Definite Constraints Research Articles

Manifold Gaussian Variational Bayes on the Precision Matrix.

We propose an optimization algorithm for variational inference (VI) in complex models. Our approach relies on natural gradient updates where the variational space is a Riemann manifold. We develop an efficient algorithm for gaussian variational inference whose updates satisfy the positive definite constraint on the variational covariance matrix. Our manifold gaussian variational Bayes on the precision matrix (MGVBP) solution provides simple update rules, is straightforward to implement, and the use of the precision matrix parameterization has a significant computational advantage. Due to its black-box nature, MGVBP stands as a ready-to-use solution for VI in complex models. Over five data sets, we empirically validate our feasible approach on different statistical and econometric models, discussing its performance with respect to baseline methods.

A warm dark matter cosmogony may yield more low-mass galaxy detections in 21-cm surveys than a cold dark matter one

ABSTRACT The 21-cm spectral line widths, $w_{50}$, of galaxies are an approximate tracer of their dynamical masses, such that the dark matter halo mass function is imprinted in the number density of galaxies as a function of $w_{50}$. Correcting observed number counts for survey incompleteness at the level of accuracy needed to place competitive constraints on warm dark matter (WDM) cosmological models is very challenging, but forward-modelling the results of cosmological hydrodynamical galaxy formation simulations into observational data space is more straightforward. We take this approach to make predictions for an ALFALFA-like survey from simulations using the EAGLE galaxy formation model in both cold (CDM) and WDM cosmogonies. We find that for WDM cosmogonies more galaxies are detected at the low-$w_{50}$ end of the 21-cm velocity width function than in the CDM cosmogony, contrary to what might naïvely be expected from the suppression of power on small scales in such models. This is because low-mass galaxies form later and retain more gas in WDM cosmogonies (with EAGLE). While some shortcomings in the treatment of cold gas in the EAGLE model preclude placing definitive constraints on WDM scenarios, our analysis illustrates that near-future simulations with more accurate modelling of cold gas will likely make strong constraints possible, especially in conjunction with new 21-cm surveys such as WALLABY.

Updated Spectral Characteristics for the Ultracool Dwarf TRAPPIST-1

A comprehensive infrared spectroscopic study of star TRAPPIST-1 is a crucial step toward the detailed examination of its planets. While the presence of Earth’s atmosphere has limited the spectral extent of such a study up to now, the Near Infrared Imager and Slitless Spectrograph (NIRISS) and the Near Infrared Spectrograph instruments aboard the James Webb Space Telescope (JWST) can now yield the 0.6–5 μm spectral energy distribution (SED) of the star. Here we translate TRAPPIST-1's SED into tight constraints on its luminosity (L bol = 0.000566 ± 0.000022 L ⊙), effective temperature (T eff = 2569 ± 28 K), and metallicity ([Fe/H] = 0.052 ± 0.073) and investigate the behavior of its gravity-sensitive indices. Through band-by-band comparisons of the NIRISS and ground-based spectra, TRAPPIST-1 exhibits a blend of both field source and intermediate-gravity spectral characteristics, suggesting that the star is likely a field-age source with spectral features reminiscent of young objects. We also employ photospheric modeling incorporating theoretical and JWST spectra to constrain stellar surface heterogeneities, finding that the limited fidelity of current stellar spectral models precludes definitive constraints on the physical parameters of the distinct spectral components giving rise to TRAPPIST-1's photospheric heterogeneity and variability. In addition, we find intermodel differences in the inferences of properties (e.g., the effective temperature) over one order of magnitude larger than the instrument-driven uncertainties (∼100 K vs. ∼4 K), pointing toward a model-driven accuracy wall. Our findings call for a new generation of stellar models to support the optimal mining of JWST data and further constraining stellar—and ultimately planetary—properties.

Differentiable microstructures design via anisotropic thermal diffusion

We propose a novel method to design differentiable microstructures. Central to our algorithm is a new representation of the mapping from the parameters to microstructures, formulated as the anisotropic thermal diffusion. A metric field governs the anisotropic diffusion. The metric associated with each point is represented as a 2 × 2 symmetric positive definite matrix that becomes the design variable. To alleviate the difficulties caused by symmetric positive definite constraints, we perform the singular value decomposition of the metric matrix so that the design variable includes a rotation angle and a diagonal matrix. Then, the positive definiteness is converted to requiring the two diagonal entries of the diagonal matrix to be positive, which is easier to deal with. The effectiveness of our algorithm is demonstrated through evaluations and comparisons over various examples.

