Visual Features and Their Own Optical Flow

Symmetries, invariances and conservation equations have always been an invaluable guide in Science to model natural phenomena through simple yet effective relations. For instance, in computer vision, translation equivariance is typically a built-in property of neural architectures that are used to solve visual tasks; networks with computational layers implementing such a property are known as Convolutional Neural Networks (CNNs). This kind of mathematical symmetry, as well as many others that have been recently studied, are typically generated by some underlying group of transformations (translations in the case of CNNs, rotations, etc.) and are particularly suitable to process highly structured data such as molecules or chemical compounds which are known to possess those specific symmetries. When dealing with video streams, common built-in equivariances are able to handle only a small fraction of the broad spectrum of transformations encoded in the visual stimulus and, therefore, the corresponding neural architectures have to resort to a huge amount of supervision in order to achieve good generalization capabilities. In the paper we formulate a theory on the development of visual features that is based on the idea that movement itself provides trajectories on which to impose consistency. We introduce the principle of Material Point Invariance which states that each visual feature is invariant with respect to the associated optical flow, so that features and corresponding velocities are an indissoluble pair. Then, we discuss the interaction of features and velocities and show that certain motion invariance traits could be regarded as a generalization of the classical concept of affordance. These analyses of feature-velocity interactions and their invariance properties leads to a visual field theory which expresses the dynamical constraints of motion coherence and might lead to discover the joint evolution of the visual features along with the associated optical flows.

Invariance Properties of the Entropy Production, and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems

This study examines the invariance properties of the thermodynamic entropy production in its global (integral), local (differential), bilinear, and macroscopic formulations, including dimensional scaling, invariance to fixed displacements, rotations or reflections of the coordinates, time antisymmetry, Galilean invariance, and Lie point symmetry. The Lie invariance is shown to be the most general, encompassing the other invariances. In a shear-flow system involving fluid flow relative to a solid boundary at steady state, the Galilean invariance property is then shown to preference a unique pair of inertial frames of reference—here termed an entropic pair—respectively moving with the solid or the mean fluid flow. This challenges the Newtonian viewpoint that all inertial frames of reference are equivalent. Furthermore, the existence of a shear flow subsystem with an entropic pair different to that of the surrounding system, or a subsystem with one or more changing entropic pair(s), requires a source of negentropy—a power source scaled by an absolute temperature—to drive the subsystem. Through the analysis of different shear flow subsystems, we present a series of governing principles to describe their entropic pairing properties and sources of negentropy. These are unaffected by Galilean transformations, and so can be understood to “lie above” the Galilean inertial framework of Newtonian mechanics. The analyses provide a new perspective into the field of entropic mechanics, the study of the relative motions of objects with friction.

Measuring Purpose in Life in College Students: An Assessment of Invariance Properties by College Year and Undergraduate School

<p style="text-align: justify;">Purpose in life is a key construct in the development of young adults, particularly college students. There are many instruments measuring sense of purpose in life, but few studies have examined their measurement properties among college students. The current study compares the measurement invariance properties of the Purpose in Life (PIL) scale and the Claremont Purpose Scale (CPS) across college year and undergraduate school. Using both a unidimensional and a two-dimensional model, we found that the PIL’s interpretability is limited among college students. Using a three-dimensional model, the CPS was invariant with respect to both grouping variables. The study suggests that the CPS can be used to make meaningful comparisons among college students categorized by school year and undergraduate school. The study also has some implications about the construct of purpose in life; namely, scale structures that work well statistically and theoretically among adults might not generalize to young adults.</p>

A Prefix Based Approach for Joint Doppler and Channel Estimation in Underwater Communication

Developing a reliable and robust underwater acoustic communication system is a difficult task, due to the complicated nature of the underwater channel, non-stationary noise, and a number of other factors. Indeed, channel estimation or equalization presents numerous challenges in this non-stationary, highly Doppler, multipath environment; as a result, traditional equalizers and PLL-based methods have limited performance. Generally, communication over such time-varying channels is accomplished via packets that contain a prefix/preamble signal for training, a payload containing the actual data, and a silent period for proper alignment. The prefix signal must be designed properly because it is used to estimate the channel and also to determine the start of packet. This paper proposes a novel prefix signal based on the hyperbolic chirp signal, where its Doppler invariance properties enable the extraction of the entire packet even when Doppler and severe multipath are present. Additionally, this proposed prefix enables an efficient and accurate method for fully characterising an underwater channel. The proposed prefix signal is used to estimate the multipath delay and amplitude, and different Doppler scales. Extensive simulations using various channel models are used to determine the proposed method robustness and efficacy under a wide range of conditions. Additionally, the proposed algorithm has been validated on a real-world channel.

The Surprising Power of Graph Neural Networks with Random Node Initialization

Graph neural networks (GNNs) are effective models for representation learning on relational data. However, standard GNNs are limited in their expressive power, as they cannot distinguish graphs beyond the capability of the Weisfeiler-Leman graph isomorphism heuristic. In order to break this expressiveness barrier, GNNs have been enhanced with random node initialization (RNI), where the idea is to train and run the models with randomized initial node features. In this work, we analyze the expressive power of GNNs with RNI, and prove that these models are universal, a first such result for GNNs not relying on computationally demanding higher-order properties. This universality result holds even with partially randomized initial node features, and preserves the invariance properties of GNNs in expectation. We then empirically analyze the effect of RNI on GNNs, based on carefully constructed datasets. Our empirical findings support the superior performance of GNNs with RNI over standard GNNs.

Reciprocal Transformations in Relativistic Gasdynamics. Lie Group Connections

Reciprocal transformations associated with admitted conservation laws were originally used to derive invariance properties in non-relativistic gasdynamics and applied to obtain reduction to tractable canonical forms. They have subsequently been shown to have diverse physical applications to nonlinear systems, notably in the analytic treatment of Stefan-type moving boundary problem and in linking inverse scattering systems and integrable hierarchies in soliton theory. Here,invariance under classes of reciprocal transformations in relativistic gasdynamics is shown to be linked to a Lie group procedure.

Note on generalized Archimedes–Borchardt algorithm

We investigate convergence and invariance properties of the generalized Archimedes–Borchardt algorithm. The main tool is reducing the problem to an appropriate Gauss iteration process.