Minimal Realization Research Articles

Lattice Structure Realization for The Design of 2-D Digital Allpass Filters With General Causality

This paper presents a lattice structure for the realization of two-dimensional (2-D) recursive digital allpass filters (DAFs) with general causality. We employ four basic lattice sections to realize 2-D recursive DAFs with wedge-shaped coefficient support region like a nonsymmetric half-plane (NSHP) support region. The theory and transfer functions of the realized 2-D lattice DAFs are derived. Some variations of the 2-D lattice structure are also presented. We use the Roesser state space model to verify the minimal realization of the proposed 2-D recursive lattice DAF. We present a least-squares design technique and a minimax design technique to solve the nonlinear optimization problems of the proposed 2-D lattice DAF structure. The novelty of the presented lattice structure is that it not only inherits the desirable attributes of 1-D Gray-Markel lattice allpass structure but also possesses the advantage of better performance over the existing 2-D lattice allpass structures. Finally, several design examples are provided for conducting illustration and comparison.

Two-channel Kondo physics in a Majorana island coupled to a Josephson junction

We study a Majorana island coupled to a bulk superconductor via a Josephson junction and to multiple external normal leads. In the absence of the Josephson coupling, the system displays a topological Kondo state, which had been largely studied recently. However, we find that this state is unstable even to small Josephson coupling, which instead leads at low temperature $T$ to a new fixed point. Most interesting is the case of three external leads, forming a minimal electronic realization of the long sought two-channel Kondo effect. While the $T=0$ conductance corresponds to simple resonant Andreev reflection, the leading $T$ dependence forms an experimental fingerprint for non-Fermi liquid properties.

Novel observer/controller identification method-based minimal realisations in block observable/controllable canonical forms and compensation improvement

ABSTRACTThis paper proposes a novel observer/controller identification method for identifying the minimally realised equivalent (reduced-order) mathematical models in the block observer/controller-canonical forms of the unknown (i) open-loop system, (ii) existing feedback/feedforward controllers and/or (iii) observer, based on available measurements of the operating closed-loop system. By skipping the singular value decomposition procedure and without involving the model conversion of the identified model from the general coordinate into the block observer/controller-canonical forms during the identification process, the proposed method is able to directly realise the identified parameters in the minimally realised block observer/controller-canonical forms. This simplifies the system identification process. The new procedures enable us to enhance the computational aspects of designing self-tuning controllers for online adaptive control of (a class of) multivariable systems and to improve the tracking performance considerably. As a result, the newly proposed compensation improvement approach is able to compensate the undesirable operating controller.

Zero textures and vanishing minor in neutrino mass models and their minimal symmetry realization.

We have made a systematical texture study on some neutrino mass models (Singh 1 et al.,2002; Singh 2 et al., 2002) which are based on diagonal charged lepton mass matrices (M l ) and Dirac neutrino mass matrices (M D ). We investigate the zero textures of the Majorana mass matrix (M R ). Interestingly we find that all the M R ’s corresponds to only one zero textures. We also observe that the one zero texture of M R propagate to the left-handed neutrino mass matrices as their vanishing minors. We perform a minimal realization of the textures under the context of an Abelian symmetric group. However in doing so, we have extended the SM to include some SU(2) singlet scalar.

Composite Higgs Dynamics on the Lattice

We investigate the spectrum of the SU(2) gauge theory with $N_f$ = 2 flavors of fermions in the fundamental representation, in the continuum, using lattice simulations. This model provides a minimal template which has been used for different strongly coupled extensions of the Standard Model ranging from composite (Goldstone) Higgs models to intriguing types of dark matter candidates, such as the SIMPs. Here we will focus on the composite Goldstone Higgs paradigm, for which this model provides a minimal UV complete realization in terms of a new strong sector with fermionic matter. After introducing the relevant Lattice methods used in our simulations, we will discuss our numerical results. We show that this model features a SU(4)/Sp(4) $\sim$ SO(6)/SO(5) flavor symmetry breaking pattern, and estimate the value of its chiral condensate. Finally, we present our results for the mass spectrum of the lightest spin one and zero resonances, analogue to the QCD $\rho$, $a_1$, $\sigma$, $\eta'$, $a_0$ resonances, which are relevant for searches of new, exotic resonances at the LHC.

Digraphs Structures Corresponding to the Analogue Realisation of Fractional Continuous-Time System

This paper presents a method of the determination of a minimal realisation of the fractional continuous-time linear system. For the proposed method, a digraph-based algorithm was constructed. In this paper, we have shown how we can perform the transfer matrix using electrical circuits consisting of resistances, capacitance and source voltages. We have also shown how after using the constant phase element method we can realize such a system. The proposed method was discussed and illustrated with some theoretical and practical numerical examples.

