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16 pages, 621 KB  
Article
Administratively Defined Functional Vulnerability and Adverse Short-Term Outcomes in Older Adults Hospitalized with Crohn’s Disease Flares: A Propensity-Matched Multicenter Cohort Study
by Noor Albusta, Mohamed Abdulla, Ali Bosta and Rehab Almarzooq
Diseases 2026, 14(7), 225; https://doi.org/10.3390/diseases14070225 (registering DOI) - 23 Jun 2026
Abstract
Background/Objectives: Functional vulnerability may identify older adults hospitalized with Crohn’s disease flares who are at increased risk for adverse outcomes, but its prognostic significance in this setting remains incompletely defined. We evaluated the association between administratively defined functional vulnerability, identified using administrative diagnostic [...] Read more.
Background/Objectives: Functional vulnerability may identify older adults hospitalized with Crohn’s disease flares who are at increased risk for adverse outcomes, but its prognostic significance in this setting remains incompletely defined. We evaluated the association between administratively defined functional vulnerability, identified using administrative diagnostic codes, and short-term clinical outcomes among adults aged ≥65 years hospitalized with Crohn’s disease flares. Methods: We conducted a retrospective cohort study using the TriNetX US Collaborative Research Network through February 2026. Functional vulnerability was identified using ICD-10-CM codes for frailty, sarcopenia, cachexia, abnormal weight loss, muscle weakness, gait/mobility abnormalities, or reduced mobility within 12 months before or during the index hospitalization. Patients coded only for nonspecific weakness or fatigue were excluded from the functional vulnerability cohort. Patients underwent 1:1 propensity score matching using demographic, comorbidity, Crohn’s disease-related, medication, nutritional, and laboratory variables. The primary outcome was 30-day all-cause mortality. Results: Among 18,420 eligible patients, 2846 met criteria for functional vulnerability, and 15,574 did not. After matching, 2720 patients remained in each cohort. Functional vulnerability was associated with higher 30-day mortality (RR 1.61, 95% CI 1.21–2.14), 90-day mortality (RR 1.40, 95% CI 1.14–1.72), bowel surgery (RR 1.29, 95% CI 1.07–1.56), sepsis (RR 1.41, 95% CI 1.18–1.68), acute kidney injury (RR 1.26, 95% CI 1.10–1.44), ICU admission (RR 1.32, 95% CI 1.13–1.55), TPN use (RR 1.47, 95% CI 1.20–1.79), and 90-day readmission (RR 1.17, 95% CI 1.07–1.29). Functionally vulnerable patients also had longer hospital stays (8.9 vs. 6.7 days; mean difference 2.2 days, 95% CI 1.9–2.5). Conclusions: Administratively defined functional vulnerability identified through diagnostic coding was associated with worse short-term outcomes among older adults hospitalized with Crohn’s disease flares. Although functional vulnerability is a recognized predictor of adverse outcomes across hospitalized populations broadly, these findings quantify its prognostic significance specifically in Crohn’s disease flare hospitalizations and suggest that functional vulnerability may identify a high-risk geriatric IBD phenotype that could benefit from early multidisciplinary assessment, nutritional optimization, rehabilitation planning, and post-discharge care coordination. Full article
15 pages, 1148 KB  
Article
Admission Serum Total Brain-Derived Neurotrophic Factor and Angiographic No-Reflow in Non-ST-Segment Elevation Myocardial Infarction Undergoing Percutaneous Coronary Intervention
by Alp Yıldırım, Mustafa Çelik, Müzeyyen Gizem Parmak, Muhammet Salih Ateş, Erdoğan Sökmen and Kenan Güçlü
Medicina 2026, 62(7), 1211; https://doi.org/10.3390/medicina62071211 (registering DOI) - 23 Jun 2026
Abstract
Background and Objectives: Angiographic no-reflow (NRF) after percutaneous coronary intervention (PCI) reflects impaired microvascular reperfusion despite successful treatment of the epicardial culprit lesion. Brain-derived neurotrophic factor (BDNF) is a neurotrophin involved in endothelial signaling, platelet biology, inflammation, and angiogenesis. Its relationship with [...] Read more.
