Combinatorial Functions Research Articles

Segmentation-based stereo matching using combinatorial similarity measurement and adaptive support region

An accurate segmentation-based algorithm using combinatorial similarity measurement and adaptive support aggregation strategy is developed for stereo matching. The advantage of our method which based on a segmentation framework is generating disparity map in textureless regions correctly and localize depth boundaries precisely. Initial disparity map is estimated by a local correspondence approach which consisting of a combinatorial similarity measurement function and an adaptive window with arbitrary shape and size. The accuracy of the initial disparity map generated by combinatorial similarity measurement is better than that generated by individual similarity measurement. The plane parameters are fitted utilizing the initial disparity map. In this process, a method named “MC-RANSAC” which consisting of mutual consistency check criterion and random sample consensus algorithm is proposed to filter out the outliers and obtain the stable disparity plane parameters. Lastly, the disparity plane is optimized by belief propagation. Experiments with stereo image pairs show the validity of the proposed method.

Linked Markovian quantum tunnels: An approximation technique for solving the bin packing problem

According to quantum mechanics there exists a small probability for a particle to pass through a barrier. The principle behind this assertion is known as Quantum Tunnelling effect because the escaping particle has to, somehow, dig a passage to the other side of the barrier. When placed in a proper context, this nonlocal phenomenon can be a powerful concept for solving combinatorial problems. The strategy used consists in simulating quantum tunnels aiming to find approximate solutions for a particular optimum of a combinatorial cost function. In this paper we present such a scheme, composed by a finite number of linked Markov Chains. Each Markov Chain is connected with its adjacent by a link that mimics a quantum tunnel. The numerical practicality of the model is demonstrated using the traditional one-dimensional Bin Packing Problem.

A combinatorial scoring function for protein-RNA docking.

Protein-RNA docking is still an open question. One of the main challenges is to develop an effective scoring function that can discriminate near-native structures from the incorrect ones. To solve the problem, we have constructed a knowledge-based residue-nucleotide pairwise potential with secondary structure information considered for nonribosomal protein-RNA docking. Here we developed a weighted combined scoring function RpveScore that consists of the pairwise potential and six physics-based energy terms. The weights were optimized using the multiple linear regression method by fitting the scoring function to L_rmsd for the bound docking decoys from Benchmark II. The scoring functions were tested on 35 unbound docking cases. The results show that the scoring function RpveScore including all terms performs best. Also RpveScore was compared with the statistical mechanics-based method derived potential ITScore-PR, and the united atom-based statistical potentials QUASI-RNP and DARS-RNP. The success rate of RpveScore is 71.6% for the top 1000 structures and the number of cases where a near-native structure is ranked in top 30 is 25 out of 35 cases. For 32 systems (91.4%), RpveScore can find the binding mode in top 5 that has no lower than 50% native interface residues on protein and nucleotides on RNA. Additionally, it was found that the long-range electrostatic attractive energy plays an important role in distinguishing near-native structures from the incorrect ones. This work can be helpful for the development of protein-RNA docking methods and for the understanding of protein-RNA interactions. RpveScore program is available to the public at http://life.bjut.edu.cn/kxyj/kycg/2017116/14845362285362368_1.html Proteins 2017; 85:741-752. © 2016 Wiley Periodicals, Inc.

On the relationship between combinatorial functions and representation theory

The paper is devoted to the study of well-known combinatorial functions on the symmetric group S n —the major index maj, the descent number des, and the inversion number inv—from the representation-theoretic point of view. We show that these functions generate the same ideal in the group algebra C[S n ], and the restriction of the left regular representation of the group S n to this ideal is isomorphic to its representation in the space of n×n skew-symmetric matrices. This allows us to obtain formulas for the functions maj, des, and inv in terms of matrices of an exceptionally simple form. These formulas are applied to find the spectra of the elements under study in the regular representation, as well as derive a series of identities relating these functions to one another and to the number fix of fixed points.

The combinatorics of LCD codes: linear programming bound and orthogonal matrices

Linear complementary dual (LCD) codes are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings Rk. We give a linear programming bound on the largest size of an LCD code of given length and minimum distance. We make a table of lower bounds for this combinatorial function for modest values of the parameters.

Deciphering Combinatorial Genetics.

