A categorial approach to reaction systems: First steps

Recently, deep learning has been successfully applied to the problem of hashing, yielding remarkable performance compared to traditional methods with hand-crafted features. However, most of existing deep hashing methods are designed for the supervised scenario and require a large number of labeled data. In this paper, we propose a novel semi-supervised hashing method for image retrieval, named Deep Hashing with a Bipartite Graph (DHBG), to simultaneously learn embeddings, features and hash codes. More specifically, we construct a bipartite graph to discover the underlying structure of data, based on which an embedding is generated for each instance. Then, we feed raw pixels as well as embeddings to a deep neural network, and concatenate the resulting features to determine the hash code. Compared to existing methods, DHBG is a universal framework that is able to utilize various types of graphs and losses. Furthermore, we propose an inductive variant of DHBG to support out-of-sample extensions. Experimental results on real datasets show that our DHBG outperforms state-of-the-art hashing methods.

The growing need to address privacy concerns when social network data is released for mining purposes has recently led to considerable interest in various techniques for graph anonymization. In this paper, we study the following problem: Given a social network modeled as an edge-labeled graph G, we aim to make a pre-specifled subset of vertices of G k-label sequence anonymous with the minimum number of edge additions. Here, the label sequence of a vertex is the sequence of labels of edges incident to it. The contributions of this paper are two fold: We provide a framework to show hardness results for different variants of social network anonymization using a common approach. We start by showing that k-label sequence anonymity of arbitrary labeled graphs is hard, and use this result to prove NP-hardness results for many other recently proposed notions of graph anonymization. Secondly, we present interesting algorithms and hardness for bipartite graphs. For unlabeled bipartite graphs, we show k-degree anonymity is in P for all k ≥ 2. For labeled bipartite graphs, we show that k-label sequence anonymity is in P for k = 2 but it is NP-hard for k ≥ 3.

Modeling and exploring high-order connectivity patterns, also called network motifs, are essential for understanding the fundamental structures that control and mediate the behavior of many complex systems. For example, in social networks, triangles have been proven to play the fundamental role in understanding social network communities; in online transaction networks, detecting directed looped transactions helps identify money laundering activities; in personally identifiable information networks, the star-shaped structures may correspond to a set of synthetic identities. Despite the ubiquity of such high-order structures, many existing graph clustering methods are either not designed for the high-order connectivity patterns, or suffer from the prohibitive computational cost when modeling high-order structures in the large-scale networks. This article generalizes the challenges in multiple dimensions. First ( Model ), we introduce the notion of high-order conductance, and define the high-order diffusion core, which is based on a high-order random walk induced by the user-specified high-order network structure. Second ( Algorithm ), we propose a novel high-order structure-preserving graph clustering framework named HOSGRAP , which partitions the graph into structure-rich clusters in polylogarithmic time with respect to the number of edges in the graph. Third ( Generalization ), we generalize our proposed algorithm to solve the real-world problems on various types of graphs, such as signed graphs, bipartite graphs, and multi-partite graphs. Experimental results on both synthetic and real graphs demonstrate the effectiveness and efficiency of the proposed algorithms.

Klein cordial trees and odd cyclic cordial friendship graphs

Random generation and enumeration of bipartite permutation graphs

Algebraic structures including multiple rank tensors, linear and non-linear operators are related to and represented with various types of graphs. Special emphasis is placed on linear operators e.g. on the Hibert space. A different graph represents the same operator depending on the basis frame used, in general non-orthonormal. All such graphs are shown to belong in one equivalence class and are termed “structurally covariant”. Crucial indices related to eigenvalues but invariant under any basis frame changes including non-orthonormal ones provide one way to characterize each class. A set of rules are given that allow one to find the graphs structurally covarinat with a given one and/or to deduce the class indices directly by simple pictorial manipulations on a graph. Applications in various fields including the quantum theory of molecules and reactions are indicated.

Although classical homogeneous Fenton reaction systems (FeII + H2O2) are widely used for organic pollutant degradation, this technology has important shortcomings such as waste generation and difficult Fe2+ recycling. These shortcomings originate secondary pollution issues and make it difficult to control the reactions. Polyoxometalates (POMs) are characterized by bearing large electron‐donating conjugate systems able to stabilize Fe2+. To explore a new kind of heterogeneous Fenton reagent, we prepared a new‐type of stable heterogeneous Fenton reagent, (H3O)3.5(H3DETA)3.5{FeII[H4MoV6O15(PO4)4]2} (DETA = diethylenetriamine) (1) by inserting FeII into the POMs. The sandwich‐type 1 was excited by ultraviolet (UV) light, showed high efficiency as a solid‐phase Fenton catalyst, and can be potentially recycled to control the reactions. The coordinating reaction mechanisms for the catalytic degradation of methyl orange (MO) over the 1 + H2O2 reaction system was studied, including photocatalysis and Fenton oxidation effects. As a contrast, another new phosphomolybdate, (H3DETA)4{ZnII[H5MoV6O15(PO4)4]2}·7.5H2O (2), which has the same sandwich‐type polyanion but ZnII acting as the sandwich‐atom, has also been synthesized, characterized. The comparative study of photocatalytically degrading MO has also been carried out. In addition, by studying the thermal decomposition behavior of 1, we revealed, for the first time, the presence of Mo4P3 as a decomposition residue of 1.

