Cancellation Problem Research Articles

Cancellation of finite-dimensional Noetherian modules

The Module Cancellation Problem solicits hypotheses that, when imposed on modules K, L, and M over a ring S, afford the implication K⊕L≅K⊕M⟹L≅M. In a well-known paper on basic element theory from 1973, Eisenbud and Evans lament the “great scarcity of strong results” in module cancellation research, expressing the wish that, “under some general hypothesis” on finitely generated modules over a commutative Noetherian ring, cancellation could be demonstrated. Singling out cancellation theorems by Bass and Dress that feature “large” projective modules, Eisenbud and Evans contend further that, although “some criteria of ‘largeness’ is certainly necessary in general […,] the need for projectivity is not clear.” In this paper, we prove that cancellation holds if K, L, and M are finitely generated modules over a commutative Noetherian ring S such that Kp⊕(1+dim⁡(S/p)) is a direct summand of Mp over Sp for every prime ideal p of S. We also weaken projectivity conditions in the cancellation theorems of Bass and Dress and a newer theorem by De Stefani–Polstra–Yao; in fact, we obtain a statement that unifies all three of these theorems while obviating a projectivity constraint in each one.

Q Control of an AFM Microcantilever With Double-Stack AlN Sensors and Actuators

Active Atomic Force Microscope (AFM) cantilevers with integrated actuator/sensor pairs display larger feedthrough than conventional base excited cantilevers operating in conjunction with optical displacement sensors. To control the Q factor of a cantilever, this feedthrough needs to be canceled or significantly reduced. We use an AFM microcantilever with a double-stack sensor/actuator pair to address the feedthrough cancellation problem. Our device provides two sensor signals: one used for displacement sensing and the other for velocity measurement, with the latter being used for feedback. A readout circuit is designed to sense the displacement signal and to implement the velocity feedback controller. With this method, we were able to reduce the Q factor from 390 to 30.

M-estimate affine projection spline adaptive filtering algorithm: Analysis and implementation

This paper investigates the M-estimate affine projection spline adaptive filtering (MAPSAF) algorithm, which utilizes a modified Huber function with robustness against impulsive interference, and employs historical regression data to update the weight and the knot vector estimates for nonlinear filtering tasks. The detailed convergence and steady-state analyses of MAPSAF are also carried out in the mean and mean-square senses. In addition, an improved MAPSAF by exploiting the combined step sizes, called the CSS-MAPSAF algorithm, is derived to speed up the convergence on the premise of low steady-state misalignment. Numerical experiments in nonlinear system identification and nonlinear acoustic echo cancellation problems corroborate the theoretical performance analysis and the superiority of the proposed algorithms.

Temporal-Structure-Aware Interference Cancellation for Asynchronous Cognitive IoT

In this paper, we investigate the interference cancellation problem for asynchronous cognitive Internet of Things (C-IoT) in the concurrent spectrum access (CSA) model. An iterative receiver together with a new clustering algorithm is employed to cancel the interference and recovers the desired signal. Since the C-IoT device and the primary user (PU) are non-cooperative, they are generally asynchronous at the symbol level and the interference signal received by the secondary user (SU) receiver (Rx) possesses a first-order Markov property over time. Therefore, we propose a new clustering algorithm named hidden Morkov model (HMM) based affinity propagation (AP) algorithm that combines the HMM and the AP algorithm to realize the clustering module. The proposed HMM-AP algorithm exploits the temporal-correlation information to improve the performance of the iterative receiver. We show that the receiver with the HMM-AP algorithm can work well in non-cooperative system and has a much better performance than the original AP.

A Proactive Flight Cancellation Problem with Stochastic Air Capacity

A Proactive Flight Cancellation Problem with Stochastic Air Capacity

A prediction-optimization approach to surgery prioritization in operating room scheduling

ABSTRACT This study proposes a mixed-integer programming model to optimize daily schedules based on surgery priority. Stacking ensemble learning is employed to predict surgery priority. The stacking algorithm is composed of K-nearest neighbor, multi-nominal logistic regression, decision tree, multi-layer perceptron, and ensemble learning. Then, the predicted priorities are fed into an optimization model. Six patient-related variables are used to predict surgery priority: surgery type, patient acuity, patient age, number of delayed days a surgery is postponed, patient age, and surgery time. The study contribution comes from integrating machine learning and optimization to propose a priority-based decision model for optimally sequencing surgeries daily. The experimental results show that the proposed approach is better than the current practice in handling unscheduled surgeries, while the scheduling cost remains nearly unchanged. We show the effectiveness of the proposed approach for handling the surgery cancellation problem in operating room systems with high surgery demands.

