Symmetric Division Research Articles

Covert Underwater Acoustic Communication Using Marine Ambient Noise Without Detectable Features

Learning from steganography, this study considers ocean ambient noise as a carrier and proposes a covert underwater acoustic communication scheme without detectable and repetitive features. We modulate the information in the parameters of the steganography operation rather than the specific signal waveforms. The steganography operation mainly includes three steps: symmetrical division, phase rotation, and time–domain inversion. The rotation phases are related to the transmitted information. The receiver demodulates by performing the same operation, like transmitter without knowing transmitted waveforms. Therefore, we can use countless ocean ambient noise signals to transmit the same information, which can avoid repetitive features. To optimize the communication performance, the relationship between the demodulation output value and the rotation phases is derived, and the optimal modulation parameter setting methods of modulation are given. Finally, the simulation and sea trial results show that the bit error ratio of the studied covert underwater acoustic communication scheme is approximately 5 × 10−4 at a signal-to-noise ratio of −4 dB, which verifies the effectiveness of the scheme, and the rate is 4 bps. And the results of cyclic spectrum, cepstrum and square frequency-doubling methods show that the signal of the studied scheme does not have any detectable features.

UNVEILING THE RELATIONSHIP BETWEEN M-POLYNOMIAL BASED TOPOLOGICAL INDICES AND INVERSE GRAPHS OF FINITE CYCLIC GROUPS: A COMPREHENSIVE STUDY

In the discipline of graph theory, topological indices are extremely important. The M-polynomial is a powerful tool for determining a graph's topological indices. The use of M-polynomials to describe macro-molecules and biochemical networking is a novel concept. Also, the M-polynomial of various micro-structural allows us to calculate a variety of topological indices. The chemical substances and biochemical networks are correlated with their chemical characteristics and bio-active compounds using these findings. In this research, we use the M-polynomial to create special essential topological indices of inverse graphs on finite cyclic groups, such as Randic, Zagreb, Augmented Zagreb, Harmonic, Inverse sum, and Symmetric division degree indices.

On Bond Incident Degree Indices of Fixed-Size Bicyclic Graphs with Given Matching Number

A connected graph with p vertices and q edges satisfying q=p+1 is referred to as a bicyclic graph. This paper is concerned with an optimal study of the BID (bond incident degree) indices of fixed-size bicyclic graphs with a given matching number. Here, a BID index of a graph G is the number BIDf(G)=∑vw∈E(G)f(dG(v),dG(w)), where E(G) represents G’s edge set, dG(v) denotes vertex v’s degree, and f is a real-valued symmetric function defined on the Cartesian square of the set of all different members of G’s degree sequence. Our results cover several existing indices, including the Sombor index and symmetric division deg index.

On Unicyclic Graphs with a Given Number of Pendent Vertices or Matching Number and Their Graphical Edge-Weight-Function Indices

Consider a unicyclic graph G with edge set E(G). Let f be a real-valued symmetric function defined on the Cartesian square of the set of all distinct elements of G’s degree sequence. A graphical edge-weight-function index of G is defined as If(G)=∑xy∈E(G)f(dG(x),dG(y)), where dG(x) denotes the degree a vertex x in G. This paper determines optimal bounds for If(G) in terms of the order of G and a parameter z, where z is either the number of pendent vertices of G or the matching number of G. The paper also fully characterizes all unicyclic graphs that achieve these bounds. The function f must satisfy specific requirements, which are met by several popular indices, including the Sombor index (and its reduced version), arithmetic–geometric index, sigma index, and symmetric division degree index. Consequently, the general results obtained provide bounds for several well-known indices.

