@article{miller_johnston_livengood_spinelli_sazdanovic_olufsen_2023, title={A topological data analysis study on murine pulmonary arterial trees with pulmonary hypertension}, volume={364}, ISSN={["1879-3134"]}, DOI={10.1016/j.mbs.2023.109056}, abstractNote={Pulmonary hypertension (PH), defined by a mean pulmonary arterial blood pressure above 20 mmHg in the main pulmonary artery, is a cardiovascular disease impacting the pulmonary vasculature. PH is accompanied by chronic vascular remodeling, wherein vessels become stiffer, large vessels dilate, and smaller vessels constrict. Some types of PH, including hypoxia-induced PH (HPH), also lead to microvascular rarefaction. This study analyzes the change in pulmonary arterial morphometry in the presence of HPH using novel methods from topological data analysis (TDA). We employ persistent homology to quantify arterial morphometry for control and HPH mice characterizing normalized arterial trees extracted from micro-computed tomography (micro-CT) images. We normalize generated trees using three pruning algorithms before comparing the topology of control and HPH trees. This proof-of-concept study shows that the pruning method affects the spatial tree statistics and complexity. We find that HPH trees are stiffer than control trees but have more branches and a higher depth. Relative directional complexities are lower in HPH animals in the right, ventral, and posterior directions. For the radius pruned trees, this difference is more significant at lower perfusion pressures enabling analysis of remodeling of larger vessels. At higher pressures, the arterial networks include more distal vessels. Results show that the right, ventral, and posterior relative directional complexities increase in HPH trees, indicating the remodeling of distal vessels in these directions. Strahler order pruning enables us to generate trees of comparable size, and results, at all pressure, show that HPH trees have lower complexity than the control trees. Our analysis is based on data from 6 animals (3 control and 3 HPH mice), and even though our analysis is performed in a small dataset, this study provides a framework and proof-of-concept for analyzing properties of biological trees using tools from Topological Data Analysis (TDA). Findings derived from this study bring us a step closer to extracting relevant information for quantifying remodeling in HPH.}, journal={MATHEMATICAL BIOSCIENCES}, author={Miller, Megan and Johnston, Natalie and Livengood, Ian and Spinelli, Miya and Sazdanovic, Radmila and Olufsen, Mette S.}, year={2023}, month={Oct} }
 @article{khovanov_sazdanovic_2023, title={Bilinear pairings on two-dimensional cobordisms and generalizations of the Deligne category}, volume={10}, ISSN={["1730-6329"]}, url={http://dx.doi.org/10.4064/fm283-8-2023}, DOI={10.4064/fm283-8-2023}, abstractNote={The Deligne category of symmetric groups is the additive Karoubi closure of the partition category. It is semisimple for generic values of the parameter t while producing categories of representations of the symmetric group when modded out by the ideal of negligible morphisms when t is a non-negative integer. The partition category may be interpreted, following Comes, via a particular linearization of the category of two-dimensional oriented cobordisms. The Deligne category and its semisimple quotients admit similar interpretations. This viewpoint coupled to the universal construction of two-dimensional topological theories leads to multi-parameter monoidal generalizations of the partition and the Deligne categories, one for each rational function in one variable.}, journal={FUNDAMENTA MATHEMATICAE}, author={Khovanov, Mikhail and Sazdanovic, Radmila}, year={2023}, month={Oct} }
 @article{chandler_sazdanovic_stella_yip_2023, title={On the strength of chromatic symmetric homology for graphs}, volume={150}, ISSN={["1090-2074"]}, url={http://dx.doi.org/10.1016/j.aam.2023.102559}, DOI={10.1016/j.aam.2023.102559}, abstractNote={In this paper, we investigate the strength of chromatic symmetric homology as a graph invariant. Chromatic symmetric homology is a lift of the chromatic symmetric function for graphs to a homological setting, and its Frobenius characteristic is a q,t generalization of the chromatic symmetric function. We exhibit three pairs of graphs where each pair has the same chromatic symmetric function but distinct homology over C as Sn-modules. We also show that integral chromatic symmetric homology contains torsion, and based on computations, conjecture that Z2-torsion in bigrading (1,0) detects nonplanarity in the graph.}, journal={ADVANCES IN APPLIED MATHEMATICS}, author={Chandler, Alex and Sazdanovic, Radmila and Stella, Salvatore and Yip, Martha}, year={2023}, month={Sep} }
 @article{chandler_sazdanovic_2022, title={<p>A broken circuit model for chromatic homology theories</p>}, volume={104}, ISSN={["1095-9971"]}, url={http://dx.doi.org/10.1016/j.ejc.2022.103538}, DOI={10.1016/j.ejc.2022.103538}, abstractNote={Using the tools of algebraic Morse theory, and the thin poset approach to constructing homology theories, we give the categorification of Whitney’s broken circuit theorem for the chromatic polynomial, and for Stanley’s chromatic symmetric function.}, journal={EUROPEAN JOURNAL OF COMBINATORICS}, author={Chandler, Alex and Sazdanovic, Radmila}, year={2022}, month={Aug} }
 @article{levitt_hajij_sazdanovic_2022, title={Big data approaches to knot theory: Understanding the structure of the Jones polynomial}, volume={11}, ISSN={["1793-6527"]}, url={http://dx.doi.org/10.1142/s021821652250095x}, DOI={10.1142/S021821652250095X}, abstractNote={ In this paper, we examine the properties of the Jones polynomial using dimensionality reduction learning techniques combined with ideas from topological data analysis. Our data set consists of more than 10 million knots up to 17 crossings and two other special families up to 2001 crossings. We introduce and describe a method for using filtrations to analyze infinite data sets where representative sampling is impossible or impractical, an essential requirement for working with knots and the data from knot invariants. In particular, this method provides a new approach for analyzing knot invariants using Principal Component Analysis. Using this approach on the Jones polynomial data, we find that it can be viewed as an approximately three-dimensional subspace, that this description is surprisingly stable with respect to the filtration by the crossing number, and that the results suggest further structures to be examined and understood. }, journal={JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS}, author={Levitt, Jesse S. F. and Hajij, Mustafa and Sazdanovic, Radmila}, year={2022}, month={Nov} }
 @article{sazdanovic_scofield_2022, title={Extremal Khovanov homology and the girth of a knot}, volume={10}, ISSN={["1793-6527"]}, url={http://dx.doi.org/10.1142/s0218216522500833}, DOI={10.1142/S0218216522500833}, abstractNote={ We show that Khovanov link homology is trivial in a range of gradings and utilize relations between Khovanov and chromatic graph homology to determine extreme Khovanov groups and corresponding coefficients of the Jones polynomial. The extent to which chromatic homology and the chromatic polynomial can be used to compute integral Khovanov homology of a link depends on the maximal girth of its all-positive graphs. In this paper, we define the girth of a link, discuss relations to other knot invariants, and describe possible values for girth. Analyzing girth leads to a description of possible all-A state graphs of any given link; e.g., if a link has a diagram such that the girth of the corresponding all-A graph is equal to [Formula: see text], then the girth of the link is equal to [Formula: see text] }, journal={JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS}, author={Sazdanovic, Radmila and Scofield, Daniel}, year={2022}, month={Oct} }
 @inbook{gasparovic_gommel_purvine_sazdanovic_wang_wang_ziegelmeier_2022, title={Local Versus Global Distances for Zigzag and Multi-Parameter Persistence Modules}, url={http://dx.doi.org/10.1007/978-3-030-95519-9_3}, DOI={10.1007/978-3-030-95519-9_3}, booktitle={Association for Women in Mathematics Series}, author={Gasparovic, Ellen and Gommel, Maria and Purvine, Emilie and Sazdanovic, Radmila and Wang, Bei and Wang, Yusu and Ziegelmeier, Lori}, year={2022} }
