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Lippo V J Lassila - One of the best experts on this subject based on the ideXlab platform.

  • polymerization shrinkage of experimental short glass fiber reinforced composite with semi inter penetrating polymer Network Matrix
    Dental Materials, 2008
    Co-Authors: Sufyan Garoushi, Pekka K. Vallittu, D C Watts, Lippo V J Lassila
    Abstract:

    OBJECTIVES: The aim of this study was to determine the magnitude of short fiber-reinforced composite resin, with a semi-IPN-polymer Matrix, on polymerization resin shrinkage-strain, shrinkage stress and marginal microleakage of the restoration. MATERIALS AND METHODS: Experimental composite FC resin was prepared by mixing 22.5 wt.% of short E-glass fibers, 22.5 wt.% of IPN-resin and 55 wt.% of silane treated silica fillers using a high speed mixing machine. As control material, commercial particulate filler composite resin (PFC) was used. Polymerization shrinkage-strain and stress of the specimens (n=5) were measured using the bonded-disc technique and tensilometer, respectively with respect to time. FC composite and PFC were placed incrementally in class II cavities sized 4 mm x 4 mm x 6 mm (n=8/group) using total-etch adhesive system according to manufacturer's instructions. After the class II restorations were completed, the specimens were finished and polished, thermocycled, stained, sectioned, and viewed under a stereo-microscope for leakage at occlusal/enamel and gingival/dentin margins. The data were analyzed using ANOVA. RESULTS: ANOVA revealed that restorations made from experimental FC composite had a significantly lower shrinkage stress and microleakage than those made from PFC (p<0.05). The data show that gingival margins had higher microleakage than that obtained from occlusal margins of restorations (p<0.05). CONCLUSIONS: The use of short fiber filler with semi-IPN polymer Matrix reduced polymerization shrinkage stress and microleakage compared to a conventional restorative composite.

  • short glass fiber reinforced composite with a semi interpenetrating polymer Network Matrix for temporary crowns and bridges
    The journal of contemporary dental practice, 2008
    Co-Authors: Sufyan Garoushi, Pekka K. Vallittu, Lippo V J Lassila
    Abstract:

    AIMS: The purpose of this study was to investigate the reinforcement effect of short E-glass fiber fillers on some mechanical properties of temporary crown and bridge (TCB) composite resin with a semi-interpenetrating polymer Network (semi-IPN). METHODS AND MATERIALS: Experimental temporary fiber reinforced (TFC) composite resin was prepared by mixing 15 wt% of short E-glass fibers (3 mm in length) with a 35 wt% of semi-IPN-resin (dual or chemical cure) with 50 wt% of silane treated particulate silica fillers using a high speed mixing device. Temporary crowns (n=6) and test specimens (2 x 2 x 25 mm3) (n=6) were made from the experimental TFC and conventional TCB composite (control, Protemp Garant, 3M-ESPE, St. Paul, MN, USA). A three-point bending test was done according to ISO standard 10477, and a compression loading test was carried out using a steel ball (O 3.0 mm) with a speed of 1.0 mm/min until fracture occurred. The degree of monomer conversion (DC%) of both composites was determined by Fourier transfer infrared (FTIR) spectrometry. RESULTS: The analysis of variance (ANOVA) revealed both dual and chemical cure experimental TFC composite resins had statistically significant (p<0.05) higher flexural strengths (117 and 99 MPa, respectively) and compressive load-bearing capacity (730 and 623 N, respectively) compared to the control TCB composite resin (72 MPa, 549 N). CONCLUSION: The use of short fiber fillers with semi-IPN polymer Matrix yielded an improved mechanical performance compared to a conventional TCB composite resin.