High-order interactions among components of interconnected genetic networks regulate complex functions in biological systems, but deciphering these interactions is challenging. New strategies are emerging to decode these combinatorial genetic interactions across a wide range of organisms. Here, we review advances in multiplexed and combinatorial genetic perturbation technologies and high-throughput profiling platforms that are enabling the systematic dissection of complex genetic networks. These rapidly evolving technologies are being harnessed to probe combinatorial gene functions in functional genomics studies and have the potential to advance our understanding of how genetic networks regulate sophisticated biological phenotypes, to generate novel therapeutic strategies, and to enable the engineering of complex artificial gene networks.

Distinct Patterns of Expression of Transcription Factors in Response to Interferonβ and Interferonλ1

After viral infection, type I and III interferons (IFNs) are coexpressed by respiratory epithelial cells (RECs) and activate the ISGF3 transcription factor (TF) complex to induce expression of a cell-specific set of interferon-stimulated genes (ISGs). Type I and III IFNs share a canonical signaling pathway, suggesting that they are redundant. Animal and in vitro models, however, have shown that they are not redundant. Because TFs dictate cellular phenotype and function, we hypothesized that focusing on TF-ISG will reveal critical combinatorial and nonredundant functions of type I or III IFN. We treated BEAS-2B human RECs with increasing doses of IFNβ or IFNλ1 and measured expression of TF-ISG. ISGs were expressed in a dose-dependent manner with a nonlinear jump at intermediate doses. At subsaturating combinations of IFNβ and IFNλ1, many ISGs were expressed in a pattern that we modeled with a cubic equation that mathematically defines this threshold effect. Uniquely, IFNβ alone induced early and transient IRF1 transcript and protein expression, while IFNλ1 alone induced IRF1 protein expression at low levels that were sustained through 24 h. In combination, saturating doses of these 2 IFNs together enhanced and sustained IRF1 expression. We conclude that the cubic model quantitates combinatorial effects of IFNβ and IFNλ1 and that IRF1 may mediate nonredundancy of type I or III IFN in RECs.

In vivo modified organic matrix for testing biomineralization-related protein functions in differentiated Dictyostelium on calcite.

This work reports an in vivo approach for identifying the function of biomineralization-related proteins. Synthetic sequences of n16N, OC-17 and perlucin with signal peptides are produced in a novel Gateway expression system for Dictyostelium under the control of the [ecmB] promoter. A fast and easy scanning electron microscopic screening method was used to differentiate on the colony level between interplay effects of the proteins expressed in the extracellular matrix (ECM). Transformed Dictyostelium, which migrated as multicellular colonies on calcite crystals and left their ECM remnants on the surface were investigated also by energy-dispersive X-ray spectroscopy (EDX). Calcium minerals with and without phosphorous accumulated very frequently within the matrix of the Dictyostelium colonies when grown on calcite. Magnesium containing phosphorous granules were observed when colonies were exposed on silica. The absence of calcium EDX signals in these cases suggests that the external calcite crystals but not living cells represent the major source of calcium in the ECM. Several features of the system provide first evidence that each protein influences the properties of the matrix in a characteristic mode. Colonies transformed with perlucin produced a matrix with cracks on the length scale of a few microns throughout the matrix patch. For colonies with OC-17, almost no cracks were observed, regardless of the length scale. The non-transformed Dictyostelium (Ax3-Orf+) produced larger cracks. The strategy presented here develops the first step toward an efficient eukaryotic screening system for the combinatorial functionalization of materials by bioengineering in close analogy to natural biomineralization concepts.

Posterior–anterior gradient of zebrafish hes6 expression in the presomitic mesoderm is established by the combinatorial functions of the downstream enhancer and 3′UTR

In vertebrates, the periodic formation of somites from the presomitic mesoderm (PSM) is driven by the molecular oscillator known as the segmentation clock. The hairy-related gene, hes6/her13.2, functions as a hub by dimerizing with other oscillators of the segmentation clock in zebrafish embryos. Although hes6 exhibits a posterior–anterior expression gradient in the posterior PSM with a peak at the tailbud, the detailed mechanisms underlying this unique expression pattern have not yet been clarified. By establishing several transgenic lines, we found that the transcriptional regulatory region downstream of hes6 in combination with the hes6 3′UTR recapitulates the endogenous gradient of hes6 mRNA expression. This downstream region, which we termed the PT enhancer, possessed several putative binding sites for the T-box and Ets transcription factors that were required for the regulatory activity. Indeed, the T-box transcription factor (Tbx16) and Ets transcription factor (Pea3) bound specifically to the putative binding sites and regulated the enhancer activity in zebrafish embryos. In addition, the 3′UTR of hes6 is required for recapitulation of the endogenous mRNA expression. Furthermore, the PT enhancer with the 3′UTR of hes6 responded to the inhibition of retinoic acid synthesis and fibroblast growth factor signaling in a manner similar to endogenous hes6. The results showed that transcriptional regulation by the T-box and Ets transcription factors, combined with the mRNA stability given by the 3′UTR, is responsible for the unique expression gradient of hes6 mRNA in the posterior PSM of zebrafish embryos.

