Fundamental Equivalence Research Articles

On Some Forgotten Formulas of L. de Broglie and the Nature of Thermal Time.

From 1948 until around 1965, Louis de Broglie, awarded the Nobel Prize for Physics in 1929 for his fundamental contributions to quantum theory, pursued a systematic study of the formal analogies between wave mechanics and the thermomechanics of Boltzmann and Helmholtz. As part of this line of research, he produced several interesting observations, which were, however, published only in French, and, therefore, had a very limited diffusion. Here, we reconsider, in particular, a result of his relating to the analogy between the internal clock (de Broglie phase) of a free particle and a cyclic isothermal process in a thermomechanical system. We show that the fundamental equivalence obtained by him can be derived under more convenient hypotheses than the original ones, essentially tied to the quantization of the action exchanged by the particle with a suitable thermostat. In this emended formulation, the relations proposed by de Broglie describe the emergence of the particle proper time from a thermal background. They also suggest a specific physical meaning of the Wick rotation, often used in quantum mechanical calculations, and the thermal time that appears in it.

Pain Score Levels Acceptable to Patients and Hospital Staff in Trauma & Orthopaedics in A Large District General Hospital

Adequate Pain control in trauma and orthopaedic wards is seen as a fundamental equivalence of the quality of medical care worldwide. Despite this, there is no official standard or numerical value of pain that is acceptable for patients. This study examines the level of pain accepted by both inpatients and staff in trauma and orthopaedics in a large district hospital.

A relationship between orthogonal regression and the coefficient of determination under rotation of data sets

In this article, we explore patterns of R 2 across data sets to reveal a fundamental equivalence. If any set of bivariate data is rotated, the R 2 value changes and defines a curve as a function of the rotation angle θ. We show that for any data set whose rotated R 2 curve has the same maximum value, the entire curve is identical up to a shift in the rotation angle. We also find that a recently introduced measure of linearity, Q 2, provides a definitive relation between these data sets, with equal Q 2 values resulting in identically rotated R 2 curves. Finally, we also show that we can consider R 2 as the combination of two components, the linearity of the data and a rotation angle. While rotating data or axes for non spatial data loses the specific meaning of the variables, these results may provide additional understanding of the relationships within the data and can reveal similarities between data sets, the role of sensitivity in correlation, and the nature of correlation itself.

A general approach to the mechanical analysis of continuous local inhomogeneity using continuum mechanics theory and a new general energy-based-model

While usually we don't know complete geometrical and physical information on the occurred inhomogeneity, but in order to study the related phenomena, continuum mechanics theory as well as exiting energy-based models need direct information from the desired system in order to A General Approach to the Mechanical Analysis of Continuous Local Inhomogeneity Using Continuum Mechanics Theory and A New General Energy-Based- Modelapply the field equations. Of course, theories and ideas based on the unification of mechanics and thermodynamics can offer other solutions. This paper establishes a general energy based model to study effects of local inhomogeneity on the mechanical behavior of materials using thermodynamic laws with a new deviation as well as new approach to the total energy. In fact, the main goal is that the established model can be used with a wide range of applications and appropriate accuracy, both theoretically and experimentally, while not getting involved with excessive computational complexity. It can be noted that the extracted formulations develop possibility to study inhomogeneity effects on the mechanical behavior without any more limiting conditions. In addition, due to that study of the stored and dissipated energy, usually, has the main role in the investigating of the inhomogeneity effects on the mechanical behavior, also the point of view in the presented model is in complete agreement to provide the conditions for this study directly. Therefore, the prediction possibility of the inhomogeneity effects on the mechanical behavior will be provided with the smallest volume of needed calculations. Also, due to that the structure and properties of the inhomogeneity are unknown usually, the formulations aren't dependent to these knowledge directly, and can be analyzed theoretically and experimentally to study the homogeneity part, as a known material. In the following, feasible processes are studied using extracted formulations. To validate the equations, a rectangular material shape with local inhomogeneity is considered, and extracted equations are developed for that. To consider our mean on the stored and dissipated energies, it is assumed that the homogeneity part of material has viscoelastic behavior, and the equations are developed to Maxwell and Kelvin viscoelastic models in different homogeneity parts of the body. In the following, classical continuum mechanic theory due to elasticity theory is used, and the field equations are developed to the considered body. Finally, results are discussed, compared as well as their differences, and corresponding capabilities for functional completion are discussed. Finally, the fundamental equivalence of the results is studied, and matching of the results between continuum mechanics theory and extracted formulations is shown.

Are cross-cultural shyness comparisons valid? Testing invariance with multigroup CFA and the alignment method across eastern and western cultures.

