Minimal Realization Research Articles

Probing Zee-Babu states at muon colliders

The Zee-Babu model is a minimal realization of radiative neutrino mass generation mechanism at the two-loop level. We study the phenomenology of this model at future multi-TeV muon colliders. After imposing all theoretical and low-energy experimental constraints on the model parameters, we find that the Zee-Babu states are expected not to reside below the TeV scale, making it challenging to probe them at the LHC. We first analyze the production rates for various channels, including multi singly charged and/or doubly charged scalars at muon colliders. For concreteness, we study several benchmark points that satisfy neutrino oscillation data and other constraints and find that most channels have large production rates. We then analyze the discovery reach of the model using two specific channels: the pair production of singly and doubly charged scalars. For the phenomenologically viable scenarios considered in this study, charged scalars with masses up to O(3–4) TeV can be probed for the center-of-mass energy of 10 TeV and total luminosity of 10 ab−1. Published by the American Physical Society 2024

A minimal and non-alternative realisation of the Cayley plane

The compact 16-dimensional Moufang plane, also known as the Cayley plane, has traditionally been defined through the lens of octonionic geometry. In this study, we present a novel approach, demonstrating that the Cayley plane can be defined in an equally clean, straightforward and more economic way using two different division and composition algebras: the paraoctonions and the Okubo algebra. The result is quite surprising since paraoctonions and Okubo algebra possess a weaker algebraic structure than the octonions, since they are non-alternative and do not satisfy the Moufang identities. Intriguingly, the real Okubo algebra has SU3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {SU}\\left( 3\\right) $$\\end{document} as automorphism group, which is a classical Lie group, while octonions and paraoctonions have an exceptional Lie group of type G2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {G}_{2}$$\\end{document}. This is remarkable, given that the projective plane defined over the real Okubo algebra is nevertheless isomorphic and isometric to the octonionic projective plane which is at the very heart of the geometric realisations of all types of exceptional Lie groups. Despite its historical ties with octonionic geometry, our research underscores the real Okubo algebra as the weakest algebraic structure allowing the definition of the compact 16-dimensional Moufang plane.

Robust tracking control of a minimal realization model of an impaired human hand for anthropomorphic coordination

Objective Physiologically relevant optimal controllers better represent the decision-making process of the central nervous system (CNS) with proper neural inputs and proprioceptor feedback. A biomechanical mathematical framework in the human palm reference frame was simulated using physiological dynamics to explore the biomechanics of movement coordination of fingers in a human hand.Method Physiological state space models include multiple zero eigenvalues, representing a redundant system. A fingertip trajectory tracking control paradigm is created by reducing the model order through the H∞ control paradigm. The external disturbances and sensory noise are included in the 21-Degrees-of-Freedom biomechanical model.Main Results An analysis is conducted on the flexion movement of the robotic finger when it is disrupted from its initial equilibrium position. The controller administers feedback force at the joints to control the movement of the robotic finger. A full order H∞ robust controller was developed, and the results were compared with the reduced-order model. The model order was reduced from 21 to 18 states. A reference trajectory is followed by the index finger in the minimal realization model, which is derived from the joint angular position profile. It stabilizes at a flexion angle of 1 rad/sec within 2 sec. Studying the simpler form of a model first gives a realistic view of the more complex model. This study has the potential to enhance our comprehension of anthropomorphic movement coordination in hands with impairments in kinesiology, ergonomics, assistive technology, and prosthetic devices.

Finite naturalness and quark-lepton unification

We study the implications of finite naturalness in Pati-Salam models where SU(3)C is embedded in SU(4). For the minimal realization at low scale of quark-lepton unification, which employs the inverse seesaw for neutrino masses, we find that radiative corrections to the Higgs boson mass are at least δmh2/mh2∼O(104). The one-loop contributions to the Higgs mass are suppressed by four powers of the hypercharge gauge coupling. We find that for the vector leptoquarks the naively leading part of the two-loop corrections cancel. We assume the Dirac Yukawa couplings for neutrinos are equal to the up-type quark Yukawa couplings as predicted in the minimal theory for quark-lepton unification. Despite these findings, the two-loop corrections still dominate the finite naturalness bound. We mention a way to relax the lower bound on the vector leptoquark mass and have δmh2/mh2∼O(102). Published by the American Physical Society 2024