New metric reconstruction scheme for gravitational self-force calculations

Inspirals of stellar-mass objects into massive black holes will be important sources for the space-based gravitational-wave detector LISA. Modelling these systems requires calculating the metric perturbation due to a point particle orbiting a Kerr black hole. Currently, the linear perturbation is obtained with a metric reconstruction procedure that puts it in a ‘no-string’ radiation gauge which is singular on a surface surrounding the central black hole. Calculating dynamical quantities in this gauge involves a subtle procedure of ‘gauge completion’ as well as cancellations of very large numbers. The singularities in the gauge also lead to pathological field equations at second perturbative order. In this paper we re-analyze the point-particle problem in Kerr using the corrector-field reconstruction formalism of Green, Hollands, and Zimmerman (GHZ). We clarify the relationship between the GHZ formalism and previous reconstruction methods, showing that it provides a simple formula for the ‘gauge completion’. We then use it to develop a new method of computing the metric in a more regular gauge: a Teukolsky puncture scheme. This scheme should ameliorate the problem of large cancellations, and by constructing the linear metric perturbation in a sufficiently regular gauge, it should provide a first step toward second-order self-force calculations in Kerr. Our methods are developed in generality in Kerr, but we illustrate some key ideas and demonstrate our puncture scheme in the simple setting of a static particle in Minkowski spacetime.

Cancellation problem for AS-Regular algebras of dimension three

Cancellation problem for AS-Regular algebras of dimension three

Asynchronous and Non-Stationary Interference Cancellation in Multiuser Interference Channels

A single antenna interference cancellation (SAIC) scheme is proposed. The scheme is motivated by the challenging asynchronous and non-stationary interference cancellation problem in wireless communications. Suppose the existence of the single-user region (SUR) of the desired signal, we propose to first recognize the SUR via a novel detection scheme. The SUR detection scheme proposed consists of the pseudo-observation matrix construction and the information theoretic criterion-based source number estimation. A basis set for the desired signal is then learnt over the SUR, via dictionary learning techniques. In the final signal recovery stage, a novel constrained sparse coding (CSC) process is proposed. The CSC reforms the conventional sparse coding (SC) via incorporating signal-specific constraints. Unlike existing SAIC algorithms, the proposed scheme is completely independent of a prior knowledge on the interferences. Numerical results are provided to demonstrate the effectiveness of the above proposed schemes under varied interference intensities and environmental noise levels. The proposed scheme outperformed competing SAIC schemes by about 5dB signal-to-interference-plus-noise ratio (SINR) improvement. The proposed CSC scheme outperformed the conventional SC by about 9dB SINR improvement, besides the superior recovery fidelity of signal property.

Verification of a fully implicit particle-in-cell method for the v ∥-formalism of electromagnetic gyrokinetics in the XGC code

A fully implicit particle-in-cell method for handling the v ∥-formalism of electromagnetic gyrokinetics has been implemented in XGC. By choosing the v ∥-formalism, we avoid introducing the nonphysical skin terms in Ampère's law, which are responsible for the well-known “cancellation problem” in the p ∥-formalism. The v ∥-formalism, however, is known to suffer from a numerical instability when explicit time integration schemes are used due to the appearance of a time derivative in the particle equations of motion from the inductive component of the electric field. Here, using the conventional δf scheme, we demonstrate that our implicitly discretized algorithm can provide numerically stable simulation results with accurate dispersive properties. We verify the algorithm using a test case for shear Alfvén wave propagation in addition to a case demonstrating the ion temperature gradient-kinetic ballooning mode (ITG-KBM) transition. The ITG-KBM transition case is compared to results obtained from other δf gyrokinetic codes/schemes, whose verification has already been archived in the literature.

Some further results on the cancellation law for partially ordered sets and T0-spaces

In this paper, we continue the study of the cancellation problem for the cartesian product of partially ordered sets (posets for short) and of T0-spaces. We first give a class of partially ordered sets satisfying the cancellation law which is different from that investigated by Banaschewski and Lowen, and then give its corresponding topological version.

