Generalized Matrix Model Research Articles

Harmonic Modeling of the Series-Connected Multipulse Rectifiers Under Unbalanced Conditions

With the promotion of high voltage direct current (HVDC) system construction around the world, the series-connected multi-pulse rectifiers (SCMPRs) have been widely used in high-power rectifying occasions in the power system. Since the certain order of harmonics cannot be effectively eliminated under the non-ideal conditions, many different phenomena, such as the unbalance of supply voltage and line/transformer parameters, the influence of background harmonics, and the non-equidistance of thyristor triggering pulses, may cause the non-characteristic harmonics (NCHs) of SCMPR. However, the existing frequency-domain harmonic model cannot be used to analyze the harmonic characteristics of the SCMPRs under non-ideal conditions. In this paper, a general frequency-domain harmonic coupling matrix model (HCMM) is proposed. The proposed HCMM can consider most of the above imbalance factors and the model can explicitly illustrate the harmonic coupling relationship between the SCMPRs supplied voltage and the generated harmonic currents. The generality of the SCMPR model under non-ideal conditions is improved accordingly. The HCMM is simplified by comparing and analyzing the effects of the transformer structure and parameters. Moreover, by analyzing the harmonic generation characteristic of the negative-sequence component, the HCMM can be further simplified. Finally, time-domain simulation and lab experimentation are performed to verify the accuracy and efficiency of the frequency-domain HCMM of SCMPRs. The results prove the generality of the proposed model and also illustrate the harmonic generating influence of unbalanced parameters from the transformer and supply voltage.

Algebraic logic for the negation fragment of classical logic

Abstract The general aim of this article is to study the negation fragment of classical logic within the framework of contemporary (Abstract) Algebraic Logic. More precisely, we shall find the three classes of algebras that are canonically associated with a logic in Algebraic Logic, i.e. we find the classes $\textrm{Alg}^*$, $\textrm{Alg}$ and the intrinsic variety of the negation fragment of classical logic. In order to achieve this, firstly, we propose a Hilbert-style axiomatization for this fragment. Then, we characterize the reduced matrix models and the full generalized matrix models of this logic. Also, we classify the negation fragment in the Leibniz and Frege hierarchies.

Modelling the responses of partially migratory metapopulations to changing seasonal migration rates: From theory to data.

Among‐individual and within‐individual variation in expression of seasonal migration versus residence is widespread in nature and could substantially affect the dynamics of partially migratory metapopulations inhabiting seasonally and spatially structured environments. However, such variation has rarely been explicitly incorporated into metapopulation dynamic models for partially migratory systems. We, therefore, lack general frameworks that can identify how variable seasonal movements, and associated season‐ and location‐specific vital rates, can control system persistence.We constructed a novel conceptual framework that captures full‐annual‐cycle dynamics and key dimensions of metapopulation structure for partially migratory species inhabiting seasonal environments. We conceptualize among‐individual variation in seasonal migration as two variable vital rates: seasonal movement probability and associated movement survival probability. We conceptualize three levels of within‐individual variation (i.e. plasticity), representing seasonal or annual variation in seasonal migration or lifelong fixed strategies. We formulate these concepts as a general matrix model, which is customizable for diverse life‐histories and seasonal landscapes.To illustrate how variable seasonal migration can affect metapopulation growth rate, demographic structure and vital rate elasticities, we parameterize our general models for hypothetical short‐ and longer‐lived species. Analyses illustrate that elasticities of seasonal movement probability and associated survival probability can sometimes equal or exceed those of vital rates typically understood to substantially influence metapopulation dynamics (i.e. seasonal survival probability or fecundity), that elasticities can vary non‐linearly, and that metapopulation outcomes depend on the level of within‐individual plasticity.We illustrate how our general framework can be applied to evaluate the consequences of variable and changing seasonal movement probability by parameterizing our models for a real partially migratory metapopulation of European shags Gulosus aristotelis assuming lifelong fixed strategies. Given observed conditions, metapopulation growth rate was most elastic to breeding season adult survival of the resident fraction in the dominant population. However, given doubled seasonal movement probability, variation in survival during movement would become the primary driver of metapopulation dynamics.Our general conceptual and matrix model frameworks, and illustrative analyses, thereby highlight complex ways in which structured variation in seasonal migration can influence dynamics of partially migratory metapopulations, and pave the way for diverse future theoretical and empirical advances.

