Lower Bound Research Articles

Deterministic One-Way Simulation of Two-Way Deterministic Finite Automata Over Small Alphabets

It is shown that a two-way deterministic finite automaton (2DFA) with [Formula: see text] states over an alphabet [Formula: see text] can be transformed to an equivalent one-way automaton (1DFA) with [Formula: see text] states, where [Formula: see text]. This reflects the fact that, by keeping the last processed symbol [Formula: see text] in memory, the simulating 1DFA can remember one of [Formula: see text] states in which the automaton moves by [Formula: see text] to the right, and a function that maps [Formula: see text] states moving to the left to [Formula: see text] states moving to the right; cf. ca. [Formula: see text] functions in the classical construction. A close lower bound of [Formula: see text] states is established using a 2-symbol alphabet, with witness languages defined by direction-determinate 2DFA. The same lower bound is also achieved with witness languages defined by sweeping 2DFA, at the expense of using a 5-symbol alphabet. In addition, the complexity of transforming a sweeping or a direction-determinate 2DFA to a 1DFA is shown to be exactly [Formula: see text].

Machine Learning-Enhanced Probabilistic Validation Techniques with Minimal Data Exposure in Distributed Systems

This article studies the distributed state estimation issue for complex networks with nonlinear uncertainty. The extended state approach is used to deal with the nonlinear uncertainty. The distributed state predictor is designed based on the extended state system model, and the distributed state estimator is designed by using the measurement of the corresponding node. The prediction error and the estimation error are derived. The prediction error covariance (PEC) is obtained in terms of the recursive Riccati equation, and the upper bound of the PEC is minimized by designing an optimal estimator gain. With the vectorization approach, a sufficient condition concerning stability of the upper bound is developed. Finally, a numerical example is presented to illustrate the effectiveness of the designed extended state estimator.

Computing sparse Fourier sum of squares on finite abelian groups in quasi-linear time

The problem of verifying the nonnegativity of a function on a finite abelian group is a long-standing challenging problem. The basic representation theory of finite groups indicates that a function f on a finite abelian group G can be written as a linear combination of characters of irreducible representations of G by f(x)=∑χ∈Gˆfˆ(χ)χ(x), where Gˆ is the dual group of G consisting of all characters of G and fˆ(χ) is the Fourier coefficient of f at χ∈Gˆ. In this paper, we show that by performing the fast (inverse) Fourier transform, we are able to compute a sparse Fourier sum of squares (FSOS) certificate of f on a finite abelian group G with complexity that is quasi-linear in the order of G and polynomial in the FSOS sparsity of f. Moreover, for a nonnegative function f on a finite abelian group G and a subset S⊆Gˆ, we give a lower bound of the constant M such that f+M admits an FSOS supported on S. We demonstrate the efficiency of the proposed algorithm by numerical experiments on various abelian groups of orders up to 107. As applications, we also solve some combinatorial optimization problems and the sum of Hermitian squares (SOHS) problem by sparse FSOS.

A generalized uniform placement of alters on spherical surface (U-PASS) for visualizing general weighted networks

Network visualization is an important tool for extracting information from the structure and configuration of a network, especially when the network includes weighted edges and nodes with attribute information. Previous studies have demonstrated an effective visualization method that projects the network onto a spherical surface. In this work, we extend this method, known as Uniform Placement of Alters on Spherical Surface (U-PASS), to general weighted networks. This extension enables the uniform distribution of network nodes across multiple layers of concentric spheres. In addition, we discuss the lower bound of a criterion called generalized spherical cap discrepancy, which is used to evaluate the uniformity of node distribution on a collapsed spherical surface.

