Position as an independent variable and the emergence of the 1/21/2-time fractional derivative in quantum mechanics

Using the position as an independent variable, and time as the dependent variable, we derive the function ${\cal P}^{(\pm)}$, which generates the space evolution under the potential ${\cal V}(q)$ and Hamiltonian ${\cal H}$. Canonically conjugated variables are the time and minus the Hamiltonian. While the classical dynamics do not change, the corresponding quantum operator naturally leads to a $1/2-$fractional time evolution, consistent with a recently proposed spacetime symmetric formalism of quantum mechanics. Using Dirac's procedure, separation of variables is possible, and while the coupled position-independent Dirac equations depend on the $1/2$-fractional derivative, the coupled time-independent Dirac equations (TIDE) lead to positive and negative shifts in the potential, proportional to the force. Both equations couple the ($\pm$) solutions of ${\cal \hat P}^{(\pm)}$ and the kinetic energy ${\cal K}_0$ is the coupling strength. We obtain a pair of coupled states for systems with finite forces. The potential shifts for the harmonic oscillator (HO) are $\pm\hbar\omega/2$, and the corresponding pair of states are coupled for ${\cal K}_0\ne 0$. No time evolution is present for ${\cal K}_0=0$, and the ground state with energy $\hbar\omega/2$ is stable. For ${\cal K}_0>0$, the ground state becomes coupled to the state with energy $-\hbar\omega/2$, and \textit{this coupling} allows to describe higher excited states. Energy quantization of the HO leads to quantization of ${\cal K}_0=k\hbar\omega$ ($k=1,2,\ldots$). For the one-dimensional Hydrogen atom, the potential shifts become imaginary and position-dependent. Decoupled case ${\cal K}_0=0$ leads to plane-waves-like solutions at the threshold. Above the threshold, we obtain a plane-wave-like solution, and for the bounded states the wave-function becomes similar to the exact solutions but squeezed closer to the nucleus.Comment: 11 pages, 6 figure

Fractional integrodifferential equations and (anti-)hermiticity of time in a spacetime-symmetric extension of nonrelativistic Quantum Mechanics

Time continues to be an intriguing physical property in the modern era. On the one hand, we have the Classical and Relativistic notion of time, where space and time have the same hierarchy, which is essential in describing events in spacetime. On the other hand, in Quantum Mechanics, time appears as a classical parameter, meaning that it does not have an uncertainty relation with its canonical conjugate. In this work, we use a recent proposed spacetime-symmetric formalism~\href{https://doi.org/10.1103/PhysRevA.95.032133}{[Phys.~Rev.~A {\bf 95}, 032133 (2017)]} that tries to solve the unbalance in nonrelativistic Quantum Mechanics by extending the usual Hilbert space. The time parameter $t$ and the position operator $\hat{X}$ in one subspace, and the position parameter $x$ and time operator $\mathbb{T}$ in the other subspace. Time as an operator is better suitable for describing tunnelling processes. We then solve the novel $1/2$-fractional integrodifferential equation for a particle subjected to strong and weak potential limits and obtain an analytical expression for the tunnelling time through a rectangular barrier. We compare to previous works, obtaining pure imaginary times for energies below the barrier and a fast-decaying imaginary part for energies above the barrier, indicating the anti-hermiticity of the time operator for tunnelling times. We also show that the expected time of arrival in the tunnelling problem has the form of an energy average of the classical times of arrival plus a quantum contribution.Comment: 11 pages, 3 figure