Reevaluating cancer stem cells and polyploid giant cancer cells from the evolutionary cancer cell biology perspective

According to the principles of Evolutionary Cancer Cell Biology (ECCB), cancer stem cells (CSCs) do not derive from normal stem cells; rather, they originate from a distinct functional phenotype of germline cells characterized by asymmetric cell division (ACD). This phenotype proliferates through ACD, producing self-renewing cells alongside non-proliferating daughter cells with CSC qualities. ECCB posits that CSCs do not proliferate. Similar to protists, there exists a close reciprocal relationship between sister cells that collectively form a germline and stem cells. These sister cells perform complementary roles: proliferating cancer germline cells generate stem cells, whereas the non-proliferating CSCs give rise to progenitor cells for the formation of new germline clones. ECCB distinguishes between primary CSCs, which are associated with carcinogenesis and primary tumors, and secondary CSCs, which are linked to metastases. This unicellular stem cell system is homologous to that of parasitic protists, such as amebae. Both CSCs and amebae stem cells are produced by an oxygen-sensitive germline and are vulnerable to damage when oxygen levels exceed 6.0% (germline hyperoxia), as elevated oxygen concentrations can harm the germline genome. Germline cells that lose their stemness quality continue to cycle through defective symmetric cell divisions (DSCD). However, to restore functionality, the DSCD genome must be repaired through hyperpolyploidization. This process occurs in native polyploid giant cancer cells, which are homologous to the multinucleated genome repair structures found in protists.

Permeability of postzygotic barriers: embryology of a partially fertile Epidendrum (Orchidaceae) hybrid

Abstract Hybrid zones offer unique insight into reproductive barriers and plant speciation mechanisms. This study investigated postzygotic reproductive isolation in the natural hybrid Epidendrum × purpureum, which occurs in sympatry with its parent species, Epidendrum denticulatum and E. orchidiflorum. We examined the development of male and female gametophytes and the events leading to seed formation in this hybrid zone. Floral buds and flowers from E. × purpureum individuals were collected at various stages of development. Both self‐pollination and backcrosses between hybrids and parental species were performed to follow ovule and seed development up to 60 days after pollination. The material was analysed using optical and confocal microscopy. In most hybrids, microsporogenesis and microgametogenesis occur regularly, forming viable male gametophytes. Non‐viable male gametophytes were also observed and are the result of symmetrical mitotic division. The development of the female gametophyte occurs after self‐pollination, and proceeds regularly, resulting in a reduced female gametophyte. Embryo development in the parental species occurs without abnormalities, while in backcrosses between hybrids and parental species, most embryos degenerate. Embryo degeneration in the crosses between hybrids can be explained by genetic incompatibilities. The co‐occurrence of viable embryos and degenerating embryos in backcrosses between hybrids and parental species point to incomplete postzygotic reproductive barriers between the hybrid and the progenitors. Our findings suggest that E. × purpureum could facilitate gene flow between parental species, as much of its embryological development occurs without abnormalities.

Mechanical power is maximized during contractile ring-like formation in a biomimetic dividing cell model

The spatial and temporal dynamics of forces in cells coordinate essential behaviors like division, polarization, and migration. While intracellular signaling initiates contractile ring assembly during cell division, how mechanical forces coordinate division and their energetic costs remain unclear. Here, we develop an in vitro model where myosin-induced stress drives division-like shape changes in giant unilamellar vesicles (GUVs, liposomes). Myosin activity is controlled by light patterns globally or locally at the equator. Global activation causes slow, shallow cleavage furrows due to a tug-of-war between the equatorial and polar forces. By contrast, local activation leads to faster, deeper, and symmetric division as equatorial forces dominate. Dissociating the actin cortex at the poles is crucial for inducing significant furrowing. During furrowing, actomyosin flows align actin filaments parallel to the division plane, forming a contractile ring-like structure. Mechanical power is not greatest during contraction, but is maximized just before furrowing. This study reveals the quantitative relationship between force patterning and mechanical energy during division-like shape changes, providing insights into cell division mechanics.

Analyzing the modified symmetric division deg index: mathematical bounds and chemical relevance

Abstract The modified symmetric division deg (MSD) index of a graph G is precisely defined as MSD ( G ) = ∑ j ∼ k 1 2 d j d k + d k d j , where d j and d k represent the degrees of j and k respectively. In this paper, we present precise bounds for the modified symmetric division deg index, expressed in the relation to the minimum and maximum degrees, the order and size of the graph, the number of pendant vertices and the minimum degree of a non-pendant vertex, the forgotten topological index, the modified second Zagreb index. We determine the upper bounds for the modified symmetric division deg index of unicyclic, bicyclic and k-cyclic graphs. Moreover, upon analyzing the modified symmetric division deg index, we observe its correlation with other well-known indices and its chemical applicability on the molecular graphs of octane isomers. At the end, we find the chemical applicability of the modified symmetric division deg index on benzenoid hydrocarbons and observe that the modified symmetric division deg index has a very strong correlation with the physical properties of benzenoid hydrocarbons.

