Emergence of Kinematic Space from Quantum Modular Geometric Tensor

Abstract We present a novel technique for the analysis of proton-proton collision events from the ATLAS and CMS experiments at the Large Hadron Collider. For a given final state and choice of kinematic variables, we build a graph network in which the individual events appear as weighted nodes, with edges between events defined by their distance in kinematic space. We then show that it is possible to calculate local metrics of the network that serve as event-by-event variables for separating signal and background processes, and we evaluate these for a number of different networks that are derived from different distance metrics. Using a supersymmetric electroweakino and stop production as examples, we construct prototype analyses that take account of the fact that the number of simulated Monte Carlo events used in an LHC analysis may differ from the number of events expected in the LHC dataset, allowing an accurate background estimate for a particle search at the LHC to be derived. For the electroweakino example, we show that the use of network variables outperforms both cut-and-count analyses that use the original variables and a boosted decision tree trained on the original variables. The stop example, deliberately chosen to be difficult to exclude due its kinematic similarity with the top background, demonstrates that network variables are not automatically sensitive to BSM physics. Nevertheless, we identify local network metrics that show promise if their robustness under certain assumptions of node-weighted networks can be confirmed.

Download Full-text

Spacetime as a quantum circuit

Journal of High Energy Physics ◽

10.1007/jhep04(2021)207 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

A. Ramesh Chandra ◽

Jan de Boer ◽

Mario Flory ◽

Michal P. Heller ◽

Sergio Hörtner ◽

...

Keyword(s):

Path Integral ◽

Constant Scalar Curvature ◽

Quantum Circuit ◽

Quantum Circuits ◽

Special Role ◽

Gravitational Action ◽

Volume Conjecture ◽

Interesting Connection ◽

Kinematic Space ◽

Boundary States

Abstract We propose that finite cutoff regions of holographic spacetimes represent quantum circuits that map between boundary states at different times and Wilsonian cutoffs, and that the complexity of those quantum circuits is given by the gravitational action. The optimal circuit minimizes the gravitational action. This is a generalization of both the “complexity equals volume” conjecture to unoptimized circuits, and path integral optimization to finite cutoffs. Using tools from holographic $$ T\overline{T} $$ T T ¯ , we find that surfaces of constant scalar curvature play a special role in optimizing quantum circuits. We also find an interesting connection of our proposal to kinematic space, and discuss possible circuit representations and gate counting interpretations of the gravitational action.

Download Full-text

Gröbner basis and resultant method for the forward displacement of 3-DoF planar parallel manipulators in seven-dimensional kinematic space

Robotica ◽

10.1017/s0263574715000259 ◽

2015 ◽

Vol 34 (11) ◽

pp. 2610-2628 ◽

Cited By ~ 1

Author(s):

Davood Naderi ◽

Mehdi Tale-Masouleh ◽

Payam Varshovi-Jaghargh

Keyword(s):

Euclidean Space ◽

Gröbner Basis ◽

Three Dimensional ◽

Parallel Manipulators ◽

Parallel Robots ◽

Dimensional Euclidean Space ◽

Grobner Basis ◽

Kinematic Space ◽

Forward Kinematic Problem ◽

Forward Kinematic

SUMMARYIn this paper, the forward kinematic analysis of 3-degree-of-freedom planar parallel robots with identical limb structures is presented. The proposed algorithm is based on Study's kinematic mapping (E. Study, “von den Bewegungen und Umlegungen,” Math. Ann.39, 441–565 (1891)), resultant method, and the Gröbner basis in seven-dimensional kinematic space. The obtained solution in seven-dimensional kinematic space of the forward kinematic problem is mapped into three-dimensional Euclidean space. An alternative solution of the forward kinematic problem is obtained using resultant method in three-dimensional Euclidean space, and the result is compared with the obtained mapping result from seven-dimensional kinematic space. Both approaches lead to the same maximum number of solutions: 2, 6, 6, 6, 2, 2, 2, 6, 2, and 2 for the forward kinematic problem of planar parallel robots; 3-RPR, 3-RPR, 3-RRR, 3-RRR, 3-RRP, 3-RPP, 3-RPP, 3-PRR, 3-PRR, and 3-PRP, respectively.

