In this paper, we analyze the complexity of topological conjugacy of pointed Cantor minimal syste... more In this paper, we analyze the complexity of topological conjugacy of pointed Cantor minimal systems from the point of view of descriptive set theory. We prove that the topological conjugacy relation on pointed Cantor minimal systems is Borel bireducible with the Borel equivalence relation ∆ + R on R N defined by x∆ + R y ⇔ {x i : i ∈ N} = {y i : i ∈ N}. Moreover, we show that ∆ + R is a lower bound for the Borel complexity of topological conjugacy of Cantor minimal systems. Finally, we interpret our results in terms of properly ordered Bratteli diagrams and discuss some applications.
These are the lecture notes of a one-week course I taught at the Nesin Mathematics Village in Şir... more These are the lecture notes of a one-week course I taught at the Nesin Mathematics Village in Şirince, İzmir, Turkey during Summer 2018. The aim of the course was to introduce various paradoxical decompositions, prove the Banach-Tarski theorem and introduce amenable groups.
These are the lecture notes of a one-week course I taught at the Nesin Mathematics Village in Şir... more These are the lecture notes of a one-week course I taught at the Nesin Mathematics Village in Şirince, İzmir, Turkey during Summer 2017. The aim of the course was to introduce some basic notions of combinatorial set theory and prove some key results regarding partition relations for cardinals and the tree property of cardinals.
F lap surgery is a common procedure in plastic surgery practice. Flaps are used for various purpo... more F lap surgery is a common procedure in plastic surgery practice. Flaps are used for various purposes including covering poorly vascularized areas in donor fields, reconstructing full-thickness defects of the eyelids, lips, nose and cheek, repairing congenital and acquired defects, and providing contour for protruding body areas (1). Various alterations, primarily in vascular balance, occur after flap elevation. Vascular support should be provided and postischemic effects should be minimized for flap viability. While blood flow at the proximal base of the flap is preserved after elevation, blood flow in the distal aspect of flap is reduced to 20% of normal values after approximately 6 h to 12 h. The entire flap circulation reaches 75% of normal values within one to two weeks, and returns to normal levels in three to four weeks (2,3). Flap necrosis occurs secondary to systemic factors (hypotension, smoking, vasoconstrictors) influencing microcirculation or secondary to physical compression of the flap (dressings, positioning, hematoma). Partial or complete flap loss has plastic surgeons seeking interventions that may decrease the amount of distal flap ischemia and subsequent flap necrosis. Chemical or surgical delay procedures are among the most common interventions (4,5). Many agents that enhance or reduce flap viability have been reported in the literature. Investigated agents improving flap viability include agents suppressing free radical production (6,7), nitric oxide (8,9), sildenafil (10,11), vascular endothelial growth factor (12) and vasonatrin peptide (13). Unfavourable effects of smoking on wound healing and flap necrosis are well known. Many studies in the literature have demonstrated that cigarettes and nicotine enhance the rate of necrosis in random pattern flaps (14-22). Possible reasons for smoking to cause necrosis in skin flaps are both multifunctional and complex. Carbon monoxide binds to the hemoglobin molecule where oxygen is supposed to bind and, thus, displaces oxygen. Moreover, affinity of carbon monoxide to hemoglobin is 250 times greater than that of oxygen (23). Blood of
Journal of plastic, reconstructive & aesthetic surgery : JPRAS, 2014
Botulinum toxin injections are previously reported to be a noninvasive alternative method for tre... more Botulinum toxin injections are previously reported to be a noninvasive alternative method for treating masseteric hypertrophy. However, there is a debate on finding an ideal place for injection. The aim of this study is to document the anatomical landmarks for defining the motor nerve entry points (MNEPs) of the masseteric nerve in the masseter for effective botulinum toxin injections. Twelve sides from six adult fixed cadavers were used for this study. The MNEPs of the masseteric nerve were defined according to standard landmark lines including the orbitomeatal line (OML) and the line (VL), which intersects the mid-distance of the OML to the tip of the angle of the mandible. All MNEPs were located 4.4 cm inferior to the OML. In addition, the average anterior distance of the MNEPs to the VL was 1.4 cm and the average posterior distance was 0.6 cm. The ideal site of Botox injection into the masseter is a rectangular area: 5 cm inferior to the OML, 1 cm anterior and posterior to the V...
The aim of the present study was to investigate the effect of ischaemic preconditioning compared ... more The aim of the present study was to investigate the effect of ischaemic preconditioning compared with the surgical delay procedure in an effort to increase the survival rate of single pedicle island venous flaps. Eighteen male Wistar albino rats (250-350 g) were included. A 3 × 4 cm flap was planned at the right lower abdomen of the rat. Superficial epigastric vein constituted the pedicle of the flap. The rats were divided into three groups, each consisting of six rats. In the control group, a single pedicle venous island flap was elevated on each rat and no other surgical procedure was performed. In the ischaemic preconditioning group, ischaemic preconditioning was performed and, in the surgical delay procedure group, the surgical delay technique was performed before flap elevation. The mean necrosis areas were 56.85 ± 14.60%, 28.73 ± 15.60%, and 12.08 ± 3.65% in the control, ischaemic preconditioning, and surgical delay procedure groups, respectively. The necrosis areas were significantly smaller in the ischaemic preconditioning group and surgical delay procedure groups compared to the control group (p = 0.004 and p < 0.001, respectively). The necrosis areas were similar in the ischaemic preconditioning and surgical delay procedure groups. Histopathological parameters including necrosis, abscess formation, and skin ulceration scores were significantly lower in the ischaemic preconditioning group than in the control group, whereas the study groups were similar. In conclusion, ischaemic preconditioning may serve as an adjuvant technique in increasing venous island flap viability.
