20 citations · 43 across the 29 of their papers we have counts for
35 papers
Posterior Frequencies and the Cost of Not Fitting: A Correction to a Memorization Lower Bound
Zhenisbek Assylbekov, Rustem Takhanov
Feldman's memorization lower bound assigns a frequency coefficient based on how often a point appears in the training sample. We give an exact three-point counterexample to its con…
New lower bounds for kissing numbers in dimensions --
Rustem Takhanov, Stanislav Yun
The kissing number in dimension is the largest number of non-overlapping congruent spheres that can simultaneously touch a central sphere of the same size. We study dimensions…
A quaternionic construction behind -point kissing arrangement in
Rustem Takhanov
Recently, a new record kissing arrangement of points in was obtained numerically by optimization (Takhanov-Assylbekov-Yun, 2026). The configuration was relea…
Structure of kissing arrangements in and a place for the st sphere
Rustem Takhanov, Zhenisbek Assylbekov, Stanislav Yun
Most currently known kissing arrangements of size in share a common structure. They consist of vectors supported on , an…
Classification of independent sets in signed Johnson graphs and applications to kissing arrangements
Rustem Takhanov, Stanislav Yun
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 analogu…
Conditional KRR: Injecting Unpenalized Features into Kernel Methods with Applications to Kernel Thresholding
Rustem Takhanov, Zhenisbek Assylbekov
Conditionally positive definite (CPD) kernels are defined with respect to a function class . It is well known that such a kernel is associated with its native spac…