Emergent order in epithelial sheets by interplay of cell divisions and cell fate regulation.

The fate choices of stem cells between self-renewal and differentiation are often tightly regulated by juxtacrine (cell-cell contact) signalling. Here, we assess how the interplay between cell division, cell fate choices, and juxtacrine signalling can affect the macroscopic ordering of cell types in self-renewing epithelial sheets, by studying a simple spatial cell fate model with cells being arranged on a 2D lattice. We show in this model that if cells commit to their fate directly upon cell division, macroscopic patches of cells of the same type emerge, if at least a small proportion of divisions are symmetric, except if signalling interactions are laterally inhibiting. In contrast, if cells are first 'licensed' to differentiate, yet retaining the possibility to return to their naive state, macroscopic order only emerges if the signalling strength exceeds a critical threshold: if then the signalling interactions are laterally inducing, macroscopic patches emerge as well. Lateral inhibition, on the other hand, can in that case generate periodic patterns of alternating cell types (checkerboard pattern), yet only if the proportion of symmetric divisions is sufficiently low. These results can be understood theoretically by an analogy to phase transitions in spin systems known from statistical physics.

Cellular and molecular mechanisms of asymmetric stem cell division in tissue homeostasis.

The asymmetric cell division determines cell diversity and distinct sibling cell fates by mechanisms linked to mitosis. Many adult stem cells divide asymmetrically to balance self-renewal and differentiation. The process of asymmetric cell division involves an axis of polarity and, second, the localization of cell fate determinants at the cell poles. Asymmetric division of stem cells is achieved by intrinsic and extrinsic fate determinants such as signaling molecules, epigenetics factors, molecules regulating gene expression, and polarized organelles. At least some stem cells perform asymmetric and symmetric cell divisions during development. Asymmetric division ensures that the number of stem cells remains constant throughout life. The asymmetric division of stem cells plays an important role in biological events such as embryogenesis, tissue regeneration and carcinogenesis. This review summarizes recent advances in the regulation of asymmetric stem cell division in model organisms.

Topological Characterization of Coronoid Structures via Valency Based Topological Indices.

The number of atoms producing a bond with an atom a in a molecular structure (graph) is regarded as the valency of a. A number of molecular structures have been topologically characterized via a large number of valency-based topological indices, which correlate certain physio-chemical properties like boiling point, stability, strain energy, and many more chemical compounds. Our intention is to perform the topological characterization of primitive coronoid structures initially on the base of seven different valency-based topological indices. Fundamentally, our purpose is to provide the universal formula by using the topological characterization of any primitive coronoid structures with any valency-based topological index. The technique of atom-bonds partitions according to the valency of atoms besides counting principals are used to find the results. Exact values of valency-based topological index, namely the Randic index, sum connectivity index, harmonic index, atom bond connectivity index, geometric arithmetic index, forgotten index, and symmetric division index are calculated coronoid structures initially constructed with at most three benzene lyres. All these indices are valency-dependent structural invariants that have been used to elaborate several chemical properties of compounds of the structure. Moreover, we provide the general formula to compute any valency-based topological index for any type of coronoid structure constructed with any number of benzene lyres.

Satellite cell dynamics during skeletal muscle hypertrophy.

Skeletal muscle stem cells (MuSCs) display distinct behavior crucial for tissue maintenance and repair. Upon activation, MuSCs exhibit distinct modes of division: symmetric division, facilitating either self-renewal or differentiation, and asymmetric division, which dictates divergent cellular fates. This review explores the nuanced dynamics of MuSC division and the molecular mechanisms governing this behavior. Furthermore, it introduces a novel phenomenon observed in a subset of MuSCs under hypertrophic stimuli termed division-independent differentiation. Insights into the underlying mechanisms driving this process are discussed, alongside its broader implications for muscle physiology.

