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Thomas Vetterlein - One of the best experts on this subject based on the ideXlab platform.
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algebras in the Positive Cone of po groups
Order, 2002Co-Authors: Anatolij Dvurečenskij, Thomas VetterleinAbstract:We systemize a number of algebras that are especially known in the field of quantum structures and that in particular arise from the Positive Cones of partially ordered groups. Generalized effect algebras, generalized difference posets, Cone algebras, commutative BCK-algebras with the relative cancellation property, and Positive minimal clans are included in the text. All these structures are conveniently characterizable as special cases of generalized pseudoeffect algebras, which we introduced in a previous paper. We establish the exact relations between all mentioned structures, thereby adding new structures whenever necessary to make the scheme of order complete. Generalized pseudoeffect algebras were under certain conditions proved to be representable by means of a po-group. From this fact, we will easily establish representation theorems for all of the structures included in discussion.
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Algebras in the Positive Cone of po-Groups
Order, 2002Co-Authors: Anatolij Dvurečenskij, Thomas VetterleinAbstract:We systemize a number of algebras that are especially known in the field of quantum structures and that in particular arise from the Positive Cones of partially ordered groups. Generalized effect algebras, generalized difference posets, Cone algebras, commutative BCK-algebras with the relative cancellation property, and Positive minimal clans are included in the text.
Anatolij Dvurečenskij - One of the best experts on this subject based on the ideXlab platform.
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algebras in the Positive Cone of po groups
Order, 2002Co-Authors: Anatolij Dvurečenskij, Thomas VetterleinAbstract:We systemize a number of algebras that are especially known in the field of quantum structures and that in particular arise from the Positive Cones of partially ordered groups. Generalized effect algebras, generalized difference posets, Cone algebras, commutative BCK-algebras with the relative cancellation property, and Positive minimal clans are included in the text. All these structures are conveniently characterizable as special cases of generalized pseudoeffect algebras, which we introduced in a previous paper. We establish the exact relations between all mentioned structures, thereby adding new structures whenever necessary to make the scheme of order complete. Generalized pseudoeffect algebras were under certain conditions proved to be representable by means of a po-group. From this fact, we will easily establish representation theorems for all of the structures included in discussion.
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Algebras in the Positive Cone of po-Groups
Order, 2002Co-Authors: Anatolij Dvurečenskij, Thomas VetterleinAbstract:We systemize a number of algebras that are especially known in the field of quantum structures and that in particular arise from the Positive Cones of partially ordered groups. Generalized effect algebras, generalized difference posets, Cone algebras, commutative BCK-algebras with the relative cancellation property, and Positive minimal clans are included in the text.
Jacob Dreiher - One of the best experts on this subject based on the ideXlab platform.
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Positive margin status in uterine cervix Cone specimens is associated with persistent recurrent high grade dysplasia
International Journal of Gynecological Pathology, 2014Co-Authors: Ruthy Shacolevy, Daniel Benharroch, Gilad Eger, Jacob Dreiher, Mihai MeirovitzAbstract:The frequency of Positive Cone margins and its significance in cervical intraepithelial neoplasia are under controversy. The purpose of the current study was to identify factors associated with Positive Cone margin status and to evaluate its clinical significance in high-grade cervical intraepithelial neoplasia. Medical records of women who underwent loop electrosurgical excision procedure at the Soroka Medical Center (January 2001-July 2011) were reviewed retrospectively. Patient age, extent of dysplasia, endocervical glands involvement, Positive margin status, type of margin involved, degree of margin involvement, and postCone endocervical curettage results were evaluated as possible factors associated with persistent/recurrent disease. A total of 376 women were included in the study. Cone margin involvement was observed in 33% (endocervical-22%, ectocervical-8%, both margins-3%). Factors significantly associated with Cone margin involvement were older age (older than 35 y), widespread dysplasia in the Cone specimen (≥4 sections) (P<0.001 for each), and endocervical glands involvement (P=0.003). Fifty patients (13%) had persistent/recurrent disease. Involvement of the Cone margins (focal: hazard ratio=17, P<0.001; extensive: hazard ratio=28, P<0.001) and older age (hazard ratio=1.18 for every 5 additional years, P=0.03) were associated with persistent/recurrent disease. We conclude that women older than 35 yr with widespread high-grade dysplasia in the Cone specimen and involvement of endocervical glands are more likely to have Positive Cone margins. Positive Cone margins, particularly when extensively involved, and increased patient age are associated with persistent/recurrent disease. These factors should be considered while planning for further management.