Gaussianity and typicality in matrix distributional semantics

Constructions in type-driven compositional distributional semantics associate large collections of matrices of size D to linguistic corpora. We develop the proposal of analysing the statistical characteristics of this data in the framework of permutation invariant matrix models. The observables in this framework are permutation invariant polynomial functions of the matrix entries, which correspond to directed graphs. Using the general 13-parameter permutation invariant Gaussian matrix models recently solved, we find, using a dataset of matrices constructed via standard techniques in distributional semantics, that the expectation values of a large class of cubic and quartic observables show high Gaussianity at levels between 90 to 99 percent. Beyond expectation values, which are averages over words, the dataset allows the computation of standard deviations for each observable, which can be viewed as a measure of typicality for each observable. There is a wide range of magnitudes in the measures of typicality. The permutation invariant matrix models, considered as functions of random couplings, give a very good prediction of the magnitude of the typicality for different observables. We find evidence that observables with similar matrix model characteristics of Gaussianity and typicality also have high degrees of correlation between the ranked lists of words associated to these observables.

Notes on matrix models (matrix musings)

In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a matrix-like fashion. We discuss the relation of matrix models to two-dimensional quantum gravity coupled to conformal matter. We provide a brief overview of a variety of more general quantum mechanical matrix models and their putative worldsheet interpretation, as well as other recent developments on large N systems. We end with a discussion of open questions and future directions.

An LDPC Approach for Chunked Network Codes

Efficient communication through a multi-hop network with packet loss requires random linear network coding schemes with low computation cost and high throughput. In this paper, we propose a low-density parity-check (LDPC)-based framework for constructing chunked code, a variation of random linear network code with low encoding/decoding computational cost and small coefficient vector overhead. Two classes of chunked codes with LDPC structures, named uniform LDPC-chunked codes and overlapped LDPC-chunked (OLC) codes, are studied under a general chunk transfer matrix model. ULC codes achieve rates close to the optimum and perform better than existing chunked codes that employ parity-check constraints. OLC codes are overlapped chunked codes, where it is not necessary to generate new packets for encoding, and demonstrate much higher rates in certain scenarios than the state-of-the-art designs of overlapped chunked codes. These results justifies the feasibility of this LDPC approach for communication through multi-hop networks with packet loss.

Quantum Hitchin Systems via $${\beta}$$ β -Deformed Matrix Models

We study the quantization of Hitchin systems in terms of $${\beta}$$ -deformations of generalized matrix models related to conformal blocks of Liouville theory on punctured Riemann surfaces. We show that in a suitable limit, corresponding to the Nekrasov–Shatashvili one, the loop equations of the matrix model reproduce the Hamiltonians of the quantum Hitchin system on the sphere and the torus with marked points. The eigenvalues of these Hamiltonians are shown to be the $${\epsilon_1}$$ -deformation of the chiral observables of the corresponding $${{\mathcal{N}=2}}$$ four dimensional gauge theory. Moreover, we find the exact wave-functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions.

Transfer matrix model of multilayer graphene nanoribbon interconnects

A general, algorithmic and exact transfer matrix model is presented for multilayer graphene nanoribbon (MLGNR) interconnects that is based on multi transmission line method (MTLM). In the proposed transfer matrix formulation the effect of Fermi level shift in GNR layers is considered. Also the capacitive and inductive coupling between the GNR layers is regarded in this matrix model. Moreover, in order to get the precise results, the block number parameter for distributed property of the interconnects is proposed for the first time. The straightforward, general and algorithmic format of the proposed matrix model causes it to be used for different technology nodes and length of the interconnects. Moreover any variation in the physical parameters can be involved simply in this formulation. Using this matrix model, one can examine different analytical prospects such as Nyquist, Bode, and Nichols stability criteria, zero and poles and step time responses for on-chip MLGNR interconnects, implemented for integrated circuit applications. Also this matrix model can be used in circuit simulators such as HSPICE in order to simulate the VLSI-ULSI circuits. As the couple of examples, we have extracted Nyquist diagrams and step time responses for 10nm, 14nm, and 22nm technology nodes. The results show that relative stability of MLGNR interconnects increases with increasing technology node and interconnect length. The results demonstrate a considerable difference between the responses obtained using traditional MLGNR interconnect formulation and the exact proposed matrix model.

Fault‐tolerant control for Markovian jump systems with general uncertain transition rates against simultaneous actuator and sensor faults

SummaryThis paper investigates the problems of simultaneous estimations of actuator faults and sensor faults, as well as fault‐tolerant control schemes for a class of Markovian jump systems with general uncertain transition rates. In a general uncertain transition rate matrix model, transition rate may be completely unknown, or one can only acquire its estimated value, which makes the design much more challenging. First, the original system is transformed into a descriptor one by extending the sensor faults to be parts of state vector. Then, a robust stochastic adaptive observer is designed for the descriptor system with the actuator fault being adjusted by an adaptive law. On the basis of the estimated states as well as estimated actuator and sensor faults, a fault‐tolerant control strategy is proposed to make the resulting closed‐loop system stable in the presence of the actuator fault. Sufficient existence conditions of the observer and controller are derived in terms of linear matrix inequalities. Finally, three practical examples are given to validate the high efficiency of our proposed method. Copyright © 2017 John Wiley & Sons, Ltd.