In this paper, we analyze the complexity of topological conjugacy of pointed Cantor minimal syste... more In this paper, we analyze the complexity of topological conjugacy of pointed Cantor minimal systems from the point of view of descriptive set theory. We prove that the topological conjugacy relation on pointed Cantor minimal systems is Borel bireducible with the Borel equivalence relation ∆ + R on R N defined by x∆ + R y ⇔ {x i : i ∈ N} = {y i : i ∈ N}. Moreover, we show that ∆ + R is a lower bound for the Borel complexity of topological conjugacy of Cantor minimal systems. Finally, we interpret our results in terms of properly ordered Bratteli diagrams and discuss some applications.
These are the lecture notes of a one-week course I taught at the Nesin Mathematics Village in Şir... more These are the lecture notes of a one-week course I taught at the Nesin Mathematics Village in Şirince, İzmir, Turkey during Summer 2018. The aim of the course was to introduce various paradoxical decompositions, prove the Banach-Tarski theorem and introduce amenable groups.
These are the lecture notes of a one-week course I taught at the Nesin Mathematics Village in Şir... more These are the lecture notes of a one-week course I taught at the Nesin Mathematics Village in Şirince, İzmir, Turkey during Summer 2017. The aim of the course was to introduce some basic notions of combinatorial set theory and prove some key results regarding partition relations for cardinals and the tree property of cardinals.
F lap surgery is a common procedure in plastic surgery practice. Flaps are used for various purpo... more F lap surgery is a common procedure in plastic surgery practice. Flaps are used for various purposes including covering poorly vascularized areas in donor fields, reconstructing full-thickness defects of the eyelids, lips, nose and cheek, repairing congenital and acquired defects, and providing contour for protruding body areas (1). Various alterations, primarily in vascular balance, occur after flap elevation. Vascular support should be provided and postischemic effects should be minimized for flap viability. While blood flow at the proximal base of the flap is preserved after elevation, blood flow in the distal aspect of flap is reduced to 20% of normal values after approximately 6 h to 12 h. The entire flap circulation reaches 75% of normal values within one to two weeks, and returns to normal levels in three to four weeks (2,3). Flap necrosis occurs secondary to systemic factors (hypotension, smoking, vasoconstrictors) influencing microcirculation or secondary to physical compression of the flap (dressings, positioning, hematoma). Partial or complete flap loss has plastic surgeons seeking interventions that may decrease the amount of distal flap ischemia and subsequent flap necrosis. Chemical or surgical delay procedures are among the most common interventions (4,5). Many agents that enhance or reduce flap viability have been reported in the literature. Investigated agents improving flap viability include agents suppressing free radical production (6,7), nitric oxide (8,9), sildenafil (10,11), vascular endothelial growth factor (12) and vasonatrin peptide (13). Unfavourable effects of smoking on wound healing and flap necrosis are well known. Many studies in the literature have demonstrated that cigarettes and nicotine enhance the rate of necrosis in random pattern flaps (14-22). Possible reasons for smoking to cause necrosis in skin flaps are both multifunctional and complex. Carbon monoxide binds to the hemoglobin molecule where oxygen is supposed to bind and, thus, displaces oxygen. Moreover, affinity of carbon monoxide to hemoglobin is 250 times greater than that of oxygen (23). Blood of
Journal of plastic, reconstructive & aesthetic surgery : JPRAS, 2014
Botulinum toxin injections are previously reported to be a noninvasive alternative method for tre... more Botulinum toxin injections are previously reported to be a noninvasive alternative method for treating masseteric hypertrophy. However, there is a debate on finding an ideal place for injection. The aim of this study is to document the anatomical landmarks for defining the motor nerve entry points (MNEPs) of the masseteric nerve in the masseter for effective botulinum toxin injections. Twelve sides from six adult fixed cadavers were used for this study. The MNEPs of the masseteric nerve were defined according to standard landmark lines including the orbitomeatal line (OML) and the line (VL), which intersects the mid-distance of the OML to the tip of the angle of the mandible. All MNEPs were located 4.4 cm inferior to the OML. In addition, the average anterior distance of the MNEPs to the VL was 1.4 cm and the average posterior distance was 0.6 cm. The ideal site of Botox injection into the masseter is a rectangular area: 5 cm inferior to the OML, 1 cm anterior and posterior to the V...
The aim of the present study was to investigate the effect of ischaemic preconditioning compared ... more The aim of the present study was to investigate the effect of ischaemic preconditioning compared with the surgical delay procedure in an effort to increase the survival rate of single pedicle island venous flaps. Eighteen male Wistar albino rats (250-350 g) were included. A 3 × 4 cm flap was planned at the right lower abdomen of the rat. Superficial epigastric vein constituted the pedicle of the flap. The rats were divided into three groups, each consisting of six rats. In the control group, a single pedicle venous island flap was elevated on each rat and no other surgical procedure was performed. In the ischaemic preconditioning group, ischaemic preconditioning was performed and, in the surgical delay procedure group, the surgical delay technique was performed before flap elevation. The mean necrosis areas were 56.85 ± 14.60%, 28.73 ± 15.60%, and 12.08 ± 3.65% in the control, ischaemic preconditioning, and surgical delay procedure groups, respectively. The necrosis areas were significantly smaller in the ischaemic preconditioning group and surgical delay procedure groups compared to the control group (p = 0.004 and p < 0.001, respectively). The necrosis areas were similar in the ischaemic preconditioning and surgical delay procedure groups. Histopathological parameters including necrosis, abscess formation, and skin ulceration scores were significantly lower in the ischaemic preconditioning group than in the control group, whereas the study groups were similar. In conclusion, ischaemic preconditioning may serve as an adjuvant technique in increasing venous island flap viability.
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