 @article{aslam_ardanza-trevijano_xiong_arsuaga_sazdanovic_2022, title={TAaCGH Suite for Detecting Cancer-Specific Copy Number Changes Using Topological Signatures}, volume={24}, ISSN={["1099-4300"]}, url={https://www.mdpi.com/1099-4300/24/7/896}, DOI={10.3390/e24070896}, abstractNote={Copy number changes play an important role in the development of cancer and are commonly associated with changes in gene expression. Persistence curves, such as Betti curves, have been used to detect copy number changes; however, it is known these curves are unstable with respect to small perturbations in the data. We address the stability of lifespan and Betti curves by providing bounds on the distance between persistence curves of Vietoris–Rips filtrations built on data and slightly perturbed data in terms of the bottleneck distance. Next, we perform simulations to compare the predictive ability of Betti curves, lifespan curves (conditionally stable) and stable persistent landscapes to detect copy number aberrations. We use these methods to identify significant chromosome regions associated with the four major molecular subtypes of breast cancer: Luminal A, Luminal B, Basal and HER2 positive. Identified segments are then used as predictor variables to build machine learning models which classify patients as one of the four subtypes. We find that no single persistence curve outperforms the others and instead suggest a complementary approach using a suite of persistence curves. In this study, we identified new cytobands associated with three of the subtypes: 1q21.1-q25.2, 2p23.2-p16.3, 23q26.2-q28 with the Basal subtype, 8p22-p11.1 with Luminal B and 2q12.1-q21.1 and 5p14.3-p12 with Luminal A. These segments are validated by the TCGA BRCA cohort dataset except for those found for Luminal A.}, number={7}, journal={ENTROPY}, author={Aslam, Jai and Ardanza-Trevijano, Sergio and Xiong, Jingwei and Arsuaga, Javier and Sazdanovic, Radmila}, year={2022}, month={Jul} }
 @article{khovanov_sazdanovic_2021, title={Diagrammatic categorification of the Chebyshev polynomials of the second kind}, volume={225}, ISSN={["1873-1376"]}, DOI={10.1016/j.jpaa.2020.106592}, abstractNote={We develop a diagrammatic categorification of the polynomial ring Z[x], based on a geometrically defined graded algebra. This construction generalizes to categorification of some special functions, such as Chebyshev polynomials. Diagrammatic algebras featured in these categorifications lead to the first topological interpretations of the Bernstein-Gelfand-Gelfand reciprocity property.}, number={6}, journal={Journal of Pure and Applied Algebra}, author={Khovanov, M. and Sazdanovic, R.}, year={2021}, month={Jun}, pages={1006592} }
 @article{khovanov_sazdanovic_2021, title={Diagrammatic categorification of the Chebyshev polynomials of the second kind}, volume={225}, url={http://www.sciencedirect.com/science/article/pii/S0022404920302930}, DOI={https://doi.org/10.1016/j.jpaa.2020.106592}, abstractNote={We develop a diagrammatic categorification of the polynomial ring Z[x], based on a geometrically defined graded algebra. This construction generalizes to categorification of some special functions, such as Chebyshev polynomials. Diagrammatic algebras featured in these categorifications lead to the first topological interpretations of the Bernstein-Gelfand-Gelfand reciprocity property.}, number={6}, journal={Journal of Pure and Applied Algebra}, author={Khovanov, Mikhail and Sazdanovic, Radmila}, year={2021}, pages={106592} }
 @inbook{adams_flapan_henrich_kauffman_ludwig_nelson_2021, title={Encyclopedia of Knot Theory}, url={http://dx.doi.org/10.1201/9781138298217}, DOI={10.1201/9781138298217}, abstractNote={theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject.
– Ed Witten, Recipient of the Fields Medal
I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field.
– Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis 
Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers.
Features

Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers
Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees
Edited and contributed by top researchers in the field of knot theory}, booktitle={Chapman and Hall/CRC}, author={Adams, Colin and Flapan, Erica and Henrich, Allison and Kauffman, Louis H. and Ludwig, Lewis D. and Nelson, Sam}, year={2021}, month={Feb} }
 @article{baldwin_dowlin_levine_lidman_sazdanovic_2021, title={Khovanov homology detects the figure‐eight knot}, volume={53}, ISSN={0024-6093 1469-2120}, url={http://dx.doi.org/10.1112/blms.12467}, DOI={10.1112/blms.12467}, abstractNote={We use Dowlin's spectral sequence from Khovanov homology to knot Floer homology to prove that reduced Khovanov homology with rational coefficients detects the figure‐eight knot.}, number={3}, journal={Bulletin of the London Mathematical Society}, publisher={Wiley}, author={Baldwin, John A. and Dowlin, Nathan and Levine, Adam Simon and Lidman, Tye and Sazdanovic, Radmila}, year={2021}, month={Jan}, pages={871–876} }
 @inbook{russell_sazdanovic_2021, title={Mathematics and Art: Unifying Perspectives}, ISBN={978-3-319-57071-6}, DOI={https://doi.org/10.1007/978-3-319-57072-3}, booktitle={Handbook of the Mathematics of the Arts and Sciences}, publisher={Springer}, author={Russell, H. and Sazdanovic, R.}, editor={Sriraman, B.Editor}, year={2021}, pages={497–525} }
 @inbook{caprau_gonzález_lee_lowrance_sazdanović_zhang_2021, title={On Khovanov Homology and Related Invariants}, url={http://dx.doi.org/10.1007/978-3-030-80979-9_6}, DOI={10.1007/978-3-030-80979-9_6}, abstractNote={This paper begins with a survey of some applications of Khovanov homology to low-dimensional topology, with an eye toward extending these results to \(\mathfrak {sl}(n)\) homologies. We extend Levine-Zemke’s ribbon concordance obstruction from Khovanov homology to \(\mathfrak {sl}(n)\) foam homologies for n ≥ 2, including the universal \(\mathfrak {sl}(2)\) and \(\mathfrak {sl}(3)\) foam homology theories. Inspired by Alishahi and Dowlin’s bounds for the unknotting number coming from Khovanov homology and relying on spectral sequence arguments, we produce bounds on the alternation number of a knot. Lee and Bar-Natan spectral sequences also provide lower bounds on Turaev genus.}, booktitle={Association for Women in Mathematics Series}, author={Caprau, Carmen and González, Nicolle and Lee, Christine Ruey Shan and Lowrance, Adam M. and Sazdanović, Radmila and Zhang, Melissa}, year={2021} }
 @article{dabkowski_harizanov_kauffman_przytycki_sazdanovic_sikora_2021, title={Preface}, volume={30}, ISSN={["1793-6527"]}, DOI={10.1142/S0218216521020016}, abstractNote={Journal of Knot Theory and Its RamificationsVol. 30, No. 14, 2102001 (2021) No AccessPrefaceMieczyslaw K. Dabkowski, Valentina Harizanov, Louis H. Kauffman, Jozef H. Przytycki, Radmila Sazdanovic, and Adam SikoraMieczyslaw K. DabkowskiUniversity of Texas at Dallas, USA, Valentina HarizanovGeorge Washington University, USA, Louis H. KauffmanUniversity of Illinois at Chicago, USA, Jozef H. PrzytyckiGeorge Washington University, USA, Radmila SazdanovicNorth Carolina State University, USA, and Adam SikoraSUNY Buffalo, USAhttps://doi.org/10.1142/S0218216521020016Cited by:0 Next This article is part of the issue: Special Issue: Dedicated to the 60th Birthday of J. H. PrzvtyckiGuest Editors: M. K. Dabkowski, V. Harizanov, L. H. Kauffman, J. H. Przytycki, R. Sazdanovic and A. Sikora AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail FiguresReferencesRelatedDetails Recommended Vol. 30, No. 14 Metrics History PDF download}, number={14}, journal={JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS}, author={Dabkowski, Mieczyslaw K. and Harizanov, Valentina and Kauffman, Louis H. and Przytycki, Jozef H. and Sazdanovic, Radmila and Sikora, Adam}, year={2021}, month={Dec} }
