Equivalent Graph Research Articles

Impact of targeted attack on the spontaneous activity in spatial and biologically-inspired neuronal networks.

We study the structural and dynamical consequences of damage in spatial neuronal networks. Inspired by real in vitro networks, we construct directed networks embedded in a two-dimensional space and follow biological rules for designing the wiring of the system. As a result, synthetic cultures display strong metric correlations similar to those observed in real experiments. In its turn, neuronal dynamics is incorporated through the Izhikevich model adopting the parameters derived from observation in real cultures. We consider two scenarios for damage, targeted attacks on those neurons with the highest out-degree and random failures. By analyzing the evolution of both the giant connected component and the dynamical patterns of the neurons as nodes are removed, we observe that network activity halts for a removal of 50% of the nodes in targeted attacks, much lower than the 70% node removal required in the case of random failures. Notably, the decrease of neuronal activity is not gradual. Both damage scenarios portray "boosts" of activity just before full silencing that are not present in equivalent random (Erdös-Rényi) graphs. These boosts correspond to small, spatially compact subnetworks that are able to maintain high levels of activity. Since these subnetworks are absent in the equivalent random graphs, we hypothesize that metric correlations facilitate the existence of local circuits sufficiently integrated to maintain activity, shaping an intrinsic mechanism for resilience.

Multiphysics Tensorial Network Analysis Applied to PCB Interconnect Fatigue Under Thermal Cycle Aggression

This paper investigates an original multiphysics KB modeling of the electrothermomechanical (ETM) phenomena in a multi-layer printed circuit board (PCB) under heat cycle aggression. The coupled thermal and intrinsic mechanical interactions with the PCB electrical response are analyzed. The via-interconnect line (IL) junction fatigue caused by the mechanical tensions is explained with tensorial equations. The ETM effects transduced between the PCB components are modeled with equivalent graphs. The multiphysics problem general tensorial relation is formulated. To validate the Kron–Branin model, the numerical application of three-layer PCB proof-of-concept under thermal cycle aggression with 0-to-70 °C variation is introduced. The tensile stresses induced by the thermal effect on the vias and ILs are calculated. The via cracking fatigue model is approximated. The PCB voltage transfer function and input impedance in the function of the thermal aggression are discussed.

Fast S-Parameter TAN Model of n-Port Lumped Structures

This paper deals with the fast S-parameter modeling of multi-port lumped structures. The developed model is based on unfamiliar formalism using the tensorial analysis of networks (TAN). The modeling methodology is described with the general abstract topology and different application cases. The methodology consists, first, in elaborating the equivalent graph topology of the considered problem. Then, it is followed by the TAN mathematical abstraction, including, successively, the branch and mesh space analyses. The problem metric can be written with the tensorial Ohm's law expressed in function of the covariant voltage, contravariant current, and the twice covariant impedance in the mesh spaces. The equivalent Z-matrix of the considered multi-port structure is established from an innovative reduction method of the mesh impedance. The S-parameter model is extracted from the Z-to-S matrix transform. The effectiveness of the established fast S-parameter TAN modeling is validated with three cases of proof of concept constituted by TT-cell, the TTT-cell two-port circuit, and four-port structure inspired from the 3D coaxial shielded cable. As expected, an excellent agreement between the S-parameters calculated from the TAN model and simulated from the commercial tools from DC to some hundred's megahertz is obtained. In the future, the developed model is outstandingly beneficial for fast and accurate applications notably for the conduced shielded cable electromagnetic compatibility analysis.

