Search

The explosive growth of spatial data and the widespread use of spatial databases emphasize the need for spatial data mining. The subsets of features frequently located together in a geographic space are called spatial co-location patterns. It is difficult to discover co-location patterns because of the huge amount of data brought by the instances of spatial features. A large fraction of the computation time is devoted to generating row instances and candidate co-location patterns. This paper makes three main contributions for mining co-location patterns. First, the definition of maximal instances is given and a row instance (RI)-tree is constructed to find maximal instances from a spatial data set. Second, a fast method for generating all row instances and candidate co-locations is proposed and the feasibility of this method is proved. Third, a maximal instance algorithm with no join operations for mining co-location patterns is proposed. Finally, experimental evaluations using synthetic data sets and a real data set show that maximal instance algorithm is feasible and has better performance.

We investigate the two problems of computing the union join graph as well as computing the subset graph for acyclic hypergraphs and their subclasses. In the union join graph G of an acyclic hypergraph H, each vertex of G represents a hyperedge of H and two vertices of G are adjacent if there exits a join tree T for H such that the corresponding hyperedges are adjacent in T. The subset graph of a hypergraph H is a directed graph where each vertex represents a hyperedge of H and there is a directed edge from a vertex u to a vertex v if the hyperedge corresponding to u is a subset of the hyperedge corresponding to v.

Recent work in weighted model counting proposed a unifying framework for dynamic-programming algorithms. The core of this framework is a project-join tree: an execution plan that specifies how Boolean variables are eliminated. We adapt this framework to compute exact literal-weighted projected model counts of propositional formulas in conjunctive normal form. Our key conceptual contribution is to define gradedness on project-join trees, a novel condition requiring irrelevant variables to be eliminated before relevant variables. We prove that building graded project-join trees can be reduced to building standard project-join trees and that graded project-join trees can be used to compute projected model counts. The resulting tool ProCount is competitive with the state-of-the-art tools \(\texttt {D4}_{\texttt {P}}\), projMC, and reSSAT, achieving the shortest solving time on 131 benchmarks of 390 benchmarks solved by at least one tool, from 849 benchmarks in total.

The Adjacency Graph is a structure used to model genomes in several rearrangement distance problems. In particular, most studies use properties of a maximum cycle packing of this graph to develop bounds and algorithms for rearrangement distance problems, such as the reversal distance and the Double Cut and Join (DCJ) distance. When each genome has no repeated genes, there exists only one cycle packing for the graph. However, when each genome may have repeated genes, the problem of finding a maximum cycle packing for the adjacency graph (Adjacency Graph Packing) is NP-hard. In this work, we developed a greedy random heuristic and a genetic algorithm heuristic for the Adjacency Graph Packing problem for genomes with repeated genes. We present experimental results and compare these heuristics with the SOAR framework. Furthermore, we show how the solutions from our algorithms can improve the estimation for the reversal distance when compared to the SOAR framework. Lastly, we applied our genetic algorithm heuristic in real genomic data to validate its practical use.

Sedona (formerly GeoSpark) is an in-memory cluster computing system for processing large-scale spatial data, which extends the core of Apache Spark to support spatial datatypes, partitioning techniques, indexes, and operations (e.g., spatial range, k Nearest Neighbor (kNN) and spatial join queries). k Nearest Neighbor Join Query (kNNJQ) finds for each object in one dataset \(\mathbb {P}\), k nearest neighbors of this object in another dataset \(\mathbb {Q}\). It is a common operation used in numerous spatial applications (e.g., GISs, location-based systems, continuous monitoring, etc.). kNNJQ is a time-consuming spatial operation, since it can be considered a hybrid of spatial join and nearest neighbor search. Given that Sedona outperforms other Spark-based spatial analytics systems in most cases and, it does not support kNN joins, including kNNJQ is a worthwhile challenge. Therefore, in this paper, we investigate how to design and implement an efficient kNNJQ algorithm in Sedona, using the most appropriate spatial partitioning technique and other improvements. Finally, the results of an extensive set of experiments with real-world datasets are presented, demonstrating that the proposed kNNJQ algorithm is efficient, scalable and robust in Sedona.

This work is dedicated to the study of an approach that allows the generation of hidden attractors based on a class of piecewise-linear (PWL) systems. The systems produced with the approach present the coexistence of self-excited attractors and hidden attractors such that hidden attractors surround the self-excited attractors. The first part of the approach consists of the generation of self-excited attractors based on pairs of equilibria with heteroclinic orbits. Then, additional equilibria are added to the system to obtain a bistable system with a second self-excited attractor with the same characteristics. It is conjectured that a necessary condition for the existence of the hidden attractor in this class of systems is the rupture of the trajectories that resemble heteroclinic orbits that join the two regions of space that surround the pairs of equilibria; these regions resemble equilibria when seen on a larger scale. With the appearance of a hidden attractor, the system presents a multistable behavior with hidden and self-excited attractors.

Real-time entity resolution (ER) is a challenging problem for large datasets. Traditional techniques of top-N join query processing are based on clean data without ER. For dirty datasets with duplicate tuples referring to the same real-world entity, these techniques may yield duplicates of top-N tuples for a query, and as a result some useful tuples may fail to be retrieved from the datasets, which leads to poor effectiveness. Based on “sorted and/or random accesses” and “no wild guesses”, in this paper, we discuss the models that integrate real-time entity resolution with top-N join queries over dirty datasets of real vectors. For finite dimensional \(\ell_{p} \) spaces and p-norm distances as nonmonotone ranking functions, using the norm equivalence theorem in Functional Analysis as a foundation, and designing buffers to join tuples with an outer-join mechanism and to cluster candidates for ER, we propose two database-friendly algorithms to answer the top-N join queries with the following two cases of data access methods: restricting sorted access and no random access. Extensive experiments are conducted to measure the effectiveness and efficiency of our approaches over various dirty datasets.