Background and Objectives: Angiographic no-reflow (NRF) after percutaneous coronary intervention (PCI) reflects impaired microvascular reperfusion despite successful treatment of the epicardial culprit lesion. Brain-derived neurotrophic factor (BDNF) is a neurotrophin involved in endothelial signaling, platelet biology, inflammation, and angiogenesis. Its relationship with NRF in non-ST-segment elevation myocardial infarction (NSTEMI) remains insufficiently characterized. Materials and Methods: This single-center prospective observational cohort study included 700 consecutive NSTEMI patients undergoing culprit-lesion PCI. Admission serum total BDNF was measured before PCI using a standardized enzyme-linked immunosorbent assay protocol. Angiographic NRF was defined as final thrombolysis in myocardial infarction (TIMI) flow <3 and/or TIMI 3 flow with myocardial blush grade (MBG) 0–1 in the absence of residual stenosis, dissection, severe spasm, or other mechanical obstruction. Four sequential logistic regression models were used to evaluate the stability of the association between BDNF and NRF: Model 1 adjusted for clinical variables; Model 2 further adjusted for laboratory and inflammatory variables; Model 3 further adjusted for cardiac injury and functional variables; and Model 4 further adjusted for angiographic and procedural variables. Discrimination, calibration, reclassification, decision-curve analysis, and internal validation were assessed. Results: NRF occurred in 114 of 700 patients (16.3%). Serum total BDNF was higher in the NRF group than in the reflow group [555 (465–688) vs. 386 (292–496) pg/mL, p < 0.001]. BDNF remained independently associated with NRF across sequential models: Model 1 OR 1.67 per 100 pg/mL (95% CI 1.43–1.96), Model 2 OR 1.49 (95% CI 1.24–1.79), Model 3 OR 1.41 (95% CI 1.16–1.72), and Model 4 OR 1.31 (95% CI 1.07–1.60). The BDNF-only AUC was 0.787, while the final BDNF-enriched Model 4 reached an AUC of 0.866. The optimism-corrected bootstrap AUC was 0.852 and the 10-fold cross-validated AUC was 0.845. Conclusions: Higher admission serum total BDNF was independently associated with angiographic NRF in NSTEMI patients undergoing PCI and improved risk discrimination when added to clinical, biochemical, cardiac, and angiographic predictors. These findings suggest that serum total BDNF may reflect a context-dependent biomarker signal related to acute thrombo-inflammatory, platelet-associated, and microvascular injury pathways; however, the observed incremental value was modest and requires external validation. Full article
(This article belongs to the Special Issue Acute Coronary Syndromes: Diagnosis, Management, and Risk Prediction)
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17 pages, 1642 KB  
Article
Metabolic Chaos After Aneurysmal Subarachnoid Haemorrhage: Longitudinal Glucose–Potassium Ratio Dynamics and Clinical Outcomes
by Adrianna Lebiedzińska, Jarosław Kędziora, Jowita Woźniak, Waldemar Goździk and Małgorzata Burzyńska
Biomedicines 2026, 14(6), 1402; https://doi.org/10.3390/biomedicines14061402 (registering DOI) - 22 Jun 2026
Abstract
Background: Hyperglycemia after aneurysmal subarachnoid hemorrhage (aSAH) is associated with poor outcome, but admission glucose may not reflect dynamic metabolic stress during neurocritical care. Unlike previous studies focused primarily on admission measurements, we evaluated longitudinal glycemic trajectories and repeated glucose–potassium ratio (GPR) assessment [...] Read more.
Background: Hyperglycemia after aneurysmal subarachnoid hemorrhage (aSAH) is associated with poor outcome, but admission glucose may not reflect dynamic metabolic stress during neurocritical care. Unlike previous studies focused primarily on admission measurements, we evaluated longitudinal glycemic trajectories and repeated glucose–potassium ratio (GPR) assessment across multiple observation windows in relation to clinical outcomes after aSAH. Methods: This retrospective single-center cohort study included 199 consecutive adults with aSAH treated between 2014 and 2025. Serial glucose and potassium measurements obtained during intensive care unit (ICU) stay were used to calculate admission values, longitudinal means across predefined observation windows, glycemic variability, hyperglycemia burden, and GPR. Primary outcomes were 30-day mortality and poor functional outcome at discharge (modified Rankin Scale ≥ 3). Secondary outcomes included delayed cerebral ischemia (DCI), delayed neurological deterioration (DND), transcranial Doppler (TCD) vasospasm, neurological deficit at ICU discharge, and length of stay. Results: Thirty-day mortality occurred in 35 patients (17.6%). Longitudinal metabolic markers demonstrated stronger associations with