Lower Bound Research Articles

Simplex slicing: An asymptotically-sharp lower bound

We show that for the regular n-simplex, the 1-codimensional central slice that's parallel to a facet will achieve the minimum area (up to a 1−o(1) factor) among all 1-codimensional central slices, thus improving the previous best known lower bound (Brzezinski 2013) by a factor of 23e≈1.27. In addition to the standard technique of interpreting geometric problems as problems about probability distributions and standard Fourier-analytic techniques, we rely on a new idea, mainly changing the contour of integration of a meromorphic function.

Auditory Steady-State Responses: Multiplexed Amplitude Modulation Frequencies to Reduce Recording Time.

This study investigated the efficiency of a multiplexed amplitude-modulated (AM) stimulus in eliciting auditory steady-state responses. The multiplexed AM stimulus was created by simultaneously modulating speech-shaped noise with three frequencies chosen to elicit different neural generators: 3.1, 40.1, and 102.1 Hz. For comparison, a single AM stimulus was created for each of these frequencies, resulting in three single AM conditions and one multiplex AM condition. Twenty-two bilaterally normal-hearing participants (18 females) listened for 8 minutes to each type of stimuli. The analysis compared the signal to noise ratios (SNRs) and amplitudes of the evoked responses to the single and multiplexed conditions. The results revealed that the SNRs elicited by single AM conditions were, on average, 1.61 dB higher than those evoked by the multiplexed AM condition ( p < 0.05). The single conditions consistently produced a significantly higher SNR when examining various stimulus durations ranging from 1 to 8 minutes. Despite these SNR differences, the frequency spectrum was very similar across and within subjects. In addition, the sensor space patterns across the scalp demonstrated similar trends between the single and multiplexed stimuli for both SNR and amplitudes. Both the single and multiplexed conditions evoked significant auditory steady-state responses within subjects. On average, the multiplexed AM stimulus took 31 minutes for the lower bound of the 95% prediction interval to cross the significance threshold across all three frequencies. In contrast, the single AM stimuli took 45 minutes and 42 seconds. These findings show that the multiplexed AM stimulus is a promising method to reduce the recording time when simultaneously obtaining information from various neural generators.

New Bounds for Quick Computation of the Lower Bound on the Gate Count of Toffoli-Based Reversible Logic Circuits

New Bounds for Quick Computation of the Lower Bound on the Gate Count of Toffoli-Based Reversible Logic Circuits

Novel flexible fixed-time stability theorem and its application to sliding mode control nonlinear systems.

For the fixed-time nonlinear system control problem, a new fixed-time stability (FxTS) theorem and an integral sliding mode surface are proposed to balance the control speed and energy consumption. We discuss the existing fixed time inequalities and set up less conservative inequalities to study the FxTS theorem. The new inequality differs from other existing inequalities in that the parameter settings are more flexible. Under different parameter settings, the exact upper bound on settling time in four cases is discussed. Based on the stability theorem, a new integral sliding mode surface and sliding mode controller are proposed. The new control algorithm is successfully applied to the fixed-time control of chaotic four-dimensional Lorenz systems and permanent magnet synchronous motor systems. By comparing the numerical simulation results of this paper's method and traditional fixed-time sliding mode control (SMC), the flexibility and superiority of the theory proposed in this paper are demonstrated. Under the same parameter settings, compared to the traditional FxTS SMC, it reduces the convergence time by 18%, and the estimated upper bound of the fixed time reduction in waiting time is 41%. In addition, changing the variable parameters can improve the convergence velocity.

On the Extremal Weighted Mostar Index of Bicyclic Graphs

Let G be a simple connected graph with edge set E(G) and vertex set V(G). The weighted Mostar index of a graph G is defined as w+Mo(G)=∑e=uv∈E(G)(dG(u)+dG(v))|nu(e)−nv(e)|, where nu(e) denotes the number of vertices closer to u than to v for an edge uv in G. In this paper, we obtain the upper bound and lower bound of the weighted Mostar index among all bicyclic graphs and characterize the corresponding extremal graphs.

