Intercollege

To address the lack of dedicated tools for analyzing the stability of bivariate functional equations in fuzzy environments, this paper investigates fixed-point theory and functional equation stability in fuzzy Banach spaces (FBSs). First, building on the Bag-Samanta fuzzy norm, we supplement and prove the "proposition on convergence preservation of linear operations for bivariate sequences," laying key technical groundwork. Second, we move beyond the constraints of traditional single-variable fixed-point theorems to develop a contraction-type fixed-point theorem for bivariate self-mappings in the FBS framework, clarifying criteria for the existence and uniqueness of fixed points when mappings satisfy contraction conditions. Finally, we apply this theorem to the Hyers-Ulam stability analysis of bivariate linear functional equations (e.g., generalized Jensen-type equations), proving that approximate solutions imply unique exact solutions with convergence error estimates. Our results enrich the FBS fixed-point theory system and provide a novel general method for stability analysis of multivariate functional equations under fuzzy uncertainty, with applications in dynamic system modeling and fuzzy optimization.

Cancer is a major public health issue worldwide. Lifestyle factors, such as body weight and physical activity (PA), significantly impact cancer risk and progression. There is strong evidence that PA reduces and obesity increases risk and mortality from numerous cancer types. Energy restriction (ER) in non-obese hosts significantly reduces tumor incidence in a variety of preclinical models, and reduces body weight and cardiometabolic risk factors in humans. Emerging data suggest that PA- and ER-induced changes in inflammatory and immune mediators may contribute to the cancer prevention effects of these interventions. A systematic literature search was conducted to identify studies that evaluated the impact of PA and ER on tumor and immune outcomes in humans and animal models. A total of 97 eligible studies were identified (68 studies reporting PA interventions and 30 studies reporting ER interventions). Thirty-one studies investigated the effect of PA on cancer immune outcomes using preclinical cancer models of breast (n=17, 55%), gastrointestinal (n=6, 19%), melanoma (n=4, 13%), and several other cancer types (n=4, 13%). Despite the heterogeneity in study designs, the majority of studies (n=23, 74%) reported positive effects of PA on tumor outcomes. Thirty-seven clinical studies investigated the effect of PA on cancer immune outcomes. None reported tumor outcomes, thus only immune outcomes were evaluated in these studies. PA studies were conducted in patients with breast (n=22, 59%), gastrointestinal (n=5, 14%), prostate (n=2, 5%), esophageal (n=1, 3%), lung (n=1, 3%) cancer, leukemia (n=1, 3%), or mixed cancer types (n=5, 14%). Twenty-two studies investigated the effect of ER interventions on cancer immune outcomes using preclinical cancer models including breast (n=5, 23%), gastrointestinal (n=5, 23%), lung (n=2, 9%), liver (n=2, 9%), pancreatic (n=2, 9%), and several other cancer types (n=6, 27%). Positive effects of ER on tumor outcomes were reported in 21 of 22 studies. Six clinical studies investigated the effect of ER (in combination with PA) on tumor immune outcomes in cancer patients with overweight or obesity. Five were conducted in breast cancer patients, and one recruited patients of a mix of cancer types. A wide range of immunological parameters including immune cell phenotype and function, cytokines, and other immune and inflammatory markers were assessed in multiple tissue compartments (blood, spleen, lymph nodes and tumor) in the included studies. Results from preclinical and clinical studies suggest that both PA and ER exert heterogeneous effects on circulating factors and systemic immune responses. PA + ER alters the gene expression profile and immune infiltrates in the tumor which may result in a reduction in immune suppressive factors. However, additional studies are needed to better understand the effect of PA and/or ER on immunomodulation, particularly in the tumor microenvironment (TME).

The intima-media thickness (IMT) of the common carotid artery (CCA) is an established indicator of cardiovascular disease (CVD). There have been reports about the difference between the left and the right sides of the CCA IMT and their relation with CVD. In this paper, we propose an automated system based on image normalization, speckle reduction filtering, and snakes segmentation, for segmenting the CCA, perform IMT measurements, and provide the differences between the left and the right sides. The study was performed on 1104 longitudinal-section ultrasound images acquired from 568 men and 536 women out of which 125 had cardiovascular symptoms (CVD). A cardiovascular expert manually delineated the IMT for the normal and the CVD groups. The corresponding (normal versus CVD) IMT mean ± standard deviation values for the left and the right sides were 0.74 ± 0.24 versus 0.87 ± 0.24 mm and 0.70 ± 0.17 versus 0.80 ± 0.18 mm, respectively. The main findings of this paper can be summarized as follows: 1) there was no significant difference between the CCA left side IMT and the right side IMT. These findings suggest that the measurement of the CCA IMT on one side only is needed for the normal group (and this is in agreement with other studies); 2) there were statistical significant differences for the IMT measurements between the normal group and the CVD group for both the left and the right sides; 3) there was an increasing linear relationship of the left and the right IMT measurements with age for the normal group; and to a lesser extend for the CVD group; 4) no statistical significant differences were found between the manual and the automated IMT measurements for both sides; and 5) the best result for classification disease modeling, using support vector machines, to discriminate between the normal and the CVD groups was a 64%±3.5% correct classifications score when using both the left and the right IMT automated measurements. Further research is required for estimating differences and similarities between left and right intima media complex structure and morphology and their variability with texture features for differentiating between the normal and the CVD group.

The recent emergence of the high-efficiency video coding (HEVC) standard promises to deliver significant bitrate savings over current and prior video compression standards, while also supporting higher resolutions that can meet the clinical acquisition spatiotemporal settings. The effective application of HEVC to medical ultrasound necessitates a careful evaluation of strict clinical criteria that guarantee that clinical quality will not be sacrificed in the compression process. Furthermore, the potential use of despeckle filtering prior to compression provides for the possibility of significant additional bitrate savings that have not been previously considered. This paper provides a thorough comparison of the use of MPEG-2, H.263, MPEG-4, H.264/AVC, and HEVC for compressing atherosclerotic plaque ultrasound videos. For the comparisons, we use both subjective and objective criteria based on plaque structure and motion. For comparable clinical video quality, experimental evaluation on ten videos demonstrates that HEVC reduces bitrate requirements by as much as 33.2% compared to H.264/AVC and up to 71% compared to MPEG-2. The use of despeckle filtering prior to compression is also investigated as a method that can reduce bitrate requirements through the removal of higher frequency components without sacrificing clinical quality. Based on the use of three despeckle filtering methods with both H.264/AVC and HEVC, we find that prior filtering can yield additional significant bitrate savings. The best performing despeckle filter (DsFlsmv) achieves bitrate savings of 43.6% and 39.2% compared to standard nonfiltered HEVC and H.264/AVC encoding, respectively.