Generalized bases of finite groups

Motivated by recent results on the minimal base of a permutation group, we introduce a new local invariant attached to arbitrary finite groups. More precisely, a subset $$\Delta $$ Δ of a finite group G is called a p-base (where p is a prime) if $$\langle \Delta \rangle $$ ⟨ Δ ⟩ is a p-group and $$\mathrm {C}_G(\Delta )$$ C G ( Δ ) is p-nilpotent. Building on results of Halasi–Maróti, we prove that p-solvable groups possess p-bases of size 3 for every prime p. For other prominent groups, we exhibit p-bases of size 2. In fact, we conjecture the existence of p-bases of size 2 for every finite group. Finally, the notion of p-bases is generalized to blocks and fusion systems.

local invariant surface

local invariant surface

Bag-of-Visual-Words for Cattle Identification from Muzzle Print Images

Cattle, buffalo and cow identification plays an influential role in cattle traceability from birth to slaughter, understanding disease trajectories and large-scale cattle ownership management. Muzzle print images are considered discriminating cattle biometric identifiers for biometric-based cattle identification and traceability. This paper presents an exploration of the performance of the bag-of-visual-words (BoVW) approach in cattle identification using local invariant features extracted from a database of muzzle print images. Two local invariant feature detectors—namely, speeded-up robust features (SURF) and maximally stable extremal regions (MSER)—are used as feature extraction engines in the BoVW model. The performance evaluation criteria include several factors, namely, the identification accuracy, processing time and the number of features. The experimental work measures the performance of the BoVW model under a variable number of input muzzle print images in the training, validation, and testing phases. The identification accuracy values when utilizing the SURF feature detector and descriptor were 75%, 83%, 91%, and 93% for when 30%, 45%, 60%, and 75% of the database was used in the training phase, respectively. However, using MSER as a points-of-interest detector combined with the SURF descriptor achieved accuracies of 52%, 60%, 67%, and 67%, respectively, when applying the same training sizes. The research findings have proven the feasibility of deploying the BoVW paradigm in cattle identification using local invariant features extracted from muzzle print images.