Quantum Dynamics, Minkowski-Hilbert space, and A Quantum Stochastic Duhamel Principle

In this paper we shall re-visit the well-known Schr\"odinger and Lindblad dynamics of quantum mechanics. However, these equations may be realized as the consequence of a more general, underlying dynamical process. In both cases we shall see that the evolution of a quantum state $P_\psi=\varrho(0)$ has the not so well-known pseudo-quadratic form $\partial_t\varrho(t)=\mathbf{V}^\star\varrho(t)\mathbf{V}$ where $\mathbf{V}$ is a vector operator in a complex Minkowski space and the pseudo-adjoint $\mathbf{V}^\star$ is induced by the Minkowski metric $\boldsymbol{\eta}$. The interesting thing about this formalism is that its derivation has very deep roots in a new understanding of the differential calculus of time. This Minkowski-Hilbert representation of quantum dynamics is called the \emph{Belavkin Formalism}; a beautiful, but not well understood theory of mathematical physics that understands that both deterministic and stochastic dynamics may be `unraveled' in a second-quantized Minkowski space. Working in such a space provided the author with the means to construct a QS (quantum stochastic) Duhamel principle and known applications to a Schr\"odinger dynamics perturbed by a continual measurement process are considered. What is not known, but presented here, is the role of the Lorentz transform in quantum measurement, and the appearance of Riemannian geometry in quantum measurement is also discussed

Harbor Security System

Harbors and ports provide the infrastructure for commercial trade and naval facilities. It is vital to ensure the safety of these locations. The Harbor Security System provides an optical ‘gate’ using underwater lasers and photodetectors. This system allows monitoring of both surface and submarine vessels traveling into and out of the harbor. Also, the system provides real time alerts when unauthorized vessels enter the harbor. This project provides a proof of concept for a Harbor Security System to be implemented in Portsmouth Harbor. A scaled model of the detection system was constructed and tested. This detection system is capable of detecting surface and submarine vessels along with their velocity and length. Results of the study showed that the average error of the size estimate was 15% and the average error of the velocity estimation ratio(slope) was 9%

Low-Shot Learning with Imprinted Weights

Human vision is able to immediately recognize novel visual categories after seeing just one or a few training examples. We describe how to add a similar capability to ConvNet classifiers by directly setting the final layer weights from novel training examples during low-shot learning. We call this process weight imprinting as it directly sets weights for a new category based on an appropriately scaled copy of the embedding layer activations for that training example. The imprinting process provides a valuable complement to training with stochastic gradient descent, as it provides immediate good classification performance and an initialization for any further fine-tuning in the future. We show how this imprinting process is related to proxy-based embeddings. However, it differs in that only a single imprinted weight vector is learned for each novel category, rather than relying on a nearest-neighbor distance to training instances as typically used with embedding methods. Our experiments show that using averaging of imprinted weights provides better generalization than using nearest-neighbor instance embeddings.Comment: CVPR 201

Long-Term Dynamics and the Orbital Inclinations of the Classical Kuiper Belt Objects

We numerically integrated the orbits of 1458 particles in the region of the classical Kuiper Belt (41 AU < a < 47 AU) to explore the role of dynamical instabilities in sculpting the inclination distribution of the classical Kuiper Belt Objects (KBOs). We find that the selective removal of low-inclination objects by overlapping secular resonances (nu_17 and nu_18) acts to raise the mean inclination of the surviving population of particles over 4 billion years of interactions with Jupiter, Saturn, Uranus and Neptune, though these long-term dynamical effects do not themselves appear to explain the discovery of KBOs with inclinations near 30 degrees. Our integrations also imply that after 3 billion years of interaction with the massive planets, high inclination KBOs more efficiently supply Neptune-encountering objects, the likely progenitors of short-period comets, Centaurs, and scattered KBOs. The secular resonances at low inclinations may indirectly cause this effect by weeding out objects unprotected by mean motion resonances during the first 3 billion years.Comment: 23 pages, including 10 figures. Accepted for publication in A

Nonrigid Optical Flow Ground Truth for Real-World Scenes with Time-Varying Shading Effects

In this paper we present a dense ground truth dataset of nonrigidly deforming real-world scenes. Our dataset contains both long and short video sequences, and enables the quantitatively evaluation for RGB based tracking and registration methods. To construct ground truth for the RGB sequences, we simultaneously capture Near-Infrared (NIR) image sequences where dense markers - visible only in NIR - represent ground truth positions. This allows for comparison with automatically tracked RGB positions and the formation of error metrics. Most previous datasets containing nonrigidly deforming sequences are based on synthetic data. Our capture protocol enables us to acquire real-world deforming objects with realistic photometric effects - such as blur and illumination change - as well as occlusion and complex deformations. A public evaluation website is constructed to allow for ranking of RGB image based optical flow and other dense tracking algorithms, with various statistical measures. Furthermore, we present an RGB-NIR multispectral optical flow model allowing for energy optimization by adoptively combining featured information from both the RGB and the complementary NIR channels. In our experiments we evaluate eight existing RGB based optical flow methods on our new dataset. We also evaluate our hybrid optical flow algorithm by comparing to two existing multispectral approaches, as well as varying our input channels across RGB, NIR and RGB-NIR.Comment: preprint of our paper accepted by RA-L'1

Contingency Model Predictive Control for Automated Vehicles

We present Contingency Model Predictive Control (CMPC), a novel and implementable control framework which tracks a desired path while simultaneously maintaining a contingency plan -- an alternate trajectory to avert an identified potential emergency. In this way, CMPC anticipates events that might take place, instead of reacting when emergencies occur. We accomplish this by adding an additional prediction horizon in parallel to the classical receding MPC horizon. The contingency horizon is constrained to maintain a feasible avoidance solution; as such, CMPC is selectively robust to this emergency while tracking the desired path as closely as possible. After defining the framework mathematically, we demonstrate its effectiveness experimentally by comparing its performance to a state-of-the-art deterministic MPC. The controllers drive an automated research platform through a left-hand turn which may be covered by ice. Contingency MPC prepares for the potential loss of friction by purposefully and intuitively deviating from the prescribed path to approach the turn more conservatively; this deviation significantly mitigates the consequence of encountering ice.Comment: American Control Conference, July 2019; 6 page

Symplectic structures on right-angled Artin groups: between the mapping class group and the symplectic group

We define a family of groups that include the mapping class group of a genus g surface with one boundary component and the integral symplectic group Sp(2g,Z). We then prove that these groups are finitely generated. These groups, which we call mapping class groups over graphs, are indexed over labeled simplicial graphs with 2g vertices. The mapping class group over the graph Gamma is defined to be a subgroup of the automorphism group of the right-angled Artin group A_Gamma of Gamma. We also prove that the kernel of the map Aut A_Gamma to Aut H_1(A_Gamma) is finitely generated, generalizing a theorem of Magnus.Comment: 45 page