Polarization due to rotational distortion in the bright star Regulus

This is the full published article (retrieved from the 6 months post-publication posting on arXiv) including the Methods and Supplementary Information sections: 33 pages, 10 figures, 8 tablesPolarization in stars was first predicted by Chandrasekhar [1] who calculated a substantial linear polarization at the stellar limb for a pure electron-scattering atmosphere. This polarization will average to zero when integrated over a spherical star but could be detected if the symmetry is broken, for example by the eclipse of a binary companion. Nearly 50 years ago, Harrington and Collins [2] modeled another way of breaking the symmetry and producing net polarization - the distortion of a rapidly rotating hot star. Here we report the first detection of this effect. Observations of the linear polarization of Regulus, with two different high-precision polarimeters, range from +42 parts-per-million (ppm) at a wavelength of 741 nm to -22 ppm at 395 nm. The reversal from red to blue is a distinctive feature of rotation-induced polarization. Using a new set of models for the polarization of rapidly rotating stars we find that Regulus is rotating at 96.5(+0.6/-0.8)% of its critical angular velocity for breakup, and has an inclination greater than 76.5 degrees. The rotation axis of the star is at a position angle of 79.5+/-0.7 degrees. The conclusions are independent of, but in good agreement with, the results of previously published interferometric observations of Regulus [3]. The accurate measurement of rotation in early-type stars is important for understanding their stellar environments [4], and course of their evolution [5].Peer reviewedFinal Accepted Versio

Characterisation of feline renal cortical fibroblast cultures and their transcriptional response to transforming growth factor beta 1

Chronic kidney disease (CKD) is common in geriatric cats, and the most prevalent pathology is chronic tubulointerstitial inflammation and fibrosis. The cell type predominantly responsible for the production of extra-cellular matrix in renal fibrosis is the myofibroblast, and fibroblast to myofibroblast differentiation is probably a crucial event. The cytokine TGF-β1 is reportedly the most important regulator of myofibroblastic differentiation in other species. The aim of this study was to isolate and characterise renal fibroblasts from cadaverous kidney tissue of cats with and without CKD, and to investigate the transcriptional response to TGF-β1

How Mistimed and Unwanted Pregnancies Affect Timing of Antenatal Care Initiation in three Districts in Tanzania

Early antenatal care (ANC) initiation is a doorway to early detection and management of potential complications associated with pregnancy. Although the literature reports various factors associated with ANC initiation such as parity and age, pregnancy intentions is yet to be recognized as a possible predictor of timing of ANC initiation. Data originate from a cross-sectional household survey on health behaviour and service utilization patterns. The survey was conducted in 2011 in Rufiji, Kilombero and Ulanga districts in Tanzania on 910 women of reproductive age who had given birth in the past two years. ANC initiation was considered to be early only if it occurred in the first trimester of pregnancy gestation. A recently completed pregnancy was defined as mistimed if a woman wanted it later, and if she did not want it at all the pregnancy was termed as unwanted. Chisquare was used to test for associations and multinomial logistic regression was conducted to examine how mistimed and unwanted pregnancies affect timing of ANC initiation. Although 49.3% of the women intended to become pregnant, 50.7% (34.9% mistimed and 15.8% unwanted) became pregnant unintentionally. While ANC initiation in the 1st trimester was 18.5%, so was 71.7% and 9.9% in the 2nd and 3rd trimesters respectively. Multivariate analysis revealed that ANC initiation in the 2nd trimester was 1.68 (95% CI 1.10‒2.58) and 2.00 (95% CI 1.05‒3.82) times more likely for mistimed and unwanted pregnancies respectively compared to intended pregnancies. These estimates rose to 2.81 (95% CI 1.41‒5.59) and 4.10 (95% CI 1.68‒10.00) respectively in the 3rd trimester. We controlled for gravidity, age, education, household wealth, marital status, religion, district of residence and travel time to a health facility. Late ANC initiation is a significant maternal and child health consequence of mistimed and unwanted pregnancies in Tanzania. Women should be empowered to delay or avoid pregnancies whenever they need to do so. Appropriate counseling to women, especially those who happen to conceive unintentionally is needed to minimize the possibility of delaying ANC initiation.\u

Human-robot sensor interface for cardiac rehabilitation.