Short certificates for chromatic equivalence

The chromatic polynomial gives the number of proper colourings of a graph in terms of the number of available colours. In general, calculating chromatic polynomials is #P-hard. Two graphs are chromatically equivalent if they have the same chromatic polynomial. At present, determining if two graphs are chromatically equivalent involves computation and comparison of their chromatic polynomials, or similar computational effort. In this paper we investigate a new approach, certificates of chromatic equivalence, first proposed by Morgan and Farr. These give proofs of chromatic equivalence, without directly computing the polynomials. The lengths of these proofs may provide insight into the computational complexity of chromatic equivalence and related problems including chromatic factorisation and chromatic uniqueness. For example, if the lengths of shortest certificates of chromatic equivalence are bounded above by a polynomial in the size of the graphs, then chromatic equivalence belongs to NP. After establishing some links of this type between certificate length and computational complexity, we give some theoretical and computational results on certificate length. We prove that, if the number of different chromatic polynomials falls well short of the number of different graphs, then for all sufficiently large $n$ there are pairs of chromatically equivalent graphs on $n$ vertices with certificate of chromatic equivalence of length $\Omega(n^2/\log n)$. We give a linear upper bound on shortest certificate length for trees. We designed and implemented a program for finding short certificates of equivalence using a minimal set of certificate steps. This program was used to find the shortest certificates of equivalence for all pairs of chromatically equivalent graphs of order $n\leq 7$.

Designing a system to extract and interpret timed causal sentences in medical reports

ABSTRACTCausal sentences are a main part of the medical explanations, providing the causes of diseases or showing the effects of medical treatments. In medicine, causal association is frequently related to time restrictions. So, some drugs must be taken before or after meals, being ‘after’ and ‘before’ temporary constraints. Thus, we conjecture that medical papers include a lot of time causal sentences. Causality involves a transfer of qualities from the cause to the effect, denoted by a directed arrow. An arrow connecting the node cause with the node effect is a causal graph. Causal graphs are an imagery way to show the causal dependencies that a sentence shows using plain text. In this article, we provide several programs to extract time causal sentences from medical Internet resources and to convert the obtained sentences in their equivalent causal graphs, providing an enlightening image of the relations that a text describes, showing the cause-effect links and the temporary constraints affecting their interpretation.

Local equivalence of complete bipartite and repeater graph states

Classifying locally equivalent graph states, and stabilizer states more broadly, is a significant problem in the theories of quantum information and multipartite entanglement. A special focus is given to those graph states for which equivalence through local unitaries implies equivalence through local Clifford unitaries (LU $\Leftrightarrow$ LC). Identification of locally equivalent states in this class is facilitated by a convenient transformation rule on the underlying graphs and an efficient algorithm. Here we investigate the question of local equivalence of the graph states behind the all-photonic quantum repeater. We show that complete bipartite graph (biclique) states, imperfect repeater graph states and small "crazy graph" states satisfy LU $\Leftrightarrow$ LC. We continue by discussing biclique states more generally and placing them in the context of counterexamples to the LU-LC Conjecture. To this end, we offer some alternative proofs and clarifications on existing results.

Elementary matrix equivalence and core transformation graphs for Parikh matrices

The introduction of the Parikh matrix mapping by Mateescu et al. in 2001 gave rise to the injectivity problem, that is, the characterization of words having the same Parikh matrix. Certain elementary rewriting rules have been successful in solving this problem for the binary alphabet, yet they do not suffice for the general case. This paper studies these elementary rewriting rules exclusively for the ternary alphabet. Certain labeled graphs, termed as core transformation graphs, are introduced and used to study the structural changes in ternary words upon applications of these elementary rewriting rules. For an arbitrary core transformation graph, all possibilities of the labels on its edges are exhausted and, for each label, the pairs of vertices forming the corresponding edges are characterized. Finally, we obtain results relating core transformation graphs to elementarily matrix equivalent words.

Computer aided compound identification based on a highly selective topological index

As the number of natural and synthesized compounds quickly increases, the management of compounds in large databases is becoming a challenging work. Especially for a compound that can be represented by several different graphs such as benzene can be drawn in single and double bonds, or aromatic bonds. These different graphs are the same for the chemists and are called equivalent chemical graphs or equivalent chemical structures herein (H atoms are found at more than one locations are not called equivalent chemical structures such as enol form and keto form). Researchers mostly hope that each group of equivalent chemical structures (represented by different graphs) could be denoted by the same value, and make them easy to be deal with. For this goal a highly discriminating index ATID (adjacent topology identification), which was derived from a graph theoretical index – 3-EAID, was suggested. In order to reduce the chance that the different compounds were mistaken for duplicate compounds, the uniqueness test of ATID was performed by over 60 million alkanes and over 19 million benzenoids with high similarity, and the results indicate that ATID possesses high discriminating ability. Finally, the ATID was successfully applied to retrieval of duplicate compounds in large databases. The results indicate that the ATID could be a valuable tool for chemical information administration. The ATID can give comparable results with InChI (International Chemical Identifier) dependent on atom number and derived from complicated rules.

