Search Results (136)

We analyze long-range dependence (LRD) for word time series, understood as a slower than exponential decay of the two-point Shannon mutual information. We achieve this by examining the decay of the cosine correlation, a proxy object defined in terms of the cosine similarity between word2vec embeddings of two words, computed by an analogy to the Pearson correlation. By the Pinsker inequality, the squared cosine correlation between two random vectors lower bounds the mutual information between them. Using the Standardized Project Gutenberg Corpus, we find that the cosine correlation between word2vec embeddings exhibits a readily visible stretched exponential decay for lags roughly up to 1000 words, thus corroborating the presence of LRD. By contrast, for the Human vs. LLM Text Corpus entailing texts generated by large language models, there is no systematic signal of LRD. Our findings may support the need for novel memory-rich architectures in large language models that exceed not only hidden Markov models but also Transformers. Full article

In this study, we investigate the impact of rising time on alternating current (AC) stress-induced degradation in amorphous indium–tin–gallium–zinc oxide (a-ITGZO) TFTs through both experiments and simulations. When AC bias stresses with rising and falling times (t_r-f) of 400 ns, 200 ns, and 100 ns were applied to the a-ITGZO TFTs, the threshold voltage (V_TH) shifted positively by 0.97 V, 2.68 V, and 2.83 V, respectively. These experimental results align with a stretched exponential model, which attributes the V_TH to electron trapping in bulk dielectric states or at interface traps. The simulation results further validate the stretched exponential model by illustrating the potential distribution across the dielectric and channel layers as a function of t_r-f and the density of states in the a-ITGZO TFT. Full article

This study presents an analytical solution to examine the mechanical behavior of an incompressible, functionally graded hyperelastic cylinder under combined extension and torsion. The exp-exp strain energy density function characterizes the hyperelastic material, with parameters varying exponentially along the radial direction. To validate the solution, finite element simulations using a custom UHYPER in ABAQUS are performed. The analytical and numerical results show strong agreement across different stretch and twist levels. The stress distribution and maximum stress are significantly influenced by the exponential parameter governing material gradients. Unlike axial stretch, torsion induces a more intricate longitudinal stress distribution, with large twisting producing two extrema that shift toward the cylinder’s center and outer surface. Longitudinal stress primarily governs von Mises stress and strain energy density variations across the radial direction. A critical axial stretch is identified, below which torsion-induced axial force transitions to compression, elongating the cylinder during twisting. Beyond this stretch, the axial force shifts from tensile to compressive with increasing twist, causing initial shortening before further elongation. Full article

This work develops a unified size-dependent shear deformation theory (SDSDT) to analyze the free vibration behavior of a functionally graded (FG) magneto-electro-elastic (MEE) microplate under fully simply supported conditions, open- or closed-circuit surface conditions, biaxial compression, magnetic and electric potentials, and uniform temperature changes based on consistent couple stress theory (CCST). The FG-MEE microplate is composed of BaTiO₃ (a piezoelectric material) and CoFe₂O₄ (a magnetostrictive material). Various CCST-based SDSDTs, considering couple stress and thickness stretching effects, can be reproduced by employing a generalized shape function that characterizes shear deformation distributions along the thickness direction within the unified SDSDT. These CCST-based SDSDTs encompass the size-dependent classical plate theory (CPT), first-order shear deformation theory (SDT), Reddy’s refined SDT, exponential SDT, sinusoidal SDT, and hyperbolic SDT. The unified SDSDT is validated by comparing its solutions with relevant three-dimensional solutions available in the literature. After validation and comparison studies, we conduct a parametric study, whose results indicate that the effects of thickness stretching, material length-scale parameter, inhomogeneity index, and length-to-thickness ratio, as well as the magnitude of biaxial compressive forces, electric potential, magnetic potential, and uniform temperature changes significantly impact the microplate’s natural frequency. Full article