Holocene surface-rupturing paleo-earthquakes along the Kachchh Mainland Fault: shaping the seismic landscape of Kachchh, Western India

This study explores the seismotectonics of Kachchh in western India, a region with a low-to-moderate strain rate and a history of significant earthquakes, notably the 1819, Mw 7.8 Allah Bund, and the 2001, Mw 7.6 Bhuj. Despite its substantial seismic risk, comprehensive studies on Kachchh’s seismogenic sources are scarce. This is attributed to the concealed nature of active structures, hindering definitive age constraints in paleoseismological research. Our research comprises a detailed paleoseismic analysis of the north-verging, reverse Jhura Fault underlying the Jhura anticline, a segment of the Kachchh Mainland Fault. This fault segment shows evidence of surface-rupturing earthquakes in the area south of the Great Rann of Kachchh. The investigation reveals three paleoseismic events: Event I before 9.72 ka B.P., Event II between 8.63–8.20 ka B.P., and Event III between 6.20–6.09 ka B.P. The elapsed time since the last event on this fault is > 8000 years, suggesting that the area is exposed to a significant earthquake hazard. This highlights the need for more precise characterization of individual seismogenic sources for future earthquake preparedness.

Performance Degradation Estimation Mechanisms for Networked Control Systems Under DoS Attacks and its Application to Autonomous Ground Vehicle.

This article examines the mechanisms by which aperiodic denial-of-service (DoS) attacks can exploit vulnerabilities in the TCP/IP transport protocol and its three-way handshake during communication data transmission to hack and cause data loss in networked control systems (NCSs). Such data loss caused by DoS attacks can eventually lead to system performance degradation and impose network resource constraints on the system. Therefore, estimating system performance degradation is of practical importance. By formulating the problem as an ellipsoid-constrained performance error estimation (PEE) problem, we can estimate the system performance degradation caused by DoS attacks. We propose a new Lyapunov-Krasovskii function (LKF) using the fractional weight segmentation method (FWSM) to examine the sampling interval and introduce a relaxed, positive definite constraint to optimize the control algorithm. We also propose a relaxed, positive definite constraint that reduces the initial constraints to optimize the control algorithm. Next, we introduce an alternate direction algorithm (ADA) to solve the optimal trigger threshold and design an integral-based event-triggered controller (IETC) to estimate the error performance of NCSs with limited network resources. Finally, we verify the effectiveness and feasibility of the proposed method using the Simulink joint platform autonomous ground vehicle (AGV) model.

Relaxed criteria on admissibility analysis for singular Markovian jump systems with time delay

This article studies the problem of admissibility analysis for singular Markovian jump systems with time delay. Without introducing more variables, an augmented Lyapunov–Krasovskii functional (LKF) is presented, which does not require all matrices to satisfy the positive definite constraint. Inspired by free-matrix-based inequality, an improved version is proposed to obtain more accurate estimation of the integral term. Based on the novel LKF and the improved inequality, some relaxed stochastic admissibility criteria are proposed, which are less conservative. Finally, several examples are offered to verify the effectiveness of the proposed results.

Multivariate probit linear mixed models for multivariate longitudinal binary data.

When analyzing multivariate longitudinal binary data, we estimate the effects on the responses of the covariates while accounting for three types of complex correlations present in the data. These include the correlations within separate responses over time, cross-correlations between different responses at different times, and correlations between different responses at each time point. The number of parameters thus increases quadratically with the dimension of the correlation matrix, making parameter estimation difficult; the estimated correlation matrix must also meet the positive definiteness constraint. The correlation matrix may additionally be heteroscedastic; however, the matrix structure is commonly considered to be homoscedastic and constrained, such as exchangeable or autoregressive with order one. These assumptions are overly strong, resulting in skewed estimates of the covariate effects on the responses. Hence, we propose probit linear mixed models for multivariate longitudinal binary data, where the correlation matrix is estimated using hypersphere decomposition instead of the strong assumptions noted above. Simulations and real examples are used to demonstrate the proposed methods. An open source R package, BayesMGLM, is made available on GitHub at https://github.com/kuojunglee/BayesMGLM/ with full documentation to produce the results.

