Navigating complex social environments requires understanding how individuals are connected within social networks. People are highly efficient at integrating dyadic relationships into larger network structures. However, social networks are embedded within different types of groups (e.g., task groups vs. social categories), raising the question of how group typology shapes the learning and representation of social networks. Across four experiments, we demonstrate that group-related network schemas-specifically, expectations that task groups are more interconnected and centralized than social categories-systematically guide social network learning and representation. Participants exhibited prior expectations about the relational structure of different group types, and memory for social relationships was enhanced when the learned network structure aligned with these schematic expectations, producing a matching effect that was correlated with schema strength (Experiment 1). This effect was causally driven by schema strength: Weakening group-related schemas through explicit descriptions attenuated the matching effect (Experiment 2). Critically, the effect was domain specific: When social relationships were replaced with nonsocial connections (airport-flight networks), the matching effect disappeared despite comparable structural properties and task demands (Experiment 3). Computational modeling using the Successor Representation framework further revealed that schema-structure misalignment reduced multistep abstraction, reflected in lower successor discount parameters (γ), yielding less integrated global representations of social networks (Experiment 4). Together, these findings show that social network learning is guided by top-down group-related schemas. It advances our understanding of social network cognition by highlighting the importance of schema-driven abstraction and by bridging local learning mechanisms with global representational structure. (PsycInfo Database Record (c) 2026 APA, all rights reserved).

Integral representation for a product of two Jacobi functions of the second kind

Universality in nonlinear nonequilibrium systems is typically expressed through scaling laws that render macroscopic behavior insensitive to microscopic details. Whether such universality survives when periodic forcing and nonlocal dissipative memory act simultaneously remains an open question in driven open dynamics. Here, we demonstrate that barrier-crossing processes in periodically driven dissipative systems are governed not merely by modified exponential scaling but by an explicit two-parameter universal response function. Within a semiclassical instanton framework incorporating Floquet modulation and Ohmic environmental coupling, the tunneling exponent factorizes into a system-dependent static contribution and a universal function of two dimensionless control parameters: the normalized driving frequency and the dissipation strength. This factorization arises from the combined modification of a single saddle-point trajectory and does not introduce additional independent scaling variables. Weak-to-moderate dissipation acts as a smooth dynamical renormalization of the effective action, preserving saddle-point structure and enabling controlled analytical expansion. In the high-frequency regime, the response exhibits universal dynamical averaging, while an explicit integral representation establishes a continuous adiabatic-Floquet crossover. Direct numerical evaluation of the nonlocal instanton action confirms that the normalized tunneling exponent exhibits a universal dependence on the driving parameter that is robust across different model systems, demonstrating that driven dissipative barrier crossing defines a distinct two-parameter universality class within nonlinear nonequilibrium dynamics. These results elevate tunneling universality from scaling behavior to a predictive functional description and provide a unifying framework for response phenomena in driven systems with memory.

Two dimensional integral representations via branches of the Bruhat-Tits tree

Melanoma-patient-derived xenograft multi-omics resource melPDomiX maps gain- and loss-of-function alterations.

A short-term memory (STM) version of the Deese/Roediger-McDermott (DRM) paradigm was employed to investigate how true and false recognition evolved as STM contents were lost over a short time window immediately after initial encoding. Presentations of five-word DRM lists were followed by list-specific recognition tests applied either immediately or after a distractor-filled retention interval of 3, 9, or 27 s. Results showed a decrease in the probability of true recognition and an increase in the probability of false recognition as the retention interval grew longer. Based on the fuzzy-trace theory, we suggest that this pattern emerged from the different durability of item-specific phonological representations, which would play a dual role of supporting true memory and preventing false recognition, and integrative semantic representations, whose overlap with the critical items would give rise to the DRM illusion. As a further contribution, our study helps to establish the DRM illusion in STM as a genuine and robust phenomenon by showing that it can be observed even with no delay and no intervening distraction between study and test, and that it occurs when participants are explicitly warned about the presence of semantically related distractors and instructed not to be misled by them.