Time-varying characteristics analysis of bridge under moving vehicle using a modified time-frequency method with limited sensors

Investigating the bridge dynamic characteristics under operational traffic load is critical for bridge health monitoring. As vehicles traverse the bridge, the bridge frequencies present time-varying characteristics owing to the effect of vehicle-bridge dynamic interaction. The recently introduced variational nonlinear chirp mode decomposition (VNCMD) demonstrates significant benefits in identifying structural instantaneous frequencies (IFs) from the measured responses. However, its practical application is limited by the requirement for artificially setting priori parameters (i.e., upper bound of noise level and number of modal components). In this study, a modified VNCMD (MVNCMD) is proposed to overcome this limitation and is employed to identify the IFs of the bridge under moving vehicle using single sensor data. First, by modifying the optimization function, the proposed MVNCMD adopts a novel algorithm framework that eliminates the necessity for presetting the upper bound of noise level. An autoregressive spectrum-based method is then introduced to preset the number of modal components. The proposed MVNCMD is evaluated using a synthetic non-stationary signal, demonstrating its effectiveness in identifying IFs and overcoming the limitations of the original VNCMD. Furthermore, the numerical simulation involving different parameter analysis and laboratory experiments of the coupled vehicle-bridge system are conducted to validate the effectiveness of the proposed method. It is to be shown that the proposed MVNCMD method is capable of identifying the IFs of the bridge under moving vehicle using single sensor data and outperforms other time-frequency methods in terms of identification accuracy, which provides a robust tool for analyzing the time-varying characteristics of the vehicle-bridge interaction system.

Fixed‐time prescribed performance control method for nonlinear systems with unknown time‐varying parameters

AbstractIn this study, it is considered that the question of adaptive tracking control of nonlinear systems containing unknown time‐varying parameters. To optimize the control effect, a fixed‐time control strategy is adopted, in which the upper bound of the settling time is connected with the designed parameters, but not to the initial conditions. In the design, the unknown time‐varying parameters are treated as the multiplication of known and unknown vectors, and the adaptive laws are constructed to estimate the mean value of the components in the unknown ones, which availably solve the difficulty of unknown control gains. Besides, the application of command filtered technique, which combined with the compensation signals containing the adaptive parameters, effectively avoids the “complexity explosion” problem. Further, Lyapunov stability theory verifies that the tracking error can always be kept within the boundaries of the performance functions, and converges to a designated neighbourhood of the origin within a fixed time, beyond that all signals of the closed‐loop system are bounded. Finally, the simulation results prove the effectiveness of the proposed control scheme.

Cardiovascular safety of pimitespib in patients with advanced solid tumors: An open-label, nonrandomized, phase 1 study.

Pimitespib (TAS-116), a first-in-class, oral, selective heat-shock protein 90 inhibitor, is approved as fourth-line treatment for gastrointestinal stromal tumors in Japan. This phase 1 study evaluated the cardiac safety of pimitespib. In this open-label, nonrandomized, multicenter study, Japanese patients (aged ≥20 years) with refractory, advanced solid tumors received placebo on day -1, then pimitespib 160 mg daily on days 1-5 of the cardiac safety evaluation period. Electrocardiograms were conducted at baseline, and on days -2, -1, 1, and 5; and blood samples were collected on days 1 and 5. Patients then received once-daily pimitespib for 5 days every 3 weeks. The primary end point was the time-matched difference in QT interval corrected for heart rate using the Fridericia correction (QTcF) between pimitespib and placebo. Pharmacokinetics, safety, and preliminary efficacy were also assessed. Of the 22 patients in the cardiac safety-evaluable population, no clinically relevant QTc prolongation was observed; the upper bound of the one-sided 95% confidence interval for the time-matched difference in change from baseline in QTcF was <20 msec at all time points on days 1 and 5. Pimitespib pharmacokinetic parameters were consistent with previous data, and the time-matched difference in change from baseline in QTcF showed no marked increase as plasma concentrations increased. The safety profile was acceptable; 40% of patients experienced grade 3 or greater adverse drug reactions, mostly diarrhea (20%). The median progression-free survival was 3.1 months. In Japanese patients with refractory, advanced solid tumors, pimitespib was not associated with clinically relevant QTc prolongation, and there were no cardiovascular safety concerns. Pimitespib is a new anticancer drug that is being used to treat cancer in the stomach or intestines (gastrointestinal stromal tumors). This study demonstrated that pimitespib had no marked effect on heart rhythm or negative effects on the heart or blood vessels and had promising anticancer effects in Japanese patients with advanced solid tumors who were unable to tolerate or benefit from standard treatment.

