Lower Bound Research Articles

Binary Graph Convolutional Network With Capacity Exploration.

The current success of Graph Neural Networks (GNNs) usually relies on loading the entire attributed graph for processing, which may not be satisfied with limited memory resources, especially when the attributed graph is large. This paper pioneers to propose a Binary Graph Convolutional Network (Bi-GCN), which binarizes both the network parameters and input node attributes and exploits binary operations instead of floating-point matrix multiplications for network compression and acceleration. Meanwhile, we also propose a new gradient approximation based back-propagation method to properly train our Bi-GCN. According to the theoretical analysis, our Bi-GCN can reduce the memory consumption by an average of ∼31x for both the network parameters and input data, and accelerate the inference speed by an average of ∼51x, on three citation networks, i.e., Cora, PubMed, and CiteSeer. Besides, we introduce a general approach to generalize our binarization method to other variants of GNNs, and achieve similar efficiencies. Although the proposed Bi-GCN and Bi-GNNs are simple yet efficient, these compressed networks may also possess a potential capacity problem, i.e., they may not have enough storage capacity to learn adequate representations for specific tasks. To tackle this capacity problem, an Entropy Cover Hypothesis is proposed to predict the lower bound of the width of Bi-GNN hidden layers. Extensive experiments have demonstrated that our Bi-GCN and Bi-GNNs can give comparable performances to the corresponding full-precision baselines on seven node classification datasets and verified the effectiveness of our Entropy Cover Hypothesis for solving the capacity problem.

Assessing quality of selection procedures: Lower bound of false positive rate as a function of inter-rater reliability.

Inter-rater reliability (IRR) is one of the commonly used tools for assessing the quality of ratings from multiple raters. However, applicant selection procedures based on ratings from multiple raters usually result in a binary outcome; the applicant is either selected or not. This final outcome is not considered in IRR, which instead focuses on the ratings of the individual subjects or objects. We outline the connection between the ratings' measurement model (used for IRR) and a binary classification framework. We develop a simple way of approximating the probability of correctly selecting the best applicants which allows us to compute error probabilities of the selection procedure (i.e., false positive and false negative rate) or their lower bounds. We draw connections between the IRR and the binary classification metrics, showing that binary classification metrics depend solely on the IRR coefficient and proportion of selected applicants. We assess the performance of the approximation in a simulation study and apply it in an example comparing the reliability of multiple grant peer review selection procedures. We also discuss other possible uses of the explored connections in other contexts, such as educational testing, psychological assessment, and health-related measurement, and implement the computations in the R package IRR2FPR.

Trade-off relations of quantum resource theory in Heisenberg models

Studying the relations between entanglement and coherence is essential in many quantum information applications. For this, we consider the concurrence, intrinsic concurrence and first-order coherence, and evaluate the proposed trade-off relations between them. In particular, we study the temporal evolution of a general two-qubit XYZ Heisenberg model with asymmetric spin-orbit interaction under decoherence and analyze the trade-off relations of quantum resource theory. For XYZ Heisenberg model, we confirm that the trade-off relation between intrinsic concurrence and first-order coherence holds. Furthermore, we show that the lower bound of intrinsic concurrence is universally valid, but the upper bound is generally not. These relations in Heisenberg models can provide a way to explore how quantum resources are distributed in spins, which may inspire future applications in quantum information processing.

Some closer estimations for Tsallis relative operator entropy

In this paper, we find some new and refined bounds for the Tsallis relative operator entropy. We give the lower and upper bounds for the Tsallis relative operator entropy such that the lower bound is an ascending sequence that ascends to the Tsallis relative operator entropy and the upper bound is a descending sequence that descends to the Tsallis relative operator entropy. Moreover, we present some new and refined bounds for the relative operator entropy and the generalized relative operator entropy.

