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Nikolai Yu. Zolotykh

Publications and source records attributed to Nikolai Yu. Zolotykh.

7 recordsLinked to original sources

CL-CLIP: CLIP-Based Continual Learning Framework with Cost-Volume Category Decoupling for Object Detection

Continual Object Detection (COD) requires a detector to acquire new categories over time while preserving previously learned ones. This goal is closely related to open-vocabulary detection, since both settings require reasoning over categories that are not fully covered by the annotations available at the current training stage. Recent CLIP-based open-vocabulary detectors have shown strong zero-shot generalization, and frameworks such as F-ViT demonstrate that vision-language pretraining can provide powerful zero-shot detection ability for unseen categories. However, real-world deployments cannot remain purely zero-shot: once these detectors are continually updated on newly introduced categories, they suffer severe catastrophic forgetting and quickly lose their previously calibrated detection ability. We therefore propose CL-CLIP, a CLIP-based COD framework that equips open-vocabulary detectors with better continual learning ability through cost-volume-guided category decoupling. Specifically, following CAT-Seg, we compute a CLIP image-text similarity cost volume, defined as dense category-wise response maps between visual tokens and class text embeddings. This zero-shot spatial prior decomposes shared region features into class-specific pathways, which are then processed by a Multi-Expert RoI head. Extensive experiments on PASCAL VOC and MS-COCO show that CL-CLIP substantially improves the F-ViT baseline under continual fine-tuning and achieves competitive performance with existing continual object detectors, especially in adapting to newly introduced categories while preserving competitive base-class performance.

cs.CV

LUDB: a new open-access validation tool for electrocardiogram delineation algorithms

We report Lobachevsky University Database (LUDB) of ECG signals, an open tool for validating ECG delineation algorithms, that is superior to the existing publicly available data bases in several aspects. LUDB contains 200 recordings of 10-second 12-lead electrocardiograms (ECG) from different subjects, representative of a variety of signal morphologies. The boundaries and peaks of QRS complexes and P and T waves are manually annotated by cardiologists for all recordings and independently for each lead, and all records received an expert classification by abnormalities. We present a case study for the recently proposed wavelet-based algorithm and the broadly used ecg-kit tool, and demonstrate the advantage of multi-lead ECG data analysis. LUDB contributes to the diversity of public databases employed in developing and validating novel ECG analysis algorithms, including the most advanced based on deep learning neural networks.

q-bio.QM

Linear read-once and related Boolean functions

It is known that a positive Boolean function f depending on n variables has at least n + 1 extremal points, i.e. minimal ones and maximal zeros. We show that f has exactly n + 1 extremal points if and only if it is linear read-once. The class of linear read-once functions is known to be the intersection of the classes of read-once and threshold functions. Generalizing this result we show that the class of linear read-once functions is the intersection of read-once and Chow functions. We also find the set of minimal read-once functions which are not linear read-once and the set of minimal threshold functions which are not linear read-once. In other words, we characterize the class of linear read-once functions by means of minimal forbidden subfunctions within the universe of read-once and the universe of threshold functions. Within the universe of threshold functions the importance of linear read-once func- tions is due to the fact that they attain the minimum value of the specification number, which is n + 1 for functions depending on n variables. In 1995 Anthony et al. conjec- tured that for all other threshold functions the specification number is strictly greater than n + 1. We disprove this conjecture by exhibiting a threshold non-linear read-once function depending on n variables whose specification number is n + 1.

math.CO

Alcuin's Propositiones de Civitatibus: the Earliest Packing Problems

We consider three problems about cities from Alcuin's_Propositiones ad acuendos juvenes_. These problems can be considered as the earliest packing problems difficult also for modern state-of-the-art packing algorithms. We discuss the Alcuin's solutions and give the known (to the author) best solutions to these problems.

math.HO

Specifying a positive threshold function via extremal points

An extremal point of a positive threshold Boolean function $f$ is either a maximal zero or a minimal one. It is known that if $f$ depends on all its variables, then the set of its extremal points completely specifies $f$ within the universe of threshold functions. However, in some cases, $f$ can be specified by a smaller set. The minimum number of points in such a set is the specification number of $f$. It was shown in [S.-T. Hu. Threshold Logic, 1965] that the specification number of a threshold function of $n$ variables is at least $n+1$. In [M. Anthony, G. Brightwell, and J. Shawe-Taylor. On specifying Boolean functions by labelled examples. Discrete Applied Mathematics, 1995] it was proved that this bound is attained for nested functions and conjectured that for all other threshold functions the specification number is strictly greater than $n+1$. In the present paper, we resolve this conjecture negatively by exhibiting threshold Boolean functions of $n$ variables, which are non-nested and for which the specification number is $n+1$. On the other hand, we show that the set of extremal points satisfies the statement of the conjecture, i.e., a positive threshold Boolean function depending on all its $n$ variables has $n+1$ extremal points if and only if it is nested. To prove this, we reveal an underlying structure of the set of extremal points.

math.CO

On the minimal teaching sets of two-dimensional threshold functions

It is known that a minimal teaching set of any threshold function on the twodimensional rectangular grid consists of 3 or 4 points. We derive exact formulae for the numbers of functions corresponding to these values and further refine them in the case of a minimal teaching set of size 3. We also prove that the average cardinality of the minimal teaching sets of threshold functions is asymptotically 7/2. We further present corollaries of these results concerning some special arrangements of lines in the plane.

math.CO