Non-adaptive Case Research Articles

Adaptive isogeometric topology optimization of shell structures based on PHT-splines

This paper proposes an adaptive isogeometric topology optimization framework for shell structures by utilizing a continuous density field represented as Polynomial splines over Hierarchical T-meshes (PHT-splines). This framework ensures an exact representation of shell structures, eliminating the geometric inaccuracies commonly associated with topology optimization. In the meanwhile, the meshes used for design and analysis are refined adaptively and locally along the density boundary to achieve a smooth material layout with reduced degrees of freedom (DOF). The adaptive sensitivity filter is tailored to the characteristics of PHT-splines, where the filter radius is determined automatically and adaptively, without the need to specify parameters in advance. Numerical experiments conducted on various shell structures validate the efficacy of the proposed adaptive framework. In comparison with isogeometric topology optimization based on non-adaptive cases (i.e. B-splines), the proposed adaptive framework demonstrates a notable enhancement in computational efficiency, with a 50%−80% reduction in running time and a 30%−60% reduction in DOF. Additionally, we offer a detailed comparison between PHT-splines and other locally refinable splines in the context of shell topology optimization. Numerical experiments exhibit that the efficient and localized refinement capability of PHT-splines provides advantages in both computational efficiency and structural performance for topology optimization.

Diagonalization Games

We study several variants of a combinatorial game which is based on Cantor’s diagonal argument. The game is between two players called Kronecker and Cantor. The names of the players are motivated by the known fact that Leopold Kronecker did not appreciate Georg Cantor’s arguments about the infinite, and even referred to him as a “scientific charlatan.” In the game Kronecker maintains a list of m binary vectors, each of length n, and Cantor’s goal is to produce a new binary vector which is different from each of Kronecker’s vectors, or prove that no such vector exists. Cantor does not see Kronecker’s vectors but he is allowed to ask queries of the form What is bit number j of vector number i? What is the minimal number of queries with which Cantor can achieve his goal? How much better can Cantor do if he is allowed to pick his queries adaptively, based on Kronecker’s previous replies? The case when m = n is solved by diagonalization using n (nonadaptive) queries. We study this game more generally, and prove an optimal bound in the adaptive case and nearly tight upper and lower bounds in the nonadaptive case.

Cartesian mesh adaptation: Immersed boundary method based on high-order discontinuous Galerkin method

Immersed boundary method (IBM) can easily distinguish fluid and solid regions in the computational region, thereby the workload of complex grid generation can be reduced. To accurately characterize the solid geometry, a large number of cells are required near the solid surface. The h-adaptive algorithm is adopted to reduce the requirement for the number of cells. In addition, considering the inherent adaptability to the h-adaptive Cartesian grids of the discontinuous Galerkin method, a high-order discontinuous Galerkin solver with an IBM is developed. To validate the h-adaptive algorithm and the solver, three cases are tested, including the steady flow past the National Advisory Committee for Aeronautics 0012 airfoil, the steady flow past a cylinder, and the unsteady flow past a cylinder. Compared with the non-adaptive cases, the h-adaptive cases need smaller total number of cells, and the numerical accuracy is significantly improved with an increasing degree of mesh refinement.

Adapting to My User, Engaging with My Robot: An Adaptive Affective Architecture for a Social Assistive Robot

Affective feedback from social robots is a useful technique for communicating to people whether they are interacting “well” with the robot or not. However, some users, such as people with physical or cognitive difficulties, may not be able to interact in all the desired ways. In these cases, affective feedback from the robot could be excessively negative—an “unhappy” robot, leading to an unrewarding experience for the user. This paper presents a motivation-based architecture for an autonomous multimodal social robot, that incorporates an affective feedback mechanism which generates an affective state by combining the internal needs of the robot and the social interaction quality. The balance between these two factors can dynamically change, allowing the robot to adapt its affective feedback to the user’s interaction style and capabilities. We have implemented this architecture in a simulation and in a MiRo social robot, and report experiments examining the behavior of the system in interactions with different experimental user profiles. The results show that the adaptive mechanism allows the robot to change its affective feedback to give more positive encouragement to users than in non-adaptive cases.