 @article{sazdanovic_summers_2021, title={Torsion in the magnitude homology of graphs}, volume={16}, ISSN={["1512-2891"]}, url={http://dx.doi.org/10.1007/s40062-021-00281-9}, DOI={10.1007/s40062-021-00281-9}, abstractNote={Magnitude homology is a bigraded homology theory for finite graphs defined by Hepworth and Willerton, categorifying the power series invariant known as magnitude which was introduced by Leinster. We analyze the structure and implications of torsion in magnitude homology. We show that any finitely generated abelian group may appear as a subgroup of the magnitude homology of a graph, and, in particular, that torsion of a given prime order can appear in the magnitude homology of a graph and that there are infinitely many such graphs. Finally, we provide complete computations of magnitude homology of a class of outerplanar graphs and focus on the ranks of the groups along the main diagonal of magnitude homology.}, number={2}, journal={JOURNAL OF HOMOTOPY AND RELATED STRUCTURES}, author={Sazdanovic, Radmila and Summers, Victor}, year={2021}, month={Jun}, pages={275–296} }
 @article{chandler_lowrance_sazdanović_summers_2021, title={Torsion in thin regions of Khovanov homology}, volume={74}, ISSN={0008-414X 1496-4279}, url={http://dx.doi.org/10.4153/s0008414x21000043}, DOI={10.4153/S0008414X21000043}, abstractNote={Abstract}, number={3}, journal={Canadian Journal of Mathematics}, publisher={Canadian Mathematical Society}, author={Chandler, Alex and Lowrance, Adam M. and Sazdanović, Radmila and Summers, Victor}, year={2021}, month={Jan}, pages={1–27} }
 @inbook{sazdanovic_2021, place={Münster, Germany}, series={Kultur: Forschung und Wissenschaft}, title={Visualizations and visual thinking in mathematics}, ISBN={9783643905352}, booktitle={On visualization: A multicentric critique beyond inforgraphics}, publisher={LIT Verlag}, author={Sazdanovic, R.}, editor={Fiorentini, Erna and Elinks, JamesEditors}, year={2021}, collection={Kultur: Forschung und Wissenschaft} }
 @book{khovanov_sazdanovic_2020, title={Bilinear pairings on two-dimensional cobordisms and generalizations of the Deligne category}, number={2007.11640}, author={Khovanov, M. and Sazdanovic, R.}, year={2020}, month={Jul} }
 @book{sazdanovic_scofield_2020, title={Extremal Khovanov homology and the girth of a knot}, number={2003.05074}, author={Sazdanovic, R. and Scofield, D.}, year={2020}, month={Mar} }
 @inbook{sazdanovic_2020, title={Khovanov Link Homology}, ISBN={9781138297845}, booktitle={Encyclopedia of Knot Theory}, publisher={Chapman & Hall}, author={Sazdanovic, R.}, editor={Adams, C. and Flapan, E. and Henrich, A. and Kauffman, L.H. and Ludwig, L.D. and Nelson, S.Editors}, year={2020}, month={Dec}, pages={Chapter 70} }
 @inproceedings{caprau_gonzalez_lee_lowrance_sazdanovic_zhang_2020, title={On Khovanov Homology and Related Invariants}, booktitle={Proceedings of the Research Collaboration Conference of the Women in Symplectic and Contact Geometry and Topology}, publisher={Springer}, author={Caprau, C. and Gonzalez, N. and Lee, Christine Ruey Shan and Lowrance, A. and Sazdanovic, R. and Zhang, M.}, year={2020}, month={Feb} }
 @article{adamaszek_adams_gasparovic_gommel_purvine_sazdanovic_wang_wang_ziegelmeier_2020, title={On homotopy types of Vietoris–Rips complexes of metric gluings}, volume={4}, ISSN={2367-1726 2367-1734}, url={http://dx.doi.org/10.1007/s41468-020-00054-y}, DOI={10.1007/s41468-020-00054-y}, abstractNote={Given a sample of points $X$ in a metric space $M$ and a scale $r>0$, the Vietoris-Rips simplicial complex $\mathrm{VR}(X;r)$ is a standard construction to attempt to recover $M$ from $X$ up to homotopy type. A deficiency of this approach is that $\mathrm{VR}(X;r)$ is not metrizable if it is not locally finite, and thus does not recover metric information about $M$. We attempt to remedy this shortcoming by defining a metric space thickening of $X$, which we call the \emph{Vietoris-Rips thickening} $\mathrm{VR}^m(X;r)$, via the theory of optimal transport. When $M$ is a complete Riemannian manifold, or alternatively a compact Hadamard space, we show that the the Vietoris-Rips thickening satisfies Hausmann's theorem ($\mathrm{VR}^m(M;r)\simeq M$ for $r$ sufficiently small) with a simpler proof: homotopy equivalence $\mathrm{VR}^m(M;r)\to M$ is canonically defined as a center of mass map, and its homotopy inverse is the (now continuous) inclusion map $M\hookrightarrow\mathrm{VR}^m(M;r)$. Furthermore, we describe the homotopy type of the Vietoris-Rips thickening of the $n$-sphere at the first positive scale parameter $r$ where the homotopy type changes.}, number={3}, journal={Journal of Applied and Computational Topology}, publisher={Springer Science and Business Media LLC}, author={Adamaszek, Michał and Adams, Henry and Gasparovic, Ellen and Gommel, Maria and Purvine, Emilie and Sazdanovic, Radmila and Wang, Bei and Wang, Yusu and Ziegelmeier, Lori}, year={2020}, month={May}, pages={425–454} }
 @inbook{gonzalez_ushakova_sazdanovic_arsuaga_2020, title={Prediction in Cancer Genomics Using Topological Signatures and Machine Learning}, ISBN={9783030434076 9783030434083}, ISSN={2193-2808 2197-8549}, url={http://dx.doi.org/10.1007/978-3-030-43408-3_10}, DOI={10.1007/978-3-030-43408-3_10}, abstractNote={Copy Number Aberrations, gains and losses of genomic regions, are a hallmark of cancer and can be experimentally detected using microarray comparative genomic hybridization (aCGH). In previous works, we developed a topology based method to analyze aCGH data whose output are regions of the genome where copy number is altered in patients with a predetermined cancer phenotype. We call this method Topological Analysis of array CGH (TAaCGH). Here we combine TAaCGH with machine learning techniques to build classifiers using copy number aberrations. We chose logistic regression on two different binary phenotypes related to breast cancer to illustrate this approach. The first case consists of patients with over-expression of the ERBB2 gene. Over-expression of ERBB2 is commonly regulated by a copy number gain in chromosome arm 17q. TAaCGH found the region 17q11-q22 associated with the phenotype and using logistic regression we reduced this region to 17q12-q21.31 correctly classifying 78% of the ERBB2 positive individuals (sensitivity) in a validation data set. We also analyzed over-expression in Estrogen Receptor (ER), a second phenotype commonly observed in breast cancer patients and found that the region 5p14.3-12 together with six full arms were associated with the phenotype. Our method identified 4p, 6p and 16q as the strongest predictors correctly classifying 76% of ER positives in our validation data set. However, for this set there was a significant increase in the false positive rate (specificity). We suggest that topological and machine learning methods can be combined for prediction of phenotypes using genetic data.}, booktitle={Topological Data Analysis}, publisher={Springer International Publishing}, author={Gonzalez, Georgina and Ushakova, Arina and Sazdanovic, Radmila and Arsuaga, Javier}, year={2020}, pages={247–276} }
 @book{chandler_sazdanovic_2019, title={A Broken Circuit Model for Chromatic Homology Theories}, number={1911.13226}, author={Chandler, A. and Sazdanovic, R.}, year={2019} }
 @article{adams_gordon_jones_kauffman_lambropoulou_millett_przytycki_ricca_sazdanovic_2019, title={Knots, low-dimensional topology and applications Preface}, volume={28}, ISSN={["1793-6527"]}, DOI={10.1142/S0218216519020012}, abstractNote={Journal of Knot Theory and Its RamificationsVol. 28, No. 11, 1902001 (2019) No AccessPreface: Knots, low-dimensional topology and applicationshttps://doi.org/10.1142/S0218216519020012Cited by:0 Next This article is part of the issue: Special Issue: Knots, Low-Dimensional Topology and Applications — Part I AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail FiguresReferencesRelatedDetails Recommended Vol. 28, No. 11 Metrics History PDF download}, number={11}, journal={JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS}, author={Adams, Colin C. and Gordon, Cameron McA and Jones, Vaughan F. R. and Kauffman, Louis H. and Lambropoulou, Sofia and Millett, Kenneth and Przytycki, Jozef H. and Ricca, Renzo and Sazdanovic, Radmila}, year={2019}, month={Oct} }
 @article{adams_gordon_jones_kauffman_lambropoulou_millett_przytycki_ricca_sazdanovic_2019, title={Knots, low-dimensional topology and applications Preface}, volume={28}, ISSN={["1793-6527"]}, DOI={10.1142/S0218216519030019}, number={13}, journal={JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS}, author={Adams, Colin C. and Gordon, Cameron McA and Jones, Vaughan F. R. and Kauffman, Louis H. and Lambropoulou, Sofia and Millett, Kenneth and Przytycki, Jozef H. and Ricca, Renzo and Sazdanovic, Radmila}, year={2019}, month={Nov} }
