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In this paper, we consider the quasilinear Schrödinger equation − Δ u + V (x) u − u Δ (u 2) = g (u) , x ∈ R 3 , where V and g are continuous functions. Without the coercive condition on V or the monotonicity condition on g , we show that the problem above has a least energy sign-changing solution and infinitely many sign-changing solutions. Our results especially solve the problem above in the case where g (u) = | u | p − 2 u (2 < p < 4) and complete some recent related works on sign-changing solutions, in the sense that, in the literature only the case g (u) = | u | p − 2 u (p ≥ 4) was considered. The main results in the present paper are obtained by a new perturbation approach and the method of invariant sets of descending flow. In addition, in some cases where the functional merely satisfies the Cerami condition, a deformation lemma under the Cerami condition is developed. [ABSTRACT FROM AUTHOR]

For positive integers u and v , let L u = [ 1 0 u 1 ] and R v = [ 1 v 0 1 ]. Let G u , v be the group generated by L u and R v. In a previous paper, the authors determined a characterization of matrices M = [ a b c d ] in G u , v when u , v ≥ 3 in terms of the short continued fraction representation of b / d. We extend this result to the case where u v ≥ 5. Additionally, we compute [ G u , v : G u , v ] where G u , v = { [ 1 + u v n 1 v n 2 u n 3 1 + u v n 4 ] ∈ SL 2 (Z) : (n 1 , n 2 , n 3 , n 4) ∈ Z 4 } for u , v ≥ 1 , extending a result of Chorna, Geller, and Shpilrain and solving the membership problem for G u , v with u , v ≥ 1. [ABSTRACT FROM AUTHOR]

A general strategy is proposed to solve the problem of efficient and controlled removal of droplets from solid surfaces. Droplet departure size on magnetic responsive polydimethylsiloxane superhydrophobic microplates (MPSM) was significantly reduced compared to the static structure, resulting in a 60% increase in the efficiency of fog collection at 15 min to meet a wide range of fields. [Display omitted] Efficient removal of droplets from solid surfaces is significant in various fields, including fog collection and condensation heat transfer. However, droplets removal on common surfaces with static structures often occurs passively, which limits the possibility of increasing removal efficiency and lacks intelligent controllability. In this paper, an active strategy based on extrusion ejection is proposed and demonstrated on the magnetic responsive polydimethylsiloxane (PDMS) superhydrophobic microplates (MPSM). The MPSM can reversibly transit between the upright and tilted state as the external magnetic field is alternately applied and removed. Under the magnetic field, the direction and trajectories of droplets departure can be intelligently controlled, demonstrating excellent controllability. More importantly, compared with the static structure where the droplet must reach a certain size before departure, droplets can be ejected at smaller sizes as the MPSM is tilted. These advantages are of great significance in many fields, such as a highly efficient fog harvesting system. This strategy of extrusion ejection based on dynamic surface structure control reported in this work may provide fresh ideas for efficient droplet manipulation. [ABSTRACT FROM AUTHOR]

An out-branching B u + (in-branching B u −) in a digraph D is a connected spanning subdigraph of D in which every vertex except the vertex u , called the root, has in-degree (out-degree) one. A good (u,v) - pair in D is a pair of branchings B u + , B v − which have no arc in common. Thomassen proved that it is NP-complete to decide if a digraph has any good pair. A digraph is semicomplete if it has no pair of non-adjacent vertices. A semicomplete composition is any digraph D which is obtained from a semicomplete digraph S by substituting an arbitrary digraph H x for each vertex x of S. Recently the authors of this paper gave a complete classification of semicomplete digraphs which have a good (u , v) -pair, where u , v are prescribed vertices. They also gave a polynomial algorithm which for a given semicomplete digraph D and vertices u , v of D , either produces a good (u , v) -pair in D or a certificate that D has no such pair. In this paper we show how to use the result for semicomplete digraphs to completely solve the problem of characterizing semicomplete compositions which have a good (u , v) -pair for given vertices u , v. Our solution implies that the problem of deciding the existence of a good (u , v) -pair and finding such a pair when it exists is polynomially solvable for all semicomplete compositions. We also completely solve the problem of deciding the existence of a good (u , v) -pair and finding one when it exists for digraphs that are compositions of transitive digraphs. Combining these two results we obtain a polynomial algorithm for deciding whether a given quasi-transitive digraph D has a good (u , v) -pair for given vertices u , v of D. This proves a conjecture of Bang-Jensen and Gutin from 1998. [ABSTRACT FROM AUTHOR]

Arc stability determines welding quality, so it is important to study arc stability online detection. In order to solve the problem, a rotating arc stability sensor is developed in this paper, which can realize the online detection of arc stability. Firstly, the general model of the input and output mapping relationship of the rotating arc stability sensor and its parameter determination method have been studied. Then, the parameter adaptive mathematical model establishment method based on the objective optimal neural network has been studied, and the parameter adaptive model of the rotating arc stability sensor has been established based on the objective optimal neural network, so that the parameters of the model can be automatically adjusted online according to the uncertain and changing welding state. Finally, the online detection method of arc stability has been studied based on the parameter adaptive model of the rotating arc stability sensor. Using the method designed in this paper, arc stability detection experiments were conducted under different welding current, welding voltage, and weld shape conditions. The experimental results showed that the detected arc stability and welding deviation were consistent with the actual welding results. Therefore, the method designed in this paper can accurately and reliably detect the arc stability. [ABSTRACT FROM AUTHOR]

Object detection technology is significant for automatic fish monitoring and intelligent aquaculture. Deep learning fish detection provides great convenience for aquaculture with its unique advantages. However, it still faces several challenges in practical applications. For example, due to the perspective projection effect, the different scales of non-rigid fish will cause difficulties in the identification and location. Also, when labelled data collection is expensive or not feasible, domain shifts due to differences in data distribution can severely limit the practical deployment of algorithms in aquaculture. Hence, this paper proposes a decoupled multi-scale discriminant model especially for cross-domain fish detection to solve these problems, termed DMDnet. The model is divided into three components: multi-scale feature enhancement detector, category adaptive module, and adaptive regression module. An enhanced feature pyramid is embedded into the detector to alleviate the multi-scale problem of fish and improve the discrimination of the whole model. Category and regression adaptors with independent parameters are also introduced to avoid the damage of adversarial training on the detector's discriminability. These two adaptors are separated from the detector, to improve transferability. The cross-domain experiments were carried out on underwater fish images collected from various scenes and aquaculture conditions. The results verify that this method can improve the detector's generalisation performance significantly in the unlabelled new domain. Hence, this method can reduce the cost and increase the efficiency of aquaculture, which has a better application prospect. • Decoupled domain adaptation model proposed for underwater fish detection. • Enhanced feature pyramid introduced to solve the multi-scale of the fish. • Adaptors decoupled from detector to avoid interference between different tasks. • Method can improve generalisation of cross-domain detection in aquaculture. • Cross-domain experiments performed to verify the method and prove its validity. [ABSTRACT FROM AUTHOR]