Dynamics of dark matter misalignment through the Higgs portal

A light singlet scalar field feebly coupled through the super-renormalizable Higgs portal provides a minimal and well-motivated realization of ultra-light bosonic dark matter. We study the cosmological production of dark matter in this model by elucidating the dynamics of two sources of scalar field misalignment generated during the radiation era. For large scalar masses (above O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(10−3 eV)), dark matter is produced through thermal misalignment, by which the scalar field is driven towards large field values as a result of the finite-temperature effective potential. The dominance of thermal misalignment in this mass range leads to a sharp relic abundance prediction which is, to a significant extent, insensitive to the initial conditions of the scalar field. On the other hand, for low mass scalars (below O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(10−5 eV)), dark matter is produced via VEV misalignment, which is caused by the induced scalar field vacuum expectation value triggered by the electroweak phase transition. We show that the relic abundance in this low mass range is sensitive to the scalar field initial conditions. In the intermediate mass range, the relic abundance is a consequence of a competition between thermal misalignment and VEV misalignment, which can potentially lead to novel forced resonance effects which cause a recurring enhancement and suppression in the late time oscillation amplitude as a function of the scalar mass. We compare our relic abundance predictions with constraints and projections from equivalence principle and inverse square law tests, stellar cooling, resonant molecular absorption, and observations of extra-galactic background light and diffuse X-ray backgrounds. New experimental ideas are needed to probe most of the cosmologically motivated regions of parameter space.

Minimal model of fermion FIMP dark matter

We investigate a simple extension of the standard model in which the dark matter consists of a feebly interacting fermion, charged under a new Z4 symmetry, that is produced in the early Universe by the freeze-in mechanism. The only other new particle included in the model is a singlet scalar, also charged under the Z4, which couples to the fermion via Yukawa interactions and to the standard model Higgs. The model is truly minimal, as it admits just five free parameters: two masses and three dimensionless couplings. Depending on their values, the freeze-in mechanism can be realized in different ways, each characterized by its own production processes. For all of them, we numerically study the relic density as a function of the free parameters of the model and determine the regions consistent with the dark matter constraint. Our results show that this scenario is viable over a wide range of couplings and dark matter masses. This model, therefore, not only offers a novel solution to the dark matter problem, but it also provides a minimal realization of freeze-in for fermion dark matter. Published by the American Physical Society 2024

Addressing the occupancy problem of Soekarno-Hatta Airport rail link during its first five years of operation

Airport rail links have long been acknowledged as a crucial component of the modern transportation system. Their attractiveness among air travellers stems from their convenience, speed, and environmental benefits. Despite their advantages, these services often face several occupancy problems that hinder their effectiveness and efficiency. Soekarno-Hatta airport rail link’s operation in 2018-2022 has been marked by low occupancy. This study aims to assess the realisations of several critical attributes of a successful airport rail link service according to TRB studies in the context of the Soekarno-Hatta airport rail link. In this context, it was shown that only four of the seven key attributes have met the minimal level to attain such goals. Despite numerous strategies undertaken during the period, which coincides with the COVID-19 pandemic, most fall under the operating or service adjustments category. The minimal realisations of the seven key attributes confirm the low occupancy levels, yet efforts to increase the ridership were limited during the pandemic. These findings provide avenues for a more successful transfer of operations from PT Railink to PT Kereta Commuter Indonesia with the clear intention of boosting the rail link’s ridership. Alongside several expansion plans by the Directorate General of Railways, the findings shall help public policymakers promote a modal shift and pave the way towards a broader integration with other modes of public transportation in the Jabodetabek region.

