Showing papers on "Skew published in 2016"

Finite mixtures of canonical fundamental skew $$t$$t-distributions

Abstract: This paper introduces a finite mixture of canonical fundamental skew $$t$$t (CFUST) distributions for a model-based approach to clustering where the clusters are asymmetric and possibly long-tailed (in: Lee and McLachlan, arXiv:1401.8182 [statME], 2014b). The family of CFUST distributions includes the restricted multivariate skew $$t$$t and unrestricted multivariate skew $$t$$t distributions as special cases. In recent years, a few versions of the multivariate skew $$t$$t (MST) mixture model have been put forward, together with various EM-type algorithms for parameter estimation. These formulations adopted either a restricted or unrestricted characterization for their MST densities. In this paper, we examine a natural generalization of these developments, employing the CFUST distribution as the parametric family for the component distributions, and point out that the restricted and unrestricted characterizations can be unified under this general formulation. We show that an exact implementation of the EM algorithm can be achieved for the CFUST distribution and mixtures of this distribution, and present some new analytical results for a conditional expectation involved in the E-step.

Widely Linear Equalization for IQ Imbalance and Skew Compensation in Optical Coherent Receivers

Abstract: In this paper, an alternative approach to design linear equalization algorithms for optical coherent receivers is introduced. Using widely linear (WL) complex analysis, a general analytical model it is shown, where In-phase/quadrature (IQ) imbalances and IQ skew at the coherent receiver front-end are naturally included in channel equalization problem. Next, the problem of chromatic dispersion (CD) compensation after imbalanced and skewed coherent detection is analyzed. Based on the analytical models obtained it is demonstrated that, under the presence of such receiver front-end imperfections, the complexity of the channel equalization filter which is able to provide optimal performance, on the minimum mean square error sense, will scale proportionally to twice the complexity of CD compensation, if standard zero-forcing equalization of CD is applied as first equalization procedure. For the last, it is shown that, by applying the WL complex analysis, one can derive a complex-valued adaptive equalizer structure which is able to compensate for linear IQ-mixing effects at the receiver front-end. By extensive numerical simulations, the performance versus complexity of the proposed equalizer is shown to match the predictions of the analytical models derived.

Flow-Join: Adaptive skew handling for distributed joins over high-speed networks

Abstract: Modern InfiniBand interconnects offer link speeds of several gigabytes per second and a remote direct memory access (RDMA) paradigm for zero-copy network communication. Both are crucial for parallel database systems to achieve scalable distributed query processing where adding a server to the cluster increases performance. However, the scalability of distributed joins is threatened by unexpected data characteristics: Skew can cause a severe load imbalance such that a single server has to process a much larger part of the input than its fair share and by this slows down the entire distributed query. We introduce Flow-Join, a novel distributed join algorithm that handles attribute value skew with minimal overhead. Flow-Join detects heavy hitters at runtime using small approximate histograms and adapts the redistribution scheme to resolve load imbalances before they impact the join performance. Previous approaches often involve expensive analysis phases, which slow down distributed join processing for non-skewed workloads. This is especially the case for modern high-speed interconnects, which are too fast to hide the extra computation. Other skew handling approaches require detailed statistics, which are often not available or overly inaccurate for intermediate results. In contrast, Flow-Join uses our novel lightweight skew handling scheme to execute at the full network speed of more than 6 GB/s for InfiniBand 4×FDR, joining a skewed input at 11.5 billion tuples/s with 32 servers. This is 6.8× faster than a standard distributed hash join using the same hardware. At the same time, Flow-Join does not compromise the join performance for non-skewed workloads.

