Topological Connectedness and Behavioral Assumptions on Preferences: A Two-Way Relationship

This paper offers a comprehensive treatment of the question as to whether a binary relation can be consistent (transitive) without being decisive (complete), or decisive without being consistent, or simultaneously inconsistent or indecisive, in the presence of a continuity hypothesis that is, in principle, non-testable. It identifies topological connectedness of the (choice) set over which the continuous binary relation is defined as being crucial to this question. Referring to the two-way relationship as the Eilenberg-Sonnenschein (ES) research program, it presents four synthetic, and complete, characterizations of connectedness, and its natural extensions; and two consequences that only stem from it. The six theorems are novel to both the economic and the mathematical literature: they generalize pioneering results of Eilenberg (1941), Sonnenschein (1965), Schmeidler (1971) and Sen (1969), and are relevant to several applied contexts, as well as to ongoing theoretical work.Comment: 47 pages, 4 figure

On the consistency and the decisiveness of the double-minded decision-maker

Under a continuity hypothesis on bi-preferences defined on a topologically-connected choice-set, as formalized by Giarlotta-Greco (2013), this letter reports that a mildly consistent, double-minded decision-maker is single-minded in the sense of being fully consistent and decisive. The results generalize recent work of Giarlotta-Watson (2019), and thereby provide a far-reaching generalization of a result of Schmeidler (1971) that has received considerable recent attention, and extend to mixture-sets of Herstein-Milnor (1953). They give another perspective on the authors’ work on the Eilenberg-Sonnenschein (ES) research program embracing both the topological and algebraic registers in choice theory

Fixed-point approaches to the proof of the Bondareva–Shapley Theorem

We provide two new proofs of the Bondareva–Shapley theorem, which states that the core of a transferable utility cooperative game has a nonempty core if and only if the game is balanced. Both proofs exploit the fixed points of self-maps of the set of imputations, applying elementary existence arguments typically associated with noncooperative games to cooperative games

On an extension of a theorem of Eilenberg and a characterization of topological connectedness

On taking a non-trivial and semi-transitive bi-relation constituted by two (hard and soft) binary relations, we report a (i) p-continuity assumption that guarantees the completeness and transitivity of its soft part, and a (ii) characterization of a connected topological space in terms of its attendant properties on the space. Our work generalizes antecedent results in applied mathematics, all following Eilenberg [14], and now framed in the context of a parametrized-topological space. This re-framing is directly inspired by the continuity assumption in Wold [50] and the mixture-space structure proposed in Herstein and Milnor [27], and the unifying synthesis of these pioneering but neglected papers that it affords may have independent interest

Can Human Recombinant Epidermal Growth Factor Improve Ischemia and Induce Healing of Anastomosis in an Experimental Study in a Rabbit Model?

Purpose: Anastomotic leaks following intestinal operations may cause devastating effects on patients. Ischemia may also occur at the intestinal walls in the presence of strangulations. In this study, we examined the effects of human recombinant (Hr)-epidermal growth factor (EGF) given at a single intramural dose into the intestinal walls and daily intraperitoneal cavity on ischemia and the healing process of anastomosis. Materials and Methods: Sixteen male New Zeland white rabbits were randomly divided into four groups (n = 4 in each group). In Group 1, two different segments of ileum were identified and, then, transected and the free ends were sutured each other. In the other groups, ischemia was induced by ligating the mesenteric vascular arcade. After the ischemic induction, Group 2 received intramural injections of %0.9 saline, Group 3 received intramural injections of a single dose of EGF, and Group 4 received intramural and intraperitoneal injections of EGF. Bursting pressures and tissue hydroxyproline levels were analyzed. Necrosis, fibroblastic activity, collagen deposition and neovascularization were also studied. Results: The mean levels of bursting pressures in Group 4 (148.6 ± 25.3 mmHg) were higher than Group 2 (70 ± 21.5 mmHg) (p = 0.001). The mean level of bursting pressures was not statistically significant between Group 1 (170.1 ± 35 mmHg) and Group 4 (p = 0.073). Hydroxyproline levels in Group 2 were lower than Groups 3 and 4. There was a statistically significant difference in the mucosal ischemia, mucosal healing and degree of adhesion, but not in the mural anastomotic healing among the groups. Conclusions: Intramural injection with daily intraperitoneal administration of low-dose EGF enhances the bursting pressure and collagen accumulation in ischemic anastomosis, improving many histological variables associated with ischemic intestinal anastomosis

Salivary and serum oxidative stress biomarkers and advanced glycation end products in periodontitis patients with or without diabetes: A cross-sectional study