Temperament/personality research has been largely based on an imposed-etic strategy: Self-report temperament/personality inventories created in and reflecting American culture were tacitly assumed to apply in other countries and cultures. Correspondingly, invariance tests on the underlying phenomena and their associated constructs have been rarely applied in cross-cultural studies and in those instances unsuccessfully. To explore this oversight, we investigated whether a western-based anxious shyness measure was equivalent across eastern-western cultures (Chinese, n = 816, 47.2% male; Canadian, n = 995, 30.8% male). In the first instance, we used the well-established multigroup confirmatory factor analysis (MGCFA) to show that there was measurement noninvariance in the one factor shyness scale across the two countries and the two countries by sex. We further examined the issue of noninvariance using the newer alignment method, an approach providing detailed information on noninvariance for each country model by parameter (across intercepts and loadings) as an alternative to the MGCFA restrictive assessment of whole scale construct validation. The findings suggested acceptable approximate invariance in the shyness scale to support an unbiased comparison of mean levels between the two countries and the two countries by sex. Chinese young adults had significantly higher mean levels of shyness than Canadian young adults. Despite some limited noninvariance, we were able to conclude that the underlying construct of shyness as measured in this study was equivalent across Chinese and Canadian cultures. Findings illustrated the difficulties and importance of first establishing fundamental measurement properties and equivalence in personality constructs before inferring cross-cultural universality in complex traits and characteristics. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Generalized approach to matched filtering using neural networks

Gravitational wave science is a pioneering field with rapidly evolving data analysis methodology currently assimilating and inventing deep learning techniques. The bulk of the sophisticated flagship searches of the field rely on the time-tested matched filtering principle within their core. In this paper, we make a key observation on the relationship between the emerging deep learning and the traditional techniques: matched filtering is formally equivalent to a particular neural network. This means that a neural network can be constructed analytically to exactly implement matched filtering, and can be further trained on data or boosted with additional complexity for improved performance. Moreover, we show that the proposed neural network architecture can outperform matched filtering, both with or without knowledge of a prior on the parameter distribution. When a prior is given, the proposed neural network can approach the statistically optimal performance. We also propose and investigate two different neural network architectures MNet-Shallow and MNet-Deep, both of which implement matched filtering at initialization and can be trained on data. MNet-Shallow has simpler structure, while MNet-Deep is more flexible and can deal with a wider range of distributions. Our theoretical findings are corroborated by experiments using real LIGO data and synthetic injections, where our proposed methods significantly outperform matched filtering at false positive rates above $5\times 10^{-3}\%$. The fundamental equivalence between matched filtering and neural networks allows us to define a "complexity standard candle" to characterize the relative complexity of the different approaches to gravitational wave signal searches in a common framework. Finally, our results suggest new perspectives on the role of deep learning in gravitational wave detection.

Bisimilarity on Basic Parallel Processes

The main aim of this paper is to give a simple transparent proof of the result showing that the problem of bisimulation equivalence on the class of Basic Parallel Processes (BPP), denoted by BPP-Bisim, can be decided by a polynomial-space algorithm. This result (by the author) has been previously only presented in a conference version, in a rather technical form that is not easily readable and verifiable. Since the result has clarified the complexity of the problem BPP-Bisim, namely its PSPACE-completeness (using the lower bound by Srba), and the problem deals with a fundamental behavioural equivalence and with one of the simplest models that naturally extend finite-state systems into infinite-state ones, it seems appropriate to have a transparent version of the proof.

Fundamental local equivalences in quantum geometric Langlands

In quantum geometric Langlands, the Satake equivalence plays a less prominent role than in the classical theory. Gaitsgory and Lurie proposed a conjectural substitute, later termed the fundamental local equivalence. With a few exceptions, we prove this conjecture and its extension to the affine flag variety by using what amount to Soergel module techniques.

Quantum steering as a witness of quantum scrambling

Quantum information scrambling describes the delocalization of local information to global information in the form of entanglement throughout all possible degrees of freedom. A natural measure of scrambling is the tripartite mutual information (TMI), which quantifies the amount of delocalized information for a given quantum channel with its state representation, i.e., the Choi state. In this work, we show that quantum information scrambling can also be witnessed by temporal quantum steering for qubit systems. We can do so because there is a fundamental equivalence between the Choi state and the pseudo-density matrix formalism used in temporal quantum correlations. In particular, we propose a quantity as a scrambling witness, based on a measure of temporal steering called temporal steerable weight. We justify the scrambling witness for unitary qubit channels by proving that the quantity vanishes whenever the channel is non-scrambling.