A negative imaginary lemma and state-feedback negative imaginary synthesis for commensurate fractional-order systems

This article focuses on negative imaginariness of commensurate fractional-order linear time-invariant systems. Enlightened by the generalized Kalman–Yakubovic–Popov lemma, minimal state-space realization based necessary and sufficient conditions are developed to characterize negative imaginariness of commensurate fractional-order systems for both 0<α<1 and 1<α<2 cases. Meanwhile, the problem of negative-imaginary state-feedback controller synthesis for fractional-order systems is addressed. A fractional-order viscoelastic system, a fractional-order RLC circuit network and a numerical example are used as illustrative examples to demonstrate the main developed theory.

Neutrinos, dark matter and Higgs vacua in parity solutions of the strong CP problem

The strong CP problem can be solved if the laws of nature are invariant under a space-time parity exchanging the Standard Model with its mirror copy. We review and extend different realizations of this idea with the aim of discussing Dark Matter, neutrino physics, leptogenesis and collider physics within the same context. In the minimal realization of ref. [1] the mirror world contains a massless dark photon, which leads to a rather interesting cosmology. Mirror electrons reproduce the dark matter abundance for masses between 500–1000 GeV with traces of strongly interacting dark matter. This scenario also predicts deviations from cold dark matter, sizable ∆Neff and colored states in the TeV range that will be tested in a variety of upcoming experiments. We also explore scenarios where the mirror photon is massive and the mirror particles are charged under ordinary electromagnetism with very different phenomenology. We also show that, for the measured values of the SM parameters, the Higgs effective potential can give rise to a second minimum at large field value as required to break spontaneously the parity symmetry.

Minimal Realizations of Nonlinear Time-Delay Systems

The problem of finding a minimal realization of a single-input single-output nonlinear retarded time-delay input-output equation with constant commensurable delays is addressed. First, an algorithm is given to find an observable realization of dimension <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> of a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -th order input-output equation. Then, this algorithm is modified under two technical assumptions to find a realization of lower dimension, which is observable and accessible. It is shown that under the same technical assumptions an observable and accessible realization has minimal possible state-space dimension among all possible realizations. An algebraic approach based on polynomial tools and modules of differential 1-forms is used to derive the results.

Effective spin filtering in correlated semiconductor nanostructures

A new theoretical concept of an electrically controllable single-electron spin filter (polarizator) based on the exchange interaction in the system of interacting quantum dots or impurity atoms is proposed. The sign of the spin polarization of the current flowing through the device can be effectively controlled in two ways (i) by changing the applied bias and (ii) by tuning the tunnel coupling via an external gate. The minimal realization involves three bound state levels coupled to the contact leads. One of these levels is occupied by a single electron with a certain spin and the two-electron occupation is prohibited by a strong on-site Coulomb repulsion. Interestingly, while the spin polarization of this state is fixed, the sign of the single-electron current spin polarization flowing between the contacts through two consistent bound state levels can be switched.

Zakat Literacy Level of Residents and Muhammadiyah Sympathists in Krajan Village

Krajan Village is a village with a majority Muhammadiyah population located in Banyumas Regency, however one of the institutions under the auspices of Muhammadiyah namely LazisMu Krajan Village is claimed to be in a passive condition, even though LazisMu Krajan Village as an institutional structure is under the auspices of LazisMu Banyumas Regency which is LazisMu with a myriad of achievements, starting from 2018 to 2022 Lazismu Banyumas Regency won several awards as the best amil zakat infak and shodaqoh institution at provincial to national levels. This phenomenon prompted researchers to measure the zakat literacy level of residents and Muhammadiyah sympathizers in Krajan Village and to measure the phenomena that affect the level of zakat literacy. The scope of this research lies in the residents of Krajan Village, Banyumas Regency, the majority of whom are Muhammadiyah sympathizers and members. This study uses a descriptive qualitative method with primary data obtained from interviews with Krajan Village residents who are classified as Muhammadiyah members and sympathizers regarding matters related to zakat literacy. The results of this study indicate that the level of literacy among Muhammadiyah residents and sympathizers in Krajan Village is still classified as poor in terms of knowledge and practice of zakat, this phenomenon is inseparable from the poor condition of LazisMu in Krajan Village, as evidenced by the poor management of the institution, to the minimal realization of the program. which then significantly affects the literacy quality of the citizens and Muhammadiyah sympathizers. The results of this study can be used as a general description of the literacy quality of the Krajan Village community to be used as a reference in improving professional institutional governance, and increasing the realization of programs for collecting, utilizing, and distributing zakat for LazisMu Krajan Village.