Given a record of geo-tagged activities, how can we suggest groups, or cohorts of likely companions? A brute-force approach is to perform a spatio-temporal join over past activity traces to find groups of users recorded as moving together; yet such an approach is inherently unscalable. In this paper, we propose that we can identify and predict such cohorts by leveraging information on social ties along with past geo-tagged activities, i.e., geo-social information. In particular, we find groups of users that (i) form cliques of friendships and (ii) maximize a function of common pairwise activities on record among their members. We show that finding such groups is an \(\mathbf {NP}\)-hard problem, and propose a nontrivial algorithm, COVER, which works as if it were enumerating maximal social cliques, but guides its exploration by a pruning-intensive activity driven criterion in place of a clique maximality condition. Our experimental study with real world data demonstrates that COVER outperforms a brute-force baseline in terms of efficiency and surpasses an adaptation of previous work in terms of prediction accuracy regarding groups of companions, including groups that do not appear in the training set, thanks to its use of a social clique constraint.

Given a finite group G, we denote by Δ(G) the graph whose vertices are the proper subgroups of G and in which two vertices H and K are joined by an edge if and only if G = ⟨H, K⟩. We prove that if there exists a finite nilpotent group X with Δ(G) ≅ Δ(X), then G is supersoluble.

Group pattern mining based on spatio-temporal trajectories have gained significant attentions due to the prevalence of location-acquisition devices and tracking technologies. Representative work includes convoy, swarm, travelling companion, gathering, and platoon. However, these works based on Euclidean space cannot handle group pattern discovery in non-planar space, such as urban road networks. In this paper, we propose a new group pattern, named converging, and its mining method in road networks. Unlike the aforementioned group patterns, a converging indicates that a group of moving objects converge from different directions for a certain time period. Motivated by this, we formalize the concept of a converging based on cluster containment relationship. Since the process of discovering convergings over large scale road network constrained trajectories is quite lengthy, we propose a density clustering algorithm based on road networks (DCRN) and a cluster containment join (CCJ) algorithm to improve the performance. Specifically, DCRN adopts the well-known filter-refinement-verification framework for efficiently identifying core points, which utilizes the upper bound property for \(\varepsilon \)-neighbourhood of point set on an edge to dramatically reduce the candidate core points. To process the neighbourhood queries efficiently, we further develop a vertex-neighbourhood based index, which precomputes the \(\varepsilon \)-neighbourhoods of all vertices, to facilitate neighbourhood queries of all points in road networks. In addition, to process the CCJ efficiently, we develop a signature tree based on road network partition index to organize the clusters in road networks hierarchically, which enable us to prune enormous unqualified candidates in an efficient way. Finally, extensive experiments with real and synthetic datasets show that our proposed methods achieve superior performance and good scalability.

For an ordered subset \(W = \{w_1, w_2, \ldots , w_k \}\) of vertices in a connected graph G and a vertex v of G, the metric representation of v with respect to W is the k-vector \(r(v|W) = (d(v, w_1), \ldots , d(v, w_k ))\), where \(d(v,w_i)\) is the distance of the vertices v and \(w_i\) in G. The set W is called a resolving set of G if \(r(u|W)=r(v|W)\) implies \(u=v\). A resolving set of G with minimum cardinality is called a metric basis of G. The metric dimension of G, denoted by \(\beta (G)\), is the cardinality of a metric basis of G.

The eccentric graph \({G}_{e}\) corresponding to a graph \(G\) is a derived graph with the same vertex set of \(G\) and two vertices in \({G}_{e}\) are neighbours if one of them is the eccentric vertex of the other. Motivated by the studies on derived graphs and graph operations, in this article, the eccentric graph of the join of two graphs is analysed based on the variations in the radius. The notion of eccentric join of two graphs with at least one of them having radius \(1\), is introduced. The eccentric graph of eccentric join of graphs is also examined. Finally, the concept of r-eccentric join of graphs is also introduced. This study is analytical in nature, which involves deductive and logical reasoning.

The study of graphs and networks accomplished by topological measures plays an applicable task to obtain their hidden topologies. This procedure has been greatly used in cheminformatics, bioinformatics, and biomedicine, where estimations based on graph invariants have been made available for effectively communicating with the different challenging tasks. Irregularity measures are mostly used for the characterization of the nonregular graphs. In several applications and problems in various areas of research like material engineering and chemistry, it is helpful to be well-informed about the irregularity of the underline structure. Furthermore, the irregularity indices of graphs are not only suitable for quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) studies but also for a number of chemical and physical properties, including toxicity, enthalpy of vaporization, resistance, boiling and melting points, and entropy. In this article, we compute the irregularity measures including the variance of vertex degrees, the total irregularity index, the σ irregularity index, and the Gini index of a new graph operation.

The weighted visual cryptographic scheme (WVCS) is a secret sharing technology, where weights are assigned to each shadow (participant) according to its importance. Among WVCS, the random grid-based WVCS (RGWVCS) is a frequently visited subject. It considers the premise of equality of all participants, without taking into account the existence of privileged people in reality. To address this problem of RGWVCS, this paper designs a new model, named as (k, m, n)-RGWVCS (where m < k < n ), in which the secret is encrypted into n shares and sent to k participants. In the recovery end, the secret could be reconstructed by minimum m shares when the privileged join in; otherwise, k shares are needed. The experimental results show that our method has the advantage of no pixel expansion and no codebook design by means of random grid. Moreover, the contrast of our model increased by 32.85% on average compared with that of other WVCS.