 @book{gasparovic_gommel_purvine_sazdanovic_wang_wang_ziegelmeier_2019, title={Local Versus Global Distances for Zigzag Persistence Modules}, number={1903.08298}, author={Gasparovic, E. and Gommel, M. and Purvine, E. and Sazdanovic, R. and Wang, B. and Wang, Y. and Ziegelmeier, L.}, year={2019} }
 @article{cooper_silva_sazdanovic_2019, title={On configuration spaces and simplicial complexes}, volume={25}, journal={New York J. Math}, author={Cooper, Andrew A and Silva, Vin and Sazdanovic, Radmila}, year={2019}, pages={723–744} }
 @book{chandler_sazdanovic_stella_yip_2019, title={On the Strength of Chromatic Symmetric Homology for graphs}, number={1911.13297}, author={Chandler, A. and Sazdanovic, R. and Stella, S. and Yip, M.}, year={2019} }
 @article{nelson_oyamaguchi_sazdanovic_2019, title={Psyquandles, Singular Knots and Pseudoknots}, volume={42}, ISSN={["0387-3870"]}, DOI={10.3836/tjm/1502179287}, abstractNote={We generalize the notion of biquandles to psyquandles and use these to define invariants of oriented singular links and pseudolinks. In addition to psyquandle counting invariants, we introduce Alexander psyquandles and corresponding invariants such as Alexander psyquandle polynomials and Alexander-Gr\"obner psyquandle invariants of oriented singular knots and links. We consider the relationship between Alexander psyquandle colorings of pseudolinks and p-colorings of pseudolinks. As a special case we define a generalization of the Alexander polynomial for oriented singular links and pseudolinks we call the Jablan polynomial and compute the invariant for all pseudoknots with up to five crossings and all 2-bouquet graphs with up to 6 classical crossings.}, number={2}, journal={TOKYO JOURNAL OF MATHEMATICS}, author={Nelson, Sam and Oyamaguchi, Natsumi and Sazdanovic, Radmila}, year={2019}, month={Dec}, pages={405–429} }
 @article{gasparovic_gommel_purvine_sazdanovic_wang_wang_ziegelmeier_2019, title={The relationship between the intrinsic Čech and persistence distortion distances for metric graphs}, url={https://jocg.org/index.php/jocg/article/view/3082}, DOI={10.20382/JOCG.V10I1A16}, abstractNote={Metric graphs are meaningful objects for modeling complex structures that arise in many real-world applications, such as road networks, river systems, earthquake faults, blood vessels, and filamentary structures in galaxies. To study metric graphs in the context of comparison, we are interested in determining the relative discriminative capabilities of two topology-based distances between a pair of arbitrary finite metric graphs: the persistence distortion distance and the intrinsic Cech distance. We explicitly show how to compute the intrinsic Cech distance between two metric graphs based solely on knowledge of the shortest systems of loops for the graphs. Our main theorem establishes an inequality between the intrinsic Cech and persistence distortion distances in the case when one of the graphs is a bouquet graph and the other is arbitrary. The relationship also holds when both graphs are constructed via wedge sums of cycles and edges.}, journal={Journal of Computational Geometry}, publisher={Journal of Computational Geometry}, author={Gasparovic, Ellen and Gommel, Maria and Purvine, Emilie and Sazdanovic, Radmila and Wang, Bei and Wang, Yusu and Ziegelmeier, Lori}, year={2019}, month={Nov}, pages={Vol. 10 No. 1 (2019)} }
 @article{gasparovic_gommel_purvine_sazdanovic_wang_wang_ziegelmeier_2019, title={The relationship between the intrinsic Čech and persistence distortion distances for metric graphs}, volume={10}, number={1}, journal={Journal of Computational Geometry}, author={Gasparovic, E. and Gommel, M. and Purvine, E. and Sazdanovic, R. and Wang, B. and Wang, Y. and Ziegelmeier, L.}, year={2019}, pages={477–499} }
 @book{sazdanovic_summers_2019, title={Torsion in the Magnitude homology of graphs}, number={1912.13483}, author={Sazdanovic, R. and Summers, V.}, year={2019} }
 @article{gasparovic_gommel_purvine_sazdanovic_wang_wang_ziegelmeier_2018, title={A Complete Characterization of the One-Dimensional Intrinsic Čech Persistence Diagrams for Metric Graphs}, DOI={10.1007/978-3-319-89593-2_3}, abstractNote={Metric graphs are special types of metric spaces used to model and represent simple, ubiquitous, geometric relations in data such as biological networks, social networks, and road networks. We are interested in giving a qualitative description of metric graphs using topological summaries. In particular, we provide a complete characterization of the one-dimensional intrinsic Čech persistence diagrams for finite metric graphs using persistent homology. Together with complementary results by Adamaszek et al., which imply the results on intrinsic Čech persistence diagrams in all dimensions for a single cycle, our results constitute the important steps toward characterizing intrinsic Čech persistence diagrams for arbitrary finite metric graphs across all dimensions.}, journal={Research in Computational Topology}, publisher={Springer International Publishing}, author={Gasparovic, Ellen and Gommel, Maria and Purvine, Emilie and Sazdanovic, Radmila and Wang, Bei and Wang, Yusu and Ziegelmeier, Lori}, year={2018}, pages={33–56} }
 @article{sazdanovic_yip_2018, title={A categorification of the chromatic symmetric function}, volume={154}, ISSN={0097-3165}, url={http://dx.doi.org/10.1016/j.jcta.2017.08.014}, DOI={10.1016/j.jcta.2017.08.014}, abstractNote={The Stanley chromatic symmetric function XG of a graph G is a symmetric function generalization of the chromatic polynomial and has interesting combinatorial properties. We apply the ideas from Khovanov homology to construct a homology theory of graded Sn-modules, whose graded Frobenius series FrobG(q,t) specializes to the chromatic symmetric function at q=t=1. This homology theory can be thought of as a categorification of the chromatic symmetric function, and it satisfies homological analogues of several familiar properties of XG. In particular, the decomposition formula for XG discovered recently by Orellana, Scott, and independently by Guay-Paquet, is lifted to a long exact sequence in homology.}, journal={Journal of Combinatorial Theory, Series A}, publisher={Elsevier BV}, author={Sazdanovic, Radmila and Yip, Martha}, year={2018}, month={Feb}, pages={218–246} }
 @article{sazdanovic_2018, title={Khovanov homology and torsion}, ISBN={["978-3-11-057148-6"]}, DOI={10.1515/9783110571493-005}, abstractNote={The present chapter gives an overview on results for discrete knot energies. These discrete energies are designed to make swift numerical computations and thus open the field to computational methods. Additionally, they provide an independent, geometrically pleasing and consistent discrete model that behaves similarly to the original model. We will focus on M\"obius energy, integral Menger curvature and thickness.}, journal={NEW DIRECTIONS IN GEOMETRIC AND APPLIED KNOT THEORY}, author={Sazdanovic, Radmila}, year={2018}, pages={125–137} }
 @article{sazdanovic_scofield_2018, title={Patterns in Khovanov link and chromatic graph homology}, volume={27}, ISSN={["1793-6527"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85044463913&partnerID=MN8TOARS}, DOI={10.1142/s0218216518400072}, abstractNote={Khovanov homology of a link and chromatic graph homology are known to be isomorphic in a range of homological gradings that depend on the girth of a graph. We discuss patterns shared by these two homology theories. In particular, we improve the bounds for the homological span of chromatic homology by Helme–Guizon, Przytycki and Rong. An explicit formula for the rank of the third chromatic homology group on the main diagonal is given and used to compute the corresponding Khovanov homology group and the fourth coefficient of the Jones polynomial for links with certain diagrams.}, number={3}, journal={JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS}, publisher={World Scientific Pub Co Pte Lt}, author={Sazdanovic, Radmila and Scofield, Daniel}, year={2018}, month={Mar} }
 @article{dabkowski_harizanov_kauffman_przytycki_sazdanovic_sikora_2018, title={Special Issue - Devoted to the 60th birthday of J. H. Przytycki; Guest Editors: M. K. Dabkowski, V. Harizanov, L. H. Kauffman, J. H. Przytycki, R. Sazdanovic and A. Sikora Preface}, volume={27}, number={3}, journal={Journal of Knot Theory and its Ramifications}, author={Dabkowski, M. K. and Harizanov, V. and Kauffman, L. H. and Przytycki, J. H. and Sazdanovic, R. and Sikora, A.}, year={2018} }