Distributed predefined-time secondary control under directed networks for DC microgrids

DC microgrids (MGs) have gained significant attention due to their ability to complement renewable energy generation. In order to improve the operational stability of DC MGs, a predefined-time-based secondary controller is proposed to restore voltage drops caused by droop control and achieve current allocation among agents according to expected ratios. To conserve communication resources, the communication topology is established as a directed network. Each distributed generator (DG) receives voltage and current information from neighboring devices and uses its own current and voltage regulators to achieve control objectives. Compared to existing controllers, the convergence time upper bound of the proposed approach is independent of the initial value and can be directly adjusted as a parameter. The stability of the proposed control strategy is then verified using Lyapunov theory. Finally, hardware-in-loop test results are conducted to validate the performance of the control strategy, and its superiority is demonstrated through comparison with existing control methods.

Blanchfield pairings and Gordian distance

A lower bound of the Gordian distance is presented in terms of the Blanchfield pairing. Our approach, in particular, allows us to show at least for [Formula: see text] pairs of unoriented nontrivial prime knots with up to [Formula: see text] crossings that their Gordian distance is equal to [Formula: see text], most of which are difficult to treat otherwise.

Guaranteed cost control for a class of composite hybrid aerial/terrestrial precise manipulator with stochastic switching payloads

AbstractThis article investigates the modeling and attitude control of a class of composite hybrid aerial/terrestrial precise manipulator (Chat‐PM) with stochastic switching payloads when attaching to a vertical surface. The dynamics of the Chat‐PM for aerial locomotion are modeled by transferring the force and moment of the end‐effector to the body based on the recursive Newton–Euler equations. Furthermore, the attitude dynamics of the Chat‐PM under the wall‐attachment condition is obtained by limiting the attitude angle/angular velocity and introducing the friction torque acting on the passive wheels for the first time. Taking into consideration the complexity of the task and the stochastic nature of environmental changes, the payload attached to the end‐effector is modeled as a continuous‐time Markov process with mode‐dependent fixed sojourn time in this study. The proposed guaranteed cost controller results in the Chat‐PM capable of stably attaching to a wall under random switching loads, while guaranteeing the quadratic performance cost with an attainable upper bound. Additionally, a convex‐optimization‐based guaranteed cost controller is proposed to optimize the performance cost in the random switching part. Finally, the effectiveness of the proposed guaranteed cost controllers is demonstrated by illustrative examples.

An improved upper bound for the online graph exploration problem on unicyclic graphs

The online graph exploration problem, which was proposed by Kalyanasundaram and Pruhs (Theor Comput Sci 130(1):125–138, 1994), is defined as follows: Given an edge-weighted undirected connected graph and a specified vertex (called the origin), the task of an algorithm is to compute a path from the origin to the origin which contains all the vertices of the given graph. The goal of the problem is to find such a path of minimum weight. At each time, an online algorithm knows only the weights of edges each of which consists of visited vertices or vertices adjacent to visited vertices. Fritsch (Inform Process Lett 168:1006096, 2021) showed that the competitive ratio of an online algorithm is at most three for any unicyclic graph. On the other hand, Brandt et al. (Theor Comput Sci 839:176–185, 2020) showed a lower bound of two on the competitive ratio for any unicyclic graph. In this paper, we showed the competitive ratio of an online algorithm is at most 5/2 for any unicyclic graph.