Analyzing Secrecy Outage in Hybrid Full-Duplex Attack While Exploiting CSI of Legitimate Link

The growing concern of secure communication becomes more challenging when encountering a hybrid Full-duplex (FD) attacker possessing the dual capability to perform eavesdropping and jamming simultaneously. To analyze secrecy outage performance in the presence of such a potential attacker, the proposed work assumes complete information of the legitimate link only. It considers unavailability of complete information of all the ungoverned communication links including eavesdropping, jamming and self-interference link of attacker. FD operation is associated with the problem of imperfect self-interference cancellation. Our proposed analysis considers residual self-interference at the attacker's end in its modelling. The closed-form expressions have been obtained for secrecy outage probability under generalized as well as special cases. The results obtained facilitate in investigating the impact of fading under FD attack and provide important insights about source power, jamming power, attacker's location. Approximate closed-form results also help in reducing computation time by more than 55%.

Tokamak ITG-KBM transition benchmarking with the mixed variables/pullback transformation electromagnetic gyrokinetic scheme

Electromagnetic gyrokinetic simulation of high temperature plasma is required to predict confinement in magnetic fusion devices and has posed challenges for existing codes. In this paper, we demonstrate successful global gyrokinetic simulation of the ion temperature gradient-driven mode-kinetic ballooning mode transition in a toroidal fusion plasma test case using the mixed variables/pullback transformation (MV/PT) scheme with the particle-in-cell codes XGC and ORB5, and compare to results from a conventional continuum code from the literature. The MV/PT scheme combines explicit time integration with mitigation of the well-known electromagnetic gyrokinetic “cancelation problem.” We calculate eigenmodes in the electrostatic and parallel vector potentials, and find good agreement in growth rate, real frequency, and the normalized plasma pressure of mode transition.

Removal of Cochannel Interference Using Probabilistic Latent Component Analysis in Passive Bistatic Radar

This paper examines the problem of cancellation of cochannel interference (CCI) present in the same frequency channel as the signal of interest, which may bring a reduction in the performance of target detection, in passive bistatic radar. We propose a novel approach based on probabilistic latent component analysis for CCI removal. The highlight is that removing CCI is considered as reconstruction, and extraction of Doppler-shifted and time-delayed replicas of the reference signal exploited fully as training data. The results of the simulation show that the developed method is effective.

Automorphisms of Danielewski varieties

In 2007, Dubouloz introduced Danielewski varieties. Such varieties generalize Danielewski surfaces and provide counterexamples to generalized Zariski cancellation problem in arbitrary dimension. In the present work we describe the automorphism group of a Danielewski variety. This result is a generalization of a description of automorphisms of Danielewski surfaces due to Makar-Limanov.

Modified covariance beamformer for solving MEG inverse problem in the environment with correlated sources

Magnetoencephalography (MEG) is a neuroimaging method ideally suited for non-invasive studies of brain dynamics. MEG’s spatial resolution critically depends on the approach used to solve the ill-posed inverse problem in order to transform sensor signals into cortical activation maps. Over recent years non-globally optimized solutions based on the use of adaptive beamformers (BF) gained popularity.When operating in the environment with a small number of uncorrelated sources the BFs perform optimally and yield high spatial resolution. However, the BFs are known to fail when dealing with correlated sources acting like poorly tuned spatial filters with low signal-to-noise ratio (SNR) of the output timeseries and often meaningless cortical maps of power distribution.This fact poses a serious limitation on the broader use of this promising technique especially since fundamental mechanisms of brain functioning, its inherent symmetry and task-based experimental paradigms result into a great deal of correlation in the activity of cortical sources. To cope with this problem, we developed a novel data covariance modification approach that allows for building beamformers that maintain high spatial resolution when operating in the environments with correlated sources.At the core of our method is a projection operation applied to the vectorized sensor-space covariance matrix. This projection does not remove the activity of the correlated sources from the sensor-space covariance matrix but rather selectively handles their contributions to the covariance matrix and creates a sufficiently accurate approximation of an ideal data covariance that could hypothetically be observed should these sources be uncorrelated. Since the projection operation is reciprocal to the PSIICOS method developed by us earlier (Ossadtchi et al., 2018) we refer to the family of algorithms presented here as ReciPSIICOS.We assess the performance of the novel approach using realistically simulated MEG data and show its superior performance in comparison to the classical BF approaches and well established MNE as a method immune to source synchrony by design. We have also applied our approach to the MEG datasets from the two experiments involving two different auditory tasks.The analysis of experimental MEG datasets showed that beamformers from ReciPSIICOS family, but not the classical BF, discovered the expected bilateral focal sources in the primary auditory cortex and detected motor cortex activity associated with the audio-motor task. In most cases MNE managed well but as expected produced more spatially diffuse source distributions. Notably, ReciPSIICOS beamformers yielded cortical activity estimates with SNR several times higher than that obtained with the classical BF, which may indirectly indicate the severeness of the signal cancellation problem when applying classical beamformers to MEG signals generated by synchronous sources.