outcomes than admission values. Mean 30-day GPR was independently associated with mortality (OR 2.56, 95% CI 1.66–4.16; p < 0.001) and poor functional outcome (OR 2.90, 95% CI 1.80–5.03; p < 0.001). Hyperglycemia burden was associated with mortality (OR 1.10 per additional hyperglycemic day, 95% CI 1.02–1.20; p = 0.020) and poor functional outcome (OR 1.39, 95% CI 1.19–1.71; p < 0.001). Early GPR during the early brain injury period was associated with DCI (OR 1.40, 95% CI 1.01–1.93; p = 0.043), whereas 30-day GPR was associated with DND (OR 1.47, 95% CI 1.08–2.07; p = 0.019). ICU-specific GPR was associated with neurological deficit at ICU discharge (OR 2.06, 95% CI 1.29–3.50; p = 0.004), but not with TCD-defined vasospasm. Addition of GPR improved mortality prediction compared with the clinical model alone (AUC 0.86 vs. 0.77; p = 0.002). Conclusions: Longitudinal metabolic dysregulation after aSAH is strongly associated with mortality and neurological outcomes. Persistent hyperglycemia and repeated GPR assessment provide prognostic information beyond admission glucose, with early abnormalities associated with DCI and sustained disturbances linked to mortality and disability. Full article
(This article belongs to the Section Neurobiology and Clinical Neuroscience)
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11 pages, 306 KB  
Article
Reduced Indocyanine Green Clearance Is Associated with Enteral Feeding Intolerance in Septic Patients Without Overt Liver Injury
by Yingying Hao, Ming Yan, Rujing Bai, Chenyu Li, Chen Qu, Zhuxi Yu, Wenkui Yu, Ning Liu, Tao Gao and Ying Xu
J. Clin. Med. 2026, 15(12), 4820; https://doi.org/10.3390/jcm15124820 (registering DOI) - 21 Jun 2026
Viewed by 78
Abstract
Background/Objectives: The gut–liver axis is central to sepsis, but assessing mesenteric perfusion remains challenging. Indocyanine green (ICG) clearance reflects hepatic blood flow. Since portal flow is derived from mesenteric circulation and supplies most of the liver, reduced ICG clearance may indicate mesenteric [...] Read more.
Background/Objectives: The gut–liver axis is central to sepsis, but assessing mesenteric perfusion remains challenging. Indocyanine green (ICG) clearance reflects hepatic blood flow. Since portal flow is derived from mesenteric circulation and supplies most of the liver, reduced ICG clearance may indicate mesenteric hypoperfusion, which can lead to enteral feeding intolerance (EFI). This study examines whether reduced ICG clearance in septic patients without overt liver injury is associated with EFI. Methods: This study is a secondary analysis of a prospective cohort study (March–May 2024, 20-bed ICU). Septic patients without sepsis-related liver injury or recent abdominal surgery were included. ICG plasma disappearance rate (ICG-PDR) was measured at admission; patients were grouped by ICG-PDR (≤18%/min vs. >18%/min). The primary outcome was EFI within 7 days. Multivariate logistic regression and correlation analyses were performed. Results: Among 77 patients (44 with ICG-PDR > 18%/min, 33 with ≤18%/min), the decreased ICG-PDR group had higher SOFA scores (8.4 ± 4.2 vs. 5.4 ± 3.5, p = 0.001) and higher EFI rates (66.7% vs. 43.1%, p = 0.041). Univariate analysis showed ICG-PDR ≤ 18%/min associated with EFI (OR = 2.632, p = 0.043), but this was attenuated after SOFA adjustment (OR = 2.247, p = 0.171). Reduced ICG-PDR correlated with central venous pressure (CVP) (r = 0.626, p < 0.001) but not with mean arterial pressure (r = −0.175, p = 0.129). Conclusions: In septic patients with preserved hepatocyte function, reduced ICG clearance is associated with EFI, but this relationship is largely explained by disease severity (SOFA). Reduced ICG clearance correlates with CVP; however, ICG-PDR cannot distinguish between portal venous and arterial inflow components. The exact mechanism remains speculative. Full article
(This article belongs to the Section Gastroenterology & Hepatopancreatobiliary Medicine)
14 pages, 998 KB  
Article
Early Dynamics of Body Temperature in Acute Stroke: Insights into Outcomes and Management
by Crhistian-Mario Oblitas, María Luz Alonso-Alonso, Antonio J. Mosqueira, Manuel Rodríguez-Yáñez, Iria López-Dequidt, Francisco Campos, Tomás Sobrino, José Castillo, Pablo Hervella and Ramón Iglesias-Rey
J. Clin. Med. 2026, 15(12), 4786; https://doi.org/10.3390/jcm15124786 (registering DOI) - 19 Jun 2026
Viewed by 160
Abstract
Background: Following a stroke, body and brain temperatures are closely linked. Elevated temperature may reflect the severity of brain injury rather than infection. The significance of admission temperature remains unclear, and hypothermia treatment lacks proven efficacy and safety. Administering paracetamol (acetaminophen) above 36.5 [...] Read more.
