Restricted Map Research Articles

Insertion Algorithms for Gelfand $$S_n$$-Graphs

Abstract The two tableaux assigned by the Robinson–Schensted correspondence are equal if and only if the input permutation is an involution, so the RS algorithm restricts to a bijection between involutions in the symmetric group and standard tableaux. Beissinger found a concise way of formulating this restricted map, which involves adding an extra cell at the end of a row after a Schensted insertion process. We show that by changing this algorithm slightly to add cells at the end of columns rather than rows, one obtains a different bijection from involutions to standard tableaux. Both maps have an interesting connection to representation theory. Specifically, our insertion algorithms classify the molecules (and conjecturally the cells) in the pair of W-graphs associated with the unique equivalence class of perfect models for a generic symmetric group.

Adaptive robust control for biped walking under uncertain external forces

Adaptability and robustness are important expressions of the intelligent walking ability of biped robots. This paper is concerned with the problem of dynamical biped walking and robust control of biped robots under external forces. Due to the characteristics of strong coupling and hybrid, the robotic system is modeled as a rigid kinematic chain with Lagrange equations. A novel adaptive feedback controller is proposed based on sliding mode control (SMC) and hybrid zero dynamics. The novelty of the proposed work lies in taking the uncertainty of upper-bound error into consideration. The hybrid robust control is mentioned to approximate unknown dynamic functions with the adaptive weight. The restricted Poincare return map is utilized to analyze the stability of a nonlinear impulsive system. It ensures that the flow of the continuous subsystem can pass through the impact cross section. Finally, the simulation results illustrate that the proposed adaptive SMC control system can favorably track the reference trajectories, even when a fault occurs, which verifies the effectiveness of the proposed method.

Unsupervised cycle-consistent network using restricted subspace field map for removing susceptibility artifacts inEPI.

To design an unsupervised deep neural model for correcting susceptibility artifacts in single-shot Echo Planar Imaging (EPI) and evaluate the model for preclinical and clinical applications. This work proposes an unsupervised cycle-consistent model based on the restricted subspace field map to take advantage of both the deep learning (DL) and the reverse polarity-gradient (RPG) method for single-shot EPI. The proposed model consists of three main components: (1) DLRPG neural network (DLRPG-net) to obtain field maps based on a pair of images acquired with reversed phase encoding; (2) spin physical model-based modules to obtain the corrected undistorted images based on the learned field map; and (3) cycle-consistency loss between the input images and back-calculated images from each cycle is explored for network training. In addition, the field maps generated by DLRPG-net belong to a restricted subspace, which is a span of predefined cubic splines to ensure the smoothness of the field maps and avoid blurring in the corrected images. This new method is trained and validated on both preclinical and clinical datasets for diffusion MRI. The proposed network could effectively generate smooth field maps and correct susceptibility artifacts in single-shot EPI. Simulated and in vivo preclinical/clinical experiments demonstrated that our method outperforms the state-of-the-art susceptibility artifact correction methods. Furthermore, the ablation experiments of the cycle-consistent network and the restricted subspace in generating field maps did show the advantages of DLRPG-net. The proposed method (DLRPG-net) can effectively correct susceptibility artifacts for preclinical and clinical single-shot EPI sequences.

