12 research outputs found
Critical sets of PL and discrete Morse theory: a correspondence
No full textPiecewise-linear (PL) Morse theory and discrete Morse theory are used in shape analysis tasks to investigate the topological features of discretized spaces. In spite of their common origin in smooth Morse theory, various notions of critical points have been given in the literature for the discrete setting, making a clear understanding of the relationships occurring between them not obvious. This paper aims at providing equivalence results about critical points of the two discretized Morse theories. First of all, we prove the equivalence of the existing notions of PL critical points. Next, under an optimality condition called relative perfectness, we show a dimension agnostic correspondence between the set of PL critical points and that of discrete critical simplices ofthe combinatorial approach. Finally, we show how a relatively perfect discrete gradient vector field can be algorithmically built up to dimension 3. This way, we guarantee a formal and operative connection between critical sets in the PL and discrete theories
Perfect discrete morse functions on connected sums
No full textLet be a finite, regular cell complex and be a real valued function on . Then is called a textit{discrete Morse function} if for all -cell , the following conditions hold: begin{align*} displaystyle n_{1}=# {tau > sigma mid f(tau)leq f(sigma)} leq 1, \ n_{2}=# {nu < sigma mid f(nu)geq f(sigma)}leq 1. end{align*} A -cell is called a textit{critical -cell} if . A discrete Morse function is called a textit{perfect discrete Morse function} if the number of critical -cells of equals to the -th Betti number of with reference to the coefficient group. The main purpose of this thesis is to compose and decompose perfect discrete Morse functions on connected sums of closed, connected manifolds. We will first discuss the existence of perfect discrete Morse functions on finite complexes and closed, connected, triangulated -manifolds. Secondly, we will show that if the components of a connected sum of closed, connected, triangulated -manifolds admit a perfect discrete Morse function, then admits a perfect discrete Morse function that coincides with the perfect discrete Morse functions on the components. Next, we will find a separating sphere on a connected sum of closed, connected, triangulated surfaces and -manifolds if admits a perfect discrete Morse function . Finally, we will prove that can be decomposed as perfect discrete Morse functions on each component of after some local modifications of it
Perfect discrete Morse functions on connected sums
No full textWe study perfect discrete Morse functions on closed, connected, oriented n-dimensional manifolds. We show how to compose such functions on connected sums of manifolds of arbitrary dimensions and how to decompose them on connected sums of closed oriented surfaces
Homological properties of persistent homology
No full textIn this paper, we investigate to what extent persistent homology benefits from the properties of a homology theory. We show that persistent homology benefits from a Mayer-Vietoris sequence and a long exact sequence for a pair if one works with graded persistence modules. We also give concrete examples showing that the same is not the case for persistent homology groups
Kalıcı Homoloji
No full textKalıcı homoloji(persistent homoloji), verilerin(üzerinde bir metrik tanımlı olan ayrık noktalar kümesi) topolojik özelliklerini(bileşenleri, üzerindeki delikler, çizge yapısı vb.) anlamak için kullanılan cebirsel bir metottur. Bu projedeki amacımız, homoloji gruplarının temel özelliklerini (ikililer icin tam diziler, dualite, evrensel katsayılar vb.) kalıcı homoloji bağlamında ele alıp, bu özelliklerin hangi formlarda kalıcı homolojiye genişletilebileceğini araştırmaktır
Elementary Methods for Persistent Homotopy Groups
No full textIn this paper, we study the basic properties of persistent homotopy groups.