Certifiable Lower Bounds of Wigner Negativity Volume and Non-Gaussian Entanglement with Conditional Displacement Gates

Certifiable Lower Bounds of Wigner Negativity Volume and Non-Gaussian Entanglement with Conditional Displacement Gates

On one-sided testing affine subspaces

We study the query complexity of one-sided ϵ-testing the class of Boolean functions f:Fn→{0,1} that describe affine subspaces and Boolean functions that describe axis-parallel affine subspaces, where F is any finite field. We give polynomial-time ϵ-testers that ask O˜(1/ϵ) queries. This improves the query complexity O˜(|F|/ϵ) in [14]. The almost optimality of the algorithms follows from the lower bound of Ω(1/ϵ) for the query complexity proved by Bshouty and Goldreich [3].We then show that any one-sided ϵ-tester with proximity parameter ϵ<1/|F|d for the class of Boolean functions that describe (n−d)-dimensional affine subspaces and Boolean functions that describe axis-parallel (n−d)-dimensional affine subspaces must make at least Ω(1/ϵ+|F|d−1log⁡n) and Ω(1/ϵ+|F|d−1n) queries, respectively. This improves the lower bound Ω(log⁡n/log⁡log⁡n) that is proved in [14] for F=GF(2). We also give testers for those classes with query complexity that almost match the lower bounds.1

Finite-Time Disturbance Observer-Based Adaptive Course Control for Surface Ships

In this paper, a finite-time disturbance observer-based adaptive control strategy is proposed for the ship course control system subject to input saturation and external disturbances. Based on the Gaussian error function, a smooth saturation model is designed to avoid the input saturation of the system and reduce steering engine vibrations, and an auxiliary dynamic system is introduced to compensate for the effect of the rudder angle input inconsistency on the system. By constructing an auxiliary dynamic, a finite-time disturbance observer is designed to approximate the external disturbance of the system; an adaptive updating law is also constructed to estimate the upper bound of the derivative of the external disturbance. Combining the finite-time disturbance observer with the auxiliary dynamic system, a novel adaptive ship course control law is proposed by using the hyperbolic tangent function. Moreover, according to LaSalle’s Invariance Principle, a system stability analysis method with loose stability conditions and easy realizations is designed, while the stability of the closed-loop system and the ultimately uniformly boundedness of all its signals are proven. Finally, the course control simulation analysis of a surface ship is carried out. The results show that the proposed control law has a strong resistance to external disturbances and a strong non-fragility to system parameter perturbations, which ensure that the course control system has great control performance.

Molecular Docking of Gamma Amino Butyric Acid GABA on Rattus Norvegicus B-receptor as Antidiabetic

Earlier research reported that GABA had a correlation with diabetes in processes of glucose homeostasis. This study aims to identify the validity of B-receptor Rattus norvegicus as GABA protein target, modeling the structure and knowing the binding affinity between GABA and B-receptor Rattus norvegicus through molecular docking. The research was carried out using in-silico method. The interaction of GABA with the target protein was determined using SuperPred, followed by modeling the protein target using SwissadMe. Ramachandran Plot and Errat Procheck are used to determine the validity of the protein target. Molecular docking was determined using Pyrx and PyMol. The results showed that GABA binding to the B- receptor Rattus norvegicus has biological activity as glucose oxidase inhibitor and antidiabetic. The conclusion are: B-receptor Rattus norvegicus is a valid protein target for binding to GABA; there are four 3-dimensional models of B-receptor Rattus norvegicus and the best model has 98.43% sequence identity; the binding affinity of GABA (ligand) on B-receptor Rattus norvegicus from the best model is -3.4 kcal/mol energy, 1.773 RMSD lower bound, and 1.81 RMSD upper bound. It is suggested that this research might be used as an empirical basis to further investigate GABA as antidiabetic.