We describe a practical algorithm for computing normal forms for semigroups and monoids with finite presentations satisfying so-called small overlap conditions. Small overlap conditions are natural conditions on the relations in a presentation, which were introduced by J. H. Remmers and subsequently studied extensively by M. Kambites. Presentations satisfying these conditions are ubiquitous; Kambites showed that a randomly chosen finite presentation satisfies the C (4) condition with probability tending to 1 as the sum of the lengths of relation words tends to infinity. Kambites also showed that several key problems for finitely presented semigroups and monoids are tractable in C (4) monoids: the word problem is solvable in O (min ⁡ { | u | , | v | }) time in the size of the input words u and v ; the uniform word problem for 〈 A | R 〉 is solvable in O (N 2 min ⁡ { | u | , | v | }) where N is the sum of the lengths of the words in R ; and a normal form for any given word u can be found in O (| u |) time. Although Kambites' algorithm for solving the word problem in C (4) monoids is highly practical, it appears that the coefficients in the linear time algorithm for computing normal forms are too large in practice. In this paper, we present an algorithm for computing normal forms in C (4) monoids that has time complexity O (| u | 2) for input word u , but where the coefficients are sufficiently small to allow for practical computation. Additionally, we show that the uniform word problem for small overlap monoids can be solved in O (N min ⁡ { | u | , | v | }) time. [ABSTRACT FROM AUTHOR]

For the famous Camassa-Holm equation, the well-posedness in C ([ 0 , T ] ; B p , 1 1 + 1 p (R)) with 1 ≤ p ≤ 2 and the ill-posedness in C ([ 0 , T ] ; B ∞ , 1 1 (R)) had been studied in [15,16,23]. That is to say, it left an open problem in the critical case C ([ 0 , T ] ; B p , 1 1 + 1 p (R)) with 2 < p < + ∞ proposed by Danchin in [15,16]. In this paper, we solve this problem and obtain the local well-posedness for the Camassa-Holm equation in critical Besov spaces C ([ 0 , T ] ; B p , 1 1 + 1 p (R)) with 1 ≤ p < + ∞. It is worth mentioning that our method is suitable for many Camassa-Holm type equations, such as the Novikov equation and the two-component Camassa-Holm system, and can also improve their index of the local well-posedness. [ABSTRACT FROM AUTHOR]

Dujmović et al. [ J. ACM '20] proved that every planar graph is isomorphic to a subgraph of the strong product of a bounded treewidth graph and a path. Analogous results were obtained for graphs of bounded Euler genus or apex-minor-free graphs. These tools have been used to solve longstanding problems on queue layouts, non-repetitive colouring, p -centered colouring, and adjacency labelling. This paper proves analogous product structure theorems for various non-minor-closed classes. One noteable example is k -planar graphs (those with a drawing in the plane in which each edge is involved in at most k crossings). We prove that every k -planar graph is isomorphic to a subgraph of the strong product of a graph of treewidth O (k 5) and a path. This is the first result of this type for a non-minor-closed class of graphs. It implies, amongst other results, that k -planar graphs have non-repetitive chromatic number upper-bounded by a function of k. All these results generalise for drawings of graphs on arbitrary surfaces. In fact, we work in a more general setting based on so-called shortcut systems, which are of independent interest. This leads to analogous results for certain types of map graphs, string graphs, graph powers, and nearest neighbour graphs. [ABSTRACT FROM AUTHOR]

Crane swing & relevant vibration are critical safety and efficiency issues to be addressed in construction automation, involving various disturbance and uncertainties. This paper presents for the first time a controller designed for 5-DOF tower crane systems with no velocity signals, and its effectiveness is experimentally verified. Compared to previous controllers, the new design utilizes an adaptive output feedback control method with accurate online gravity compensation, which solves the problems of unavailability velocity, noise amplification by numerical difference, and steady state error of cable in tower crane control. Additionally, the saturated control inputs are guaranteed by employing bounded functions. The results of this study unveil that the controller proposed in this paper can simultaneously achieve accurate trolley/jib/cable positioning, rapid payload swing suppression and elimination, as well as precise payload mass estimation, and guarantee control inputs constraints. This study provides a new approach for accurate control of tower crane systems. [ABSTRACT FROM AUTHOR]

In this paper, the parallel machine scheduling problem with DeJong's learning effect, is addressed. The objective function to be minimized is the makespan. This problem is proofed to be NP-Hard in the strong sense. This is the challenging theoretical side of the studied problem. Furthermore, several real-life situations in manufacturing and computer science are modeled using the current problem. Several algorithms intended to solve the studied problem within a reasonable computing time are proposed in literature. Among these algorithms the exact methods, which failed to solve the studied problem to optimality even for small size instances. In this paper several new heuristics and meta-heuristics are proposed. These heuristics are classified into three types. The first type is based on Longest Processing Time (LPT) rule. The innovation is the modification of the LPT rule in a way to cope efficiently with the learning effect concept, by randomizing the selection of the next scheduled job. The second type of heuristics, is taking advantage of an exact Branch and Bound algorithm, developed originally for the classical parallel machine scheduling problem. The contribution for this kind of heuristics is lying in the modification of the processing time values, according to a prefixed selected functions. The third type of methods is based in an adaptation of the Genetic Algorithm to the learning effect concept. This adaptation consists in enlarging the area of selection of the parameters values. To assess the performance and the efficiency of the proposed heuristics, a newly developed lower bound is proposed. This lower bound is based on a relaxation of the studied problem, which allows to obtain a minimum cost flow problem. Finally, an extensive experimental study is conducted over a benchmark test problems. The obtained results provide strong evidence that the proposed procedures outperform the earlier existing ones. • Modeling the learning effect in parallel machine scheduling problem. • Development of dispatching rules based heuristics. • Development of heuristics based on the resolution of NP-Hard problems. • Development of new tight lower bounds based on the maximum allowed position. • Caring out an extensive experimental study that confirms the efficiency of the proposed procedures. [ABSTRACT FROM AUTHOR]

In this paper we consider lower order perturbations of the critical Lane-Emden system posed on a bounded smooth domain Ω ⊂ R N , with N ≥ 3 , inspired by the classical results of Brezis and Nirenberg [4]. We solve the problem of finding a positive solution for all dimensions N ≥ 4. For the critical dimension N = 3 we show a new phenomenon, not observed for scalar problems. Namely, there are parts on the critical hyperbola where solutions exist for all 1-homogeneous or subcritical superlinear perturbations and parts where there are no solutions for some of those perturbations. [ABSTRACT FROM AUTHOR]

