Search Results (7)

For a graph G, the zero forcing number of G, $Z\left(G\right)$, is defined to be the minimum cardinality of a set S of vertices for which repeated applications of the forcing rule results in all vertices being in S. The forcing rule is as follows: if a vertex v is in S, and exactly one neighbor u of v is not in S, then the vertex u is added to S in the subsequent iteration. Now, the failed zero forcing number of a graph is defined to be the maximum size of a set of vertices which does not force all of the vertices in the graph. A similar type of forcing is called skew zero forcing, which is defined so that if there is exactly one neighbor u of v that is not in S, then the vertex u is added to S in the next iteration. The key difference is that vertices that are not in S can force other vertices. The failed skew zero forcing number of a graph is denoted by $F^{-}\left(G\right)$. At its core, the problem we consider is how to identify the tipping point at which information or infection will spread through a network or a population. The graphs we consider are where computers/routers or people are arranged in a linear or circular formation with varying proximities for contagion. Here, we present new results for failed skew zero forcing numbers of path powers and circulant graphs. Furthermore, we found that the failed skew zero forcing numbers of these families form interesting sequences with increasing n. Full article

Photoplethysmography (PPG) is widely used to assess cardiovascular health. Yet, its effectiveness is often hindered by external factors like contact force (CF), which significantly affects the accuracy and reliability of measurements. This study investigates how variations in the CF at the index fingertips influence six signal quality indices (SQIs)—including the perfusion index, skewness, kurtosis, entropy, zero-crossing rate, and relative power—using data from 11 healthy participants. Our analysis of normalized CF values reveals that lower CF ranges (0.2 to 0.4) may be optimal for extracting information about perfusion and blood flow. However, they may not be the best range to capture all the physiological details within the PPG pulse. In contrast, higher CF ranges (0.4 to 0.6) enable capturing more complex signals that could be physiologically representative. The findings underscore the necessity of considering viscoelastic tissue properties and individual biomechanical differences, advocating for both the normalization of CF for improved cross-subject comparison and personalized CF calibration to adapt PPG devices to diverse populations. These strategies ensure measurement reliability and consistency, thereby advancing the accuracy of cardiac and vascular assessments. Our study offers guidelines for adjusting the CF levels to balance signal detail and perfusion quality, customized to meet specific analytical requirements, with direct implications for both clinical and research environments. Full article

Interior permanent magnet (IPM) motors in traction applications often employ discrete rotor skewing constructions to reduce torsional excitations and back-EMF harmonics. Although skewing is very effective in reducing cogging torque, the impact on torque ripple is not well understood and can vary significantly over the operating envelope of a motor. Skewing also leads to the creation of a non-zero axial force that may compromise the bearing life if not considered. This paper introduces a holistic methodology for analyzing the effect of skewing, aiming to minimize torsional excitations, axial forces and back-EMF harmonics whilst mitigating the impact on performance and costs. Firstly, analytical models are employed for calculating cogging torque, torque ripple and axial forces. Then, 2D and 3D finite element analysis are used to incorporate the influence of non-linear material behavior. A detailed structural model of the powertrain is employed to calculate the radiated noise and identify key areas allowing a motor designer to reduce noise, vibration and harshness (NVH). A meticulous selection process for the skewing angle, the number of skew stacks and the orientation of skew stacks is developed, giving particular attention to the effect of the selected pattern on NVH in both forward and reverse rotating directions. Full article