A generalized collaborative functional link adaptive filter for nonlinear active noise control

This paper derives a collaborative control algorithm called generalized collaborative functional link adaptive filter (GCFLAF) for nonlinear active noise control (NANC). The algorithm adopts the collaborative scheme by handling the noise cancellation problem divisionally and parallelly, and working coordinately. It takes the characteristics of different nonlinear components into consideration and handles them separately. And a hierarchical adaption law is adopted in which linear filter is always prior to nonlinear filters no matter whether nonlinear distortions arise from the primary path as required by the filtering scenario. Thus the proposed scheme can tailor to different nonlinear characters arising from the primary path and can hierarchically adapt to the influences of the distinct nonlinearities. Particularly, since the zero-memory nonlinearity and memory nonlinearity are often unavoidable in NANC, it employs two shrinkage parameters to regulate the contribution of the different degrees of memory and zero-memory nonlinearity as required by the filtering scenario, aiming to achieve a better convergence performance and robustness to nonlinear distortions. Some numerical simulation results in the context of random noises as well as the real noise signals verify the improved convergence behavior of the presented architecture in NANC scenarios.

Probability estimation model for the cancellation of container slot booking in long-haul transports of intercontinental liner shipping services

The intercontinental liner shipping services transport containers between two continents and they are crucial for the profitability of a global liner shipping company. In the daily operations of an intercontinental liner shipping service, however, container slot bookings from customers can be freely cancelled during a booking period, which causes loss of revenue and low utilization of ship capacity. Though a pain-point of the liner shipping industry, the container slot cancellation problem has not yet been well investigated in the literature. To fill this research gap, this study aims to estimate the probability for the cancellation of container slot booking in the long haul transports of the intercontinental liner shipping service by considering the primary influential factors of cancellation behavior. To achieve the objective, a container slot booking data-driven model is developed by means of a time-to-event modeling technique. To incorporate the effect of booking region on the cancellation probability, we introduce the frailty term in the model to capture the regionality of the container shipping market. Our case study with real slot booking data shows that the developed model performs well in forecasting the loaded containers of the slot booking requests. In addition, we shed light on how the internal factors of slot booking and external factors of shipping market influence the probability of cancellation.

Two‐stage clutter and interference cancellation method in passive bistatic radar

Target echoes are inevitably contaminated by the direct-path signal, multipath signal and possible interference in passive bistatic radar (PBR). Cancellation performance is deteriorated as the interference signal is irrelevant to the transmitted signal and the target echoes are submerged by in the sidelobe of the spread clutter echoes. In this study, the cancellation problem is addressed, involving clutter and interference. In this method, the spread clutter echoes are cancelled by constructing a tailored clutter subspace. Besides, the interference is also cancelled by constructing a tailored interference subspace. The sample of the interference signal is obtained from the beam channel after clutter cancellation. The performance of the proposed method is first verified by the simulation result. Then its effectiveness is also demonstrated with the application of the real data collected from an experimental PBR system.

A cancellation problem in hybrid particle-in-cell schemes due to finite particle size

The quasi-neutral hybrid particle-in-cell algorithm with kinetic ions and fluid electrons is a popular model to study multi-scale problems in laboratory, space, and astrophysical plasmas. Here, it is shown that the different spatial discretizations of ions as finite-spatial-size particles and electrons as a grid-based fluid can lead to significant numerical wave dispersion errors in the long wavelength limit (kdi≪1, where k is the wavenumber and di is the ion skin-depth). The problem occurs when high-order particle-grid interpolations, or grid-based smoothing, spreads the electric field experienced by the ions across multiple spatial cells and leads to inexact cancellation of electric field terms in the total (ion + electron) momentum equation. Practical requirements on the mesh spacing Δx/di are suggested to bound these errors from above. The accuracy impact of not respecting these resolution constraints is shown for a non-linear shock problem.