 @inproceedings{adamaszek_adams_gasparovic_gommel_purvine_sazdanovic_wang_wang_ziegelmeier_2018, title={Vietoris-rips and čech complexes of metric gluings}, volume={99}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85048959293&partnerID=MN8TOARS}, DOI={10.4230/LIPIcs.SoCG.2018.3}, abstractNote={We study Vietoris-Rips and Cech complexes of metric wedge sums and metric gluings. We show that the Vietoris-Rips (resp. Cech) complex of a wedge sum, equipped with a natural metric, is homotopy equivalent to the wedge sum of the Vietoris-Rips (resp. Cech) complexes. We also provide generalizations for certain metric gluings, i.e. when two metric spaces are glued together along a common isometric subset. As our main example, we deduce the homotopy type of the Vietoris-Rips complex of two metric graphs glued together along a sufficiently short path. As a result, we can describe the persistent homology, in all homological dimensions, of the Vietoris-Rips complexes of a wide class of metric graphs.}, booktitle={Leibniz International Proceedings in Informatics, LIPIcs}, author={Adamaszek, M. and Adams, H. and Gasparovic, E. and Gommel, M. and Purvine, E. and Sazdanovic, R. and Wang, B. and Wang, Y. and Ziegelmeier, L.}, year={2018}, pages={32–315} }
 @inproceedings{adamaszek_adams_gasparovic_gommel_purvine_sazdanovic_wang_wang_ziegelmeier_2018, place={Wadern, Germany}, series={LIPIcs - Leibniz International Proceedings in Informatics}, title={Vietoris–Rips and Cech Complexes of Metric Gluings}, volume={3}, number={1-3}, booktitle={34th International Symposium on Computational Geometry (SoCG 2018)}, publisher={Wadern Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH}, author={Adamaszek, M. and Adams, H. and Gasparovic, E. and Gommel, M. and Purvine, E. and Sazdanovic, R. and Wang, B. and Wang, Y. and Ziegelmeier, L.}, editor={Speckmann, Bettina and Toth, Csaba D.Editors}, year={2018}, pages={218–246}, collection={LIPIcs - Leibniz International Proceedings in Informatics} }
 @article{lowrance_sazdanovic_2017, title={Chromatic homology, Khovanov homology, and torsion}, volume={222}, ISSN={["1879-3207"]}, DOI={10.1016/j.topol.2017.02.078}, abstractNote={In the first few homological gradings, there is an isomorphism between the Khovanov homology of a link and the categorification of the chromatic polynomial of a graph related to the link. In this article, we show that all torsion in the categorification of the chromatic polynomial is of order two, and hence all torsion in Khovanov homology in the gradings where the isomorphism is defined is of order two. We also prove that odd Khovanov homology is torsion-free in its first few homological gradings.}, journal={TOPOLOGY AND ITS APPLICATIONS}, publisher={Elsevier BV}, author={Lowrance, Adam M. and Sazdanovic, Radmila}, year={2017}, month={May}, pages={77–99} }
 @inproceedings{guan_tang_krim_keiser_rindos_sazdanovic_2016, title={A topological collapse for document summarization}, volume={2016-August}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84984653594&partnerID=MN8TOARS}, DOI={10.1109/spawc.2016.7536867}, abstractNote={As a useful tool to summarize documents, keyphrase extraction extracts a set of single or multiple words, called keyphrases, that capture the primary topics discussed in a document. In this paper we propose DoCollapse, a topological collapse-based unsupervised keyphrase extraction method that relies on networking document by semantic relatedness of candidate keyphrases. A semantic graph is built with candidates keyphrases as vertices and then reduced to its core using topological collapse algorithm to facilitate final keyphrase selection. Iteratively collapsing dominated vertices aids in removing noisy candidates and revealing important points. We conducted experiments on two standard evaluation datasets composed of scientific papers and found that DoCollapse outperforms state-of-the-art methods. Results show that simplifying a document graph by homology-preserving topological collapse benefits keyphrase extraction.}, booktitle={2016 IEEE 17th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)}, publisher={IEEE}, author={Guan, Hui and Tang, Wen and Krim, Hamid and Keiser, James and Rindos, Andrew and Sazdanovic, Radmila}, year={2016}, month={Jul} }
 @article{jablan_sazdanovic_2016, title={From Conway Notation to LinKnot}, volume={670}, ISBN={["978-1-4704-2257-8"]}, ISSN={["1098-3627"]}, DOI={10.1090/conm/670/13445}, journal={KNOT THEORY AND ITS APPLICATIONS}, publisher={American Mathematical                    Society}, author={Jablan, Slavik V. and Sazdanovic, Radmila}, year={2016}, pages={63–92} }
 @article{radovic_gerdes_jablan_sazdanovic_2016, title={Plaited polyhedra: A knot theory point of view}, volume={25}, ISSN={["1793-6527"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84980383623&partnerID=MN8TOARS}, DOI={10.1142/s0218216516410066}, abstractNote={Plaited polyhedra, discovered by P. Gerdes in African dance rattle capsules are analyzed from the knot-theory point of view. Every plaited polyhedron can be derived from a knot or link diagram as its dual. In the attempt to classify obtained plaited polyhedra, we propose different methods based on families of knots and links in Conway notation or their corresponding braid families, both leading to the notion of families of plaited polyhedra.}, number={9}, journal={JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS}, publisher={World Scientific Pub Co Pte Lt}, author={Radovic, Ljiljana and Gerdes, Paulus and Jablan, Slavik and Sazdanovic, Radmila}, year={2016}, month={Aug} }
 @article{kauffman_lambropoulou_sazdanovic_2016, title={Remembering Slavik Jablan}, volume={25}, ISSN={["1793-6527"]}, DOI={10.1142/s0218216516020028}, abstractNote={Journal of Knot Theory and Its RamificationsVol. 25, No. 09, 1602002 (2016) Special Issue for Slavic Jablan; Guest Editors: L. H. Kauffman, R. Sazdanovic and S. LambropoulouNo AccessRemembering Slavik JablanLouis H. Kauffman, Sofia Lambropoulou, and Radmila SazdanovicLouis H. KauffmanUniversity of Illinois at Chicago, USA, Sofia LambropoulouNational Technology University of Athens, Greece, and Radmila SazdanovicNorth Carolina State University, USAhttps://doi.org/10.1142/S0218216516020028Cited by:0 Next AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail References 1. S. Jablan, A new method of generating plane groups of simple and multiple antisymmetry, Acta Cryst. A 42 (1986) 209–212. Crossref, ISI, Google Scholar2. S. Jablan, A new method of deriving and cataloguing simple and Multiple G3l space groups, Acta Cryst. A 43 (1987) 326–337. Crossref, ISI, Google Scholar3. S. Jablan, Algebra of antisymmetric characteristics, Publ. Inst. Math. 47(61) (1990) 39–55. Google Scholar4. S. Jablan, Mackay groups, Acta Cryst. A 49 (1993) 132–137. Crossref, ISI, Google Scholar5. S. Jablan and A. F. Palistrant, Space groups of simple and multiple colored antisymmetry, kristallografiya 38(2) (1993) 4–11. Google Scholar6. S. Jablan, Edge-bicolorings of regular polyhedra, Z. Kristall 210 (1995) 173–176. Crossref, Google Scholar7. S. V. Jablan, Geometry of links, Novi Sad J. Math. 29(3) (1999) 121–139. Google Scholar8. S. V. Jablan, New knot tables, Filomat (Nis), (2002), 141–152, http://www.mi.sanu. ac.rs/jablans/knotab/index.html. Google Scholar9. S. Jablan and R. Sazdanovic, Unlinking number and unlinking gap, J. Knot Theory Ramification 16(10) (2007) 1331–1355. Link, ISI, Google Scholar10. S. Jablan and R. Sazdanovic, Braid family representatives, J. Knot Theory Ramification 17(7) (2008) 817–833. Link, ISI, Google Scholar11. S. Jablan, Lj. Radović and R. Sazdanovic, Tutte and jones polynomials of link families, Filomat 24(3) (2010) 19–33. Crossref, ISI, Google Scholar12. S. Jablan, Lj. Radović and R. Sazdanovic, Adequacy of link families, Publ. Inst. Math. 88(102) (2010) 21–52. Crossref, Google Scholar13. S. Jablan, Lj. Radović and R. Sazdanovic, Pyramidal knots and links and their invariants, MATCH-Commun. Math. Comput. Chem. 65(3) (2011) 541–580. ISI, Google Scholar14. S. Jablan, Lj. Radović and R. Sazdanovic, Knots and links derived from prismatic graphs, MATCH-Commun. Math. Comput. Chem. 66(1) (2011) 65–92. ISI, Google