Dynamic data structures for twin-ordered matrices

We present a dynamic data structure for representing binary $n\times n$ matrices that are $d$-twin-ordered, for a~fixed parameter $d$. Our structure supports cell queries and single-cell updates both in $\text{Oh}(\log \log n)$ expected worst case time, while using ${\text{Oh}}_d(n)$ memory; here, the ${\text{Oh}}_d(\cdot )$ notation