Our study evaluated airborne microplastics (MPs) captured by spider webs (Agelenidae) in an urban environment (Wrocław, Poland). GC-MS was used to characterize extractable organic compounds linked to MPs, while ATR-FTIR spectroscopy enabled detection of polymer-related signals in solid residues after solvent extraction. All samples contained compounds associated with polymeric materials, including rubber- and silicone-related components, with rubber signals detected at all sites. No significant differences were observed between central and suburban locations, indicating a relatively uniform distribution of airborne MPs. ATR-FTIR results further suggested the occurrence of tire-derived materials in all samples, along with polyamides (Nylon 6; 40%), polypropylene-related materials (including Epcar 5875; ~20%), polyvinyl alcohol (20%), and polyethylene (LDPE; 13%), expressed as frequency of occurrence across samples. Overall, the results demonstrate that spider webs can serve as accessible passive samplers, providing a qualitative and integrative representation of airborne microplastic contamination in urban environments.

A new structure of Hermite polynomials associated with the Mittag–Leffler function is introduced in this paper. A generating function in terms of Mittag–Leffler function is obtained. Several differential recurrence relations are established. Pure recurrence relations are derived without the use of differential recurrence relations. Properties of the gamma function are used to obtain integral representations and integral duplication formulae.

This study investigates transient heat conduction in a separable class of anisotropic functionally graded materials with spatially and temporally varying thermal properties and an internal heat source term. The governing transient heat equation with variable coefficients is first transformed into an equivalent form with constant coefficients through an appropriate variable transformation under prescribed separability conditions on the material properties. The resulting equation is then mapped into the Laplace domain to eliminate the time derivative and simplify the transient formulation. A fundamental solution in the Laplace space is employed to reformulate the transformed equation into a boundary integral representation containing source-related domain integrals, which serves as the basis for the boundary element formulation. The resulting integral equations are discretized using boundary elements, while the domain integrals are evaluated numerically through domain discretization in conjunction with particular solutions. The transient solution in the physical time domain is recovered by applying the Stehfest numerical inversion technique for the Laplace transform. Several benchmark test problems with known analytical solutions are presented to assess the accuracy, convergence, and stability of the proposed approach. Numerical results demonstrate that the developed boundary element formulation provides accurate and consistent solutions for transient heat conduction problems in anisotropic functionally graded materials satisfying the prescribed transformation conditions.

I obtain an integral representation of the exponential function exp ⁡ ( − γ ) using an elementary reduction to the Gaussian integral in a lively and engaging manner.

In this paper, we consider the operational calculus of Mellin transforms of the Faxén, Macdonald and Whittaker functions to establish some identities in terms of the Airy functions. The convolution-type integrals involving these functions provide us to derive the Mellin–Barnes integrals coinciding with the Mellin–Barnes integrals of the Airy functions. The Legendre duplication formula is the main tool for simplifications of the products and ratios of gamma functions in our computations.

Single-cell multi-omics technologies enable simultaneous interrogation of transcriptional and epigenomic states at single-cell resolution, providing powerful means to dissect cellular heterogeneity and regulatory mechanisms. However, effective integration of single-cell multi-omics data remains challenging due to extreme sparsity, high dimensionality, and cross-modal heterogeneity, which often lead to distorted similarity structures, information loss, and limited biological interpretability in existing methods. Here, we propose scFNSA, a factorized node-set attentive framework for integrative analysis of single-cell multi-omics data that explicitly decouples modality-specific feature learning from graph-based relational modeling. scFNSA first learns aligned low-dimensional representations for individual modalities through multi-view variational inference and subsequently models complex cellular dependencies via attention-guided graph learning with structured node masking. This design enables robust cross-modal structural alignment while effectively mitigating noise propagation and oversmoothing commonly encountered in deep graph neural networks. Across multiple single-cell multi-omics datasets, scFNSA consistently improves integrative representation quality and cell type resolution compared with state-of-the-art approaches. By decoupling feature extraction from relational inference, scFNSA provides a robust and interpretable framework for single-cell multi-omics integration, facilitating more accurate characterization of cellular states and underlying regulatory landscapes.

