Uzhhorod National University

This study investigates the preparation and properties of Ag7+x(P1-xGex)S6 solid solutions, specifically comparing the impact of nanopowder dispersion and heterovalent P+5→Ge+4 substitution on the properties of resulting ceramic materials. Nanopowders were prepared via ball milling for 30 and 60 minutes, achieving crystallite sizes of 126–180 nm (30 min) and 98–140 nm (60 min). The ceramics were fabricated by cold pressing (400 MPa) with subsequent annealing. It has been established that the use of nanocrystalline precursors leads to a highly homogeneous ceramic microstructure without distinct intercrystalline boundaries. The subsequent phase transitions during cooling induce microdefects and microcracks that influence mechanical and electrical performance. Microhardness investigation of the ceramics revealed the presence of a normal indentation size effect. The microhardness of ceramics is in the range 0.57–0.94 GPa (P = 1.5 N) and the compositional dependence of microhardness shows nonlinear behavior. The electrical investigations reveal that the ionic conductivity is non-monotonic, reaching a maximum value of 4.96 × 10-2 S cm–1 for composition Ag7.5P0.5Ge0.5S6. It has been established that reducing the powder grain size to the nanoscale did not significantly increase the maximum ionic conductivity compared to microcrystalline versions, but it lead to a notable decrease in activation energy for compositions Ag7.25P0.75Ge0.25S6 (0.190 eV) and Ag7.33P0.67Ge0.33S6 (0.183 eV). These findings demonstrate that Ag7+x(P1-xGex)S6 ceramics are promising high-conductivity electrolytes where functional properties can be tuned through both chemical substitution and the control of precursor dispersion.

Sparse Mixture-of-Experts (MoE) models scale parameters while fixing active computation per token, but the specialization of individual experts remains opaque. In a companion paper we showed that routing topology is quality-neutral: five structurally different configurations converge to statistically equivalent language modeling quality. Here we show that expert identity is nonetheless causally meaningful: individual rank-1 experts are monosemantic by construction, and cosine-similarity routing in a low-dimensional metric space makes their specialization directly inspectable. We present four lines of evidence. First, projecting expert output vectors through the unembedding matrix yields a Semantic Dictionary: 15 MoE expert-level specialization is a first-class interpretability primitive: architecturally monosemantic, causally validated, and controllable at inference with zero overhead.

Sparse Mixture-of-Experts (MoE) architectures employ increasingly sophisticated routing mechanisms – learned routers, multi-hop trajectories, token-dependent gating. We ask: does routing topology actually determine language modeling quality? We build a geometric MoE (ST-MoE) using cosine-similarity routing against learned centroids in a low-dimensional space (d_space = 64), requiring 80

We describe the R package EstemPMM, which implements the Polynomial Maximization Method (PMM) for parameter estimation under non-Gaussian errors. PMM exploits higher-order cumulants of the error distribution – specifically the third standardized moment gamma_3 and fourth standardized moment gamma_4 – to construct estimators that outperform ordinary least squares (OLS) whenever the errors are asymmetric or leptokurtic. The package provides a unified interface for linear regression (lm_pmm2, lm_pmm3), autoregressive and moving-average time-series models (ar_pmm2, ma_pmm2, arma_pmm2, arima_pmm2, and seasonal variants), a data-driven dispatch function (pmm_dispatch) that automatically selects OLS, PMM2, or PMM3 based on the sample skewness and excess kurtosis, and Monte Carlo comparison utilities. The implementation uses R's S4 class system and follows standard generic interfaces (coef, fitted, residuals, predict, summary, AIC, logLik, vcov, confint). Asymptotic efficiency is characterised by Kunchenko-style coefficients g_2, g_3 in [0,1], defined as the ratios of the asymptotic variance of the PMM2 and PMM3 estimators to that of OLS. Monte Carlo experiments confirm the theoretical values and a WTI crude-oil case study illustrates the dispatcher and parameter-precision benefits of PMM2 on real heavy-tailed data. EstemPMM version 0.3.2 is available from CRAN at https://CRAN.R-project.org/package=EstemPMM under the GPL-3 licence.

Sequential change-point detection in non-Gaussian stochastic processes is challenging because the underlying densities are rarely known in real time. Classical parametric procedures such as CUSUM lose optimality under distributional mismatch, whereas nonparametric alternatives often react slowly. We develop a unified framework that approximates the log-likelihood ratio (LLR) on a generalized stochastic basis – polynomial, logarithmic, or fractional-power – using only moments up to order 3s, with no analytic form of the distribution, and thereby adapts the classical CUSUM, GRSh, and SRP procedures to non-Gaussian data. The convergence functional J(s) = K^T Y is interpreted as the projection of the Kullback-Leibler divergence onto the basis span, yielding a formal criterion for selecting the approximation order. We target the regime of small relative change-points, where the signal energy changes little but the shape of the distribution – tail structure and modality – does. A robust threshold follows from Kunchenko's probability-error bound (KU-PE), which controls the false-alarm rate without empirical tuning. On nine public benchmarks across four domains, the method is, to our knowledge, the only one operative on extremely heavy-tailed data (excess kurtosis gamma_4 > 20), where classical methods produce 100