The search and rescue game on a cycle

We consider a search and rescue game introduced recently by the first author. An immobile target or targets (for example, injured hikers) are hidden on a graph. The terrain is assumed to be dangerous, so that when any given vertex of the graph is searched, there is a certain probability that the search will come to an end, otherwise with the complementary success probability the search can continue. A Searcher searches the graph with the aim of finding all the targets with maximum probability. Here, we focus on the game in the case that the graph is a cycle. In the case that there is only one target, we solve the game for equal success probabilities, and for a class of games with unequal success probabilities. For multiple targets and equal success probabilities, we give a solution for an adaptive Searcher and a solution in a special case for a non-adaptive Searcher. We also consider a continuous version of the model, giving a full solution for an adaptive Searcher and approximately optimal solutions in the non-adaptive case.

Adaptive isogeometric topology optimization using PHT splines

This paper presents a novel adaptive isogeometric topology optimization methodology using the Geometry Independent Field approximaTion (GIFT) framework for Polynomial splines over Hierarchical T-meshes (PHT)-splines. Under the philosophy of the GIFT framework, industry-standard multi-patch Non-Uniform Rational B-Splines (NURBS) definition of the geometry is considered, and the adaptive discretization is achieved with the help of PHT-splines. The approach tracks the variation of density of an element, refining the sub-domains such that the boundary between the material and the non-material domain has a proper resolution. The proposed approach has threefold merits: (i) Complex multi-patch NURBS geometries could be constructed in any professional computer-aided design package and exported for analysis; (ii) The topology optimization problem could initially be solved on a relatively coarse mesh and refined progressively for substantial computational gains; (iii) Taking benefit of the GIFT framework, we can exactly represent conic sections in our computational model, thus altogether avoiding any geometric error during refinement. The accuracy and computational efficiency of the proposed framework are studied by comparing the adaptive solution to the non-adaptive solution. The proposed approach achieves a 30%–60% reduction in degree’s-of-freedom and an 80%–90% reduction in CPU time compared to the non-adaptive case.

Adaptation to Unknown Leader Velocity in Vector-Field UAV Formation

This article presents a new adaptive method for formation control of unmanned aerial vehicles (UAVs) with limited leader information and communication. We study a formation control protocol in the framework of vector-field guidance where the leader can communicate its position and orientation but not its velocity. A practical motivation for this scenario is the so-called congestion-aware control, in which tradeoffs between the density of unmanned vehicles and communication interference caused by many communicating vehicles arise: these tradeoffs may require to reduce the communication load to avoid interference. To compensate for the lack of knowledge of the leader velocity, each UAV makes use of a local estimation mechanism. The resulting method is an adaptive control method, whose stability can be established using Lyapunov stability. We show that the method can be extended to a distributed communication setting with a few neighboring UAVs in place of the leader. Extensive simulations with different formation shapes (Y, V, and T formation) show that the proposed adaptation mechanism effectively achieves the formation despite the unknown leader velocity. The proposed mechanism has a very similar performance to the ideal case when the leader velocity is perfectly known, and outperforms all the nonadaptive cases in which the followers have an incorrect knowledge of the leader velocity.

Posted Price Mechanisms and Optimal Threshold Strategies for Random Arrivals

The classic prophet inequality states that, when faced with a finite sequence of nonnegative independent random variables, a gambler who knows the distribution and is allowed to stop the sequence at any time, can obtain, in expectation, at least half as much reward as a prophet who knows the values of each random variable and can choose the largest one. In this work, we consider the situation in which the sequence comes in random order. We look at both a nonadaptive and an adaptive version of the problem. In the former case, the gambler sets a threshold for every random variable a priori, whereas, in the latter case, the thresholds are set when a random variable arrives. For the nonadaptive case, we obtain an algorithm achieving an expected reward within at least a 0.632 fraction of the expected maximum and prove that this constant is optimal. For the adaptive case with independent and identically distributed random variables, we obtain a tight 0.745-approximation, solving a problem posed by Hill and Kertz in 1982. We also apply these prophet inequalities to posted price mechanisms, and we prove the same tight bounds for both a nonadaptive and an adaptive posted price mechanism when buyers arrive in random order.