The error bounds of Gaussian quadratures for one rational modification of Chebyshev measures

Abstract For an analytic integrand, the error term in the Gaussian quadrature can be represented as a contour integral, where the contour is commonly taken to be an ellipse. Thus, finding its upper bound can be reduced to finding the maximum of the modulus of the kernel on the ellipse. The location of this maximum was investigated in many special cases, particularly, for the Gaussian quadrature with respect to the Chebyshev measures modified by a quadratic divisor (known as the Bernstein–Szeg̋ measures). Here, for the Gaussian quadratures with respect to the Chebyshev measures modified by a linear over linear rational factor, we examine the kernel and describe sufficient conditions for the maximum to occur on the real axis. Furthermore, an assessment of the kernel is made in each case, since in some cases the true maximum is hard to reach. Hence, we derive the error bounds for these quadrature formulas. The results are illustrated by the numerical examples. An alternative approach for estimating the error of the Gaussian quadrature with respect to the same measure can be found in [Djukić, D. L., Djukić, R. M. M., Reichel, L. &amp; Spalević, M. M. (2023, Weighted averaged Gaussian quadrature rules for modified Chebyshev measure. Appl. Numer. Math., ISSN 0168-9274)].

A new bound for the orthogonality defect of HKZ reduced lattices

Hermite–Korkin–Zolotarev (HKZ) reduction is an important notion of lattice reduction which plays a significant role in number theory (particularly the geometry of numbers), and more recently in coding theory and post-quantum cryptography. In this work, we determine a sharp upper bound on the orthogonality defect of HKZ reduced bases up to dimension 3. Using this result, we determine a general upper bound for the orthogonality defect of HKZ reduced bases of arbitrary rank. This upper bound is sharper than existing bounds in literature, such as the one determined by Lagarias, Lenstra and Schnorr [3].

The picker routing problem in mixed-shelves, multi-block warehouses

Unlike conventional warehouses, where the inventory of an item is concentrated on a single shelf, the inventory in mixed-shelves warehouses is broken down into units and dispersed throughout the warehouse. As a result, the locations from where items are to be retrieved must be chosen when designing the picker tour. The rare research on the picker routing problem (PRP) in mixed-shelves warehouses focuses on (and heavily exploits the properties of) 1-block warehouses, which are warehouses with only two cross aisles. Here, we tackle the more general PRP in mixed-shelves, multi-block warehouses. To solve the problem, we propose a logic-based Benders decomposition method whereby the master problem selects the locations from where each item is retrieved and the subproblem designs the associated picker tour. We introduce tailored optimality cuts and prove their validity. In addition, we propose a set of various techniques to enhance the performance of the logic-based Benders decomposition, including a lower bounding function and valid inequalities. We show the efficiency and effectiveness of the proposed method through extensive computational experiments carried out on both standard instances from the literature (for the 1-block setting) and newly generated instances (for our case). We also leverage our algorithms to generate managerial insights into the benefits of multi-block layouts and mixed-shelves policies in warehousing.