A Robust Adaptive Pre-Distortion Method for Optical Communication Transmitters

Abstract: Present and next generation optical communication systems are constantly being developed to operate at higher baud rates and higher modulation formats. It then becomes inevitable to consider the various linear and nonlinear effects due to the imperfect components at the transmitter. State-of-the-art digital-to-analog converters, high bandwidth driver amplifiers, and dual-polarization (DP) Mach–Zehnder modulators are far from being ideal and present distortions in the form of bandwidth limitation, transmitter I/Q skew, and nonlinear effects. In this letter, we propose a new robust pre-distortion method to mitigate the undesirable linear and non-linear distortions of all electrical and optical transmitter components simultaneously. A step-by-step derivation and implementation of the algorithm are discussed and put forward. The performance of the algorithm is experimentally assessed across DP-4QAM, DP-8QAM, DP-16QAM, DP-32QAM, and DP-64QAM up to the signaling rates of 56 GBd. Significant improvements in the required optical signal-to-noise ratio at bit-error rate (BER) of $10^{-2}$ are demonstrated.

Tsunami-Induced Forces on Skewed Bridges

Abstract: Research on the influence of tsunamis on bridges has been based almost exclusively on the results of field surveys and of two-dimensional analysis. Although these analyses can provide estimates of forces and moments on the structure, they do not account for three-dimensional (3D) phenomena, such as channelization, or geometric effects, such as bridge skew. Using a 3D computational fluid dynamics approach, this work analyzes the temporal and spatial dynamics of a bore-type tsunami loading on a model bridge and shows how the skew angle of the bridge relative to the incoming wave can affect the loading history. The analyses found that, unlike a bridge without skew, (1) the bore impact forces on the skewed deck do not all occur at the same time; (2) the skewed bridge is subjected to a force perpendicular to its abutments, which could lead to unseating; and (3) the skewed bridge is subjected to pitching and spinning moments. These effects combine to lead to increased horizontal reactions in the substru...

An Efficient Method for Skew Estimation and Compensation in Coherent Receivers

Abstract: The performance of coherent optical systems can be seriously degraded when in-phase and quadrature (IQ) components experience misalignments crossing certain critical limits. The critical limits of IQ phase, gain, and skew misalignments are lower at higher modulation formats and in narrowband systems. In this letter, frequency-domain skew-estimation algorithm and time-domain skew-compensation technique are proposed. When compared with other published methods, the new architecture improves timing performance and relaxes requirements for a multiple-input multiple-output time-domain equalizer at low implementation price. We discuss IQ imperfections on both transmitter and receiver sides and provide an efficient compensation procedure.

Rotor skew pattern design and optimisation for cogging torque reduction

Abstract: This study examines the effects of different rotor skew patterns on the cogging torque, the excitation torque ripple, the average torque, and the axial force in an interior permanent magnet synchronous motor. A genetic algorithm is used to minimise the cogging torque for different skew patterns based on analytical functions. The optimal design obtained is verified with finite element analysis. The results show that the linear skew patterns reduce the cogging torque, but increase the axial force. Four- and five-step symmetric skew, herring-bone skew, and five-step W-shaped skew patterns provide an adequate reduction in the cogging torque and axial force, but they have higher excitation torque ripple compared with the linear skew pattern.

Write Skew and Zipf Distribution: Evidence and Implications

Abstract: Understanding workload characteristics is essential to storage systems design and performance optimization. With the emergence of flash memory as a new viable storage medium, the new design concern of flash endurance arises, necessitating a revisit of workload characteristics, in particular, of the write behavior. Inspired by Web caching studies where a Zipf-like access pattern is commonly found, we hypothesize that write count distribution at the block level may also follow Zipf’s Law. To validate this hypothesis, we study 48 block I/O traces collected from a wide variety of real and benchmark applications. Through extensive analysis, we demonstrate that the Zipf-like pattern indeed widely exists in write traffic provided its disguises are removed by statistical processing. This finding implies that write skew in a large class of applications could be analytically expressed and, thus, facilitates design tradeoff explorations adaptive to workload characteristics.

Sum uncertainty relations based on Wigner---Yanase skew information

Abstract: We study sum uncertainty relations for arbitrary finite N quantum mechanical observables. Some uncertainty inequalities are presented by using skew information introduced by Wigner and Yanase. These uncertainty inequalities are nontrivial as long as the observables are mutually noncommutative. The relations among these new and existing uncertainty inequalities have been investigated. Detailed examples are presented.