We consider the divided-difference operator D ω , the q-derivative one H q and the algebraic equation x 2 u = λxv , λ ∈ C ∖ { 0 } , in the regular case for the forms u and v. We study the D ω -semiclassical character and the variation of the class s ~ of u (respectively the H q -semiclassical case) where v is a symmetric D ω -semiclassical form of class s (respectively a symmetric H q -semiclassical form of class s). Some illustrative examples are highlighted in the two cases and integral representations or discrete one's are obtained.

Purpose This study aims to investigate how stakeholder cocreation in 3D city mapping initiatives can extend the role of digital urban platforms beyond administrative efficiency toward the negotiation and enhancement of place attractiveness. Drawing on a participatory case study of Trollhättan, Sweden, the paper explores the needs, expectations and aspirations articulated by diverse stakeholder groups regarding collaborative 3D mapping, and examines how these perspectives, when enacted through cocreation processes, shape and negotiate place attractiveness in small- and mid-sized cities. Design/methodology/approach The study adopts an abductive case-study design, integrating the social construction of technology (SCOT) theory, participatory design and place attractiveness research into an analytical framework. Primary data were generated through eight cocreation workshops involving 32 participants across five stakeholder clusters in Trollhättan. Data were analyzed using a three-step thematic coding process of open, axial and selective coding, supported by a coding matrix linking empirical themes to theoretical constructs. The case-study approach enables contextualized understanding of complex socio-technical dynamics in a small- and mid-sized city context. Findings The findings show that stakeholders interpret the 3D map not merely as an administrative visualization tool but as an evolving socio-technical platform through which diverse needs, expectations and aspirations are articulated and place attractiveness is negotiated and coproduced. Across six themes, stakeholders articulated diverse expectations related to visualization, usability, data integration, real-time responsiveness, civic dialogue and temporal representation. These interpretations reflect distinct technological frames shaped by stakeholders’ institutional roles and lived experiences. The analysis demonstrates that identical technical features acquire multiple meanings, activating different dimensions of place attractiveness. Consequently, collaborative 3D mapping functions as a participatory infrastructure in which urban value is continuously negotiated, extending place attractiveness beyond static representations toward dynamic, socio-technical engagement. Originality/value The study makes three contributions. An integrated analytical framework combining SCOT, participatory design and place attractiveness research is developed to explain how stakeholder cocreation on digital urban platforms shapes multiple dimensions of place attractiveness. Place attractiveness theory is advanced by introducing a temporal dimension, arguing that attractiveness in digital contexts spans past, present and future rather than reflecting present-state evaluations alone. Finally, participation is reframed not as input preceding design decisions, but as an ongoing process in which urban meaning is continuously negotiated within, and partly constituted by, the platform itself.

This paper investigates pricing formulas for geometric average and arithmetic average Asian call and put options under an uncertain exponential Ornstein–Uhlenbeck stock model. Employing the α-path technique from uncertainty theory, we derive closed-form integral representations for all four option types and rigorously establish their monotonicity properties with respect to the strike price, interest rate, time to expiration, and initial stock price. A comparative analysis with Liu’s standard uncertain stock model and a discussion of the option Greeks are also provided. Numerical examples are given to illustrate the practical applicability of the proposed formulas.