Fractal Architecture of the Universe Based on Primary-Centric World-View - A Post Copernican Conjecture

This paper investigates the fractal architecture of our Universe based on Primary-Centric Theoretical Formulation. Through theoretical analysis of Earth-Moon System, I arrived at the planetary satellite dynamics which was found to apply equally well to Solar and Exo-solar systems. This gave the theoretical foundation of the New Perspective of the birth and evolution of Exo-solar Systems. This was further extended to the theoretical analysis of star pairs and Neutron-Star pairs. This laid down the Primarycentric World View which I postulate as the physical process which has been shaping the evolution of the Universe and the hot-spots of the Cosmic Microwave Background Radiation right from 380,000 yrs after the Big Bang to date in top-down model resulting into Super-clusters, Clusters, Galaxies and Solar Systems. Primary-centric analysis corresponds to keplerian Analysis for negligibly small mass ratio less than 0.001. In the Copernican Framework, Kepler’s Third Law places no restriction on the orbit of the secondary component in a celestial pair. In Primary Centric Framework there is a very definite constraint on the permitted stable orbit, introduced due to periodic tidal deformations . There are two Clarke’s Orbits which are fully circularized and synchronized and hence nondissipative and equilibrium orbits called inner and outer Clarke's orbits equivalent to two geosynchronous orbits in Earth-Moon scenario. Outer Clarke’s Orbit is permissible as a stable orbit if the mass ratio of secondary to primary is greater than 0.2, Inner Clarke’s Orbit is permissible if mass ratio is less than 10-4 . If the mass ratio is between 10-4 to 0.2 then secondary spirals-out from inner Clarke’s Orbit to outer Clarke’s Orbit if it tumbles into super-synchronous orbit and spirals-in if it tumbles into sub-synchronous orbit destined to be destroyed by the primary. My conjecture states that every cosmological sub-system has a Monarch (or dominant) Primary (M_primary) Component anchoring the given sub-system and this Primary decides the stable equilibrium orbits of the secondary/secondaries. Planet-Satellite has a Planet as the M_primary, Solar System and exo-Solar Systems have a planet hosting star (PHS) as the M_primary, Galaxy has a Super-Massive Black Hole(SMBH) as the M_primary, Cluster has a cD galaxy (central dominant Galaxy) which is also known as Brightest Cluster Galaxy(BCG) as the M_primary, Super-Cluster has a massive Cluster hosting a QUASER/Blazer as the M_primary. This goes adinfinitum until a Cosmic Web is woven with Cosmic filaments. This conjecture gains a definite credence after the recent discoveries of the over-massive Black Holes in M_Galaxies namely Messier 87 in Virgo Cluster, NGC 3842 in Leo Cluster, NGC 4889 in Coma Cluster[68] and NGC 1277 in Perseus Cluster[66] which had been proposed as M_Galaxies on general considerations even before the confirmation of over-massive black holes. In 2011, a group of floating planets have been discovered. This is a transitory event and is an exception to this conjecture.

Aperiodic Sampled-Data-Based Control for T-S Fuzzy Systems: An Improved Fuzzy-Dependent Adaptive Event-Triggered Mechanism

This paper is devoted to designing a novel aperiodic sampled-data-based event-triggered control strategy for Takagi-Sugeno (T-S) fuzzy systems. Firstly, via taking the structural features of fuzzy subsystems and the available information of fuzzy membership functions (FMFs) into consideration, an improved fuzzy-dependent adaptive event-triggered mechanism (FDAETM), which designs different adaptive event-triggered mechanisms for corresponding fuzzy subsystems, is proposed to provide extra design flexibility and further optimize communication efficiency. Then, the two-side looped-functional method (TSLFM) and dynamic partitioning approach are introduced in the construction of the novel Lyapunov-Krasovskii functional (LKF). These two methods contribute to deriving preferable stability criterion and stabilization approach via relaxing the positive definite constraint on LKF and fully utilizing the inner system state during the whole aperiodic sampling interval. Eventually, two simulation examples are introduced to verify the effectiveness of the proposed control strategy and its advantages in lightening communication frequency.

