts, suggesting that changes in both glandular epithelial cells and their surrounding microenvironment contribute to age-related degeneration.

These discoveries suggest that targeting Hh and EGFR signaling to stimulate stem cell activity in the meibomian glands could be a potential therapeutic option to treat evaporative dry eye disease.

A team of researchers has identified stem cell populations and mechanisms underlying age-related degeneration in glands that are vital to eye function. The findings, published in Nature Communications, may lead to new therapeutic approaches for evaporative dry eye disease, a common condition in older people.

Meibomian glands, tiny oil glands along the edges of the eyelids, secrete lipid-rich meibum to prevent tear evaporation and protect the eye surface. Aging-related shrinkage of the meibomian glands may result, in part, from stem cell exhaustion and is associated with evaporative dry eye disease, a common condition that causes swollen eyelids, itchy eyes, or blurred vision. Symptoms may be lessened with warm compressions, artificial tears, and thermal pulsation, but these treatments are only partially effective.

The researchers identified markers for stem cell populations that maintain distinct regions of the meibomian glands, and uncovered the hedgehog (Hh) cell-cell signaling pathway, which is broadly important in development and disease, as a key regulator of meibomian gland stem cell proliferation and tissue regeneration.

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UCLA Health researchers have helped to develop a new digital toolbox to create a “common language” for brain network studies, potentially accelerating new discoveries and treatments for neurological and psychiatric conditions.

In a study recently published in the journal Nature Communications, the authors say the open-source software will help researchers worldwide overcome a longstanding hurdle in brain imaging research.

“As long as people have been interested in studying the brain, they have tried to map it out by answering a basic question: how many brain regions are there?” said study senior author Lucina Uddin, a UCLA Health Psychiatry and Biobehavioral Sciences Professor and Director of the UCLA Brain Connectivity and Cognition Laboratory.

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An international team of astronomers reports the detection of four new gamma-ray millisecond pulsars using the Murriyang radio telescope at the Parkes Observatory in Australia. The discovery was detailed in a research paper published March 16 on the arXiv preprint server.

Pulsars are highly magnetized, rotating emitting a beam of electromagnetic radiation. The most rapidly rotating pulsars, with rotation periods below 30 milliseconds, are known as millisecond pulsars (MSPs). Astronomers assume that they are formed in binary systems when the initially more massive component turns into a neutron star that is then spun up due to accretion of matter from the secondary star.

Now, a group of led by Matthew Kerr of the Naval Research Laboratory (NRL) in Washington, DC, has detected four new MSPs with spin periods below four milliseconds. The discovery was made using the Murriyang radio telescope as part of the search for .

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A research team has successfully developed a technology that utilizes Large Language Models (LLMs) to predict the synthesizability of novel materials and interpret the basis for such predictions. The team was led by Seoul National University’s Professor Yousung Jung and conducted in collaboration with Fordham University in the United States.

The findings of this research are expected to contribute to the novel material design process by filtering out material candidates with low synthesizability in advance or optimizing previously challenging-to-synthesize materials into more feasible forms.

The study, with Postdoctoral Researcher Seongmin Kim as the first author, was published in two chemistry journals: the Journal of the American Chemical Society on July 11, 2024, and Angewandte Chemie International Edition on February 13, 2025.

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