Measurement-induced nonlocality based on Wigner-Yanase skew information

Abstract: Measurement-induced nonlocality (MIN), which describes the maximum global effect caused by locally invariant measurements, was introduced by Luo and Fu (Phys. Rev. Lett. , 106 (2011) 120401). In this paper, a new measure of MIN based on Wigner-Yanase skew information is proposed. It is shown that this measure not only has good computability but also eliminates the noncontractivity problem appearing in the original measure of MIN defined by the Hilbert-Schmidt norm. The analytical formulas of MIN based on Wigner-Yanase skew information for any pure states, -dimensional mixed states, and some higher-dimensional symmetric states are presented. Furthermore, the tight upper bound to MIN based on Wigner-Yanase skew information in the general case is also derived.

Detection and alignment of dual-polarization optical quadrature amplitude transmitter IQ and XY skews using reconfigurable interference

Abstract: Dual-polarization quadrature amplitude modulation (DP-QAM) is one of the feasible paths towards 100-Gb/s, 400-Gb/s and 1-Tb/s optical fiber communications systems. For DP-QAM transmitter, the time mismatch between the in-phase and quadrature (IQ) or x-polarized and y-polarized (XY) tributary channels is known as the IQ or XY skew. Large uncompensated IQ or XY skew can significantly degrade the optical fiber communications system performance. Sometimes, time-interleaved return-to-zero (RZ) DP signal is preferred with lower nonlinear polarization scattering induced penalty. In this work, detection and alignment of DP-QAM transmitter IQ and XY skews using reconfigurable interference is experimentally demonstrated. For IQ skew detection, a total dynamic range of 26.4 dB is achieved with ~1-dB power change for 0.5-ps skew from well alignment. For XY skew detection, it shows 23.2-dB dynamic range, and ~1.5-dB power change is achieved for 1-ps XY skew. Fast detection algorithm for arbitrary skew is also proposed and experimentally verified. The scheme is compatible with different modulation formats, flexible data sequences, and variable waveforms.

Eigenvalue analysis of an irreversible random walk with skew detailed balance conditions

Abstract: An irreversible Markov-chain Monte Carlo (MCMC) algorithm with skew detailed balance conditions originally proposed by Turitsyn et al. is extended to general discrete systems on the basis of the Metropolis-Hastings scheme. To evaluate the efficiency of our proposed method, the relaxation dynamics of the slowest mode and the asymptotic variance are studied analytically in a random walk on one dimension. It is found that the performance in irreversible MCMC methods violating the detailed balance condition is improved by appropriately choosing parameters in the algorithm.

Anchor-Aided Joint Localization and Synchronization Using SOOP: Theory and Experiments

Abstract: We consider the problem of tracking a receiver using signals-of-opportunity (SOOPs) from beacons and a reference anchor with known positions and velocities, and where all devices have asynchronous local clocks or oscillators. We model the clock drift at individual devices by a two-state model with unknown clock offset and clock skew and analyze the biases introduced by clock asynchronism in the received signals. Based on an extended Kalman filter, we propose a sequential estimator to jointly track the receiver location, velocity, and its clock parameters using altitude information together with time-difference-of-arrival and frequency-difference-of-arrival measurements obtained from the SOOP samples collected by the receiver and a reference anchor. The receiver was implemented on a software-defined radio testbed, and field experiments are carried out using Iridium satellites as the SOOP beacons. The experiment and simulation results demonstrate that our measurement model has a good fit, and our proposed estimator can successfully track both the receiver location, velocity, and the relative clock offset and skew with respect to the reference anchor with good accuracy.

