An adaptive algorithm solving the on-line parameter estimation problem for a broad class of linear systems is proposed. The approach can be applied to systems with delay, distributed-parameter systems, fractional order systems, and others which are stable or stabilized by linear feedback. The proposed scheme can be applied to simultaneously track sufficiently slow changes in process gains, delays, time-constants, diffusivity and other parameters. The proposed method is gradient-based and it yields a relatively efficient numerical implementation. Convergence and robustness of the algorithm are investigated through Lyapunov analysis, yielding explicit convergence conditions which generalize the well-known “Persistence of Excitation” (P. E.) and identifiability requirements arising in conventional adaptive estimation. The method is illustrated by several examples.

Background/Objectives: The number of individuals with lower limb loss (LLL) is rising. Therefore, identifying the walking potential in individuals with LLL and prescribing adequate prosthetic systems are crucial. Various factors can influence participants’ walking ability, to different extents. The aim of the present study was to apply machine learning methods to develop a predictive mode. This model can assist rehabilitation and limb loss care teams in making informed decisions regarding prosthesis prescription and predicting walking ability in individuals with LLL. Methods: The present study was designed as a prospective cross-sectional study encompassing 104 consecutively recruited participants with LLL (average age 62.1 ± 10.9 years, 80 (76.9%) men) at the Medical Rehabilitation Clinic. Demographic, physical, psychological, and social status data of patients were collected at the beginning of the rehabilitation program. At the end of the treatment, K-level estimation of functional ability, a Timed Up and Go Test (TUG), and a Two-Minute Walking Test (TMWT) were performed. Support vector machines (SVM) were used to develop the prediction model. Results: Three decision trees were created, one for each output, as follows: K-level, TUG, and TMWT. For all three outputs, there were eight significant predictors (balance, body mass index, age, Beck depression inventory, amputation level, muscle strength of the residual extremity hip extensors, intact extremity (IE) plantar flexors, and IE hip extensors). For the K-level, the ninth predictor was The Multidimensional Scale of Perceived Social Support (MSPSS). Conclusions: Using the SVM model, we can predict the K-level, TUG, and TMWT with high accuracy. These clinical assessments could be incorporated into routine clinical practice to guide clinicians and inform patients of their potential level of ambulation.

The present paper proposes a framework for the systematic and fruitful application of complex-order operators for modeling and control applications. We emphasize that special care must be taken when using complex-order elements to ensure that their responses to real-valued stimuli are real-valued themselves. The proposed complex-order real-valued elements enable the seamless generalization of their conventional real and integer-order counterparts. We further demonstrate how any linear operator can be extended in much the same way as the differintegral, by “raising” it to a power of a complex order, while ensuring that its kernel remains real-valued. The applicability of our considerations is demonstrated by a model of a compressed natural gas injection system.

Social sustainability in urban and architectural design depends on inclusive, participatory processes that empower communities to actively engage in shaping their environments. This study investigates how emerging digital platforms, specifically Augmented Reality (AR) and decentralized platforms built on blockchain technology (Web3), can function as instruments for broadening public participation and enhancing perceptual access to urban art proposals. An original algorithm generated nine digital abstract sculptures, each with descriptive attributes forming the basis for qualitative analysis across different visualization modes: traditional renderings, Augmented Reality environments, and NFT-based Web3 representations. Through participant voting, each digital sculpture accumulated a measurable level of preference that served to identify which sculpture was perceived as most successful within each visualization context. Comparative analysis revealed how distinct digital interactions shape perception, engagement, and inclusivity of feedback processes. Regression models further predicted voting outcomes, showing that different sculptural attributes played a dominant role depending on the type of visualization. Findings indicate that platform-specific technological affordances substantially shape participatory outcomes. Consequently, the study argues that careful analysis and selection of the digital platform must precede any participatory process, as platform-specific affordances fundamentally condition the inclusivity, accessibility, and overall effectiveness of public engagement in socially sustainable design.

Background and Objectives: Carotid artery stenosis is a significant risk factor for ischemic stroke due to impaired cerebral blood flow (CBF). Even asymptomatic unilateral stenosis can induce subclinical cerebrovascular changes, potentially affecting both hemispheres through collateral circulation. This study aimed to systematically assess cerebral perfusion in asymptomatic individuals with unilateral carotid artery stenosis by comparing ipsilateral and contralateral hemispheres with healthy controls, challenging the assumption that the contralateral hemisphere remains unaffected. Materials and Methods: This cross-sectional study included 114 participants, comprising 54 asymptomatic individuals (mean age 65.5) with significant unilateral carotid stenosis and 60 age-matched controls (mean age 64.8). Cerebral perfusion was assessed using 1.5T Magnetic Resonance Imaging (MRI) with pseudo-continuous arterial spin labeling (pCASL). CBF was measured bilaterally in four predefined middle cerebral artery (MCA) regions: precentral gyrus, lentiform nucleus, insular cortex, and temporal cortex. Statistical analyses included multivariate analysis of variance (MANOVA), analysis of variance (ANOVA), paired t-tests, and discriminant analysis (DA). Results: Significant bilateral reductions in CBF were observed in individuals with carotid stenosis compared to controls (MANOVA and ANOVA, p < 0.001). The greatest perfusion deficit was in the ipsilateral insular cortex (49.88 ± 10.83 mL/100 g/min), followed by intermediate contralateral perfusion (51.49 ± 8.86 mL/100 g/min) and higher control values (58.78 ± 10.44 mL/100 g/min). DA indicated the insular cortex as the region with the highest discriminative contribution (64.7%). Conclusions: Unilateral carotid artery stenosis in asymptomatic individuals is associated with significant bilateral cerebral hypoperfusion, suggesting widespread hemodynamic effects. Pronounced perfusion deficits in the insular cortex underline its vulnerability. The observed contralateral perfusion reductions challenge the traditional use of the contralateral hemisphere as a reference standard, underscoring the need for comprehensive perfusion assessment in carotid artery disease.