The paper is concerned with gradient blowup behavior for a semilinear parabolic equation u t − Δ u = δ m (x) | ∇ u | p + Λ in Ω × (0 , T) with the zero Dirichlet condition. Two results with p > m + 2 and m ⩾ 0 are established. One of which is that any gradient blowup solution follows a global ODE type behavior, with domination of normal derivatives over the tangential derivatives. The other is about time-increasing solutions. Zhang and Hu (2010) [50] obtained the precise gradient blowup rate in one-dimensional case, but the higher dimensional case was left as an open problem. Here we solve this problem by establishing the gradient blowup rate, for any small γ > 0 , C (T − t) − m + 1 p − m − 2 ⩽ ‖ ∇ u ‖ ∞ ⩽ C γ (T − t) − m + 1 p − m − 2 − γ for suitable ranges of p and m , which extends the result of (Attouchi and Souplet (2020) [3]) to the case m ≠ 0. As an important by-product which is of independent interests itself, the gradient estimate near boundary for the corresponding elliptic equation is derived under weaker assumptions on the inhomogeneous term. [ABSTRACT FROM AUTHOR]

In this paper, we consider an eigenvalue problem defined on a two-patch domain. Our first aim is to show that the two-patch eigenvalue problem is equivalent to the eigenvalue problem of a measure differential equation defined on an one-patch domain. Our second aim is to study the existence of principal eigenvalue of the measure differential equation, and we will prove the principal eigenvalue is continuously depending on the weight measure in the weak⁎ topology of the measure space. Our third aim is to solve a minimization problem on principal eigenvalues. Some main results of this paper have interesting relations with population dynamics. We will interpret these results in terms of survival chances and optimal distribution of resources. [ABSTRACT FROM AUTHOR]

• A novel unscented Kalman filter without direct feedthrough is proposed for the identification of joint input-system without direct feedthrough. • According to the uncertainty of the identified unknown inputs, two algorithms of the proposed method are presented. • The proposed method is verified by linear/nonlinear hysteretic shear structures under external or seismic excitations. Given the difficulty of accurately measuring external inputs acting on structures, the research on joint input-system identification has gained significant attention in recent years. Among them, several unscented Kalman filters under unknown input (UKF-UI) based methods have been proposed for joint input and system identification. However, the existing UKF-UI methods require unknown inputs to be presented in the observation equations, which is not always available in practical engineering. To solve this problem, an unscented Kalman filter under unknown input without direct feedthrough (UKF-UI-WDF) is proposed in this paper for real-time joint input and system identification of structural systems without direct feedthrough using limited response measurements. The proposed UKF-UI-WDF is derived for recursive identification of the structural states, parameters, and unknown inputs by integrating unknown input estimation into the conventional UKF framework. In each identification step, the unknown inputs are first identified by minimizing posterior residuals of measurements, and then the structural states and parameters are identified by a traditional unscented Kalman filtering using the identified unknown inputs. According to whether the uncertainty of the identified unknown inputs can be quantitatively described or not, two implementation algorithms are provided in this paper. In algorithm 1, only the mean values of unknown inputs can be identified. In algorithm 2, the unknown inputs are identified as a set of sigma points, so not only the mean values but also the variance of the unknown inputs can be estimated. The effectiveness of the proposed method is examined by the joint input and system identification of various case studies of linear and nonlinear hysteretic shear structures subjected to unknown external or base excitations, respectively. The results show that the proposed UKF-UI-WDF method can effectively perform real-time joint input-system identification of structural systems without direct feedthrough using limited response measurements. [ABSTRACT FROM AUTHOR]

• In this paper, we propose a distorted pulse detection method based on odd function for pulse decomposition, to solve the problem of optical path mismatch in UWFBG array. • In theory, we build a mathematical model of the distortion pulse and derive the corresponding odd function. • Then, we analyze the peak trajectory obtained by the difference curve by simulation, and determine the optimal interference position of the distorted pulse. • Finally, we use the vibrating liquid column method to carry out underwater acoustic sensing experiments, under different conditions of optical path mismatch. • The results show that, when the distance between adjacent UWFBGs is 50 m and pulse width with 100 ns, the gain of harmonic SNR and average PSD is improved from 2.3 dB and 1.8 dB to 11.2 dB and 10.0 dB respectively, under different circumstances with length difference for 1 m, 1.5 m, and 2 m respectively. In this paper, we propose a distorted pulse detection method based on odd function for pulse decomposition, to solve the problem of optical path mismatch in UWFBG array. In theory, we build a mathematical model of the distortion pulse and derive the corresponding odd function. Then, we analyze the peak trajectory obtained by the difference curve by simulation, and determine the optimal interference position of the distorted pulse. Finally, we use the vibrating liquid column method to carry out underwater acoustic sensing experiments, under different conditions of optical path mismatch. The results show that, when the distance between adjacent UWFBGs is 50 m and pulse width with 100 ns, the gain of harmonic SNR and average PSD is improved from 2.3 dB and 1.8 dB to 11.2 dB and 10.0 dB respectively, under different circumstances with length difference for 1 m, 1.5 m, and 2 m respectively. So, the algorithm is more robust to length mismatch, and verifies the effectiveness of the algorithm, and has potential significance for reducing the difficulty of designing the UWFBG array interferometer. [ABSTRACT FROM AUTHOR]

With the evolving application demands, the inherent immutability of consortium blockchains hinders their widespread adoption. For example, expired data stored on the chain cannot be deleted, and erroneous data cannot be redacted, seriously limiting the flexibility of consortium blockchains. However, existing redactable blockchain solutions need to be improved in aspects of decentralization, efficiency, and fault tolerance. This paper develops a new v erifiable d istributed c hameleon h ash (VDCH) function to solve the above problems. With VDCH, nodes share chameleon keys with a secure multi-party computation protocol based on a verifiable key-sharing scheme, and the collision shares can be verified with a Schnorr non-interactive zero-knowledge proof protocol, which enhances the fault tolerance of the consortium chain while maintaining its decentralized nature. Then, this paper proposes a consensus protocol called CVTSS based on verifiable threshold signatures, which provides protocol support for collaborative hash collision computation by multiple nodes using VDCH, thus avoiding the dependence on Nakamoto consensus and improving the redaction efficiency. Meanwhile, CVTSS uses threshold signatures to prevent malicious nodes from tampering with data using one-time chameleon keys. Finally, this paper constructs an efficient, practical, and secure redactable consortium chain scheme based on VDCH and CVTSS. Theoretical analysis and experimental results show that the proposed scheme can operate safely in the presence of malicious nodes with an acceptable time cost. • This paper proposes a verifiable distributed chameleon hash function - VDCH. • VDCH makes the process of computing hash collisions fault-tolerant. • This paper proposes a threshold signature-based consensus protocol - CVTSS. • The feasibility and security of our scheme are proven by both theoretical analysis and experimental evaluations. • Experiments show that our scheme is fault-tolerant and highly efficient. [ABSTRACT FROM AUTHOR]