Adaptive consensus of multi-agent systems under quantized measurements via the edge Laplacian

This paper investigates consensus problems for a first-order nonlinear multi-agent system with unknown non-identical parameters when quantized measurements are available. We explore the utility of edge Laplacian for designing adaptive consensus protocol with quantized state information. A tree structure plays an important role in designing adaptive control with quantized information. Then, all agents achieve consensus mainly based on tree edges information. The proposed protocol has the advantage of using an equivalent simpler graph to avoid the redundant edge information in the cycle structure of the graph. Furthermore, when the multi-agent systems have unknown identical control directions, a Nussbaum-type item is used in the protocol for each agent to seek control direction adaptively and cooperatively. Finally, simulation examples are given to illustrate the effectiveness of the proposed method in this article.

Computationally Efficient Nonlinear Bell Inequalities for Quantum Networks.

The correlations in quantum networks have attracted strong interest with new types of violations of the locality. The standard Bell inequalities cannot characterize the multipartite correlations that are generated by multiple sources. The main problem is that no computationally efficient method is available for constructing useful Bell inequalities for general quantum networks. In this work, we show a significant improvement by presenting new, explicit Bell-type inequalities for general networks including cyclic networks. These nonlinear inequalities are related to the matching problem of an equivalent unweighted bipartite graph that allows constructing a polynomial-time algorithm. For the quantum resources consisting of bipartite entangled pure states and generalized Greenberger-Horne-Zeilinger (GHZ) states, we prove the generic nonmultilocality of quantum networks with multiple independent observers using new Bell inequalities. The violations are maximal with respect to the presented Tsirelson's bound for Einstein-Podolsky-Rosen states and GHZ states. Moreover, these violations hold for Werner states or some general noisy states. Our results suggest that the presented Bell inequalities can be used to characterize experimental quantum networks.

A graphical equivalent to mandated nutrition information tables

PurposeThe purpose of this paper is to explore understanding of a graphic equivalent to mandatory nutrition information tables.Design/methodology/approachThe horizontal bar graphic’s single number shows the per cent content of the dominant nutrient, marked “Most”, contrasting with “Least” at the origin. A separate bar for energy is expressed as percentage of 3,700 kJ, the energy in 100 g of fat. Six randomised table and equivalent graph images were shown to subjects who answered questions about the foods’ energy, dominant nutrient and per cent content, and relative abundance of seven mandated nutrients. One trial tested 40 food science students, another 100 online Australasian consumers. Scores were compared by the χ2 test. Liking of the two formats was compared by t-test.FindingsCorrect online consumer responses were: energy – 18 per cent (tables), 71 per cent (graphics); dominant nutrient – 81, 96 per cent; per cent dominant nutrient – 43, 82 per cent. All differences were highly significant. Relative abundance questions created a 7 nutrient × 6 food matrix (42 combinations) where tables were more accurately understood 14 times (3 significant) and graphics 28 times (12 significant). Responses in the student trial paralleled the consumer trial; differences were less marked but with similar statistical significances. Consumers liked the graphic more.Practical implicationsThe graphic format was more understandable than the table format, and would be useful in internet-based applications.Originality/valueThe graphic format represents a huge advance in understanding of mandatory nutrient information.