Viability and Arbitrage Under Knightian Uncertainty

We reconsider the microeconomic foundations of financial economics. Motivated by the importance of Knightian uncertainty in markets, we present a model that does not carry any probabilistic structure ex ante, yet is based on a common order. We derive the fundamental equivalence of economic viability of asset prices and absence of arbitrage. We also obtain a modified version of the fundamental theorem of asset pricing using the notion of sublinear pricing measures. Different versions of the efficient market hypothesis are related to the assumptions one is willing to impose on the common order.

The Operational Choi-Jamiołkowski Isomorphism.

In this article, I use an operational formulation of the Choi–Jamiołkowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be understood as a means of drawing conclusions about the intratheoretic causal structure of quantum mechanics which are independent of any specific ontological picture. I then give an operational formulation of the Choi–Jamiołkowski isomorphism and show that, in an operational theory which exhibits this isomorphism, several features of the theory which are usually regarded as properties of the quantum state can be derived from constraints on non-local correlations. This demonstrates that there is no need to postulate states to be the bearers of these properties, since they can be understood as consequences of a fundamental equivalence between multipartite and temporal correlations.

𝒦-convergence as a new tool in numerical analysis

Abstract We adapt the concept of $\mathscr{K}$-convergence of Young measures to the sequences of approximate solutions resulting from numerical schemes. We obtain new results on pointwise convergence of numerical solutions in the case when solutions of the limit continuous problem possess minimal regularity. We apply the abstract theory to a finite volume method for the isentropic Euler system describing the motion of a compressible inviscid fluid. The result can be seen as a nonlinear version of the fundamental Lax equivalence theorem.

Satellite Laser-Ranging as a Probe of Fundamental Physics

Satellite laser-ranging is successfully used in space geodesy, geodynamics and Earth sciences; and to test fundamental physics and specific features of General Relativity. We present a confirmation to approximately one part in a billion of the fundamental weak equivalence principle (“uniqueness of free fall”) in the Earth’s gravitational field, obtained with three laser-ranged satellites, at previously untested range and with previously untested materials. The weak equivalence principle is at the foundation of General Relativity and of most gravitational theories.

Nanoparticles in dilute gases: Fundamental equivalence between momentum accommodation and surface adsorption.

Momentum accommodation is a key factor governing the transport of particles in gases from electric mobility and Brownian diffusion to thermophoresis. This paper explores the relationship between momentum accommodation of nanoparticles in dilute gases and surface adsorption. We demonstrate that the momentum accommodation factor is fundamentally equal to the probability of surface adsorption. Molecular dynamics simulations show that surface adsorption is the key mechanism behind the diffuse scattering model, and that upon gas-particle collision the immediate reflection dynamics and surface adsorption events are governed by the kinetic energy distribution of the rebounding gas molecules. This distribution determines the transition of the dominant mode of molecular scattering off a particle surface from diffuse to specular elastic reflection as the particle approaches the realm of molecular size. The kinetics and equilibrium of physisorption are examined to shed light on the effect of the lifetime of surface adsorbates on momentum transfer. A statistical treatment is proposed for the adsorption and hence the gas-nanoparticle momentum accommodation coefficient. The validity of the theoretical treatment is examined by comparing its prediction against experimental mobility data of silver nanoparticles.

$H_v$-Normal subgroups and $H_v$-quotient groups

‎A larger class of algebraic hyperstructures satisfying the group-like axioms is the class of $H_v$-groups‎. ‎In this paper‎, ‎without any condition and in general‎, ‎we define the $H_v$-normal subgroup and the $H_v$-quotient group of a $H_v$-group‎. ‎We introduce the fundamental equivalence relation of a $H_v$-quotient group and prove the first and third isomorphism theorems for $H_v$-groups‎.

The fundamental Lepage form in variational theory for submanifolds

The multiple-integral variational functionals for finite-dimensional immersed submanifolds are studied by means of the fundamental Lepage equivalent of a homogeneous Lagrangian, which can be regarded as a generalization of the well-known Hilbert form in the classical mechanics. The notion of a Lepage form is extended to manifolds of regular velocities and plays a basic role in formulation of the variational theory for submanifolds. The theory is illustrated on the minimal submanifolds problem, including analysis of conservation law equations.

Testing the Equivalence between Spatial Averaging and Temporal Averaging in Highly Dilute Solutions.

