Kuru Ratnavelu

You are already at the latest version For a real correlation matrix \(C\), the self-conjugate specialization of Chollet's conjecture asserts \permanent(C\circ C)\leq\permanent(C)^2$.

You are already at the latest version Let \( p\geq 5 \) be prime. The theorem of Yu obtained from permanent rank proves the Alon--Jaeger--Tarsi conjecture over \( F_p \) in dimensions \( n<2^{p-2} \). We close the missing boundary: the conjecture holds for every \( n\leq 2^{p-2} \). In particular, for every \( M\in GL_8(F_5) \) there is a vector \( x\in(F_5^*)^8 \) such that \( Mx\in(F_5^*)^8 \). The proof separates according to the permanent rank of \( M \).

Let G?=?(V, E) be a network where and are sets of nodes and edges. In the SSCLPA, nodes are divided into two types, known as the solo and grouped nodes. Solo nodes refer to nodes that are not yet assigned into any community yet, while grouped nodes mean otherwise. Solo and grouped nodes are denoted by and , respectively. The labels of V and V are updated separately in two propagation processes in the SSCLPA.