Reproducibly oriented cell divisions pattern the prothallus to set up dorsoventrality and de novo meristem formation in Marchantia polymorpha

Land plant bodies develop from stem cells located in meristems. However, we know little about how meristems initiate from non-meristematic cells. The haploid body of bryophytes develops from unicellular spores in isolation from the parental plant, which allows all stages of development to be observed. We discovered that the Marchantia spore undergoes a series of reproducibly oriented cell divisions to generate a flat prothallus on which a meristem later develops de novo. The young sporeling comprises an early cell mass. One cell of the early cell mass elongates and undergoes a formative division that produces the prothalloblast, which initiates prothallus formation. A symmetric division of the prothalloblast followed by two transverse divisions generates a four-celled plate that expands into a flat disc through oblique divisions in three of the four plate-cell-derived quadrants. One quadrant gives rise to a flat flabellum. A notch with a meristem and apical stem cell develops at the margin of the flabellum. The transcription factor Marchantia class III homeodomain-leucine-zipper (MpC3HDZ) is a marker of the first flat prothallus structure and polarizes to the dorsal tissues of flabella and meristems. Mpc3hdz mutants are defective in setting up dorsoventrality and thallus body flatness. We report how a regular set of cell divisions forms the prothallus-the first dorsoventral structure-and how cells on the margin of the prothallus develop a dorsoventralized meristem de novo.

Loss of symmetric cell division of apical neural progenitors drives DENND5A-related developmental and epileptic encephalopathy

Developmental and epileptic encephalopathies (DEEs) feature altered brain development, developmental delay and seizures, with seizures exacerbating developmental delay. Here we identify a cohort with biallelic variants in DENND5A, encoding a membrane trafficking protein, and develop animal models with phenotypes like the human syndrome. We demonstrate that DENND5A interacts with Pals1/MUPP1, components of the Crumbs apical polarity complex required for symmetrical division of neural progenitor cells. Human induced pluripotent stem cells lacking DENND5A fail to undergo symmetric cell division with an inherent propensity to differentiate into neurons. These phenotypes result from misalignment of the mitotic spindle in apical neural progenitors. Cells lacking DENND5A orient away from the proliferative apical domain surrounding the ventricles, biasing daughter cells towards a more fate-committed state, ultimately shortening the period of neurogenesis. This study provides a mechanism for DENND5A-related DEE that may be generalizable to other developmental conditions and provides variant-specific clinical information for physicians and families.

Loss of PRICKLE1 leads to abnormal endometrial epithelial architecture, decreased embryo implantation, and reduced fertility in mice.

Conservative cell division is essential to maintain apical-basal polarity and proper epithelial function in the uterus. Wnt/ Planar cell polarity signaling molecules are hypothesized to provide the spatial cues to organize unicellular, 2-dimensional sheet of epithelium in a plane orthogonal to the apical-basal polarity. Conditional ablation of Prickle1 , a crucial Wnt/ PCP gene, in mouse uterine epithelium results in aberrant expression of epithelial cadherin, altered plane of cell division, incomplete cytokinesis leading to binucleated/ multinucleated cells, epithelial - mesenchymal transition, and defective implantation. Role of Prickle1 in maintaining symmetric uterine epithelial cell division and tissue architecture is unique among Wnt/PCP genes, including previously described mouse models for Vangl2, Ror2, and Wnt5a . Classification: Biological Sciences (Major) Cell Biology (Minor), Physiology (Minor).

Stem Cell Division and Its Critical Role in Mammary Gland Development and Tumorigenesis: Current Progress and Remaining Challenges.