Spectral decoupled correction algorithm for multi-input multi-output random vibration control

The multi-output response spectral replication correction algorithms for the multi-shaker random vibration test are investigated. In the existing matrix power correction algorithm, the control of auto and cross spectral densities is coupled which may bring some unexpected errors. The ideal spectral correction mode is that the control of auto and cross spectral densities should be independent of each other. For this purpose, a novel spectral decoupled correction algorithm is proposed with a spectral decoupling decomposition method in this work. Two lower triangular matrices are introduced to modify the auto and cross spectral densities separately during equalization procedure. Due to the positive definite constraint for the power spectral matrix, the coherence coefficient and phase difference in the cross spectral densities cannot be controlled independently when the number of the control channels is more than two. A simulation example is provided and the control results with the matrix power correction algorithm and proposed spectral decoupled correction algorithm are compared. Finally, a tri-axial shaker random vibration test is carried out and the results prove the effectiveness and feasibility of the proposed method.

Geochronology, pyrite trace elements, and in-situ S isotopes of the giant Nagengkangqie’er silver deposit in the Eastern Kunlun Orogenic Belt, Northern Tibetan Plateau

The Nagengkangqie'er (Nageng) silver deposit, situated in the Eastern Kunlun Orogenic Belt (EKOB), Northwestern China. It contains 5,070 tons of contained silver at a silver grade of 325 g/t. Nonetheless, the genesis of the Nageng silver deposit is still under debate, due to the absence of definitive constraints the mineralization age and the metal sources. The U-Pb data analysis of a post-ore calcite vein established the minimum age of the mineralization at 207 ± 3 Ma, whereas the maximum age of 217 ± 4 Ma was determined from zircon U-Pb data obtained from the altered and mineralized rhyolitic porphyry host-rock. These temporal limitations suggest that the mineralization formed at ca. 217–207 Ma, and it is associated with the post-collisional setting of the Paleo-Tethys evolution in the EKOB. The distinct textural patterns, as revealed by petrographic observations, suggest three types of pyrites: py1 is composed of euhedral pyrite in the early barren quartz vein at stage 1, py2 is represented by subhedral-anhedral grains in massive ore veins at stage 2, and py3 forms euhedral crystals of varying sizes, which are interspersed with early-formed marcasite in the quartz + calcite + silver-bearing sulfosalt-dominated veins at stage 3. In-situ δ34S values of pyrites range between −2.33 ‰ and −0.37 ‰, indicating a dominantly magmatic origin. EPMA studies have revealed that silver in the Nageng deposit predominantly occurs as silver-bearing galena at stage 2, whereas silver is enriched in sulfosalts of stage 3. From py1 to py3, a decrease in the Co-content indicates a decrease in the ore-forming fluid temperatures. The presence of stage 3 sulfide, sliver-bearing sulfosalt, and calcite-quartz in a fracture-filled vein indicates low-pressure conditions during its formation, compared to stages 1 and 2. In summary, the Nageng deposit is a typical magmatic-hydrothermal vein-type Ag-Pb-Zn deposit. Fluid cooling and decrease in pressure, coupled with decreases in fO2 and fS2, are the parameters inferred to have led to a decrease of silver solubility in the hydrothermal fluids and, successively, promoted extensive Ag deposition.

Nonfragile Memory-Based PD-Like Sampled-Data Consensus Control for Nonlinear Multiagent Systems With Time-Varying Communication Delays

In this article, the consensus problem of nonlinear multiagent systems (MASs) with time-varying communication delays (TVCDs) is addressed by proposing a novel nonfragile memory-based sampled-data control approach. Different from the existing sampled-data control schemes, an improved memory-based proportional derivative like a sampled-data control scheme based on the information of neighbors is proposed. Besides, considering the inaccuracy and perturbation of controller, a nonfragile control method is also adopted to design the controller. Then, instead of the general quadratic type of the Lyapunov–Krasovskii functional, a delay-product-type quadratic is presented by taking full advantage of the information of TVCDs, and the positive definite constraint in the entire time domain is weakened to the sampled instants on account of adopting the two-sided looped-functional approach. Furthermore, less-conservative consensus criteria for MASs are developed. By solving linear matrix inequalities, the desired control gain matrices and larger sampled-data periods are achieved. Finally, illustrative examples are employed to demonstrate the effectiveness of the designed control strategy.

