Sharif Digital Repository

Background: It is now possible to analyze cellular heterogeneity at the single-cell level thanks to the rapid developments in single-cell sequencing technologies. The clustering of cells is a fundamental and common step in heterogeneity analysis. Even so, accurate cell clustering remains a challenge due to the high levels of noise, the high dimensions, and the high sparsity of data. Results: Here, we present SCEA, a clustering approach for scRNA-seq data. Using two consecutive units, an encoder based on MLP and a graph attention auto-encoder, to obtain cell embedding and gene embedding, SCEA can simultaneously achieve cell low-dimensional representation and clustering performing various... 

The application of nanobiotechnology in biomolecule detection can provide fast and accurate tests for diagnosing molecular changing-associated diseases. The use of AuNPs-thiolated probe conjugates has long been considered as an alternative method for the detection of specific DNA/RNA targets. Here, we present a colorimetric direct detection method for the SOX2OT transcript, long noncoding RNAs (lncRNAs), by using a poly guanine tail (G12) as a template for in situ synthesis of gold nanoparticles (AuNPs) without any chemical modification or DNA labeling. We have then developed this proposed detection system based on two complementary sequences of long noncoding RNA SOX2OT with an extra strand... 

Let G = {g1,...,gn} be a finite abelian group. Consider the complete graph with the vertex set {g1.....,.....g n}. The G-coloring of Kn is a proper edge coloring in which the color of edge {gi,gj} gi g i + gj, 1 ≤ i < 3 ≤ n. We prove that in the G-coloring of the complete graph Kn, there exists a multicolored Hamilton path if G is not an elementary abelian 2-group. Furthermore, we show that if n is odd, then the G-coloring of Kn can be decomposed into multicolored 2-factors and there are exactly lr/2 multicolored r-uniform 2-factors in this decomposition where lr is the number of elements of order r in G, 3 ≤ r ≤ n. This provides a generalization of a recent result due to Constantine which... 

A unique approach is introduced for constructing gold nanocrystals (AuNCs) with RNA motif–directed morphologies in a sequence-independent manner and its applications in the clinical area are described. By using this method, a label-free LSPR-based detection method for the SOX2OT transcript, long non-coding RNAs (lncRNAs), which is a prognostic indicator of poor survival in lung cancer patients is presented. For the first time, we examined how the structural changes of RNA after the heteroduplex formation with a specific DNA probe can change the morphology and LSPR band of AuNCs. Using this method, is was possible to differentiate lung squamous cell carcinoma from adenocarcinoma samples... 

For every natural number h, a graph G is said to be h-magic if there exists a labelling l:E(G)→Zh{0} such that the induced vertex set labelling l+:V(G)→Zh defined byl+(v)=∑uv∈E(G)l(uv), is a constant map. When this constant is zero, it is said that G admits a zero-sum h-magic labelling. The null set of a graph G, denoted by N(G), is the set of all natural numbers h∈N such that G admits an h-zero-sum magic labelling. In 2007, E. Salehi determined the null set of complete bipartite graphs. In this paper we generalize this result by obtaining the null set of complete multipartite graphs  

Let R be a commutative ring with unity. The cozero-divisor graph of R, denoted by Γ′(R), is a graph with vertex set W*(R), where W*(R) is the set of all nonzero and nonunit elements of R, and two distinct vertices a and b are adjacent if and only if a ∉ Rb and b ∉ Ra, where Rc is the ideal generated by the element c in R. Recently, it has been proved that for every nonlocal finite ring R, Γ′(R) is a unicyclic graph if and only if R ≅ ℤ2 × ℤ4, ℤ3 × ℤ3, ℤ2 × ℤ2[x]/(x 2). We generalize the aforementioned result by showing that for every commutative ring R, Γ′(R) is a unicyclic graph if and only if R ≅ ℤ2 × ℤ4, ℤ3 × ℤ3, ℤ2 × ℤ2[x]/(x 2), ℤ2[x, y]/(x, y)2, ℤ4[x]/(2x, x 2). We prove that for every... 

Let R be a commutative ring with unity. The cozero-divisor graph of R denoted by Γ'(R) is a graph with the vertex set W*(R), where W*(R) is the set of all nonzero and non-unit elements of R, and two distinct vertices a and b are adjacent if and only if a ∉ Rb and b ∉ Ra, where Rc is the ideal generated by the element c in R. Let α(Γ'(R)) and γ(Γ'(R)) denote the independence number and the domination number of Γ'(R), respectively. In this paper, we prove that if α(Γ'(R)) is finite, then R is Artinian if and only if R is Noetherian. Also, we prove that if α(Γ'(R)) is finite, then R/P is finite, for every prime ideal P. Moreover, we prove that if R is a Noetherian ring, γ(Γ'(R)) is finite and... 

Let R be a commutative ring with unity. The cozero-divisor graph of R denoted by Γ′(R) is a graph with the vertex set W*-(R), where W*-(R) is the set of all nonzero and non-unit elements of R, and two distinct vertices a and b are adjacent if and only if a*‰Rb and b*‰Ra. Let ω(Γ′(R)) and χ(Γ′(R)) denote the clique number and the chromatic number of Γ′(R), respectively. In this paper, we prove that if R is a finite commutative ring, then Γ′(R) is perfect. Also, we prove that if R is a commutative Artinian non-local ring and ω(Γ′(R)) is finite, then χ(Γ′(R)) = ω(Γ′(R)). For Artinian local ring, we obtain an upper bound for the chromatic number of cozero-divisor graph. Among other results, we... 