Scholar15. S. Jablan and Lj. Radović, Do you like paleolithic Op-Art? Kybernetes 40(7–8) (2011) 1045–1054 Crossref, ISI, Google Scholar16. S. Jablan, Lj. Radović and R. Sazdanovic, Tute and Jones polynomials of links, polyominoes and graphical recombination patterns, J. Math. Chem. 49(1) (2011) 79–94. Crossref, ISI, Google Scholar17. S. Jablan, Lj. Radović and R. Sazdanovic, Nonplanar graphs derived from gauss codes of virtual knots and links, J. Math. Chem. 49(10) (2011) 2250–2267. Crossref, ISI, Google Scholar18. S. Jablan, Lj. Radović, R. Sazdanovic and A. Zekovic, Mirror-curves and knot mosaics, Comput. Math. Appl. 64(4) (2012) 527–543. Crossref, ISI, Google Scholar19. L. Kauffman, S. Jablan, Lj. Radović and R. Sazdanovic, Reduced relative tutte, Kauffman bracket and Jones polynomials of virtual link families, J. Knot Theory Ramifications 22(4) (2013). Link, ISI, Google Scholar20. A. Henrich, R. Hoberg, S. Jablan, L. Johnson, E. Minten and Lj. Radović, The theory of pseudoknots, J. Knot Theory Ramifications 22(7) (2013). Link, ISI, Google Scholar21. S. Jablan, L. H. Kauffman and P. Lopes, On the maximum number of colors for links, J. Knot Theory Ramifications, 22(3) (2013). Link, ISI, Google Scholar22. L. H. Kauffman and S. V. Jablan, A note on amphicheiral alternating links, J. Knot Theory Ramifications, 22(1) (2013). Link, ISI, Google Scholar23. S. Jablan, Lj. Radović, Unknotting numbers of alternating knot and link families, Publ. Inst. Math. 95(109) (2014) 87–99. Crossref, Google Scholar24. A. Henrich and S. V. Jablan, On the coloring of Pseudoknots, J. Knot Theory Ramifications 23(12) (2014). Link, ISI, Google Scholar25. Lj. Radović and S. Jablan, Meander knots and links, Filomat 29(10) (2015) 2381–2392. Crossref, ISI, Google Scholar26. S. Jablan, L. H. Kauffman and P. Lopes, The Delunification process and minimal diagrams, Topology Appl. 193 (2015) 270–289. Crossref, Google Scholar FiguresReferencesRelatedDetails Recommended Vol. 25, No. 09 Metrics History PDF download}, number={9}, journal={JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS}, author={Kauffman, Louis H. and Lambropoulou, Sofia and Sazdanovic, Radmila}, year={2016}, month={Aug} }
 @article{sazdanovic_kauffman_radovic_2016, title={Remembrance Slavik Jablan (1952-2015)}, volume={25}, ISSN={["1793-6527"]}, DOI={10.1142/s021821651602003x}, number={9}, journal={JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS}, author={Sazdanovic, Radmila and Kauffman, Louis H. and Radovic, Ljiljana}, year={2016}, month={Aug} }
 @article{zekovic_jablan_kauffman_sazdanovic_stosic_2016, title={Unknotting and maximum unknotting numbers}, volume={25}, ISSN={["1793-6527"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84979240749&partnerID=MN8TOARS}, DOI={10.1142/s0218216516410108}, abstractNote={ We introduce concepts of the maximum unknotting number and the mixed unknotting number, taking into consideration the Bernhard–Jablan Conjecture about computing the unknotting number based only on minimal knot diagrams. The existence of Kauffman knots (alternating knots, such that a crossing change does not change their minimal crossing number) was first suggested by Kauffman. We extend the concept and offer three related classes of knots named: Kauffman knots, Zeković knots and Taniyama knots. }, number={9}, journal={JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS}, publisher={World Scientific Pub Co Pte Lt}, author={Zekovic, Ana and Jablan, Slavik and Kauffman, Louis and Sazdanovic, Radmila and Stosic, Marko}, year={2016}, month={Aug} }
 @inproceedings{khovanov_sazdanovic_2015, title={A Categorification of One-Variable Polynomials}, booktitle={Discrete Mathematics and Theoretical Computer Science}, author={Khovanov, M. and Sazdanovic, R.}, year={2015}, pages={937–948} }
 @inproceedings{sazdanovic_yip_2015, title={A categorification of the chromatic symmetric polynomial}, booktitle={Discrete Mathematics and Theoretical Computer Science}, author={Sazdanovic, R. and Yip, M.}, year={2015}, pages={631–642} }
 @article{khovanov_sazdanovic_2015, title={Categorifications of the polynomial ring}, volume={230}, ISSN={["1730-6329"]}, DOI={10.4064/fm230-3-3}, abstractNote={We develop a diagrammatic categorification of the polynomial ring $Z[x]$. Our categorification satisfies a version of Bernstein-Gelfand-Gelfand reciprocity property with the indecomposable projective modules corresponding to $x^n$ and standard modules to $(x-1)^n$ in the Grothendieck ring.}, number={3}, journal={FUNDAMENTA MATHEMATICAE}, publisher={Institute of Mathematics, Polish Academy of Sciences}, author={Khovanov, Mikhail and Sazdanovic, Radmila}, year={2015}, pages={251–280} }
 @article{crowe_darvas_huylebrouck_kappraff_kauffman_lambropoulou_przytycki_radovic_sazdanovic_spinadel_et al._2015, title={In Memoriam: Slavik Jablan 1952-2015 Obituary}, volume={7}, ISSN={["2073-8994"]}, DOI={10.3390/sym7031261}, abstractNote={After a long and brave battle with a serious illness, our dear friend and colleague Slavik Jablan passed away on 26 February 2015. [...]}, number={3}, journal={SYMMETRY-BASEL}, author={Crowe, Donald and Darvas, Gyoergy and Huylebrouck, Dirk and Kappraff, Jay and Kauffman, Louis and Lambropoulou, Sofia and Przytycki, Jozef and Radovic, Ljiljana and Sazdanovic, Radmila and Spinadel, Vera W. and et al.}, year={2015}, month={Sep}, pages={1261–1274} }
 @article{przytycki_sazdanovic_2014, title={Torsion in Khovanov homology of semi-adequate links}, volume={225}, ISSN={["1730-6329"]}, DOI={10.4064/fm225-1-13}, abstractNote={The goal of this paper is to address A. Shumakovitch's conjecture about the existence of $\Z_2$-torsion in Khovanov link homology. We analyze torsion in Khovanov homology of semi-adequate links via chromatic cohomology for graphs which provides a link between the link homology and well-developed theory of Hochschild homology. In particular, we obtain explicit formulae for torsion and prove that Khovanov homology of semi-adequate links contains $Z_2$-torsion if the corresponding Tait-type graph has a cycle of length at least 3. Computations show that torsion of odd order exists but there is no general theory to support these observations. We conjecture that the existence of torsion is related to the braid index.}, number={1}, journal={FUNDAMENTA MATHEMATICAE}, publisher={Institute of Mathematics, Polish Academy of Sciences}, author={Przytycki, Jozef H. and Sazdanovic, Radmila}, year={2014}, pages={277–303} }
 @article{kauffman_jablan_radović_sazdanović_2013, title={REDUCED RELATIVE TUTTE, KAUFFMAN BRACKET AND JONES POLYNOMIALS OF VIRTUAL LINK FAMILIES}, volume={22}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84877608644&partnerID=MN8TOARS}, DOI={10.1142/s0218216513400038}, abstractNote={ This paper contains general formulae for the reduced relative Tutte, Kauffman bracket and Jones polynomials of families of virtual knots and links given in Conway notation and discussion of a counterexample to the Z-move conjecture of Fenn, Kauffman and Manturov. }, number={04}, journal={Journal of Knot Theory and Its Ramifications}, publisher={World Scientific Pub Co Pte Lt}, author={KAUFFMAN, LOUIS H. and JABLAN, SLAVIK and RADOVIĆ, LJILJANA and SAZDANOVIĆ, RADMILA}, year={2013}, month={Apr}, pages={1340003} }
 @article{nanda_sazdanović_2013, title={Simplicial Models and Topological Inference in Biological Systems}, DOI={10.1007/978-3-642-40193-0_6}, abstractNote={This article is a user’s guide to algebraic topological methods for data analysis with a particular focus on applications to datasets arising in experimental biology. We begin with the combinatorics and geometry of simplicial complexes and outline the standard techniques for imposing filtered simplicial structures on a general class of datasets. From these structures, one computes topological statistics of the original data via the algebraic theory of (persistent) homology. These statistics are shown to be computable and robust measures of the shape underlying a dataset. Finally, we showcase some appealing instances of topology-driven inference in biological settings, from the detection of a new type of breast cancer to the analysis of various neural structures.}, journal={Discrete and Topological Models in Molecular Biology}, publisher={Springer Berlin Heidelberg}, author={Nanda, Vidit and Sazdanović, Radmila}, year={2013}, month={Oct}, pages={109–141} }
