Classical Frame Research Articles

Geodetic innovation in Chilean mining: The evolution from static to kinematic reference frame in seismic zones

Abstract The use of regional kinematic reference frames (mRFs) in seismic zones is uncommon worldwide. This article proposes a solution implemented for Chilean mining, whose current projects are based on the classic reference frames (PSAD56 and SAD69). The approach is to move from a classic reference frame to an mRF in seismic countries where earthquakes constantly alter the frame. Our research group calculated an mRF (REDGEOMIN) that includes interseismic, coseismic, and postseismic deformation using CORS with open data from 2009 to 2022 and processed with scientific standards global navigation satellite system. REDGEOMIN consists of a deformation model (ADELA) with an interpolation approach through thin plate spline, allowing the greatest deformation to be modelled at campaign points. The relationship between classical and modern systems was explored with conformal transformations and NTv2 grids to include deformations, especially coming from PSAD56 and SAD69. The results demonstrate that REDGEOMIN aligns with the IGb14 reference frame (<1.0 mm), SIRGAS (ENU = 1.0, 1, 0, 2.0 mm), and the Chilean national reference frame SIRGASChile@2021.00 (ENU = 1, 2, 1, 6, 4.3 mm) aligns with millimetric precision. ADELA deformation model accurately models period locations to within 5 mm. Densification of REDGEOMIN@2022.00 at passive points PSAD56/SAD69 shows centimetric precision. PSAD56/SAD69, adjusted in the 1970s, are outdated due to crustal movement and seismic events and have metric errors. Therefore, different types of transformations were evaluated between PSAD56/SAD69 and REDGEOMIN@2022, whose RMS is between 1.57 and 1.69 m, and national grid transformations (NTv2) with an RMS of 0.23 and 0.16 m for PSAD56 and SAD69, respectively. The relationship between the classic systems and REDGEOMIN allows the transformation of the entire Chilean mining cadastre to epoch 2022.00. Starting in 2022.00, REDGEOMIN/ADELA offers millimetre precision, which is crucial in seismic zones. Furthermore, it paves the way to implement an updated national-level mRF in case of seismic events. Currently, Chilean mining laws are rigid, geodesically speaking. Therefore, legal-technical suggestions for implementing REDGEOMIN are also included in this article.

On special curves in Lie groups with Myller configuration

In this study, we determine a new type comprehensive frame, which is called the generalized Frenet‐type frame in three‐dimensional Lie groups with Myller configurations, and it includes several special and classical type frames for Euclidean 3‐space and three‐dimensional Lie groups. After constructing this new comprehensive frame, we obtain derivative formulas with the help of the Lie curvature. In addition, we define some special type curves. The geometry of versor fields along a curve with Frenet‐type frame in three‐dimensional Lie groups with Myller configurations is a generalization of the usual theory of curves. Since this particular relationship, the osculating‐type and rectifying‐type curves with Frenet‐type frame in three‐dimensional Lie groups with Myller configurations include some special cases for osculating and rectifying curves in different spaces.

An Efficient Inexact Gauss–Seidel-Based Algorithm for Image Restoration with Mixed Noise

A challenge in image restoration is to recover a clear image from the blurry observation in the presence of different types of noise. There are few works addressing image deblurring under mixed noise. To handle this issue, we propose a general model based on classical wavelet tight frame regularization. We utilize a convexity-preserving term to obtain a component-wise convex model under a mild condition. Indeed, to reduce the cost of solving subproblems, the inexact Gauss–Seidel-based majorized semi-proximal alternating direction method of multipliers (sGS-imsPADMM) with relative error control is developed. Besides, the global convergence of sGS-imsPADMM is demonstrated. Numerical results for the image restoration problems show that the proposed model and solving approach are superior to some state-of-the-art methods both in numerical analysis and visual quality.