Realisation of Linear Continuous-Time Fractional Singular Systems Using Digraph-Based Method. First approach.

In this paper, a new method for computation of a minimal realisation of a given proper transfer function of fractional continuous-time singular one-dimensional linear systems using one-dimensional digraphs theory D has been presented. For the proposed method, an algorithm was constructed. The proposed solution allows minimal digraphs construction for any one-dimensional system. The proposed method was discussed and illustrated with numerical examples.

On domains of noncommutative rational functions

In this paper the stable extended domain of a noncommutative rational function is introduced and it is shown that it can be completely described by a monic linear pencil from the minimal realization of the function. This result amends the singularities theorem of Kalyuzhnyi-Verbovetskyi and Vinnikov. Furthermore, for noncommutative rational functions which are regular at a scalar point it is proved that their domains and stable extended domains coincide.

Minimal realization of ℓ-conformal Galilei algebra, Pais-Uhlenbeck oscillators and their deformation

We present the minimal realization of the $\ell$-conformal Galilei group in 2+1 dimensions on a single complex field. The simplest Lagrangians yield the complex Pais-Uhlenbeck oscillator equations. We introduce a minimal deformation of the $\ell$=1/2 conformal Galilei (a.k.a. Schr\"odinger) algebra and construct the corresponding invariant actions. Based on a new realization of the d=1 conformal group, we find a massive extension of the near-horizon Kerr-dS/AdS metric.

Ultrafast exciton migration in an HJ-aggregate: Potential surfaces and quantum dynamics

Quantum dynamical and electronic structure calculations are combined to investigate the mechanism of exciton migration in an oligothiophene HJ aggregate, i.e., a combination of oligomer chains (J-type aggregates) and stacked aggregates of such chains (H-type aggregates). To this end, a Frenkel exciton model is parametrized by a recently introduced procedure [Binder et al., J. Chem. Phys. 141, 014101 (2014)] which uses oligomer excited-state calculations to perform an exact, point-wise mapping of coupled potential energy surfaces to an effective Frenkel model. Based upon this parametrization, the Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method is employed to investigate ultrafast dynamics of exciton transfer in a small, asymmetric HJ aggregate model composed of 30 sites and 30 active modes. For a partially delocalized initial condition, it is shown that a torsional defect confines the trapped initial exciton, and planarization induces an ultrafast resonant transition between an HJ-aggregated segment and a covalently bound “dangling chain” end. This model is a minimal realization of experimentally investigated mixed systems exhibiting ultrafast exciton transfer between aggregated, highly planarized chains and neighboring disordered segments.

Electron electric dipole moment in Inverse Seesaw models

We consider the contribution of sterile neutrinos to the electric dipole moment of charged leptons in the most minimal realisation of the Inverse Seesaw mechanism, in which the Standard Model is extended by two right-handed neutrinos and two sterile fermion states. Our study shows that the two pairs of (heavy) pseudo-Dirac mass eigenstates can give significant contributions to the electron electric dipole moment, lying close to future experimental sensitivity if their masses are above the electroweak scale. The major contribution comes from two-loop diagrams with pseudo-Dirac neutrino states running in the loops. In our analysis we further discuss the possibility of having a successful leptogenesis in this framework, compatible with a large electron electric dipole moment.

Electroweak interactions and dark baryons in the sextet BSM model with a composite Higgs particle

The Electroweak interactions of a strongly coupled gauge theory are discussed with outlook beyond the Standard Model (BSM) under global and gauge anomaly constraints. The theory is built on a minimal massless fermion doublet of the SU(2) BSM flavor group (bsm-flavor) with a confining gauge force at the TeV scale in the two-index symmetric (sextet) representation of the BSM SU(3) color gauge group (bsm-color). The intriguing possibility of near-conformal sextet gauge dynamics could lead to the minimal realization of the composite Higgs mechanism with a light $0^{++}$ scalar, far separated from strongly coupled resonances of the confining gauge force in the 2-3 TeV range, distinct from Higgsless Technicolor. In previous publications we have presented results for the meson spectrum of the theory, including the light composite scalar, perhaps the emergent Higgs impostor. Here we discuss the critically important role of the baryon spectrum in the sextet model investigating its compatibility with what we know about thermal evolution of the early Universe including its galactic and terrestrial relics. For an important application, we report the first numerical results on the baryon spectrum of this theory from non-perturbative lattice simulations with baryon correlators in the staggered fermion implementation of the strongly coupled gauge sector. The quantum numbers of composite baryons and their spectroscopy from lattice simulations are required inputs for exploring dark matter contributions of the sextet BSM model, as outlined for future work.

