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Multipartite secret sharing schemes are those having a multipartite access structure, in which the set of participants is divided into several parts and all participants in the same part play an equivalent role. Secret sharing schemes for multipartite access structures have received considerable attention due to the fact that multipartite secret sharing can be seen as a natural and useful generalization of threshold secret sharing.

Multipartite bacteria have one chromosome and one or more chromid. Chromids are believed to have properties that enhance genomic flexibility, making them a favored integration site for new genes. However, the mechanism by which chromosomes and chromids jointly contribute to this flexibility is not clear. To shed light on this, we analyzed the openness of chromosomes and chromids of the two bacteria, Vibrio and Pseudoalteromonas, both which belong to the Enterobacterales order of Gammaproteobacteria, and compared the genomic openness with that of monopartite genomes in the same order. We applied pangenome analysis, codon usage analysis and the HGTector software to detect horizontally transferred genes. Our findings suggest that the chromids of Vibrio and Pseudoalteromonas originated from two separate plasmid acquisition events. Bipartite genomes were found to be more open compared to monopartite. We found that the shell and cloud pangene categories drive the openness of bipartite genomes in Vibrio and Pseudoalteromonas. Based on this and our two recent studies, we propose a hypothesis that explains how chromids and the chromosome terminus region contribute to the genomic plasticity of bipartite genomes.

In Monras et al. (Phys. Rev. A, 2011, 84(1):012301 2011), the authors presented an entanglement measure for bipartite pure states based on local unitary operations. In this paper, motivated by this idea, we obtained an entanglement measure for multipartite quantum states with respect to k-partitions, which is called mirror entanglement measure for multipartite k-nonseparable states, it is simply denoted by k-MEM. We show that this measure is well-defined, i.e., it satisfies some necessary conditions of entanglement measure including vanishes iff the multipartite quantum states are k-separable, invariance under local unitary operation and monotonicity under local quantum operation and classical communication.

Interpersonal communication is so important in everyday life that it is desirable everyone who participates in the conversation is satisfied. However, every participant of the conversation cannot be satisfied in such cases as those wherein only one person cannot keep up with the conversation and feels alienated, or wherein someone cannot communicate non-verbal expressions with his/her conversation partner adequately. In this study, we have focused on facial direction and gaze among the various factors that are said to affect conversational satisfaction. We have attempted to lessen any sense of non-participation in the conversation and increase the conversational satisfaction of the non-participant in a tripartite conversation by modulating the visual information in such a way that the remaining two parties turn toward the non-participating party. In the experiments we have conducted in VR environments, we have reproduced a conversation of two male adults recorded in actual environments using two avatars. The experimental subjects have watched this over their HMDs. The experiments have found that visually modulating the avatars’ faces and gazes such that they appear to turn toward the subjects has increased the subjects’ sense of participation in the conversation. Nevertheless, the experiments have not increased the subjects’ conversational enjoyment, a component of the factors for conversational satisfaction.

The purpose of this paper was to introduce the concepts of very thin multigroup, nondistributive (very thin) multirings, zero-divisor elements of multirings and zero-divisor graphs based on zero-divisor elements of multirings. In order to realize the article’s goals, we consider the relationship between finite nondistributive (very thin) multirings and multirings and construct nondistributive (very thin) multirings based on given ring. By some conditions on prime numbers, finite (nondistributive) very thin multirings are constructed. Zero-divisor graph based on zero-divisor set of (nondistributive) (very thin) multirings are introduced, so we investigate of some necessity and sufficiency conditions such that compute of order and size of these zero-divisor graphs. Also, the notations of derivable zero-divisor graphs and derivable zero-divisor subgraphs are introduced and is showed that some multipartite graphs are derivable zero-divisor graphs, all complete graphs, and cyclic graphs are derivable zero-divisor subgraphs.

We look into multipartite quantum states on which quantum cryptographic protocols including quantum key distribution and quantum secret sharing can be perfectly performed, and define the quantum cryptographic resource distillable rate as the asymptotic rate at which such multipartite state can be distilled from a given multipartite state. Investigating several relations between entanglement and the rate, we show that there exists a multipartite bound entangled state whose quantum cryptographic resource distillable rate is strictly positive, that is, there exists a multipartite entangled state which is not distillable, but can be useful for quantum cryptography such as quantum key distribution and quantum secret sharing., 9 pages, 2 figures