Info-Geometric Analysis of Gamma Distribution Manifold with Gamma Distribution Impact to Advance Satellite Earth Observations

This study aims to reveal the revolutionary Gamma Distribution Manifold (GDM) info-geometric analysis combined with potential Gamma distribution (GD) applications to advance Satellite Earth Observations (SEOs). An exposition of the GDM Fisher Information Matrix (FIM) was undertaken, together with the analytic investigation of the existence of FIM’s inverse. The derivation of GDM’s Geodesic Equations (GEs) is undertaken. The solution of the obtained Geodesic Equations is optimally complicated, and it provides more extensions to numerous open problems. Notably, the current paper provides a first-time unification between three multi-interdisciplinary fields, namely, information geometry theory, probability theory, and Satellite earth observations. Looking at the other side of the coin, the provided revolutionary approach in this current work reports the significant impact of info-geometric analysis on the probabilistic dynamics as well as the influential role of information geometry in the satellite and space industry. This poses numerous open issues that initiate a new form of contemporary unification between these inter-disciplinaries to discover another visionary thinking out of traditional statistical frames. In other words, refraining ourselves from using classical statistical frames of thinking and delving into a new info-geometric vision of statistical distributions as well as examining real-life applications of information geometry to advance satellite earth observations. The curtain is drawn on this paper by providing several challenging open problems in combination with a concluding remark and the next phase of research.

Gravitational quantum switch on a superposition of spherical shells

In the absence of a complete theory of quantum gravity, phenomenological models built upon minimal assumptions have been explored for the analysis of possible quantum effects in gravitational systems. Implications of a superposition of geometries have been considered in such models, including the occurrence of processes with indefinite order. In a gravitational quantum switch, in particular, the order of operations applied by two agents on a target system is entangled with the state of the geometry. We consider a model describing the superposition of geometries produced by distinct arrangements of spherical mass shells, and show that a protocol for the implementation of a gravitational quantum switch can be formulated in such a system. The geometries in superposition are identical in an exterior region outside a given radius, and differ within such a radius. The exterior region provides a classical frame from which the superposition of geometries in the interior region can be probed. One of the agents crosses the interior region and becomes entangled with the geometry, which is explored as a resource for the implementation of the quantum switch. Novel features of the protocol include the superposition of nonisometric geometries, the existence of a region with a definite geometry, and the fact that the agent that experiences the superposition of geometries is in free fall, preventing information on the global geometry to be obtained from within its laboratory.

Group Actions on Manifolds

In this paper some Riemann Geometry aspects will be gathered with classical time, the study naturally concentrate to PDE’s from the relation outside geometry. The classical frame work of differential geometry (intending smooth manifolds) and later it endured with Riemannian metric is briefly described in one of the sections that were formed to be essential for our understanding of the inner structure of the space.

An alternative to the Navier–Stokes equation based on the conservation of acceleration

The derivation of the Navier–Stokes equation in continuum mechanics leads to a number of consequences which are discussed in depth. In spite of its very high representativity of real flows, this equation presents some artefacts due to the whole notion of the continuous medium. An alternative to the Navier–Stokes equation is proposed, based on the conservation of energy per unit mass instead of momentum. The classical inertial frame of reference is replaced by a set of local frames of reference where interactions are treated as cause and effect. Invoking the principle of equivalence between energy and mass, the latter is eliminated from the quantities used in this new formalism. All quantities, variables and physical properties are thus expressed in units of mass. The law of motion is established in the form of the conservation of acceleration, an energy per unit of mass and length. The acceleration is thus written in the form of a Helmholtz–Hodge decomposition, in two terms, the first curl-free and the second divergence-free as a function of two potentials, scalar and vector. Maxwell's idea of federating the laws of electrodynamics and magnetism to establish electromagnetism is taken up here to establish the new law of motion as a nonlinear wave equation. This approach makes it possible to demonstrate that this law is relativistic from the start. The form of the equation of motion in two Lagrangians gives access to symmetries related to the conservation of certain quantities according to Noether's theorem.

Investigation of the feasibility of using aluminum honeycomb cores in the design of the fin of the aircraft

The issues related to the use of a honeycomb cores in the design, the weight ratio of the empennage units are considered on the example of the fin of an aircraft. The article provides a comparative qualitative assessment of the weight efficiency, manufacturability of the design and design features of the fin with the use of honeycomb panels, compared with the classical frame construction of fin units. In addition, the article discusses the problems associated with the operation and repair of honeycomb core constructions. In the article the calculations of mass determination of honeycomb panel and transverse set for cases the thickness of the profile C=13%, C=8%, C=4% were carried out. Using he method of sequential calculations of each structural part of the honeycomb panel or the frame construction, the resulting masses of units were obtained. Based on the results, we can conclude that the use of three-layer panels in the construction of the fin with a given area and construction height is not justified, since the difference in weight is negligible, and honeycomb panels have several disadvantages.