On Breaking Truss-based and Core-based Communities

We introduce the general problem of identifying a smallest edge subset of a given graph whose deletion makes the graph community-free. We consider this problem under two community notions that have attracted significant attention: k -truss and k -core. We also introduce a problem variant where the identified subset contains edges incident to a given set of nodes and ensures that these nodes are not contained in any community: k -truss or k -core, in our case. These problems are directly applicable in social networks: The identified edges can be hidden by users or sanitized from the output graph; or in communication networks: the identified edges correspond to vital network connections. We present a series of theoretical and practical results. On the theoretical side, we show through non-trivial reductions that the problems we introduce are NP-hard and, in fact, hard to approximate. For the k -truss-based problems, we also show exact exponential-time algorithms, as well as a non-trivial lower bound on the size of an optimal solution. On the practical side, we develop a series of heuristics that are sped up by efficient data structures that we propose for updating the truss or core decomposition under edge deletions. In addition, we develop an algorithm to compute the lower bound. Extensive experiments on 11 real-world and synthetic graphs show that our heuristics are effective, outperforming natural baselines, and also efficient (up to two orders of magnitude faster than a natural baseline), thanks to our data structures. Furthermore, we present a case study on a co-authorship network and experiments showing that the removal of edges identified by our heuristics does not substantially affect the clustering structure of the input graph. This work extends a KDD 2021 paper, providing new theoretical results as well as introducing core-based problems and algorithms.

On stability and H∞ control synthesis of sampled‐data systems: A multiple convex function approximation approach

AbstractThis article deals with the stability and control synthesis for a class of linear sampled‐data systems. First, a novel integral inequality with the cubic term of integral interval length instead of reciprocal one of integral interval length is constructed by non‐orthogonal polynomials. This can make full use of slack matrix variables and additional information about sawtooth structural sampling pattern. Then, on the basis of the constructed integral inequality, a cubic‐term‐dependent discontinuous exponent Lyapunov–Krasovskii Functional (LKF) is developed containing additional information about system states to design an sampled‐data state feedback controller. To better estimate the upper bound of the derivative of LKF, a kind of multiple convex function approximation approach is developed, which can be used to deal with the two‐variable polynomial negative definite issue by dividing the variable interval into multiple subintervals. By the constructed integral inequality and multiple convex function approximation approach, sufficient conditions with less conservatism are deduced for the feasibility of sampled‐data state feedback controller. Moreover, by the inner convex approximation solution technique and proposed iterative algorithm, the bilinear matrix inequalities can be transformed into linear matrix ones, which can be easily tackled, to obtain the desired sampled‐data controller gain. Finally, by comparing with existing results, the advantages and superiority of our proposed approaches can be confirmed via two numerical examples.

On the Upper Bound of Near Potential Differential Games

This letter presents an extended analysis and a novel upper bound of the subclass of Linear Quadratic Near Potential Differential Games (LQ NPDG). LQ NPDGs are a subclass of potential differential games, for which there is a distance between an LQ exact potential differential game and the LQ NPDG. LQ NPDGs exhibit a unique characteristic: The smaller the distance from an LQ exact potential differential game, the more closer their dynamic trajectories. This letter introduces a novel upper bound for this distance. Moreover, a linear relation between this distance and the resulting trajectory errors is established, opening the possibility for further application of LQ NPDGs.

An upper bound for the inter-exit time of two jobs in an m-machine flow shop

AbstractThis paper addresses the class of permutation flow shop scheduling where jobs, after their completion, must be grouped in batches. This is a common scheme in industrial environments, where products undergo multiple process steps in different shops and, when completed, must be transported to customers or the next production step. A new optimisation criterion is used, the inter-exit time, i.e., the difference between the completion times of two jobs. An upper bound is proposed and demonstrated for a general permutation flow shop with m machines.

Upper Bound of Barrow Entropy Index from Black Hole Fragmentation

Both classical and quantum arguments suggest that if Barrow entropy is correct, its index δ must be energy-dependent, which would affect the very early universe. Based on thermodynamic stability that sufficiently large black holes should not fragment, we argue that Barrow entropy correction must be small, except possibly at the Planckian regime. Furthermore, the fact that a solar mass black hole does not fragment implies an upper bound δ≲O(10−3), which surprisingly lies in the same range as the bound obtained from some cosmological considerations assuming fixed δ. This indicates that allowing δ to run does not raise its allowed value. We briefly comment on the case of Kaniadakis entropy.