A bifurcation theorem for evolutionary matrix models with multiple traits.

One fundamental question in biology is population extinction and persistence, i.e., stability/instability of the extinction equilibrium and of non-extinction equilibria. In the case of nonlinear matrix models for structured populations, a bifurcation theorem answers this question when the projection matrix is primitive by showing the existence of a continuum of positive equilibria that bifurcates from the extinction equilibrium as the inherent population growth rate passes through 1. This theorem also characterizes the stability properties of the bifurcating equilibria by relating them to the direction of bifurcation, which is forward (backward) if, near the bifurcation point, the positive equilibria exist for inherent growth rates greater (less) than 1. In this paper we consider an evolutionary game theoretic version of a general nonlinear matrix model that includes the dynamics of a vector of mean phenotypic traits subject to natural selection. We extend the fundamental bifurcation theorem to this evolutionary model. We apply the results to an evolutionary version of a Ricker model with an added Allee component. This application illustrates the theoretical results and, in addition, several other interesting dynamic phenomena, such as backward bifurcation induced strong Allee effects.

Performance and emission reduction potential of renewable energy aided coal-fired power generation systems

A renewable energy aided coal-fired power generation system (REACPGS) is proposed to provide a meaningful and promising way for energy conservation and emission reduction. General matrix models of the heat balance and exergy losses of REACPGS are established, and the thermo-economic performance, energy conservation and emission reduction potentials are investigated. The effects of system capacity, shunt coefficient and the acting position of auxiliary steam-generating system (ASS) on the overall performance are examined. Results show that the increments of thermal performance indicators in a 300 MW system are higher than those in a 600 MW system; it is a preferred choice to upgrade a 300 MW system integrated with ASS. The exergy loss coefficient of No.5 heater is the largest in all heaters, followed by that of No.2 heater; both No.5 and No.2 heaters dominate the critical energy conservation potential. Because the quality of bled steam for No.5 heater is inferior to that for No.2 heater, the benefits as ASS acting on No.2 heater are over than those on No.5 heater. Thermo-economic performance indicators are distinctly improved with increasing shunt coefficient, and reach the maximal values under the case of bled steam totally supplanted by ASS.

Flowing in Group Field Theory Space: a Review

We provide a non-technical overview of recent extensions of renormalization methods and techniques to Group Field Theories (GFTs), a class of combinatorially non-local quantum field theories which generalize matrix models to dimension $d \geq 3$. More precisely, we focus on GFTs with so-called closure constraint, which are closely related to lattice gauge theories and quantum gravity spin foam models. With the help of recent tensor model tools, a rich landscape of renormalizable theories has been unravelled. We review our current understanding of their renormalization group flows, at both perturbative and non-perturbative levels.

An OSp extension of the canonical tensor model

Tensor models are generalizations of matrix models, and are studied as discrete models of quantum gravity for arbitrary dimensions. Among them, the canonical tensor model (CTM for short) is a rank-three tensor model formulated as a totally constrained system with a number of first-class constraints, which have a similar algebraic structure as the constraints of the ADM formalism of general relativity. In this paper, we formulate a super-extension of CTM as an attempt to incorporate fermionic degrees of freedom. The kinematical symmetry group is extended from $O(N)$ to $OSp(N,\tilde N)$, and the constraints are constructed so that they form a first-class constraint super-Poisson algebra. This is a straightforward super-extension, and the constraints and their algebraic structure are formally unchanged from the purely bosonic case, except for the additional signs associated to the order of the fermionic indices and dynamical variables. However, this extension of CTM leads to the existence of negative norm states in the quantized case, and requires some future improvements as quantum gravity with fermions. On the other hand, since this is a straightforward super-extension, various results obtained so far for the purely bosonic case are expected to have parallels also in the super-extended case, such as the exact physical wave functions and the connection to the dual statistical systems, i.e. randomly connected tensor networks.

Physical states in the canonical tensor model from the perspective of random tensor networks

Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the algebra of which resembles the Dirac algebra of general relativity. When quantized, the physical states are defined to be vanished by the quantized constraints. In explicit representations, the constraint equations are a set of partial differential equations for the physical wave-functions, which do not seem straightforward to be solved due to their non-linear character. In this paper, after providing some explicit solutions for N = 2, 3, we show that certain scale-free integration of partition functions of statistical systems on random networks (or random tensor networks more generally) provides a series of solutions for general N. Then, by generalizing this form, we also obtain various solutions for general N. Moreover, we show that the solutions for the cases with a cosmological constant can be obtained from those with no cosmological constant for increased N. This would imply the interesting possibility that a cosmological constant can always be absorbed into the dynamics and is not an input parameter in the canonical tensor model. We also observe the possibility of symmetry enhancement in N = 3, and comment on an extension of Airy function related to the solutions.