Considering a superposition of classical reference frames

A ubiquitous feature of quantum mechanical theories is the existence of states of superposition. This is expected to be no different for a quantum gravity theory. Guided by this consideration and others we consider a framework in which classical reference frames may be in superposition relative to one another. Mirroring standard quantum mechanics we introduce a complex-valued wavefunctional, which takes as input the transformations between the coordinates, Ψ[x(x′)], with the interpretation that an interaction between the reference frames may select a particular transformation with probability distribution given by the Born rule — P[x(x′)] = probability distribution functional ≡ |Ψ[x(x′)]|2. The cases of two and three reference frames in superposition are considered explicitly. It is shown that the set of transformations is closed. A rule for transforming wavefunctions from one system to another system in superposition is proposed and consistency with the Schrodinger equation is demonstrated.

Shear thickening in presence of adhesive contact forces: The singularity of cornstarch

Hypothesis: A number of dense particle suspensions experience a dramatic increase in viscosity with the shear stress, up to a solid-like response. This shear-thickening process is understood as a transition under flow of the nature of the contacts – from lubricated to frictional – between initially repellent particles. Most systems are now assumed to fit in with this scenario, which is questionable.Experiment: Using an in-house pressure sensor array, we provide a spatio-temporal map of the normal stresses in the flows of two shear-thickening fluids: a stabilized calcium carbonate suspension, known to fit in with the standard scenario, and a cornstarch suspension, which spectacular thickening behavior remains poorly understood.Findings: We evidence in cornstarch a unique, stable heterogeneous structure, which moves in the velocity direction and does not appear in calcium carbonate. Its nature changes from a stress wave to a rolling solid jammed aggregate at high solid fraction and small gap width. The modeling of these heterogenities points to an adhesive force between cornstarch particles at high stress, also evidenced in microscopic measurements. Cornstarch being also attractive at low stress, it stands out of the classical shear-thickening frame, and might be part of a larger family of adhesive and attractive shear-thickening fluids.

Analyzing the Narrative Framing Pitfalls of Social Media Based on Propaganda Model

Social media is a product of the web 2.0 era. It has always been regarded as a symbol of the spirit of "freedom" and "sharing" in this period. Early media optimists believed that social media would free democracy from the encroachment of mass media and expand the sphere of public opinion. With the development of digital technology and social media, the information content produced by the public on social media has the same dissemination ability as mass media to a certain extent. From a neoliberal perspective, such changes herald the overall rise of press freedom and freedom of opinion on social media. However, it remains to be seen whether social media can break through the social framework constructed by the mass media to achieve freedom of expression. Therefore, this paper explores this issue based on the classical theoretical frame in the political economy of the media-the Propaganda Model (PM). By selecting the "Bucha massacre" in the Russia-Ukraine conflict as the research object, and collecting and conducting qualitative research on the data of social media platforms, the results of this paper guide to an answer: with strong control from the mass media and social elites, it is difficult for social media to fulfill the expected breakthrough task it was entrusted with. The more serious situation is that contemporary social media has a great possibility of becoming a link in the propaganda framework.

Generalized frame operator, lower semiframes, and sequences of translates

AbstractGiven an arbitrary sequence of elements of a Hilbert space , the operator is defined as the operator associated to the sesquilinear form , for . This operator is in general different from the classical frame operator but possesses some remarkable properties. For instance, is always self‐adjoint with regard to a particular space, unconditionally defined, and, when ξ is a lower semiframe, gives a simple expression of a dual of ξ. The operator and lower semiframes are studied in the context of sequences of integer translates of a function of . In particular, an explicit expression of is given in this context, and a characterization of sequences of integer translates, which are lower semiframes, is proved.

The hands’ default location guides tactile spatial selectivity

Our skin is a two-dimensional sheet that can be folded into a multitude of configurations due to the mobility of our body parts. Parts of the human tactile system might account for this flexibility by being tuned to locations in the world rather than on the skin. Using adaptation, we scrutinized the spatial selectivity of two tactile perceptual mechanisms for which the visual equivalents have been reported to be selective in world coordinates: tactile motion and the duration of tactile events. Participants' hand position-uncrossed or crossed-as well as the stimulated hand varied independently across adaptation and test phases. This design distinguished among somatotopic selectivity for locations on the skin and spatiotopic selectivity for locations in the environment, but also tested spatial selectivity that fits neither of these classical reference frames and is based on the default position of the hands. For both features, adaptation consistently affected subsequent tactile perception at the adapted hand, reflecting skin-bound spatial selectivity. Yet, tactile motion and temporal adaptation also transferred across hands but only if the hands were crossed during the adaptation phase, that is, when one hand was placed at the other hand's typical location. Thus, selectivity for locations in the world was based on default rather than online sensory information about the location of the hands. These results challenge the prevalent dichotomy of somatotopic and spatiotopic selectivity and suggest that prior information about the hands' default position -right hand at the right side-is embedded deep in the tactile sensory system.

