Stitching Data: Recovering a Manifold’s Geometry from Geodesic Intersections

Let (M, g) be a Riemannian manifold with boundary. We show that knowledge of the length of each geodesic, and where pairwise intersections occur along the corresponding geodesics allows for recovery of the geometry of (M, g) (assuming (M, g) admits a Riemannian collar of a uniform radius). We call this knowledge the ‘stitching data’. We then pose a boundary measurement problem called the ‘delayed collision data problem’ and apply our result about the stitching data to recover the geometry from the collision data (with some reasonable geometric restrictions on the manifold).

Measured distribution of cloud chamber tracks from radioactive decay: a new empirical approach to investigating the quantum measurement problem

Using publicly available video of a diffusion cloud chamber with a very smallradioactive source, I measure the spatial distribution of where tracks start, and consider possibleimplications. This is directly relevant to the quantum measurement problem and its possibleresolution, and appears never to have been done before. The raw data are relatively uncontrolled,leading to caveats that should guide future, more tailored experiments. Results may suggest amodification to Born’s rule at very small wavefunction, with possibly profound implications forthe detection of extremely rare events such as proton decay. I introduce two candidate smallwavefunctionBorn rule modifications, a hard cutoff and an offset model; the data may favor theoffset model, which has a stronger underlying physical rationale. Track distributions from decaysin cloud chambers represent a previously unappreciated way to probe the foundations of quantummechanics, and a novel case of wavefunctions with macroscopic signatures.

Using photoelectron spectroscopy to measure resonant inelastic X-ray scattering: a computational investigation

Resonant inelastic X-ray scattering (RIXS) has become an important scientific tool. Nonetheless, conventional high-resolution (few hundred meV or less) RIXS measurements, especially in the soft X-ray range, require low-throughput grating spectrometers, which limits measurement accuracy. Here, the performance of a different method for measuring RIXS, i.e. photoelectron spectrometry for analysis of X-rays (PAX), is computationally investigated. This method transforms the X-ray measurement problem of RIXS to an electron measurement problem, enabling use of high-throughput, compact electron spectrometers. X-rays to be measured are incident on a converter material and the energy distribution of the resultant photoelectrons, the PAX spectrum, is measured with an electron spectrometer. A deconvolution algorithm for analysis of such PAX data is proposed. It is shown that the deconvolution algorithm works well on data recorded with ∼0.5 eV resolution. Additional simulations show the potential of PAX for estimation of RIXS features with smaller widths. For simulations using the 3d levels of Ag as a converter material, and with 105 simulated detected electrons, it is estimated that features with a few hundred meV width can be accurately estimated in a model RIXS spectrum. For simulations using a sharp Fermi edge to encode RIXS spectra, it is estimated that one can accurately distinguish 100 meV FWHM peaks separated by 45 meV with 105 simulated detected electrons that were photoemitted from within 0.4 eV of the Fermi level.

Error analysis of prospective mathematics teachers in solving of applying radian measurement problem in trigonometry courses

This research aims to describe the mistakes of the prospective teachers in solving the application of radian measurement problems and their causes. This type of research is qualitative descriptive research with a case study approach. The types of data collection in this research consisted of the results of the subject's work and transcripts of interviews with research subjects. By following the type of data, this research instrument consists of one question about the problem of applying radian measurement and interview guidelines developed by the researchers. Data analysis of the subject's work is carried out by classifying the types of errors to know the types of errors that arise in solving the problem of applying the radian measurements. While the transcript analysis of the interview results was carried out by coding the words to determine the factors causing the errors that appeared. The results of the research indicate that the error in solving the problem of applying the radian measurement are misconceptions and factual errors. This misconception is generally caused by intuitive thinking, while this factual error is generally caused by not paying careful attention to the information in the question. The solution to these errors is to analyze the elements of the circle that are interconnected in solving the problem of applying the radian measurements and to be careful in writing the information that is known in the question.

How Do the Probabilities Arise in Quantum Measurement?

A satisfactory resolution of the persistent quantum measurement problem remains stubbornly unresolved in spite of an overabundance of efforts of many prominent scientists over the decades. Among others, one key element is considered yet to be resolved. It comprises of where the probabilities of the measurement outcome stem from. This article attempts to provide a plausible answer to this enigma, thus eventually making progress toward a cogent solution of the longstanding measurement problem.Quanta 2021; 10: 65–74.

Application of spectral analysis for determine the phase shift of signals with equal amplitudes using full-wave transformation when measuring the characteristics of weapons

The article defines the list of technical characteristics of armaments and military equipment (ARM), the value of which is measured using phase methods. An analysis of known methods that have found wide application in measuring technology, which is designed to determine the technical characteristics associated with the measurement of phase shift during the development, manufacture and operation of weapons. Based on this analysis, it was determined that the measuring systems are designed to determine the phase shift of two harmonic signals in their composition have two channels of information transmission. This architecture of the implementation of measuring systems leads to the fact that a significant impact on the accuracy of the proposed measurement problem, makes a component of the error due to the phase symmetry of the signal transmission channels, as well as internal and external noise. As an alternative approach to solving the measurement problem of determining the phase shift of two harmonic signals, which will significantly reduce the error component due to phase asymmetry of information transmission channels, it is proposed to use the signal obtained by summing harmonic signals after full-wave transformation followed by spectral analysis. In order to implement the above approach, a measurement problem was set to determine the phase shift of two harmonic signals, using spectral analysis of the signal obtained by summing the harmonic signals after their full-wave transformation. A list of assumptions required for the synthesis of analytical relations that establish the relationship between the spectra of phases and amplitudes (power) of the signal obtained by summing harmonic signals after their full-wave transformation and phase shift of two harmonic signals. Analytical relationships are proposed that establish the relationship between the above characteristics. It is shown that the values of the spectrum of phases and amplitudes, which are calculated using the proposed expressions, differ from the values obtained in the calculations using the Fourier series coefficients, not more than 0.1%.