Layout of Detection Array Based on Multi-Strategy Fusion Improved Adaptive Mayfly Algorithm in Bearing-Only Sensor Network

The various applications of bearing-only sensor networks for detection and localization are becoming increasingly widespread and important. The array layout of the bearing-only sensor network seriously impacts the detection performance. This paper proposes a multi-strategy fusion improved adaptive mayfly algorithm (MIAMA) in a bearing-only sensor network to perform layout planning on the geometric configuration of the optimal detection. Firstly, the system model of a bearing-only sensor network was constructed, and the observability of the system was analyzed based on the Cramer–Rao Lower Bound and Fisher Information Matrix. Then, in view of the limitations of the traditional mayfly algorithm, which has a single initial population and no adaptability and poor global search capabilities, multi-strategy fusion improvements were carried out by introducing Tent chaos mapping, the adaptive inertia weight factor, and Random Opposition-based Learning. Finally, three simulation experiments were conducted. Through comparison with the Particle Swarm Optimization (PSO) algorithm, Mayfly Algorithm (MA), and Genetic Algorithm (GA), the effectiveness and superiority of the proposed MIAMA were validated.

Lower Bounds on Ground-State Energies of Local Hamiltonians through the Renormalization Group

Lower Bounds on Ground-State Energies of Local Hamiltonians through the Renormalization Group

A Population Pharmacokinetic Assessment of the Effect of Food on Selumetinib in Patients with Neurofibromatosis Type 1-Related Plexiform Neurofibromas and Healthy Volunteers.

Selumetinib is clinically used for pediatric patients with neurofibromatosis type 1 and symptomatic, inoperable plexiform neurofibromas. Until recently, selumetinib had to be taken twice daily, after 2 hours of fasting and followed by 1 hour of fasting, which could be inconvenient. This population analysis evaluated the effect of low- and high-fat meals on the pharmacokinetic (PK) parameters of selumetinib and its active metabolite N-desmethyl selumetinib. The dataset comprised 511 subjects from 15 clinical trials who received ≥1 dose of selumetinib and provided ≥1 measurable postdose concentration of selumetinib and N-desmethyl selumetinib. A 2-compartment model with sequential 0- and 1st-order delayed absorption and 1st-order elimination adequately described selumetinib PK characteristics. A 1-compartment model reasonably described N-desmethyl selumetinib PK characteristics over time simultaneously with selumetinib. Selumetinib geometric mean area under the concentration-time curveratio (1-sided 90% confidence interval [CI] lower bound) was 76.9% (73.3%) with a low-fat meal and 79.3% (76.3%) with a high-fat meal versus fasting. The lower bound of the 1-sided 90% CI demonstrated a difference of <30% between fed and fasted states. Considering the flat exposure-response relationship within the dose range (20-30mg/m2), the observed range of exposure, and the variability in the SPRINT trial, this was not considered clinically relevant.

Lyapunov Drift-Plus-Penalty-Based Cooperative Uplink Scheduling in Dense Wi-Fi Networks

In high-density network environments with multiple access points (APs) and stations, individual uplink scheduling by each AP can severely interfere with the uplink transmissions of neighboring APs and their associated stations. In congested areas where concurrent uplink transmissions may lead to significant interference, it would be beneficial to deploy a cooperative scheduler or a central coordinating entity responsible for orchestrating cooperative uplink scheduling by assigning several neighboring APs to support the uplink transmission of a single station within a proximate service area to alleviate the excessive interference. Cooperative uplink scheduling facilitated by cooperative information sharing and management is poised to improve the likelihood of successful uplink transmissions in areas with a high concentration of APs and stations. Nonetheless, it is crucial to account for the queue stability of the stations and the potential delays arising from information exchange and the decision-making process in uplink scheduling to maintain the overall effectiveness of the cooperative approach. In this paper, we propose a Lyapunov drift-plus-penalty framework-based cooperative uplink scheduling method for densely populated Wi-Fi networks. The cooperative scheduler aggregates information, such as signal-to-interference-plus-noise ratio (SINR) and queue status. During the aggregation procedure, propagation delays are also estimated and utilized as a value of expected cooperation delays in scheduling decisions. Upon aggregating the information, the cooperative scheduler calculates the Lyapunov drift-plus-penalty value, incorporating a predefined model parameter to adjust the system accordingly. Among the possible scheduling candidates, the proposed method proceeds to make uplink decisions that aim to reduce the upper bound of the Lyapunov drift-plus-penalty value, thereby improving the network performance and stability without a severe increase in cooperation delay in highly congested areas. Through comprehensive performance evaluations, the proposed method effectively enhances network performance with an appropriate model parameter. The performance improvement is particularly notable in highly congested areas and is achieved without a severe increase in cooperation delays.