Pauli-type coupling of spinors and curved spacetime

Abstract In this study we prove that the Pauli interaction---which is associated with a length parameter---emerges when the minimal coupling recipe is applied to the non-degenerate Dirac Lagrangian.&amp;#xD;The conventional Dirac Lagrangian is rendered non-degenerate if supplemented by a particular term quadratic in the derivatives of the spinors.&amp;#xD;For dimensional reasons, this non-degenerate Dirac Lagrangian is associated with a length parameter $\ell$.&amp;#xD;It yields---just as the conventional degenerate Dirac Lagrangian---the standard free Dirac equation in Minkowski space as the $\ell$ terms cancel when setting up the Euler-Lagrange equations.&amp;#xD;However, if the Dirac spinor is minimally coupled to gauge fields, then the length parameter~$\ell$ becomes a physical coupling constant yielding novel interactions.&amp;#xD;For the U($1$) symmetry the Pauli coupling of fermions to electromagnetic fields arises, modifying the fermion's magnetic moment.&amp;#xD;We discuss the impact of these findings on electrodynamics, and estimate the upper bound of the length parameter~$\ell$ from the yet existing discrepancy between the (SM) theory and measurement of the anomalous magnetic moment of light leptons.&amp;#xD;This, and also recent studies of the renormalization theory, suggest that the Pauli coupling of leptons to the electromagnetic field is a necessary ingredient in QED, supporting the notion of a fundamental nature of the non-degenerate Dirac Lagrangian.&amp;#xD;&amp;#xD;In a second step we then investigate how analogous ``Pauli-type'' couplings of gravity and matter arise if fermions are embedded in curved spacetime.&amp;#xD;The diffeomorphism and Lorentz invariance of that system leads to an anomalous spin-torsion interaction and a curvature-dependent mass correction.&amp;#xD;We calculate the mass correction in the De~Sitter geometry of vacuum with the cosmological constant $\Lambda$.&amp;#xD;Possible implications for the existence of effective non-zero rest masses of neutrinos are addressed.&amp;#xD;Finally, an outlook on the impact of mass correction on the physics of ``Big Bang'' cosmology, black holes, and of neutron stars is provided.

Preparation of KH560‐UiO‐66‐NH2/Pebax mixed matrix membranes and CO2 separation

AbstractMetal–organic frame UiO‐66‐NH2 was modified by 3‐glycidyl ether oxypropyl trimethoxysilane (KH560), and KH560‐UiO‐66‐NH2 was synthetized and added to Pebax to prepare KH560‐UiO‐66‐NH2/Pebax mixed matrix membranes (MMMs). The epoxy group of KH560 had an amine‐epoxidation reaction with the NH2 in UiO‐66‐NH2, which prevented UiO‐66‐NH2 from agglutinating in the MMMs. In addition, the NH bond and OH bond of KH560‐UiO‐66‐NH2 could theoretically form hydrogen bonds with CO and NH bonds in the main chain of polymerization, respectively, so as to improve the interfacial compatibility between fillers and polymers. The structure and properties of the filler particles and MMMs were evaluated by Fourier transform infrared spectrometer, x‐ray diffraction, scanning electron microscopy, and thermogravimetric analyzer. The results showed that the filler particles were successfully synthesized, and had good crystallinity, uniform size distribution, and good thermal stability. The inorganic and organic interfaces of MMMs had no obvious interface defects. The obtained KH560‐UiO‐66‐NH2/Pebax MMMs showed CO2 permeability of 111.52 Barre and CO2/N2 selectivity of 92.16, which were 85.65% and 88.73% higher than that of pristine membranes, respectively. The gas separation performance of MMMs was significantly improved, exceeding the upper bound of 2008 Robeson.

Adaptive Kriging-Based Heat Production Performance Optimization for a Two-Horizontal-Well Geothermal System

Optimizing heat generation capacity is crucial for geothermal system design and evaluation. Computer simulation is a valuable approach for determining the influence of various parameter combinations on a geothermal system’s ability to produce heat. However, computer simulation evaluations are often computationally demanding since all potential parameter combinations must be examined, posing significant hurdles for heat generation performance evaluation and optimization. This research proposes an adaptive Kriging-based heat generation performance optimization method. Firstly, a two-horizontal-well geothermal system with rectangular multi-parallel fractures is constructed. The heat production performance optimization problem is then established, and the temperature and enthalpy of the outlet water are calculated using computer simulation and Kriging. A parameterized lower confidence bounding sampling scheme (PLCB) is developed to adaptively update Kriging in order to strike a compromise between optimization accuracy and computation burden. The outcomes of the optimization are compared to those of the Kriging-based optimization approach and other common infill options to demonstrate the efficiency of the proposed method. The outlet temperature curve obtained with PLCB-AKO-1 rose for a longer time and the heat generation power curve reached a stable output without a downward trend. According to the Friedman and Wilcoxon signed ranks tests, the PLCB-1-AKO technique is statistically superior to alternative strategies.