The origin of breast cancer (BC) has traditionally been a focus of medical research. It is widely acknowledged that BC originates from immortal mammary stem cells and that these stem cells participate in two division modes: symmetric cell division (SCD) and asymmetrical cell division (ACD). Although both of these modes are key to the process of breast development and their imbalance is closely associated with the onset of BC, the molecular mechanisms underlying these phenomena deserve in-depth exploration. In this review, we first outline the molecular mechanisms governing ACD/SCD and analyze the role of ACD/SCD in various stages of breast development. We describe that the changes in telomerase activity, the role of polar proteins, and the stimulation of ovarian hormones subsequently lead to two distinct consequences: breast development or carcinogenesis. Finally, gene mutations, abnormalities in polar proteins, modulation of signal-transduction pathways, and alterations in the microenvironment disrupt the balance of BC stem cell division modes and cause BC. Important regulatory factors such as mammalian Inscuteable mInsc, Numb, Eya1, PKCα, PKCθ, p53, and IL-6 also play significant roles in regulating pathways of ACD/SCD and may constitute key targets for future research on stem cell division, breast development, and tumor therapy.

Stochastic journeys of cell progenies through compartments and the role of self-renewal, symmetric and asymmetric division

Division and differentiation events by which cell populations with specific functions are generated often take place as part of a developmental programme, which can be represented by a sequence of compartments. A compartment is the set of cells with common characteristics; sharing, for instance, a spatial location or a phenotype. Differentiation events are transitions from one compartment to the next. Cells may also die or divide. We consider three different types of division events: (i) where both daughter cells inherit the mother’s phenotype (self-renewal), (ii) where only one of the daughters changes phenotype (asymmetric division), and (iii) where both daughters change phenotype (symmetric division). The self-renewal probability in each compartment determines whether the progeny of a single cell, moving through the sequence of compartments, is finite or grows without bound. We analyse the progeny stochastic dynamics with probability generating functions. In the case of self-renewal, by following one of the daughters after any division event, we may construct lifelines containing only one cell at any time. We analyse the number of divisions along such lines, and the compartment where lines terminate with a death event. Analysis and numerical simulations are applied to a five-compartment model of the gradual differentiation of hematopoietic stem cells and to a model of thymocyte development: from pre-double positive to single positive (SP) cells with a bifurcation to either SP4 or SP8 in the last compartment of the sequence.

On unicyclic graphs with a given girth and their minimum symmetric division deg index

On unicyclic graphs with a given girth and their minimum symmetric division deg index

HB-EGF activates EGFR to induce reactive neural stem cells in the mouse hippocampus after seizures.

Hippocampal seizures mimicking mesial temporal lobe epilepsy cause a profound disruption of the adult neurogenic niche in mice. Seizures provoke neural stem cells to switch to a reactive phenotype (reactive neural stem cells, React-NSCs) characterized by multibranched hypertrophic morphology, massive activation to enter mitosis, symmetric division, and final differentiation into reactive astrocytes. As a result, neurogenesis is chronically impaired. Here, using a mouse model of mesial temporal lobe epilepsy, we show that the epidermal growth factor receptor (EGFR) signaling pathway is key for the induction of React-NSCs and that its inhibition exerts a beneficial effect on the neurogenic niche. We show that during the initial days after the induction of seizures by a single intrahippocampal injection of kainic acid, a strong release of zinc and heparin-binding epidermal growth factor, both activators of the EGFR signaling pathway in neural stem cells, is produced. Administration of the EGFR inhibitor gefitinib, a chemotherapeutic in clinical phase IV, prevents the induction of React-NSCs and preserves neurogenesis.

Computation of differential and integral operators using [formula omitted]-polynomials of gold crystal

Gold is generally considered a noble metal since it is inherently inert in its bulk state. However, gold demonstrates reactivity when it is in its ionic state. The inherent inertness of bulk gold has resulted in its widespread recognition as a vital raw material in various biomedical processes. The applications of these technologies include drug delivery microchips, dental prostheses, reconstructive surgery, culinary additives, and cardiovascular stents. Gold can also exist in molecules or ions, particularly gold ions, which facilitates the production of gold nanomaterials. In this paper, we have computed differential and integral operators by using the M-Polynomial of gold crystals and by utilizing this polynomial, we have also computed eleven topological indices like 1st Zagreb, 2nd Zagreb, Hyper, Sigma, Second Modified, General Randic, General Reciprocal Randic, 3rd Redefined Zagreb, Symmetric Division Degree, Harmonic, Inverse Sum indices for the structure of Gold crystal.