Background: Following a stroke, body and brain temperatures are closely linked. Elevated temperature may reflect the severity of brain injury rather than infection. The significance of admission temperature remains unclear, and hypothermia treatment lacks proven efficacy and safety. Administering paracetamol (acetaminophen) above 36.5 °C is considered safe, though its clinical benefit is modest. This study aimed to examine how admission temperature, peak temperature in the first 24 h, and temperature fluctuations affect three-month functional outcomes. Methods: We conducted a retrospective study using data from a prospective stroke registry, including 5883 patients (4830 with ischemic stroke [IS] and 1053 with hemorrhagic stroke [HS]). Temperature at admission, maximum temperature within the first 24 h, and the temperature increase during the first day were assessed. Patients with a temperature ≥ 37.5 °C received 3 g of paracetamol per day until normothermia was achieved. Results: Baseline temperature was not associated with 3-month functional outcomes. In IS patients, an increasing temperature during the first 24 h was associated with a 10-fold higher risk of poor functional outcome (sensitivity 81%, specificity 64%); whereas in HS, the risk increased sevenfold (sensitivity 88%, specificity 53%). The most reliable predictor of therapeutic response was the temperature increase on the first day, with sensitivities of 89% and 83%, and specificities of 84% and 71%, for IS and HS, respectively. Conclusions: An increase in temperature during the first 24 h, rather than a single measurement, is the most reliable temperature-based biomarker for predicting poor functional outcomes and guiding the initiation of antihyperthermic treatment. Full article
(This article belongs to the Section Clinical Neurology)
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14 pages, 312 KB  
Article
Association of Urea-to-Creatinine Ratio with Functional Outcomes in Patients with Traumatic Brain Injury
by Valentina Blažinčić, Anđela Grgić, Kristina Kralik, Ivica Ščurić, Ivana Klepo and Duško Cerovec
J. Clin. Med. 2026, 15(12), 4766; https://doi.org/10.3390/jcm15124766 (registering DOI) - 19 Jun 2026
Viewed by 188
Abstract
Background: In patients with traumatic brain injury (TBI), proteins are considered the main source of energy. Previous studies have suggested that an increase in the urea-to-creatinine ratio (UCR) indicates the onset of protein catabolism. Therefore, we aimed to investigate the associations of [...] Read more.
Background: In patients with traumatic brain injury (TBI), proteins are considered the main source of energy. Previous studies have suggested that an increase in the urea-to-creatinine ratio (UCR) indicates the onset of protein catabolism. Therefore, we aimed to investigate the associations of the UCR with the functional independence measure (FIM). Methods: This single-center retrospective study included 291 patients aged 17–87 years who underwent inpatient rehabilitation within the first 6 months post-TBI. Their demographic, clinical, neuroradiological, and laboratory data (eGFR, urea, creatinine, UCR) were collected. Spearman’s correlation and hierarchical multivariate regression analyses adjusted for clinical covariates were performed. Results: The strongest significant positive correlation was found between the Glasgow Coma Scale (GCS) and FIM at admission (ρ = 0.488, p < 0.001) and between GCS and FIM at discharge (ρ = 0.340, p < 0.001). A significant negative correlation was found between the discharge UCR and FIM at discharge (ρ = −0.262, p < 0.003), as well as with the change in FIM (ρ = −0.207, p < 0.02). Patients with UCRs ≥ 80 had a significantly lower discharge FIM compared to patients with UCRs < 80 (median 27 vs. 40; p = 0.02). The significant independent predictors of discharge FIM were the nutritional route (NGT/PEG), level of consciousness, and FIM at admission. The UCR did not remain independently associated with the discharge FIM (ΔR2 = 0.004, Cohen’s f2 = 0.014). Conclusions: Although UCR is associated with functional outcomes measured by FIM in TBI patients, it is not an independent predictor of these outcomes but rather a biomarker of catabolic burden. Full article
(This article belongs to the Section Brain Injury)
13 pages, 2045 KB  
Article
Functional Outcome and Hip Survival Rate in Traumatic Femoral Head Fractures
by Christian Prangenberg, Thomas Loy, Alberto Alfieri Zellner, Jonas Roos, Sebastian Scheidt, Lisa Roder, Soufian Ben Amar and Kristian Welle
J. Clin. Med. 2026, 15(12), 4741; https://doi.org/10.3390/jcm15124741 - 18 Jun 2026
Viewed by 147
Abstract
Objective: Femoral head fractures are rare and severe injuries often associated with high-energy trauma. Early recognition and rapid, stable reduction are essential for successful treatment to prevent complications and morbidity. This retrospective study aims to describe and analyze long-term outcomes and survival rates [...] Read more.