Algebraic Properties of Quantum Reference Frames: Does Time Fluctuate?

Quantum reference frames are expected to differ from classical reference frames because they have to implement typical quantum features such as fluctuations and correlations. Here, we show that fluctuations and correlations of reference variables, in particular of time, are restricted by their very nature of being used for reference. Mathematically, this property is implemented by imposing constraints on the system to make sure that reference variables are not physical degrees of freedom. These constraints not only relate physical degrees of freedom to reference variables in order to describe their behavior, they also restrict quantum fluctuations of reference variables and their correlations with system degrees of freedom. We introduce the notion of “almost-positive” states as a suitable mathematical method. An explicit application of their properties to examples of recent interest in quantum reference frames reveals previously unrecognized restrictions on possible frame–system interactions. While currently discussed clock models rely on assumptions that, as shown here, make them consistent as quantum reference frames, relaxing these assumptions will expose the models to new restrictions that appear to be rather strong. Almost-positive states also shed some light on a recent debate about the consistency of relational quantum mechanics.

Emotional body postures affect inhibitory control only when task-relevant.

A classical theoretical frame to interpret motor reactions to emotional stimuli is that such stimuli, particularly those threat-related, are processed preferentially, i.e., they are capable of capturing and grabbing attention automatically. Research has recently challenged this view, showing that the task relevance of emotional stimuli is crucial to having a reliable behavioral effect. Such evidence indicated that emotional facial expressions do not automatically influence motor responses in healthy young adults, but they do so only when intrinsically pertinent to the ongoing subject's goals. Given the theoretical relevance of these findings, it is essential to assess their generalizability to different, socially relevant emotional stimuli such as emotional body postures. To address this issue, we compared the performance of 36 right-handed participants in two different versions of a Go/No-go task. In the Emotional Discrimination task, participants were required to withhold their responses at the display of emotional body postures (fearful or happy) and to move at the presentation of neutral postures. Differently, in the control task, the same images were shown, but participants had to respond according to the color of the actor/actress' t-shirt, disregarding the emotional content. Results showed that participants made more commission errors (instances in which they moved even though the No-go signal was presented) for happy than fearful body postures in the Emotional Discrimination task. However, this difference disappeared in the control task. Such evidence indicates that, like facial emotion, emotional body expressions do not influence motor control automatically, but only when they are task-relevant.

A SiC MOSFET Isolated DC/DC Converter for a Hybrid Vehicle

This article deals with development of a DC/DC converter for use as a device for charging the traction storage batteries of an unmanned vehicle with a solid-oxide fuel cell stack. A phase shift controlled 8 kW full-bridge DC/DC converter was modeled, developed, manufactured, and tested within the frame of a research work. The device operation principle is described. The device control system developed on the basis of the Cortex ARM STM32F407VGT6 controller uses original software. The software supports the converter operation in an automatic mode by receiving, from the central processor device, operation mode setting commands (including the current, voltage, and power setpoints) and transmitting the remote measurement data (input and output circuit voltages, and the power switches and housing temperatures). Communication with the vehicle central processor is performed using the CAN protocol as per the SAE J1939 standard. The CAN is a standard serial communication protocol (its support for real-time distributed control with multiplexing allows information to be exchanged between various vehicle components). The classic CAN frame format allows data transmission rates up to 1 Mbps and payloads up to 8 bytes per frame. However, the recently introduced format (a CAN flexible data transmission rate frame format) allows higher data transmission rates and payloads higher and longer than these ordinary values. The transmission rate in the developed converter is 250 kbps. The converter operates in the input voltage range from 180 to 250 V and output voltage range from 500 to 800 V. The output current limit is 10 A. The converter efficiency was estimated to be 93%.