In an era where social media shapes public opinion, understanding information spreading is key to grasping its broader impact. This paper explores the intricacies of information diffusion on Twitter, emphasizing the significant influence of content saturation on user engagement and retweet behaviors. We introduce a diffusion model that quantifies the likelihood of retweeting relative to the number of accounts a user follows. Our findings reveal a significant negative correlation where users following many accounts are less likely to retweet, suggesting a saturation effect in which exposure to information overload reduces engagement. We validate our model through simulations, demonstrating its ability to replicate real-world retweet network characteristics, including diffusion size and structural properties. Additionally, we explore this saturation effect on the temporal behavior of retweets, revealing that retweet intervals follow a stretched exponential distribution, which better captures the gradual decline in engagement over time. Our results underscore the competitive nature of information diffusion in social networks, where tweets have short lifespans and are quickly replaced by new information. This study contributes to a deeper understanding of content propagation mechanisms, offering a model with broad applicability across contexts, and highlights the importance of information overload in structural and temporal social media dynamics. Full article

Compared to natural and shale gas, studies on predicting production specific to coalbed methane (CBM) are still relatively limited, and mainly use decline curve methods such as Arps, Stretched Exponential Decline Model, and Duong’s model. In recent years, machine learning (ML) methods applied to CBM production prediction have focused on the significant data characteristics of production, achieving more accurate predictions. However, throughout the application process, these models require a large amount of data for training and can only achieve accurate forecasts over a short period, such as 30 days. This study constructs a hybrid ML model by integrating a long short-term memory (LSTM) network and Transformer architecture. The model is trained using the mean absolute error (MAE) loss function, optimized using the Adam optimizer, and finally evaluated using metrics such as MAE, root mean square error (RMSE), and R squared (R²) scores. The results show that the LSTM-Attention (LSTM-A) hybrid model based on small training datasets can accurately capture the CBM production trend and is superior to traditional methods and the LSTM model regarding prediction accuracy and effective prediction time interval. The methodologies established and the results obtained in this study are of great significance to accurately predict CBM production. It is also helpful to better understand the mechanisms of CBM production. Full article

This study investigates the functionalization of a poplar biochar (PB), obtained by high-temperature pyrolysis, under oxidative conditions typically used in organic synthesis. In particular, concentrated nitric acid, a sulfonitric mixture and a piranha mixture were applied as oxidants at different temperatures and reaction times. In order to assess the outcome of the reaction conditions on the characteristics of the resultant products, these were characterized by a combination of imaging (SEM), spectroscopic (ATR-FTIR, RAMAN) and FFC-NMR relaxometric techniques. The latter techniques, rationalized in terms of the Kohlrausch-type stretched exponential kinetic model, were analyzed using a recently developed heuristic Monte Carlo method, providing insights into the water dynamics within material pore networks. Additionally, the water-holding capacity of the modified biochars and their abilities to adsorb some model dyes were evaluated. The results clarify the relationship between oxidative treatment conditions and biochar properties, highlighting their impact on both structural modifications and water dynamics within the porous network, and enabling us to identify the best reaction conditions for optimizing the features of the oxidized product. Full article

Understanding mixing patterns in urban networks is crucial for exploring the connectivity relationships between nodes and revealing the connection tendencies. Based on multi-source data (Baidu index data, investment data of listed companies, high-speed rail operation data, and highway network data) from 2017 to 2019 across seven national-level urban agglomerations, this study introduces complex network assortativity coefficients to analyze the mechanisms of urban relationship formation from two dimensions, structural features and socioeconomic attributes, to evaluate how these features shape urban agglomeration networks and reveal the distribution of network assortativity coefficients across urban agglomerations to classify diverse developmental patterns. The results show that the sampled cities exhibit heterogeneous characteristics following a stretched exponential distribution in urban structural features and a log-normal distribution in socioeconomic attributes, demonstrating significant resource mixing patterns. Different types of urban agglomeration networks display distinct assortativity characteristics. Information network mixing patterns within urban agglomerations are insignificant; investment relationships, high-speed rail, and highway networks demonstrate significant centripetal mixing patterns. The assortativity coefficients of urban agglomerations follow a unified general probability density distribution, suggesting that urban agglomerations objectively tend toward centripetal agglomeration. Full article