• A novel mistuning identification method based on proper orthogonal modes is proposed. • The BTT data can be used as input information for the identification process. • The method can be applied to online mistuning identification and model updating. To solve the problem of online mistuning identification of bladed disks, this paper proposes a novel mistuning identification method based on proper orthogonal modes (POM-ID) and the response data. Firstly, the proposed method is analyzed by numerical simulation technology, and the influence of related parameters on the identification results is discussed. Compared with the traditional method, the effectiveness of the proposed method is verified. Secondly, the POM-ID method is applied to identify the mistuning parameters of an actual bladed disk based on the blade tip timing test data. Finally, the identification results of the rotating bladed disk are verified by using static test results, and the dynamic model of the bladed disk is updated. The accuracy of the updated model is confirmed by the aspects of natural frequency and vibration coupling effect. The results indicate that the natural frequency error of the modified model is less than 1%, and the vibration coupling law between blades is consistent with the test results. The mistuning identification method proposed in this paper is especially suitable for test data of the rotating bladed disk and is expected to be applicable for online dynamic updating of the bladed disk model. [ABSTRACT FROM AUTHOR]

This paper is concerned with the inverse eigenvalue problem (IEP) for "fixed–fixed" mass–spring–inerter systems. Unlike the "fixed–free" case, a "fixed–fixed" system has its both ends attached to the ground. This brings some essential differences in the IEP. We find that the construction strategy proposed in Liu et al. (2022) cannot be readily applied here. So we endeavor to develop a new strategy in this paper to solve the problem and accordingly derive a necessary and sufficient condition for the "fixed–fixed" case. [ABSTRACT FROM AUTHOR]

This paper aims to study linear sets of minimum size on the projective line, that is F q -linear sets of rank k in PG (1 , q n) admitting one point of weight one and having size q k − 1 + 1. Examples of these linear sets have been found by Lunardon and the second author (2000) and, more recently, by Jena and Van de Voorde (2021). However, classification results for minimum size linear sets are known only for k ≤ 5. In this paper we provide classification results for minimum size linear sets admitting two points with complementary weights. We construct new examples (not necessarily with complementary weights) and also study the related Γ L (2 , q n) -equivalence issue. These results solve an open problem posed by Jena and Van de Voorde. The main tool relies on two results by Bachoc, Serra and Zémor (2017 and 2018) on the linear analogues of Kneser's and Vosper's theorems. We then conclude the paper pointing out a connection between critical pairs and linear sets, obtaining also some classification results for critical pairs. [ABSTRACT FROM AUTHOR]

Recently, Federated Learning (FL) has been explored as a new paradigm that preserves both data privacy and end-users knowledge while reducing latency during model training. While often applied between a central server and the edge devices, FL deals with a wide range of end-user applications and devices. Given the Internet of Things (IoT) current popularity, its relevance and its penetration in several new application domains, this work examines the new challenges faced when combining IoT with the classic FL model. The limited resources of IoT edge devices require careful adaptation of the way how FL should be structured in this scenario. In addition, since FL is a distributed paradigm that shares deep learning artifacts through a network, there are also communication issues reminiscent to IoT networks that need special consideration. Thus, it is necessary to optimize the use of both processing and communication resources when considering the use of IoT edge devices as part of a FL. This paper systematically reviews current advances and steps taken towards dealing with resource optimization when using FL as part of IoT scenarios. We examine the published works over the last ten years and discuss the main goals, scenarios, and developed solutions to solve the problems encountered. We also present the main metrics used to quantify the effectiveness and to evaluate the performance of existing IoT based architectures with FL support. • Federated Learning preserves data privacy and end-users knowledge. • Federated Learning deals with a wide range of end-user applications and devices. • Internet of Things application offers a substantial source of data. • Federated Learning is seen as a suitable approach for building smart IoT systems. • Federated Learning and IoT integration present peculiar IoT-scenario challenges. [ABSTRACT FROM AUTHOR]

Nonblocking data structures are an essential part of many parallel applications in that they can help to improve fault tolerance and performance. Although there are scores of nonblocking data structures, such as stacks, queues, double-ended queues (deques), lists, widely used in practice, most of them are designed to be used on shared-memory machines only, and cannot be used in a distributed-memory setting. Several recent studies focus on the development of novel tailor-made nonblocking distributed data structures and omit the potential for adapting a great wealth of existing nonblocking shared-memory ones for the distributed-memory case. Hence, we propose a general approach for bridging the gap between most existing nonblocking data structures and distributed-memory machines in this work. Several challenges, such as safe memory reclamation and solving the ABA problem, must be overcome. To address these issues, we present a global memory management scheme. The scheme takes advantage of hazard pointers which are widely used to tackle the problems in shared-memory environments. To demonstrate our general approach, we take stacks as a typical example of nonblocking data structures. This work also provides a survey of well-known nonblocking stack algorithms along with our analysis and evaluation in distributed-memory environments. Moreover, this paper depicts how to improve performance of a stack algorithm by making use of node locality. Besides, a cost model based on worst cases is devised to help gain a better understanding into experimental results of nonblocking distributed data structures, along with our analysis of the influence of two popular lock-free programming patterns on performance. • A general remedy porting nonblocking data structures to distributed memory. • A global memory manager reusing reclaimed global memory, avoiding the ABA problem. • A node-aware design of the elimination-backoff stack for distributed memory. • Experimental results and an analysis of nonblocking stacks for distributed memory. • Performance implications of lock-free programming patterns for distributed memory. [ABSTRACT FROM AUTHOR]

In this paper, we study a free boundary problem modeling solid tumor growth with vasculature which supplies nutrients to the tumor; this is characterized in the Robin boundary condition. It was recently established [Discrete Cont. Dyn. Syst. 39 (2019) 2473-2510] that for this model, there exists a threshold value μ ⁎ such that the unique radially symmetric stationary solution is linearly stable under non-radial perturbations for 0 < μ < μ ⁎ and linearly unstable for μ > μ ⁎. In this paper we further study the nonlinear stability of the radially symmetric stationary solution, which introduces a significant mathematical difficulty: the center of the limiting sphere is not known in advance owing to the perturbation of mode 1 terms. We prove a new fixed point theorem to solve this problem, and finally obtain that the radially symmetric stationary solution is nonlinearly stable for 0 < μ < μ ⁎ when neglecting translations. [ABSTRACT FROM AUTHOR]