An asymmetric Lyapunov–Krasovskii functional and its application to stochastic admissibility analysis of time-delay singular Markovian jump systems

This paper investigates the stochastic admissibility of time-delay singular Markovian jump systems (SMJSs). A new asymmetric Lyapunov–Krasovskii functional (LKF) is built to obtain new sufficient conditions for ensuring stochastic admissibility. The merits of our method are that we remove the positive definite constraint of some matrix variables to reduce the conservativeness. Finally, a numerical example is provided to verify the less conservativeness of our result.

Hybrid Policy Model in the Land Acquisition Decision-Making Process for Toll Road Project in West Sumatra, Indonesia

This research is related to the social phenomenon of land acquisition for toll road construction. It is necessary to enrich knowledge about policy politics, especially in the decision-making process of land acquisition policies, by involving the participation of widely affected communities (hybrid policy). The implementation of land acquisition for the Sicincin-Padang toll road construction in West Sumatra relatively encounters challenges such as issues of compensation, disputes over customary land, coordination between stakeholders, and such. The purpose of this research is to formulate a hybrid policy model for the decision-making process of land acquisition for the construction of toll roads in West Sumatra. The research approach is a mixed method, a kind of concurrent triangulation, namely two-sided research conducted simultaneously so that both sides have the same emphasis (data collection and analysis techniques). Data were collected from relevant informants and respondents from affected communities (325 respondents). Data were analyzed using a soft system methodology consisting of root definition, customers, actors, transformation, worldview, owners, and environmental constraints (CATWOE) analysis. The study results explain that the implementation of land acquisition for toll roads in Indonesia and the Sicincin-Padang section of toll roads in West Sumatra has not been optimal; there are still problems such as refusal of compensation value, road alignment issues, land acquisition administration, and coordination between the central government, local government, and the community. Furthermore, based on the above findings, a hybrid policy model for land acquisition policy (especially at the planning stage) is formulated as a novel concept that can be an alternative solution to the problem of toll road land acquisition.
 
 Received: 15 January 2023 / Accepted: 20 April 2023 / Published: 5 May 2023

A Multiple Objective Genetic Algorithm Approach for Stochastic Open Pit Production Scheduling Optimisation

ABSTRACT The conventional approach to mine planning is to use a single estimated orebody model as the basis for production scheduling. This approach, however, does not consider grade uncertainties associated with grade estimation. These uncertainties have a significant impact on the net present value (NPV) and can only be accounted for when modelled as part of the production scheduling optimisation problem. In this research, a set of equally probable simulated orebodies generated through Sequential Gaussian Simulation is used as input to a stochastic optimisation model solved with genetic algorithm (GA). Grade variability is considered as part of the stochastic model. The problem definition and resource constraints are formulated and optimised using a specially designed mining-specific GA. This GA is employed to handle partial block processing through a specialised chromosome encoding technique resulting in near-optimal solutions. Two case studies are presented which compare results from the stochastic model solved with GA (SGA) and a Stochastic Mixed Integer Linear Programming (SMILP) model solved with CPLEX. For the second case study, while the SMILP model was at an optimality gap of 101% after 28 days, the SGA model generated an NPV of $10,045 M at 10.16% optimality gap after 1.5 h.

Novel stability analysis methods for generalized neural networks with interval time-varying delay

This paper deals with the stability analysis of generalized neural networks (GNN) with interval time-varying delay, and some novel stability criteria are proposed. For the delay, more specifically, it has the upper and lower bounds but the information of its derivative is unknown (or itself is not differentiable). Firstly, a new Lyapunov-Krasovskii functional (LKF) is constructed to obtain the less conservative stability results. Then, in order to cooperate with the introduced LKF, the free-matrix-based inequality (FMBI) is employed in the estimation of the integral quadratic terms. Next, by utilizing the new negative definite conditions (NDCs) of matrix-valued cubic polynomials, the stability conditions are presented in the form of linear matrix inequalities (LMIs). In addition, in the establishment process of these conditions, no extra state variables are introduced and the positive definite constraint on the LKF is relaxed. Finally, the validity and advantages of the proposed conditions are illustrated with some classical numerical examples.