Fixed-time consensus of leader-following multi-agent systems subject to failed follower: Reconstructed topology approach

This paper considers fixed-time leader-following consensus of multi-agent systems subject to failed follower. Firstly, the issue is addressed for the system without failed follower, and an upper bound of the fixed-time, which is not affected by initial states, is derived. If a follower fails, it will lose the communication ability in the topology and impede its neighbors from obtaining the information regarding the failed follower. If its neighbors continue to use the last state of the failed follower, the remaining agents may be unable to achieve consensus. For such issue, the topology is reconstructed by removing the failed follower and reconnecting the neighbors of the failed follower to the remaining agents according to the position in topology. In sequel, fixed-time leader-following consensus is concerned applying reconstructed topology approach. Finally, theoretical results are verified by numerical simulations considering the cases with and without failed follower.

State‐dependent dynamic tube MPC: A novel tube MPC method with a fuzzy model of model of disturbances

AbstractMost real‐world systems are affected by external disturbances, which may be impossible or costly to measure. For instance, when autonomous robots move in dusty environments, the perception of their sensors is disturbed. Moreover, uneven terrains can cause ground robots to deviate from their planned trajectories. Thus, learning the external disturbances and incorporating this knowledge into the future predictions in decision‐making can significantly contribute to improved performance. Our core idea is to learn the external disturbances that vary with the states of the system, and to incorporate this knowledge into a novel formulation for robust tube model predictive control (TMPC). Robust TMPC provides robustness to bounded disturbances considering the known (fixed) upper bound of the disturbances, but it does not consider the dynamics of the disturbances. This can lead to highly conservative solutions. We propose a new dynamic version of robust TMPC (with proven robust stability), called state‐dependent dynamic TMPC (SDD‐TMPC), which incorporates the dynamics of the disturbances into the decision‐making of TMPC. In order to learn the dynamics of the disturbances as a function of the system states, a fuzzy model is proposed. We compare the performance of SDD‐TMPC, MPC, and TMPC via simulations, in designed search‐and‐rescue scenarios. The results show that, while remaining robust to bounded external disturbances, SDD‐TMPC generates less conservative solutions and remains feasible in more cases, compared to TMPC.

Optimal Local Identifying and Local Locating-dominating Codes

We introduce two new classes of covering codes in graphs for every positive integer r. These new codes are called local r-identifying and local r-locating-dominating codes and they are derived from r-identifying and r-locating-dominating codes, respectively. We study the sizes of optimal local 1-identifying codes in binary hypercubes. We obtain lower and upper bounds that are asymptotically tight. Together the bounds show that the cost of changing covering codes into local 1-identifying codes is negligible. For some small n optimal constructions are obtained. Moreover, the upper bound is obtained by a linear code construction. Also, we study the densities of optimal local 1-identifying codes and local 1-locating-dominating codes in the infinite square grid, the hexagonal grid, the triangular grid and the king grid. We prove that seven out of eight of our constructions have optimal densities.

Deviation analysis in transient response of fractional-order systems: An elementary function-based lower bound

In this paper, transient response of commensurate fractional-order systems with non-zero initial conditions is investigated in the viewpoint of the existence of deviation from initial condition. In particular, firstly peak effect for a class of linear fractional order systems is inspected by presenting a lower bound for their responses. Such a lower bound is described by an elementary function, where the commensurate order of the system is considered as a rational number. Furthermore, it has been demonstrated that under particular circumstances the derived lower bound can be extended to apply for deviation analysis in response of a class of fractional-order nonlinear systems. Moreover, included are various illustrative examples intended to assess the applicability of the obtained lower bound in prediction of the deviation value and the time instance at which the peak effect occurs.