Cosmological Density and Power Spectrum from Peculiar Velocities: Nonlinear Corrections and PCA

We allow for nonlinear effects in the likelihood analysis of galaxy peculiar velocities, and obtain ~35%-lower values for the cosmological density parameter Om and the amplitude of mass-density fluctuations. The power spectrum in the linear regime is assumed to be a flat LCDM model (h=0.65, n=1, COBE) with only Om as a free parameter. Since the likelihood is driven by the nonlinear regime, we "break" the power spectrum at k_b=0.2 h/Mpc and fit a power law at k>k_b. This allows for independent matching of the nonlinear behavior and an unbiased fit in the linear regime. The analysis assumes Gaussian fluctuations and errors, and a linear relation between velocity and density. Tests using proper mock catalogs demonstrate a reduced bias and a better fit. We find for the Mark3 and SFI data Om_m=0.32+-0.06 and 0.37+-0.09 respectively, with sigma_8*Om^0.6 = 0.49+-0.06 and 0.63+-0.08, in agreement with constraints from other data. The quoted 90% errors include cosmic variance. The improvement in likelihood due to the nonlinear correction is very significant for Mark3 and moderately so for SFI. When allowing deviations from LCDM, we find an indication for a wiggle in the power spectrum: an excess near k=0.05 and a deficiency at k=0.1 (cold flow). This may be related to the wiggle seen in the power spectrum from redshift surveys and the second peak in the CMB anisotropy. A chi^2 test applied to modes of a Principal Component Analysis (PCA) shows that the nonlinear procedure improves the goodness of fit and reduces a spatial gradient of concern in the linear analysis. The PCA allows addressing spatial features of the data and fine-tuning the theoretical and error models. It shows that the models used are appropriate for the cosmological parameter estimation performed. We address the potential for optimal data compression using PCA.Comment: 18 pages, LaTex, uses emulateapj.sty, ApJ in press (August 10, 2001), improvements to text and figures, updated reference

Accurate and linear time pose estimation from points and lines

The final publication is available at link.springer.comThe Perspective-n-Point (PnP) problem seeks to estimate the pose of a calibrated camera from n 3Dto-2D point correspondences. There are situations, though, where PnP solutions are prone to fail because feature point correspondences cannot be reliably estimated (e.g. scenes with repetitive patterns or with low texture). In such scenarios, one can still exploit alternative geometric entities, such as lines, yielding the so-called Perspective-n-Line (PnL) algorithms. Unfortunately, existing PnL solutions are not as accurate and efficient as their point-based counterparts. In this paper we propose a novel approach to introduce 3D-to-2D line correspondences into a PnP formulation, allowing to simultaneously process points and lines. For this purpose we introduce an algebraic line error that can be formulated as linear constraints on the line endpoints, even when these are not directly observable. These constraints can then be naturally integrated within the linear formulations of two state-of-the-art point-based algorithms, the OPnP and the EPnP, allowing them to indistinctly handle points, lines, or a combination of them. Exhaustive experiments show that the proposed formulation brings remarkable boost in performance compared to only point or only line based solutions, with a negligible computational overhead compared to the original OPnP and EPnP.Peer ReviewedPostprint (author's final draft

Some open questions in "wave chaos"

The subject area referred to as "wave chaos", "quantum chaos" or "quantum chaology" has been investigated mostly by the theoretical physics community in the last 30 years. The questions it raises have more recently also attracted the attention of mathematicians and mathematical physicists, due to connections with number theory, graph theory, Riemannian, hyperbolic or complex geometry, classical dynamical systems, probability etc. After giving a rough account on "what is quantum chaos?", I intend to list some pending questions, some of them having been raised a long time ago, some others more recent

Alpha-N: Shortest Path Finder Automated Delivery Robot with Obstacle Detection and Avoiding System

Alpha N A self-powered, wheel driven Automated Delivery Robot is presented in this paper. The ADR is capable of navigating autonomously by detecting and avoiding objects or obstacles in its path. It uses a vector map of the path and calculates the shortest path by Grid Count Method of Dijkstra Algorithm. Landmark determination with Radio Frequency Identification tags are placed in the path for identification and verification of source and destination, and also for the recalibration of the current position. On the other hand, an Object Detection Module is built by Faster RCNN with VGGNet16 architecture for supporting path planning by detecting and recognizing obstacles. The Path Planning System is combined with the output of the GCM, the RFID Reading System and also by the binary results of ODM. This PPS requires a minimum speed of 200 RPM and 75 seconds duration for the robot to successfully relocate its position by reading an RFID tag. In the result analysis phase, the ODM exhibits an accuracy of 83.75 percent, RRS shows 92.3 percent accuracy and the PPS maintains an accuracy of 85.3 percent. Stacking all these 3 modules, the ADR is built, tested and validated which shows significant improvement in terms of performance and usability comparing with other service robots.Comment: 12 pages, 7 figures, To be appear in the proceedings of 12th Asian Conference on Intelligent Information and Database Systems 23-26 March 2020 Phuket, Thailan

