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Combinatorial and analytic aspects of independence polynomials of zero divisor graphs
arXiv:2606.04789v1 Announce Type: cross Abstract: The independence polynomial of a graph encapsulates all independent sets of differing sizes, a task classified as NP-hard in theoretical computer science. This article examines the independence polynomial of zero divisor graphs in commutative rings. We demonstrate that the independent sets, represented as a sequence of coefficients of the independence polynomial, exhibit unimodality and log-concavity.
Why researcher independence doesn't start or end with a PhD
Why researcher independence doesn't start or end with a PhD Gaby Clark Scientific Editor Andrew Zinin Lead Editor A Ph.D. is often treated as the point where scholars become "independent." Yet, a new study by Hiroshima University shows that achieving independence is far less simple and tidy, unfolding instead as a long, uneven, river-like journey shaped by relationships, risks and resilience. The study was published in Innovations in Education and Teaching International on May 18, 2026.
Identifiability and Estimation for Unlabeled Finite Mixtures under Marginal Independence
arXiv:2606.07914v1 Announce Type: cross Abstract: We study component recovery and mixing-matrix estimation from unlabeled finite mixtures whose observable distributions share the same latent components but have unknown mixing weights. The main identifying signal is marginal independence: each component is assumed to be independent on at least one coordinate pair, but no labels, clean component samples, or mixing weights are observed. We first prove a structural result for product components:...
Outgoing chair Powell delivers defence of Fed independence
Outgoing chair Powell delivers defence of Fed independence WASHINGTON: Outgoing US Federal Reserve chair Jerome Powell on Sunday (May 31) delivered a staunch defence of the need for the central bank to maintain independence and credibility, as it comes under assault from President Donald Trump. "Like many other institutions, the Fed has been undergoing a stress test," he said as he accepted an award from the John F Kennedy Library Foundation.
Kyra Sedgwick says knowing her ancestor signed the Declaration of Independence 'means a lot' to her
Kyra Sedgwick is sharing why the upcoming 250th anniversary of America's independence is special to her. During a recent appearance on "Today," the 60-year-old actress revealed that one of her ancestors signed the Declaration of Independence, telling the hosts that knowing that "means a lot.""I mean, as an American, democracy means a lot to me.
ATG7 function promotes pancreatic cancer progression independently of autophagy
Autophagy is a cellular degradation process that recycles dysfunctional components to maintain cellular homeostasis. Beyond this canonical role, autophagy-related proteins, such as the essential autophagy initiation protein ATG7, are increasingly recognized to have autophagy independent functions in diverse biological processes and disease contexts, including cancer progression and metastasis. However, the mechanisms underlying these autophagy independent functions remain unclear.
Cheng Li-wun talks Trump, Taiwan independence and a future leadership run
Taiwan’s main opposition leader hailed US President Donald Trump’s recent comments opposing the island’s independence as a “relatively positive first step” towards reducing tensions. Cheng Li-wun, chairwoman of the Kuomintang (KMT), told the South China Morning Post on Sunday in an exclusive interview: “The ‘one China’ principle and opposition to Taiwan independence have always been the Kuomintang’s stance. “On this political basis, the status quo across the Taiwan Strait can be maintained,...
Non-association independent schools inspections and outcomes: management information
Non-association independent schools inspections and outcomes: management information Management information aggregating in-year and most recent inspections and outcomes. - From: - Ofsted - Published - 20 February 2018 - Last updated - 9 June 2026 — See all updates For the latest individual inspection reports, please visit our reports website.
Classification of independent sets in signed Johnson graphs and applications to kissing arrangements
Announce Type: new Abstract: Johnson graph are a family of graphs that play an important role in the theory of constant-weight codes, extremal combinatorics, and combinatorial geometry. We study signed analogues of classical Johnson graphs, denoted by $J_\pm(n,k)$, whose vertices are vectors of the form $\pm e_{i_1}\pm\cdots\pm e_{i_k}$, where two vertices are adjacent whenever their dot product equals $k-1$. We are particularly interested in maximum independent sets in the case $k=4$. An...
Screenings for Independent’s new film documenting the kidnap and torture of LGBTQ+ people in Nigeria
Screenings for Independent’s new film documenting the kidnap and torture of LGBTQ+ people in Nigeria To mark Pride Month, The Arzner cinema will screen our film on how aid cuts are severing lifelines for vulnerable people. A second screening will follow at the Institute for Contemporary Arts - Bookmark - CommentsGo to comments Amid unprecedented global aid cuts, which are hurting some of the most vulnerable people across the world, The Arzner cinema and the Institute of Contemporary Arts...