Handling data skew in join algorithms using MapReduce

Abstract: We introduce a skew handling algorithm, called multi-dimensional range partitioning.The proposed algorithm is more efficient than traditional MapReduce-based join algorithms.The proposed algorithm is scalable regardless of the size of input data. One of the major obstacles hindering effective join processing on MapReduce is data skew. Since MapReduce's basic hash-based partitioning method cannot solve the problem properly, two alternatives have been proposed: range-based and randomized methods. However, they still remain some drawbacks: the range-based method does not handle join product skew, and the randomized method performs worse than the basic hash-based partitioning when input relations are not skewed. In this paper, we present a new skew handling method, called multi-dimensional range partitioning (MDRP). The proposed method overcomes the limitations of traditional algorithms in two ways: 1) the number of output records expected at each machine is considered, which leads to better handling of join product skew, and 2) a small number of input records are sampled before the actual join begins so that an efficient execution plan considering the degree of data skew can be created. As a result, in a scalar skew experiment, the proposed join algorithm is about 6.76 times faster than the range-based algorithm when join product skew exists and about 5.14 times than the randomized algorithm when input relations are not skewed. Moreover, through the worst-case analysis, we show that the input and the output imbalances are less than or equal to 2. The proposed algorithm does not require any modification to the original MapReduce environment and is applicable to complex join operations such as theta-joins and multi-way joins.

Nonlinear Skew Lie Triple Derivations between Factors

Abstract: Let A be a factor. For A, B ∈ A, define by [A, B]* = AB − BA* the skew Lie product of A and B. In this article, it is proved that a map Φ: A → A satisfies Φ([[A, B]*, C]*) = [[Φ(A), B]*, C]* + [[A, Φ(B)]*, C]* + [[A, B]*, Φ(C)]* for all A, B, C ∈ A if and only if Φ is an additive *-derivation.

Hook formulas for skew shapes II. Combinatorial proofs and enumerative applications

Abstract: The Naruse hook-length formula is a recent general formula for the number of standard Young tableaux of skew shapes, given as a positive sum over excited diagrams of products of hook-lengths. In 2015 we gave two different $q$-analogues of Naruse's formula: for the skew Schur functions, and for counting reverse plane partitions of skew shapes. In this paper we give an elementary proof of Naruse's formula based on the case of border strips. For special border strips, we obtain curious new formulas for the Euler and $q$-Euler numbers in terms of certain Dyck path summations.

Skew mirrors, methods of use, and methods of manufacture

Abstract: An optical reflective device referred to as a skew mirror, having a reflective axis that need not be constrained to surface normal, is described. Examples of skew mirrors are configured to reflect light about substantially constant reflective axes across a relatively wide range of wavelengths. In some examples, a skew mirror has substantially constant reflective axes across a relatively wide range of angles of incidence. Exemplary methods for making and using skew mirrors are also disclosed. Skew mirrors include a grating structure, which in some examples comprises a hologram.

Dynamic Resource Allocation for MapReduce with Partitioning Skew

Abstract: MapReduce has become a prevalent programming model for building data processing applications in the cloud. While being widely used, existing MapReduce schedulers still suffer from an issue known as partitioning skew, where the output of map tasks is unevenly distributed among reduce tasks. Existing solutions follow a similar principle that repartitions workload among reduce tasks. However, those approaches often incur high performance overhead due to the partition size prediction and repartitioning. In this paper, we present DREAMS, a framework that provides run-time partitioning skew mitigation. Instead of repartitioning workload among reduce tasks, we cope with the partitioning skew problem by controlling the amount of resources allocated to each reduce task. Our approach completely eliminates the repartitioning overhead, yet is simple to implement. Experiments using both real and synthetic workloads running on a 21-node Hadoop cluster demonstrate that DREAMS can effectively mitigate the negative impact of partitioning skew, thereby improving the job completion time by up to a factor of $2.29$ over the native Hadoop YARN. Compared to the state-of-the-art solution, DREAMS can improve the job completion time by a factor of $1.65$ .

Impact of the transmitter IQ-skew in multi-subcarrier coherent optical systems

Abstract: We show that the impact of non-ideal time synchronization between in-phase and quadrature electrical signals can be critical in multi-subcarrier systems. We propose the use of an 8×8 real-valued butterfly equalizer structure to mitigate it.

