Search Results (89)

The volumetric mass transfer coefficient ($k_{L}a$) governs the design, operation, and scale-up of aerobic bioprocesses, yet its dependence on reactor geometry, impeller design, operating conditions, and fluid properties limits prediction by empirical correlations. Machine learning (ML) improves accuracy but faces two barriers in bioprocess practice: selecting the best model among many candidates requires expertise, and small, highly multicollinear data make models chosen based on test error alone prone to overfitting. Using a browser-based, no-code platform, we trained 14 regression algorithms under an identical pipeline on a published $k_{L}a$ dataset, and introduced a composite objective, the generalization-penalized error (GPE), which is the test RMSE plus the absolute train–test RMSE gap. Minimizing GPE rather than test RMSE expanded the top statistically equivalent group to include not only boosting ensembles but also simpler, interpretable models, indicating that black-box models hold no clear advantage once train–test consistency is assessed. Sensitivity analysis showed that tree models produce discontinuous responses, whereas algebraic learning via elastic net (ALVEN) yields smooth surfaces. Shapley additive explanations (SHAP) and an ontology graph, interpreted by a retrieval-augmented language-model agent, identified rotational speed and gas flow rate as dominant, reproducing the established mass transfer mechanism. The framework offers a reproducible, interpretable, expertise-light route to bioprocess model selection. Full article

We develop a comparative synthesis of quantum-information geometry beyond complex numbers, with emphasis on what different algebraic frameworks contribute to information-processing structure rather than on their formal novelty alone. The organizing idea is a layer-by-layer test of the standard complex Hilbert-space formalism: each non-complex or deformed framework modifies the scalar field, phase group, projective state space, Born-probability semantics, composition rule, measurement geometry, symmetry algebra or representation category. The central thesis is that such frameworks are physically meaningful when they identify which assumptions make complex quantum mechanics operationally stable: positive probabilities, associative multipartite composition, reversible dynamics, experimentally testable phases, locality constraints, informationally complete measurements, error bases and clear operational semantics. Real quantum theory probes the necessity of complex phases and local tomography; quaternionic quantum mechanics probes non-Abelian phase while retaining associativity and admitting complex embeddings; octonionic proposals probe the boundary where exceptional geometry survives but generic circuit composition is obstructed by non-associativity; Jordan algebras test ordered probabilistic state spaces; Clifford algebras and Bott periodicity provide the spinorial and topological grammar connecting gates, Hopf maps and periodic dimensions; and quantum-group or q-deformed constructions probe coproducts, braiding and representation categories rather than scalar amplitudes. We distinguish three roles that are often conflated: genuine hypercomplex kinematics, Hopf-fibration coordinates for ordinary complex multipartite entanglement, and deformed algebraic or categorical structures. The resulting map separates established equivalence and experimental-constraint results from useful representation tools and speculative programs, while identifying concrete open problems for non-complex quantum information. Full article

Calculating the number of spanning trees in a graph is a crucial problem in combinatorics and physics that has been thoroughly researched for many years by mathematicians and physicists. The higher the quality and perfection of the network, the greater the number of trees spanning it, leading to greater possibilities for connection between two vertices and ensuring good rigidity and resistance. In this work, we use matrix theory and linear algebra techniques to derive simple explicit formulas for calculating the complexity of various products of two complete bipartite graphs, including the Cartesian product, tensor product, normal product, composition product, symmetric product, disjunction, and strong sum. Full article

Rapid urbanization in semi-arid cities intensifies heat exposure, air pollution, and land-surface degradation, yet these stressors are often assessed separately. This study develops a scale-aware Urban Environmental Stress (UES) framework for Jaipur, India, using multi-sensor Earth observation data. The framework explicitly addresses indicator redundancy, weighting bias, short time-series interpretation, and temporal comparability. The final primary UES surface uses twelve retained stress-oriented indicators on a 500 m common analysis grid, excludes NDBI because it is algebraically redundant with NDMI when both are computed from the same NIR/SWIR bands, and applies equal weights so that built fraction does not dominate the composite. Entropy weighting is reported only as a sensitivity diagnostic. The resulting UES map identifies high relative stress in Jaipur’s dense urban core and transport-industrial corridors, with lower stress along the Aravalli flank and peri-urban green or water-adjacent areas. The framework is presented as a relative spatial prioritization tool rather than an absolute physical time series; temporal claims are limited to independently reported land-cover and individual-indicator trajectories unless fixed multi-year normalization and fixed weights are applied. Full article

