Characterization Of Diversity Research Articles

Topology and Dynamics of Transcriptome (Dys)Regulation.

RNA transcripts play a crucial role as witnesses of gene expression health. Identifying disruptive short sequences in RNA transcription and regulation is essential for potentially treating diseases. Let us delve into the mathematical intricacies of these sequences. We have previously devised a mathematical approach for defining a "healthy" sequence. This sequence is characterized by having at most four distinct nucleotides (denoted as nt≤4). It serves as the generator of a group denoted as fp. The desired properties of this sequence are as follows: fp should be close to a free group of rank nt-1, it must be aperiodic, and fp should not have isolated singularities within its SL2(C) character variety (specifically within the corresponding Groebner basis). Now, let us explore the concept of singularities. There are cubic surfaces associated with the character variety of a four-punctured sphere denoted as S24. When we encounter these singularities, we find ourselves dealing with some algebraic solutions of a dynamical second-order differential (and transcendental) equation known as the Painlevé VI Equation. In certain cases, S24 degenerates, in the sense that two punctures collapse, resulting in a "wild" dynamics governed by the Painlevé equations of an index lower than VI. In our paper, we provide examples of these fascinating mathematical structures within the context of miRNAs. Specifically, we find a clear relationship between decorated character varieties of Painlevé equations and the character variety calculated from the seed of oncomirs. These findings should find many applications including cancer research and the investigation of neurodegenative diseases.

Mixed Hodge structures on character varieties of nilpotent groups

AbstractLet $$\textsf{Hom}^{0}(\Gamma ,G)$$ Hom 0 ( Γ , G ) be the connected component of the identity of the variety of representations of a finitely generated nilpotent group $$\Gamma $$ Γ into a connected reductive complex affine algebraic group G. We determine the mixed Hodge structure on the representation variety $$\textsf{Hom}^{0}(\Gamma ,G)$$ Hom 0 ( Γ , G ) and on the character variety $$\textsf{Hom}^{0}(\Gamma ,G)/\!\!/G$$ Hom 0 ( Γ , G ) / / G . We obtain explicit formulae (both closed and recursive) for the mixed Hodge polynomial of these representation and character varieties.

An Implementation on: A Game technology using ROBLOX Studio

A thrilling ROBLOX adventure called "Hide and Seek - Ultimate" invites players of all stripes to interact, form connections, and experience the excitement of the timeless Hide and Seek game. This project sets out to accomplish two goals: create a thriving gaming community and enthrall gamers with immersive gameplay. The unique aspects of the game constitute its core. Because each character has special abilities, the gameplay gains depth and a degree of strategy. The Hide and Seek experience is improved by the wide variety of characters that players can choose from, each of which has unique powers. The game's dynamic architectural structures, complex terrain, and eye-catching visuals are just a few of the innovative design features. Additionally, "Hide and Seek - Ultimate" includes a fascinating game economy. Participants

Symplectic Geometry of Character Varieties and SU(2) Lattice Gauge Theory I

Symplectic Geometry of Character Varieties and SU(2) Lattice Gauge Theory I

Valuations on the character variety: Newton polytopes and residual Poisson bracket

Valuations on the character variety: Newton polytopes and residual Poisson bracket

Coordinate rings of some $\mathrm{SL}_2$-character varieties

Coordinate rings of some $\mathrm{SL}_2$-character varieties

The Use of Short Stories to improve English proficiency in Sixth Graders

Existing research suggests that short stories are an engaging and immersive experience that actively stimulates foreign language students' imagination and promotes their interest in language acquisition; they can also foster empathy, critical thinking, and creativity, all of which are essential tools for language development. By bringing short stories into the language classroom, a variety of narratives, characters, and cross-cultural experiences might be met. This research examines English as a Foreign Language (EFL) students’ improvement and perceptions of the implementation of short stories into their English classes after a six-week period of exposure to it as a teaching-learning strategy. The findings of the investigation showed a slight difference in students’ language improvement after comparing the pre- and post-test results; however, students’ perceptions of the implementation of short stories could bring insights into the English classrooms to enhance students’ language skills, promoting passion for reading, and encouraging critical thinking.