A 2-edge-coloured graph G is supereulerian if G contains a spanning closed trail in which the edges alternate in colours. We show that for general 2-edge-coloured graphs it is NP-complete to decide whether the graph is supereulerian. An eulerian factor of a 2-edge-coloured graph is a collection of vertex-disjoint induced subgraphs which cover all the vertices of G such that each of these subgraphs is supereulerian. We give a polynomial algorithm to test whether a 2-edge-coloured graph has an eulerian factor and to produce one when it exists. A 2-edge-coloured graph is (trail-)colour-connected if it contains a pair of alternating (u, v)-paths ((u, v)-trails) whose union is an alternating closed walk for every pair of distinct vertices u, v. We prove that a 2-edge-coloured complete bipartite graph is supereulerian if and only if it is colour-connected and has an eulerian factor. A 2-edge-coloured graph is M-closed if xz is an edge of G whenever some vertex u is joined to both x and z by edges of the same colour. M-closed 2-edge-coloured graphs, introduced in Contreras-Balbuena et al. (Discret Math Theoret Comput Sci 21:1, 2019), form a rich generalization of 2-edge-coloured complete graphs. We show that if G is obtained from an M-closed 2-edge-coloured graph H by substituting independent sets for the vertices of H, then G is supereulerian if and only if G is trail-colour-connected and has an eulerian factor. Finally we discuss 2-edge-coloured complete multipartite graphs and show that such a graph may not be supereulerian even if it is trail-colour-connected and has an eulerian factor.

In his paper "Kings in Bipartite Hypertournaments" (Graphs $\&$ Combinatorics 35, 2019), Petrovic stated two conjectures on 4-kings in multipartite hypertournaments. We prove one of these conjectures and give counterexamples for the other.

Multipartite secret sharing schemes are those that have multipartite access structures. The set of the participants in those schemes is divided into several parts, and all the participants in the same part play the equivalent role. One type of such access structure is the compartmented access structure, and the other is the hierarchical access structure. We propose an efficient compartmented multisecret sharing scheme based on the linear homogeneous recurrence (LHR) relations. In the construction phase, the shared secrets are hidden in some terms of the linear homogeneous recurrence sequence. In the recovery phase, the shared secrets are obtained by solving those terms in which the shared secrets are hidden. When the global threshold is t , our scheme can reduce the computational complexity of the compartmented secret sharing schemes from the exponential time to polynomial time. The security of the proposed scheme is based on Shamir’s threshold scheme, i.e., our scheme is perfect and ideal. Moreover, it is efficient to share the multisecret and to change the shared secrets in the proposed scheme.

Attributed network embedding has attracted plenty of interest in recent years. It aims to learn task-independent, low-dimensional, and continuous vectors for nodes preserving both topology and attribute information. Most of the existing methods, such as random-walk based methods and GCNs, mainly focus on the local information, i.e., the attributes of the neighbours. Thus, they have been well studied for assortative networks (i.e., networks with communities) but ignored disassortative networks (i.e., networks with multipartite, hubs, and hybrid structures), which are common in the real world. To model both assortative and disassortative networks, we propose a block-based generative model for attributed network embedding from a probability perspective. Specifically, the nodes are assigned to several blocks wherein the nodes in the same block share the similar linkage patterns. These patterns can define assortative networks containing communities or disassortative networks with the multipartite, hub, or any hybrid structures. To preserve the attribute information, we assume that each node has a hidden embedding related to its assigned block. We use a neural network to characterize the nonlinearity between node embeddings and node attributes. We perform extensive experiments on real-world and synthetic attributed networks. The results show that our proposed method consistently outperforms state-of-the-art embedding methods for both clustering and classification tasks, especially on disassortative networks.

It is well known that the quantum mutual information and its conditional version do not increase under local channels. I this paper we show that the recently established lower semicontinuity of the quantum conditional mutual information implies (in fact, is equivalent to) the lower semicontinuity of the loss of the quantum (conditional) mutual information under local channels considered as a function on the Cartesian product of the set of all states of a composite system and the sets of all local channels (equipped with the strong convergence). Some applications of this property are considered. New continuity conditions for the quantum mutual information and for the squashed entanglement in both bipartite and multipartite infinite-dimensional systems are obtained. It is proved, in particular, that the multipartite squashed entanglement of any countably-non-decomposable separable state with finite marginal entropies is equal to zero. Special continuity properties of the information gain of a quantum measurement with and without quantum side information are established that can be treated as robustness (stability) of these quantities w.r.t. perturbation of the measurement and the measured state., Comment: 32 pages, preliminary version, any comments and references are welcome

We present a new quantum-memory-assisted entropic uncertainty relation for multipartite systems which shows the uncertainty principle of quantum mechanics. Notably, our results recover some well-known entropic uncertainty relations for two arbitrary incompatible observables that demonstrate the uncertainties about the results of two measurements. This uncertainty relation might play a critical role in the foundations of quantum theory.