In a real-world network, overlapping structures are essential for understanding the community. In many different situations, a node may join or leave, and this defines sub-communities of varying size. In this paper, we propose a preference implication based-method for generating overlapping structures based on a local function optimization approach. We introduce some parameters in our novel method to design the communities according to a threshold. This method allows us to control the size and number of these overlapping regions. The \(\nu \) will enable us to design the sub-communities. This framework can easily detect communities in a scale-free network case. We set our experiments using artificial and real network data with a size between \({\approx }15\) to \({\approx }10000\). In our findings, we found a good relationship between \(\nu \) and overlapping nodes in communities. We control our procedure using \(\alpha \) parameter as well. We can say that the preference is stronger when \(\nu \) is greater than 0.5, and a value of \(\alpha \) between 0.20 and 0.80. The third parameter \(\delta \), which controls the intensity of community membership, defines the degree of relationship of a node to a community. The communities detected by the preference implication method obey a power law in the community size distribution.

This paper explores a model of group membership formation in which agents decide to join or not multiple social groups. The membership formation process induces a bipartite graph structure with social groups listed on one side and agents listed on the other side. Among members of multiple social groups, we consider two decisive types of agents: the grand star and the mini star. The former type is the unique agent in a society who participates in all social groups. The latter type includes agents who participate in more than one, but not all, social groups such that every social group pair has one and only one common member. We analyze the efficiency and stability conditions of group membership formation, and we establish sufficient conditions under which a connected graph that contains either a grand star or a set of mini stars becomes the unique strongly efficient and stable graph.

In 2011, Caro et al. introduced the monochromatic connection of graphs. An edge-coloring of a connected graph $G$ is called a monochromatically connecting (MC-coloring, for short) if there is a monochromatic path joining any two vertices. The monochromatic connection number $\operatorname{mc}(G)$ of a graph $G$ is the maximum integer $k$ such that there is a $k$-edge-coloring, which is an MC-coloring of $G$. Clearly, a monochromatic spanning tree can monochromatically connect any two vertices. So for a graph $G$ of order $n$ and size $m$, $\operatorname{mc}(G) \geq m-n+2$. Caro et al. proved that both triangle-free graphs and graphs of diameter at least three meet the lower bound. ¶ In this paper, we consider the monochromatic connectivity of graphs containing triangles which meet the lower bound too. Also, in order to study the graphs of diameter two, we present the formula for the monochromatic connectivity of join graphs. This will be helpful to solve the problem for graphs of diameter two.

The purpose of this paper is to study the Sasakian geometry on odd dimensional sphere bundles over a smooth projective algebraic variety $N$ with the ultimate, but probably unachievable goal of understanding the existence and non-existence of extremal and constant scalar curvature Sasaki metrics. We apply the fiber join construction of Yamazaki \cite{Yam99} for K-contact manifolds to the Sasaki case. This construction depends on the choice of $d+1$ integral K\"ahler classes $[\omega_j]$ on $N$ that are not necessarily colinear in the K\"ahler cone. We show that the colinear case is equivalent to a subclass of a different join construction orginally described in \cite{BG00a,BGO06}, applied to the spherical case by the authors in \cite{BoTo13,BoTo14a} when $d=1$, and known as cone decomposable \cite{BHLT16}. The non-colinear case gives rise to infinite families of new inequivalent cone indecomposable Sasaki contact CR on certain sphere bundles. We prove that the Sasaki cone for some of these structures contains an open set of extremal Sasaki metrics and, for certain specialized cases, the regular ray within this cone is shown to have constant scalar curvature. We also compute the cohomology groups of all such sphere bundles over a product of Riemann surfaces., Comment: 49 pages

The Zagreb indices for a graph are defined as sum of the square of the degrees of all the vertices of the graph and sum of the product of degrees of all the pair of adjacent vertices of that graph. In this study, the Zagreb indices of two recently introduced graph operations, called double join of graphs based on the total graph and double corona of graphs based on the total graph are computed in terms of different topological indices of their factor graphs and hence some application of the derived results are also discussed.

For a given variety V of algebras, we define a class relation to be a binary relation R subset of S(2)which is of the form R = S-2 boolean AND K for some congruence class K on A(2), where A is an algebra in V such that S subset of A. In this paper we study the following property of V : every reflexive class relation is an equivalence relation. In particular, we obtain equivalent characterizations of this property analogous to well-known equivalent characterizations of congruence-permutable varieties. This property determines a Mal'tsev condition on the variety and in a suitable sense, it is a join of Chajda's egg-box property as well as Duda's direct decomposability of congruence classes. South African National Research FoundationNational Research Foundation - South Africa Centre for Mathematics of the University of Coimbra - Portuguese Government through FCT/MEC [UID/MAT/00324/2019] European Regional Development Fund through the Partnership Agreement PT2020 info:eu-repo/semantics/publishedVersion

We study in s general way the construction of string bit Hamiltonians which are supersymmetric, We construct several quadratic and quartic polynomials in string bit creation and annihilation operators ϕ¯a1⋯anA, ϕa1⋯anA, which commute with the supersymmetry generators Qa. Among these operators are ones with the spinor tensor structure required to provide the lightcone worldsheet vertex insertion factors needed to give the correct interactions for the IIB superstring, whenever a closed string separates into two closed strings or two closed strings join into one.