  • Short glass fiber-reinforced composite with a semi-interpenetrating polymer Network Matrix for temporary crowns and bridges.
    The journal of contemporary dental practice, 2008
    Co-Authors: Sufyan Garoushi, Pekka K. Vallittu, Lippo V J Lassila
    Abstract:

    AIMS The purpose of this study was to investigate the reinforcement effect of short E-glass fiber fillers on some mechanical properties of temporary crown and bridge (TCB) composite resin with a semi-interpenetrating polymer Network (semi-IPN). METHODS AND MATERIALS Experimental temporary fiber reinforced (TFC) composite resin was prepared by mixing 15 wt% of short E-glass fibers (3 mm in length) with a 35 wt% of semi-IPN-resin (dual or chemical cure) with 50 wt% of silane treated particulate silica fillers using a high speed mixing device. Temporary crowns (n=6) and test specimens (2 x 2 x 25 mm3) (n=6) were made from the experimental TFC and conventional TCB composite (control, Protemp Garant, 3M-ESPE, St. Paul, MN, USA). A three-point bending test was done according to ISO standard 10477, and a compression loading test was carried out using a steel ball (O 3.0 mm) with a speed of 1.0 mm/min until fracture occurred. The degree of monomer conversion (DC%) of both composites was determined by Fourier transfer infrared (FTIR) spectrometry. RESULTS The analysis of variance (ANOVA) revealed both dual and chemical cure experimental TFC composite resins had statistically significant (p

  • short glass fiber reinforced restorative composite resin with semi inter penetrating polymer Network Matrix
    Dental Materials, 2007
    Co-Authors: Sufyan Garoushi, Pekka K. Vallittu, Lippo V J Lassila
    Abstract:

    Abstract Objectives The purpose of this study was to investigate the reinforcing effect of short E-glass fiber fillers on some mechanical properties of dental composite resin with interpenetrating polymer Network (IPN)-polymer Matrix. Materials and methods Experimental composite resin was prepared by mixing short fibers (3 mm in length) with a fraction of 22.5 wt% and IPN-resin 22.5 wt% with silane treated silica filler 55 wt% using high speed mixing machine. Test specimens (2 mm × 2 mm × 25 mm) and (9.5 mm × 5.5 mm × 3 mm) were made from the experimental composite (FC) and conventional particulate composite resin (control, Z250, 3M-ESPE). The test specimens ( n  = 6) were either dry stored or water stored (37 °C for 30 days) before the mechanical tests. Three-point bending test was carried out according to ISO 10477 and compression loading test was carried out using a steel ball (O3.0 mm) with speed of 1.0 mm/min until fracture. Degree of monomer conversion (DC %) of both composites was determined by FTIR spectrometry. Water sorption and solubility of specimens were also measured. Scanning electron microscopy was used to evaluate the microstructure of the composite. Results ANOVA revealed that experimental fiber composite had statistically significantly higher mechanical performance of flexural strength (210 MPa) and compressive load-bearing capacity (1881 N) ( p Significance The use of short fiber fillers with IPN-polymer Matrix yielded improved mechanical performance compared to conventional restorative composite.

  • Polymerization shrinkage of experimental short glass fiber-reinforced composite with semi-inter penetrating polymer Network Matrix
    Dental materials : official publication of the Academy of Dental Materials, 2007
    Co-Authors: Sufyan Garoushi, Pekka K. Vallittu, D C Watts, Lippo V J Lassila
    Abstract:

    OBJECTIVES: The aim of this study was to determine the magnitude of short fiber-reinforced composite resin, with a semi-IPN-polymer Matrix, on polymerization resin shrinkage-strain, shrinkage stress and marginal microleakage of the restoration. MATERIALS AND METHODS: Experimental composite FC resin was prepared by mixing 22.5 wt.% of short E-glass fibers, 22.5 wt.% of IPN-resin and 55 wt.% of silane treated silica fillers using a high speed mixing machine. As control material, commercial particulate filler composite resin (PFC) was used. Polymerization shrinkage-strain and stress of the specimens (n=5) were measured using the bonded-disc technique and tensilometer, respectively with respect to time. FC composite and PFC were placed incrementally in class II cavities sized 4 mm x 4 mm x 6 mm (n=8/group) using total-etch adhesive system according to manufacturer's instructions. After the class II restorations were completed, the specimens were finished and polished, thermocycled, stained, sectioned, and viewed under a stereo-microscope for leakage at occlusal/enamel and gingival/dentin margins. The data were analyzed using ANOVA. RESULTS: ANOVA revealed that restorations made from experimental FC composite had a significantly lower shrinkage stress and microleakage than those made from PFC (p

Pekka K. Vallittu - One of the best experts on this subject based on the ideXlab platform.

