National Institute for Mathematical Sciences

Every negative amphichiral knot is rationally slice

In 2009, Kawauchi proved that every strongly negative amphichiral knot is rationally slice. However, as shown by Hartley in 1980, there are examples of negative amphichiral knots that are not strongly negative amphichiral. In this paper, we prove that every negative amphichiral l...

Towards a universal ovarian cancer biomarker model: clinical validation of Trx1 and CA125 dual strategy

Abstract Background Ovarian cancer is the fifth leading cause of cancer-related mortality in women, with early detection being critical for improving patient outcomes. Current diagnostic biomarkers, including Cancer antigen 125 (CA125), human epididymis protein 4 (HE4), and their...

Three Topological Phases of the Elliptic Ginibre Ensembles with a Point Charge

Abstract We consider the complex and symplectic elliptic Ginibre matrices of size $$(c+1)N \times (c+1)N$$ ( c + 1 ) N × ( c + 1 ) N , conditioned to have a deterministic eigenvalue at $$ p \in \mathbb {R} $$ p ∈ R with multiplicity cN . We show that their limiting spectrum is ei...

Minimal rank of primitively n-universal integral quadratic forms over local rings

Abstract Let F be a local field and let R be its ring of integers. For a positive integer n , an integral quadratic form defined over R is called primitively n -universal if it primitively represents all quadratic forms of rank n . It was proved in [7] that the minimal rank of pr...

Calderón–Zygmund estimates for generalized double phase equations with matrix weights

Abstract We prove Calderón–Zygmund estimates for generalized double phase equations with Orlicz growth and variable matrix weights. The operator combines a nonuniformly elliptic double phase structure with a degenerate or singular matrix weight satisfying a small log‐ condition....

Evaluating the impact of incomplete contact tracing data on urban epidemic dynamics

Contact tracing (CT) is a frontline measure against emerging epidemics, yet in practice it is never complete. The quantitative impact of missing information—such as untraced cases or unnotified contacts—on the effectiveness of CT remains insufficiently understood. Using a stochas...

On the Order of Intersecting Hypergraphs

Abstract. Determining the maximum number of edges in an intersecting hypergraph on a fixed ground set under additional constraints is one of the central topics in extremal combinatorics. In contrast, there are few results on analogous problems concerning the maximum order of such...