Further Stability Criteria for Sampled-Data-Based Interval Type-2 Fuzzy Systems via a Refined Two-Side Looped-Functional Method

This article investigates the stability and stabilization problem of aperiodic sampled-data nonlinear systems in the framework of interval type-2 (IT-2) fuzzy models. First, by introducing two adjustable parameters and splitting the sampling intervals into four nonuniform intervals, a refined two-side looped-functional method is constructed to fully utilize inner state information during the whole aperiodic sampling interval. Simultaneously, the positive definiteness constraint for the individual matrix in Lyapunov–Krasovskii functional can be further relaxed. Then, via constructing a novel fuzzy Lyapunov–Krasovskii functional (FLKF) together with a fuzzy-dependent-switching scheme, the available features of fuzzy membership functions (FMFs) can be further taken into consideration to increase the design flexibility. Consequently, the stability condition and corresponding controller design approach for aperiodic sampled-data IT-2 fuzzy systems can be obtained with less design conservatism and larger sampling intervals. Finally, two simulation examples are employed to demonstrate the validity and superiority of the proposed method.

Excitations in the Ordered and Paramagnetic States of Honeycomb Magnet Na_{2}Co_{2}TeO_{6}.

Na_{2}Co_{2}TeO_{6} is a proposed approximate Kitaev magnet, yet its actual magnetic interactions are elusive due to a lack of knowledge on the full excitation spectrum. Here, using inelastic neutron scattering and single crystals, we determine the system's temperature-dependent magnetic excitations over the entire Brillouin zone. Without committing to specific models, we unveil a distinct signature of the third-nearest-neighbor coupling in the spin waves, which signifies the associated distance as an emerging effective link in the ordered state. The presence of at least six nonoverlapping spin-wave branches is at odds with all models proposed to date. Above the ordering temperature, persisting dynamic correlations can be described by equal-time magnetic structure factors of a hexagonal cluster, which reveal the leading instabilities. Our result sets definitive constraints on theoretical models for Na_{2}Co_{2}TeO_{6} and provides new insight for the materialization of the Kitaev model.

A comparison of L2 and L1 speakers’ production of adverb positions in the Cardiff variety of Welsh

The grammaticality of adverb positions varies by language. Consequently, L2 and L1 speakers may differ from each other in their acquisition of adverb positions. Given that L2 Welsh speakers outnumber L1 Welsh speakers in Wales, differences in acquisition may change which adverb positions occur in contemporary Welsh. This study compares which adverb positions L2 and L1 speakers produce in the spoken data from Cardiff in the CorCenCC corpus (Knight et al., 2020) in order to identify any differences in acquisition. Comparisons of L2 and L1 English speakers find that L2 speakers consistently acquire novel adverb positions yet they frequently use ungrammatical adverb positions. They also do not acquire additional constraints on adverb positions. This study largely reinforces these findings. First, L2 Welsh speakers produce every adverb position that L1 speakers produce. Secondly, although the definiteness constraint that Borsley et al. (2009: 50) describe is not productive in the sample of Cardiff Welsh speakers, L1 speakers exhibit a heaviness constraint on V-Adv-O that L2 speakers do not. Therefore, L1 transfer neither inhibits the acquisition of adverb positions nor facilitates the acquisition of additional constraints. However, unlike L2 English speakers, L2 Welsh speakers do not produce ungrammatical adverb positions. This likely derives from the lack of transferable adverb positions between Welsh and English rather than a lack of transfer. Therefore, this sample of Cardiff Welsh reinforces the crosslinguistic consistency of L2 speakers’ acquisition of adverb positions. It also suggests that L2 Welsh speakers most likely diverge from L1 speakers in the contexts in which they use adverb positions rather than the adverb positions that they use.