Asymptotic Analysis and Spatial Coupling of Counter Braids

A counter braid (CB) is a novel counter architecture introduced by Lu et al. in 2007 for per-flow measurements on high-speed links which can be decoded with low complexity using message passing (MP). CBs achieve an asymptotic compression rate (under optimal decoding) that matches the entropy lower bound of the flow size distribution. In this paper, we apply the concept of spatial coupling to CBs to improve the performance of the original CBs and analyze the performance of the resulting spatially-coupled CBs (SC-CBs). We introduce an equivalent bipartite graph representation of CBs with identical iteration-by-iteration finite-length and asymptotic performance. Based on this equivalent representation, we then analyze the asymptotic performance of single-layer CBs and SC-CBs under the MP decoding algorithm proposed by Lu et al. . In particular, we derive the potential threshold of the uncoupled system and show that it is equal to the area threshold. We also derive the Maxwell decoder for CBs and prove that the potential threshold is an upper bound on the Maxwell decoding threshold, which, in turn, is a lower bound on the maximum a posteriori (MAP) decoding threshold. We then show that the area under the extended MP extrinsic information transfer curve (defined for the equivalent graph), computed for the expected residual CB graph when a peeling decoder equivalent to the MP decoder stops, is equal to zero precisely at the area threshold. This, combined with the analysis of the Maxwell decoder and simulation results, leads us to the conjecture that the potential threshold is, in fact, equal to the Maxwell decoding threshold and hence a lower bound on the MAP decoding threshold. Interestingly, SC-CBs do not show the well-known phenomenon of threshold saturation of the MP decoding threshold to the potential threshold characteristic of spatially-coupled low-density parity-check codes and other coupled systems. However, SC-CBs yield better MP decoding thresholds than their uncoupled counterparts. Finally, we also consider SC-CBs as a compressed sensing scheme and show that low undersampling factors can be achieved.

Calculating Competitive Intransitivity: Computational Challenges.

Intransitive (or "rock-paper-scissors") competition is compelling because it promotes species coexistence and because recent work suggests that it may be common in natural systems. One class of intransitivity indices works by considering s, the minimum number of competitive reversals to convert a given competitive community (i.e., a "tournament") to a hierarchy. The most straightforward example of such "reversal-based" indices is Petraitis's index, [Formula: see text], where M is the maximum s across all possible n-species tournaments. Using exhaustive searches, we prove that Petraitis's formula for M (and, therefore, t) does not hold for [Formula: see text]. Furthermore, determination of s for even moderate values of n may prove difficult, as the equivalent graph theoretical problem is NP (nondeterministic polynomial time) hard; there is no known computationally feasible way to compute an exact answer for anything but small values of n, let alone a closed-form solution. Petraitis's t is a valuable index of intransitivity; however, at present its use is limited to relatively species-poor systems. More broadly, reversal-based indices, while intuitive, may be problematic because of this computability issue.

Direct Time-Domain TAN Model of 3D Multilayer Hybrid PCB: Experimental Validation

The multilayer technology constitutes the ultimate solution for the design of high-density printed circuit board (PCB). Challenging modeling method is required to predict the signal integrity (SI) of the multilayer PCB. This paper addresses an unfamiliar direct time-domain model of a 3-D multilayer hybrid PCB. The subnetwork primitive elements of the equivalent graph are constituted by lumped components, interconnect lines, vias, pads, and anti-pads. The tensorial analysis of networks (TANs) is used to solve the problem related to the graph topology in the function of the PCB design parameters. The TAN concept is based on the interaction between the primitive elements. The mesh currents constitute the proposed computational unknowns. The unfamiliar model is validated with a three-port network prototype constituted by the six-layer PCB, including passive SMD components. In the frequency domain, S-parameter validation from 100 kHz to 5 GHz is presented. By using 80-Mb/s and 0.5-Gb/s rate data patterns, the proposed TAN model is validated by both simulations and measurements in the time domain. The transient results present vector magnitude relative error accuracy lower than 15%. Thanks to the computation speed and adaptability to multilayer hybrid structures, the TAN model is a prominent approach for the SI and power integrity analyses of 3-D multilayer structures.

Enumeration of spanning trees in the sequence of Dürer graphs

Abstract In this paper, we calculate the number of spanning trees in the sequence of Dürer graphs with a special feature that it has two alternate states. Using the electrically equivalent transformations, we obtain the weights of corresponding equivalent graphs and further derive relationships for spanning trees between the Dürer graphs and transformed graphs. By algebraic calculations, we obtain a closed-form formula for the number of spanning trees with regard to iteration step. Finally we compare the entropy of our graph with other studied graphs and see that its value of entropy lies in the interval of those of graphs with average degree being 3 and 4.

Graph-based representation of design properties in creating building floorplans

This paper proposes a framework for supporting the design process by defining design requirements over graph-based representations of designs. First, hierarchical layout hypergraphs (HL-graphs) representing designs and hierarchical layout graph grammars generating them are specified. Then, local and global graph requirements over HL-graphs, which correspond to design constraints, are defined. The proposed ontological interpretations transform first-order and monadic second-order logic formulas expressing design criteria into equivalent local and global graph requirements. The satisfiability of graph requirements by representations of designs allows for checking correctness of design solutions. The approach is illustrated on examples of designing floor layouts of buildings.