Diffusion relates the flux of particles to the local gradient of the particle density in a deterministic way. The question arises as to what happens when the particle density is so low that the local gradient becomes an ill-defined concept. The dilemma was resolved early last century by analyzing the average motion of particles subject to random forces whose magnitude is such that the particles are always in thermal equilibrium with their environment. The diffusion dynamics is now described in terms of the probability density of finding a particle at some position and time and the probabilistic flux density, which is proportional to the gradient of the probability density. In a time average sense, the system thus behaves exactly like the ensemble average. Here, we report on an experimental method and test this fundamental equivalence principle in statistical physics. In the experiment, we study the flux distribution of 20 nm radius polystyrene particles impinging on a circular sink of micrometer dimensions. The particle concentration in the water suspension is approximately 1 particle in a volume element of the dimension of the sink. We demonstrate that the measured flux density is exactly described by the solution of the diffusion equation of an infinite system, and the flux statistics obeys a Poissonian distribution as expected for a Markov process governing the random walk of noninteracting particles. We also rigorously show that a finite system behaves like an infinite system for very long times despite the fact that a finite system converges to a zero flux empty state.

Implicitly Coupled Electromechanical and Electromagnetic Transient Analysis Using a Frequency-Dependent Network Equivalent

This paper presents an improved solution of the implicitly coupled electromechanical and electromagnetic transient analysis problem using a frequency-dependent network equivalent (FDNE). In previous work, the fundamental frequency equivalent was used as the network equivalent of the external system. While simple, this fundamental frequency equivalent is only accurate for a single frequency, the fundamental frequency. This may lead to an inaccurate equivalent of the transient stability (TS) network. This paper extends previous work by using an FDNE derived from the vector-fitting technique. The FDNE is able to resolve the transient behavior over a wider frequency spectrum leading to a more accurate representation of the TS network. Results demonstrating the accuracy of the proposed scheme are presented on a 3-bus test system and the IEEE 118-bus system.

A Fundamental Equivalence between Randomized Experiments and Observational Studies

Abstract A fundamental probabilistic equivalence between randomized experiments and observational studies is presented. Given a detailed scenario, the reader is asked to consider which of two possible study designs provides more information regarding the expected difference in an outcome due to a time-fixed treatment. A general solution is described, and a particular worked example is also provided. A mathematical proof is given in the appendix. The demonstrated equivalence helps to clarify common ground between randomized experiments and observational studies, and to provide a foundation for considering both the design and interpretation of studies.

US Surveillance Law, Safe Harbor, and Reforms Since 2013

This White Paper is a submission to the Belgian Privacy Authority for its December 18, 2015 Forum on “The Consequences of the Judgment in the Schrems Case.” The Forum discusses the decision by the European Court of Justice in Schrems v. Data Protection Commissioner that the EU/US Safe Harbor was unlawful under the EU Data Protection Directive, particularly due to concerns about US surveillance law.For the Forum, I have been asked to comment on two issues:1) Is US surveillance law fundamentally compatible with EU data protection law? 2) What actions and reforms has the US taken since the Snowden revelations began in June 2013?The White Paper draws on my background as a scholar of both EU data protection law and US surveillance law. It addresses serious misunderstandings of US national security law, reflected in official statements made in the Schrems case and elsewhere. It has three chapters:(1) The fundamental equivalence of the United States and EU member States as constitutional democracies under the rule of law. In the Schrems decision, the US was criticized for failing to ensure “a level of protection of fundamental rights essentially equivalent to that guaranteed in the EU legal order.” This chapter critiques that finding, instead showing that the United States has strict rule of law, separation of powers, and judicial oversight of law enforcement and national security surveillance, which together make the US legal order “essentially equivalent” to the EU legal order.(2) The Section 702 PRISM and Upstream programs are reasonable and lawful responses to changing technology. The Advocate General’s opinion in the Schrems case said that the PRISM program gave the NSA “unrestricted access to mass data” stored in the US, and that Section 702 enabled NSA access “in a generalised manner” for “all persons and all means of electronic communications.” This chapter refutes those claims, which appear to be based in part on incorrect stories in the press. Instead, the Section 702 programs operate with judicial supervision and subject to numerous safeguards and limitations. They examine the communications only of targeted individuals, and only for listed foreign intelligence purposes. The total number of individuals targeted under Section 702 in 2013 was 92,707, a tiny fraction of Internet users in the EU or globally.(3) The US Congress and executive branch have instituted two dozen significant reforms to surveillance law and practice since 2013. The Schrems decision said that US privacy protections must be evaluated in the “current factual and legal context,” but did not address the numerous changes put in place since 2013. This chapter provides a readable explanation of each of these actions, which together constitute the biggest set of pro-privacy actions in US surveillance law since creation of the Foreign Intelligence Surveillance Act in 1978.