A new method is proposed for automatic classification of seismoacoustic emission sources in fiber optic monitoring systems based on the principles of optic

We study a deterministic finite-scale geometric index associated with the Poincaré ball. The index is defined through the volume growth of hyperbolic balls along the outward radial direction. For a fixed Euclidean radial step ε in the interval (0,1) and a point whose radial coordinate r satisfies 0 ≤ r < 2 arctanh(1 − ε), we prove that the corresponding outward radial hyperbolic step δ+(r, ε) strictly increases with r. Consequently, the composition Gε(r) = φ(δ+(r, ε)), where φ is the logarithmic derivative of the volume of a hyperbolic ball, is strictly increasing in r for dimension n ≥ 2. The quantity Gε(r) is a deterministic, direction-dependent finite-scale geometric index. It should not be identified with local intrinsic dimensionality (LID) in the sense of Houle, and the Riemannian dimension of the space equals n at every point. However, under a Lipschitz condition on a sampling density p with constant L, we establish a multiplicative envelope: the population finite-scale LID at the matched scale δ = δ+(r, ε) lies between exp(−2Lδ) Gε(r) and exp(2Lδ) Gε(r). A conjectural finite-sample extension is briefly discussed without the status of a theorem. Open problems are stated in a compact form.

We extend the finite-scale radial monotonicity result for the Poincaré ball to three settings: the inward radial direction, the tangential direction, and the case of a variable Euclidean step \(\varepsilon(r)\). In the inward case we show that the hyperbolic step \(\delta_-(r,\varepsilon)\) is strictly increasing in \(r\) on the domain \(r>2\mathrm{arctanh}(\varepsilon)\). In the tangential case, interpreting the hyperbolic step as the hyperbolic distance to the displaced point, we prove strict monotonicity of \(\delta_\perp(r,\varepsilon)\) on the domain \(a^2+\varepsilon^2<1\), where \(a=\tanh(r/2)\). We then establish a sphere-averaged analogue \(\bar{\delta}(r,\varepsilon)\) on the restricted domain \(\varepsilon<a<1-\varepsilon\) (which requires \(\varepsilon<1/2\)), where pointwise monotonicity holds for every direction of the displacement, and a volume-based characterization \(\delta_{\mathrm{vol}}(r,\varepsilon)\) on the full outward domain \(0\leq r<2\mathrm{arctanh}(1-\varepsilon)\). Finally, for a variable step \(\varepsilon(r)\) we derive a necessary and sufficient criterion for monotonicity of \(\delta_+(r,\varepsilon(r))\), show that it holds automatically whenever \(\varepsilon'(r)\geq0\), and exhibit an explicit counterexample of the form \(\varepsilon(r)=c(1-\|z\|)\) with \(c\in(0,1)\) for which monotonicity fails. The extension of the sphere-averaged result to the full domain \(a+\varepsilon<1\) remains open.

We proposed a new approach to solving the problem of operational analysis and medium-term forecasting of the greenhouse gas generation (CO₂, CH₄) intensity in a certain area of the cryolithozone using data from a geographically distributed network of multimodal measuring stations. A network of measuring stations, capable of functioning autonomously for long periods of time, continuously generated a data flow of the CO₂, CH₄ concentration, soil moisture, and temperature, as well as a number of other parameters. These data, taking into account the type of soil, were used to build a spatially distributed dynamic model of greenhouse gas emission intensity of the permafrost area depending on the temperature and moisture of the soil. This article presented models for estimating and medium-term predicting ground greenhouse gases emission intensity, which are based on artificial intelligence methods. The results of the numerical simulations were also presented, which showed the adequacy of the proposed approach for predicting the intensity of greenhouse gas emissions.