Let $K_n$ be the set of all nonsingular $n\times n$ lower triangular $(0,1)$-matrices. Hong and Loewy (2004) introduced the numbers $$ c_n={\rm min}\{\lambda\mid \lambda~\text{is an eigenvalue of}~XX^{\rm T},~X\in K_n\},\quad n\in\mathbb{Z}_+. $$ A related family of numbers was considered by Ilmonen, Haukkanen, and Merikoski (2008): $$ C_n={\rm max}\{\lambda\mid \lambda~\text{is an eigenvalue of}~XX^{\rm T},~X\in K_n\},\quad n\in\mathbb{Z}_+. $$ These numbers can be used to bound the singular values of matrices belonging to $K_n$ and they appear, e.g., in eigenvalue bounds for power GCD matrices, lattice-theoretic meet and join matrices, and related number-theoretic matrices. In this paper, it is shown that for $n$ odd, one has the lower bound $$ c_n\geq \frac{1}{\sqrt{\frac{1}{25}\varphi^{-4n}+\frac{2}{25}\varphi^{-2n}-\frac{2}{5\sqrt{5}}n\varphi^{-2n}-\frac{23}{25}+n+\frac{2}{25}\varphi^{2n}+\frac{2}{5\sqrt{5}}n\varphi^{2n}+\frac{1}{25}\varphi^{4n}}}, $$ and for $n$ even, one has $$ c_n\geq \frac{1}{\sqrt{\frac{1}{25}\varphi^{-4n}+\frac{4}{25}\varphi^{-2n}-\frac{2}{5\sqrt{5}}n\varphi^{-2n}-\frac{2}{5}+n+\frac{4}{25}\varphi^{2n}+\frac{2}{5\sqrt{5}}n\varphi^{2n}+\frac{1}{25}\varphi^{4n}}}, $$ where $\varphi$ denotes the golden ratio. These lower bounds improve the estimates derived previously by Mattila (2015) and Altini\c{s}ik et al. (2016). The sharpness of these lower bounds is assessed numerically and it is conjectured that $c_n\sim 5\varphi^{-2n}$ as $n\to\infty$. In addition, a new closed form expression is derived for the numbers $C_n$, viz. $$ C_n=\frac14 \csc^2\bigg(\frac{\pi}{4n+2}\bigg)=\frac{4n^2}{\pi^2}+\frac{4n}{\pi^2}+\bigg(\frac{1}{12}+\frac{1}{\pi^2}\bigg)+\mathcal{O}\bigg(\frac{1}{n^2}\bigg),\quad n\in\mathbb{Z}_+. $$, Comment: 12 pages, 2 figures

It is well known that the center of mass of a tetrahedron is the intersection of the line segments that join its vertices to the centers of mass of the opposite faces, and that a similar statement holds for simplices in higher dimensions. This paper addresses the question whether this nice inductive property of the center of mass also holds for other centers. It proves that the center of mass is the only center that has this property, and investigates in detail the situation for the other well known centers, namely, the Gergonne center, the Nagel center, the Lemoine center, the incenter, the orthocenter, the Fermat-Torricelli center, and the circumcenter. Some questions for further research are raised.

We present spectroscopic and photometric monitoring of NGC 3783 conducted throughout the first half of 2020. Time delays between the continuum variations and the response of the broad optical emission lines were clearly detected, and we report reverberation measurements for H$\beta$, HeII $\lambda 4686$, H$\gamma$, and H$\delta$. From the time delay in the broad H$\beta$ emission line and the line width in the variable portion of the spectrum, we derive a black hole mass of $M_{\rm BH} = 2.34^{+0.43}_{-0.43} \times 10^7$ M$_{\odot}$. This is slightly smaller than, but consistent with, previous determinations. However, our significantly improved time sampling ($T_{\rm med}=1.7$ days compared to $T_{\rm med}=4.0$ days) has reduced the uncertainties on both the time delay and the derived mass by $\sim 50$%. We also detect clear velocity-resolved time delays across the broad H$\beta$ profile, with shorter lags in the line wings and a longer lag in the line core. Future modeling of the full velocity-resolved time delay response will further improve the reverberation-based mass for NGC 3783, adding it to the small but growing sample of AGNs for which we have direct, primary black hole mass measurements. Upcoming MUSE observations at VLT will also allow NGC 3783 to join the smaller sample of black holes where reverberation masses and masses from stellar dynamical modeling may be directly compared., Comment: Accepted for publication in ApJ; 9 pages, 2 tables and 6 figures. V2 includes minor edits after refereeing

This paper investigates the monetary regime choice between a monetary union and a flexible exchange rate regime in a large open economy framework. The classical approach argues that a monetary union should be established between countries with positively correlated shocks so that the cost of the one-size-fits-all monetary policy in a monetary union is minimized. This study suggests that this criterion is insufficient to determine optimal monetary unions. A country has a signi cant incentive to choose a monetary union over a flexible exchange rate regime if prospective or existing member countries have larger or proportional cost-push shocks relative to domestic ones. In reverse, a country has a signi cant incentive to choose a flexibleexchange rate regime if domestic cost-push shocks are relatively larger. For this reason, the relative variance of cost-push shocks between countries should be accounted for in the monetary regime choice. The classical criterion should be updated: countries with positively correlated efficient shocks and proportional cost-push shocks should form monetary unions.