FRACTAL DIMENSIONS FOR THE MIXED (κ,s)-RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL OF BIVARIATE FUNCTIONS

The research object of this paper is the mixed [Formula: see text]-Riemann–Liouville fractional integral of bivariate functions on rectangular regions, which is a natural generalization of the fractional integral of univariate functions. This paper first indicates that the mixed integral still maintains the validity of the classical properties, such as boundedness, continuity and bounded variation. Furthermore, we investigate fractal dimensions of bivariate functions under the mixed integral, including the Hausdorff dimension and the Box dimension. The main results indicate that fractal dimensions of the graph of the mixed [Formula: see text]-Riemann–Liouville integral of continuous functions with bounded variation are still two. The Box dimension of the mixed integral of two-dimensional continuous functions has also been calculated. Besides, we prove that the upper bound of the Box dimension of bivariate continuous functions under [Formula: see text] order of the mixed integral is [Formula: see text] where [Formula: see text].

Enhancing CO2/N2 and CO2/CH4 separation in mixed matrix membrane: A comprehensive study on Pebax®1657 with SSMMP/IL for improved efficiency

AbstractMixed matrix membranes (MMMs) have been proposed as a solution to surmount Robeson's trade‐off curves and have demonstrated efficacy in gas separation processes, particularly for CO2 capture. In this study, MMMs based on Pebax®1657 were obtained utilizing synthetic silico‐metallic mineral particles (SSMMP) functionalized with ionic liquids (ILs). The objective was to attain enhanced CO2 separation performance, thereby showcasing the potential to mitigate the environmental repercussions of industrial processes that entail greenhouse gas emissions. For membrane production, an ethanol/water mixture was used as solvent, with the SSMMP/IL content varying from 0.5 to 20% by weight of the polymer. The primary aim of this study was to assess the effect of filler addition on permeability and selectivity for CO2, CH4, and N2. Comprehensive analyses, including SEM, FTIR, TGA, DSC, and DMA were conducted to evaluate the properties of the produced membranes. Gas permeability and ideal selectivity were measured at 25°C and different pressures, ranging from 1 to 7 bar. Characterization results demonstrate that the glass transition temperature (Tg) of MMMs increased compared to pure Pebax®1657, indicating that the addition of SSMMP/IL reduces the flexibility of the PEO chains, forming a rigid interface at the polymer/filler, which may enhance selectivity. This effect, corroborated by gas permeation, was observed for both CO2/N2 and CO2/CH4. For CO2/N2, the highest selectivity was achieved at lower filler concentrations, gradually decreasing as the filler load increased. MMM‐0.5 wt% achieved the highest selectivity of 91.96. The membrane CO2 permeability rose with an elevated filler content, rising from 84.21 for pure Pebax®1657 to 192.17 Barrer for MMM‐20 wt% at 4 bar. The permeability results were influenced by the gas diffusion coefficients of the MMMs, which increased with increasing SSMMP/IL content. The effect of feed pressure on MMM‐5 wt% was also assessed, revealing that CO2 permeability increased with increasing pressure, from 126.72 Barrer at 1 bar to 165.56 Barrer at 7 bar. This work showcased the viability of MMMs incorporating SSMMP/IL for industrial use, as they displayed separation capabilities that exceeded the 2008 Robeson upper bound.Highlights Mixed matrix membranes based on Pebax®1657 and SSMMP‐20%‐[bmim][Tf2N] were prepared. CO2 permeability of the MMMs was increased by 128% and CO2/N2 selectivity by 83%. Higher CO2 pressures increase MMMs permeability. The obtained MMMs have separation performances above the Robeson upper Bound.

