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© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. ; In this paper, we consider the problem of estimating and tracking an R-dimensional subspace with relevant information embedded in an N-dimensional ambient space, given that N»R. We focus on a formulation of the signal subspace that interprets the problem as a least squares optimization. The approach we present relies on the geometrical concepts behind the Affine Projection Algorithms (APA) family to obtain the Affine Projection Subspace Tracking (APST) algorithm. This on-line solution possesses various desirable tracking capabilities, in addition to a high degree of configurability, making it suitable for a large range of applications with different convergence speed and computational complexity requirements. The APST provides a unified framework that generalises other well-known techniques, such as Oja's rule and stochastic gradient based methods for subspace tracking. This algorithm is finally tested in a few synthetic scenarios against other classical adaptive methods. ; This work has been supported by the Spanish Ministry of Science and Innovation through project RODIN (PID2019-105717RB-C22 / AEI / 10.13039/501100011033) and by the Catalan Government (AGAUR) under grant 2017 SGR 578. ; Peer Reviewed ; Postprint (author's final draft)

CBO projection and SPF mean forecast diverge, by nearly a percentage point in 2024. Figure 1: Ten year Treasury yield (black), projected by CBO (tan), SPF mean (blue), TIPS ten year (red), all in %. NBER peak-to-trough recession dates shaded gray. Source: Treasury via FRED, CBO, Philadelphia Fed, NBER. CBO's projection is based on current […]

1593 1605 66 8 ; S ; [EN] Let R be a unital ring with involution. In Section 2, for given two core invertible elements a, b. R, we investigate mainly the absorption law for the core inverse in virtue of the equality of the projections aa and .In Section 3, we study several relations concerning the projections a a and bb , where a . a{1, 2, 4} and b . b{1, 2, 3}. Some well- known results are extended to the *- reducing ring case. As an application, EP elements in a *- reducing ring are considered. This research was supported by the National Natural Science Foundation of China [grant number 11371089]. The first author is grateful to China Scholarship Councilor giving him a scholarship for his further study in Universitat Politecnica de Valencia Spain. Xu, S.; Chen, C.; Benítez López, J. (2018). Projections for generalized inverses. Linear and Multilinear Algebra. 66(8):1593-1605. https://doi.org/10.1080/03081087.2017.1364339

Abstract
Beliefs about the world affect language processing and interpretation in several empirical domains. In two experiments, we tested whether subjective prior beliefs about the probability of utterance content modulate projection, that is, listeners' inferences about speaker commitment to that content. We find that prior beliefs predict projection at both the group and the participant level: the higher the prior belief in a content, the more speakers are taken to be committed to it. This result motivates the integration of formal analyses of projection with cognitive theories of language understanding.

Julius Caesar is a play that has been performed for hundreds of years, but in our modern adaptation we've used technology and the art of projections to give this classic play a modernistic flair and demonstrate the parallels between the political turmoil of that time and our own.