Lower Bound Research Articles

Contextual Dynamic Pricing with Strategic Buyers

Personalized pricing, which involves tailoring prices based on individual characteristics, is commonly used by firms to implement a consumer-specific pricing policy. In this process, buyers can also strategically manipulate their feature data to obtain a lower price, incurring certain manipulation costs. Such strategic behavior can hinder firms from maximizing their profits. In this article, we study the contextual dynamic pricing problem with strategic buyers. The seller does not observe the buyer’s true feature, but a manipulated feature according to buyers’ strategic behavior. In addition, the seller does not observe the buyers’ valuation of the product, but only a binary response indicating whether a sale happens or not. Recognizing these challenges, we propose a strategic dynamic pricing policy that incorporates the buyers’ strategic behavior into the online learning to maximize the seller’s cumulative revenue. We first prove that existing nonstrategic pricing policies that neglect the buyers’ strategic behavior result in a linear Ω ( T ) regret with T the total time horizon, indicating that these policies are not better than a random pricing policy. We then establish an O ( T ) regret upper bound of our proposed policy and an Ω ( T ) regret lower bound for any pricing policy within our problem setting. This underscores the rate optimality of our policy. Importantly, our policy is not a mere amalgamation of existing dynamic pricing policies and strategic behavior handling algorithms. Our policy can also accommodate the scenario when the marginal cost of manipulation is unknown in advance. To account for it, we simultaneously estimate the valuation parameter and the cost parameter in the online pricing policy, which is shown to also achieve an O ( T ) regret bound. Extensive experiments support our theoretical developments and demonstrate the superior performance of our policy compared to other pricing policies that are unaware of the strategic behaviors. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Upper Bound Limit Analysis of Deep Tunnel Face Support Pressure with Nonlinear Failure Criterion under Pore Water Conditions

Based on the nonlinear failure criterion and modified tangential technique, the upper bound solutions of the critical supporting pressure on the deep tunnel face were obtained under pore water pressure conditions. The influence of parameters on the critical supporting pressure and collapse range was investigated according to the unlimited block failure mechanism. It was found that the upper bound solutions of the critical supporting pressure increase with the growth of the nonlinear coefficient and pore water pressure coefficient. The collapse range of the tunnel face scales out with the increase in the nonlinear coefficient and shrinks with an increasing pore water pressure coefficient. Moreover, with the increase in the nonlinear coefficient, the impact strength on critical supporting pressure and collapse range declines gradually. According to the calculated results, both the pore water pressure and nonlinear criterion factors have negative impacts on the stability of the tunnel face. Thus, more attention should be paid to these parameters to ensure face stability in deep tunnel construction.

The diameter of sum basic equilibria games

We study the sum basic network creation game introduced in 2010 by Alon, Demaine, Hajiaghai and Leighton. In this game, an undirected and unweighted graph G is said to be a sum basic equilibrium if and only if, for every edge uv and any vertex v′ in G, swapping edge uv with edge uv′ does not decrease the total sum of the distances from u to all the other vertices. This concept lies at the heart of the network creation games, where the central problem is to understand the structure of the resulting equilibrium graphs, and in particular, how well they globally minimize the diameter. In this sense, in 2013 Alon et al. showed an upper bound of 2O(log⁡n) on the diameter of sum basic equilibria, and they also proved that if a sum basic equilibrium graph is a tree, then it has diameter at most 2. In this paper, we prove that the upper bound of 2 also holds for bipartite graphs and even for some non-bipartite classes like block graphs and cactus graphs.

Hierarchical and defect-free metal-organic framework membranes deep-rooted within flexible nanofiber substrate