Variance estimation in adaptive sequential Monte Carlo

Sequential Monte Carlo (SMC) methods represent a classical set of techniques to simulate a sequence of probability measures through a simple selection/mutation mechanism. However, the associated selection functions and mutation kernels usually depend on tuning parameters that are of first importance for the efficiency of the algorithm. A standard way to address this problem is to apply adaptive sequential Monte Carlo (ASMC) methods, which consist in exploiting the information given by the history of the sample to tune the parameters. This article is concerned with variance estimation in such ASMC methods. Specifically, we focus on the case where the asymptotic variance coincides with the one of the “limiting” sequential Monte Carlo algorithm as defined by Beskos et al. (Ann. Appl. Probab. 26 (2016) 1111–1146). We prove that, under natural assumptions, the estimator introduced by Lee and Whiteley (Biometrika 105 (2018) 609–625) in the nonadaptive case (i.e., SMC) is also a consistent estimator of the asymptotic variance for ASMC methods. To do this, we introduce a new estimator that is expressed in terms of coalescent tree-based measures, and explain its connection with the previous one. Our estimator is constructed by tracing the genealogy of the associated interacting particle system. The tools we use connect the study of particle Markov chain Monte Carlo methods and the variance estimation problem in SMC methods. As such, they may give some new insights when dealing with complex genealogy-involved problems of interacting particle systems in more general scenarios.

Target Detection via Cognitive Radars Using Change-Point Detection, Learning, and Adaptation

Many radar detection algorithms that assume a stationary environment (clutter) have been proposed and analyzed over the years. However, in practice, changes in the nonstationary environment can perturb the parameters of the clutter distribution, or even alter the clutter distribution family, which can greatly deteriorate the target detection capability. To avoid such potential performance degradation, cognitive radar systems are envisioned which are required to rapidly realize the nonstationarity, accurately learn the new characteristics of the environments, and adaptively update the detector. In this paper, aiming to develop a fully cognitive radar for target detection in nonstationary environments, we propose a unifying framework that integrates (i) change-point detection of clutter distributions by using a data-driven cumulative sum (CUSUM) algorithm and its extended version, (ii) learning/identification of clutter distribution by applying sparse theory and kernel density estimation methods, and (iii) adaptive target detection by automatically modifying the likelihood-ratio test and corresponding detection threshold. Further, with extensive numerical examples, we demonstrate the achieved improvements in detection performance due to the proposed framework in comparison with a nonadaptive case, an adaptive matched filter method, and the clairvoyant case. We also use Wilcoxon rank-sum tests to evaluate the statistical significance of the performance improvements.

Neighborhood Matters: Influence Maximization in Social Networks with Limited Access

Influence maximization (IM) aims at maximizing the spread of influence by offering discounts to influential users (called seeding). In many applications, due to user's privacy concern, overwhelming network scale etc., it is hard to target any user in the network as one wishes. Instead, only a small subset of users is initially accessible. Such access limitation would significantly impair the influence spread, since IM often relies on seeding high degree users, which are particularly rare in such a small subset due to the power-law structure of social networks. In this paper, we attempt to solve the limited IM in real-world scenarios by the adaptive approach with seeding and diffusion uncertainty considered. Specifically, we consider fine-grained discounts and assume users accept the discount probabilistically. The diffusion process is depicted by the independent cascade model. To overcome the access limitation, we prove the set-wise friendship paradox (FP) phenomenon that neighbors have higher degree in expectation, and propose a two-stage seeding model with the FP embedded, where neighbors are seeded. On this basis, for comparison we formulate the non-adaptive case and adaptive case, both proven to be NP-hard. In the non-adaptive case, discounts are allocated to users all at once. We show the monotonicity of influence spread w.r.t. discount allocation and design a two-stage coordinate descent framework to decide the discount allocation. In the adaptive case, users are sequentially seeded based on observations of existing seeding and diffusion results. We prove the adaptive submodularity and submodularity of the influence spread function in two stages. Then, a series of adaptive greedy algorithms are proposed with constant approximation ratio.