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Post‐conization endocervical curettage for estimating the risk of persistent or recurrent high‐grade dysplasia
International journal of gynaecology and obstetrics: the official organ of the International Federation of Gynaecology and Obstetrics, 2013Co-Authors: Ruthy Shaco-levy, Mihai Meirovitz, Gilad Eger, Daniel Benharroch, Jacob DreiherAbstract:Abstract Objective To evaluate the association between post-Cone endocervical curettage (ECC) results, either alone or with Cone margin status, and persistent/recurrent high-grade dysplasia after conization. Methods The medical records of 250 women who underwent a loop electrosurgical excision procedure with post-Cone ECC at Soroka Medical Center, Be'er Sheva, Israel, between January 2001 and July 2011 were reviewed retrospectively. Results Thirty-one women (12.4%) had evidence of high-grade dysplasia in the ECC sample. Factors associated with Positive ECC were being older than 35 years (P = 0.004) and Positive margin status (P = 0.001). Twenty-nine patients (11.6%) had persistent/recurrent high-grade dysplasia. Both high-grade dysplasia in the ECC sample (hazard ratio, 2.31; P = 0.032) and Positive Cone margins (hazard ratio, 23.4; P Conclusion High-grade dysplasia in the ECC sample was associated with Positive Cone margin status. These 2 factors were both associated with persistent/recurrent disease. Among patients with Positive Cone margins, a combination of margin status and ECC was superior to margin status alone for estimating the probability of persistent/recurrent disease. For women with negative Cone margins, ECC was less useful. Because ECC is valuable for assessing the risk of persistent/recurrent high-grade dysplasia in many cases, post-Cone ECC should be performed routinely with conization.
Mihai Meirovitz - One of the best experts on this subject based on the ideXlab platform.
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Positive margin status in uterine cervix Cone specimens is associated with persistent recurrent high grade dysplasia
International Journal of Gynecological Pathology, 2014Co-Authors: Ruthy Shacolevy, Daniel Benharroch, Gilad Eger, Jacob Dreiher, Mihai MeirovitzAbstract:The frequency of Positive Cone margins and its significance in cervical intraepithelial neoplasia are under controversy. The purpose of the current study was to identify factors associated with Positive Cone margin status and to evaluate its clinical significance in high-grade cervical intraepithelial neoplasia. Medical records of women who underwent loop electrosurgical excision procedure at the Soroka Medical Center (January 2001-July 2011) were reviewed retrospectively. Patient age, extent of dysplasia, endocervical glands involvement, Positive margin status, type of margin involved, degree of margin involvement, and postCone endocervical curettage results were evaluated as possible factors associated with persistent/recurrent disease. A total of 376 women were included in the study. Cone margin involvement was observed in 33% (endocervical-22%, ectocervical-8%, both margins-3%). Factors significantly associated with Cone margin involvement were older age (older than 35 y), widespread dysplasia in the Cone specimen (≥4 sections) (P<0.001 for each), and endocervical glands involvement (P=0.003). Fifty patients (13%) had persistent/recurrent disease. Involvement of the Cone margins (focal: hazard ratio=17, P<0.001; extensive: hazard ratio=28, P<0.001) and older age (hazard ratio=1.18 for every 5 additional years, P=0.03) were associated with persistent/recurrent disease. We conclude that women older than 35 yr with widespread high-grade dysplasia in the Cone specimen and involvement of endocervical glands are more likely to have Positive Cone margins. Positive Cone margins, particularly when extensively involved, and increased patient age are associated with persistent/recurrent disease. These factors should be considered while planning for further management.