These are lecture notes for a short course given at the Les Houches Summer School on ``Integrability in Atomic and Condensed Matter Physics'', in summer 2018. Here, I pedagogically discuss recent advances in the study of the entanglement spreading during the non-equilibrium dynamics of isolated integrable quantum systems. I first introduce the idea that the stationary thermodynamic entropy is the entanglement accumulated during the non-equilibrium dynamics and then join such an idea with the quasiparticle picture for the entanglement spreading to provide quantitive predictions for the time evolution of the entanglement entropy in arbitrary integrable models, regardless of the interaction strength., Comment: 33 pages, 2 figures, Lectures for Les Houches Summer School on "Integrability in Atomic and Condensed Matter Physics", summer 2018

In this paper we prove that the inductively defined graph dimension has a simple additive property under the join operation. The dimension of the join of two simple graphs is one plus the sum of the dimensions of the component graphs: $\mathrm{dim}\, (G_1+ G_2) = 1 +\mathrm{dim}\, G_1+ \mathrm{dim}\, G_2$. We use this formula to derive an expression for the inductive dimension of an arbitrary finite simple graph from its minimum edge clique cover. A corollary of the formula is that any arbitrary finite simple graph whose maximal cliques are all of order $N$ has dimension $N-1$. We finish by finding lower and upper bounds on the inductive dimension of a simple graph in terms of its clique number., Comment: arXiv admin note: substantial text overlap with arXiv:1903.02523 author note: this version was meant to be a replacement of arXiv:1903.02523, but due to submission mistake it appeared as a new submission

Tensor Core Units (TCUs) are hardware accelerators developed for deep neural networks, which efficiently support the multiplication of two dense \(\sqrt{m}\times \sqrt{m}\) matrices, where m is a given hardware parameter. In this paper, we show that TCUs can speed up similarity search problems as well. We propose algorithms for the Johnson-Lindenstrauss dimensionality reduction and for similarity join that, by leveraging TCUs, achieve a \(\varOmega (\sqrt{m})\) speedup up with respect to traditional approaches.

In the present contribution we study a viscous Cahn-Hilliard system where a further leading term in the expression for the chemical potential $ \mu$ is present. This term consists of a subdifferential operator $S$ in $L^2(\Omega)$ (where $\Omega$ is the domain where the evolution takes place) acting on the difference of the phase variable $\varphi$ and a given state $\varphi^* $, which is prescribed and may depend on space and time. We prove existence and continuous dependence results in case of both homogeneous Neumann and Dirichlet boundary conditions for the chemical potential $\mu$. Next, by assuming that $S=\rho\,$sign, a multiple of the sign operator, and for smoother data, we first show regularity results. Then, in the case of Dirichlet boundary conditions for $\mu$ and under suitable conditions on $\rho$ and $\Omega$, we also prove the sliding mode property, that is, that $\varphi$ is forced to join the evolution of $\varphi^* $ in some time $T^*$ lower than the given final time $T$. We point out that all our results hold true for a very general and possibly singular multi-well potential acting on $\varphi$., Comment: Key words: viscous Cahn-Hilliard equation, state-feedback control law, initial-boundary value problem, well-posedness, regularity, sliding mode property

The aim of decentralized gradient descent (DGD) is to minimize a sum of $n$ functions held by interconnected agents. We study the stability of DGD in open contexts where agents can join or leave the system, resulting each time in the addition or the removal of their function from the global objective. Assuming all functions are smooth, strongly convex, and their minimizers all lie in a given ball, we characterize the sensitivity of the global minimizer of the sum of these functions to the removal or addition of a new function and provide bounds in $ O\left(\min \left(\kappa^{0.5}, \kappa/n^{0.5},\kappa^{1.5}/n\right)\right)$ where $\kappa$ is the condition number. We also show that the states of all agents can be eventually bounded independently of the sequence of arrivals and departures. The magnitude of the bound scales with the importance of the interconnection, which also determines the accuracy of the final solution in the absence of arrival and departure, exposing thus a potential trade-off between accuracy and sensitivity. Our analysis relies on the formulation of DGD as gradient descent on an auxiliary function. The tightness of our results is analyzed using the PESTO Toolbox., Comment: 8 pages, 2 figures, 3 pdf files for the figures

In coalition formation games self-organized coalitions are created as a result of the strategic interactions of independent agents. For each couple of agents $(i,j)$, weight $w_{i,j}=w_{j,i}$ reflects how much agents $i$ and $j$ benefit from belonging to the same coalition. We consider the modified fractional hedonic game, that is a coalition formation game in which agents' utilities are such that the total benefit of agent $i$ belonging to a coalition (given by the sum of $w_{i,j}$ over all other agents $j$ belonging to the same coalition) is averaged over all the other members of that coalition, i.e., excluding herself. Modified fractional hedonic games constitute a class of succinctly representable hedonic games. We are interested in the scenario in which agents, individually or jointly, choose to form a new coalition or to join an existing one, until a stable outcome is reached. To this aim, we consider common stability notions, leading to strong Nash stable outcomes, Nash stable outcomes or core stable outcomes: we study their existence, complexity and performance, both in the case of general weights and in the case of 0-1 weights. In particular, we completely characterize the existence of the considered stable outcomes and show many tight or asymptotically tight results on the performance of these natural stable outcomes for modified fractional hedonic games, also highlighting the differences with respect to the model of fractional hedonic games, in which the total benefit of an agent in a coalition is averaged over all members of that coalition, i.e., including herself., Comment: A conference version of this paper has been accepted at AAMAS 2018: Gianpiero Monaco, Luca Moscardelli, and Yllka Velaj. 2018. Stable Outcomes in Modified Fractional Hedonic Games. In Proc. of the 17th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2018), Stockholm, Sweden, July 10-15, 2018, IFAAMAS, 9 pages