Ergodic Measure and Potential Control of Anomalous Diffusion.

In statistical mechanics, the ergodic hypothesis (i.e., the long-time average is the same as the ensemble average) accompanying anomalous diffusion has become a continuous topic of research, being closely related to irreversibility and increasing entropy. While measurement time is finite for a given process, the time average of an observable quantity might be a random variable, whose distribution width narrows with time, and one wonders how long it takes for the convergence rate to become a constant. This is also the premise of ergodic establishment, because the ensemble average is always equal to the constant. We focus on the time-dependent fluctuation width for the time average of both the velocity and kinetic energy of a force-free particle described by the generalized Langevin equation, where the stationary velocity autocorrelation function is considered. Subsequently, the shortest time scale can be estimated for a system transferring from a stationary state to an effective ergodic state. Moreover, a logarithmic spatial potential is used to modulate the processes associated with free ballistic diffusion and the control of diffusion, as well as the minimal realization of the whole power-law regime. The results presented suggest that non-ergodicity mimics the sparseness of the medium and reveals the unique role of logarithmic potential in modulating diffusion behavior.

Modeling and Simulation of a Micro strip Antenna in Annular Geometry

In the last decade, the study of multidimensional systems for signal filtering purpose has attracted the attention of many research teams, which are motivated by various interesting real world applications such Image processing, video signal filtering processing, video signal filtering Computational tomography, distributed parameters systems. The representation of the state space realization for two-dimensional (2D) filters by a transfer function, with minimal delays is a crucial problem; the minimal realization can avoidmathematical complexities as well as technical benefit to hardware requirement. Unfortunately, it is not possible to find the minimal state space realization for every 2D system other than the 1D system, but we can find it for a specific cases of all-pole or the all-zero. Lattice filter is classified as an important structure in digital signal processing. In fact, it minimizes the computation complexity, reduces the finite word length and requires less hardware compared to the direct form digital filter with similar design specifications. The authors in two delay units z1-1 , z2-1 are used. In this paper we propose a new lattice-ladder structure of 2-D digital filter, composed of a delay units z1-1 and a basic lattice section z1 and z2-1 - Using matrix representation of the basic lattice sections and we derived transfer functions of the proposed 2-D digital ladder-lattice filters. The proposed structure is composed by a minimal number of delays and a minimal number of basic lattice sections. Furthermore, we have considered the description of the proposed lattice structure by using a state-space n-D Roesser form description presented in below and the implementations suggested by the authors in literatures. Besides, the state space equations for 2-D digital filter are presented, where the dimension of the matrices of the proposed lattice structure verify the minimal state space realization. The remainder of the paper is organized as follows; first is devoted to the proposed -D lattice-ladder structure and realization and in the second is dedicated to the state space realization. As conclusion this work has allowed us to approach a field that has experienced a great growth in recent years which is constantly evolving in order to improve, understanding and control the complex systems and processes that surround us.

Sparse representation learning with modified q-VAE towards minimal realization of world model

Extraction of low-dimensional latent space from high-dimensional observation data is essential to construct a real-time robot controller with a world model on the extracted latent space. However, there is no established method for tuning the dimension size of the latent space automatically, suffering from finding the necessary and sufficient dimension size, i.e. the minimal realization of the world model. In this study, we analyze and improve Tsallis-based variational autoencoder (q-VAE), and reveal that, under an appropriate configuration, it always facilitates making the latent space sparse. Even if the dimension size of the pre-specified latent space is redundant compared to the minimal realization, this sparsification collapses unnecessary dimensions, allowing for easy removal of them. We experimentally verified the benefits of the sparsification by the proposed method that it can easily find the necessary and sufficient six dimensions for a reaching task with a mobile manipulator that requires a six-dimensional state space. Moreover, by planning with such a minimal-realization world model learned in the extracted dimensions, the proposed method was able to exert a more optimal action sequence in real-time, reducing the reaching accomplishment time by around 20%.