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Post‐conization endocervical curettage for estimating the risk of persistent or recurrent high‐grade dysplasia
International journal of gynaecology and obstetrics: the official organ of the International Federation of Gynaecology and Obstetrics, 2013Co-Authors: Ruthy Shaco-levy, Mihai Meirovitz, Gilad Eger, Daniel Benharroch, Jacob DreiherAbstract:Abstract Objective To evaluate the association between post-Cone endocervical curettage (ECC) results, either alone or with Cone margin status, and persistent/recurrent high-grade dysplasia after conization. Methods The medical records of 250 women who underwent a loop electrosurgical excision procedure with post-Cone ECC at Soroka Medical Center, Be'er Sheva, Israel, between January 2001 and July 2011 were reviewed retrospectively. Results Thirty-one women (12.4%) had evidence of high-grade dysplasia in the ECC sample. Factors associated with Positive ECC were being older than 35 years (P = 0.004) and Positive margin status (P = 0.001). Twenty-nine patients (11.6%) had persistent/recurrent high-grade dysplasia. Both high-grade dysplasia in the ECC sample (hazard ratio, 2.31; P = 0.032) and Positive Cone margins (hazard ratio, 23.4; P Conclusion High-grade dysplasia in the ECC sample was associated with Positive Cone margin status. These 2 factors were both associated with persistent/recurrent disease. Among patients with Positive Cone margins, a combination of margin status and ECC was superior to margin status alone for estimating the probability of persistent/recurrent disease. For women with negative Cone margins, ECC was less useful. Because ECC is valuable for assessing the risk of persistent/recurrent high-grade dysplasia in many cases, post-Cone ECC should be performed routinely with conization.
Masakazu Kojima - One of the best experts on this subject based on the ideXlab platform.
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Extension of Completely Positive Cone Relaxation to Moment Cone Relaxation for Polynomial Optimization
Journal of Optimization Theory and Applications, 2015Co-Authors: Naohiko Arima, Sunyoung Kim, Masakazu KojimaAbstract:We propose the moment Cone relaxation for a class of polynomial optimization problems to extend the results on the completely Positive Cone programming relaxation for the quadratic optimization model by Arima, Kim and Kojima. The moment Cone relaxation is constructed to take advantage of sparsity of the polynomial optimization problems, so that efficient numerical methods can be developed in the future. We establish the equivalence between the optimal value of the polynomial optimization problem and that of the moment Cone relaxation under conditions similar to the ones assumed in the quadratic optimization model.
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A Quadratically Constrained Quadratic Optimization Model for Completely Positive Cone Programming
SIAM Journal on Optimization, 2013Co-Authors: Naohiko Arima, Sunyoung Kim, Masakazu KojimaAbstract:We propose a class of quadratic optimization problems which can be reformulated by completely Positive Cone programming with the same optimal values. The objective function can be any quadratic form. The constraints of each problem are described in terms of quadratic forms with no linear terms, and all constraints are homogeneous equalities, except one inhomogeneous equality where a quadratic form is set to be a Positive constant. For the equality constraints, “a hierarchy of copositvity” condition is assumed. This model is a generalization of the standard quadratic optimization problem of minimizing a quadratic form over the standard simplex, and covers many of the existing quadratic optimization problems studied for exact coPositive Cone and completely Positive Cone programming relaxations. In particular, it generalizes the recent results on quadratic optimization problems by Burer and the set-semidefinite representation by Eichfelder and Povh [Optim. Lett., 7 (2013), pp. 1373--1386].
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B-471 Extension of Completely Positive Cone Relaxation to Polynomial Optimization
2013Co-Authors: Naohiko Arima, Sunyoung Kim, Masakazu KojimaAbstract:We propose the moment Cone relaxation for a class of polynomial optimiza- tion problems (POPs) to extend the results on the completely Positive Cone programming relaxation for the quadratic optimization (QOP) model by Arima, Kim and Kojima. The moment Cone relaxation is constructed to take advantage of sparsity of the POPs, so that efficient numerical methods can be developed in the future. We establish the equivalence between the optimal value of the POP and that of the moment Cone relaxation under conditions similar to the ones assumed in the QOP model. The proposed method is compared with the canonical convexification procedure recently proposed by Pena, Vera and Zuluaga for POPs. The moment Cone relaxation is theoretically powerful, but nu- merically intractable. For tractable numerical methods, the doubly nonnegative Cone relaxation is derived from the moment Cone relaxation. Exploiting sparsity in the doubly nonnegative Cone relaxation and its incorporation into Lasserre's semidefinite relaxation are briefly discussed.