We show that the persistent fundamental group benefits from the Van Kampen
theorem, and the interleaving distance between total spaces is less than or
equal to the maximum of the interleaving distances between subspaces. We also
prove excision and Hurewicz theorems for persistent homotopy groups. As an
application, we analyze the sublevelset persistent homotopy groups of the
energy landscape of alkane molecules.Comment: 29 pages, 20 figure
The transfection efficiency of newly developed calcium phosphate nanoparticles in reprogramming of fibroblast cells
No full textInduced pluripotent stem cells (iPSCs) represent a groundbreaking advancement in stem cell research, offering new avenues for regenerative therapy and disease modeling. This study explores the application of calcium phosphate (CaP) nanoparticles in gene transfer studies involving iPSCs. By meticulously analyzing the characteristics of CaP nanoparticles—such as mean particle size and zeta potential—using dynamic light scattering (DLS), the research provides insights into their potential application in iPSC-related research. In addition, in vitro assessments were conducted on L929 mouse fibroblast cells to evaluate the biocompatibility of CaP nanoparticles, further demonstrating their potential utility. The results from the MTT assay indicate no significant toxic effects across various concentrations (ranging from 5 to 25 µg/µL), highlighting their safety profile and supporting their use in iPSC-related studies. Additionally, the CaP nanoparticle group exhibited lower total oxidant levels, suggesting potential antioxidant properties or the ability to mitigate oxidative stress. This reduction in oxidant levels may contribute to maintaining cell health and normal cellular functions, complemented by higher total antioxidant levels observed in the CaP group. Moreover, increased levels of cyclin D1 in the CaP group indicate enhanced cellular activity in proliferation and division processes, particularly significant during the G1 phase of the cell cycle. In summary, calcium phosphate nanoparticles play a multifaceted role in iPSC-related research, showcasing antioxidant properties, supporting cell proliferation, and potentially enhancing cell survival by inhibiting apoptosis. This research underscores their efficacy as non-viral carriers for genetic studies and sheds light on their application in gene transfer experiments. Successful transfection of L929 cells with a selected plasmid encoding Oct4-Sox2-Klf4-Myc-GFP demonstrates the effectiveness of CaP nanoparticles in delivering genetic material into cells. With a transfection efficiency persisting at 85% (± 3.4%) over a 72-h observation period, coupled with significant expression levels of key genes OCT-4 and SSEA-4 detected via flow cytometry (88%), CaP nanoparticles emerge as a promising tool for facilitating cellular reprogramming. Graphical Abstract: (Figure presented.)
A virus-free vector for the transfection of somatic cells to obtain IPSC
No full textReprogramming of somatic cells to induced pluripotent stem cells (iPSCs) is a promising tool for regenerative medicine. The fibroblast cells are the most commonly used cell type for this purpose thanks to their easy accessibility. In this study, we used the fibroblast cell line to introduce the main transcription factors (Oct4, Klf4, Sox2) for reprogramming. Controversy to literature, we used a virus-free method for introduction OKS. We developed an octadecylamine-based cationic lipid nanoparticle as a nonviral carrier. The cationic nanoparticle was prepared via the emulsion-solvent evaporation method. We used the formulation OLN32 with 29.7 +/- 3.16 mV zeta potential and 118.3 +/- 3.05 nm size for introducing OKS. The fibroblast L929 cell line was transfected with OLN-OKS conjugates, and the transfection efficiency was followed by observing GFP expression. The transfection efficiency was found at 72%. The expression of OKS was detected by RT-qPCR and the transfection factors were determined to be amplified after the 11th cycle
Decomposing perfect discrete Morse functions on connected sum of 3-manifolds
No full textIn this paper, we show that if a closed, connected, oriented 3-manifold M = M-1 # M-2 admits a perfect discrete Morse function, then one can decompose this function as perfect discrete Morse functions on M-1 and M-2. We also give an explicit construction of a separating sphere on M corresponding to such a decomposition
3-Hydroxyhexanoate-based polycationic nanoparticle system for delivering reprogramming factors
No full textAim: In this study, we aimed to develop a polycationic non-viral carrier for the delivery of the reprogramming factors to the L929 fibroblast cell. Methods: We have prepared (3-hydroxybutyrate-co-3-hydroxyhexanoate) PHBHHx-based nanoparticles with the solvent diffusion method. Cytotoxicity of PXNs was determined via MTT assay. Transfection efficiency was evaluated via screening GFP expression by fluorescence microscopy. The expression of reprogramming factors (Oct4, Klf4, and Sox2) was determined by RT-qPCR. Results: PXNs with 32.9 +/- 0.41 mV zeta potential and 177.6 +/- 0.80 nm size were used for transfection of L929 Fbroblast cells. The percentage of cell viability of PXN were between 91.8%(+/- 2.9) and 42.1%(+/- 1.3). The transfection efficiency was found as 71.6%(+/- 3,5). According to RT-qPCR data, the rate of transfection factors was significantly increased after the 11th cycle compared to non-transfected cells. Based on these results, it can be concluded that newly developed PXN is thought to be an effective tool for reprogramming cells