Objective: Femoral head fractures are rare and severe injuries often associated with high-energy trauma. Early recognition and rapid, stable reduction are essential for successful treatment to prevent complications and morbidity. This retrospective study aims to describe and analyze long-term outcomes and survival rates of the femoral head after a Pipkin fracture. Methods: Between 2012 and 2021, all patients with a femoral head fracture who were treated in a Level I Trauma Center were assessed and analyzed. Two examiners performed a physical examination and radiological control of patients and called the patients for a final follow-up. Anterior and posterior fracture-dislocations and femoral head fractures were classified according to Pipkin’s classification system. The functional outcome was assessed using the Harris Hip Score (HHS). Results: Over a 10-year period, n = 15 patients were diagnosed with a femoral head fracture. All patients were male; the average age at admission was 41.3 years. The mean follow-up was 43.7 months ± 46 months. No complications occurred in three patients (20%). Twelve patients had complications. The most common complications were nerve lesions and posttraumatic osteoarthritis. Regarding the outcome, no data were available for two patients; one patient died, and two of four patients remained with a Girdlestone resection arthroplasty at the follow-up. The mean score in HHS was 76.69 ± 20.3 (mean ± standard deviation). Conclusions: An overall complication rate of 80% was observed; however, functional outcomes were generally moderate at final follow-up. These findings highlight the considerable risk of complications associated with femoral head fractures, particularly nerve injury and posttraumatic osteoarthritis. Notably, six of 15 patients no longer retained their native hip joint at the time of assessment. The study is a Level 2b study. Full article
(This article belongs to the Section Orthopedics)
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14 pages, 2609 KB  
Article
Investigating Performance, Functional Outcomes, and Patient Autonomy in a Rural Community Hospital: A Real-Life Descriptive Cohort Study of Territorial Intermediate Care
by Fabio Del Duca, Luca Casertano, Luca Di Sarra, Arturo Cavaliere, Paola Frati, Gennaro Scialò, Emiliano Cingolani and Aniello Maiese
Healthcare 2026, 14(12), 1757; https://doi.org/10.3390/healthcare14121757 - 18 Jun 2026
Viewed by 472
Abstract
Background/Objectives: Community hospitals can be a valuable and cost-effective resource for elderly people, especially in rural areas. Their aim is to promote self-reliance, prevent unnecessary hospital admissions, and facilitate rapid recovery after acute illness. The widespread adoption of intermediate care facilities helps [...] Read more.
Background/Objectives: Community hospitals can be a valuable and cost-effective resource for elderly people, especially in rural areas. Their aim is to promote self-reliance, prevent unnecessary hospital admissions, and facilitate rapid recovery after acute illness. The widespread adoption of intermediate care facilities helps alleviate hospital overcrowding by preventing clinical deterioration through advanced and continuous nursing care. An intermediate care unit was established in a rural area of central Italy. This study aims to describe the impact of a community hospital on patients’ functional status from admission to discharge, describing a real-life model. Methods: This single-center descriptive study examines trends in the quality of care provided. Data were retrieved from anonymized electronic clinical records. Statistical analyses were performed using descriptive statistics, paired t-tests, and Pearson correlation coefficients. Results: A total of 532 residents (mean age 80.7 ± 13.2 years; 61% female) were admitted to the community hospital between January 2022 and September 2025. The mean length of stay was 15.2 ± 7.6 days, with a mean improvement in Modified Barthel Index score of 5.24 ± 7.95 (p < 0.05). Most patients (81.8%) were discharged home, while 6.0% required hospitalization. No readmissions were recorded in 2025. Clinical risk events occurred only in 1.2% of the total. Nursing specialization increased during the study period, correlating with improved patient outcomes (R = 0.88). Conclusions: This descriptive cross-sectional study in a rural nurse-led intermediate care unit found relatively short lengths of stay, high rates of home discharges and modest, but statistically significant, improvements in functional autonomy. Full article
(This article belongs to the Special Issue Challenges and Opportunities for Nurses in Modern Clinical Practice)
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4 pages, 151 KB  
Proceeding Paper
Evaluating the Effectiveness of AI Chatbots in University Admissions: Exploring Student Assistance and Satisfaction
by Shah Asim Azhar, Malik Shafaq Mahmood and Ayesha Iftikhar
Proceedings 2026, 142(1), 10; https://doi.org/10.3390/proceedings2026142010 - 17 Jun 2026
Viewed by 51
Abstract
Universities increasingly rely on digital self-service channels to manage high volumes of time-sensitive admissions enquiries. AI enabled chatbots represent a prominent solution because they can provide round-the-clock responses, standardize guidance, and potentially reduce uncertainty for applicants. Yet evidence on whether such chatbots meaningfully [...] Read more.
