Necklaces,Convolutions, and X+Y

We give subquadratic algorithms that, given two necklaces each with n beads at arbitrary positions, compute the optimal rotation of the necklaces to best align the beads. Here alignment is measured according to the ? _p norm of the vector of distances between pairs of beads from opposite necklaces in the best perfect matching. We show surprisingly different results for p=1, p even, and p=∞. For p even, we reduce the problem to standard convolution, while for p=∞ and p=1, we reduce the problem to (min,+) convolution and $(\operatorname {median},+)$ convolution. Then we solve the latter two convolution problems in subquadratic time, which are interesting results in their own right. These results shed some light on the classic sorting X+Y problem, because the convolutions can be viewed as computing order statistics on the antidiagonals of the X+Y matrix. All of our algorithms run in o(n ²) time, whereas the obvious algorithms for these problems run in Θ(n ²) time.     

Picture-Hanging Puzzles

We show how to hang a picture by wrapping rope around n nails, making a polynomial number of twists, such that the picture falls whenever any k out of the n nails get removed, and the picture remains hanging when fewer than k nails get removed. This construction makes for some fun mathematical magic performances. More generally, we characterize the possible Boolean functions characterizing when the picture falls in terms of which nails get removed as all monotone Boolean functions. This construction requires an exponential number of twists in the worst case, but exponential complexity is almost always necessary for general functions.     

Indoor Radio Propagation and Interference in 2.4 GHz Wireless Sensor Networks: Measurements and Analysis

In wireless sensor networks (WSNs), the performance and lifetime are significantly affected by the indoor propagation and the interference from other technologies using the 2.4 GHz band. Next to an overview of the propagation and coexistence issues in the literature, we present a model for analysing these effects in WSNs. We also present our measurements results on the indoor propagation, the interference of the microwave oven (MWO) and their impact on the performance of the WSN. The propagation measurements reveal significant influence of the multipath: changing a node position with a few centimetres or changing the communication channel can lead up to 30 dB difference in the received power. The power leakage of MWO has been observed around $-$ 20 dBm at 1 m distances to the oven. This leads to extra retries of the 802.15.4 messages which matches our simulation results: the packet success ratio at first try decreases to 30–40 %, which increases the average active time of the sensor, closely located to the MWO. We observe that the ON–OFF pattern of the MWO could be exploited by WSNs to improve the performance.     

Solving the Hamiltonian path problem with a light-based computer

In this paper we propose a special computational device which uses light rays for solving the Hamiltonian path problem on a directed graph. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes. In each node the rays are uniquely marked so that they can be easily identified. At the destination node we will search only for particular rays that have passed only once through each node. We show that the proposed device can solve small and medium instances of the problem in reasonable time.     

Algebraic structures for fuzzy numbers from categorial point of view

Using a classic algebraic construction additive and multiplicative structures (as commutative monoids) for fuzzy numbers are obtained. Moreover, we realize here an isomorphism between these structures.     

Criteria for Identifying the Major Risks Associated with Tailings Ponds in Romania

Damage caused by accidents at hydraulic structures, due to natural hazards or human causes (e.g. terrorist sabotage) can be comparable to those caused by natural disasters. The paper identifies the major advantages of a common methodology for risk identification and quantification regarding the potential impact of accidents at tailings dams on the environment. Relevant Romanian and EU legislation and regulations enacted following the “Baia Mare” accident in 2000 are reviewed, along with a common risk evaluation methodology that can be applied by the mining sector to tailings dams.     

Online state of health prediction method for lithium-ion batteries,based on gated recurrent unit neural networks

Online state of health (SOH) prediction of lithium-ion batteries remains a very important problem in assessing the safety and reliability of battery-powered systems. Deep learning techniques based on recurrent neural networks with memory, such as the long short-term memory (LSTM) and gated recurrent unit (GRU), have very promising advantages, when compared to other SOH estimation algorithms. This work addresses the battery SOH prediction based on GRU. A complete BMS is presented along with the internal structure and configuration parameters. The neural network was highly optimized by adaptive moment estimation (Adam) algorithm. Experimental data show very good estimation results for different temperature values, not only at room value. Comparisons performed against other relevant estimation methods highlight the performance of the recursive neural network algorithms such as GRU and LSTM, with the exception of the battery regeneration points. Compared to LSTM, the GRU algorithm gives slightly higher estimation errors, but within similar prediction error range, while needing significantly fewer parameters (about 25% fewer), thus making it a very suitable candidate for embedded implementations.     

The effects of cathode flow channel size and operating conditions on PEM fuel performance: A CFD modelling study and experimental demonstration

A comprehensive 3D, multiphase, and nonisothermal model for a proton exchange membrane fuel cell has been developed in this study. The model has been used to investigate the effects of the size of the parallel‐type cathode flow channel on the fuel cell performance. The flow‐field plate, with the numerically predicted best performing cathode flow channel, has been built and experimentally tested using an in‐house fuel cell test station. The effects of the operating conditions of relative humidity, pressure, and temperature have also been studied. The results have shown that the fuel cell performs better as the size of the cathode flow channel decreases, and this is due to the increased velocity that assists in removing liquid water that may hinder the transport of oxygen to the cathode catalyst layer. Further, the modelled fuel cell was found to perform better with increasing pressure, increasing temperature, and decreasing relative humidity; the respective results have been presented and discussed. Finally, the agreement between the modelling and the experimentally data of the best performing cathode flow channel was found to be very good.     

Highly predictable execution support for critical applications with HARETICK kernel

In this paper, the problem of providing a fully predictable execution environment for critical and hard real-time applications on embedded and DSP-based platforms is studied from the viewpoint of system architecture and operation.We introduce a set of homogenous models for time, signals and tasks, which will further serve as a basis for describing the architecture and operation of a particular hard real-time kernel – “HARETICK”. The kernel provides support for concurrent operation of hard real-time tasks (the HRT execution environment), using non-preemptive scheduling algorithms, along with soft real-time tasks (the SRT environment), using classical, preemptive, priority-based scheduling algorithms.A set of applications has been developed to test the correct operation of the HARETICK kernel according to the theoretical models and to evaluate its abilities to provide high predictability of execution for critical applications. Some of the main testing results are also discussed in the paper.     

Comparative node selection‐based localization technique for wireless sensor networks: A bilateration approach

Wireless sensor networks find extensive applications, such as environmental and smart city monitoring, structural health, and target location. To be useful, most sensor data must be localized. We propose a node localization technique based on bilateration comparison (BACL) for dense networks, which considers two reference nodes to determine the unknown position of a third node. The mirror positions resulted from bilateration are resolved by comparing their coordinates with the coordinates of the reference nodes. Additionally, we use network clustering to further refine the location of the nodes. We show that BACL has several advantages over Energy Aware Co‐operative Localization (EACL) and Underwater Recursive Position Estimation (URPE): (1) BACL uses bilateration (needs only two reference nodes) instead of trilateration (that needs three reference nodes), (2) BACL needs reference (anchor) nodes only on the field periphery, and (3) BACL needs substantially less communication and computation. Through simulation, we show that BACL localization accuracy, as root mean square error, improves by 53% that of URPE and by 40% that of EACL. We also explore the BACL localization error when the anchor nodes are placed on one or multiple sides of a rectangular field, as a trade‐off between localization accuracy and network deployment effort. Best accuracy is achieved using anchors on all field sides, but we show that localization refinement using node clustering and anchor nodes only on one side of the field has comparable localization accuracy with anchor nodes on two sides but without clustering.