When examined at the nanometer length scale, metallic liquids exhibit extensive ordering. Bonding enthalpies are balanced against entropic tendencies resulting in a rich complicated behavior that leads to clustering that depends on temperature but evolves on picosecond time scales. The structural organization of metallic liquids affects their thermophysical properties, such as viscosity and density, thus influencing the ability of a metallic liquid to form useful technological phases, such as metallic glasses. The time-dependent pair correlation function (the Van Hove function) was determined for metallic-glass forming Cu₄₉Zr₄₅Al₆ at 1060 °C from time-of-flight inelastic neutron scattering measurements made using the Neutron Electrostatic Levitation facility at the Spallation Neutron Source. The time for changes in local atomic connectivity, which is the timescale of atomic ordering, was determined by examining the decay of the nearest neighbor peak. The results of rigorous statistical analyses were used to distinguish between competing models of ordering, suggesting that a stretched exponential model of coordination number change is valid for this system. Full article

Non-linear least squares (NLS) methods are commonly used for quantitative magnetic resonance imaging (MRI), especially for multi-exponential T1ρ mapping, which provides precise parameter estimation for different relaxation models in tissues, such as mono-exponential (ME), bi-exponential (BE), and stretched-exponential (SE) models. However, NLS may suffer from problems like sensitivity to initial guesses, slow convergence speed, and high computational cost. While deep learning (DL)-based T1ρ fitting methods offer faster alternatives, they often face challenges such as noise sensitivity and reliance on NLS-generated reference data for training. To address these limitations of both approaches, we propose the HDNLS, a hybrid model for fast multi-component parameter mapping, particularly targeted for T1ρ mapping in the knee joint. HDNLS combines voxel-wise DL, trained with synthetic data, with a few iterations of NLS to accelerate the fitting process, thus eliminating the need for reference MRI data for training. Due to the inverse-problem nature of the parameter mapping, certain parameters in a specific model may be more sensitive to noise, such as the short component in the BE model. To address this, the number of NLS iterations in HDNLS can act as a regularization, stabilizing the estimation to obtain meaningful solutions. Thus, in this work, we conducted a comprehensive analysis of the impact of NLS iterations on HDNLS performance and proposed four variants that balance estimation accuracy and computational speed. These variants are Ultrafast-NLS, Superfast-HDNLS, HDNLS, and Relaxed-HDNLS. These methods allow users to select a suitable configuration based on their specific speed and performance requirements. Among these, HDNLS emerges as the optimal trade-off between performance and fitting time. Extensive experiments on synthetic data demonstrate that HDNLS achieves comparable performance to NLS and regularized-NLS (RNLS) with a minimum of a 13-fold improvement in speed. HDNLS is just a little slower than DL-based methods; however, it significantly improves estimation quality, offering a solution for T1ρ fitting that is fast and reliable. Full article

The direct discharge of cationic surfactants into environmental matrices has exponentially increased due to their wide application in many products. These compounds and their degraded products disrupt microbial dynamics, hinder plant survival, and affect human health. Therefore, there is an urgent need to develop electroanalytical assessment techniques for their identification, determination, and monitoring. In our study, ZnO-PANI nanocomposites were electrodeposited on a glassy carbon electrode (GCE), followed by the immobilization of laccase enzymes and the electrodeposition of polypyrrole (PPy), to form a biosensor that was used for the detection of CTAB. A UV-Vis analysis showed bands corresponding to the π-π* transition of benzenoid and quinoid rings, π-polaron band transition and n-π*polaronic transitions associated with the extended coil chain conformation of PANI, and the presence and interaction of ZnO with PANI and type 3 copper in the laccase enzymes. The FTIR analysis exhibited peaks corresponding to N-H and C-N stretches and bends for amine, C=C stretches for conjugated alkenes, and a C-H bend for aromatic compounds. A high-resolution scanning electron microscopy (HRSEM) analysis proved that PANI and ZnO-PANI were deposited as fibres with hairy topography resulting from covalent bonding with the laccase enzymes. The modified electrode (PPy-6/GCE) was used as a platform for the detection of CTAB with three linear ranges of 0.5–100 µM, 200–500 µM, and 700–1900 µM. The sensor displayed a high sensitivity of 0.935 μA μM⁻¹ cm⁻², a detection limit of 0.0116 µM, and acceptable recoveries of 95.02% and 87.84% for tap water and wastewater, respectively. Full article