  • Original and Repair Bulk Fracture Resistance of Particle Filler and Short Fiber–Reinforced Composites
    Operative dentistry, 2018
    Co-Authors: Jasmina Bijelic-donova, S Uctasli, Pekka K. Vallittu, L.v. Lassila
    Abstract:

    Clinical Relevance Longevity of repaired direct composite restorations may be improved by including a short E-glass fiber–reinforced composite with a semi-interpenetrating Network Matrix as the substrate material in bilayered restorations.

  • polymerization shrinkage of experimental short glass fiber reinforced composite with semi inter penetrating polymer Network Matrix
    Dental Materials, 2008
    Co-Authors: Sufyan Garoushi, Pekka K. Vallittu, D C Watts, Lippo V J Lassila
    Abstract:

    OBJECTIVES: The aim of this study was to determine the magnitude of short fiber-reinforced composite resin, with a semi-IPN-polymer Matrix, on polymerization resin shrinkage-strain, shrinkage stress and marginal microleakage of the restoration. MATERIALS AND METHODS: Experimental composite FC resin was prepared by mixing 22.5 wt.% of short E-glass fibers, 22.5 wt.% of IPN-resin and 55 wt.% of silane treated silica fillers using a high speed mixing machine. As control material, commercial particulate filler composite resin (PFC) was used. Polymerization shrinkage-strain and stress of the specimens (n=5) were measured using the bonded-disc technique and tensilometer, respectively with respect to time. FC composite and PFC were placed incrementally in class II cavities sized 4 mm x 4 mm x 6 mm (n=8/group) using total-etch adhesive system according to manufacturer's instructions. After the class II restorations were completed, the specimens were finished and polished, thermocycled, stained, sectioned, and viewed under a stereo-microscope for leakage at occlusal/enamel and gingival/dentin margins. The data were analyzed using ANOVA. RESULTS: ANOVA revealed that restorations made from experimental FC composite had a significantly lower shrinkage stress and microleakage than those made from PFC (p<0.05). The data show that gingival margins had higher microleakage than that obtained from occlusal margins of restorations (p<0.05). CONCLUSIONS: The use of short fiber filler with semi-IPN polymer Matrix reduced polymerization shrinkage stress and microleakage compared to a conventional restorative composite.

  • short glass fiber reinforced composite with a semi interpenetrating polymer Network Matrix for temporary crowns and bridges
    The journal of contemporary dental practice, 2008
    Co-Authors: Sufyan Garoushi, Pekka K. Vallittu, Lippo V J Lassila
    Abstract:

    AIMS: The purpose of this study was to investigate the reinforcement effect of short E-glass fiber fillers on some mechanical properties of temporary crown and bridge (TCB) composite resin with a semi-interpenetrating polymer Network (semi-IPN). METHODS AND MATERIALS: Experimental temporary fiber reinforced (TFC) composite resin was prepared by mixing 15 wt% of short E-glass fibers (3 mm in length) with a 35 wt% of semi-IPN-resin (dual or chemical cure) with 50 wt% of silane treated particulate silica fillers using a high speed mixing device. Temporary crowns (n=6) and test specimens (2 x 2 x 25 mm3) (n=6) were made from the experimental TFC and conventional TCB composite (control, Protemp Garant, 3M-ESPE, St. Paul, MN, USA). A three-point bending test was done according to ISO standard 10477, and a compression loading test was carried out using a steel ball (O 3.0 mm) with a speed of 1.0 mm/min until fracture occurred. The degree of monomer conversion (DC%) of both composites was determined by Fourier transfer infrared (FTIR) spectrometry. RESULTS: The analysis of variance (ANOVA) revealed both dual and chemical cure experimental TFC composite resins had statistically significant (p<0.05) higher flexural strengths (117 and 99 MPa, respectively) and compressive load-bearing capacity (730 and 623 N, respectively) compared to the control TCB composite resin (72 MPa, 549 N). CONCLUSION: The use of short fiber fillers with semi-IPN polymer Matrix yielded an improved mechanical performance compared to a conventional TCB composite resin.