MODL-39. CHARACTERIZING NON-ENHANCING TUMOR USING MULTI-SHELL DIFFUSION MRI

Abstract Characterizing infiltration in the non-enhancing tumor (NET) is clinically crucial as infiltration leads to progression, and a reduction in survival times. As voxel-wise biopsy of these regions is infeasible, a non-invasive MRI-based identification of infiltration would be a significant contribution. Diffusion MRI (dMRI), with its ability to model different levels of water restriction, as is caused by infiltration and edema, is well positioned to model the NET. This is achieved via multicomparment modeling (MCM) of the dMRI where infiltration, vasogenic edema and healthy tissue (with complex fibers) form the different compartments. Current MCM approaches are either not designed for NET or rely on advanced MRI scans currently not feasible in the clinic. The simplest ball-tensor models, including Hoy 2014 using multi-shell data and FERNET 2020 for single-shell data, consists of a free water compartment that models vasogenic edema and a tensor modeling underlying tissue. These single-tensor methods cannot model complex WM fibers. Our proposed model consists of two steps. First, two bundles are fit: an isotropic bundle with two balls that model isotropic free diffusivity and restricted diffusivity, and a bundle containing stick and zeppelin, corresponding to intra-cellular and extra-cellular diffusion of axons, respectively. Next, a fiber orientation distribution (FOD) is estimated from the fitted parameters. We applied our modeling to multi-shell data from eight patients with glioblastoma, and one patient with a metastatic brain tumor. Our method produces maps corresponding to free water (CSF), restricted diffusion, intra-cellular, and extra-cellular volume fractions. Preliminary results show that restricted diffusivity map of NET comprises 46% of vasogenic metastatic edema compare to 15% of infiltrated GBM edema. In conclusion, we demonstrate that our proposed model shows promise to characterize the NET region of various brain tumors, and distinguishing tumor types. These compartments will provide invaluable radiomic features that no other modality can capture.

Prospective comparison of restriction spectrum imaging and non-invasive biomarkers to predict upgrading on active surveillance prostate biopsy.

Protocol-based active surveillance (AS) biopsies have led to poor compliance. To move to risk-based protocols, more accurate imaging biomarkers are needed to predict upgrading on AS prostate biopsy. We compared restriction spectrum imaging (RSI-MRI) generated signal maps as a biomarker to other available non-invasive biomarkers to predict upgrading or reclassification on an AS biopsy. We prospectively enrolled men on prostate cancer AS undergoing repeat biopsy from January 2016 to June 2019 to obtain an MRI and biomarkers to predict upgrading. Subjects underwent a prostate multiparametric MRI and a short duration, diffusion-weighted enhanced MRI called RSI to generate a restricted signal map along with evaluation of 30 biomarkers (14 clinico-epidemiologic features, 9 molecular biomarkers, and 7 radiologic-associated features). Our primary outcome was upgrading or reclassification on subsequent AS prostate biopsy. Statistical analysis included operating characteristic improvement using AUROC and AUPRC. The individual biomarker with the highest area under the receiver operator characteristic curve (AUC) was RSI-MRI (AUC = 0.84; 95% CI: 0.71-0.96). The best non-imaging biomarker was prostate volume-corrected Prostate Health Index density (PHI, AUC = 0.68; 95% CI: 0.53-0.82). Non-imaging biomarkers had a negligible effect on predicting upgrading at the next biopsy but did improve predictions of overall time to progression in AS. RSI-MRI, PIRADS, and PHI could improve the predictive ability to detect upgrading in AS. The strongest predictor of clinically significant prostate cancer on AS biopsy was RSI-MRI signal output.

Efficient Obstacle Detection and Tracking Using RGB-D Sensor Data in Dynamic Environments for Robotic Applications.

Obstacle detection is an essential task for the autonomous navigation by robots. The task becomes more complex in a dynamic and cluttered environment. In this context, the RGB-D camera sensor is one of the most common devices that provides a quick and reasonable estimation of the environment in the form of RGB and depth images. This work proposes an efficient obstacle detection and tracking method using depth images to facilitate quick dynamic obstacle detection. To achieve early detection of dynamic obstacles and stable estimation of their states, as in previous methods, we applied a u-depth map for obstacle detection. Unlike existing methods, the present method provides dynamic thresholding facilities on the u-depth map to detect obstacles more accurately. Here, we propose a restricted v-depth map technique, using post-processing after the u-depth map processing to obtain a better prediction of the obstacle dimension. We also propose a new algorithm to track obstacles until they are within the field of view (FOV). We evaluate the performance of the proposed system on different kinds of data sets. The proposed method outperformed the vision-based state-of-the-art (SoA) methods in terms of state estimation of dynamic obstacles and execution time.