Connected bipartite permutation graphs without vertex labels are investigated. First, the number of connected bipartite permutation graphs of n vertices is given. Based on the number, a simple algorithm that generates a connected bipartite permutation graph uniformly at random up to isomorphism is presented. Finally an enumeration algorithm of connected bipartite permutation graphs is proposed. The algorithm is based on the reverse search, and it outputs each connected bipartite permutation graph in \(\mbox{\cal O}(1)\) time.

Fine-Grained Parallel and Distributed Spatial Stochastic Simulation of Biological Reactions

Assigning an integer to a vertices or edges is called a vertex or edge labeling respectively. Suppose G is a simple graph. Consider the function f for the edge set . For each vertex t , define f(t)= (mod2). The function f is known as an E-cordial labeling (E-CL) of G if , and where , and , are the number of edges and vertices labeled with 0 and labeled by 1 respectively. A graph that admits E-CL is said to be E-cordial graphs (E-CG). Based on the above definition we propose a novel labeling known as SP Mean E-cordial labeling (E-CL). In this paper, we study SP Mean E-CL of several families of graphs such as complete bipartite graphs, complete graphs, wheels, etc.

The combination of algebraic structures and graphs was carried out by investigating thoroughly the relation among the algebraic structure and the graph theoretic properties. Moreover, it needs to explore algebraic structure. The results of the combination of algebraic structures and graphs have many applications in the fields of Internet modeling, coding, etc. For example, the famous Cayley graph was constructed from groups and widely used in network models. Das introduced the subspace inclusion graph on finite-dimensional vector space over a finite filed, and studied that the graph is bipartite and some special properties if the dimension of the vector space is 3. In this paper, this bipartite inclusion graph in the case of 3-dimensional is extended to more general dimensional bipartite inclusion graph. The diameter, girth, clique number, covering number, independence number and matching number are studied and the properties are shown, such as regular, planar and Eulerian. Moreover, the authors also introduce a new results about the structure and the number of 1-dimensional and n-1-dimensional subspaces on n-dimensional vector space.

We introduce a new type of model framework which is part stochastic and part deterministic. The starting point is a finite size particle system within a single reaction volume, with type exchanges modelled by a contact process. Inside the reaction volume, each particle can interact with every other particle with the same probability. This is the setting of a classical reaction system simulated with a Gillespie algorithm. Such systems can be used to describe other than chemistry type exchanges, like an infection process, and therefore are already very versatile. Their advantage is that they are able to be used where small size effects can play a role, like extinction events, which are impossible to model with differential equations, including stochastic differential equations. However finite size and single reaction volume settings for reaction systems are too restrictive in other ways. We might like to add internal or external states to the particles. These states are coordinates in a position space. An example of an internal position/state space is age (since entering the system), an example for an external position/state space is geographical location. The particles then can also change their positions in these state spaces, according to some probability distribution which evolution is modelled deterministically. The classical example for a transport process is a partial differential equation like the heat equation, or more general parabolic advection-diffusion equations. We assume that the distribution of the particles in position space is not influencing the evolution of the probability distribution driving in turn the evolution of the particles’ positions. The model framework with its finite-size particle population approach can very accurately model situations where finite-size effects take place, however provides in addition detailed descriptions of both internal and external particle state spaces where needed. The framework can therefore be used in addition to traditional established models, like transport PDEs or internally structured population models, when the computation of the statistics of finite-size effects is important.

Suppose that an n-vertex graph has a distinct labeling with the integers {1, . . . ,n}. Such a graph is radial level planar if it admits a crossings-free drawing under two constraints. First, each vertex lies on a concentric circle such that the radius of the circle equals the label of the vertex. Second, each edge is drawn with a radially monotone curve. We characterize the set of unlabeled radial level planar(URLP) graphs that are radial level planar in terms of 7 and 15 forbidden subdivisions depending on whether the graph is disconnected or connected, respectively. We also provide linear-time drawing algorithms for any URLP graph.

Total edge irregularity strength of complete graphs and complete bipartite graphs

Consider a collection of particles of various types, and a set of reactions that are allowed to take place among these particles. Each reaction is defined by an input linear combination of particle types, and an output linear combination of particle types. This framework (which is a Petri net) is shown to model the cost of updating several standard data structures, the amortized cost of counting in various number systems and the space consumption of persistent data structures. A proof that the system of reactions is guaranteed to terminate gives a bound on the cost of the corresponding data structure problem. I show how linear programming can be used to analyze these systems.