arXiv subjects

Svetlana Shirokovskikh

Publications and source records attributed to Svetlana Shirokovskikh.

4 recordsLinked to original sources

arXiv2026

Matrix-tree theorem for cohomological electrical networks

We introduce a new type of boundary condition for electrical networks by specifying a cohomology class on the underlying cell complex. As special and limiting cases, we recover the Dirichlet boundary condition, multiport condition, and prescribed voltage drops along nontrivial cycles on a surface. In this setting, we obtain a combinatorial formula for minors of the response matrix, generalizing the matrix-tree theorem, the Kenyon-Wilson formula, and a recently discovered formula for networks on surfaces due to Lam et al. To prove this formula, we develop a statistical-physics toolbox, including a new parafermionic observable for the uniform spanning tree model. This is the first parafermionic observable that is intrinsic, in the sense that it does not require an embedding of the graph in the plane or on a surface. Other ingredients are an intrinsic Temperley correspondence and source-synchronized networks, the latter providing a completely elementary reformulation of our results.

math.CO↗

arXiv2026

Fast and Feasible: Permutation-based Constrained Reranking for Revenue Maximization

Search and recommender systems have produced highly relevant search results. A natural next step in the development of such systems in e-commerce is to rerank these results to increase the platform's revenue from paid promotion products. However, maximizing revenue alone may degrade the user experience by reducing relevance or increasing fraud risk. To avoid this, we state the reranking problem as an integer linear program ($ILP$) that maximizes revenue subject to per-query constraints on other metrics, e.g., relevance. Since solving $ILP$ exactly for every query is slow for deployment to the online service, we propose a lightweight permutation-based reranking approximation algorithm PermR. At each step, the algorithm selects a pair of neighboring items and swaps them to either improve the objective or repair a violated constraint. We evaluate PermR across multiple categories of a large classified platform in offline and online settings. PermR achieves about 63\% of the ILP revenue improvement, within production latency limits, preserving all constraints. In a 14-day online A/B test over 56 million search queries, PermR increased revenue by $2$\%.

cs.IR↗

arXiv2025

Superport networks

We study multiport networks, common in electrical engineering. They have boundary conditions different from electrical networks: the boundary vertices are split into pairs and the sum of the incoming currents is set to be zero in each pair. If one sets the voltage difference for each pair, then the incoming currents are uniquely determined. We generalize Kirchhoff's matrix-tree theorem to this setup. Different forests now contribute with different signs, making the proof subtle. In particular, we use the formula for the response matrix minors by R. Kenyon-D. Wilson, determinantal identities, and combinatorial bijections. We introduce superport networks, generalizing both ordinary networks and multiport ones.

math.CO↗

arXiv2022

Transformations of 2-port networks and tiling by rectangles

In this paper, we study 2-port networks and introduce new concepts of voltage drop and $Π$-equivalence. The main result is that each planar network is $Π$-equivalent to a network with no more than 5 edges. This implies that if an octagon in the shape of the letter $Π$ can be tiled by squares then it can be tiled by no more than 5 rectangles with rational aspect ratios. Kenyon's theorem from 1998 proves this only for 6 rectangles.

math.CO↗