The joint effect of framing and defaults on choice behavior

The framing effect leads people to prefer a sure alternative over a risky one (risk aversion) when alternatives are described as potential gains compared to a context-dependent reference point. The reverse (risk propensity) happens when the same alternatives are described as potential losses. The default effect is the tendency to prefer a preselected alternative over other non-preselected given options, without facilitating nor incentivizing the choice. These two effects have mainly been studied separately. Here we provided novel empirical evidence of additive effects due to the application of both framing and default within the same decision problem in a large sample size (N = 960). In the baseline condition, where no default was provided, we measured the proportion of risky choices in life-or-death and financial decisions both presented in terms of potential gains or losses following the structure of the Asian disease problem. In the sure default condition, the same layout was proposed with a flag on the sure option, whereas in the risky default condition, the flag was on the risky option. In both default conditions, we asked participants whether they wanted to change the preselected option. Overall, the comparison between these conditions revealed three distinct main effects: (i) a classic framing effect, (ii) a larger risk propensity in the life-or-death scenario than in the financial one, and (iii) a larger default effect when the flag was on the risky, rather than on the sure, option. Therefore, we conclude that default options can enhance risk propensity. Finally, individual beliefs about the source of the default significantly moderated the strength of the effect. Underlying mechanisms and practical implications are discussed considering prominent theories in this field.

Short Frame Transmission at Very Low SNR by Associating CCSK Modulation With NB-Code

In this paper, we present a frame structure that can be viewed as a preamble for the detection and synchronization process (leading to low cost receiver) and as an encoded codeword carrying the transmitted message (leading to reliable transmission). This duality facilitates an ALOHA protocol avoiding preamble overhead. The frame structure, named Quasi-Cyclic Short Packet (QCSP), is based on the association of a Cyclic Code Shift Keying (CCSK) modulation and a non-binary error control code. The detection/correction algorithm of the QCSP system is presented, its performance is theoretically derived and discussed for different parameters. A QCSP frame can be transmitted and received correctly with an error probability of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {10^{-4}}$ </tex-math></inline-formula> , distanced by <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.2</b> dB from Polyanskiy’s bound (an estimated Shannon’s limit for small packet size) at −11 dB of SNR for a payload of 360 bits. Compared to a classical preamble-based frame using a modern binary error control code, the size of a QCSP frame is reduced by 23%. Moreover, detecting a QCSP frame requires a lower complexity than detecting a longer classical preamble.

A Rhetorical Reading of Self–Other Polarities in Counsel Arguments made before the Trials of Major Criminals at Nuremberg and Tokyo

Abstract An argumentative narrative apart from positive rules appeared in early international criminal law (ICL). This article argues that a complex narrative pertaining to Self–Other polarities can be identified from the arguments presented by the counsel, whether prosecution or defence, in their respective case’s opening and closing arguments before the major war criminals’ trials at the Nuremberg International Military Tribunal, on the one hand, and at the International Military Tribunal for the Far East, on the other. This article proposes a fourfold taxonomy to explain said Self–Other narratives. It is further argued that these narratives could be explained through a classical rhetorical frame as aimed at enhancing the persuasion (by appealing, in particular, to logos, ethos and pathos) of the respective sides’ arguments. The article finally reflects on possible reasons why counsel appearing before these early ICL tribunals took recourse to these narratives to persuade. The constitution of the respective intended target audiences to be persuaded are considered in the process as well.

Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system

Symmetry principles are fundamental in physics, and while they are well understood within Lagrangian mechanics, their impact on quantum channels has a range of open questions. The theory of asymmetry grew out of information-theoretic work on entanglement and quantum reference frames, and allows us to quantify the degree to which a quantum system encodes coordinates of a symmetry group. Recently, a complete set of entropic conditions was found for asymmetry in terms of correlations relative to infinitely many quantum reference frames. However, these conditions are difficult to use in practice and their physical implications unclear. In the present theoretical work, we show that this set of conditions has extensive redundancy, and one can restrict to reference frames forming any closed surface in the state space that has the maximally mixed state in its interior. This in turn implies that asymmetry can be reduced to just a single entropic condition evaluated at the maximally mixed state. Contrary to intuition, this shows that we do not need macroscopic, classical reference frames to determine the asymmetry properties of a quantum system, but instead infinitesimally small frames suffice. Building on this analysis, we provide simple, closed conditions to estimate the minimal depolarization needed to make a given quantum state accessible under channels covariant with any given symmetry group.