Adaptive Relay Configuration Based on the Novel Hyperchaotic Three-Components Oscillator Operating at High Frequency: Global Synchronization

This article is investigating from one of best control technique known as periodically intermittent discrete observation control (PIDOC), the problem of global synchronization based on a relay configuration of three novel hyperchaotic oscillators of three-components (NHO) operating at high frequency. Contrary to traditional periodically intermittent control based on continuous-time state observations, PIDOC used here, chooses discrete-time state observations in work time during a control period. Our analysis has been limited to a range of parameters for which the NHO-type oscillator exhibits bursting oscillations. The global conditions of stability for non-adaptive and adaptive cases have been proven analytically. To the best of our knowledge and in the literature of the relay coupling system, no work has been carried out concerning the study of the stability of adaptive synchronization case. The Synchronization of the system is analysed in terms of its control gain by using time series. The numerical results show that there is global synchronization between the three relay coupled NHO-type oscillators for both non-adaptive and adaptive synchronizations. Moreover, PSpice based simulations of the analog electronic circuit for the non-adaptive case are in good accordance with both theoretical and numerical results.

Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps

We study the problem of testing unateness of functions $f:\{0,1\}^d \to \mathbb{R}.$ We give a $O(\frac{d}{\epsilon} \cdot \log\frac{d}{\epsilon})$-query nonadaptive tester and a $O(\frac{d}{\epsilon})$-query adaptive tester and show that both testers are optimal for a fixed distance parameter $\epsilon$. Previously known unateness testers worked only for Boolean functions, and their query complexity had worse dependence on the dimension both for the adaptive and the nonadaptive case. Moreover, no lower bounds for testing unateness were known. We also generalize our results to obtain optimal unateness testers for functions $f:[n]^d \to \mathbb{R}$. Our results establish that adaptivity helps with testing unateness of real-valued functions on domains of the form $\{0,1\}^d$ and, more generally, $[n]^d$. This stands in contrast to the situation for monotonicity testing where there is no adaptivity gap for functions $f:[n]^d \to \mathbb{R}$.

Single-Bit Millimeter Wave Beam Alignment Using Error Control Sounding Strategies

Millimeter wave technology is an essential component of most solutions that address the coverage and throughput demands of next-generation cellular networks. To overcome the high propagation losses however, it is necessary to deploy large antenna arrays for spatial localization of energy by beamforming. This imposes a significant communication overhead, especially when channel reciprocity does not hold. In this work, we study the problem of successive one-bit feedback-assisted beam alignment. We exploit the sparse nature of the millimeter wave channel to pose the beamforming problem as a questioning strategy. We consider both adaptive ( closed-loop ) and non-adaptive ( open-loop ) channel sounding techniques which are robust to erroneous feedback signals caused by noisy quantization. In the adaptive case, we formulate new sounding signals by drawing a parallel with the well known Ulam's problem. In the non-adaptive case, the beams are designed in accordance to an open-loop code. We demonstrate that multiple paths can also be resolved by using ideas from group testing. Finally, we show the efficacy of our proposed techniques via simulations.

Noisy Adaptive Group Testing: Bounds and Algorithms

The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of possibly noisy tests, and is relevant in applications such as medical testing, communication protocols, pattern matching, and many more. One of the defining features of the group testing problem is the distinction between the non-adaptive and adaptive settings. In the non-adaptive case, all tests must be designed in advance, whereas in the adaptive case, each test can be designed based on the previous outcomes. While tight information-theoretic limits and near-optimal practical algorithms are known for the adaptive setting in the absence of noise, surprisingly little is known in the noisy adaptive setting. In this paper, we address this gap by providing information-theoretic achievability and converse bounds under various noise models, as well as a slightly weaker achievability bound for a computationally efficient variant. These bounds are shown to be tight or near-tight in a broad range of scaling regimes, particularly at low noise levels. The algorithms used for the achievability results have the notable feature of only using two or three stages of adaptivity.

The impact of spike-frequency adaptation on balanced network dynamics.

A dynamic balance between strong excitatory and inhibitory neuronal inputs is hypothesized to play a pivotal role in information processing in the brain. While there is evidence of the existence of a balanced operating regime in several cortical areas and idealized neuronal network models, it is important for the theory of balanced networks to be reconciled with more physiological neuronal modeling assumptions. In this work, we examine the impact of spike-frequency adaptation, observed widely across neurons in the brain, on balanced dynamics. We incorporate adaptation into binary and integrate-and-fire neuronal network models, analyzing the theoretical effect of adaptation in the large network limit and performing an extensive numerical investigation of the model adaptation parameter space. Our analysis demonstrates that balance is well preserved for moderate adaptation strength even if the entire network exhibits adaptation. In the common physiological case in which only excitatory neurons undergo adaptation, we show that the balanced operating regime in fact widens relative to the non-adaptive case. We hypothesize that spike-frequency adaptation may have been selected through evolution to robustly facilitate balanced dynamics across diverse cognitive operating states.