Finite-Time Adaptive Synchronization and Fixed-Time Synchronization of Fractional-Order Memristive Cellular Neural Networks with Time-Varying Delays

Asymptotic synchronization requires continuous external control of the system, which is unrealistic considering the cost of control. Adaptive control methods have strong robustness to uncertainties such as disturbances and unknowns. On the other hand, for finite-time synchronization, if the initial value of the system is unknown, the synchronization time of the finite-time synchronization cannot be estimated. This paper explores the finite-time adaptive synchronization (FTAS) and fixed-time synchronization (FDTS) of fractional-order memristive cellular neural networks (FMCNNs) with time-varying delays (TVD). Utilizing the properties and principles of fractional order, we introduce a novel lemma. Based on this lemma and various analysis techniques, we establish new criteria to guarantee FTAS and FDTS of FMCNNs with TVD through the implementation of a delay-dependent feedback controller and fractional-order adaptive controller. Additionally, we estimate the upper bound of the synchronization setting time. Finally, numerical simulations are conducted to confirm the validity of the finite-time and fixed-time stability theorems.

A Lower Bound on the Growth of Minimal Graphs

A Lower Bound on the Growth of Minimal Graphs

ACTOR: Adaptive Control of Transmission Power in RPL.

RPL-Routing Protocol for Low-Power and Lossy Networks (usually pronounced "ripple")-is the de facto standard for IoT networks. However, it neglects to exploit IoT devices' full capacity to optimize their transmission power, mainly because it is quite challenging to do so in parallel with the routing strategy, given the dynamic nature of wireless links and the typically constrained resources of IoT devices. Adapting the transmission power requires dynamically assessing many parameters, such as the probability of packet collisions, energy consumption, the number of hops, and interference. This paper introduces Adaptive Control of Transmission Power for RPL (ACTOR) for the dynamic optimization of transmission power. ACTOR aims to improve throughput in dense networks by passively exploring different transmission power levels. The classic solutions of bandit theory, including the Upper Confidence Bound (UCB) and Discounted UCB, accelerate the convergence of the exploration and guarantee its optimality. ACTOR is also enhanced via mechanisms to blacklist undesirable transmission power levels and stabilize the topology of parent-child negotiations. The results of the experiments conducted on our 40-node, 12-node testbed demonstrate that ACTOR achieves a higher packet delivery ratio by almost 20%, reduces the transmission power of nodes by up to 10 dBm, and maintains a stable topology with significantly fewer parent switches compared to the standard RPL and the selected benchmarks. These findings are consistent with simulations conducted across 7 different scenarios, where improvements in end-to-end delay, packet delivery, and energy consumption were observed by up to 50%.

The entropy formula of shrinking target problem in nonautonomous dynamical systems

This paper is devoted to studying the topological entropy of shrinking target problem in nonautonomous dynamical systems (NDSs). After providing the shrinking target problem of the topological version in NDSs, we obtain a general formula for computing the topological entropy of it. More precisely, we show that the entropy distribution principle still holds in NDSs and apply it to estimate the lower bound of the formula. In addition to the specification property, the concept of control non-decreasing property about the Bowen metric proposed by us is taken as a supplementary condition. Furthermore, we get the connection about the topological entropy between the shrinking target problem and the whole system. This extends the result of Ma et al. [Discrete Contin. Dyn. Syst. 39(5) (2019), pp. 2455–2471], corresponding to the case when the maps are the same as the more general case of different maps.

Tight Lower Bound on Differential Entropy for Mixed Gaussian Distributions

In this paper, a tight lower bound for the differential entropy of the Gaussian mixture model is presented. First, the probability model of mixed Gaussian distribution that is created by mixing both discrete and continuous random variables is investigated in order to represent symmetric bimodal Gaussian distribution using the hyperbolic cosine function, on which a tighter upper bound is set. Then, this tight upper bound is used to derive a tight lower bound for the differential entropy of the Gaussian mixture model introduced. The proposed lower bound allows to maintain its tightness over the entire range of the model's parameters and shows more tightness when compared with other bounds that lose their tightness over certain parameter ranges. The presented results are then extended to introduce a more general tight lower bound for asymmetric bimodal Gaussian distribution, in which the two modes have a symmetric mean but differ in terms of their weights.