PD40-07 CLINICAL DECISION ALGORITHM USING RESTRICTION SPECTRUM IMAGING AND BIOMARKERS TO PREDICT UPGRADING IN ACTIVE SURVEILLANCE

You have accessJournal of UrologyCME1 May 2022PD40-07 CLINICAL DECISION ALGORITHM USING RESTRICTION SPECTRUM IMAGING AND BIOMARKERS TO PREDICT UPGRADING IN ACTIVE SURVEILLANCE Stefan Eng, Benjamin Basasie, Alfonso Lam, John Semmes, Dean Troyer, Geoffrey Clarke, Abhijit Sunnapwar, Robin Leach, Teresa Johnson-Pais, Lori Sokoll, Daniel Chan, Jeffrey Tosoian, Javed Siddiqui, Arul Chinnaiyan, Paul Boutros, and Michael Liss Stefan EngStefan Eng More articles by this author , Benjamin BasasieBenjamin Basasie More articles by this author , Alfonso LamAlfonso Lam More articles by this author , John SemmesJohn Semmes More articles by this author , Dean TroyerDean Troyer More articles by this author , Geoffrey ClarkeGeoffrey Clarke More articles by this author , Abhijit SunnapwarAbhijit Sunnapwar More articles by this author , Robin LeachRobin Leach More articles by this author , Teresa Johnson-PaisTeresa Johnson-Pais More articles by this author , Lori SokollLori Sokoll More articles by this author , Daniel ChanDaniel Chan More articles by this author , Jeffrey TosoianJeffrey Tosoian More articles by this author , Javed SiddiquiJaved Siddiqui More articles by this author , Arul ChinnaiyanArul Chinnaiyan More articles by this author , Paul BoutrosPaul Boutros More articles by this author , and Michael LissMichael Liss More articles by this author View All Author Informationhttps://doi.org/10.1097/JU.0000000000002601.07AboutPDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareFacebookLinked InTwitterEmail Abstract INTRODUCTION AND OBJECTIVE: To determine the relative value and optimal combination of radiologic and molecular biomarkers to predict prostate cancer progression in men on active surveillance. METHODS: We prospectively enrolled 123 men with prostate cancer on active surveillance who were undergoing repeat biopsy to obtain an MRI and non-invasive biomarkers that predict the risk of upgrading. Subjects underwent a prostate multiparametric MRI and a short duration, diffusion-weighted enhanced MRI called restriction spectrum imaging (RSI) to generate a restricted signal map (RSM) along with evaluation of 30 features (14 clinico-epidemiologic features, 9 molecular biomarkers and 7 radiologic-associated features). Our primary outcome was upgrading to higher grade disease on subsequent active surveillance prostate biopsy. Statistical analysis evaluated AUROC and AUPRC, and improvements in these. Using the data, we then devised a clinical decision algorithm to best predict upgrading using the tested biomarkers. RESULTS: RSM (RSI-MRI biomarker) was the most accurate single biomarker in predicting upgrading at the subsequent active surveillance biopsy (AUROC=0.84; 95%CI: 0.71-0.96). RSI improved a baseline clinical model that included MRI PIRADSv2 scores from an AUROC of 0.74 (95%CI 0.69-0.80) to 0.84 (95% CI 0.79–0.89). The best non-imaging biomarker was the prostate volume corrected Prostate Health Index (PHI) density (AUROC=0.68; 95%CI: 0.53-0.82). Combining these with age as a clinical decision tree to perform or not perform a biopsy using cross validated statistics we reach an AUC of the model at 0.8 (SD 0.18). CONCLUSIONS: Enhancement of diffusion-weighted imaging using RSI in addition to standard PIRADSv2 scoring, PHI, and age provides improvement to the predictive ability of MRI to detect upgrading in active surveillance. A combination of multiple biomarkers in a clinical decision tree improves prediction of groups at high risk for future upgrading. Source of Funding: Department of Defense © 2022 by American Urological Association Education and Research, Inc.FiguresReferencesRelatedDetails Volume 207Issue Supplement 5May 2022Page: e686 Advertisement Copyright & Permissions© 2022 by American Urological Association Education and Research, Inc.MetricsAuthor Information Stefan Eng More articles by this author Benjamin Basasie More articles by this author Alfonso Lam More articles by this author John Semmes More articles by this author Dean Troyer More articles by this author Geoffrey Clarke More articles by this author Abhijit Sunnapwar More articles by this author Robin Leach More articles by this author Teresa Johnson-Pais More articles by this author Lori Sokoll More articles by this author Daniel Chan More articles by this author Jeffrey Tosoian More articles by this author Javed Siddiqui More articles by this author Arul Chinnaiyan More articles by this author Paul Boutros More articles by this author Michael Liss More articles by this author Expand All Advertisement PDF DownloadLoading ...