Let A be the classical, singly-graded Steenrod algebra over the prime order field F 2 and let P ⊗ h : = F 2 [ t 1 , ... , t h ] denote the polynomial algebra on h generators, each of degree 1, viewed as a module over A. Write G L h for the usual general linear group of rank h over F 2. As well known, the (mod 2) cohomology groups of the Steenrod algebra, Ext A h , h + ⁎ (F 2 , F 2) is still largely mysterious for all homological degrees h ≥ 6. The h -th algebraic transfer T r h A : (F 2 ⊗ G L h Ann A ‾ [ P ⊗ h ] ⁎) n ⟶ Ext A h , h + n (F 2 , F 2) , defined by William Singer [28] , is a helpful tool to describe that Ext groups. Singer conjectured that this transfer is a monomorphism, but it remains open for any h ≥ 5. There is currently no information on the conjecture for h = 6. In this paper, we verify Singer's conjecture for homological degree h = 6 and the internal degree of the general form n s : = 6 (2 s − 1) + 10 ⋅ 2 s. This result is important, since it tells us that the non-zero elements h 2 2 g 1 = h 4 P h 2 ∈ Ext A 6 , 6 + n 1 (F 2 , F 2) , and D 2 ∈ Ext A 6 , 6 + n 2 (F 2 , F 2) are not in the image of the sixth algebraic transfer. This Note is a continuation of our previous one [22] , which will refer to as Part I. Our approach is based on explicitly solving the hit problem for the Steenrod algebra in the case h = 6 and degree n s. This extends a result in Mothebe, Kaelo and Ramatebele [13]. At the same time, we also use this obtained result to establish the dimension result for the space of the unhit elements, F 2 ⊗ A P ⊗ 7 in a certain general degree. [ABSTRACT FROM AUTHOR]

The use of multiple independent spanning trees (ISTs) for data broadcasting in networks provides a number of advantages, including the increase of fault-tolerance and secure message distribution. Thus, the designs of multiple ISTs on several classes of networks have been widely investigated. Kao et al. (2019) [18] proposed an algorithm to construct independent spanning trees in bubble-sort networks. The algorithm is executed in a recursive function and thus is hard to parallelize. In this paper, we focus on the problem of constructing ISTs in bubble-sort networks B n and present a non-recursive algorithm. Our approach can be fully parallelized, i.e., every vertex can determine its parent in each spanning tree in constant time. This solves the open problem from the paper by Kao et al. Furthermore, we show that the total time complexity O (n ⋅ n !) of our algorithm is asymptotically optimal, where n is the dimension of B n and n ! is the number of vertices of the network. • We present an algorithm for constructing multiple independent spanning trees in bubble-sort networks. • Our approach can be fully parallelized, thus solving an open problem from Kao et al. (2019). • We show that the total time complexity of our algorithm is asymptotically optimal. [ABSTRACT FROM AUTHOR]

[Display omitted] • A tristable nonlinear energy sink (TNES) is proposed for suppressing strong excitation vibration. • The TNES can eliminate the detached resonance curve and enlarge the effective range of the NES. • The TNES can perform chaotic inter-well oscillation and suppress strong excitation vibration. As well known, the vibration reduction efficiency of the nonlinear energy sink (NES) is poor under strong excitation. In this paper, a tristable NES (TNES) is proposed. The TNES can degenerate into bistable and mono-stable NES by adjusting the geometric parameters of the springs. The governing equations of a linear oscillator coupled with the TNES under harmonic excitation are derived. The approximate analytical solution of the coupled system is obtained by using the harmonic balance method and verified numerically. The vibration suppression efficiency of TNES and NES is compared. The dynamic behavior of TNES under strong excitation is demonstrated. The results show that the nonlinear restoring force is softened due to the wide distribution of the three stable points of TNES. Therefore, compared with NES, the proposed TNES can suppress stronger excitation vibration. In addition, the low side barrier depth is conducive to TNES to perform chaotic inter-well oscillation, which can effectively suppress the strong excitation vibration and obtain good vibration reduction performance. As a result, the proposed TNES can eliminate the detached resonance curve and enlarge the effective range of the NES. Under relatively weak excitation, the vibration suppression efficiency of TNES is slightly lower than that of NES, although the TNES is also relatively significant. Therefore, this paper reveals the vibration suppression mechanism of TNES, and provides a way to effectively solve the problem of low vibration reduction efficiency of NES under strong excitation. [ABSTRACT FROM AUTHOR]

In this paper a new method for solving complex estimation problems for systems governed by partial differential equations and characterized by non-uniqueness (or equifinality) is presented. For such problems, the usefulness of the MAP estimates is doubtful, especially if the available prior information is very limited or not plausible in general. Thus, the posterior mean or median estimates would be more appropriate, which implies that the Bayesian approach has to be preferred. Since the direct use of the Bayesian approach involving computationally expensive models is not feasible a hybrid method which combines the Bayesian and variational elements in a unique way is suggested. The main idea of the method is to find one particular posterior mode out of a possibly infinite set, which would have the global properties (its first moments, for example) consistent with the available prior information and close to those of the posterior mean. The method is implemented in the form of a cyclic algorithm including the Bayesian estimation part for the lumped global (hidden, latent) variables describing the moments of the spatially distributed or time-dependent variables and the variational estimation part for the invariant 'shape' functions. The method has been numerically validated for two different applications: one including the Saint-Venant hydraulic model, and another one including the nonlinear convection-diffusion transport model. The results for the former are reported in a separate paper (reference provided), for the latter - in the present paper. These results confirm the expected properties of the suggested algorithm, such as improved robustness and accuracy, in comparison to the MAP estimator represented by the variational estimation algorithm. • We consider composite estimation problems for distributed parameter systems. • These problems are often characterized by non-uniqueness (equifinality). • We present a new Bayesian Variational Cyclic method designed for solving such problems. • The method is validated using the convection-diffusion and Saint-Venant models. • It shows improved robustness and accuracy in comparison to variational estimators. [ABSTRACT FROM AUTHOR]