  • Short glass fiber-reinforced composite with a semi-interpenetrating polymer Network Matrix for temporary crowns and bridges.
    The journal of contemporary dental practice, 2008
    Co-Authors: Sufyan Garoushi, Pekka K. Vallittu, Lippo V J Lassila
    Abstract:

    AIMS The purpose of this study was to investigate the reinforcement effect of short E-glass fiber fillers on some mechanical properties of temporary crown and bridge (TCB) composite resin with a semi-interpenetrating polymer Network (semi-IPN). METHODS AND MATERIALS Experimental temporary fiber reinforced (TFC) composite resin was prepared by mixing 15 wt% of short E-glass fibers (3 mm in length) with a 35 wt% of semi-IPN-resin (dual or chemical cure) with 50 wt% of silane treated particulate silica fillers using a high speed mixing device. Temporary crowns (n=6) and test specimens (2 x 2 x 25 mm3) (n=6) were made from the experimental TFC and conventional TCB composite (control, Protemp Garant, 3M-ESPE, St. Paul, MN, USA). A three-point bending test was done according to ISO standard 10477, and a compression loading test was carried out using a steel ball (O 3.0 mm) with a speed of 1.0 mm/min until fracture occurred. The degree of monomer conversion (DC%) of both composites was determined by Fourier transfer infrared (FTIR) spectrometry. RESULTS The analysis of variance (ANOVA) revealed both dual and chemical cure experimental TFC composite resins had statistically significant (p

  • short glass fiber reinforced restorative composite resin with semi inter penetrating polymer Network Matrix
    Dental Materials, 2007
    Co-Authors: Sufyan Garoushi, Pekka K. Vallittu, Lippo V J Lassila
    Abstract:

    Abstract Objectives The purpose of this study was to investigate the reinforcing effect of short E-glass fiber fillers on some mechanical properties of dental composite resin with interpenetrating polymer Network (IPN)-polymer Matrix. Materials and methods Experimental composite resin was prepared by mixing short fibers (3 mm in length) with a fraction of 22.5 wt% and IPN-resin 22.5 wt% with silane treated silica filler 55 wt% using high speed mixing machine. Test specimens (2 mm × 2 mm × 25 mm) and (9.5 mm × 5.5 mm × 3 mm) were made from the experimental composite (FC) and conventional particulate composite resin (control, Z250, 3M-ESPE). The test specimens ( n  = 6) were either dry stored or water stored (37 °C for 30 days) before the mechanical tests. Three-point bending test was carried out according to ISO 10477 and compression loading test was carried out using a steel ball (O3.0 mm) with speed of 1.0 mm/min until fracture. Degree of monomer conversion (DC %) of both composites was determined by FTIR spectrometry. Water sorption and solubility of specimens were also measured. Scanning electron microscopy was used to evaluate the microstructure of the composite. Results ANOVA revealed that experimental fiber composite had statistically significantly higher mechanical performance of flexural strength (210 MPa) and compressive load-bearing capacity (1881 N) ( p Significance The use of short fiber fillers with IPN-polymer Matrix yielded improved mechanical performance compared to conventional restorative composite.

Joachim M. Buhmann - One of the best experts on this subject based on the ideXlab platform.

  • AIME - Unsupervised mitral valve segmentation in echocardiography with neural Network Matrix factorization.
    Artificial Intelligence in Medicine, 2019
    Co-Authors: Luca Corinzia, Jesse Provost, Alessandro Candreva, Maurizio Tamarasso, Francesco Maisano, Joachim M. Buhmann
    Abstract:

    Mitral valve segmentation specifies a crucial first step to establish a machine learning pipeline that can support practitioners into performing diagnosis of mitral valve diseases, surgical planning, and intraoperative procedures. To this end, we propose a totally automated and unsupervised mitral valve segmentation algorithm, based on a low-dimensional neural Network Matrix factorization of echocardiography videos. The method is evaluated in a collection of echocardiography videos of patients with a variety of mitral valve diseases and exceeds the state-of-the-art method in all the metrics considered.