WaveCRN: An Efficient Convolutional Recurrent Neural Network for End-to-End Speech Enhancement

Due to the simple design pipeline, end-to-end (E2E) neural models for speech enhancement (SE) have attracted great interest. In order to improve the performance of the E2E model, the local and sequential properties of speech should be efficiently taken into account when modelling. However, in most current E2E models for SE, these properties are either not fully considered or are too complex to be realized. In this letter, we propose an efficient E2E SE model, termed WaveCRN. Compared with models based on convolutional neural networks (CNN) or long short-term memory (LSTM), WaveCRN uses a CNN module to capture the speech locality features and a stacked simple recurrent units (SRU) module to model the sequential property of the locality features. Different from conventional recurrent neural networks and LSTM, SRU can be efficiently parallelized in calculation, with even fewer model parameters. In order to more effectively suppress noise components in the noisy speech, we derive a novel restricted feature masking approach, which performs enhancement on the feature maps in the hidden layers; this is different from the approaches that apply the estimated ratio mask to the noisy spectral features, which is commonly used in speech separation methods. Experimental results on speech denoising and compressed speech restoration tasks confirm that with the SRU and the restricted feature map, WaveCRN performs comparably to other state-of-the-art approaches with notably reduced model complexity and inference time.

Finite-time stabilization of periodic orbits for under-actuated biped walking with hybrid zero dynamics

This paper is concerned with the problem of finite-time stable walking for a 5-link under-actuated biped robot. Due to instantaneous change of 2 legs and complex dynamics during the walking process, the robot can be regarded as a nonlinear impulsive system. In order to make impulsive control of the robotic system, it is modeled as a rigid kinematic chain with Lagrange equations, which is strong coupling and hybrid. A novel finite-time feedback controller is proposed to realize finite-time stability of the nonlinear impulsive system. The controller is designed based on finite-time stabilizing control Lyapunov function (FTS-CLF) and hybrid zero dynamics (HZD). By establishing a finite-time stable periodic orbit, the controller can make the output of virtual constraints converge to zero rapidly. Restricted Poincare return map is then utilized to analyze the finite-time stability of nonlinear impulsive system. It ensures that the flow of the continuous subsystem can pass through the impact cross section. Additionally, a periodic walking gait planning is further investigated, and the existence of the gait is proved, which satisfy the joint trajectory tracking. Finally, the effectiveness of the mentioned method is illustrated by simulations.

Exponentially stable periodic walking of under-actuated biped robot

The biped robots have characteristics of strong environmental adaptability, complex structure and difficult motion control. This paper addresses the problem of exponential stable walking of a five-link under-actuated biped robot (RABBIT) through control Lyapunov function and hybrid zero dynamics. The walking system is input-output linearized after the full-order dynamic model is described with Lagrange dynamic equations. Based on hybrid zero dynamics, a state feedback controller is then utilized to realize exponential stability of periodic orbit by designing control Lyapunov function, which is proved to be exponentially stable by restricted Poincare Return Map. The effectiveness of the mentioned method is illustrated by simulations.