Distributed Independent Sets in Interval and Segment Intersection Graphs

The Maximum Independent Set problem is well-studied in graph theory and related areas. An independent set of a graph is a subset of non-adjacent vertices of the graph. A maximum independent set is an independent set of maximum size. This paper studies the Maximum Independent Set problem in some classes of geometric intersection graphs in a distributed setting. More precisely, we study the Maximum Independent Set problem on two geometric intersection graphs, interval and axis-parallel segment intersection graphs, and present deterministic distributed algorithms in a model that is similar but a little weaker than the local communication model. We compute the maximum independent set on interval graphs in [Formula: see text] rounds and [Formula: see text] messages, where [Formula: see text] is the size of the maximum independent set and [Formula: see text] is the number of nodes in the graph. We provide a matching lower bound of [Formula: see text] on the number of rounds, whereas [Formula: see text] is a trivial lower bound on message complexity. Thus, our algorithm is both time and message-optimal. We also study the Maximum Independent Set problem in interval count [Formula: see text] graphs, a special case of the interval graphs where the intervals have exactly [Formula: see text] different lengths. We propose an [Formula: see text]-approximation algorithm that runs in [Formula: see text] round. For axis-parallel segment intersection graphs, we design an [Formula: see text]-approximation algorithm that obtains a solution in [Formula: see text] rounds. The results in this paper extend the results of Molla et al. [J. Parallel Distrib. Comput. 2019].

A novel branch‐and‐bound algorithm for solving linear multiplicative programming problems

AbstractThis article proposes a rectangular branch‐and‐bound algorithm for solving linear multiplication problems (LMP) globally. In order to obtain a reliable lower bound of the original problem, this article designs a novel linear relaxation programming problem (LRP) that has not been seen in the existing literature. Based on the basic framework of the rectangular branch and bound algorithm, this article proposes an algorithm that can obtain a global solution. According to the structure of linear relaxation programming, the article designs a region reduction technology to improve the efficiency of the algorithm. This article also provides convergence analysis to ensure the reliability of the algorithm. Finally, several numerical experiments are used to demonstrate the effectiveness and robustness of the algorithm.

Specific target pinning control of complex dynamical networks based on semidefinite programming strategy

Pinning control of complex networks aims to force the states of all nodes to reach the desired goal by controlling a few nodes in the network. The easiness of a pinning strategy can be measured by the minimum eigenvalue λ1 of the specific matrix L+Γ, where L is the Laplacian matrix of the underlying network and Γ is a diagonal matrix with Γi,i=1 if node i is pinned. A larger value λ1 indicates a smaller coupling strength. We here are interested in two key questions on this issue. The first one is, what is the minimum number of pinned nodes to achieve system synchronization when individual node dynamics and the coupling strength of the network are given? We show an upper bound of the minimum eigenvalue λ1, by which a lower bound of the number of pinned nodes is presented. The second one is, which nodes should be pinned such that the system achieves synchronization much easier if a potential pinning target node set S0 (instead of the whole node set) and the number of pinned nodes l (l<|S0| ) are both restricted beforehand? This specific target pinning control problem is raised for the first time. By transforming it into a semi-definite programming problem, we then use a convex optimization tool to solve this problem. Experimental results show that the strategy is more effective than other classical node selection indices.

Optimizing environmental costs and economic benefits in new energy vehicle production: A case study of FAW Hongqi in China

This study focuses on the environmental cost accounting and economic benefit optimization of China’s FAW Hongqi New Energy Vehicle manufacturing enterprise under uncertain conditions, within the context of the emission permit system This study calculates the pollution situation throughout the manufacturing and production process of FAW Hongqi new energy vehicles, and constructs a multi-level environmental cost evaluation system for FAW Hongqi new energy vehicle manufacturing projects. Through the interval fuzzy model of FAW Hongqi new energy vehicle manufacturing projects, the maximum economic benefits of the enterprise are simulated. The research results indicate that the pollution emissions of enterprises are mainly concentrated in the three processes of welding, painting, and final assembly. Enterprises use their own exhaust gas and wastewater treatment devices to meet the standards for pollution emissions. At the same time, solid waste generated during the automobile manufacturing process is handed over to third-party companies for treatment. Secondly, based on the accounting results of enterprise pollution source intensity and a multi-layer environmental cost evaluation system, the environmental costs of enterprises are accounted for, and the environmental costs are represented in interval form to reduce uncertainty in the accounting process. According to the accounting results of enterprise environmental costs, the main environmental costs of enterprises are environmental remediation costs caused by normal pollution discharge and purchase costs of environmental protection facilities. Pollutant emission taxes and routine environmental monitoring costs are relatively low. Enterprises can adopt more scientific solutions from the aspects of environmental remediation and environmental protection facilities to reduce environmental costs. After optimization by the fuzzy interval uncertainty optimization model, the economic benefits of the FAW Hongqi new energy vehicle manufacturing project were [101,254.71, 6278.5413] million yuan. Compared with the interval uncertainty optimization model, the lower bound of economic benefits increased by 57.68%, and the upper bound decreased by 12.08%, shortening the results of the economic benefits interval. Clarify the current environmental pollution situation of FAW Hongqi’s new energy vehicle manufacturing enterprise, provide data support for sustainable development of the enterprise, and provide reasonable decision-making space for enterprise decision-makers.