Delayed-onset muscle soreness (DOMS), occurring 24-72 h postexercise, is characterized by pain and decreased force production. Recent evidence suggests DOMS may result from damage to muscle spindle afferents rather than to muscle fibers. We hypothesized that this type of disruption impairs the central integration of proprioceptive inputs, reducing the efficiency of body-related motor imagery. In a controlled study, young sports science students were assigned to a DOMS group (n = 47)-induced by whole body eccentric exercises-or a control group (n = 47). All participants then performed mental rotation tasks; for the DOMS group, this assessment took place 48 h postexercise. The stimuli took the form of body images (arms and legs), and there was also a control condition involving nonbody images (the number "2"). Response times and accuracy were measured. Accuracy in motor imagery tasks was unaffected by DOMS, indicating preserved body representations. However, participants with DOMS responded more slowly than control participants to the arm images (trend, P = 0.06; 1,189.3 ± 51.1 ms vs. 1,044.7 ± 42.7 ms, respectively) and leg images (P = 0.03; 1,280.2 ± 65.5 ms vs. 1,121.5 ± 42.3 ms, respectively), whereas no significant difference was observed for the number images (P = 0.55; 792.9 ± 29.5 ms vs. 831.2 ± 25.7 ms, respectively). This selective slowing suggests that DOMS transiently reduces the efficiency, but not the accuracy, of proprioceptive-motor integration. These results suggest that acute muscle soreness imposes a measurable computational cost on the sensorimotor system, requiring participants to mobilize time-consuming internal models to maintain representational accuracy in the face of peripheral proprioceptive noise.NEW & NOTEWORTHY This study demonstrates that exercise-induced muscle soreness selectively impairs the efficiency of proprioceptive integration during body-related motor imagery, but without affecting global cognitive performance. By revealing how temporary peripheral disturbances alter internal sensorimotor representations, these findings provide new insights into the neural mechanisms of sensorimotor integration. This work highlights the functional consequences of acute muscle soreness for motor planning and offers a framework for understanding how the nervous system adapts to temporary proprioceptive disruption.

A navigation-guided 3D breast ultrasound scanning and reconstruction system for automated multi-lesion spatial localization and diagnosis.

ABSTRACT In this paper, the linear theory of Moore–Gibson–Thompson (MGT) thermoelasticity for materials with voids is examined, taking into account the coupled effect of material deformation, the concept of pore volume fraction, and the MGT law of heat conduction. The basic boundary value problems (BVPs) associated with steady vibrations within this framework are investigated. Specifically, the integral representations of regular vector functions are obtained, the surface (single‐layer and double‐layer) and volume potentials are constructed, and their essential properties are established. These BVPs are reduced to singular integral equations, which are always solvable and for which Noether's theorems hold. Finally, the existence theorems for classical solutions to the internal and external BVPs are proven using the potential method and the theory of singular integral equations.

We study fractional and complex powers of a fixed directional derivative in Rd, defined via a Marchaud-type singular integral representation. Under explicit convergence assumptions, this yields a pointwise nonlocal realization along rays. We then formulate a Ramanujan–Hardy approach to fractional directional differentiation based on analytic interpolation of the directional jet at a point. This construction is local in jet space and is governed by Hardy’s formulation of Ramanujan’s Master Theorem. We emphasize that the resulting Ramanujan–Hardy derivative is defined through a Hardy-admissible interpolant of the directional jet. As an application, we investigate fractional directional derivatives of the Newtonian kernel in dimension d≥3. After a justified regularization and reduction to a Marchaud-type integral, we obtain a one-dimensional integral representation and a zonal harmonic description of the resulting function. This leads to a fractional Maxwell–Gegenbauer identity for 0<ℜ(s)<1, expressing the fractional directional derivative of ∥x∥2−d in terms of Gegenbauer functions of complex degree. In this way, the classical Maxwell multipole formula appears as the integer-order case of a continuous analytic family. Moreover, the fractional operator preserves the main structural properties of the Newtonian kernel, including homogeneity, rotational invariance, and harmonicity away from the origin. The paper thus connects Mellin analysis, Ramanujan’s Master Theorem, fractional calculus, and harmonic analysis on the sphere, while clarifying the distinction between Marchaud and jet-interpolation constructions of fractional directional operators.

This paper presents a comprehensive system of integration formulas for the generalized p-k-Mittag-Leffler function.By extending and synthesizing multiple mathematical results through the properties of the k-Gamma function, we derive general integral representations that serve as generating relations for various special functions. The resulting formulas are expressed using generalized Wright and Fox-Wright functions. Furthermore, we examine several special cases to demonstrate the functional relationship between our results and the classical and p-k-Mittag-Leffler function frameworks.