To address the voltage regulation problem of the DC-DC buck converter under multi-source disturbances, this paper proposes a composite anti-disturbance control strategy integrating a Chebyshev-based self-evolving fuzzy neural network (SECFNN) and an arctangent super-twisting sliding mode control (ASTSMC). First, to construct the composite anti-disturbance framework, a load algebraic reconstruction compensator (LARC) is utilized to analytically estimate real-time load dynamics, providing active feedforward compensation for extreme load steps. Second, targeting the unmodeled nonlinearities and parameter uncertainties, the SECFNN is deeply integrated into the control loop. It employs a bidirectional structural learning mechanism—dynamically growing and pruning fuzzy rules—to achieve high-precision adaptive approximation and intelligent compensation. Furthermore, serving as the robust inner-loop core of this composite strategy, the ASTSMC is introduced. By replacing the traditional discontinuous sign function with a continuous arctangent operator, it effectively mitigates sliding mode chattering while ensuring the rapid finite-time convergence of the current tracking error. Ultimately, by synergistically fusing feedforward disturbance rejection (LARC), intelligent nonlinear approximation (SECFNN), and robust tracking (ASTSMC), the proposed strategy significantly reduces transient voltage drops and achieves smoother steady-state performance. Comparative simulation experiments demonstrate the superiority of the proposed method, achieving a rapid startup settling time of 6.5 ms, limiting the maximum transient voltage drop to 15 mV, and completing dynamic reference tracking in 1.2 ms. Furthermore, hardware experimental results confirm its practical engineering feasibility, demonstrating a fast startup of 8.3 ms with zero overshoot, effectively mitigating transient voltage drops during load step changes, and completing dynamic tracking in just 2.2 ms, which verifies its reliable dynamic agility and strong robustness under various test conditions. Full article

This study evaluates structure-preserving neural network architectures for learning holonomically constrained mechanical dynamics in Cartesian coordinates. In contrast to methods using reduced coordinates, the full ambient phase space ${\mathbb{R}}^{2n}$ is retained with explicit algebraic constraints $C_i\left(\mathbf{q}\right)=0$ to provide a test bed for constraint-aware learning. The Constraint-Aware Hamiltonian Neural Network (CA-HNN) is proposed, which augments the standard HNN with a dedicated multiplier network ${\lambda }_{\varphi }(\mathbf{q},\mathbf{p})$ for Lagrange multipliers and a composite loss function evaluated on predicted rollouts. The theoretical framework is grounded in the geometry of constrained Hamiltonian systems: the extended phase space ${\mathbb{R}}^{2n+m}$ carries a degenerate antisymmetric structure where an m-dimensional kernel encodes constraint directions, while the symplectic structure emerges on the $2(n-m)$-dimensional reduced manifold $\Sigma$. It is proven that the physical Hamiltonian is conserved on the constraint surface under augmented flow. Benchmarks on a pendulum ($C=x^2+y^2-l^2$), double pendulum, and bead on a parabola ($C=y-x^2$) demonstrate that CA-HNN reduces constraint violations $\parallel C\left(\mathbf{q}\right)\parallel$ by $5\times$ to $2400\times$ compared to standard HNNs. While the best energy conservation is achieved by PINNs, these findings clarify the roles of architectural inductive bias, constraint augmentation, and soft physics regularization. Full article

We applied an algebraic approach, developed within the framework of the theory of a commutative monoid of self-dual symmetric polynomials, to the problem of effective isotropic conductivity ${\sigma }_e({\sigma }_1,\dots ,{\sigma }_n)$ in two-dimensional n-phase symmetric composites with partial isotropic conductivities ${\sigma }_j$. The upper $\mathsf{\Omega }({\sigma }_1,\dots ,{\sigma }_n)$ and lower $\omega ({\sigma }_1,\dots ,{\sigma }_n)$ bounds for ${\sigma }_e({\sigma }_1,\dots ,{\sigma }_n)$, found by the algebraic approach for $n=3,4$, are universal (independent of the composite microstructure) and possess all algebraic properties of ${\sigma }_e({\sigma }_1,\dots ,{\sigma }_n)$ that follow from physics: first-order homogeneity, full permutation invariance, Keller’s self-duality, positivity, and monotony. The bounds are compatible with the trivial solution ${\sigma }_e(\sigma ,\dots ,\sigma )=\sigma$ and satisfy Dykhne’s ansatz. Their comparison with previously known numerical calculations, asymptotic analysis, and exact results for the effective isotropic conductivity ${\sigma }_e({\sigma }_1,\dots ,{\sigma }_n)$ of two-dimensional three- and four-phase composites showed complete agreement. The bounds $\mathsf{\Omega }({\sigma }_1,\dots ,{\sigma }_n)$ and $\omega ({\sigma }_1,\dots ,{\sigma }_n)$ in both cases $n=3,4$ are stronger than the currently known variational bounds. Full article