In the clock network design, the trade-off between power consumption and timing closure is an important and difficult issue. The clock tree architecture has a shorter wire length and better power consumption, but it is more difficult to achieve timing closure with it. On the other hand, clock mesh architecture is easier to satisfy the clock skew constraint, but it usually has much more power consumption. Therefore, a hybrid clock network architecture that combines both the clock tree and clock mesh seems to be a promising solution. In a normal hybrid mesh/tree structure, a driving buffer is placed in the intersection of mesh lines. In this paper, we propose a novel cross-mesh architecture, and we distribute the buffers to balance the overall switching capacitance, reducing the number of registers connected to a subtree, and the load capacitance of a buffer. With the average dispersion of the overall driving force, our methodology creates small non-zero skew clock trees. In addition, we integrate clock gating, register clustering, and load balancing techniques to optimize clock skew and load capacitance simultaneously. The proposed methodology has four stages: cross-mesh planning, register clustering, mesh line connecting, and load balancing. Experimental results show that our cross-mesh architecture has high tolerance for process variation, and is robust in all the operation modes. Comparing it to the uniform mesh architecture, our methodology and algorithms reduce 28.9% of load capacitance and 80.4% of clock skew on average. Compared to the non-uniform mesh architecture, we also reduce capacitance by 22.4% and skew by 76.7% on average. This illustrates that we can obtain a feasible solution effectively and improve both power consumption and clock skew simultaneously. Full article

Given a graph G, the zero forcing number of G, $Z\left(G\right)$, is the minimum cardinality of any set S of vertices of which repeated applications of the forcing rule results in all vertices being in S. The forcing rule is: if a vertex v is in S, and exactly one neighbor u of v is not in S, then u is added to S in the next iteration. Hence the failed zero forcing number of a graph was defined to be the cardinality of the largest set of vertices which fails to force all vertices in the graph. A similar property called skew zero forcing was defined so that if there is exactly one neighbor u of v is not in S, then u is added to S in the next iteration. The difference is that vertices that are not in S can force other vertices. This leads to the failed skew zero forcing number of a graph, which is denoted by $F^{-}\left(G\right)$. In this paper, we provide a complete characterization of all graphs with $F^{-}\left(G\right)=1$. Fetcie, Jacob, and Saavedra showed that the only graphs with a failed zero forcing number of 1 are either: the union of two isolated vertices; $P_3$; $K_3$; or $K_4$. In this paper, we provide a surprising result: changing the forcing rule to a skew-forcing rule results in an infinite number of graphs with $F^{-}\left(G\right)=1$. Full article

The reluctance machine is a potential candidate for electrical vehicle propulsion because of its reliable structure, low cost, flexible flux regulation ability, and wide speed range. However, the torque density is unsatisfactory because of the poor excitation ability and low stator core utilization factor. To solve this problem, in this paper, a novel hybrid reluctance machine (HRM) with the skewed permanent magnet (PM) and the zero-sequence current is proposed for electric vehicles. The skewed PM has two magnetomotive force (MMF) components with different functions. The radial MMF component provides extra torque by the flux modulation effect. The tangential MMF component can generate a constant biased field in the stator core to relieve the saturation caused by the zero-sequence current and thus improve the utilization factor of the stator core. Therefore, torque improvement and the relief of stator core saturation can be simultaneously achieved by the skewed PM. In this paper, the machine structure and principle of the proposed machine are introduced. And ultimately, the machine’s electromagnetic performances are evaluated under different PM magnetization directions and zero-sequence current angles by using finite element analysis (FEA). Full article

In this study, a simplified model of an autonomous underwater vehicle (AUV) with input saturation based on kinematic and dynamic equations was built. Subsequently, a simplified model of the AUV was used to represent its main dynamic features. In terms of trajectory tracking, only the system’s structure (i.e., the regression matrix, which is flexible and non-unique) from the nominal model of the transformed system was required to design the proposed adaptive regression matrix-based fixed-time controller (ARM-FTC). A nonlinear auxiliary sliding surface was contained in the control design to shape the system’s frequency response. When the operating point was in the neighborhood of the zero auxiliary sliding surface, nonlinear filtering gains were increased to accelerate its tracking ability. Furthermore, the skew-symmetric property condition of the time-derivative of the inertia matrix and the Coriolis and centrifugal force matrices was not necessitated for the controller design. Under an appropriate condition for lumped uncertainties, the fixed-time convergence of the auxiliary sliding surface and the corresponding tracking error is guaranteed to go to zero by the Lyapunov stability theory. Finally, a comparative study was conducted through simulations for the AUV with external disturbance and input saturation among the known parameters, learning parameters reflecting a regression matrix, and another asymptotical robust tracking control scheme. The results validate the fast tracking ability of a desired time-varying trajectory of the proposed control scheme. Full article