Defect-free MOFs membrane on flexible substrate is challenging and promising for industrial applications. In this work, electrospun nanofiber substrates were employed to construct deep-rooted and defect-free ZIF-8 membranes by a symbiotic layer composed of interpenetrated nanofibers and ZIF-8. Nanofibers provide sufficient nucleation sites to construct an interpenetrated “symbiotic layer”, which further supports ZIF-8 growing to be defect-free. Importantly, benefiting from this symbiotic layer, the rigidity difference between substrate and ZIF-8 is well balanced, resulting in ZIF-8 membrane deep-rooted within the support. Furthermore, tannic acid (TA), was combined to modulate the surface chemistry and inter-crystalline defects of ZIF-8 membranes. Finally, a hierarchical ZIF-8 membrane with nanofibers as flexible substrates were obtained. The prepared PAN/TA2-NZIF-80.25 membrane exhibits H2 permeance of 2408 GPU and H2/CO2 selectivity of 21.80. Specifically, compared with the reported MOFs membrane for H2 separation, the H2 permeance of this work locates in a very high region, while proper H2/CO2 separation factor is still remained, exceeding the 2008 upper bound of H2/CO2 separation. Importantly, this membrane presents stable microstructures and separation performance after twisting. The proposed deep-rooted and defect-free ZIF-8 membrane on flexible substrate is competitive to achieve industrial application.

Positivity-Preserving Rational Cubic Fractal Interpolation Function Together with Its Zipper Form

In this paper, a novel class of rational cubic fractal interpolation function (RCFIF) has been proposed, which is characterized by one shape parameter and a linear denominator. In interpolation for shape preservation, the proposed rational cubic fractal interpolation function provides a simple but effective approach. The nature of shape preservation of the proposed rational cubic fractal interpolation function makes them valuable in the field of data visualization, as it is crucial to maintain the original data shape in data visualization. Furthermore, we discussed the upper bound of error and explored the mathematical framework to ensure the convergence of RCFIF. Shape parameters and scaling factors are constraints to obtain the desired shape-preserving properties. We further generalized the proposed RCFIF by introducing the concept of signature, giving its construction in the form of a zipper-rational cubic fractal interpolation function (ZRCFIF). The positivity conditions for the rational cubic fractal interpolation function and zipper-rational cubic fractal interpolation function are found, which required a detailed analysis of the conditions where constraints on shape parameters and scaling factor lead to the desired shape-preserving properties. In the field of shape preservation, the proposed rational cubic fractal interpolation function and zipper fractal interpolation function both represent significant advancement by offering a strong tool for data visualization.

Sharp lower bounds for the Laplacian Estrada index of graphs

Let G be a simple graph on n vertices, and let λ 1 , λ 2 , … , λ n be the Laplacian eigenvalues of G. The Laplacian Estrada index of G is defined as LEE ( G ) = ∑ i = 1 n e λ i . Consider a graph G with n ≥ 3 vertices, m edges, c connected components, and the largest Laplacian eigenvalue λ n . Let K n , S n , and K p , q (p + q = n) denote the complete graph, the star graph, and the complete bipartite graph on n vertices, respectively. In this paper, we establish that LEE ( G ) ≥ n e 2 m n + c + e λ n − ( c + 1 ) e λ n c + 1 . Furthermore, we show that the equality holds if and only if G ≅ K ¯ n (the complement of K n ), G ≅ ∪ i = 1 c − 1 K 1 ∪ S c + 1 if n = 2c, or G ≅ K n 2 , n 2 if G is a connected graph on an even number of vertices. As a consequence of this lower bound, we derive sharp lower bounds for the Laplacian Estrada index of a graph, considering its well-known graph parameters. This leads to improvements to some previously known lower bounds for the Laplacian Estrada index of a graph. Notably, we establish a sharp lower bound for the Laplacian Estrada index of a graph in terms of its maximum vertex degree. As an application, we demonstrate that the lower bound for the Laplacian Estrada index presented by Khosravanirad in [A Lower Bound for Laplacian Estrada Index of a Graph, MATCH Commun Math Comput Chem. 2013;70:175–180.] is not complete. Consequently, we provide a complete version of this lower bound.

Matrix hypercontractivity, streaming algorithms and LDCs: the large alphabet case