This communication discusses the problem of depositing equiatomic metal alloy films. It is shown that this problem can be solved using a magnetron equipped with a target constructed using a new “multilayer target” paradigm. This target, sputtered in an argon environment, consists of several parallel metal plates mounted on the magnetron axis. A method based on the equality of the sputtered fluxes generated by the plates is proposed for calculating the geometric dimensions of the plates. This equality leads to a system of algebraic equations, which are proposed to be solved under the assumption of a uniform discharge current density distribution in the sputtering region of the target. The communication describes two types of targets in which the plates have slots of different shapes. In one case, the slots are shaped as sectors of a ring with a given angle. In the other, the plates are shaped as rings. As examples, the geometric dimensions of targets for a balanced magnetron system intended for the deposition of films of equiatomic Ti_0.33Ta_0.33Nb_0.33 and Ti_0.25Ta_0.25Nb_0.25Mo_0.25 alloys are calculated. The presentation is accompanied by the results of individual experiments. This report is preliminary in nature; experimental verification is ongoing. The application of the new paradigm in magnetron target design facilitates the fabrication of films of nanostructured medium- and high-entropy alloys with specified chemical compositions, which is the central theme of the Special Issue devoted to functional nanomaterials. Full article

We consider Banach spaces ${\ell }_p\left(\mathcal{C}\right),$ $1\le p<\infty ,$ where the index set $\mathcal{C}$ is the classical Cantor set and study various groups of symmetries of ${\ell }_p\left(\mathcal{C}\right),$ associated with the binary representation of $\mathcal{C}.$ The main purpose of the paper is the investigation of polynomials on ${\ell }_p\left(\mathcal{C}\right)$ that are symmetric (i.e., invariant) with respect to the constructed groups $G.$ We are interested in finding systems of generators of algebras of G-symmetric polynomials for different groups G and we discuss possible applications of G-symmetric polynomials to highly composite physical systems. The generators are useful for descriptions of spectra of algebras of G-symmetric analytic functions on ${\ell }_p\left(\mathcal{C}\right),$ and for the construction of some nontrivial complex homomorphisms of these algebras. Finally, we establish the topological transitivity and hypercyclicity of some shift-like operators on ${\ell }_p\left(\mathcal{C}\right)$ and its subspaces, and translation operators on algebras of symmetric analytic functions on ${\ell }_p\left(\mathcal{C}\right).$ Full article

Background: Short-term facilitation (STF) is a key form of synaptic plasticity driven by activity-dependent increases in presynaptic release probability. However, estimating core synaptic parameters—quantal size ($q$), vesicle pool size ($N$), and release probability ($p_i$)—remains challenging due to nonlinear dynamics and unobservable presynaptic states, limiting the applicability of conventional methods. Methods: We developed a fast analytical framework based on first- and second-order statistical moments of evoked EPSCs, including mean, variance, and cross-stimulus covariance. By constructing composite moment relationships, latent variables were algebraically eliminated, yielding closed-form estimators of synaptic parameters. To improve robustness under strong facilitation, a Tsodyks–Markram (T–M) model-based calibration step was introduced to refine $N$ and $p_i$ using the estimated $q$ as a constraint. Results: Applied to hippocampal CA3–CA1 synapses, the method produced accurate and stable estimates of q across varying noise and sampling conditions. Incorporation of cross-stimulus covariance enabled effective characterization of structured variability that is neglected in classical approaches. While direct estimates of $N$ and $p_i$ showed dispersion, T–M calibration significantly improved stability and physiological consistency. Compared with mean–variance analysis, the proposed method achieved superior performance under facilitating conditions. Conclusions: This hybrid framework enables rapid and reliable estimation of synaptic parameters in STF synapses by exploiting second-order statistical structure. It provides a practical tool for investigating presynaptic mechanisms and may facilitate quantitative studies of synaptic dysfunction in neurological and psychiatric disorders. Full article