Let $H$ be the C*-algebra of a non-trivial compact quantum group acting freely on a unital C*-algebra $A$. It was recently conjectured that there does not exist an equivariant $*$-homomorphism from $A$ (type-I case) or $H$ (type-II case) to the equivariant noncommutative join C*-algebra $A\circledast^\delta H$. When $A$ is the C*-algebra of functions on a sphere, and $H$ is the C*-algebra of functions on ${\mathbb Z}/2{\mathbb Z}$ acting antipodally on the sphere, then the conjecture of type I becomes the celebrated Borsuk-Ulam theorem. Following recent work of Passer, we prove the conjecture of type I for compact quantum groups admitting a non-trivial torsion character. Next, we prove that, if a compact quantum group admits a representation whose \mbox{$K_1$-class} is non-trivial and $A$ admits a character, then a stronger version of the type-II conjecture holds: the finitely generated projective module associated with $A\circledast^\delta H$ via this representation is not stably free. In particular, we apply this result to the $q$-deformations of compact connected semisimple Lie groups and to the reduced group C*-algebras of free groups on $n>1$ generators.

Let G = (V, E) be a simple and undirected graph with |V| vertices and |E| edges. Consider a graph G with |E| ≥ |V|. An injective f from V to a set {0,1,2, . . . , |E|−1} such that the induced edge labeling given by f(xy) = g(x) + g(y) (mod |E| ) for any edge xy in the graph is also an injective function, is called harmonious labeling of a graph G. A harmonious graph is a graph which has a harmonious labeling. In this paper we show an existence of harmonious labeling on G+K¯2 and G × P2, where G is a harmonious unicyclic graph.

The heating of the real polar cap surface of radio pulsars by the bombardment of ultra-relativistic charges is studied. The real polar cap is a significantly smaller area within or close by the conventional polar cap which is encircled by the last open field lines of the dipolar field $\vec{B}_d$. It is surrounded by those field lines of the small scale local surface field $\vec{B}_s$ that join the last open field lines of $\vec{B}_d$ in a height of $\sim 10^5$ cm above the cap. As the ratio of radii of the conventional and real polar cap $R_{dip}/R_{pc}\sim 10$, flux conservation requires $B_s/B_d\sim 100$. For rotational periods $P\sim 0.5$ s, $B_s\sim 10^{14}$ G creates a strong electric potential gap that forms the inner accelerating region (IAR) in which charges gain kinetic energies $\sim 3\times 10^{14}$ eV. This sets an upper limit for the energy that back flowing charges can release as heat in the surface layers of the real polar cap. Within the IAR, which is flown through with a dense stream of extremely energetic charges, no stable atmosphere of hydrogen can survive. Therefore, we consider the polar cap as a solidified "naked" surface consisting of fully ionized iron ions. We discuss the physical situation at the real polar cap, calculate its surface temperatures $T_s$ as functions of $B_s$ and $P$, and compare the results with X-ray observations of radio pulsars., Comment: Published in MNRAS

Users create accounts on multiple social networks to get connected to their friends across these networks. We refer to these user accounts as user identities. Since users join multiple social networks, therefore, there will be cases where a pair of user identities across two different social networks belong to the same individual. We refer to such pairs as Cross-Network Linkages (CNLs). In this work, we model the social network as a graph to explore the question, whether we can obtain effective social network graph representation such that node embeddings of users belonging to CNLs are closer in embedding space than other nodes, using only the network information. To this end, we propose a modular and flexible node embedding framework, referred to as NeXLink, which comprises of three steps. First, we obtain local node embeddings by preserving the local structure of nodes within the same social network. Second, we learn the global node embeddings by preserving the global structure, which is present in the form of common friendship exhibited by nodes involved in CNLs across social networks. Third, we combine the local and global node embeddings, which preserve local and global structures to facilitate the detection of CNLs across social networks. We evaluate our proposed framework on an augmented (synthetically generated) dataset of 63,713 nodes & 817,090 edges and real-world dataset of 3338 Twitter-Foursquare node pairs. Our approach achieves an average Hit@1 rate of 98% for detecting CNLs across social networks and significantly outperforms previous state-of-the-art methods.

An interesting observation was made that only a few (far shorter than the prefix) low-frequency tokens are enough to help finding similarity pairs for processing top-k set joins. This phenomenon is ubiquitous in all real datasets we have experimented with, covering domains as varied as text, social network, protein sequence data. Possible explanations are discussed. Based on this observation, we propose an algorithm called AEtop-k for processing both approximate and exact top-k similarity join in a unified framework. Comprehensive experiments demonstrate that, compared with the state-of-the-art algorithm on a large collection of real-life datasets, the approximate version of our algorithm can achieve up to 10000\(\times \) speedup with little sacrifice on accuracy and the exact version runs up to 5\(\times \) faster than the existing algorithm.