Riemann Hypothesis and strongly Ramanujan complexes from GLn

We investigate the Riemann Hypothesis on combinatorial zeta functions associated to finite quotients of the affine building of GLn. We prove that if the quotient complex is strongly Ramanujan then these zeta functions satisfy the Riemann Hypothesis. On the other hand, we show that the converse statement is also true provided the extra generic condition. In the end, we give an example to show that this generic condition is indeed necessary.

Combinatorial functions of GATA2 and GATA3 are essential for early trophoblast development and to balance the stem vs. differentiation and angiogenic equilibrium in trophoblast lineage

Combinatorial functions of GATA2 and GATA3 are essential for early trophoblast development and to balance the stem vs. differentiation and angiogenic equilibrium in trophoblast lineage

On a new edge function on complete weighted graphs and its application for locating Hamiltonian cycles of small weight

In this paper, we define a new combinatorial function on the edges of complete weighted graphs. This function assigns to each edge of the graph the sum of the weights of all Hamiltonian cycles that contain the edge. Since this function involves the factorial function, whose exact calculation is intractable due to its superexponential asymptotic rate of increase, we also introduce a normalized version of the function that is efficiently computable. From this version, we derive an upper bound to the weight of the minimum weight Hamiltonian cycle of the graph based on the weights of the graph edges. Then we investigate the possible algorithmic applications of this normalized function using the Nearest Neighbor Heuristic and a smallest edge first heuristic. As evidence for its applicability, we show that the use of this function as a criterion for the selection of the next edge, improves the performance of both heuristics for approximating the minimum weight Hamiltonian cycles in Euclidean plane graphs. Moreover, our experimental results show that the use of the function is more suitable with the structure of the smallest edge first heuristic since it provides a solution closer to the best known solution of known hard TSP instances but in \(O(n^3)\) time.

Generalized modularity matrices

Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph clustering problems. In this paper we put in evidence certain common traits of various modularity matrices and shed light on their spectral properties that are at the basis of various theoretical results and practical spectral-type algorithms for community detection.

A brief histone in time: understanding the combinatorial functions of histone PTMs in the nucleosome context.

It has been over 50 years since Allfrey et al. proposed that histone acetylation regulates RNA synthesis, and the study of histone modifications has progressed at an extraordinary pace for the past two decades. In this review, we provide a perspective on some key events and advances in our understanding of histone modifications. We also highlight reagents and tools from past to present that facilitated progress in this research field. Using histone H3 phosphorylation as an underlying thread, we review the rationale that led to the proposal of the histone code hypothesis, as well as examples that illustrate the concepts of combinatorial histone modifications and cross-talk pathways. We further highlight the importance of investigating these mechanisms in the context of nucleosomes rather than just at the histone level and present current and developing approaches for such studies. Overall, research on histone modifications has yielded great mechanistic insights into the regulation of genomic functions, and extending these studies using nucleosomes will further elucidate the complexity of these pathways in a more physiologically relevant context.

2D Toda τ-Functions as Combinatorial Generating Functions

Two methods of constructing 2D Toda τ-functions that are generating functions for certain geometrical invariants of a combinatorial nature are related. The first involves generation of paths in the Cayley graph of the symmetric group Sn by multiplication of the conjugacy class sums Cλ ∈C(Sn) in the group algebra by elements of an abelian group of central elements. Extending the characteristic map to the tensor product C(Sn )⊗ C(Sn) leads to double expansions in terms of power sum symmetric functions, in which the coefficients count the number of such paths. Applying the same map to sums over the orthogonal idempotents leads to diagonal double Schur function expansions that are iden- tified as τ-functions of hypergeometric type. The second method is the standard construc- tion of τ-functions as vacuum-state matrix elements of products of vertex operators in a fermionic Fock space with elements of the abelian group of convolution symmetries .A homomorphism between these two group actions is derived and shown to be intertwined by the characteristic map composed with fermionization. Applications include Okounkov's generating function for double Hurwitz numbers, which count branched coverings of the Riemann sphere with specified ramification profiles at two branch points, and only simple branching at all the others, and various analogous combinatorial counting functions.