Universities increasingly rely on digital self-service channels to manage high volumes of time-sensitive admissions enquiries. AI enabled chatbots represent a prominent solution because they can provide round-the-clock responses, standardize guidance, and potentially reduce uncertainty for applicants. Yet evidence on whether such chatbots meaningfully assist students and improve their satisfaction with admissions support remains limited in many developing higher education contexts. This quantitative study evaluates the perceived effectiveness of AI chatbots used for university admissions in Pakistan, with a focus on student assistance and satisfaction as key outcomes. Using a cross-sectional survey design, data were collected from students who had recently engaged with university admissions information services (e.g., website chat widgets, messaging-based virtual assistants, and admissions enquiry portals) across private universities in Pakistan. Admissions chatbot effectiveness was measured through established information systems and service quality constructs system quality (ease of use, responsiveness, accessibility), information quality (accuracy, clarity, completeness), and service quality and trust cues (assurance, privacy confidence, and appropriateness of conversational support). Student assistance captured the extent to which chatbot interactions helped participants complete admissions related tasks and navigate application procedures. Student satisfaction reflected overall evaluation of the admissions support experience. The results indicate a positive association between perceived chatbot quality and perceived student assistance, and a further positive association between student assistance and student satisfaction with admissions support. The overall pattern suggests that student assistance functions as a key mechanism through which chatbot effectiveness translates into satisfaction. At the same time, respondents highlighted limitations in resolving complex or exception based queries, emphasizing the importance of transparent escalation to human admissions staff. The study contributes context specific evidence from Pakistan and offers an empirically grounded framework that university administrators can use to evaluate and improve admissions chatbots. Practical implications emphasize maintaining accurate knowledge bases, designing clear handoff pathways, and implementing governance practices that strengthen students’ confidence in information reliability and data privacy. Full article
37 pages, 566 KB  
Article
Admissible Reciprocally Symmetric Costs: Combiner Existence and Classification
by Sebastian Pardo-Guerra, Jonathan Washburn and Elshad Allahyarov
Mathematics 2026, 14(12), 2157; https://doi.org/10.3390/math14122157 (registering DOI) - 16 Jun 2026
Viewed by 113
Abstract
We classify the continuous reciprocally symmetric cost functions J:(0,)R with J(1)=0 and strictly convex log-substitution G(t):=J(et) (admissible costs) [...] Read more.
We classify the continuous reciprocally symmetric cost functions J:(0,)R with J(1)=0 and strictly convex log-substitution G(t):=J(et) (admissible costs) for which the symmetric compound J(xy)+J(x/y) depends on (x,y) only through (J(x),J(y)). We first prove that this dependence is automatic: for every admissible J, there exists a unique continuous combiner (the auxiliary function P that encodes the compound) P:[0,)2R with J(xy)+J(x/y)=P(J(x),J(y)) for all x,y>0 (Theorem 1); P is symmetric, non-negative, satisfies P(u,0)=2u, and inherits monotonicity and coercivity from admissibility. When P is required to be a polynomial, a growth rate comparison between two recursions for G forces degP2 (Theorem 4), so P(u,v)=cuv+2u+2v with c0, and the corresponding admissible costs are exhausted by two explicit families (Theorem 8)—the hyperbolic family J(x)=c1(xλ+xλ)2c1 (c,λ>0) and the degenerate quadratic family J(x)=a(lnx)2 (a>0)—with the latter arising as the Inönü–Wigner contraction λ0+, λ2/ca of the former (Theorem 9). Two regularity extensions are obtained: a Lebesgue-measurable cost satisfying explicit regularity hypotheses admits a continuous representative (Theorem 5), and in the entire finite-order regime, the diagonal combiner Q(u):=P(u,u), when polynomial of degree d, obeys the sharp bound d2ρ (Theorem 6), attained with equality in both classified families. The normalisations P(1,1)=6 and G(0)=1 single out the canonical representative Jcost(x)=12(x+x1)1. Full article
(This article belongs to the Section C: Mathematical Analysis)
23 pages, 1401 KB  
Article
User-Centric Analysis of Time-Consistent Strategies in Car-Sharing and Rental Platforms
by Hui Jiang, Ye Gao, Ping Sun, Yang Yu and Hongwei Gao
Mathematics 2026, 14(12), 2140; https://doi.org/10.3390/math14122140 - 15 Jun 2026
Viewed by 105
Abstract
The rapid growth of the sharing economy has improved resource utilization in car-sharing, yet it has also sharpened market competition and diversified user demand. A persistent obstacle is the low coordination efficiency between asset-heavy operating companies and traffic-driven platforms, whose misaligned objectives waste [...] Read more.
