5,586 research outputs found
COMPLEXITIES OF 3-MANIFOLDS FROM TRIANGULATIONS, HEEGAARD SPLITTINGS AND SURGERY PRESENTATIONS
No full textWe study complexities of 3-manifolds defined from triangulations, Heegaard splittings, and surgery presentations. We show that these complexities are related by linear inequalities, by presenting explicit geometric constructions. We also show that our linear inequalities are asymptotically optimal. Our results are used in another paper of the author to estimate Cheeger-Gromov L-2 rho-invariants in terms of geometric group theoretic and knot theoretic data.110sciescopu
Unknotted gropes, Whitney towers, and doubly slicing knots
No full textWe study the structure of the exteriors of gropes and Whitney towers in dimension 4, focusing on their fundamental groups. In particular we introduce a notion of unknottedness of gropes and Whitney towers in the 4-sphere. We prove that various modifications of gropes and Whitney towers preserve the unknottedness and do not enlarge the fundamental group. We exhibit handlebody structures of the exteriors of gropes and Whitney towers constructed by earlier methods of Cochran, Teichner, Horn, and the first author and use them to construct examples of unknotted gropes and Whitney towers. As an application, we introduce geometric bi-filtrations of knots which approximate the double sliceness in terms of unknotted gropes and Whitney towers. We prove that the bi-filtrations do not stabilize at any stage.11Nsciescopu
Rational Whitney tower filtration of links
No full textWe present complete classifications of links in the 3-sphere modulo framed and twisted Whitney towers in a rational homology 4-ball. This provides a geometric characterization of the vanishing of the Milnor invariants of links in terms of Whitney towers. Our result also says that the higher order Arf invariants, which are conjectured to be nontrivial, measure the potential difference between the Whitney tower theory in rational homology 4-balls and that in the 4-ball extensively developed by Conant, Schneiderman and Teichner.110sciescopu
Primary decomposition in the smooth concordance group of topologically slice knots
Full text linkWe address primary decomposition conjectures for knot concordance groups,which predict direct sum decompositions into primary parts. We show that thesmooth concordance group of topologically slice knots has a large subgroup forwhich the conjectures are true and there are infinitely many primary parts eachof which has infinite rank. This supports the conjectures for topologicallyslice knots. We also prove analogues for the associated graded groups of thebipolar filtration of topologically slice knots. Among ingredients of theproof, we use amenable -signatures, Ozsv\'ath-Szab\'o -invariants andN\'emethi's result on Heegaard Floer homology of Seifert 3-manifolds. In anappendix, we present a general formulation of the notion of primarydecomposition.<br
A user-specific activity pattern generation framework for evidence-based ABW planning
No full textTo plan successful activity-based workplaces (ABW), architects need to clearly understand user-specific activity patterns through the accurate recognition of user activity. Because user activity is closely associated with space, equipment, and users, such diverse activity-related information should be essentially considered for accurate activity recognition. However, previous activity recognition methods have limitations for accurately recognizing user activity for ABW planning, because they only relied on sensor-estimated data and are, therefore, unable to comprehensively consider diverse activity-related information. The study thus integrates site investigation and sensor estimation using a Bluetooth Low Energy beacon and accelerometer for accurately recognizing user activity based on diverse activity-related information. We defined five important items of activity-related information (user actions, number of nearby users, function of space, equipment located in space, and space use policy) and developed a user-specific activity pattern generation (UAPG) framework consisting of three stages: (1) the preparation stage, (2) sensor-estimation stage, and (3) activity pattern generation stage. The demonstration was conducted through scenario-based experiments in an academic office building. In the demonstration, the UAPG framework achieved 91.8% of activity recognition accuracy and successfully generated user-specific activity patterns. In addition, information regarding space usage, proportion of activities, and spatial preference of the user was generated based on a user-specific activity pattern. Such objective information provided by the UAPG framework enables evidence-based ABW planning that efficiently accommodates users with minimal office space, while simultaneously increasing their satisfaction and productivity.
SPLITTING NUMBERS OF LINKS
No full textThe splitting number of a link is the minimal number of crossing changes between different components required, on any diagram, to convert it to a split link. We introduce new techniques to compute the splitting number, involving covering links and Alexander invariants. As an application, we completely determine the splitting numbers of links with nine or fewer crossings. Also, with these techniques, we either reprove or improve upon the lower bounds for splitting numbers of links computed by Batson and Seed using Khovanov homology.111sciescopu
Rasmussen s-invariants of satellites do not detect slice knots
No full textWe present a large family of knots for which the Rasmussen s-invariants of arbitrary satellites do not detect sliceness. This answers a question of Hedden. The proof hinges on work of Kronheimer-Mrowka and Cochran-Harvey-Horn.111Nsciescopu
Creating spatial visualizations using fine-tuned interior design style models informed by user preferences
No full textThis study examines the automated creation of spatial visualizations for interior design, emphasizing user preferences over precision. Recognizing design as a reflection of personal identity, we utilize domain-specific, image-fine-tuned AI models to capture the qualitative aspects of various design styles. In interior architecture, design styles are often categorized by shared visual features-like material use, color combinations, and furniture arrangement-based on tacit consensus rather than explicit data. These features significantly impact both the aesthetic and functional aspects of spaces, influenced by historical, cultural, and personal factors. We advanced the field with a text-to-image model that translates descriptive text into visual representations. An extensive evaluation of the default model was conducted, generating over 15,000 images across 25 design styles, which informed the subsequent integration of detailed design knowledge into the model's training. The refinement process included data preparation, textual alignment with image content, and hyperparameter optimization to develop fine-tuned models. Implemented across multiple scenarios, this approach proved successful in combining the nuanced models with the default, creating images that align with user-defined styles. This methodology serves as a tool for generating spatial visualizations that align with user requirements, providing a range of styles that cater to diverse preferences. It highlights the potential of AI in enhancing design visualization and the shift towards personalized, user-centric design solutions.
Sinus augmentation using BMP-2 in a bovine hydroxyapatite collagen carrier in dogs
Full text link치과대학/박사Objective
The objective of this study was to determine the efficacy of bone morphogenetic protein 2 (BMP-2) in a bovine hydroxyapatite/collagen (BHC) carrier to augment bone formation in a canine nasal sinus model.
Material and Methods
Eight mongrel dogs, approximately 12 months old and 30 kg in weight were used. Following preparation of bilateral sinus access windows, BHC alone (control) or loaded with E.coli-derived BMP-2 at 0.1 mg/mL was implanted in 4 animals, and BHC loaded with E.coli-derived BMP-2 at 0.5 and 1.5 mg/mL was implanted in 4 animals. The animals were euthanized at 20 weeks when block sections were obtained for micro-computed tomography and histometric analyses.
Results
Total augmented volumes did not differ significantly between groups. Histometric analysis showed significantly enhanced bone formation for the BMP-2 groups compared with control.
Conclusion
BMP-2 in a BHC carrier, even at the low 0.1-mg/mL concentration, induces osteogenic activity, enhancing local bone formation in a canine sinus model.ope
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