Associative3D: Volumetric Reconstruction from Sparse Views

This paper studies the problem of 3D volumetric reconstruction from two views of a scene with an unknown camera. While seemingly easy for humans, this problem poses many challenges for computers since it requires simultaneously reconstructing objects in the two views while also figuring out their relationship. We propose a new approach that estimates reconstructions, distributions over the camera/object and camera/camera transformations, as well as an inter-view object affinity matrix. This information is then jointly reasoned over to produce the most likely explanation of the scene. We train and test our approach on a dataset of indoor scenes, and rigorously evaluate the merits of our joint reasoning approach. Our experiments show that it is able to recover reasonable scenes from sparse views, while the problem is still challenging. Project site: https://jasonqsy.github.io/Associative3DComment: ECCV 202

Generic 3D Representation via Pose Estimation and Matching

Though a large body of computer vision research has investigated developing generic semantic representations, efforts towards developing a similar representation for 3D has been limited. In this paper, we learn a generic 3D representation through solving a set of foundational proxy 3D tasks: object-centric camera pose estimation and wide baseline feature matching. Our method is based upon the premise that by providing supervision over a set of carefully selected foundational tasks, generalization to novel tasks and abstraction capabilities can be achieved. We empirically show that the internal representation of a multi-task ConvNet trained to solve the above core problems generalizes to novel 3D tasks (e.g., scene layout estimation, object pose estimation, surface normal estimation) without the need for fine-tuning and shows traits of abstraction abilities (e.g., cross-modality pose estimation). In the context of the core supervised tasks, we demonstrate our representation achieves state-of-the-art wide baseline feature matching results without requiring apriori rectification (unlike SIFT and the majority of learned features). We also show 6DOF camera pose estimation given a pair local image patches. The accuracy of both supervised tasks come comparable to humans. Finally, we contribute a large-scale dataset composed of object-centric street view scenes along with point correspondences and camera pose information, and conclude with a discussion on the learned representation and open research questions.Comment: Published in ECCV16. See the project website http://3drepresentation.stanford.edu/ and dataset website https://github.com/amir32002/3D_Street_Vie

A finite model of two-dimensional ideal hydrodynamics

A finite-dimensional su($N$) Lie algebra equation is discussed that in the infinite $N$ limit (giving the area preserving diffeomorphism group) tends to the two-dimensional, inviscid vorticity equation on the torus. The equation is numerically integrated, for various values of $N$, and the time evolution of an (interpolated) stream function is compared with that obtained from a simple mode truncation of the continuum equation. The time averaged vorticity moments and correlation functions are compared with canonical ensemble averages.Comment: (25 p., 7 figures, not included. MUTP/92/1

Scene Segmentation Driven by Deep Learning and Surface Fitting

This paper proposes a joint color and depth segmentation scheme exploiting together geometrical clues and a learning stage. The approach starts from an initial over-segmentation based on spectral clustering. The input data is also fed to a Convolutional Neural Network (CNN) thus producing a per-pixel descriptor vector for each scene sample. An iterative merging procedure is then used to recombine the segments into the regions corresponding to the various objects and surfaces. The proposed algorithm starts by considering all the adjacent segments and computing a similarity metric according to the CNN features. The couples of segments with higher similarity are considered for merging. Finally the algorithm uses a NURBS surface fitting scheme on the segments in order to understand if the selected couples correspond to a single surface. The comparison with state-of-the-art methods shows how the proposed method provides an accurate and reliable scene segmentation

Mass equidistribution of Hilbert modular eigenforms

Let F be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n), trivial central character and full level. We show that the mass of f equidistributes on the Hilbert modular variety as max(k_1,...,k_n) tends to infinity. Our result answers affirmatively a natural analogue of a conjecture of Rudnick and Sarnak (1994). Our proof generalizes the argument of Holowinsky-Soundararajan (2008) who established the case F = Q. The essential difficulty in doing so is to adapt Holowinsky's bounds for the Weyl periods of the equidistribution problem in terms of manageable shifted convolution sums of Fourier coefficients to the case of a number field with nontrivial unit group.Comment: 40 pages; typos corrected, nearly accepted for

Debiasing Decisions. Improved Decision Making With A Single Training Intervention

From failures of intelligence analysis to misguided beliefs about vaccinations, biased judgment and decision making contributes to problems in policy, business, medicine, law, and private life. Early attempts to reduce decision biases with training met with little success, leading scientists and policy makers to focus on debiasing by using incentives and changes in the presentation and elicitation of decisions. We report the results of two longitudinal experiments that found medium to large effects of one-shot debiasing training interventions. Participants received a single training intervention, played a computer game or watched an instructional video, which addressed biases critical to intelligence analysis (in Experiment 1: bias blind spot, confirmation bias, and fundamental attribution error; in Experiment 2: anchoring, representativeness, and social projection). Both kinds of interventions produced medium to large debiasing effects immediately (games ≥ -31.94% and videos ≥ -18.60%) that persisted at least 2 months later (games ≥ -23.57% and videos ≥ -19.20%). Games, which provided personalized feedback and practice, produced larger effects than did videos. Debiasing effects were domain-general: bias reduction occurred across problems in different contexts, and problem formats that were taught and not taught in the interventions. The results suggest that a single training intervention can improve decision making. We suggest its use alongside improved incentives, information presentation, and nudges to reduce costly errors associated with biased judgments and decisions