The quantum Frobenius for character varieties and multiplicative quiver varieties

The quantum Frobenius for character varieties and multiplicative quiver varieties

Higgs fields, non-abelian Cauchy kernels and the Goldman symplectic structure

We consider the moduli space of vector bundles of rank n and degree ng over a fixed Riemann surface of genus g⩾2 with the explicit parametrization in terms of the Tyurin data. The ‘non-abelian’ theta divisor consists of bundles such that h1⩾1 . On the complement of this divisor we construct a non-abelian (i.e. matrix) Cauchy kernel explicitly in terms of the Tyurin data. With the additional datum of a non-special divisor, we can construct a reference flat holomorphic connection which also depends holomorphically on the moduli of the bundle. This allows us to identify the bundle of Higgs fields, i.e. the cotangent bundle of the moduli space, with the affine bundle of holomorphic connections and provide a monodromy map into the GLn character variety. We show that the Goldman symplectic structure on the character variety pulls back along this map to the complex canonical symplectic structure on the cotangent bundle and hence also on the space of connections. The pull-back of the Liouville one-form to the affine bundle of connections is then shown to be a logarithmic form with poles along the non-abelian theta divisor and residue given by h 1.

Perspective of Gender Roles in Margaret Atwood’s The Penelopiad

The most actively and purposefully practiced agenda for ages has been based on mythical patterns and beliefs, which are useful in encapsulating and hiding the reality of gender. Likewise, feminist writers and philosophers have investigated the causes, methods, and effects of the longstanding systemic oppression of women through myths. This project concentrates on how modern female writers have reconstructed gender identities to benefit women. The Penelopiad, a 2005 novella by Margaret Atwood defies the conventional ideas of femininity by depicting a variety of strong female characters. The patriarchal dominance that accuses this sensitive gender of passivity and the pervasive misrepresentation of women in mythologies served as the main sources of inspiration for this work. Therefore, this project shows how Atwood reconstructs gender identities in The Penelopiad. This work is examined in this research to see what gender roles the patriarchal Greek culture has assigned to both men and women.

Minimality of rational knots C(2n + 1,2m,2)

A nontrivial knot is called minimal if its knot group does not surject onto the knot groups of other nontrivial knots. In this paper, we determine the minimality of the rational knots [Formula: see text] in the Conway notation, where [Formula: see text] and [Formula: see text] are integers. When [Formula: see text], we show that the nonabelian [Formula: see text]-character variety of [Formula: see text] is irreducible and therefore [Formula: see text] is a minimal knot. The proof of this result is an interesting application of Eisenstein’s irreducibility criterion for polynomials over integral domains.

Transitivity of normal subgroups of the mapping class groups on character varieties

Transitivity of normal subgroups of the mapping class groups on character varieties

Dynamics of Fricke–Painlevé VI Surfaces

The symmetries of a Riemann surface Σ∖{ai} with n punctures ai are encoded in its fundamental group π1(Σ). Further structure may be described through representations (homomorphisms) of π1 over a Lie group G as globalized by the character variety C=Hom(π1,G)/G. Guided by our previous work in the context of topological quantum computing (TQC) and genetics, we specialize on the four-punctured Riemann sphere Σ=S2(4) and the ‘space-time-spin’ group G=SL2(C). In such a situation, C possesses remarkable properties: (i) a representation is described by a three-dimensional cubic surface Va,b,c,d(x,y,z) with three variables and four parameters; (ii) the automorphisms of the surface satisfy the dynamical (non-linear and transcendental) Painlevé VI equation (or PVI); and (iii) there exists a finite set of 1 (Cayley–Picard)+3 (continuous platonic)+45 (icosahedral) solutions of PVI. In this paper, we feature the parametric representation of some solutions of PVI: (a) solutions corresponding to algebraic surfaces such as the Klein quartic and (b) icosahedral solutions. Applications to the character variety of finitely generated groups fp encountered in TQC or DNA/RNA sequences are proposed.

Tropical Fock–Goncharov coordinates for -webs on surfaces I: construction

Abstract For a finite-type surface $\mathfrak {S}$ , we study a preferred basis for the commutative algebra $\mathbb {C}[\mathscr {R}_{\mathrm {SL}_3(\mathbb {C})}(\mathfrak {S})]$ of regular functions on the $\mathrm {SL}_3(\mathbb {C})$ -character variety, introduced by Sikora–Westbury. These basis elements come from the trace functions associated to certain trivalent graphs embedded in the surface $\mathfrak {S}$ . We show that this basis can be naturally indexed by nonnegative integer coordinates, defined by Knutson–Tao rhombus inequalities and modulo 3 congruence conditions. These coordinates are related, by the geometric theory of Fock and Goncharov, to the tropical points at infinity of the dual version of the character variety.