The families F 1 ⊆ [ n ] k 1 , F 2 ⊆ [ n ] k 2 , ... , F r ⊆ [ n ] k r are said to be cross-intersecting if | F i ∩ F j | ⩾ 1 for any 1 ⩽ i < j ⩽ r and F i ∈ F i , F j ∈ F j . Cross-intersecting families F 1 , F 2 , ... , F r are said to be non-empty if F i ≠ 0̸ for any 1 ⩽ i ⩽ r. This paper shows that if F 1 ⊆ [ n ] k 1 , F 2 ⊆ [ n ] k 2 , ... , F r ⊆ [ n ] k r are non-empty cross-intersecting families with k 1 ⩾ k 2 ⩾ ⋯ ⩾ k r and n ⩾ k 1 + k 2 , then ∑ i = 1 r | F i | ⩽ max { n k 1 − n − k r k 1 + ∑ i = 2 r n − k r k i − k r , ∑ i = 1 r n − 1 k i − 1 }. This solves a problem posed by Shi, Frankl and Qian recently. The extremal families attaining the upper bounds are also characterized. [ABSTRACT FROM AUTHOR]

Let OG (4) denote the family of all graph-group pairs (Γ , G) where Γ is finite, 4-valent, connected, and G -oriented (G -half-arc-transitive). A subfamily of OG (4) has recently been identified as 'basic' in the sense that all graphs in this family are normal covers of at least one basic member. In this paper we provide a description of such basic pairs which have at least one G -normal quotient which is isomorphic to a cycle graph. In doing so, we produce many new infinite families of examples and solve several problems posed in the recent literature on this topic. This result completes a research project aiming to provide a description of all basic pairs in OG (4). [ABSTRACT FROM AUTHOR]

We consider the quotient module Q of the Hardy module H 2 (S) defined by an analytic set M ˜ satisfying certain conditions. Denote d = dim C M ˜. When d = 1 , Q was shown to be 1-essentially normal in [24]. An analogous problem for the case d ≥ 2 was proposed in [24] , which asks whether 2 d -antisymmetric sums of certain module operators are in the trace class. In this paper we solve this problem in the affirmative. In the case d = 1 , we derive a trace formula on Q , which answers another question raised in [24]. [ABSTRACT FROM AUTHOR]

The virtual haptics is a crucial aspect of immersive virtual reality, extending the traditional experiences of sight and hearing. The vibration can provide direct normal vibration and friction reduction, making it a promising method to realize virtual haptics. However, the optimum perceptual threshold of skin for vibration is 100 Hz to 500 Hz, resulting in a too low vibrotactile resolution. The conflict between the low perceptual frequency and high resolution still remains challenges. In this paper, a low-frequency envelope wave methodology is proposed to realize the localized vibrotactile feedback. The high-frequency components are modulated into a low-frequency envelope waveform, which provides low-frequency perception and high resolution at the same time. Due to hardware limitations, the modes must be truncated and minimized as much as possible. This requirement conflicts with achieving localized vibration at arbitrary points and further implementing complex vibration patterns. Therefore, a modal optimization algorithm is proposed to solve the inverse problem. The modal participation coefficients is obtained, basing on the evaluation index that ensures the frequency of the envelope wave and the vibration pattern quality. The localized vibration patterns including multiple points, points of proportional amplitude, bar and circle are achieved with a resolution of 3 cm and a perception frequency of about 200 Hz. This method is expected to be applied to virtual reality, blind assistance, and other potential applications to enhance tactile interaction experiences. [ABSTRACT FROM AUTHOR]

Deep generative models have shown impressive results in generating realistic images of faces. GANs managed to generate high-quality, high-fidelity images when conditioned on semantic masks, but they still lack the ability to diversify their output. Diffusion models partially solve this problem and are able to generate diverse samples given the same condition. This paper introduces a novel strategy for enhancing diffusion models through multi-conditioning, harnessing cross-attention mechanisms to utilize multiple feature sets, ultimately enabling the generation of high-quality and controllable images. The proposed method extends previous approaches by introducing conditioning on both attributes and semantic masks, ensuring finer control over the generated face images. In order to improve the training time and the generation quality, the impact of applying perceptual-focused loss weighting into the latent space instead of the pixel space is also investigated. The proposed solution has been evaluated on the CelebA-HQ dataset, and it can generate realistic and diverse samples while allowing for fine-grained control over multiple attributes and semantic regions. Experiments on the DeepFashion dataset have also been performed in order to analyze the capability of the proposed model to generalize to different domains. In addition, an ablation study has been conducted to evaluate the impact of different conditioning strategies on the quality and diversity of the generated images. • A diffusion model for face generation maximizing fidelity, quality and diversity. • A multi-conditioning mechanism using both attributes and semantic masks. • Analysis of perception prioritized training in the latent space of diffusion models. [ABSTRACT FROM AUTHOR]

• Frequency assignment of an assembled structure via links between substructures. • Implementation on a test structure comprising two substructures and six links. • Discussion of challenges, e.g., rotational receptance estimation and model build-up. • Determination of links with the right cross sections as an optimisation solution. Structural modifications for assigning desirable natural frequencies and modes are an effective passive vibration control strategy. In many assembled structures, the substructures, which may come from different manufacturers/suppliers or have intended individual functions, do not allow modifications or are difficult to modify. In such common situations, designing proper links or joints used for assembling the substructures will be an effective solution to ensure that the assembled structure possesses the right modal properties. In this paper, a receptance-based frequency assignment approach is presented, which consists of a theoretical method of frequency assignment suitable for assembled structures, an indirect method for estimating rotational recpetances and a substructuring method. It is implemented on an assembled structure, which is a simplified model of a floating raft platform installed on a ship hull. The model comprises two substructures and six links. A number of experiments are carried out to measure the required receptances systematically, including rotational receptances which are measured with the help of an auxiliary structure and two rotational accelerometers. One and two frequencies are successfully assigned by using the links with the right cross-sections determined by solving an optimisation problem. Key challenges are also discussed. This work should be practically very useful in passive vibration control of assembled structures. [ABSTRACT FROM AUTHOR]

For the famous Camassa-Holm equation, the well-posedness in B p , 1 1 + 1 p (R) with p ∈ [ 1 , ∞) and the ill-posedness in B p , r 1 + 1 p (R) with p ∈ [ 1 , ∞ ] , r ∈ (1 , ∞ ] had been studied in [13,14,16,23] , that is to say, it only left an open problem in the critical case B ∞ , 1 1 (R) proposed by Danchin in [13,14]. In this paper, we solve this problem by proving the norm inflation and hence the ill-posedness for the Camassa-Holm equation in B ∞ , 1 1 (R). Therefore, the well-posedness and ill-posedness for the Camassa-Holm equation in all critical Besov spaces B p , 1 1 + 1 p (R) with p ∈ [ 1 , ∞ ] have been completed. Finally, since the norm inflation occurs by choosing an special initial data u 0 ∈ B ∞ , 1 1 (R) but u 0 x 2 ∉ B ∞ , 1 0 (R) (an example implies B ∞ , 1 0 (R) is not a Banach algebra), we then prove that this condition is necessary. That is, if u 0 x 2 ∈ B ∞ , 1 0 (R) holds, then the Camassa-Holm equation has a unique solution u (t , x) ∈ C T (B ∞ , 1 1 (R)) ∩ C T 1 (B ∞ , 1 0 (R)) and the norm inflation will not occur. [ABSTRACT FROM AUTHOR]