 @inproceedings{jablan_sazdanovic_2012, place={Singapore}, series={Series on Knots and Everything}, title={Diagrammatic knot properties and invariants}, booktitle={Introductory lectures on knot theory : selected lectures presented at the Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology, ICTP, Trieste, Italy, 11-29 May 2009}, publisher={World Scientific}, author={Jablan, S. and Sazdanovic, R.}, year={2012}, pages={162–186}, collection={Series on Knots and Everything} }
 @article{sazdanovic_2012, title={Diagrammatics in Art and Mathematics}, volume={4}, ISSN={2073-8994}, url={http://dx.doi.org/10.3390/sym4020285}, DOI={10.3390/sym4020285}, abstractNote={This paper explores two-way relations between visualizations in mathematics and mathematical art, as well as art in general. A collection of vignettes illustrates connection points, including visualizing higher dimensions, tessellations, knots and links, plotting zeros of polynomials, and new and rapidly developing mathematical discipline, diagrammatic categorification.}, number={2}, journal={Symmetry}, publisher={MDPI AG}, author={Sazdanovic, Radmila}, year={2012}, month={May}, pages={285–301} }
 @book{sazdanovic_barallo_budin_durity_fenyvesi_jablan_takacs_radovic_stettner_2012, place={Kaposvar}, title={Experience-centered approach and Visuality in the Education of Mathematics and Physics}, ISBN={978-963-9821-52-1}, publisher={Kaposvar University}, year={2012} }
 @inproceedings{sazdanovic_2012, title={Fisheye View of Tessellations}, booktitle={Bridges: Mathematical Connections in Art, Music and Science}, author={Sazdanovic, R.}, year={2012}, pages={361–364} }
 @article{baranovsky_sazdanovic_2012, title={Graph homology and graph configuration spaces}, volume={7}, ISSN={2193-8407 1512-2891}, url={http://dx.doi.org/10.1007/S40062-012-0006-3}, DOI={10.1007/S40062-012-0006-3}, abstractNote={If R is a commutative ring, M a compact R-oriented manifold and G a finite graph without loops or multiple edges, we consider the graph configuration space M G and a Bendersky–Gitler type spectral sequence converging to the homology H *(M G , R). We show that its E 1 term is given by the graph cohomology complex C A (G) of the graded commutative algebra A = H*(M, R) and its higher differentials are obtained from the Massey products of A, as conjectured by Bendersky and Gitler for the case of a complete graph G. Similar results apply to the spectral sequence constructed from an arbitrary finite graph G and a graded commutative DG algebra $${\mathcal{A}}$$ .}, number={2}, journal={Journal of Homotopy and Related Structures}, publisher={Springer Science and Business Media LLC}, author={Baranovsky, Vladimir and Sazdanovic, Radmila}, year={2012}, month={Apr}, pages={223–235} }
 @article{jablan_radović_sazdanović_2012, title={Knots and links in architecture}, volume={7}, ISSN={1788-1994 1788-3911}, url={http://dx.doi.org/10.1556/pollack.7.2012.s.6}, DOI={10.1556/pollack.7.2012.s.6}, abstractNote={This paper contains a survey of different methods for generating knots and links based on geometric polyhedra, suitable for applications in architecture chemistry, biology (or even jewelry). We describe several ways of obtaining 4-valent polyhedral graphs and their corresponding knots and links from basic polyhedra: mid-edge construction, cross-curve and double-line covering, and edge doubling construction. These methods are implemented in the Mathematica-based program LinKnot and can be applied to the data base of basic polyhedra. In a similar way, an edge doubling construction transforms fullerene graphs into alternating knot and link diagrams. In the last part of the paper is proposed the use of virtual knots and links and the corresponding nonplanar graphs obtained from their Gauss codes.}, number={Supplement 1}, journal={Pollack Periodica}, publisher={Akademiai Kiado Zrt.}, author={Jablan, Slavik and Radović, Ljiljana and Sazdanović, Radmila}, year={2012}, month={Jan}, pages={65–76} }
 @article{jablan_radović_sazdanović_zeković_2012, title={Knots in Art}, volume={4}, ISSN={2073-8994}, url={http://dx.doi.org/10.3390/sym4020302}, DOI={10.3390/sym4020302}, abstractNote={We analyze applications of knots and links in the Ancient art, beginning from Babylonian, Egyptian, Greek, Byzantine and Celtic art. Construction methods used in art are analyzed on the examples of Celtic art and ethnical art of Tchokwe people from Angola or Tamil art, where knots are constructed as mirror-curves. We propose different methods for generating knots and links based on geometric polyhedra, suitable for applications in architecture and sculpture.}, number={2}, journal={Symmetry}, publisher={MDPI AG}, author={Jablan, Slavik and Radović, Ljiljana and Sazdanović, Radmila and Zeković, Ana}, year={2012}, month={Jun}, pages={302–328} }
 @article{jablan_radović_sazdanović_zeković_2012, title={Mirror-curves and knot mosaics}, volume={64}, ISSN={0898-1221}, url={http://dx.doi.org/10.1016/j.camwa.2011.12.042}, DOI={10.1016/j.camwa.2011.12.042}, abstractNote={Inspired by the paper on quantum knots and knot mosaics (Lomonaco and Kauffman, 2008 [18]) and grid diagrams (or arc presentations), used extensively in the computations of Heegaard–Floer knot homology (Bar-Natan, 0000 [16], Cromwell, 1995 [21], Manolescu et al., 2007 [22]), we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. Tame knot theory is equivalent to knot mosaics (Lomonaco and Kauffman, 2008 [18]), mirror-curves, and grid diagrams (Bar-Natan, 0000 [16], Cromwell, 1995 [21], Kuriya, 2008 [20], Manolescu et al., 2007 [22]). Hence, we introduce codes for mirror-curves treated as knot or link diagrams placed in rectangular square grids, suitable for software implementation. We provide tables of minimal mirror-curve codes for knots and links obtained from rectangular grids of size 3×3 and p×2 (p≤4), and describe an efficient algorithm for computing the Kauffman bracket and L-polynomials (Jablan and Sazdanović, 2007 [8], Kauffman, 2006 [11], Kauffman, 1987 [12]) directly from mirror-curve representations.}, number={4}, journal={Computers & Mathematics with Applications}, publisher={Elsevier BV}, author={Jablan, Slavik and Radović, Ljiljana and Sazdanović, Radmila and Zeković, Ana}, year={2012}, month={Aug}, pages={527–543} }
 @article{jablan_sazdanović_2011, title={DIAGRAMMATIC KNOT PROPERTIES AND INVARIANTS}, DOI={10.1142/9789814313001_0008}, abstractNote={Series on Knots and EverythingIntroductory Lectures on Knot Theory, pp. 162-186 (2011) No AccessDIAGRAMMATIC KNOT PROPERTIES AND INVARIANTSS. V. Jablan and R. SazdanovićS. V. JablanThe Mathematical Institute, Belgrade 11001, Knez Mihailova 36, P.O.Box 367, Serbia and R. SazdanovićUniversity of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104-6395, USAhttps://doi.org/10.1142/9789814313001_0008Cited by:0 (Source: Crossref) PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: We analyze relations between several knot invariants such as the unknotting (unlinking) number, adequacy, and quasi-alternating property, and the corresponding values obtained from (minimal crossing number) knot diagrams. In particular, we define the BJ-unlinking number, and compute it for various families of knots and links for which the unlinking number is unknown. Keywords: Linkknot diagramwritheunknotting numberadequacyKho-vanov homologyquasi-alternating FiguresReferencesRelatedDetails Recommended Introductory Lectures on Knot TheoryMetrics History KeywordsLinkknot diagramwritheunknotting numberadequacyKho-vanov homologyquasi-alternatingPDF download}, journal={Introductory Lectures on Knot Theory}, publisher={WORLD SCIENTIFIC}, author={Jablan, S. V. and Sazdanović, R.}, year={2011}, month={Sep}, pages={162–186} }
 @article{jablan_radovi?_sazdanovi?_2011, title={Knots and links derived from prismatic graphs}, volume={66}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-80155214125&partnerID=MN8TOARS}, number={1}, journal={Match}, author={Jablan, S. and Radovi?, L. and Sazdanovi?, R.}, year={2011}, pages={65–92} }
 @article{jablan_radović_sazdanović_2011, title={Nonplanar graphs derived from Gauss codes of virtual knots and links}, volume={49}, ISSN={0259-9791 1572-8897}, url={http://dx.doi.org/10.1007/S10910-011-9884-6}, DOI={10.1007/S10910-011-9884-6}, number={10}, journal={Journal of Mathematical Chemistry}, publisher={Springer Science and Business Media LLC}, author={Jablan, Slavik and Radović, Ljiljana and Sazdanović, Radmila}, year={2011}, month={Aug}, pages={2250–2267} }