Logical and inequality implications for reducing the size and difficulty of quadratic unconstrained binary optimization problems

The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to transform the graph representing the QUBO problem into a smaller equivalent graph is important for improving solution quality and time for both exact and metaheuristic algorithms and is a step towards mapping large scale QUBO to hardware graphs used in quantum annealing computers. In an earlier paper a set of rules was introduced that achieved significant QUBO reductions as verified through computational testing. Here this work is extended with additional rules that provide further reductions that succeed in exactly solving 10% of the benchmark QUBO problems. An algorithm and associated data structures to efficiently implement the entire set of rules is detailed and computational experiments are reported that demonstrate their efficacy.

Minimum equivalent precedence relation systems

In this paper two related simplification problems for systems of linear inequalities describing precedence relation systems are considered. Given a precedence relation system, the first problem seeks a minimum subset of the precedence relations (i.e., inequalities) which has the same solution set as that of the original system. The second problem is the same as the first one except that the “subset restriction” in the first problem is removed. This paper establishes that the first problem is NP-hard. However, a sufficient condition is provided under which the first problem is solvable in polynomial-time. In addition, a decomposition of the first problem into independent tractable and intractable subproblems is derived. The second problem is shown to be solvable in polynomial-time, with a full parameterization of all solutions described. The results in this paper generalize those in Moyles and Thompson (1969) and Aho et al. (1972) for the minimum equivalent graph problem and transitive reduction problem.

Canonical Forms for Isomorphic and Equivalent RDF Graphs

Existential blank nodes greatly complicate a number of fundamental operations on Resource Description Framework (RDF) graphs. In particular, the problems of determining if two RDF graphs have the same structure modulo blank node labels (i.e., if they are isomorphic ), or determining if two RDF graphs have the same meaning under simple semantics (i.e., if they are simple-equivalent ), have no known polynomial-time algorithms. In this article, we propose methods that can produce two canonical forms of an RDF graph. The first canonical form preserves isomorphism such that any two isomorphic RDF graphs will produce the same canonical form; this iso-canonical form is produced by modifying the well-known canonical labelling algorithm N auty for application to RDF graphs. The second canonical form additionally preserves simple-equivalence such that any two simple-equivalent RDF graphs will produce the same canonical form; this equi-canonical form is produced by, in a preliminary step, leaning the RDF graph, and then computing the iso-canonical form. These algorithms have a number of practical applications, such as for identifying isomorphic or equivalent RDF graphs in a large collection without requiring pairwise comparison, for computing checksums or signing RDF graphs, for applying consistent Skolemisation schemes where blank nodes are mapped in a canonical manner to Internationalised Resource Identifiers (IRIs), and so forth. Likewise a variety of algorithms can be simplified by presupposing RDF graphs in one of these canonical forms. Both algorithms require exponential steps in the worst case; in our evaluation we demonstrate that there indeed exist difficult synthetic cases, but we also provide results over 9.9 million RDF graphs that suggest such cases occur infrequently in the real world, and that both canonical forms can be efficiently computed in all but a handful of such cases.

Cycle Time Optimization of Deterministic Timed Weighted Marked Graphs by Transformation

Timed marked graphs, a special class of Petri nets, are extensively used to model and analyze cyclic manufacturing systems. Weighted marked graphs are convenient to model automated production systems, such as robotic work cells or embedded systems, and reduce the size of the model. The main problem for designers is to find a tradeoff between minimizing the cost of the resources and maximizing the system's throughput (also called cycle time). It is possible to apply analytical techniques for the cycle time optimization problem of such systems. The problem consists in finding an initial marking to minimize the cycle time (i.e., maximize the throughput) while the weighted sum of tokens in places is less than or equal to a given value. We transform a weighted marked graph into several equivalent marked graphs and formulate a mixed integer linear programming model to solve this problem. Moreover, several techniques are proposed to reduce the complexity of the proposed method. We show that the proposed method can always find an optimal solution.