The performance of collective communication operations determines the overall performance of MPI applications. Different algorithms have been developed and implemented for each MPI collective operation, but none proved superior in all situations. Therefore, MPI implementations have to solve the problem of selecting the optimal algorithm for the collective operation depending on the platform, the number of processes involved, the message size(s), etc. The current solution method is purely empirical. Recently, an alternative solution method using analytical performance models of collective algorithms has been proposed and proved both accurate and efficient for one-process-per-CPU configurations. The method derives the analytical performance models of algorithms from their code implementation rather than from high-level mathematical definitions, and estimates the parameters of the models separately for each algorithm. The method is network and topology oblivious and uses the Hockney model for point-to-point communications. In this paper, we extend that selection method to the case of clusters of multi-core processors, where each core of the platform runs a process of the MPI application. We present the proposed approach using Open MPI broadcast algorithms, and experimentally validate it on three different clusters of multi-core processors, Grisou, Gros and MareNostrum4. • A novel model-based method for runtime selection of optimal collective algorithms. • Application of the proposed method to the Open MPI broadcast algorithms. • Experimental validation of the method on two modern multi-core clusters. [ABSTRACT FROM AUTHOR]

Abstract In this paper, motivated by diffraction of traveling light waves, a simple mathematical model is proposed, both for the multivariate super-resolution problem and the problem of blind-source separation of real-valued exponential sums. This model facilitates the development of a unified theory and a unified solution of both problems in this paper. Our consideration of the super-resolution problem is aimed at applications to fluorescence microscopy and observational astronomy, and the motivation for our consideration of the second problem is the current need of extracting multivariate exponential features in magnetic resonance spectroscopy (MRS) for the neurologist and radiologist as well as for providing a mathematical tool for isotope separation in Nuclear Chemistry. The unified method introduced in this paper can be easily realized by processing only finitely many data, sampled at locations that are not necessarily prescribed in advance, with computational scheme consisting only of matrix-vector multiplication, peak finding, and clustering. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we study the following classical question of extremal set theory: what is the maximum size of a family of subsets of [ n ] such that no s sets from the family are pairwise disjoint? This problem was first posed by Erdős and resolved for n ≡ 0 , − 1 (mod s) by Kleitman in the 60s. Very little progress was made on the problem until recently. The only result was a very lengthy resolution of the case s = 3 , n ≡ 1 (mod 3) by Quinn, which was written in his PhD thesis and never published in a refereed journal. In this paper, we give another, much shorter proof of Quinn's result, as well as resolve the case s = 4 , n ≡ 2 (mod 4). This complements the results in our recent paper, where, in particular, we answered the question in the case n ≡ − 2 (mod s) for s ≥ 5. [ABSTRACT FROM AUTHOR]

Highlights • In our manuscript, we proposed a high-precision demodulation method based on amplitude ratio curve to instead of the FBG reflection spectrum, which can increase the sensing precision significantly. • Compared to the traditional demodulation methods, in order to improve the precision of demodulation system, we no longer concentrate on improving the resolution of the system components, but change the idea and focus on reducing the FWHM of the FBG reflection spectrum. • The experiments show that comparing with the demodulation method based on the FBG reflection spectrum, the average maximum measure error (MME) of Bragg wavelength determination is reduced from ±1.54 pm to ±0.15 pm. Abstract For the fiber Bragg grating (FBG) sensor based on the reflection peak position searching demodulation algorithms, a key problem is that the demodulation precision of measurement signal is seriously limited by the full width half maximum (FWHM) of the FBG reflection spectrum. In this paper, in order to overcome this problem and enhance the measurement precision, we proposed a high-precision demodulation method based on amplitude ratio curve to instead of the FBG reflection spectrum, which can increase the sensing precision significantly. In this method, the Bragg wavelength of FBG is modulated periodically with a sinusoidal function to obtain a series of reflection spectra. Then at each wavelength the amplitude ratio between second harmonic frequency component and fundamental frequency component is calculated to create the amplitude ratio curve. Here, we present a comprehensive theoretical analysis and experimental demonstration to verify the advantages of this method. Comparing with the demodulation method based on the FBG reflection spectrum, the average maximum measure error (MME) of Bragg wavelength is reduced from ±1.54 pm to ±0.15 pm, which improved by 10.3 times. In addition, the influence of the modulation amplitude and sampling frequency on demodulation accuracy are also studied in this paper. [ABSTRACT FROM AUTHOR]

Abstract As a result of the reporting of casual observations of the oscillation or rotation of the beacons in transmission line guard cables, some attention has been paid to the stability of the guard cables with beacons. The relatively more frequent observation of these motions has been explained in recent papers dealing with the elastic part of the problem as a consequence of the increasing number of resonant frequencies (one for each additional beacon) that can be excited by appropriate aerodynamic loads. But a model that could explain the aerodynamic forces that can give rise to this motion is still lacking. In this paper we consider the transverse motions of a single sphere in two simplified configurations, (1) hanging (tethered at one point), and (2) swing (tethered at two points) under a longitudinal flow, performing small amplitude swinging oscillations or circular-orbit autorotation about an axis parallel to the main flow direction. The dynamic model here presented is based on the motion equations, which also include a model for the aerodynamic lift and drag forces on the sphere in transverse motion, which considers the effect of changes of flow around the sphere due to the cable interference. These forces are contained in the symmetry plane of the flow relative to the sphere, and, when projected on the lateral direction, give rise to a lateral force, which can explain the existence of the azimuthal motion even at a large reduced velocity, outside the vortex induced vibration (VIV) range The conditions for stable small oscillation motion and circular-orbit autorotation of a sphere in a swing configuration are given. The results for the aerodynamic loads in transverse motion have also been applied to the case of a circular-orbit autorotation of a hanging sphere (spherical pendulum) under a vertical flow. The angular rotation speed and the orbit radius (or cable angle) have been determined as a function of aerodynamic coefficients and configuration parameters. [ABSTRACT FROM AUTHOR]

