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RICCI CURVATURE, CIRCULANTS, AND EXTENDED MATCHING CONDITIONS
Dagli, Mehmet,Olmez, Oktay,Smith, Jonathan D.H. Korean Mathematical Society 2019 대한수학회보 Vol.56 No.1
Ricci curvature for locally finite graphs, as proposed by Lin, Lu and Yau, provides a useful isomorphism invariant. A Matching Condition was introduced as a key tool for computation of this Ricci curvature. The scope of the Matching Condition is quite broad, but it does not cover all cases. Thus the current paper introduces extended versions of the Matching Condition, and applies them to the computation of the Ricci curvature of a class of circulants determined by certain number-theoretic data. The classical Matching Condition is also applied to determine the Ricci curvature for other families of circulants, along with Cayley graphs of abelian groups that are generated by the complements of (unions of) subgroups.
LINEAR AND NON-LINEAR LOOP-TRANSVERSAL CODES IN ERROR-CORRECTION AND GRAPH DOMINATION
Dagli, Mehmet,Im, Bokhee,Smith, Jonathan D.H. Korean Mathematical Society 2020 대한수학회보 Vol.57 No.2
Loop transversal codes take an alternative approach to the theory of error-correcting codes, placing emphasis on the set of errors that are to be corrected. Hitherto, the loop transversal code method has been restricted to linear codes. The goal of the current paper is to extend the conceptual framework of loop transversal codes to admit nonlinear codes. We present a natural example of this nonlinearity among perfect single-error correcting codes that exhibit efficient domination in a circulant graph, and contrast it with linear codes in a similar context.
Ricci curvature, circulants, and extended matching conditions
Mehmet Dagli,Oktay Olmez,Jonathan D. H. Smith 대한수학회 2019 대한수학회보 Vol.56 No.1
Ricci curvature for locally finite graphs, as proposed by Lin, Lu and Yau, provides a useful isomorphism invariant. A Matching Condition was introduced as a key tool for computation of this Ricci curvature. The scope of the Matching Condition is quite broad, but it does not cover all cases. Thus the current paper introduces extended versions of the Matching Condition, and applies them to the computation of the Ricci curvature of a class of circulants determined by certain number-theoretic data. The classical Matching Condition is also applied to determine the Ricci curvature for other families of circulants, along with Cayley graphs of abelian groups that are generated by the complements of (unions of) subgroups.
Collagenous Fibroma (Desmoplastic Fibroblastoma)
Muharrem Dagli,Adil Eryilmaz,Aydin Acar,Sezer Kulacoglu,Halit Akmansu 연세대학교의과대학 2004 Yonsei medical journal Vol.45 No.5
A Collagenous Fibroma (Desmoplastic Fibroblastoma) is a rare, benign, slowly growing, fibroblastic, soft tissue lesion. Here, the case of a 28-year-old woman, who presented with a 1-year history of a slowly growing painless mass in the right anterior aspect of her neck, is described. This type of tumor was first described by Evans in 1995, and named as a Desmoplastic fibroblastoma but was renamed, by Nielsen in 1996 as a Collagenous Fibroma. This type of tumor is frequently reported in men with a mean age at occurance of 50 years. Clinically, a Collagenous fibroma presents as a firm, well-circumscribed subcutaneous, or intramuscular, painless mass of long duration. They are mostly located in the neck and extremities. The tumors range in size from 1 to 20cm and predominantly occurs within the subcutaneous tissue, but fascial and skeletal muscle involvement is common. The treatment of a Collagenous Fibroma is a total surgical excision. No tumor recurrence has been reported the literature during the follow-up period and no tumor recurrence was observed in our case at the 1-year follow-up.
Linear and non-linear loop-transversal codes in error-correction and graph domination
Mehmet Dagli,임복희,Jonathan D. H. Smith 대한수학회 2020 대한수학회보 Vol.57 No.2
Loop transversal codes take an alternative approach to the theory of error-correcting codes, placing emphasis on the set of errors that are to be corrected. Hitherto, the loop transversal code method has been restricted to linear codes. The goal of the current paper is to extend the conceptual framework of loop transversal codes to admit nonlinear codes. We present a natural example of this nonlinearity among perfect single-error correcting codes that exhibit efficient domination in a circulant graph, and contrast it with linear codes in a similar context.