Toward Innovative Recognition of Handwritten Arabic Characters: A Hybrid Approach with SIFT, BoVW, and SVM classification

The goal of handwriting recognition has been a top priority for those who want to enter data into computer systems for more than thirty years. In several fields, the advent of handwriting recognition technology is highly anticipated. OCR technology has made it possible for computers to recognize characters as visual objects and collect data about their unique characteristics in recent years. In particular, several studies in this field have focused on Arabic writing. The use of machines to examine handwritten papers is the first step in the character identification process. The identification of specific Arabic characters is the main goal of this particular investigation. In computer vision, Arabic character recognition is very important since it's necessary to correctly recognize and classify Arabic letters and characters in manuscripts. In this research, an innovative approach based on identifying Arabic character characteristics using BoVW (bag of visual words) and SIFT (Scale Invariant Feature Transform) features is proposed. These features are clustered using k-means clustering to produce a dictionary. Following that, SVM (Support Vector Machine) is utilized to classify the word images in a visual codebook created using these terms. The proposed approach is an innovative method to deal with the difficulties associated with Arabic hand-writing recognition. The utilization of BoVW and SIFT features is expected to enhance the system's robustness in recognizing and classifying Arabic characters. The proposed approach will be experimentally evaluated using a dataset that includes a variety of Arabic characters written in various styles. The results of this study will offer important new perspectives on the effectiveness and practicality of the approach suggested.

A Fano compactification of the $$\textrm{SL}_2(\mathbb {C})$$ free group character variety

A Fano compactification of the $$\textrm{SL}_2(\mathbb {C})$$ free group character variety

The Monodromy Map from Differential Systems to the Character Variety Is Generically Immersive

The Monodromy Map from Differential Systems to the Character Variety Is Generically Immersive

CHARACTER VALUES OF INDEPENDENCE, HARD WORK, CREATIVITY, AND DEMOCRACY IN SERAT WEDATAMA

Rapid technological advancements facilitate human progress towards various objectives, but they also have a drawback, namely the emergence of instant culture. All things desire to be quick, simple, helpful, and satisfying. A culture that is averse to effort, care, and empathy will become hardworking due to this character. The life guidance derived from regional culture and beliefs must be rebuilt. A literary piece called Serat Wedatama, which takes the form of a macapat song, contains moral lessons. It is essential to continuously work towards fostering self-discipline, perseverance, creativity, independence, and democracy founded on sincerity, patience, and sincerity. It is possible to purify the heart and mind through selfless work, which affects behaviour that is not constrained by professional outcomes. An incentive to put in the extra effort will be a disciplined character that has become ingrained. Genuinely working hard and dedicating all of one's creations and emotions will yield satisfying results. The ability or self-intuition that generates creative ideas will awaken with sincere effort. A sense of self-confidence fostered by creative ideas can help someone become independent. Coexisting in various societal contexts is also a necessary component of independence. Humans must cooperate while putting mutual respect and appreciation first in order to establish democracy in a society with a variety of conditions and characters.

Flawed groups and the topology of character varieties

A finitely presented group Γ is called flawed if Hom(Γ,G)//G deformation retracts onto its subspace Hom(Γ,K)/K for all reductive affine algebraic groups G and maximal compact subgroups K⊂G. After discussing generalities concerning flawed groups, we show that all finitely generated groups isomorphic to a free product of nilpotent groups are flawed. This unifies and generalizes all previously known classes of flawed groups. We also provide further evidence for the authors' conjecture that RAAGs are flawed. Lastly, we show direct products between finite groups and some flawed group are also flawed. These latter two theorems enlarge the known class of flawed groups.

The Dialogic, Unfinalizable, and Heteroglossic in William Golding’s Lord of the Flies (1954): A Bakhtinian Reading

As a persistently profound source of inspiring ideas, William Golding’s Lord of the Flies (1954) continues to attract researchers with novel concepts and notions to be addressed. Whenever researchers seem to have exhausted the text in critical writings and used up its possible subjects, the novel’s supply of ever fresher and more original ideas seems to keep flowing. Therefore, the current research study intends to examine certain concepts such as dialogism, unfinalizability and heteroglossia in Lord of the Flies from a Bakhtinian perspective, which is a new approach to the novel. No research study before this one has—to the best knowledge of the researcher—addressed Lord of the Flies or these concepts from such an angle. As the title suggests, the present study explores the concepts mentioned earlier by examining the diversity, difference, and variety of characters in the novel, their views and ideas on numerous issues such as leadership, survival, rescue, fire, hunting, masking and the like. It employs Bakhtin’s views and theorizations as a theoretical reference outline for its main argument. The analysis of the paper will address the diversity, variety and multiplicity of different views, plural opinions, and assorted narrative voices as demonstrated by the novel’s characters to show their dialogic, unfinalizable and heteroglossic nature.