A sharper bound of the Hotelling–Solomons inequality

AbstractThe original Hotelling–Solomons inequality states that an upper bound of the absolute difference between the mean and median, standardised by the standard deviation, is 1. However, in this paper, we introduce a new bound that depends on the sample size, which is strictly smaller than 1.

Adaptive second-order backstepping control for a class of 2DoF underactuated systems with input saturation and uncertain disturbances

An adaptive second-order backstepping control algorithm is proposed for a kind of two degrees of freedom (2DoF) underactuated systems. The system dynamics is transformed into a nonlinear feedback cascade system with an improved global change of coordinates. Fully taking the cascade structure into consideration and in order to simplify the design process, each step in the backstepping process is designed for a second-order subsystem. Two neural networks are applied to approximate system unknown functions and two adaptive laws are designed to estimate the upper bound of the sum of approximation error and external disturbances. To overcome the explosion problem of complexity, a second-order filter is applied to produce the virtual control and its second-order derivative that is needed in the next backstepping step. Two auxiliary dynamic systems are proposed and integrated into the backstepping process to eliminate the effects of filtering error and input saturation. The system stability is analyzed by the Lyapunov stability theory and verified by numerical simulations with two 2DoF benchmark underactuated systems: the translational oscillator with a rotational actuator (TORA) and the inertial wheel pendulum (IWP).

Salbutamol, a Short Acting Beta-2 Agonist, Reduces Risk and Improves Prognosis of Prostate Cancer.

Beta-blockers, a class of drugs commonly used to manage blood pressure, have been the subject of research regarding their relationship to prostate cancer (PC) risk, prognosis, and treatment. Beta-blockers reduce risk and improve the prognosis of PC. Perioperative use of a nonselective beta-blocker improves outcomes after radical prostatectomy. However, a related class of drugs, beta-2 adrenergic agonists, has received little attention in PC. We studied the relationship of the beta-2 adrenergic agonist salbutamol to PC risk and survival. We analyzed Food and Drug Administration MedWatch data to determine whether salbutamol could influence the risk of PC. We used UK Biobank data to assess the effect of salbutamol on PC survival. Salbutamol significantly reduces PC risk, proportional reporting ratio, and 95% CI (lower bound; upper bound): 0.131 (0.11; 0.155) and improves prognosis. Mean survival was 7.35 years for subjects not taking salbutamol, and 10.5 years for subjects taking salbutamol (P = 0.041, log-rank test. To adjust for the effect of age, we performed proportional hazards regression, survival time-dependent variable, age, and salbutamol use independent variables. Salbutamol use was significantly related to survival time (P = 0.016) and independent of the significant effect of age (P < 0.001). We found a lower proportion of PCs in salbutamol-treated people, but we have not demonstrated that PC risk is reduced (there is no proof of causality). There is no causality relationship between salbutamol and the survival of patients with PC treated with salbutamol versus those not treated with the drug. Yet, there is a trend in favor of salbutamol-treated patient survival. Therefore, salbutamol and other beta-adrenergic agonists might represent a new class of drugs for the treatment of PC.