The exploration of quantum entanglement in multipartite quantum systems is of great significance to the study of quantum entanglement, maximally multi-qubit entangled state is one of the research objects. Recently, Che et al. presented a recurrence relation of multi-qubit state. According to this inspiration, we present the recurrence relation of maximally multi-qubit pure states of N-qubits for N = 6, 7, 8. Further, some new forms of the seven- and eight-qubit maximally entangled states are found with the recurrence relation.

In recent decades, multipartite mutualisms involving microorganisms such as fungi have been discovered in associations traditionally thought of as bipartite. Ant-plant mutualisms were long thought to be bipartite despite fungi being noticed in an epiphytic ant-plant over 100 years ago. We sequenced fungal DNA from the three distinct domatium chambers of the epiphytic ant-plant Myrmecodia beccarii to establish if fungal communities differ by chamber type across five geographic locations spanning 675 km. The three chamber types serve different ant-associated functions including ‘waste’ chambers, where ant workers deposit waste; ‘nursery’ chambers, where the brood is kept; and ‘ventilation’ chambers, that allow air into the domatium. Overall, fungi from the order Chaetothyriales dominated the chambers in terms of the proportion of operational taxonomic units (OTUs; 13.4%) and sequence abundances of OTUs (28% of the total); however a large portion of OTUs (28%) were unidentified at the order level. Notably, the fungal community in the waste chambers differed consistently from the nursery and ventilation chambers across all five locations. We identified 13 fungal OTUs as ‘common’ in the waste chambers that were rare or in very low sequence abundance in the other two chambers. Fungal communities in the nursery and ventilation chambers overlapped more than either did with the waste chambers but were also distinct from each other. Differences in dominance of the common OTUs drove the observed patterns in the fungal communities for each of the chamber types. This suggests a multipartite mutualism involving fungi exists in this ant-plant and that the role of fungi differs among chamber types.

The Seidel energy of a simple graph G is the sum of the absolute values of the eigenvalues of the Seidel matrix of G. In this paper we study the Seidel eigenvalues of complete multipartite graphs and find the exact value of the Seidel energy of the complete multipartite graphs.

An edge-colored graph is called rainbow if all its edges are colored distinct. The anti-Ramsey number of a graph family $${\mathcal {F}}$$ in the graph G, denoted by $$AR{(G,{\mathcal {F}})}$$ , is the maximum number of colors in an edge-coloring of G without rainbow subgraph in $${\mathcal {F}}$$ . The anti-Ramsey number for the short cycle $$C_3$$ has been determined in a few graphs. Its anti-Ramsey number in the complete graph can be easily obtained from the lexical edge-coloring. Gorgol considered the problem in complete split graphs which contains complete graphs as a subclass. In this paper, we study the problem in the complete multipartite graph which further enlarges the family of complete split graphs. The anti-Ramsey numbers for $$C_3$$ and $$C_3^{+}$$ in complete multipartite graphs are determined. These results contain the known results for $$C_3$$ and $$C_3^{+}$$ in complete and complete split graphs as corollaries.

We provide a characterization of multipartite systems constraints in terms of quantum correlations. By using the Hamming weight of the binary vectors associated with the subsystems, we give the α th power of monogamy and β th power of polygamy inequalities for general quantum correlations. Using concurrence as an application, one gets tighter inequalities than the existing ones for some classes of quantum states. Detailed examples are presented.

In any interconnection network, task allocation plays a major role in the processor speed as fair distribution leads to enhanced performance. Complete multipartite networks serve well for this purpose as the task can be split into different partites which improves the degree of reliability of the network. Such an allocation process in the network can be done by means of graph embedding. The optimal wirelength of a graph embedding helps in the distribution of deterministic algorithms from the guest graph to other host graphs in order to incorporate its unique deterministic properties on that chosen graph. In this paper, we propose an algorithm to compute the optimal wirelength of balanced complete multipartite graphs onto the Cartesian product of trees with path and cycle. Moreover, we derive the closed formulae for wirelengths in specific trees like (1-rooted) complete binary tree and sibling graphs.