Design of IPMSM Applying V-Shape Skew Considering Axial Force Distribution and Performance Characteristics According to the Rotating Direction

Abstract: Skew is a common method to reduce torque ripple and cogging torque. However, when skew is applied, unexpected axial force is produced. To reduce axial force, V-skew is used as one of the solutions. Specifically, when V-skew is applied, the magnetic flux distribution changes according to the rotating direction, which causes a difference in the performance. For the application in which the motor rotates in one direction, this phenomenon can be used to produce power with better quality torque and less losses. In this paper, the interior permanent-magnet synchronous motor (IPMSM) is designed by applying a V-skew to the stator, taking into consideration the manufacturing difficulties with applying a rotor skew to the IPMSM. The skew effect and the reduction of axial force are verified based on finite-element analysis. Moreover, torque, axial force, and losses are comparatively analyzed according to the rotating direction. All calculations and analysis are conducted based on 2-D and 3-D finite-element analysis.

Skew adjustment circuit and skew adjustment method

Abstract: A skew adjustment circuit comprises a phase adjustment circuit that adjusts a phase of a first input clock based on a predetermined phase control signal, and outputs it as an output clock, a logical circuit that performs a logical operation between signals that are input, an integral circuit that generates a predetermined voltage signal, based on a result of the logical operation by the logical circuit, a comparator that compares an electric potential of the predetermined voltage signal and an electric potential of a predetermined reference voltage signal, a first controller that generates the predetermined phase control signal based on a result of the comparison by the comparator, and a second controller that performs control for selecting a signal that is to be input to the logical circuit. The second controller, in a first mode, performs the control such that the output clock and a second input clock are selected.

On the skew-morphisms of dihedral groups

Abstract: Abstract A skew-morphism φ of a finite group G is a permutation on G such that φ ⁢ ( 1 ) = 1 ${\varphi(1)\hskip-0.853583pt=\hskip-0.853583pt1}$ and φ ⁢ ( g ⁢ h ) = φ ⁢ ( g ) ⁢ φ π ⁢ ( g ) ⁢ ( h ) ${\varphi(gh)=\varphi(g)\varphi^{\pi(g)}(h)}$ for all g , h ∈ G ${g,h\in G}$ , where π is a function from G to 𝐙 | φ | ${\mathbf{Z}_{|\varphi|}}$ , called the power function of φ. Furthermore, we say φ is of skew-type k, provided π takes on exactly k values in 𝐙 | φ | ${\mathbf{Z}_{|\varphi|}}$ , and call the set Ker ⁡ φ = { g ∈ G ∣ π ⁢ ( g ) = 1 } ${\operatorname{Ker}\varphi=\{g\in G\mid\pi(g)=1\}}$ the kernel of φ, which is actually a subgroup of G (see [6]). Though skew-morphism is a pure group theoretical concept, it is closely related to regular Cayley maps. We have a long term goal to classify all regular Cayley maps for dihedral groups. In this paper, we mainly work on the skew-morphisms of dihedral groups. Let φ be a skew-morphism of the dihedral groups D 2 ⁢ n = 〈 a , b ∣ a n = b 2 = ( a ⁢ b ) 2 = 1 〉 ${D_{2n}=\langle a,b\mid a^{n}=b^{2}=(ab)^{2}=1\rangle}$ . We prove that the kernel of φ is contained in the cyclic subgroup 〈 a 〉 ${\langle a\rangle}$ if and only if φ is of skew-type 4 and preserves 〈 a 〉 ${\langle a\rangle}$ . In the case of φ preserving 〈 a 〉 ${\langle a\rangle}$ , we give some characterizations of φ, in particular, we prove that φ is of skew-type 1, 2 or 4. Working from these characterizations, an infinite family of skew-morphisms of D 2 ⁢ n ${D_{2n}}$ are constructed, all of which are of skew-type 4 and have kernel 〈 a 2 〉 ${\langle a^{2}\rangle}$ , which gives a positive answer to an open problem raised recently by M. Conder [1].