Ad Hoc Broadcast, Trace, and Revoke

Traitor tracing schemes [Chor–Fiat–Naor, Crypto ’94] help content distributors fight against piracy and are defined with the content distributor as a trusted authority having access to the secret keys of all users. While the traditional model caters well to its original motivation, its centralized nature makes it unsuitable for many scenarios. For usage among mutually untrusted parties, a notion of *ad hoc* traitor tracing (naturally with the capability of broadcast and revocation) is proposed and studied in this work. Such a scheme allows users in the system to generate their own public/secret key pairs, without trusting any other entity. To encrypt, a list of public keys is used to identify the set of recipients, and decryption is possible with a secret key for any of the public keys in the list. In addition, there is a tracing algorithm that given a list of recipients’ public keys and a pirate decoder capable of decrypting ciphertexts encrypted to them, identifies at least one recipient whose secret key must have been used to construct the said decoder. Two constructions are presented. The first is based on functional encryption for circuits (conceptually, obfuscation) and has constant-size ciphertext, yet its decryption time is linear in the number of recipients. The second is a generic transformation that reduces decryption time at the cost of increased ciphertext size. A matching lower bound on the trade-off between ciphertext size and decryption time is shown, indicating that the two constructions achieve all possible optimal trade-offs, i.e., they fully demonstrate the Pareto front of efficiency. The lower bound also applies to broadcast encryption (hence all mildly expressive attribute-based encryption schemes) and is of independent interest.

The lower bound of weighted representation function

The lower bound of weighted representation function

Effect of strain on the photoelectric properties of molybdenum ditelluride under vacancy defects: a DFT investigation.

This study explores the impact of deformation on the electrical and optical characteristics of monolayer cadmium telluride (MoTe2) with vacancies, using the foundational principles of density functional theory. It was discovered that both strain and imperfections alter the electrical characteristics of monolayer MoTe2. Under VTe-MoTe2, a direct-to-indirect band-gap transition occurs. In DTe-MoTe2, the band-gap value reduces dramatically, the conduction band changes downward, and the carrier concentration rises. The DVTe-induced band gap state is closer to the Fermi energy level than the VTe-induced band gap state. In this paper, DTe-MoTe2 is chosen for tensile deformation. The results show that the band-gap value tends to decrease by increasing tensile deformation. When the stretching value reaches 10%, the lower bound of the conduction band and the top of the valence band overlap, and the system is converted from a semiconductor to a metal. Considering the density of states, the missing state MoTe2 is mainly contributed by the participation of Te-s, Te-p, and Mo-d orbitals. In terms of optical qualities, the absorption and reflection peaks are red-shifted and blue-shifted, respectively. It is hoped that these effects on the optoelectronic properties will be widely applied. In this study, we utilize the generalized gradient approximation plane-wave pseudopotential method, incorporating Perdew-Burke Ernzerhof (PBE) generalized functions and following the fundamental principles of the density functional theory framework. A 3 × 3 × 1 supercell was constructed as an undoped model based on a MoTe2 monolayer, which consists of 9 Mo atoms and 18 Te atoms. The vacuum flat plate was set to 15Å along the z-direction to avoid interactions between the monolayers. For electronic structure calculations, the energy cutoff was set to 450eV. Each model's computational process and structural optimization were carried out using the Monkhorst-Pack specialized K-point sampling approach. Crystal optimization computations used a 3 × 3 × 1 Monkhorst-Pack K-point grid for molybdenum ditelluride monolayers and a 9 × 9 × 1K-point grid for electronic system analysis, analyzing state density and optical characteristics, respectively. For the structural optimization, the convergence requirements for maximum force, maximum atom displacement, maximum stress, and energy change were defined at 0.03eV/Å, 0.001Å, 0.05 Gpa, and 1.0 × 10-5eV/atom, respectively.