This paper studies the problem of finding a path centdian on a tree in which vertex weights are uncertain and the uncertainty is characterized by given intervals. It is required to find a minmax regret solution, which minimizes the worst-case loss in the objective function. Puerto et al. had an O ( n 5 log ⁡ n ) -time algorithm for this problem. In this paper, we first show that there is a special case which their algorithm does not handle and it is easy to modify their algorithm to cope with this exception. Then, we further present an improved O ( n 4 ) -time algorithm. [ABSTRACT FROM AUTHOR]

In 1994, Erdős, Gyárfás and Łuczak posed the following problem: given disjoint vertex sets V 1 , ... , V n of size k , with exactly one edge between any pair V i , V j , how large can n be such that there will always be an independent transversal? They showed that the maximal n is at most (1 + o (1)) k 2 , by providing an explicit construction with these parameters and no independent transversal. They also proved a lower bound which is smaller by a 2 e -factor. In this paper, we solve this problem by showing that their upper bound construction is best possible: if n ≤ (1 − o (1)) k 2 , there will always be an independent transversal. In fact, this result is a very special case of a much more general theorem which concerns independent transversals in arbitrary partite graphs that are 'locally sparse', meaning that the maximum degree between each pair of parts is relatively small. In this setting, Loh and Sudakov provided a global maximum degree condition for the existence of an independent transversal. We show that this can be relaxed to an average degree condition. We can also use our new theorem to establish tight bounds for a more general version of the Erdős–Gyárfás–Łuczak problem and solve a conjecture of Yuster from 1997. This exploits a connection to the Turán numbers of complete bipartite graphs, which might be of independent interest. [ABSTRACT FROM AUTHOR]

Sparse polynomial interpolation, sparse linear system solving or modular rational reconstruction are fundamental problems in Computer Algebra. They come down to computing linear recurrence relations of a sequence with the Berlekamp–Massey algorithm. Likewise, sparse multivariate polynomial interpolation and multidimensional cyclic code decoding require guessing linear recurrence relations of a multivariate sequence. Several algorithms solve this problem. The so-called Berlekamp–Massey–Sakata algorithm (1988) uses polynomial additions and shifts by a monomial. The Scalar-FGLM algorithm (2015) relies on linear algebra operations on a multi-Hankel matrix, a multivariate generalization of a Hankel matrix. The Artinian Gorenstein border basis algorithm (2017) uses a Gram-Schmidt process. We propose a new algorithm for computing the Gröbner basis of the ideal of relations of a sequence based solely on multivariate polynomial arithmetic. This algorithm allows us to both revisit the Berlekamp–Massey–Sakata algorithm through the use of polynomial divisions and to completely revise the Scalar-FGLM algorithm without linear algebra operations. A key observation in the design of this algorithm is to work on the mirror of the truncated generating series allowing us to use polynomial arithmetic modulo a monomial ideal. It appears to have some similarities with Padé approximants of this mirror polynomial. As an addition from the paper published at the ISSAC conference, we give an adaptive variant of this algorithm taking into account the shape of the final Gröbner basis gradually as it is discovered. The main advantage of this algorithm is that its complexity in terms of operations and sequence queries only depends on the output Gröbner basis. All these algorithms have been implemented in Maple and we report on our comparisons. [ABSTRACT FROM AUTHOR]

Neural networks have emerged as a tool for solving differential equations in many branches of engineering and science. But their progress in frequency domain acoustics is limited by the vanishing gradient problem that occurs at higher frequencies. This paper discusses a formulation that can address this issue. The problem of solving the governing differential equation along with the boundary conditions is posed as an unconstrained optimization problem. The acoustic field is approximated to the output of a neural network which is constructed in such a way that it always satisfies the boundary conditions. The applicability of the formulation is demonstrated on popular problems in plane wave acoustic theory. The predicted solution from the neural network formulation is compared with those obtained from the analytical solution. A good agreement is observed between the two solutions. The method of transfer learning to calculate the particle velocity from the existing acoustic pressure field is demonstrated with and without mean flow effects. The sensitivity of the training process to the choice of the activation function and the number of collocation points is studied. • PINNs-based solution for problems in frequency domain acoustics is presented. • Problems associated with the existing Lagrange multiplier method are discussed. • Acoustic field is predicted in the ducts of two different cross-sections. • Mean flow and visco-thermal effects are captured with a maximum error of O (1 0 − 4). • Results show the ability of PINNs to emerge as an acoustic solver in the future. [ABSTRACT FROM AUTHOR]

The goal of this paper is to open up a new research direction aimed at understanding the power of preprocessing in speeding up algorithms that solve NP-hard problems exactly. We explore this direction for the classic Feedback Vertex Set problem on undirected graphs, leading to a new type of graph structure called antler decomposition , which identifies vertices that belong to an optimal solution. It is an analogue of the celebrated crown decomposition which has been used for Vertex Cover. We develop the graph structure theory around such decompositions and develop fixed-parameter tractable algorithms to find them, parameterized by the number of vertices for which they witness presence in an optimal solution. This reduces the search space of fixed-parameter tractable algorithms parameterized by the solution size that solve Feedback Vertex Set. [ABSTRACT FROM AUTHOR]

Parameterization of triangulated surface meshes is a crucial problem in computer graphics, computer aided geometric design and digital geometric processing. This paper addresses the problem of planar parameterization, i.e., mapping a given triangulated surface onto a planar domain. We construct an optimized algorithm for parameterization of genus-zero meshes and aim to minimize the distortion of the parameterization. An energy functional is proposed in the paper, that quantities angle and area distortions simultaneously, while the relative importance between angle and area preservation can be controlled by the user through a parameter. The method is based on an iterative procedure that incrementally flattens mesh by growing region to obtain a parameterization result with free boundary. The result is then converted to a parameterization with regular boundary by conformal mapping. Application of the method to texture mapping is presented. Experiments show that the proposed method can obtain better results than some common parameterization methods. [ABSTRACT FROM AUTHOR]

A power assignment is an assignment of transmission power to each of the wireless nodes of a wireless network, so that the induced graph satisfies some desired properties. The cost of a power assignment is the sum of the assigned powers. In this paper, we consider the dual power assignment problem, in which each wireless node is assigned a high- or low-power level, so that the induced graph is strongly connected and the cost of the assignment is minimized. We improve the best known approximation ratio from π 2 6 − 1 36 + ϵ ≈ 1.617 to 11 7 ≈ 1.571 . Moreover, we show that the algorithm of Khuller et al. [11] for the strongly connected spanning subgraph problem, which achieves an approximation ratio of 1.617, is 1.522-approximation algorithm for symmetric directed graphs. The innovation of this paper is in achieving these results by using interesting conditions for the existence of a second Hamiltonian cycle. [ABSTRACT FROM AUTHOR]