Invariance of the restricted p-power map on integrable derivations under stable equivalences

We show that the p-power maps in the first Hochschild cohomology space of finite-dimensional selfinjective algebras over a field of prime characteristic p commute with stable equivalences of Morita type on the subgroup of classes represented by integrable derivations. We show, by giving an example, that the p-power maps do not necessarily commute with arbitrary transfer maps in the Hochschild cohomology of symmetric algebras.

A real-time detector for parked vehicles based on hybrid background modeling

In this paper, a real-time detection system based on hybrid background modeling is proposed for detecting parked vehicles along the side of a road. The hybrid background model consists of three components: (1) a scene background model, (2) a computed restricted area map, and (3) a dynamic threshold curve for vehicles. By exploiting the motion information of normal activity in the scene, we propose a hybrid background model that determines the location of the road, estimates the roadside and generates the adaptive threshold of the vehicle size. The system triggers a notification when a large vehicle-like foreground object has been stationary for more than a pre-set number of video frames (or time). The proposed method is tested on the AVSS 2007 PV dataset. The results are satisfactory compared to other state-of-the-art methods.

White matter microstructure from nonparametric axon diameter distribution mapping

We report the development of a double diffusion encoding (DDE) MRI method to estimate and map the axon diameter distribution (ADD) within an imaging volume. A variety of biological processes, ranging from development to disease and trauma, may lead to changes in the ADD in the central and peripheral nervous systems. Unlike previously proposed methods, this ADD experimental design and estimation framework employs a more general, nonparametric approach, without a priori assumptions about the underlying form of the ADD, making it suitable to analyze abnormal tissue. In the current study, this framework was used on an ex vivo ferret spinal cord, while emphasizing the way in which the ADD can be weighted by either the number or the volume of the axons. The different weightings, which result in different spatial contrasts, were considered throughout this work. DDE data were analyzed to derive spatially resolved maps of average axon diameter, ADD variance, and extra-axonal volume fraction, along with a novel sub-micron restricted structures map. The morphological information contained in these maps was then used to segment white matter into distinct domains by using a proposed k-means clustering algorithm with spatial contiguity and left–right symmetry constraints, resulting in identifiable white matter tracks. The method was validated by comparing histological measures to the estimated ADDs using a quantitative similarity metric, resulting in good agreement. With further acquisition acceleration and experimental parameters adjustments, this ADD estimation framework could be first used preclinically, and eventually clinically, enabling a wide range of neuroimaging applications for improved understanding of neurodegenerative pathologies and assessing microstructural changes resulting from trauma.

On a conjecture about the norm of Lyapunov mappings

The norm properties of Lyapunov mappings and their restrictions on symmetric and skew-symmetric subspaces are investigated. For non-negative, non-positive, and tridiagonal matrices, this paper gives an affirmative answer to an open conjecture which says that the norm of a Lyapunov mapping over the space of real square matrices equals that of its restricted map over the subspace of real symmetric matrices. In addition, matrix transformation and norm relationships on certain matrices arising from the Lyapunov mapping and its restrictions are provided.

Continuity of the Maximum-Entropy Inference

We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference can be a discontinuous map from the convex set of expected values to the convex set of states because the image contains states of reduced support, while this map restricts to a smooth parametrization of a Gibbsian family of fully supported states. Here we prove for arbitrary ranking functions that the inference is continuous up to boundary points. This follows from a continuity condition in terms of the openness of the restricted linear map from states to their expected values. The openness condition shows also that ranking functions with a discontinuous inference are typical. Moreover it shows that the inference is continuous in the restriction to any polytope which implies that a discontinuity belongs to the quantum domain of non-commutative observables and that a geodesic closure of a Gibbsian family equals the set of maximum-entropy states. We discuss eight descriptions of the set of maximum-entropy states with proofs of accuracy and an analysis of deviations.

On Lusztig's map for spherical unipotent conjugacy classes

We provide an alternative description of the restriction to spherical unipotent conjugacy classes, of Lusztig's map Ψ from the set of unipotent conjugacy classes in a connected reductive algebraic group to the set of conjugacy classes of its Weyl group. For irreducible root systems, we analyze the image of this restricted map and we prove that a conjugacy class in a finite Weyl group has a unique maximal length element if and only if it has a maximum.