A Characterization of Switched Linear Control Systems With Finite $L_{2}$-Gain

Motivated by an open problem posed by J. P. Hespanha, we extend the notion of Barabanov norm and extremal trajectory to classes of switching signals that are not closed under concatenation. We use these tools to prove that the finiteness of the $L_{2}$ -gain is equivalent, for a large set of switched linear control systems, to the condition that the generalized spectral radius associated with any minimal realization of the original switched system is smaller than one.

On minimal realizations of first-degree 3D systems with separable denominators

In this paper, we focus on first-degree three-dimensional (3D) causal systems which have separable denominators. Grobner basis is applied to prove that not all first-degree 3D systems with separabl...

Minimal Realization Problems for Hidden Markov Models

This paper addresses two fundamental problems in the context of hidden Markov models (HMMs). The first problem is concerned with the characterization and computation of a minimal order HMM that realizes the exact joint densities of an output process based on only finite strings of such densities (known as HMM partial realization problem). The second problem is concerned with learning a HMM from finite output observations of a stochastic process. We review and connect two fields of studies: realization theory of HMMs, and the recent development in spectral methods for learning latent variable models. Our main results in this paper focus on generic situations, namely, statements that will be true for almost all HMMs, excluding a measure zero set in the parameter space. In the main theorem, we show that both the minimal quasi-HMM realization and the minimal HMM realization can be efficiently computed based on the joint probabilities of length $N$ strings, for $N$ in the order of ${\cal O}(\log_{d}(k))$ . In other words, learning a quasi-HMM and an HMM have comparable complexity for almost all HMMs.

Goldstones in diphotons

We study the conditions for a new scalar resonance to be observed first in diphotons at the LHC Run-2. We focus on scenarios where the scalar arises either from an internal or spacetime symmetry broken spontaneously, for which the mass is naturally below the cutoff and the low-energy interactions are fixed by the couplings to the broken currents, UV anomalies, and selection rules. We discuss the recent excess in diphoton resonance searches observed by ATLAS and CMS at 750 GeV, and explore its compatibility with other searches at Run-1 and its interpretation as Goldstone bosons in supersymmetry and composite Higgs models. We show that two candidates naturally emerge: a Goldstone boson from an internal symmetry with electromagnetic anomalies, and the scalar partner of the Goldstone of supersymmetry breaking: the sgoldstino. The dilaton from conformal symmetry breaking is instead disfavoured by present data, in its minimal natural realization.

Reduced-order modeling of human body for brain hypothermia treatment

Brain hypothermia treatment (BHT) is an active therapy for severe brain injury. It makes the temperature of the brain track a given temperature input curve so as to reduce the risk of tissue damage. BHT requires a brain-temperature control system because of environmental disturbances and changes in the human body. The thermal models of the human body devised so far are usually of a very high order and are not suitable for controlling brain temperature. This paper presents a method of finding a reducedorder thermal model of the human body for use in BHT. It combines minimal realization and balanced realization. Unlike other methods, this method yields a reduced-order model that is based on system theory and that takes the frequency characteristics of human thermal sensation into account. It features high precision in the frequency band for BHT and is suitable for the control of brain temperature.

Minimal eventually positive realizations of externally positive systems

It is a well-known fact that externally positive linear systems may fail to have a minimal positive realization. In order to investigate these cases, we introduce the notion of minimal eventually positive realization, for which the state update matrix becomes positive after a certain power. Eventually positive realizations capture the idea that in the impulse response of an externally positive system the state of a minimal realization may fail to be positive, but only transiently. As a consequence, we show that in discrete-time it is possible to use downsampling to obtain minimal positive realizations matching decimated sequences of Markov coefficients of the impulse response. In continuous-time, instead, if the sampling time is chosen sufficiently long, a minimal eventually positive realization leads always to a sampled realization which is minimal and positive.

Determination of minimal realisation of one-dimensional continuous-time fractional linear system

In this paper, a new alternative method for the determination of the set of all minimal positive and non-positive realisations of the one-dimensional fractional continuous-time linear systems based on the one-dimensional digraphs theory has been presented. In addition, all realisations in the set are minimal. For the proposed method, an algorithm was also constructed. The algorithm is based on a parallel computing method to gain needed speed and computational power for such a solution. The proposed method is discussed and illustrated with numerical examples.

Minimal realization for fuzzy behaviour: A bicategory-theoretic approach

The purpose of present work is to introduce and study two minimal realizations for a given fuzzy behaviour in bicategory- theoretic setup. One such realization is based on Myhill Nerode's theory, while the other realization is based on derivative of the given fuzzy behaviour. It is shown here that there exists a unique 2-cell in bicategory of crisp deterministic fuzzy machines between both the realizations.