We present the discovery of two new 10-day period giant planets from the Transiting Exoplanet Survey Satellite ($TESS$) mission, whose masses were precisely determined using a wide diversity of ground-based facilities. TOI-481 b and TOI-892 b have similar radii ($0.99\pm0.01$ $\rm R_{J}$ and $1.07\pm0.02$ $\rm R_{J}$, respectively), and orbital periods (10.3311 days and 10.6266 days, respectively), but significantly different masses ($1.53\pm0.03$ $\rm M_{J}$ versus $0.95\pm0.07$ $\rm M_{J}$, respectively). Both planets orbit metal-rich stars ([Fe/H]= $+0.26\pm 0.05$ dex and [Fe/H] = $+0.24 \pm 0.05$ dex, for TOI-481 and TOI-892, respectively) but at different evolutionary stages. TOI-481 is a $\rm M_{\star}$ = $1.14\pm0.02$ $\rm M_{\odot}$, $\rm R_{\star}$ = $1.66\pm0.02$ $\rm R_{\odot}$ G-type star ($T_{\rm eff}$ = $5735 \pm 72$ K), that with an age of 6.7 Gyr, is in the turn-off point of the main sequence. TOI-892, on the other hand, is a F-type dwarf star ($T_{\rm eff}$ = $6261 \pm 80$ K), which has a mass of $\rm M_{\star}$ = $1.28\pm0.03$ $\rm M_{\odot}$, and a radius of $\rm R_{\star}$ = $1.39\pm0.02$ $\rm R_{\odot}$. TOI-481 b and TOI-892 b join the scarcely populated region of transiting gas giants with orbital periods longer than 10 days, which is important to constrain theories of the formation and structure of hot Jupiters., Comment: 19 pages, 10 figures, accepted for publication in AJ

Accepted paper for the CRYPTO 2020 conference [Abstract]We introduceDynamic Decentralized Functional Encryption (DDFE), a generalization ofFunctional Encryptionwhich allows multiple users to join the system dynamically, without relying on a trusted third party or on expensive and interactiveMulti-Party Computation protocols. This notion subsumes existingmulti-user extensions of Functional Encryption, such asMulti-Input,Multi-Client, and Ad Hoc Multi-Input Functional Encryption. We define and construct schemes for various functionalities which serve as building-blocks for latter primitives and may be useful in their own right, such as a scheme for dynamically computing sums in any Abelian group. These constructions build upon simple primitives in a modular way, and have instantiations from well-studied assumptions, such as DDH or LWE. Our constructions culminate in anInner-Product schemefor computing weighted sums on aggregated encrypted data, from standard assumptions in prime-order groups in theRandom Oracle Model.

We study Hawaiian groups of the infinite dimensional Hawaiian earring which is the weak join of all finite dimensional Hawaiian earrings. We show that the structure of the 1st Hawaiian groups of the infinite dimensional Hawaiian earring and the one dimensional Hawaiian earring are isomorphic. Also, for n ≥ 2 , we prove that the nth Hawaiian group of the infinite dimensional Hawaiian earring is isomorphic to the direct product of direct sum of a family consisting of quotient of nth homotopy groups of consecutive retractions.

Intuitionistic fuzzy sets represent a generalization of the concept of fuzzy sets and has many applications to different fields of science. This paper applies the concept of intuitionistic fuzzy sets to genetics. More precisely, we consider some examples of hypergroupoids associated to biological inheritance, construct sequences of join spaces and find their intuitionistic fuzzy grades.

This paper examines tensor products of complete lattices in which one factor is completely distributive. At least five characterizations of complete distributivity involving tensor products of complete lattices are given, among them this one: M is a completely distributive lattice if and only if for every complete lattice L the tensor product $$M\otimes L$$ is order isomorphic to the partially ordered set of all join- and meet-reversing maps from the complete lattice of all upclosed subsets of L to the lattice M. Some of these characterizations are then applied to give explicit descriptions of the multiplication of the tensor product of two quantales one of which is completely distributive.

Two new borates, NaK1.5[B{B5O9(OH)}{B5O8(OH)2}1/2] (1) and Na3.5[Al{B3O6(OH)}{B5O10}1/2{BO(OH)}] (2), have been made by a solvothermal method. Structure 1 is made of two types of oxoboron clusters ([B5O9(OH)]4- and [B5O8(OH)2]3-) and BO4 tetrahedra to form a 3D porous layer, in which the [B5O9(OH)]4- clusters are bridged by BO4 groups to produce a 2D B-O layer with 11-membered ring (MR) windows, while the [B5O8(OH)2]3- clusters as 2-connected pillars join the adjacent B-O layers to make a 3-D porous layer. Structure 2 is built from two types of oxoboron clusters ([B3O6(OH)]4- and [B5O12]9-), AlO4 units and BO2(OH) triangles to produce 3D pillar-layered aluminoborate (ABO), in which the [B5O12]9- clusters are linked together to form a 2-D B-O layer; the [B3O6(OH)]4- clusters and AlO4 groups join each other to form 1D tubular ABO; and the BO2(OH) triangles act as linkers to connect the adjacent B-O layer and the ABO tubes, resulting in 3D pillar-layered ABO. Interestingly, the ABO tubes decorated with the BO2(OH) triangles act as pillars to make a 3D layer-pillared structure. UV-vis diffuse spectra indicate that both have cut-off edges below 190 nm, and the calculated band gaps are 5.75 and 5.78 eV, respectively.