Minimal Realizations of Atomic Density Functions

In this article, it is shown that Koebe inner functions and squares of singular Nevanlinna functions, so called atomic density functions, have minimal realizations in reproducing kernel Krein spaces.

Reduced realization for switched linear systems with known mode sequence

We consider switched linear systems with mode-dependent state-dimensions and/or state jumps and propose a method to obtain a switched system of reduced size with identical input–output behavior. A key feature of our method is that only the mode sequence of the switching signal needs to be known and not the exact switching times. Since simple examples show that a minimal realization will depend on the switching times, our algorithm cannot result in a minimal realization in general, but we conjecture that it results in a minimal realization for almost all switching times. Our approach is based on considering time-dependent reachability and unobservability spaces as well as suitable extended reachability and restricted unobservability spaces together with the notion of a weak Kalman decomposition.

Minimal seven‐element series‐parallel realizability of a certain positive‐real biquadratic impedance

SummaryThe minimal complexity realization of low‐order positive‐real immittances as resistor–inductor–capacitor (RLC) (or damper‐spring‐inerter) networks is an essential unsolved problem in the theory of network synthesis, and the results can be directly applied to the inerter‐based mechanical systems control. This paper solves the realizability problem of a certain class of biquadratic impedances as any seven‐element series‐parallel RLC network, where the impedance contains a repeated zero and pole of multiplicity two. In contrast to the previous results of this problem, the work in this paper considers the general case and removes the restrictions on the network structures and the number of reactive elements. The final results present a necessary and sufficient condition for the realizability of such an impedance as any seven‐element series‐parallel RLC network. A network synthesis example in suspension control design is presented to illustrate the results of this paper and the applications in inerter‐based mechanical control.

Designing Optimal Linear Detectors: A Bottom-Up Approach

This paper develops a systematic approach to realizing linear detectors with an optimized sensitivity, allowing for the detection of extremely weak signals. First, general constraints are derived on a specific class of input-output transfer functions of a linear detector. Then a physical realization of transfer functions in that class is found using the quantum network synthesis technique, which allows for the inference of the physical setup directly from the input-output transfer function. By exploring a minimal realization which has the minimum number of internal modes, it is shown that the optimal such detectors are internal squeezing schemes. Then, investigating nonminimal realizations, which is motivated by parity-time symmetric systems, a quantum nondemolition measurement is systematically recovered.

On minimal realization of topological Lorentz structures with one-loop seesaw extensions in A4 modular symmetry

The topological classification of one-loop Weinberg operator at dimension-5 leads to systematic categorization of one-loop neutrino mass models. All one-loop neutrino mass models must fall in one of these categories. Among these topological categories, loop extension of canonical seesaw scenarios is interesting in light of the current LHC run. Apart from one-loop contribution, these extensions result in dominant tree-level contribution to neutrino masses. The immediate remedy to obtain dominant one-loop contribution requires combination of flavor symmetries and enlarged field content. Alternatively, in this work, we propose a minimal way of realizing the topological structures with dominant one-loop contribution using modular variant of the permutation symmetries. In such a realization, no new fields are needed apart from those permitted by the topology itself. For the first time, we have realized one such topological Lorentz structure(T4-2-i) pertaining to one-loop extension of Type-II seesaw using modular A4 symmetry. Here, modular weights play an important role in suppressing tree-level terms and stabilizing the particles running in the loop(Ni , ρ and ϕ), thus, making them suitable dark matter candidates. In this work, we have explored the possibility of fermionic dark matter candidate where right-handed neutrino (N 1) is assumed to be lightest. We have, also, analyzed the compatibility of the model with neutrino oscillation data and obtained model predictions for effective Majorana mass Mee and CP violation. Furthermore, the predictions on relic density of dark matter and its direct detection considering bound on lepton flavor violating process, μ → eγ have, also, been investigated.