Bell nonlocality of quantum states is an important resource in quantum information and then has various applications. It is usually detected by the violation of some Bell’s inequalities and the all-versus-nothing test. In the present paper, we aim to establish some mathematical methods for proving Bell nonlocality without inequalities, inspired by the work [Phys. Rev. Lett., 89, 080402 (2002)] regarding the GHZ paradox. For self-containedness, we recall the mathematical definition of Bell nonlocality proposed in [Sci. China-Phys. Mech. Astron. 62, 030311 (2019)] and then give some basic properties on it. Then we derive some necessary conditions for a multipartite state to be Bell local and obtain some sufficient conditions for a state to be Bell nonlocal in terms of “expectations” of local observables without invoking Bell inequalities. Unlike the standard approach to nonlocality detection based on violation of Bell inequalities, the obtained criteria are formulated in terms of certain relations for expectation values of local observables that are constructed from the well-known GHZ paradoxes.

Rhizobium leguminosarum symbiovar trifolii strains TA1 and CC275e are nitrogen-fixing microsymbionts of Trifolium spp. and have been used as commercial inoculant strains for clovers in pastoral agriculture in Australia and New Zealand. Here we present the complete genome sequences of both strains, resolving their multipartite genome structures and allowing for future studies using genomic approaches. [Formula: see text] Copyright © 2021 The Author(s). This is an open access article distributed under the CC BY 4.0 International license .

An interconnection network is a complex connection of a set of processors and communication links between different processors which is utilized to exchange data between processors in the parallel computing system. Graph embedding is a vital tool used to run parallel algorithms in computer networks in which placing different modules on the board is one of the main cost criteria. By finding the optimal layout, the placement problem in circuit designs which does not have any deterministic algorithms can be solved. The complete multipartite graph is a widely used network topology with a high degree of reliability due to its flexible choice of network size. Recently a study was made by computing the optimal layout of balanced complete multipartite graphs into host graphs taken from the Cartesian product of elements in the set {path, cycle}, but leaving the case of product of paths as an open problem. This paper aims to solve such an open problem and the key idea is to locate suitable optimal sets in balanced complete multipartite graphs with respect to maximizing the number of edges in the located sets. Besides, we compute the layout in the case of host graphs like k-rooted complete binary trees, k-rooted sibling trees and the Cartesian product of path P 2 and complete binary trees.

Pure quantum spin-s states can be represented by 2s points on the sphere, as shown by Majorana (Nuovo Cimento 9:43–50, 1932)—the description has proven particularly useful in the study of rotational symmetries of the states, and a host of other properties, as the points rotate rigidly on the sphere when the state undergoes an SU(2) transformation in Hilbert space. We present here an extension of this representation to multipartite, totally antisymmetric (under exchange of any two qudits) states, widely known in the form of Slater determinants, and linear combinations thereof. Such states generally involve a superposition of various spin values, giving rise to a family of Majorana-like constellations, that captures their rotational transformation properties. We also point out that our results apply equally well to the characterization of degenerate linear subspaces of the Hilbert space of a single spin, of the type that appear in the Wilczek–Zee effect, and comment on potential applications to holonomic quantum computing.

We calculate spin correlation functions using IBM quantum processors, accessed online. We demonstrate the rotational invariance of the singlet state, interesting properties of the triplet states, and surprising features of a state of three entangled qubits. This exercise is ideal for remote learning and generates data with real quantum mechanical systems that are impractical to investigate in the local laboratory. Students learn a wide variety of skills, including calculation of multipartite spin correlation functions, design and analysis of quantum circuits, and remote measurement with real quantum processors.

Generalized multipartite networks consist in the joint observation of several networks implying some common pre-specified groups of individuals. Such complex networks arise commonly in social sciences, biology, ecology, etc. We propose a flexible probabilistic model named Multipartite Block Model (MBM) able to unravel the topology of multipartite networks by identifying clusters (blocks) of nodes sharing the same patterns of connectivity across the collection of networks they are involved in. The model parameters are estimated through a variational version of the Expectation–Maximization algorithm. The numbers of blocks are chosen using an Integrated Completed Likelihood criterion specifically designed for our model. A simulation study illustrates the robustness of the inference strategy. Finally, two datasets respectively issued from ecology and ethnobiology are analyzed with the MBM in order to illustrate its flexibility and its relevance for the analysis of real datasets. The inference procedure is implemented in an R -package GREMLIN , available on Github ( https://github.com/Demiperimetre/GREMLINhttps://github.com/Demiperimetre/GREMLIN ).