The rapid growth of the sharing economy has improved resource utilization in car-sharing, yet it has also sharpened market competition and diversified user demand. A persistent obstacle is the low coordination efficiency between asset-heavy operating companies and traffic-driven platforms, whose misaligned objectives waste social resources. This paper uses differential game theory to analyze their dynamic coordination strategies and benefit allocation mechanisms. The Nerlove–Arrow model captures the evolution of brand goodwill, while the company’s decisions on station layout, vehicle dispatch, and pricing, together with the platform’s advertising investment, form the core decision variables in a two-party game framework linking the asset side and the traffic side. Compared with the non-cooperative Nash equilibrium, the cooperative mode removes the double marginalization effect, strengthens the investment incentives of both parties, and raises the system’s steady-state goodwill and total profit, achieving a Pareto improvement. To ground the cooperative framework in rigorous theory, we supply a verification theorem confirming that the linear candidate value functions satisfy the Hamilton–Jacobi–Bellman equations over the entire admissible state space. A formal proof of instantaneous rationality ensures that neither party falls into a cooperation trap on the horizon [0,T], and the asymptotic stability of the steady-state goodwill trajectory is established. We further endogenize the revenue-sharing coefficient through a generalized Nash bargaining model that admits asymmetric bargaining structures, and introduce a Stackelberg leadership benchmark as a third comparative regime. Sensitivity analyses with respect to the discount rate and user heterogeneity confirm the robustness of the findings. A dedicated discussion section bridges the gap between idealized parameterization and data-driven calibration, describing practical pathways via A/B testing, user churn metrics, and econometric estimation of demand parameters. The results offer a scientific decision-making reference for strategic cooperation in the car-sharing industry. Full article
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22 pages, 602 KB  
Article
Differential Subordination and Superordination Related to Admissible Functions for Multivalent Functions Associated with Borel Distribution
by Shahad Kareem Atiyah, Abbas Kareem Wanas and Alina Alb Lupas
Symmetry 2026, 18(6), 1015; https://doi.org/10.3390/sym18061015 - 12 Jun 2026
Viewed by 164
Abstract
In this paper, we consider some differential subordination and superordination results for analytic and multivalent functions in the open unit disk related to Borel distribution through investigating appropriate families of admissible functions. These results are applied to obtain differential sandwich results. Full article
(This article belongs to the Special Issue Symmetry in Complex Analysis Operators Theory)
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17 pages, 668 KB  
Article
H Control Designs for Continuous-Time Singular Systems
by Badreddine El Haiek, Hicham El Aiss, Taha Zoulagh and Fernando Tadeo
Symmetry 2026, 18(6), 1014; https://doi.org/10.3390/sym18061014 - 12 Jun 2026
Viewed by 145
Abstract
This paper investigates some H control problems for linear continuous-time singular systems. The objective is to design controllers that guarantee the admissibility of the closed-loop system and simultaneously achieve a prescribed H disturbance attenuation level. To this end, a framework based [...] Read more.
This paper investigates some H control problems for linear continuous-time singular systems. The objective is to design controllers that guarantee the admissibility of the closed-loop system and simultaneously achieve a prescribed H disturbance attenuation level. To this end, a framework based on novel strict LMIs (Linear Matrix Inequalities) is developed using a Lyapunov function approach for the analysis of admissibility and H performance. In particular, an additional scalar parameter α is introduced to generalize the condition reported in previous results in the literature, providing greater flexibility. Then, sufficient LMI conditions are derived for the synthesis of both state-feedback and static output-feedback controllers. Finally, some numerical examples demonstrate the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Symmetry in Fuzzy Systems and Control: A Path to Innovative Solutions)
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14 pages, 11573 KB  
Case Report
Spontaneous Bilateral Renal Forniceal Rupture Secondary to Acute Urinary Retention in a Patient with Prior Prostate Radiotherapy: A Case Report
by Timoleon Giannakas, Dimitrios Deligiannis, Panagiotis Mitsos, Anna Papakonstantinou, Marios Stavropoulos and Aris Kaltsas
Reports 2026, 9(2), 184; https://doi.org/10.3390/reports9020184 - 12 Jun 2026
Viewed by 235
Abstract
Background and Clinical Significance: Spontaneous renal forniceal rupture is an uncommon complication of obstructive uropathy and is classically associated with ureteric calculi rather than distal urinary retention. Bilateral retention-related rupture appears to be exceptionally rare and may be diagnostically challenging when renal function [...] Read more.