 @article{jablan_radovi?_sazdanovi?_2011, title={Pyramidal knots and links and their invariants}, volume={65}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-80051537311&partnerID=MN8TOARS}, number={3}, journal={Match}, author={Jablan, S. and Radovi?, L. and Sazdanovi?, R.}, year={2011}, pages={541–580} }
 @phdthesis{sazdanović_2010, title={Categorification of Knot and Graph Polynomials and the Polynomial Ring, Electronic dissertation published by ProQuest}, url={http://surveyor.gelman.gwu.edu/.}, author={Sazdanović, R.}, year={2010} }
 @article{jablan_radović_sazdanović_2010, title={Tutte and Jones polynomials of links, polyominoes and graphical recombination patterns}, volume={49}, ISSN={0259-9791 1572-8897}, url={http://dx.doi.org/10.1007/S10910-010-9731-1}, DOI={10.1007/S10910-010-9731-1}, number={1}, journal={Journal of Mathematical Chemistry}, publisher={Springer Science and Business Media LLC}, author={Jablan, S. and Radović, Lj. and Sazdanović, R.}, year={2010}, month={Oct}, pages={79–94} }
 @article{jablan_sazdanović_2008, title={BRAID FAMILY REPRESENTATIVES}, volume={17}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-49449083565&partnerID=MN8TOARS}, DOI={10.1142/s0218216508006427}, abstractNote={ Imposing different conditions on minimality of reduced braid words and new criteria on their representatives, we define braid family representatives and establish one-to-one correspondence with families of knots and links given in Conway notation. }, number={07}, journal={Journal of Knot Theory and Its Ramifications}, publisher={World Scientific Pub Co Pte Lt}, author={JABLAN, SLAVIK and SAZDANOVIĆ, RADMILA}, year={2008}, month={Jul}, pages={817–833} }
 @article{pabiniak_przytycki_sazdanović_2008, title={On the first group of the chromatic cohomology of graphs}, volume={140}, ISSN={0046-5755 1572-9168}, url={http://dx.doi.org/10.1007/S10711-008-9307-4}, DOI={10.1007/S10711-008-9307-4}, abstractNote={The Hochschild homology of the algebra of truncated polynomials $${{\mathcal {A}_m=\mathbb {Z}[x]/(x^m)}}$$ is closely related to the Khovanov-type homology as shown by the second author. In the present paper we utilize this in the study of the first graph cohomology group of an arbitrary graph G with v vertices. The complete description of this group is given for m = 2, 3. For the algebra $${\mathcal {A}_2}$$ we relate the chromatic graph cohomology with the Khovanov homology of adequate links. We describe the chromatic cohomology over the algebra $${\mathcal {A}_3}$$ using the homology of a cell complex built on the graph G. In particular we prove that $${{H_{\mathcal {A}_{3}}^{1,2v-3}(G)}}$$ can be isomorphic to any finite abelian group. Moreover, we give a characterization of graphs which have torsion in cohomology $${{H_{\mathcal {A}_{3}}^{1,2v-3}(G)}}$$ and construct graphs which have the same (di)chromatic polynomial but different $${{H_{\mathcal {A}_{3}}^{1,2v-3}(G)}}$$ .}, number={1}, journal={Geometriae Dedicata}, publisher={Springer Science and Business Media LLC}, author={Pabiniak, Milena D. and Przytycki, Józef H. and Sazdanović, Radmila}, year={2008}, month={Nov}, pages={19–48} }
 @article{jablan_sazdanović_2007, title={Knots, Links, and Self-avoiding Curves}, volume={22}, number={1}, journal={Forma}, author={Jablan, S. and Sazdanović, R.}, year={2007}, pages={5–13} }
 @book{jablan_sazdanović_2007, title={Linknot - Knot Theory by Computer}, DOI={10.1142/9789812772244}, abstractNote={Basic Graph Theory Shadows of KLs Notation of Knots and Links (KLs) Gauss and Dowker Code KL Diagrams Reidemeister Moves Conway Notation Classification of KLs Chirality of KLs Unlinking Number and Unlinking Gap KLs with Unlinking Number One Non-Invertible KLs Braids Braid Family Representatives Borromean Links Recognition and Generation of KLs Polynomial Invariants Experimenting with KLs Derivation and Classification of KLs Basic Polyhedra, Polyhedral KLs, and Non-Algebraic Tangles Non-Alternating and Almost Alternating KLs Families of Undetectable KLs Detecting Chirality of KLs by Polynomial Invariants History of Knot Theory and Its Applications Mirror Curves KLs and Fullerenes KLs and Mathematical Logic Self-Referential Systems KL Automata.}, journal={Series on Knots and Everything}, publisher={World Scientific Publishing Co. Pte. Ltd.}, author={Jablan, Slavik and Sazdanović, Radmila}, year={2007} }
 @article{jablan_sazdanović_2007, title={UNLINKING NUMBER AND UNLINKING GAP}, volume={16}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-38549182277&partnerID=MN8TOARS}, DOI={10.1142/s0218216507005828}, abstractNote={ Computing unlinking number is usually very difficult and complex problem, therefore we define BJ-unlinking number and recall Bernhard–Jablan conjecture stating that the classical unknotting/unlinking number is equal to the BJ-unlinking number. We compute BJ-unlinking number for various families of knots and links for which the unlinking number is unknown. Furthermore, we define BJ-unlinking gap and construct examples of links with arbitrarily large BJ-unlinking gap. Experimental results for BJ-unlinking gap of rational links up to 16 crossings, and all alternating links up to 12 crossings are obtained using programs LinKnot and K2K. Moreover, we propose families of rational links with arbitrarily large BJ-unlinking gap and polyhedral links with constant non-trivial BJ-unlinking gap. Computational results suggest existence of families of non-alternating links with arbitrarily large BJ-unlinking gap. }, number={10}, journal={Journal of Knot Theory and Its Ramifications}, publisher={World Scientific Pub Co Pte Lt}, author={JABLAN, SLAVIK and SAZDANOVIĆ, RADMILA}, year={2007}, pages={1331–1355} }
 @article{basic polyhedra in knot theory_2005, volume={28 }, journal={Kragujevac Journal of Mathematics}, year={2005}, pages={155–164} }
 @article{jablan_sazdanovic_2004, title={Discovering symmetry of knots by using program LinKnot}, volume={1-4}, journal={The Journal of ISIS-Symmetry}, author={Jablan, S. and Sazdanovic, R.}, year={2004}, pages={102–106} }
 @article{kappraff_jablan_adamson_sazdanović_2004, title={Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices}, volume={19}, number={4}, journal={Forma}, author={Kappraff, J. and Jablan, S. and Adamson, G.W. and Sazdanović, R.}, year={2004}, pages={367–387} }
 @article{sazdanovic_sremcević_2004, title={Hyperbolic Tessellations by tess}, journal={Symmetry: Art and Science (The Quarterly of ISIS Symmetry)}, author={Sazdanovic, R. and Sremcević, M.}, year={2004}, pages={1–4 226–229} }
 @inproceedings{sarhangi_jablan_sazdanovic_2004, title={Modularity in Medieval Persian Mosaics: Textual, Empirical, Analytical and Theoretical Considerations, Bridges}, booktitle={Mathematical Connections in Art, Music and Science, Conference Proceedings}, author={Sarhangi, R. and Jablan, S. and Sazdanovic, R.}, year={2004}, pages={281–293} }
 @article{jablan_sazdanovic_2004, title={Visualizing symmetry of knots by using program LinKnot, Symmetry: Art and Science}, volume={1-4}, journal={The Journal of ISIS-Symmetry}, author={Jablan, S. and Sazdanovic, R.}, year={2004}, pages={106–110} }
 @article{barrallo_sazdanovic_2002, title={Computer Sculpture: A Journey Through Mathematics,Bridges: Mathematical Connections in Art}, volume={54}, journal={Music and Science, Conference Proceedings}, author={Barrallo, J. and Sazdanovic, R.}, year={2002} }
 @article{sazdanovic_sremcevic_2002, title={Tessellations of the Euclidean, Elliptic and Hyperbolic Plane, Symmetry}, volume={2}, journal={Art and Science}, author={Sazdanovic, R. and Sremcevic, M.}, year={2002}, pages={229–304} }
 @article{jablan_radovic_sazdanovic, place={PO BOX 60, RADOJA DOMANOVICA 12, KRAGUJEVAC 34000, SERBIA}, title={BASIC POLYHEDRA IN KNOT THEORY}, volume={28}, journal={KRAGUJEVAC JOURNAL OF MATHEMATICS}, publisher={UNIV KRAGUJEVAC, FAC SCIENCE}, author={Jablan, Slavik V. and Radovic, Ljiljana M. and Sazdanovic, Radmila}, pages={{155–164}} }
 @book{levitt_hajij_sazdanovic, title={Big Data approaches to knot theory: Understanding the structure of the Jones polynomial}, number={1912.10086}, author={Levitt, J.S. and Hajij, M. and Sazdanovic, R.} }