Background Non-invasive methods for periodontitis diagnosis would be a clinically important tool. This cross-sectional study aimed to investigate the association between oxidative stress, glycation, and inflammation markers and periodontal clinical parameters in periodontitis and periodontally healthy patients with type 2 diabetes and corresponding systemically healthy controls. Material and methods Sixty-seven periodontally healthy (DM-H, n = 32) and periodontitis (DM-P, n = 35) patients with type 2 diabetes, and 54 systemically healthy periodontitis (H-P, n = 26) and periodontally healthy (H-H, n = 28) controls were included. Clinical periodontal parameters, body mass index, fasting glucose, hemoglobin A1c (HbA1c), along with saliva and serum 8-hydroxy-2 '-deoxyguanosine (8-OHdG), malondialdehyde (MDA), 4-hydroxy-2-nonenal (4-HNE), advanced glycation end products (AGE), AGE receptor (RAGE) and high sensitivity C-reactive protein (hsCRP) levels were recorded and analyzed. Results Salivary 8-OHdG levels were significantly higher in periodontitis compared to periodontally healthy patients, regardless of systemic status (P < 0.001). Salivary MDA levels were significantly higher in all disease groups compared to H-H group (P <= 0.004). Serum AGE levels were significantly higher in diabetic groups than systemically healthy groups (P < 0.001) and in H-P compared to H-H (P < 0.001). Bleeding on probing (BOP) and clinical attachment level (CAL) strongly correlated with salivary 8-OHdG and serum hsCRP (P < 0.001). In systemically healthy patients, salivary 8-OHdG was the most accurate marker to differentiate periodontitis from controls (AUC = 0.84). In diabetics salivary 4-HNE and RAGE were the most accurate (AUC = 0.85 for both). Conclusion Salivary 8-OHdG alone or in combination with 4-HNE, AGE and RAGE for diabetics, and salivary 8-OHdG alone or in combination with MDA and hsCRP for systemically healthy persons, could potentially serve as non-invasive screening marker(s) of periodontitis.Ankara University Scientific Research Projects Office, Ankara, Turkey [12B3334002]; Ankara University Department of Periodontology and Department of Endocrinology; Ohio State University Division of PeriodontologyThis study was supported by the Ankara University Scientific Research Projects Office, Ankara, Turkey (12B3334002). The authors declare that they have no conflicts of interest.; Ankara University Department of Periodontology and Department of Endocrinology; Ohio State University Division of Periodontolog

Salivary and serum oxidative stress biomarkers and advanced glycation end products in periodontitis patients with or without diabetes: A cross-sectional study.

Background: Non-invasive methods for periodontitis diagnosis would be a clinically important tool. This cross-sectional study aimed to investigate the association between oxidative stress, glycation, and inflammation markers and periodontal clinical parameters in periodontitis and periodontally healthy patients with type 2 diabetes and corresponding systemically healthy controls. Material and methods: Sixty-seven periodontally healthy (DM-H, n = 32) and periodontitis (DM-P, n = 35) patients with type 2 diabetes, and 54 systemically healthy periodontitis (H-P, n = 26) and periodontally healthy (H-H, n = 28) controls were included. Clinical periodontal parameters, body mass index, fasting glucose, hemoglobin A1c (HbA1c), along with saliva and serum 8-hydroxy-2'-deoxyguanosine (8-OHdG), malondialdehyde (MDA), 4-hydroxy-2-nonenal (4-HNE), advanced glycation end products (AGE), AGE receptor (RAGE) and high sensitivity C-reactive protein (hsCRP) levels were recorded and analyzed. Results: Salivary 8-OHdG levels were significantly higher in periodontitis compared to periodontally healthy patients, regardless of systemic status (P < 0.001). Salivary MDA levels were significantly higher in all disease groups compared to H-H group (P ≤ 0.004). Serum AGE levels were significantly higher in diabetic groups than systemically healthy groups (P < 0.001) and in H-P compared to H-H (P < 0.001). Bleeding on probing (BOP) and clinical attachment level (CAL) strongly correlated with salivary 8-OHdG and serum hsCRP (P < 0.001). In systemically healthy patients, salivary 8-OHdG was the most accurate marker to differentiate periodontitis from controls (AUC = 0.84). In diabetics salivary 4-HNE and RAGE were the most accurate (AUC = 0.85 for both). Conclusion: Salivary 8-OHdG alone or in combination with 4-HNE, AGE and RAGE for diabetics, and salivary 8-OHdG alone or in combination with MDA and hsCRP for systemically healthy persons, could potentially serve as non-invasive screening marker(s) of periodontitis

Clinical and genetic spectrum from a prototype of ciliopathy: Joubert syndrome

Objective: Joubert syndrome is a neurodevelopmental disorder with a distinctive hindbrain malformation called molar tooth sign, causing motor and cognitive impairments. More than 40 genes have been associated with Joubert syndrome. We aim to describe a group of Joubert syndrome patients clinically and genetically emphasizing organ involvement. Methods: We retrospectively collected clinical information and molecular diagnosis data of 22 patients with Joubert syndrome from multiple facilities. Clinical exome or whole-exome sequencing were performed to identify causal variations in genes. Results: The most common variants were in the CPLANE1, CEP290, and TMEM67 genes, and other causative genes were AHI1, ARMC9, CEP41, CSPP1, HYLS1, KATNIP, KIAA0586, KIF7, RPGRIP1L, including some previously unreported variants in these genes. Multi-systemic organ involvement was observed in nine (40%) patients, with the eye being the most common, including Leber's congenital amaurosis, ptosis, and optic nerve coloboma. Portal hypertension and esophageal varices as liver and polycystic kidney disease and nephronophthisis as kidney involvement was encountered in our patients. The HYLS1 gene, which commonly causes hydrolethalus syndrome 1, was also associated with Joubert syndrome in one of our patients. A mild phenotype with hypophyseal hormone deficiencies without the classical molar tooth sign was observed with compound heterozygous and likely pathogenic variants not reported before in the KATNIP gene. Conclusion: Some rare variants that display prominent genetic heterogeneity with variable severity are first reported in our patients. In our study of 22 Joubert syndrome patients, CPLANE1 is the most affected gene, and Joubert syndrome as a ciliopathy is possible without a classical molar tooth sign, like in the KATNIP gene-affected patients