  • Unsupervised mitral valve segmentation in echocardiography with neural Network Matrix factorization.
    EasyChair Preprints, 2019
    Co-Authors: Luca Corinzia, Jesse Provost, Alessandro Candreva, Maurizio Tamarasso, Francesco Maisano, Joachim M. Buhmann
    Abstract:

    Mitral valve segmentation is a crucial first step to establish a machine learning pipeline that can support practitioners into performing the diagnosis of mitral valve diseases, surgical planning, and intraoperative procedures. To this end, we propose a totally automated and unsupervised mitral valve segmentation algorithm, based on a neural Network low-dimension Matrix factorization of the echocardiography video. The method is evaluated in a collection of echocardiography video of patients with a variety of mitral valve diseases and exceeds the state-of-the-art method in all the metrics considered.

Sufyan Garoushi - One of the best experts on this subject based on the ideXlab platform.

  • polymerization shrinkage of experimental short glass fiber reinforced composite with semi inter penetrating polymer Network Matrix
    Dental Materials, 2008
    Co-Authors: Sufyan Garoushi, Pekka K. Vallittu, D C Watts, Lippo V J Lassila
    Abstract:

    OBJECTIVES: The aim of this study was to determine the magnitude of short fiber-reinforced composite resin, with a semi-IPN-polymer Matrix, on polymerization resin shrinkage-strain, shrinkage stress and marginal microleakage of the restoration. MATERIALS AND METHODS: Experimental composite FC resin was prepared by mixing 22.5 wt.% of short E-glass fibers, 22.5 wt.% of IPN-resin and 55 wt.% of silane treated silica fillers using a high speed mixing machine. As control material, commercial particulate filler composite resin (PFC) was used. Polymerization shrinkage-strain and stress of the specimens (n=5) were measured using the bonded-disc technique and tensilometer, respectively with respect to time. FC composite and PFC were placed incrementally in class II cavities sized 4 mm x 4 mm x 6 mm (n=8/group) using total-etch adhesive system according to manufacturer's instructions. After the class II restorations were completed, the specimens were finished and polished, thermocycled, stained, sectioned, and viewed under a stereo-microscope for leakage at occlusal/enamel and gingival/dentin margins. The data were analyzed using ANOVA. RESULTS: ANOVA revealed that restorations made from experimental FC composite had a significantly lower shrinkage stress and microleakage than those made from PFC (p<0.05). The data show that gingival margins had higher microleakage than that obtained from occlusal margins of restorations (p<0.05). CONCLUSIONS: The use of short fiber filler with semi-IPN polymer Matrix reduced polymerization shrinkage stress and microleakage compared to a conventional restorative composite.

  • short glass fiber reinforced composite with a semi interpenetrating polymer Network Matrix for temporary crowns and bridges
    The journal of contemporary dental practice, 2008
    Co-Authors: Sufyan Garoushi, Pekka K. Vallittu, Lippo V J Lassila
    Abstract:

    AIMS: The purpose of this study was to investigate the reinforcement effect of short E-glass fiber fillers on some mechanical properties of temporary crown and bridge (TCB) composite resin with a semi-interpenetrating polymer Network (semi-IPN). METHODS AND MATERIALS: Experimental temporary fiber reinforced (TFC) composite resin was prepared by mixing 15 wt% of short E-glass fibers (3 mm in length) with a 35 wt% of semi-IPN-resin (dual or chemical cure) with 50 wt% of silane treated particulate silica fillers using a high speed mixing device. Temporary crowns (n=6) and test specimens (2 x 2 x 25 mm3) (n=6) were made from the experimental TFC and conventional TCB composite (control, Protemp Garant, 3M-ESPE, St. Paul, MN, USA). A three-point bending test was done according to ISO standard 10477, and a compression loading test was carried out using a steel ball (O 3.0 mm) with a speed of 1.0 mm/min until fracture occurred. The degree of monomer conversion (DC%) of both composites was determined by Fourier transfer infrared (FTIR) spectrometry. RESULTS: The analysis of variance (ANOVA) revealed both dual and chemical cure experimental TFC composite resins had statistically significant (p<0.05) higher flexural strengths (117 and 99 MPa, respectively) and compressive load-bearing capacity (730 and 623 N, respectively) compared to the control TCB composite resin (72 MPa, 549 N). CONCLUSION: The use of short fiber fillers with semi-IPN polymer Matrix yielded an improved mechanical performance compared to a conventional TCB composite resin.