Duality on Fock spaces and combinatorial energy functions

We generalize in a combinatorial way the notion of the energy function of affine type A on a sequence of row or column tableaux to the case of a more general class of modules over a general linear Lie superalgebra g based on a Howe duality of type (g,gln) on various Fock spaces.

A modular analysis of the auxin signalling network.

Auxin is essential for plant development from embryogenesis onwards. Auxin acts in large part through regulation of transcription. The proteins acting in the signalling pathway regulating transcription downstream of auxin have been identified as well as the interactions between these proteins, thus identifying the topology of this network implicating 54 Auxin Response Factor (ARF) and Aux/IAA (IAA) transcriptional regulators. Here, we study the auxin signalling pathway by means of mathematical modeling at the single cell level. We proceed analytically, by considering the role played by five functional modules into which the auxin pathway can be decomposed: the sequestration of ARF by IAA, the transcriptional repression by IAA, the dimer formation amongst ARFs and IAAs, the feedback loop on IAA and the auxin induced degradation of IAA proteins. Focusing on these modules allows assessing their function within the dynamics of auxin signalling. One key outcome of this analysis is that there are both specific and overlapping functions between all the major modules of the signaling pathway. This suggests a combinatorial function of the modules in optimizing the speed and amplitude of auxin-induced transcription. Our work allows identifying potential functions for homo- and hetero-dimerization of transcriptional regulators, with ARF:IAA, IAA:IAA and ARF:ARF dimerization respectively controlling the amplitude, speed and sensitivity of the response and a synergistic effect of the interaction of IAA with transcriptional repressors on these characteristics of the signaling pathway. Finally, we also suggest experiments which might allow disentangling the structure of the auxin signaling pathway and analysing further its function in plants.

Unimodal sequences and “strange” functions: a family of quantum modular forms

We construct an infinite family of quantum modular forms from combinatorial rank “moment” generating functions for strongly unimodal sequences. The first member of this family is Kontsevich’s “strange” function studied by Zagier. These results rely upon the theory of mock Jacobi forms. As a corollary, we exploit the quantum and mock modular properties of these combinatorial functions in order to obtain asymptotic expansions.

The Arabidopsis cytosolic Acyl-CoA-binding proteins play combinatory roles in pollen development.

In Arabidopsis, six acyl-CoA-binding proteins (ACBPs) have been identified and they have been demonstrated to function in plant stress responses and development. Three of these AtACBPs (AtACBP4-AtACBP6) are cytosolic proteins and all are expressed in floral organs as well as in other tissues. The roles of cytosolic AtACBPs in floral development were addressed in this study. To this end, a T-DNA insertional knockout mutant of acbp5 was characterized before use in crosses with the already available acbp4 and acbp6 T-DNA knockout mutants to examine their independent and combinatory functions in floral development. The single-gene knockout mutations did not cause any significant phenotypic changes, while phenotypic deficiencies affecting siliques and pollen were observed in the double mutants (acbp4acbp6 and acbp5acbp6) and the acbp4acbp5acbp6 triple mutant. Vacuole accumulation in the acbp4acbp6, acbp5acbp6 and acbp4acbp5acbp6 pollen was the most severe abnormality occurring in the double and triple mutants. Furthermore, scanning electron microscopy and transmission electron microscopy revealed exine and oil body defects in the acbp4acbp5acbp6 mutant, which also displayed reduced ability in in vitro pollen germination. Transgenic Arabidopsis expressing β-glucuronidase (GUS) driven from the various AtACBP promoters indicated that AtACBP6pro::GUS expression overlapped with AtACBP4pro::GUS expression in pollen grains and with AtACBP5pro::GUS expression in the microspores and tapetal cells. Taken together, these results suggest that the three cytosolic AtACBPs play combinatory roles in acyl-lipid metabolism during pollen development.

A combinatorial condition and Boolean functions with optimal algebraic immunity

This paper first proposes an infinite class of 2k-variable Boolean functions with high non- linearity and high algebraic degree. Then an infinite class of balanced Boolean functions are proposed by modifying the above Boolean functions. This class of balanced Boolean functions have optimal al- gebraic degree and high nonlinearity. Both classes have optimal algebraic immunity based on a general combinatorial conjecture.