Modeling and Simulation of the Multiple Robot’s Applications

This paper explains and demonstrates how can designed one multi robots application with many tasks and some different type of modular collaborative robots. Was described the general mathematical model for the direct and inverse kinematics to controlling the robots and how can solve the inverse kinematics of multiple tasks by using the priority of tasks or serial tasks composed by sum of the weighted several tasks. Some collaborative multi robots applications with parallel, serial or composed robots configurations were shown. The general mathematical matrix model of the robot application point with three translations and three rotations to the world Cartesian coordinates of the application map was defined. The designed method, the animation programs and the used LabVIEW proper virtual instruments open the way to easily define the multi robots application map, establish the constraints of the used robots and of the environment to avoid the singular points and tests the manipulation programs for collaborative application.

The double scaling limit of random tensor models

Tensor models generalize matrix models and generate colored triangulations of pseudo-manifolds in dimensions D ≥ 3. The free energies of some models have been recently shown to admit a double scaling limit, i.e. large tensor size N while tuning to criticality, which turns out to be summable in dimension less than six. This double scaling limit is here extended to arbitrary models. This is done by means of the Schwinger-Dyson equations, which generalize the loop equations of random matrix models, coupled to a double scale analysis of the cumulants.

Confinement and Mayer cluster expansions

In this paper, we study a class of grand-canonical partition functions with a kernel depending on a small parameter ϵ. This class is directly relevant to Nekrasov partition functions of 𝒩 = 2 SUSY gauge theories on the 4d Ω-background, for which ϵ is identified with one of the equivariant deformation parameter. In the Nekrasov–Shatashvili limit ϵ→0, we show that the free energy is given by an on-shell effective action. The equations of motion take the form of a TBA equation. The free energy is identified with the Yang–Yang functional of the corresponding system of Bethe roots. We further study the associated canonical model that takes the form of a generalized matrix model. Confinement of the eigenvalues by the short-range potential is observed. In the limit where this confining potential becomes weak, the collective field theory formulation is recovered. Finally, we discuss the connection with the alternative expression of instanton partition functions as sums over Young tableaux.

Notes on Mayer expansions and matrix models

Mayer cluster expansion is an important tool in statistical physics to evaluate grand canonical partition functions. It has recently been applied to the Nekrasov instanton partition function of N=2 4d gauge theories. The associated canonical model involves coupled integrations that take the form of a generalized matrix model. It can be studied with the standard techniques of matrix models, in particular collective field theory and loop equations. In the first part of these notes, we explain how the results of collective field theory can be derived from the cluster expansion. The equalities between free energies at first orders is explained by the discrete Laplace transform relating canonical and grand canonical models. In a second part, we study the canonical loop equations and associate them with similar relations on the grand canonical side. It leads to relate the multi-point densities, fundamental objects of the matrix model, to the generating functions of multi-rooted clusters. Finally, a method is proposed to derive loop equations directly on the grand canonical model.

Backward bifurcations and strong Allee effects in matrix models for the dynamics of structured populations

In nonlinear matrix models, strong Allee effects typically arise when the fundamental bifurcation of positive equilibria from the extinction equilibrium at r=1 (or R0=1) is backward. This occurs when positive feedback (component Allee) effects are dominant at low densities and negative feedback effects are dominant at high densities. This scenario allows population survival when r (or equivalently R0) is less than 1, provided population densities are sufficiently high. For r>1 (or equivalently R0>1) the extinction equilibrium is unstable and a strong Allee effect cannot occur. We give criteria sufficient for a strong Allee effect to occur in a general nonlinear matrix model. A juvenile–adult example model illustrates the criteria as well as some other possible phenomena concerning strong Allee effects (such as positive cycles instead of equilibria).

The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders

Random tensor models for a generic complex tensor generalize matrix models in arbitrary dimensions and yield a theory of random geometries. They support a 1/N expansion dominated by graphs of spherical topology. Their Schwinger Dyson equations, generalizing the loop equations of matrix models, translate into constraints satisfied by the partition function. The constraints have been shown, in the large N limit, to close a Lie algebra indexed by colored rooted D-ary trees yielding a first generalization of the Virasoro algebra in arbitrary dimensions. In this paper we complete the Schwinger Dyson equations and the associated algebra at all orders in 1/N. The full algebra of constraints is indexed by D-colored graphs, and the leading order D-ary tree algebra is a Lie subalgebra of the full constraints algebra.