The Concept of Effective Organization for Quality Performance of Public Administration: For New Democracies

The article considers a possible public administration performance measurement regarding to political organization situation in Croatia. The first performance measurement problem comes from multilevel responsibility and co-production implementations. Second comes with emergence of multilevel products origin. Thirdly, state is very open and integrated in the EU and globalization influence. Therefore, it is crucially important to identify products and the evaluation indicators of the public administration, according with the public goals and social values. The article considers the performance measurement and management methodological at an organizational frame and it also considers the social values influence on a methodology and the role of the public administration in fulfilment of the public policy. Finally, effective organization possible could be built and improved by measuring effectiveness. The paper has tried to show the public service complexity work and the purpose, but first of all the importance public administration for achieving public goals.

Universe as Klein–Gordon eigenstates

We formulate Friedmann’s equations as second-order linear differential equations. This is done using techniques related to the Schwarzian derivative that selects the$$\beta $$ β -times $$t_\beta :=\int ^t a^{-2\beta }$$ t β : = ∫ t a - 2 β , where a is the scale factor. In particular, it turns out that Friedmann’s equations are equivalent to the eigenvalue problems $$\begin{aligned} O_{1/2} \Psi =\frac{\Lambda }{12}\Psi , \quad O_1 a =-\frac{\Lambda }{3} a , \end{aligned}$$ O 1 / 2 Ψ = Λ 12 Ψ , O 1 a = - Λ 3 a , which is suggestive of a measurement problem. $$O_{\beta }(\rho ,p)$$ O β ( ρ , p ) are space-independent Klein–Gordon operators, depending only on energy density and pressure, and related to the Klein–Gordon Hamilton–Jacobi equations. The $$O_\beta $$ O β ’s are also independent of the spatial curvature, labeled by k, and absorbed in $$\begin{aligned} \Psi =\sqrt{a} e^{\frac{i}{2}\sqrt{k}\eta } . \end{aligned}$$ Ψ = a e i 2 k η . The above pair of equations is the unique possible linear form of Friedmann’s equations unless $$k=0$$ k = 0 , in which case there are infinitely many pairs of linear equations. Such a uniqueness just selects the conformal time $$\eta \equiv t_{1/2}$$ η ≡ t 1 / 2 among the $$t_\beta $$ t β ’s, which is the key to absorb the curvature term. An immediate consequence of the linear form is that it reveals a new symmetry of Friedmann’s equations in flat space.

Quantitative Digitography Solves the Remote Measurement Problem in Parkinson's disease

Background: Assessment of motor signs in Parkinson's disease (PD) has required an in-person examination. However, 50% of people with PD do not have access to a neurologist. Wearable sensors can provide remote measures of some motor signs but require continuous data acquisition for several days. A major unmet need is reliable metrics of all cardinal motor signs, including rigidity, from a simple short active task that can be performed remotely or in the clinic. Objective: Investigate whether thirty seconds of repetitive alternating finger tapping (RAFT) on a portable quantitative digitography (QDG) device, which measures amplitude and timing, produces reliable metrics of all cardinal motor signs in PD Methods: Ninety-six individuals with PD and forty-two healthy controls performed a thirty-second QDG-RAFT task and clinical motor assessment. Eighteen individuals were followed longitudinally with repeated assessments for an average of three years and up to six years. Results: QDG-RAFT metrics differentiated individuals with PD from controls and provided validated metrics for total motor disability (MDS-UPDRS III) and for rigidity, bradykinesia, tremor, gait impairment and freezing of gait (FOG). Additionally, QDG-RAFT tracked disease progression over several years off therapy, and differentiated akinetic rigid from tremor dominant phenotypes, as well as people with from those without FOG. Conclusions: QDG is a reliable technology, which will improve access to care, allows complex remote disease management, and accurate monitoring of disease progression over time in PD. QDG-RAFT also provides the comprehensive PD motor metrics needed for therapeutic trials.

Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility

Wigner functions, allowing for a reformulation of quantum mechanics in phase space, are of central importance for the study of the quantum-classical transition. A full understanding of the quantum-classical transition, however, also requires an explanation for the absence of macroscopic superpositions to solve the quantum measurement problem. Stochastic reformulations of quantum mechanics based on spontaneous collapses of the wavefunction are a popular approach to this issue. In this article, we derive the dynamic equations for the four most important spontaneous collapse models—Ghirardi–Rimini–Weber (GRW) theory, continuous spontaneous localization (CSL) model, Diósi-Penrose model, and dissipative GRW model—in the Wigner framework. The resulting master equations are approximated by Fokker–Planck equations. Moreover, we use the phase-space form of GRW theory to test, via molecular dynamics simulations, David Albert’s suggestion that the stochasticity induced by spontaneous collapses is responsible for the emergence of thermodynamic irreversibility. The simulations show that, for initial conditions leading to anti-thermodynamic behavior in the classical case, GRW-type perturbations do not lead to thermodynamic behavior. Consequently, the GRW-based equilibration mechanism proposed by Albert is not observed.