We prove a hypercontractive inequality for matrix-valued functions defined over large alphabets. In order to do so, we prove a generalization of the powerful 2-uniform convexity inequality for trace norms of Ball, Carlen, Lieb (Inventiones Mathematicae’94). Using our hypercontractive inequality, we present upper and lower bounds for the communication complexity of the Hidden Hypermatching problem defined over large alphabets. We then consider streaming algorithms for approximating the value of Unique Games on a hypergraph with t -size hyperedges. By using our communication lower bound, we show that every streaming algorithm in the adversarial model achieving an ( r − ε)-approximation of this value requires Ω ( n 1 − 2/ t ) quantum space, where r is the alphabet size. We next present a lower bound for locally decodable codes ( \(\mathsf {LDC} \) ) \(\mathbb {Z}_r^n\rightarrow \mathbb {Z}_r^N \) over large alphabets with recoverability probability at least 1/ r + ε. Using hypercontractivity, we give an exponential lower bound \(N= 2^{\Omega (\varepsilon ^4 n/r^4)} \) for 2-query (possibly non-linear) \(\mathsf {LDC} \) s over \(\mathbb {Z}_r \) and using the non-commutative Khintchine inequality we prove an improved lower bound of \(N= 2^{\Omega (\varepsilon ^2 n/r^2)} \) .

On two-variable guarded fragment logic with expressive local Presburger constraints

We consider the extension of the two-variable guarded fragment logic with local Presburger quantifiers. These are quantifiers that can express properties such as "the number of incoming blue edges plus twice the number of outgoing red edges is at most three times the number of incoming green edges" and captures various description logics with counting, but without constant symbols. We show that the satisfiability problem for this logic is EXP-complete. While the lower bound already holds for the standard two-variable guarded fragment logic, the upper bound is established by a novel, yet simple deterministic graph-based algorithm.

Width and Local Homology Dimension for Triangulated Categories

Let T be a compactly generated triangulated category. In this paper, the width and local homology dimension of an object X with respect to a homogeneous ideal a, widthR(a,X) and hd(a,X), respectively, are introduced. The local nature and some basic properties of widthR(a,X) and hd(a,X) are provided. In addition, we give an upper bound and lower bound of widthR(a,X). What is more, we give the relationship between the local homology dimension hd(a,X) and the arithmetic rank of a and dimR.

Comparative efficacy of subcutaneous versus intravenous natalizumab on annualized relapse rate: A post-hoc analysis of the REFINE study

BackgroundThe non-inferiority of the efficacy of subcutaneous (SC) vs intravenous (IV) administration of natalizumab (NTZ) once every 4 weeks in relapsing-remitting multiple sclerosis (RRMS) was recently demonstrated on the primary outcome of the REFINE study, i.e. MRI “combined unique active lesions number” (CUAL). To provide further evidence on the comparative efficacy of the two NTZ formulations, the effect of NTZ-SC vs NTZ-IV on annualized relapse rate (ARR) was investigated re-analysing the REFINE dataset. MethodsPost-hoc analysis of the REFINE study dataset aimed at exploring the non-inferiority of the efficacy of NTZ-SC vs NTZ-IV on ARR, i.e. the main secondary outcome of the REFINE study. Robustness of the non-inferiority analysis on CUAL with respect to the presence of cases from the SC arm who received a rescue treatment, including NTZ-IV, was also assessed by sensitivity analyses. Three non-inferiority margins were selected, corresponding to 25 %, 33 %, and 50 % fractions of the effect size of NTZ-IV vs placebo observed in the AFFIRM study on ARR (i.e. 0.125, 0.170, and 0.250). ResultsNinety-nine RRMS patients were included. The mean difference in the effect of NTZ-SC vs NTZ-IV on ARR was close to 0. The lower bound of the 95 % confidence interval (worst case scenario) was –0.119, corresponding to 25 % (p = 0.025) of the effect of NTZ-IV vs placebo on ARR. Sensitivity analyses confirmed the results of the primary non-inferiority analysis on the outcome CUAL. ConclusionsNTZ-SC resulted not inferior to NTZ-IV on ARR for all the non-inferiority margins. The non-inferiority analysis of the efficacy of NTZ-SC vs NTZ-IV on CUAL was demonstrated to be robust with respect to rescued patients.

A matrix-separation-based integral inequality for aperiodic sampled-data synchronization of delayed neural networks considering communication delay

This paper achieves the synchronization of delayed neural networks (DNNs) considering aperiodic sampled-data control and communication delay. First of all, based on the master-slave DNNs with aperiodic sampling synchronization controller, a synchronization error system is constructed. Then, an augmented functional containing both the error state and its derivative is constructed. Compared with the existing researches, the augmented functional introduces more cross information of error states to the criterion. Next, an integral inequality based on the separation of internal integral variable and matrix is developed. Compared to the inequalities that treat the internal variable and the matrix as unified ones, the developed inequality provides a tighter estimate of the derivative of the augmented functional. On this basis, a criterion with less conservative is developed for the aperiodic sampled-data synchronization of DNNs considering communication delay. Finally, to indicate the superiority of the developed method on improving the acceptable sampling upper bound of synchronization, three numerical examples are provided.