In this paper we design a deterministic controllable quantum communication protocol for remotely preparing three-qubit GHZ-type and four-qubit W-type entangled states at two different locations at the same time. Two parties (the preparers) along with a third party (the controller) are connected through a proper multipartite entangled resource. The states to be prepared are not physically available, only the classical information of each state is known by a party who intends to remotely prepare it at the end of the other party under the same control of a third party. Concretely, it is a multi-tasking protocol in which remote preparations of the two inequivalent states are accomplished not only simultaneously but also controllably through execution of a single protocol by utilizing an eleven-qubit entangled state as shared quantum resource. We also propose a generation process of the multipartite quantum resource used.

The human face is complex and multipartite, and characterization of its genetic architecture remains challenging. Using a multivariate genome-wide association study meta-analysis of 8,246 European individuals, we identified 203 genome-wide-significant signals (120 also study-wide significant) associated with normal-range facial variation. Follow-up analyses indicate that the regions surrounding these signals are enriched for enhancer activity in cranial neural crest cells and craniofacial tissues, several regions harbor multiple signals with associations to different facial phenotypes, and there is evidence for potential coordinated actions of variants. In summary, our analyses provide insights into the understanding of how complex morphological traits are shaped by both individual and coordinated genetic actions. ispartof: Nature Genetics vol:53 issue:1 ispartof: location:United States status: Published online

This article studies a consensus protocol, which is called a multipartite average consensus, of a multiagent system over signed undirected networks in which all agents could be partitioned into multiple subgroups and all agents in the same group converge to the average of their initial values. The proposed protocol is based on results from a matrix-weighted consensus. It is shown that a matrix-weighted consensus can be transformed into a multipartite average consensus. We then discuss a method to combine some subgroups or all subgroups into a union group in order that all agents in the union group reach an average consensus. Finally, we provide examples and simulations to validate the statement.

The skewness of a graph G, denoted by sk(G), is the minimum number of edges in G whose removal results in a planar graph. It is an important parameter that measures how close a graph is to planarity, and it is complementary, and computationally equivalent, to the Maximum Planar Subgraph Problem. For any connected graph G on p vertices and q edges with girth g, one can easily verify that sk(G) ≥ π(G), where $$\pi(G)=\lceil q-\frac{g}{g-2}(p-2)\rceil$$ , and the graph G is said to be π-skew if equality holds. The concept of π-skew was first proposed by G. L. Chia and C. L. Lee. The π-skew graphs with girth 3 are precisely the graphs that contain a triangulation as a spanning subgraph. The purpose of this paper is to explore the properties of π-skew graphs. Some families of π-skew graphs are obtained by applying these properties, including join of two graphs, complete multipartite graphs and Cartesian product of two graphs. We also discuss the threshold for the existence of a spanning triangulation. Among other results some sufficient conditions regarding the regularity and size of a graph, which ensure a spanning triangulation, are given.

Descrying all aspects of the quantum entanglement of multipartite quantum systems is an essential part when researching the quantum entanglement. Maximally multi-qubit entangled state is one of the research objects. Recently, attracted by a criterion for maximally entangled nine-qubit state and construct a nine-qubit maximally entangled state, we construct a new genuine maximally nine-qubit entangled state via the recurrence relation. Further, nine-qubit entangled state is found which can be seen as a new form maximally nine-qubit entangled state. There are 108 of purity equal to 1/16, 18 of purity equal to 1/8 in observation. We believe the result could provide a new idea for constructing more new maximally multi-qubit states.

The interaction of a three-level atom with two quantum field modes has been studied analytically. Strong quantum entanglement between individual parts of the considered multipartite system has been revealed and the possibility of its controlled variation has been demonstrated. Methods of the transmission and exchange of phase information between field modes, as well as of direct measurement of the phase characteristics of an unknown state of the input field, have been developed on the basis of quantum entanglement between initially independent quantum fields interacting with an atom.

Synthetic biology relies on rapid and efficient methods to stably integrate DNA payloads encoding for synthetic biological systems into the genome of living cells. The size of designed biological systems increases with their complexity, and novel methods are needed that enable efficient and simultaneous integration of multiple payloads into single cells. By assembling natural and synthetic protein-protein dimerization domains, we have engineered a set of multipartite transcription factors for driving heterologous target gene expression. With the distribution of single parts of multipartite transcription factors on piggyback transposon-based donor plasmids, we have created a logic genome integration control (LOGIC) system that allows for efficient one-step selection of stable mammalian cell lines with up to three plasmids. LOGIC significantly enhances the efficiency of multiplexed payload integration in mammalian cells compared to traditional cotransfection and may advance cell line engineering in synthetic biology and biotechnology., ACS Synthetic Biology, 9 (11), ISSN:2161-5063