Let 1 < ti < t2 < ••• < th < n. A Toeplitz graph G = (V,E) denoted by Tn(tiy ..., f) is a graph where V = {1,. .. ,n} and E = {(m) I i-JI. • • >}}•this paper, we classify all regular Toeplitz graphs. Here, we present some conditions under which a Toeplitz graph has no cut-edge and cut-vertex  

The energy of a graph G, denoted by E(G), is defined as the sum of absolute values of all eigenvalues of G. A graph of order n, whose energy is less than n, i.e., E(G) < n, is said to be hypoenergetic. Graphs for which E(G) ≥ n are called non-hypoenergetic. A graph of order n is said to be orderenergetic, if its energy and its order are equal, i.e., E(G) = n. In this paper, we characterize non-hypoenergetic graphs with nullity 2. It is proved that except two graphs, every connected graph with nullity 2 is non-hypoenergetic. © 2021 University of Kragujevac, Faculty of Science. All rights reserved  

We study graphs whose adjacency matrices have determinant equal to 1 or -1, and characterize certain subclasses of these graphs. Graphs whose adjacency matrices are totally unimodular are also characterized. For bipartite graphs having a unique perfect matching, we provide a formula for the inverse of the corresponding adjacency matrix, and address the problem of when that inverse is diagonally similar to a nonnegative matrix. Special attention is paid to the case that such a graph is unicyclic. © 2006 Elsevier Inc. All rights reserved  

The energy of a graph G, denoted by E(G), is defined as the sum of absolute values of all eigenvalues of G. A graph of order n, whose energy is less than n, i.e., E(G) < n, is said to be hypoenergetic. Graphs for which E(G) ≥ n are called non-hypoenergetic. A graph of order n is said to be orderenergetic, if its energy and its order are equal, i.e., E(G) = n. In this paper, we characterize non-hypoenergetic graphs with nullity 2. It is proved that except two graphs, every connected graph with nullity 2 is non-hypoenergetic. © 2021 University of Kragujevac, Faculty of Science. All rights reserved  

Let G = (V,E) be a simple undirected graph. For a given set L ⊂ ℝ, a function ω: E → L is called an L-flow. Given a vector γ ∈ ℝv, ω is a γ-L-flow if for each υ ∈ V, the sum of the values on the edges incident to υ is γ(υ). If γ(υ) = c, for all υ ∈ V, then the γ-L-flow is called a c-sum L-flow. In this paper, the existence of γ-L-flows for various choices of sets L of real numbers is studied, with an emphasis on 1-sum flows. Let L be a subset of real numbers containing 0 and denote L*:= L {0}. Answering a question from [S. Akbari, M. Kano, and S. Zare. A generalization of 0-sum flows in graphs. Linear Algebra Appl., 438:3629-3634, 2013.], the bipartite graphs which admit a 1-sum ℝ*-flow or... 

Let G be a graph with no isolated vertex. A total dominating set of G is a set S of vertices of G such that every vertex is adjacent to at least one vertex in S. The total domatic number of a graph is the maximum number of total dominating sets which partition the vertex set of G. In this paper we provide a criterion under which a cubic graph has total domatic number at least two  

Let G be a graph with n vertices and m edges and assume that f : V ( G ) → N is a function with ∑v ∈ V ( G ) f ( v ) = m + n. We show that, if we can assign to any vertex v of G a list Lv of size f ( v ) such that G has a unique vertex coloring with these lists, then G is f-choosable. This implies that, if ∑v ∈ V ( G ) f ( v ) > m + n, then there is no list assignment L such that | Lv | = f ( v ) for any v ∈ V ( G ) and G is uniquely L-colorable. Finally, we prove that if G is a connected non-regular multigraph with a list assignment L of edges such that for each edge e = u v, | Le | = max { d ( u ), d ( v ) }, then G is not uniquely L-colorable and we conjecture that this result holds for... 

We construct counterexamples to the conjecture of Xu (1990, J. Combin. Theory Ser. B50, 319-320) that every uniquely r-colorable graph of order n with exactly (r-1)n-(r2) edges must contain a Kr. © 2001 Academic Press  

For every h ∈ ℕ, a graph G with the vertex set V (G) and the edge set E(G) is said to be h-magic if there exists a labeling l: E(G) → ℤh{0} such that the induced vertex labeling s: V (G) → ℤh, defined by s(v) = Puv∈E(G) l(uv) is a constant map. When this constant is zero, we say that G admits a zero-sum h-magic labeling. The null set of a graph G, denoted by N(G), is the set of all natural numbers h ∈ ℕ such that G admits a zero-sum h-magic labeling. In 2012, the null sets of 3-regular graphs were determined. In this paper we show that if G is an r-regular graph, then for even r (r > 2), N(G) = ℕ and for odd r (r ≠ 5), ℕ {2, 4} ⊆ N(G). Moreover, we prove that if r is odd and G is a 2-edge...