RH-ECBS: enhanced conflict-based search for MRPP with region heuristics

Abstract This paper proposes a novel two-layer framework based on conflict-based search and regional divisions to improve the efficiency of multi-robot path planning. The high-level layer targets the reduction of conflicts and deadlocks, while the low-level layer is responsible for actual path planning. Distinct from previous dual-level search frameworks, the novelties of this work are (1) subdivision of planning regions for each robot to decrease the number of conflicts encountered during planning; (2) consideration of the number of robots in the region during planning in the node expansion stage of A*, and (3) formal proof demonstrating the nonzero probability of the proposed method in obtaining a solution, along with providing the upper bound of the solution in a special case. Experimental comparisons with Enhanced Conflict-Based Search demonstrate that the proposed method not only reduces the number of conflicts but also achieves a computation time reduction of over 30%.

Distributed nonlinear fusion filtering for multi-sensor networked systems with random varying parameter matrix and missing measurements

This paper is concerned with the distributed fusion filtering algorithm design problem for multi-sensor nonlinear networked systems (MSNNSs) subject to multiplicative noises, random varying parameter matrix and missing measurements (MMs). In particular, we utilize the Bernoulli random variable with certain statistical features to describe and characterize the MMs phenomenon. By introduce a fictitious noise, the effects from process noise as well as random varying parameter matrix are addressed and a new nonlinear stochastic networked system is obtained. The primary purpose of this paper is to develop a novel fusion filtering scheme of the distributed way and provide the corresponding boundedness evaluation criterion. Firstly, specific upper bounds of filtering error covariance (FEC) are identified and locally minimized at each sampling instant. Subsequently, based on the obtained local filters, a distributed fusion filtering algorithm is designed via adopting the inverse covariance intersection (ICI) fusion idea. Furthermore, the analysis with respect to the upper bound of local FEC is discussed and examined by proposing a sufficient condition under certain constraints regarding the related parameters. Eventually, with the help of the simulation experiments, the usefulness of the proposed fusion filtering algorithm is illustrated.

Sharp Waiting-Time Bounds for Multiserver Jobs

Multiserver jobs, which are jobs that occupy multiple servers simultaneously during service, are prevalent in today’s computing clusters. But, little is known about the delay performance of systems with multiserver jobs. We consider queueing models for multiserver jobs in scaling regimes where the system load becomes heavy and meanwhile, the total number of servers in the system and the number of servers that a job needs become large. Prior work has derived upper bounds on the queueing probability in this scaling regime. However, without proper lower bounds, the existing results cannot be used to differentiate between policies. In this paper, we study the delay performance by establishing sharp bounds on the steady-state mean waiting time of multiserver jobs, where the waiting time of a job is the time spent in queueing rather than in service. We first characterize the exact order of the mean waiting time under the first come, first serve (FCFS) policy. Then, we prove a lower bound on the mean waiting time of all policies, which has an order gap with the mean waiting time under FCFS. We show that the lower bound is achievable by a priority policy that we call smallest need first (SNF). Funding: This research was supported in part by the National Science Foundation [Grant ECCS-2145713]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/stsy.2023.0006 .

Stream salinity prediction in data-scarce regions: Application of transfer learning and uncertainty quantification