Stabilization of Periodic Orbits for Planar Walking With Noninstantaneous Double-Support Phase

This paper presents an analytical approach to design a continuous time-invariant two-level control scheme for asymptotic stabilization of a desired period-one trajectory for a hybrid model describing walking by a planar biped robot with noninstantaneous double-support phase and point feet. It is assumed that the hybrid model consists of both single- and double-support phases. The design method is based on the concept of hybrid zero dynamics. At the first level, parameterized continuous within-stride controllers, including single- and double-support-phase controllers, are employed. These controllers create a family of 2-D finite-time attractive and invariant submanifolds on which the dynamics of the mechanical system is restricted. Moreover, since the mechanical system during the double-support phase is overactuated, the feedback law during this phase is designed to be minimum norm on the desired periodic orbit. At the second level, parameters of the within-stride controllers are updated by an event-based update law to achieve hybrid invariance, which results in a reduced-order hybrid model for walking. By these means, stability properties of the periodic orbit can be analyzed and modified by a restricted Poincare return map. Finally, a numerical example for the proposed control scheme is presented.

Walking and steering control for a 3D biped robot considering ground contact and stability

This paper presents a stable walking control method for a 3D bipedal robot with 14 joint actuators. The overall control law consists of a ZMP (zero moment point) controller, a swing ankle rotation controller and a partial joint angles controller. The ZMP controller guarantees that the stance foot remains in flat contact with the ground. The swing ankle rotation controller ensures a flat foot impact at the end of the swinging phase. Each of these controllers creates 2 constraints on joint accelerations. As a consequence, the partial joint angles controller is implemented to track only 10 independent outputs. These outputs are defined as a linear combination of the 14 joint angles. The most important question addressed in this paper is how this linear combination can be defined in order to ensure walking stability. The stability of the walking gait under closed loop control is evaluated with the linearization of the restricted Poincare map of the hybrid zero dynamics. As a result, the robot can achieve an asymptotically stable and periodic walking along a straight line. Finally, another feedback controller is supplemented to adjust the walking direction of the robot and some examples of the robot steered to walk along different paths with mild curvature are given.

Accelerated water–fat imaging using restricted subspace field map estimation and compressed sensing

Water-fat separation techniques play an important role in a variety of clinical and research applications. In particular, multiecho separation methods remain a topic of great interest due to their ability to resolve water and fat images in the presence of B(0)-field inhomogeneity. However, these methods are inherently slow as they require multiple measurements. An accelerated technique with reduced k-space sampling is desirable to decrease the scan time. This work presents a new method for water-fat separation from accelerated multiecho acquisitions. The proposed approach does not require the region-growing or region-merging schemes that are typically used for field map estimation. Instead, the water, fat, and field map signals are estimated directly from the undersampled k-space measurements. In this work, up to 2.5×-acceleration is demonstrated in a water-fat phantom, ankle, knee, and liver.

Restricted Trees: Simplifying Networks with Bottlenecks

Suppose N is a phylogenetic network indicating a complicated relationship among individuals and taxa. Often of interest is a much simpler network, for example, a species tree T, that summarizes the most fundamental relationships. The meaning of a species tree is made more complicated by the recent discovery of the importance of hybridizations and lateral gene transfers. Hence, it is desirable to describe uniform well-defined procedures that yield a tree given a network N. A useful tool toward this end is a connected surjective digraph (CSD) map φ: N → N' where N' is generally a much simpler network than N. A set W of vertices in N is "restricted" if there is at most one vertex u ∉ W from which there is an arc into W, thus yielding a bottleneck in N. A CSD map φ: N → N' is "restricted" if the inverse image of each vertex in N' is restricted in N. This paper describes a uniform procedure that, given a network N, yields a well-defined tree called the "restricted tree" of N. There is a restricted CSD map from N to the restricted tree. Many relationships in the tree can be proved to appear also in N.