We study a quantum cone, a novel structure composed of multiple quantum dots with gradually decreasing diameters from the base to the top. The dot distribution leads to a dispersive radiated spectrum. The blue edge of the spectrum is determined by the quantum confinement of excitons on top of the cones, while the red edge is determined by the bandgap of a semiconductor. We observe the kinetics of photoluminescence by obeying the stretch-exponential law from quantum cones formed on the surface of diamond-like carbon (DLC). They are explained by an increase in the lifetime of excitons along the height of the cone from the top to the base of the cone and an increasing concentration of excitons at the base due to their drift in the quasi-built-in electric field of the quantum cone. The possible visualization of the quantum cone tops of DLC using irradiation by a UV light source is shown. A quantum cone is an innovative nano-source of light because it substitutes for two elements in a conventional spectrometer: a source of light and a dispersive element—an ultrafast monochromator. These features enable the building of a nano-spectrometer to measure the absorbance spectra of virus and molecule particles. Full article

The behavior of polyzwitterions, constituted by dipole-like zwitterionic monomers, is significantly different from that of uniformly charged polyelectrolytes. The origin of this difference lies in the intrinsic capacity of polyzwitterions to self-associate intramolecularly and associate with interpenetrating chains driven by dominant dipolar interactions. Earlier attempts to treat polyzwitterions implicitly assume that the dipoles of zwitterion monomers are randomly oriented. At ambient temperatures, the dipolar zwitterion monomers can readily align with each other generating quadrupoles and other multipoles and thus generating heterogeneous structures even in homogeneous solutions. Towards an attempt to understand the role of such dipolar associations, we present a mean field theory of solutions of polyzwitterions. Generally, we delineate a high-temperature regime where the zwitterion dipoles are randomly oriented from a low-temperature regime where quadrupole formation is significantly prevalent. We present closed-form formulas for: (1) Coil-globule transition in the low-temperature regime, the anti-polyelectrolyte effect of chain expansion upon addition of low molar mass salt, and chain relaxation times in dilute solutions. (2) Spontaneous formation of a mesomorphic state at the borderline between the high-temperature and low-temperature regimes and its characteristics. A universal law is presented for the radius of gyration of the microgel, as a proportionality to one-sixth power of the polymer concentration. (3) Swelling equilibrium of chemically cross-linked polyzwitterion gels in both the high temperature and low-temperature regimes. Addressing the hierarchical internal dynamics of polyzwitterion gels, we present a general stretched exponential law for the time-correlation function of gel displacement vector, that can be measured in dynamic light scattering experiments. The present theory is of direct experimental relevance and additional theoretical developments to all polyzwitterion systems, and generally to biological macromolecular systems such as intrinsically disordered proteins. Full article

Thermoplastic polymers exhibit relatively limited surface energies and this results in poor adhesion when bonded to other materials. Plasma surface modification offers the potential to overcome this challenge through the functionalisation of the polymer surfaces. In this study, three polymers of differing hydrophobicity (HDPE, PA12, and PA6) were subjected to a novel, atmospheric, μPlasma surface treatment technique, and its effectiveness at increasing the surface energies was evaluated via measurement of the contact angle. To characterise the physical and chemical changes following μPlasma surface modification, the surface morphology was observed using atomic force microscopy (AFM), and the functionalisation of the surface was evaluated using infrared spectroscopy. Immediately after treatment, the contact angle decreased by 47.3° (HDPE), 42.6° (PA12), and 50.1° (PA6), but the effect was not permanent in that there was a pronounced relaxation or ageing phenomenon in operation. The ageing process over five hours was modelled using a modified stretched exponential function Kohlrausch–Williams–Watts (KWW) model, and it was found that the ageing rate was dependent on the hydrophilicity of polymers, with polyamides ageing more rapidly than polyethylene. Full article

In a previous investigation, the authors proposed nitrogen as a possible candidate for exploiting the donor spin in silicon quantum devices. This system is characterized by a ground state deeper than the other group V impurities in silicon, offering less stringent requirements on the device temperature necessary to access the unionized state. The nitrogen donor is slightly displaced from the substitutional site, and upon heating, the system undergoes a motional transition. In the present article, we show the results from our investigation on the spin–relaxation times in ^natSi and ²⁸Si substrates and discuss the motional effects on relaxation. The stretched exponential relaxation observed is interpreted as a distribution of spin–lattice relaxation times, whose origin is also discussed. This information greatly contributes to the assessment of a nitrogen-doped silicon system as a potential candidate for quantum devices working at temperatures higher than those required for other group V donors in silicon. Full article