Scarcity of stream salinity data poses a challenge to understanding salinity dynamics and its implications for water supply management in water-scarce salt-prone regions around the world. This paper introduces a framework for generating continuous daily stream salinity estimates using instance-based transfer learning (TL) and assessing the reliability of the synthetic salinity data through uncertainty quantification via prediction intervals (PIs). The framework was developed using two temporally distinct specific conductance (SC) datasets from the Upper Red River Basin (URRB) located in southwestern Oklahoma and Texas Panhandle, United States. The instance-based TL approach was implemented by calibrating Feedforward Neural Networks (FFNNs) on a source SC dataset of around 1200 instantaneous grab samples collected by United States Geological Survey (USGS) from 1959 to 1993. The trained FFNNs were subsequently tested on a target dataset (1998-present) of 220 instantaneous grab samples collected by the Oklahoma Water Resources Board (OWRB). The framework's generalizability was assessed in the data-rich Bird Creek watershed in Oklahoma by manipulating continuous SC data to simulate data-scarce conditions for training the models and using the complete Bird Creek dataset for model evaluation. The Lower Upper Bound Estimation (LUBE) method was used with FFNNs to estimate PIs for uncertainty quantification. Autoregressive SC prediction methods via FFNN were found to be reliable with Nash Sutcliffe Efficiency (NSE) values of 0.65 and 0.45 on in-sample and out-of-sample test data, respectively. The same modeling scenario resulted in an NSE of 0.54 for the Bird Creek data using a similar missing data ratio, whereas a higher ratio of observed data increased the accuracy (NSE = 0.84). The relatively narrow estimated PIs for the North Fork Red River in the URRB indicated satisfactory stream salinity predictions, showing an average width equivalent to 25 % of the observed range and a confidence level of 70 %.

Zero gradient sum algorithm of arbitrary initial value with constraints and communication delay based on directed graph

The distributed convex optimisation issue with inequality constraints and box constraints on the directed communication topology is examined in this paper. In the case of the communication delay between agents, we propose a piecewise zero-gradient-sum triggered control algorithm that allows arbitrary initial values. Using the log-barrier penalty method, we only need to study an unconstrained approximation problem of the original problem. Firstly, each agent's state converges to the optimal value of the related local objective function in a fixed time. Simultaneously, the upper bound of fixed time in this paper is smaller than some existing results. Then, in the case of communication delay, time-triggered and event-triggered methods with non-uniform sampling interval are proposed in this paper, which make the communication cost lower and the application broader. Using the Lyapunov function method, the sufficient conditions for each agent's state to converge to the optimal point are given, and the Zeno behaviour is excluded. Finally, to confirm the algorithm's effectiveness, we provide two numerical examples and one machine learning example as demonstrations.

On the Consistency of Circuit Lower Bounds for Non-Deterministic Time

On the Consistency of Circuit Lower Bounds for Non-Deterministic Time

Uniform Stabilization and Asymptotic Behavior with a Lower Bound of the Maximal Existence Time of a Coupled System’s Semi-Linear Pseudo-Parabolic Equations

Uniform Stabilization and Asymptotic Behavior with a Lower Bound of the Maximal Existence Time of a Coupled System’s Semi-Linear Pseudo-Parabolic Equations

Super-Oscillating Diffractive Optical Spot Generators

The prior discrete Fourier transform (PDFT) is applied to the design of super-oscillating diffractive optical elements with rotational symmetry. Numerical simulations of the filter response are used to demonstrate the potential of the PDFT-based approach, which includes a regularization method for improved numerical and functional stability of the filter design. For coherent monochromatic illumination, the Strehl ratio of spot generators as a function of the spot radius is compared to the theoretical upper bound. It is shown that the performance of the PDFT design varies significantly depending on the aperture function and the encoding as a phase-only diffractive element. Experimental results are in good agreement with simulations and demonstrate the moderate demands to implement super-oscillating diffractive optical elements.

Robust optimization algorithm for integrated crane assignment and scheduling in slab yard with uncertain arrival time

A slab yard served as a key component of the iron and steel plant. Effective slab yard crane assignment and scheduling directly affect the overall efficiency of the steel production process. This work addresses an uncertain slab yard crane assignment and scheduling problem (SYCAS) with the fluctuating arrival time. A stochastic programming model is established to obtain a robust solution that minimises the completion time of slab groups under uncertainty. Due to its NP-hardness, we developed an improved column and cut generation method (IC&CG), which divides the problem into a relaxed master problem (RMP) and a slave problem (SP). A new initialisation strategy for obtaining high-quality solutions and an acceleration strategy for discarding irrelevant scenarios are proposed. We use small-size instances to compare the performance of IC&CG with CPLEX and a generalised column and cut generation method in both deterministic and uncertain environments to validate the effectiveness of the method. For large-size instances, a lower bound (LB) of the optimal objective function is proposed to show the effectiveness of IC&CG. Furthermore, we prove the robustness of the method by sensitive analysis.