Cardiovascular disease is the leading cause of death in the world. A program of cardiac rehabilitation (CR) is related to physical activities or exercises to regain the optimal quality of life. CR relies on the necessity to evaluate, control and supervise a patient's status and progress. This work has two objectives: on the one hand, provide a tool for clinicians to assess the patient's status during CR. On the other hand, there is evidence that robots can motivate patients during therapeutic procedures. Our sensor interface explores the possibility to integrate a robotic agent into cardiac therapy. This work presents an exploratory experiment for on-line assessment of typical CR routines

Sensor Interface for Cardiac Rehabilitation Monitoring: Pilot Clinical Study

In this paper, is presented a pilot clinical study of a monitoring system designed for cardiac rehabilitation (CR). The system allows measuring three main metrics: cardiovascular, spatiotemporal gait and difficulty in physical activity parameters. In this study, the sensor interface was used with two volunteer patients from the phase II of CR. During the experiment, the monitoring system was used to report the parameters and store the information from the patients without interrupting the session. It was found that there is no difference between the data from the interface and the measurements that are normally taken by physiatrists. Additionally, the system allows the continuous measurement and visualization of the status of the patient, which might prove useful for physiatrists. This work presents an exploratory experiment for an on-line assessment method for CR sessions, which in turn, opens the possibility of implementing different biofeedback methods to improve the rehabilitation effects of CR

Rudimentary G-Quadruplex-Based Telomere Capping In Saccharomyces Cerevisiae

Telomere capping conceals chromosome ends from exonucleases and checkpoints, but the full range of capping mechanisms is not well defined. Telomeres have the potential to form G-quadruplex (G4) DNA, although evidence for telomere G4 DNA function in vivo is limited. In budding yeast, capping requires the Cdc13 protein and is lost at nonpermissive temperatures in cdc13-1 mutants. Here, we use several independent G4 DNA-stabilizing treatments to suppress cdc13-1 capping defects. These include overexpression of three different G4 DNA binding proteins, loss of the G4 DNA unwinding helicase Sgs1, or treatment with small molecule G4 DNA ligands. In vitro, we show that protein-bound G4 DNA at a 3\u27 overhang inhibits 5\u27-\u3e 3\u27 resection of a paired strand by exonuclease I. These findings demonstrate that, at least in the absence of full natural capping, G4 DNA can play a positive role at telomeres in vivo

Preference Transitivity and Symbolic Representation in Capuchin Monkeys (Cebus apella)

BACKGROUND: Can non-human animals comprehend and employ symbols? The most convincing empirical evidence comes from language-trained apes, but little is known about this ability in monkeys. Tokens can be regarded as symbols since they are inherently non-valuable objects that acquire an arbitrarily assigned value upon exchange with an experimenter. Recent evidence suggested that capuchin monkeys, which diverged from the human lineage 35 million years ago, can estimate, represent and combine token quantities. A fundamental and open question is whether monkeys can reason about symbols in ways similar to how they reason about real objects. METHODOLOGY/PRINCIPAL FINDINGS: Here we examined this broad question in the context of economic choice behavior. Specifically, we assessed whether, in a symbolic context, capuchins' preferences satisfy transitivity--a fundamental trait of rational decision-making. Given three options A, B and C, transitivity holds true if A > or = B, B > or = C and A > or = C (where > or = indicates preference). In this study, we trained monkeys to exchange three types of tokens for three different foods. We then compared choices monkeys made between different types of tokens with choices monkeys made between the foods. Qualitatively, capuchins' preferences revealed by the way of tokens were similar to those measured with the actual foods. In particular, when choosing between tokens, monkeys displayed strict economic preferences and their choices satisfied transitivity. Quantitatively, however, values measured by the way of tokens differed systematically from those measured with the actual foods. In particular, for any pair of foods, the relative value of the preferred food increased when monkeys chose between the corresponding tokens. CONCLUSIONS/SIGNIFICANCE: These results indicate that indeed capuchins are capable of treating tokens as symbols. However, as they do so, capuchins experience the cognitive burdens imposed by symbolic representation