A new version of the linear integral representation method is developed for solving inverse problems in geophysics. This approach is applied to the interpretation of anomalous time-dependent field data. The reconstruction of field elements is reduced to solving a system of linear algebraic equations (SLAE) with an approximately given right-hand side. Since the matrix elements of this system are derived analytically, the modeling process is significantly simplified. The article also analyzes how the approximation quality of a non-stationary field element depends on the observation network geometry, enabling its optimization for more accurate detection of geological properties. The proposed method for solving inverse problems for hyperbolic partial differential equations with constant coefficients can also be applied to data described by systems of nonlinear PDEs, provided the target field is represented as a composition of components differing in magnitude. Finally, the results of non-stationary gravity field modeling are presented. Full article

Reliable data transmission over noisy channels requires effective error-correcting codes. While classical algebraic constructions, such as Bose–Chaudhuri–Hocquenghem (BCH) codes, remain industry standards, structured alternatives based on discrete wavelet transforms offer potential benefits in terms of implementation complexity and error resilience. This study presents a comparative analysis of BCH and wavelet-based linear block codes, focusing on their error-correction capability and overall performance under realistic wireless channel conditions. This work evaluates both coding schemes across five channel models: additive white Gaussian noise (AWGN), Rayleigh fading, sinusoidal attenuation, multiplicative Gaussian noise, and a composite Rayleigh-plus-sinusoid channel. Performance is assessed using bit error rate (BER), frame error rate (FER), and decoding reliability across a range of signal-to-noise ratios. Results show that wavelet codes achieve error-correction performance comparable to or slightly better than BCH in most channels. Notably, they demonstrate a consistent advantage in scenarios with periodic or slow-varying interference, outperforming BCH starting from the 1.5 dB SNR threshold where the wavelet code achieves a BER reduction of up to 48% and a 37.5% improvement in FER, significantly enhancing decoding reliability in structured noise environments. These findings indicate that wavelet-based codes are not only viable but, in specific practical environments characterized by structured noise, represent a superior alternative for robust and reliable communication systems. Full article

Colour algebras are noncommutative Jordan algebras and closely related to octonion algebras. They initially emerged in physics since the multiplication of a colour algebra over the real or complex numbers describes the colour symmetry of the Gell–Mann quark model. Over fields of characteristic not equal to two, their structure is now well-known. We initiate the study of colour algebras over a unital commutative base ring R where two is an invertible element, and show when colour algebras can be constructed canonically by employing nondegenerate ternary hermitian forms with trivial determinant. We investigate their structure, their automorphism group and their derivations. We show that there is again a close connection between the colour algebras obtained from hermitian forms and certain types of octonion algebras. Full article

An n-color composition is a colored composition in which a part of size m may come in m colors. This paper gives a new set of n-color-type compositions that admits exhaustive conjugation of its members. Previous attempts at conjugation of n-color compositions have yielded partial results at best. Instead of importing the coloring scheme previously used for partitions, we apply colors directly to the parts of compositions while treating any maximal string of ones as a single part under color assignment. This leads to the definition of n-color compositions of the second kind. As with ordinary compositions, a conjugate may be found using equivalent techniques: symbolic algebra, zig-zag graphs, and line graphs. We conclude with a derivation of the relevant enumeration formulas. Full article

We introduce Recognition Geometry (RG), an axiomatic framework in which geometric structure is not assumed a priori but derived. The starting point of the theory is a configuration space together with recognizers that map configurations to observable events. Observational indistinguishability induces an equivalence relation, and the observable space is obtained as a recognition quotient. Locality is introduced through a neighborhood system, without assuming any metric or topological structure. A finite local resolution axiom formalizes the fact that any observer can distinguish only finitely many outcomes within a local region. We prove that the induced observable map $\overline{R}:{\mathcal{C}}_R\to \mathcal{E}$ is injective, establishing that observable states are uniquely determined by measurement outcomes with no hidden structure. The framework connects deeply with existing approaches: C^*-algebraic quantum theory, information geometry, categorical physics, causal set theory, noncommutative geometry, and topos-theoretic foundations all share the measurement-first philosophy, yet RG provides a unified axiomatic foundation synthesizing these perspectives. Comparative recognizers allow us to define order-type relations based on operational comparison. Under additional assumptions, quantitative notions of distinguishability can be introduced in the form of recognition distances, defined as pseudometrics. Several examples are provided, including threshold recognizers on ${\mathbb{R}}^n$, discrete lattice models, quantum spin measurements, and an example motivated by Recognition Science. In the last part, we develop the composition of recognizers, proving that composite recognizers refine quotient structures and increase distinguishing power. We introduce symmetries and gauge equivalence, showing that gauge-equivalent configurations are necessarily observationally indistinguishable, though the converse does not hold in general. A significant part of the axiomatic framework and the main constructions are formalized in the Lean 4 proof assistant, providing an independent verification of logical consistency. Full article