Download Full-text

Reactive navigation for non-holonomic robots using the ego-kinematic space

Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292) ◽

10.1109/robot.2002.1013699 ◽

2003 ◽

Cited By ~ 8

Author(s):

J. Minguez ◽

L. Montano ◽

J. Santos-Victor

Keyword(s):

Reactive Navigation ◽

Kinematic Space

Download Full-text

Mapping Together Kinetic and Kinematic Abilities of the Hand

Journal of Biomechanical Engineering ◽

10.1115/1.4044141 ◽

2019 ◽

Vol 142 (2) ◽

Author(s):

Joshua P. Drost ◽

Hyokyoung G. Hong ◽

Tamara Reid Bush

Keyword(s):

Hand Function ◽

Coordinate Space ◽

Loss Of Function ◽

Limited Data ◽

Kinematic Space ◽

Load Cells ◽

Finger Forces ◽

Finger Posture ◽

Force Data ◽

Force Characteristics

Abstract Millions of people have reduced hand function; this loss of function can be due to injury, disease, or aging. Loss of hand function is identified as reduced motion abilities in the fingers or a decrease in the ability of the fingers to generate force. Unfortunately, there are limited data available regarding each finger's ability to produce force and how those force characteristics vary with changes in finger posture. To relate motion and force abilities of the fingers, first, an approach to measure and map them together is needed. The goal of this work was to develop and demonstrate a method to quantify the force abilities of the fingers and map these forces to the kinematic space associated with each finger. Using motion capture and multiaxis load cells, finger forces were quantified at different positions over their ranges of motion. These two sets of data were then converted to the same coordinate space and mapped together. Further, the data were normalized for the index finger and mapped as a population space model. The ability to quantify motion and force data for each finger and map them together will provide an improved understanding of the effects of treatments and rehabilitation, identifying functional loss due to injury or disease, and device design.

Download Full-text

Quantitative Examinations of Internal Representations for Arm Trajectory Planning: Minimum Commanded Torque Change Model

Journal of Neurophysiology ◽

10.1152/jn.1999.81.5.2140 ◽

1999 ◽

Vol 81 (5) ◽

pp. 2140-2155 ◽

Cited By ~ 206

Author(s):

Eri Nakano ◽

Hiroshi Imamizu ◽

Rieko Osu ◽

Yoji Uno ◽

Hiroaki Gomi ◽

...

Keyword(s):

Trajectory Planning ◽

Computational Models ◽

Change Model ◽

Trajectory Data ◽

Internal Representations ◽

Muscle Dynamics ◽

Kinematic Space ◽

Wide Range ◽

Flexion Extension ◽

Intrinsic Dynamic

Quantitative examinations of internal representations for arm trajectory planning: minimum commanded torque change model. A number of invariant features of multijoint planar reaching movements have been observed in measured hand trajectories. These features include roughly straight hand paths and bell-shaped speed profiles where the trajectory curvatures between transverse and radial movements have been found to be different. For quantitative and statistical investigations, we obtained a large amount of trajectory data within a wide range of the workspace in the horizontal and sagittal planes (400 trajectories for each subject). A pair of movements within the horizontal and sagittal planes was set to be equivalent in the elbow and shoulder flexion/extension. The trajectory curvatures of the corresponding pair in these planes were almost the same. Moreover, these curvatures can be accurately reproduced with a linear regression from the summation of rotations in the elbow and shoulder joints. This means that trajectory curvatures systematically depend on the movement location and direction represented in the intrinsic body coordinates. We then examined the following four candidates as planning spaces and the four corresponding computational models for trajectory planning. The candidates were as follows: the minimum hand jerk model in an extrinsic-kinematic space, the minimum angle jerk model in an intrinsic-kinematic space, the minimum torque change model in an intrinsic-dynamic-mechanical space, and the minimum commanded torque change model in an intrinsic-dynamic-neural space. The minimum commanded torque change model, which is proposed here as a computable version of the minimum motor command change model, reproduced actual trajectories best for curvature, position, velocity, acceleration, and torque. The model’s prediction that the longer the duration of the movement the larger the trajectory curvature was also confirmed. Movements passing through via-points in the horizontal plane were also measured, and they converged to those predicted by the minimum commanded torque change model with training. Our results indicated that the brain may plan, and learn to plan, the optimal trajectory in the intrinsic coordinates considering arm and muscle dynamics and using representations for motor commands controlling muscle tensions.

Download Full-text