  • Short glass fiber-reinforced composite with a semi-interpenetrating polymer Network Matrix for temporary crowns and bridges.
    The journal of contemporary dental practice, 2008
    Co-Authors: Sufyan Garoushi, Pekka K. Vallittu, Lippo V J Lassila
    Abstract:

    AIMS The purpose of this study was to investigate the reinforcement effect of short E-glass fiber fillers on some mechanical properties of temporary crown and bridge (TCB) composite resin with a semi-interpenetrating polymer Network (semi-IPN). METHODS AND MATERIALS Experimental temporary fiber reinforced (TFC) composite resin was prepared by mixing 15 wt% of short E-glass fibers (3 mm in length) with a 35 wt% of semi-IPN-resin (dual or chemical cure) with 50 wt% of silane treated particulate silica fillers using a high speed mixing device. Temporary crowns (n=6) and test specimens (2 x 2 x 25 mm3) (n=6) were made from the experimental TFC and conventional TCB composite (control, Protemp Garant, 3M-ESPE, St. Paul, MN, USA). A three-point bending test was done according to ISO standard 10477, and a compression loading test was carried out using a steel ball (O 3.0 mm) with a speed of 1.0 mm/min until fracture occurred. The degree of monomer conversion (DC%) of both composites was determined by Fourier transfer infrared (FTIR) spectrometry. RESULTS The analysis of variance (ANOVA) revealed both dual and chemical cure experimental TFC composite resins had statistically significant (p

  • short glass fiber reinforced restorative composite resin with semi inter penetrating polymer Network Matrix
    Dental Materials, 2007
    Co-Authors: Sufyan Garoushi, Pekka K. Vallittu, Lippo V J Lassila
    Abstract:

    Abstract Objectives The purpose of this study was to investigate the reinforcing effect of short E-glass fiber fillers on some mechanical properties of dental composite resin with interpenetrating polymer Network (IPN)-polymer Matrix. Materials and methods Experimental composite resin was prepared by mixing short fibers (3 mm in length) with a fraction of 22.5 wt% and IPN-resin 22.5 wt% with silane treated silica filler 55 wt% using high speed mixing machine. Test specimens (2 mm × 2 mm × 25 mm) and (9.5 mm × 5.5 mm × 3 mm) were made from the experimental composite (FC) and conventional particulate composite resin (control, Z250, 3M-ESPE). The test specimens ( n  = 6) were either dry stored or water stored (37 °C for 30 days) before the mechanical tests. Three-point bending test was carried out according to ISO 10477 and compression loading test was carried out using a steel ball (O3.0 mm) with speed of 1.0 mm/min until fracture. Degree of monomer conversion (DC %) of both composites was determined by FTIR spectrometry. Water sorption and solubility of specimens were also measured. Scanning electron microscopy was used to evaluate the microstructure of the composite. Results ANOVA revealed that experimental fiber composite had statistically significantly higher mechanical performance of flexural strength (210 MPa) and compressive load-bearing capacity (1881 N) ( p Significance The use of short fiber fillers with IPN-polymer Matrix yielded improved mechanical performance compared to conventional restorative composite.

  • Polymerization shrinkage of experimental short glass fiber-reinforced composite with semi-inter penetrating polymer Network Matrix
    Dental materials : official publication of the Academy of Dental Materials, 2007
    Co-Authors: Sufyan Garoushi, Pekka K. Vallittu, D C Watts, Lippo V J Lassila
    Abstract:

    OBJECTIVES: The aim of this study was to determine the magnitude of short fiber-reinforced composite resin, with a semi-IPN-polymer Matrix, on polymerization resin shrinkage-strain, shrinkage stress and marginal microleakage of the restoration. MATERIALS AND METHODS: Experimental composite FC resin was prepared by mixing 22.5 wt.% of short E-glass fibers, 22.5 wt.% of IPN-resin and 55 wt.% of silane treated silica fillers using a high speed mixing machine. As control material, commercial particulate filler composite resin (PFC) was used. Polymerization shrinkage-strain and stress of the specimens (n=5) were measured using the bonded-disc technique and tensilometer, respectively with respect to time. FC composite and PFC were placed incrementally in class II cavities sized 4 mm x 4 mm x 6 mm (n=8/group) using total-etch adhesive system according to manufacturer's instructions. After the class II restorations were completed, the specimens were finished and polished, thermocycled, stained, sectioned, and viewed under a stereo-microscope for leakage at occlusal/enamel and gingival/dentin margins. The data were analyzed using ANOVA. RESULTS: ANOVA revealed that restorations made from experimental FC composite had a significantly lower shrinkage stress and microleakage than those made from PFC (p

Yegor Zenkevich - One of the best experts on this subject based on the ideXlab platform.

  • Anomaly in RTT relation for DIM algebra and Network Matrix models
    Nuclear Physics B, 2017
    Co-Authors: Hidetoshi Awata, Andrei Mironov, Andrey Morozov, Alexei Morozov, Hiroaki Kanno, Yusuke Ohkubo, Yegor Zenkevich
    Abstract:

    We discuss the recent proposal of arXiv:1608.05351 about generalization of the RTT relation to Network Matrix models. We show that the RTT relation in these models is modified by a nontrivial, but essentially abelian anomaly cocycle, which we explicitly evaluate for the free field representations of the quantum toroidal algebra. This cocycle is responsible for the braiding, which permutes the external legs in the q  -deformed conformal block and its 5d/6d5d/6d gauge theory counterpart, i.e. the non-perturbative Nekrasov functions. Thus, it defines their modular properties and symmetry. We show how to cancel the anomaly using a construction somewhat similar to the anomaly matching condition in gauge theory. We also describe the singular limit to the affine Yangian (4d Nekrasov functions), which breaks the spectral duality.

  • ding iohara miki symmetry of Network Matrix models
    Physics Letters B, 2016
    Co-Authors: A Mironov, Yegor Zenkevich, A Morozov
    Abstract:

    Abstract Ward identities in the most general “Network Matrix model” from [1] can be described in terms of the Ding–Iohara–Miki algebras (DIM). This confirms an expectation that such algebras and their various limits/reductions are the relevant substitutes/deformations of the Virasoro/W-algebra for ( q , t ) and ( q 1 , q 2 , q 3 ) deformed Network Matrix models. Exhaustive for these purposes should be the Pagoda triple-affine elliptic DIM, which corresponds to Networks associated with 6d gauge theories with adjoint matter (double elliptic systems). We provide some details on elliptic qq -characters.

  • Explicit examples of DIM constraints for Network Matrix models
    Journal of High Energy Physics, 2016
    Co-Authors: Hidetoshi Awata, Andrei Mironov, Andrey Morozov, Alexei Morozov, Hiroaki Kanno, Yusuke Ohkubo, Takuya Matsumoto, Yegor Zenkevich
    Abstract:

    A bstractDotsenko-Fateev and Chern-Simons Matrix models, which describe Nekrasov functions for SYM theories in different dimensions, are all incorporated into Network Matrix models with the hidden Ding-Iohara-Miki (DIM) symmetry. This lifting is especially simple for what we call balanced Networks. Then, the Ward identities (known under the names of Virasoro/ W $$ \mathcal{W} $$ -constraints or loop equations or regularity condition for qq -characters) are also promoted to the DIM level, where they all become corollaries of a single identity.

  • Ding–Iohara–Miki symmetry of Network Matrix models
    Physics Letters B, 2016
    Co-Authors: A. D. Mironov, Alexei Morozov, Yegor Zenkevich
    Abstract:

    Abstract Ward identities in the most general “Network Matrix model” from [1] can be described in terms of the Ding–Iohara–Miki algebras (DIM). This confirms an expectation that such algebras and their various limits/reductions are the relevant substitutes/deformations of the Virasoro/W-algebra for ( q , t ) and ( q 1 , q 2 , q 3 ) deformed Network Matrix models. Exhaustive for these purposes should be the Pagoda triple-affine elliptic DIM, which corresponds to Networks associated with 6d gauge theories with adjoint matter (double elliptic systems). We provide some details on elliptic qq -characters.