Young diagrams can be parameterized with the help of hook variables, which is well known but never studied in big detail. We demonstrate that this is the most adequate parameterization for many physical applications: from the Schur functions, conventional, skew and shifted, which all satisfy their own kinds of determinant formulas in these coordinates, to KP/Toda integrability and related basis of cut-and-join $\hat W$-operators, which are both actually expressed through the single-hook diagrams. In particular, we discuss a new type of multi-component KP $\tau$-functions, Matisse $\tau$-functions. We also demonstrate that the Casimir operators, which are responsible for integrability, are single-hook, with the popular basis of "completed cycles" being distinguished by especially simple coefficients in the corresponding expansion. The Casimir operators also generate the $q=t$ Ruijsenaars Hamiltonians. However, these properties are broken by the naive Macdonald deformation, which is the reason for the loss of KP/Toda integrability and related structures in $q$-$t$ matrix models., Comment: 15 pages

Randall and others [2] used the intrinsic join product to express the index of a k-field with finite singularities on the total space of a smooth fiber bundle F ↪ M ⟶ B , for 1 k ≤ 4 . The k-field with finite singularities on the total space M arises from k-fields with finite singularities given on the fiber F and on the base B. The index of the k-field on M is the join product of indices of the k-fields with finite singularities defined on F and on B. In this work we extend the results of [2] for the cases where k = 5 and 6. We present tables for the join product of generators of π m − 1 ( V m , k ) for k = 5 and 6, where V m , k denotes the real Stiefel manifold of k-frames in R m . The index of a k-field with finite singularities on a smooth, closed, oriented manifold, for k = 5 and 6, is given precisely in terms of the characteristic numbers of the manifold as coefficients of the generators of π m − 1 ( V m , k ) .

A graph is well-covered if all its maximal independent sets are of the same size (Plummer, 1970). A graph G belongs to class Wn if every n pairwise disjoint independent sets in G are included in n pairwise disjoint maximum independent sets (Staples, 1975). Clearly, W1 is the family of all well-covered graphs. Staples showed a number of ways to build graphs in Wn, using graphs from Wn or Wn+1. In this paper, we construct some more infinite subfamilies of the class W2 by means of corona, join, and rooted product of graphs.

The purpose of this study is to investigate an M/M/R retrial queue with geometric loss and Bernoulli feedback, in which all servers are subject to breakdowns and starting failures. After the completion of service, unsatisfied customers can join the retrial group with probability p or depart from the system with probability 1 − p. All servers may breakdown at any time, and the failed server undergoes repair immediately when a breakdown occurs. An arriving customer finding all servers unavailable (busy or down), will either join the orbit with probability b or leave the system with probability 1 − b. For such a queuing model, the authors apply the matrix-geometric method to compute the stationary probabilities and develop system performance measures in the steady state. Moreover, they construct a cost model and formulate an optimisation problem of minimising the expected cost per unit time. Finally, numerical results are given for illustrative purposes.

We consider the Type 1 and Type 2 noncommutative Borsuk-Ulam conjectures of Baum, D$\k{a}$browski, and Hajac: there are no equivariant morphisms $A \to A \circledast_\delta H$ or $H \to A \circledast_\delta H$, respectively, when $H$ is a nontrivial compact quantum group acting freely on a unital $C^*$-algebra $A$. Here $A \circledast_\delta H$ denotes the equivariant noncommutative join of $A$ and $H$; this join procedure is a modification of the topological join that allows a free action of $H$ on $A$ to produce a free action of $H$ on $A \circledast_\delta H$. For the classical case $H = \mathcal{C}(G)$, $G$ a compact group, we present a reduction of the Type 1 conjecture and counterexamples to the Type 2 conjecture. We also present some examples and conditions under which the Type 2 conjecture does hold., Comment: 15 pages. Version 4 has an expanded commentary in section 3, including the equivalence of a topological conjecture with a certain noncommutative generalization. To appear in Proceedings of the American Mathematical Society

We study computably enumerable equivalence relations (or, ceers), under computable reducibility ≤, and the halting jump operation on ceers. We show that every jump is uniform join-irreducible, and thus join-irreducible. Therefore, the uniform join of two incomparable ceers is not equivalent to any jump. On the other hand there exist ceers that are not equivalent to jumps, but are uniform join-irreducible: in fact above any non-universal ceer there is a ceer which is not equivalent to a jump, and is uniform join-irreducible. We also study transfinite iterations of the jump operation. If a is an ordinal notation, and E is a ceer, then let E ( a ) denote the ceer obtained by transfinitely iterating the jump on E along the path of ordinal notations up to a. In contrast with what happens for the Turing jump and Turing reducibility, where if a set X is an upper bound for the A-arithmetical sets then X ( 2 ) computes A ( ω ) , we show that there is a ceer R such that R ≥ Id ( n ) , for every finite ordinal n, but, for all k, R ( k ) ≱ Id ( ω ) (here Id is the identity equivalence relation). We show that if a , b are notations of the same ordinal less than ω 2 , then E ( a ) ≡ E ( b ) , but there are notations a , b of ω 2 such that Id ( a ) and Id ( b ) are incomparable. Moreover, there is no non-universal ceer which is an upper bound for all the ceers of the form Id ( a ) where a is a notation for ω 2 .

The class CR of completely regular semigroups considered as algebras with binary multiplication and unary operation of inversion forms a variety. Kernel, trace, local and core relations, denoted by K, T, L and C, respectively, are quite useful in studying the structure of the lattice L(CR) of subvarieties of CR. They are equivalence relations whose classes are intervals. Their ends are used for defining operators on L(CR). Starting with a few band varieties, we repeatedly apply operators induced by upper ends of classes of these relations and characterize corresponding classes up to certain variety low in the lattice L(CR). We consider only varieties whose origin are “central” band varieties, that is those in the middle column of the lattice L(B) of band varieties. Several diagrams represent the (semi)lattices studied.

The adjacent-eccentric distance sum and the eccentric-adjacency index are two newly defined degree-distance based topological descriptors. In this paper, we compute these topological descriptors of the join and corona products of graphs.