Background and Clinical Significance: Spontaneous renal forniceal rupture is an uncommon complication of obstructive uropathy and is classically associated with ureteric calculi rather than distal urinary retention. Bilateral retention-related rupture appears to be exceptionally rare and may be diagnostically challenging when renal function begins to improve after bladder decompression; Case Presentation: An 82-year-old man with a history of prostate cancer treated five years earlier with external beam radiotherapy and androgen deprivation therapy presented with acute abdominal pain radiating to both flanks and inability to void. Bedside ultrasonography showed urinary retention and bilateral hydronephrosis, and a 16-Fr Foley catheter drained 900 mL of urine. Admission evaluation showed severe acute kidney injury, microscopic hematuria, minimal leukocyturia, and elevated inflammatory markers. Post-obstructive diuresis developed after bladder decompression. CT urography with excretory-phase imaging on hospital day 3 demonstrated severe bilateral hydroureteronephrosis with bilateral renal forniceal rupture and associated urinomas, including a larger left-sided collection extending toward the psoas compartment. Bilateral percutaneous nephrostomies were placed on hospital day 4 for upper-tract diversion. Immediate nephrostography showed no active contrast extravasation. At one-month follow-up, combined CT and nephrostographic assessment confirmed complete resolution of the bilateral urinomas without persistent leak, and the nephrostomy tubes were removed; Conclusions: This case suggests that urinary retention in an older man with prior prostate radiotherapy may reflect radiation-associated outlet pathology and/or impaired detrusor function rather than simple prostate enlargement. Delayed-phase CT urography was essential for diagnosis, and active bilateral diversion was justified by bilateral rupture, acute kidney injury, and the extent of urinary extravasation. The report expands the limited PubMed-indexed literature on retention-related upper urinary tract rupture and supports cautious follow-up aimed at defining the underlying mechanism of retention. Full article
(This article belongs to the Special Issue When Urology Surprises: Educational and Rare Clinical Cases)
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Article
HPT Axis Dysregulation in Mood and Anxiety Disorders: The Clinical Utility of Routine Hormonal Dosing in Psychiatric In-Patients
by Georgiana-Adriana Toma, Elena Coman, Antonia Ioana Vasile and Simona Trifu
Diseases 2026, 14(6), 211; https://doi.org/10.3390/diseases14060211 - 11 Jun 2026
Viewed by 259
Abstract
Background/Objectives: Thyroid dysfunction is frequently associated with mood and anxiety disorders, yet the directionality and diagnostic specificity of this relationship remain debated. Although numerous studies have examined major depressive disorder (MDD) and bipolar disorder (BD) separately, comparative data including generalized anxiety disorder (GAD) [...] Read more.
Background/Objectives: Thyroid dysfunction is frequently associated with mood and anxiety disorders, yet the directionality and diagnostic specificity of this relationship remain debated. Although numerous studies have examined major depressive disorder (MDD) and bipolar disorder (BD) separately, comparative data including generalized anxiety disorder (GAD) and accounting for non-thyroidal illness (NTI) effects remain scarce. This study aimed to evaluate thyroid function and its correlation with affective symptom severity across MDD, GAD, and BD in an inpatient cohort. Methods: Eighty-eight hospitalized patients with MDD, GAD, or BD were included in the study (MDD = 30, GAD = 30, BD = 28). Serum levels of TSH, FT4, and FT3 were measured 24–48 h after admission to minimize the influence of NTI. Psychiatric assessment included the Montgomery-Åsberg Depression Rating Scale (MADRS), Hamilton Anxiety Scale (HAM-A), and Young Mania Rating Scale (YMRS). Between-group differences were analyzed using ANOVA, and associations between thyroid parameters and symptom severity were examined using correlation and regression analyses. Results: ANOVA revealed that patients with MDD had significantly higher TSH levels compared with those with GAD and BD (p < 0.01). MDD patients also showed a higher prevalence of subclinical hypothyroidism (33.3%) than patients with GAD (13.3%) and BD (7.1%), as well as a higher prevalence of overt hypothyroidism (13.3%) compared with GAD (0%) and BD (7.1%). TSH levels correlated positively with MADRS scores (r = 0.45, p < 0.05) and HAM-A scores (r = 0.38, p < 0.05), particularly within the MDD group. In BD, FT4 and FT3 levels were elevated and positively correlated with YMRS scores (FT4: r = 0.30, p < 0.05; FT3: r = 0.42, p < 0.05). In regression analysis within the MDD subgroup, both hypothyroidism and male sex were independently associated with higher MADRS scores, indicating greater depressive symptom severity. Conclusions: These findings suggest diagnosis-specific patterns of thyroid dysfunction among psychiatric inpatients. Higher TSH levels and increased rates of hypothyroidism were most prominent in MDD and were associated with greater depressive and anxiety symptom severity, whereas elevated FT4 and FT3 levels in BD were associated with manic symptom severity. The results support systematic thyroid screening in depressive admissions, hormone-informed monitoring in bipolar disorder, and a more integrated endocrine–psychiatric approach to clinical care. Full article
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