Computationally Simple MMSE (A-Optimal) Adaptive Beam-Pattern Design for MIMO Active Sensing Systems via a Linear-Gaussian Approximation

This paper presents an approximate minimum mean squared error (MMSE) adaptive beam-pattern design (ABD) method for MIMO active sensing systems. The proposed approximate MMSE ABD method leverages the physics of the MIMO arrays to provide a linear-Gaussian approximation that is specific to MIMO active sensing systems, and yields a computationally simple optimization problem. Computational complexity analysis confirms this theoretical reduction in the number of floating-point operations required, most notably that evaluation of the proposed approximate optimization cost function grows polynomially with the number of targets being tracked, whereas for evaluation of the exact cost the growth is exponential. Additionally, numerical results indicate that, even for a simple scenario with a single target being tracked, the proposed approximate MMSE ABD method does indeed reduce the mean squared error of target parameter estimation compared to the nonadaptive case, with a reduction in computation time of four orders of magnitude compared to exact MMSE ABD.

Determination of the intersegmental plane using the slip-knot method.

Visualization of intersegmental planes in the lung is desirable for precise anatomical lung segmentectomy. We developed the slip-knot method for creating inflation-deflation lines. This study aimed to assess relevant data for thoracoscopic segmentectomy performed using this method. In the slip-knot method, the objective segmental bronchus is looped with a monofilament thread. One end of the thread is then pulled during temporary bilateral ventilation, causing the knot to slip toward the bronchus. Thereafter, bronchial ligation is tightened to block the outflow of segmental air, ensuring that the segment remains expanded while the other reserved segments collapse on resumption of unilateral ventilation. Data from 221 patients who underwent thoracoscopic pulmonary segmentectomy between 2010 and 2016 were analyzed. A total of 147 patients (67%) were indicated for the slip-knot method, and 74 cases (33%) were non-adaptive cases. Ninety six percent of 147 cases were well adapted to the slip-knot method, which allowed us to obtain good inflation-deflation line images to determine the intersegmental plane. The mean operative time was 171±51 min (range, 71-367 min). The mean duration of chest tube insertion was 1.5±1.2 days (range, 1-7 days). Three cases (2.0%) had prolonged air-leakage and one (0.7%) case had readmission for late air-leakage. Our method enables determination of anatomical intersegmental planes using only one monofilament thread, thus facilitating thoracoscopic pulmonary anatomical segmentectomy.

Semi‐global cooperative output regulation of a class of nonlinear uncertain multi‐agent systems under switching networks

SummaryIn this paper, we consider the semi‐global cooperative output regulation problem for a class of nonlinear uncertain multi‐agent systems under switching networks. At first, we study the nonadaptive case when the exosystem has no parametric uncertainties and construct a common Lyapunov function to achieve the output regulation for general switching connected networks. Next, we study the case when the exosystem contains some parametric uncertainties. To solve the problem, we establish a stability result for a class of time‐varying system, which is then used in the design of distributed adaptive internal model‐based control. Then we construct multiple Lyapunov functions for the switching signal with its average dwell time lower bounded by a given constant. Throughout the paper, we treat the closed‐loop multi‐agent system from the viewpoint of singular perturbation. In fact, the singular perturbation‐based method provides an effective tool to handle the multi‐agent system under switching networks. Finally, we give numerical simulations based on Duffing systems and flexible manipulator systems to illustrate the effectiveness of our method. Copyright © 2017 John Wiley & Sons, Ltd.

Strong converses for group testing from finite blocklength results

We prove new strong converse results in a variety of group testing settings, generalizing a result of Baldassini, Johnson and Aldridge. These results are proved by two distinct approaches, corresponding to the non-adaptive and adaptive cases. In the non-adaptive case, we mimic the hypothesis testing argument introduced in the finite blocklength channel coding regime by Polyanskiy, Poor and Verd\'{u}. In the adaptive case, we combine a formulation based on directed information theory with ideas of Kemperman, Kesten and Wolfowitz from the problem of channel coding with feedback. In both cases, we prove results which are valid for finite sized problems, and imply capacity results in the asymptotic regime. These results are illustrated graphically for a range of models.