Comparative analysis of visual analog scales for assessing acute pain in women after radical mastectomy

BACKGROUND: Effective quantitative assessment of acute pain as an urgent problem in clinical medicine. One of the solutions to this problem is a color discrete scale (CDS). AIM: To determine the efficacy of the clinical usage of color discrete scale compared with linear visual analog scale to assess acute pain in women after radical mastectomy. MATERIALS AND METHODS: This study includes a prospective, observational, and non-randomized clinical trial. A total of 110 females who underwent radical mastectomy (RM) were interviewed. We used a 100-point linear visual analog scale (lVAS) and CDS with monotonic (mCDS) and random (rCDS) color arrangement. Pain was assessed 2, 6, 12, 24, 48, and 72 h after surgery. RESULTS: Pain scores obtained 2 h after RM were 6 (0; 30), 12 (0; 24), 8 (0; 20) points according to IVAS, mCDS, and rCDS, respectively (p 0.05). Furthermore, the pain scores were gradually reduced on all three scales and had no statistically significant difference (p 0.05). In women who underwent paravertebral blockade (PVB), pain scores were significantly less at 2, 6, 12, and 48 h after surgery (p 0.05). Spearmans correlation coefficient for lVAS and mCDS is 0.90, 0.86 for lVAS and rCDS, and 0.90 for mCDS and rCDS (all p 0.05). CONCLUSIONS: The CDS is an alternative, independent, and sufficient tool for quantifying pain. A strong correlation was found between the pain assessments according to CDS and lVAS. PVB significantly improves the quality of pain relief after RM.

The Altes Family of Log-Periodic Chirplets and the Hyperbolic Chirplet Transform

This work revisits a class of biomimetically inspired waveforms introduced by R.A. Altes in the 1970s for use in sonar detection. Similar to the chirps used for echolocation by bats and dolphins, these waveforms are log-periodic oscillations, windowed by a smooth decaying envelope. Log-periodicity is associated with the deep symmetry of discrete scale invariance in physical systems. Furthermore, there is a close connection between such chirping techniques, and other useful applications such as wavelet decomposition for multi-resolution analysis. Motivated to uncover additional properties, we propose an alternative, simpler parameterisation of the original Altes waveforms. From this, it becomes apparent that we have a flexible family of hyperbolic chirps suitable for the detection of accelerating time-series oscillations. The proposed formalism reveals the original chirps to be a set of admissible wavelets with desirable properties of regularity, infinite vanishing moments and time-frequency localisation. As they are self-similar, these “Altes chirplets” allow efficient implementation of the scale-invariant hyperbolic chirplet transform (HCT), whose basis functions form hyperbolic curves in the time-frequency plane. Compared with the rectangular time-frequency tilings of both the conventional wavelet transform and the short-time Fourier transform, the HCT can better facilitate the detection of chirping signals, which are often the signature of critical failure in complex systems. A synthetic example is presented to illustrate this useful application of the HCT.

The Weight Formula

In this chapter the Law of Balancing, one of the two laws in A Theory of Constitutional Law (2002), is transformed into a mathematical formula, the Weight Formula. This formula allows a clear identification of the three factors that pertain to balancing: intensity of interference, abstract weight, and epistemic reliability of the premises standing behind these two classifications, and this on both sides of the principles collision. This is not possible without scaling. A geometric and discrete scale is proposed. Discrete scales are necessary. Geometric scales have advantages with respect to arithmetic scales. Cases are considered, and, in the last part of the text, open questions are presented.

A Local-Feedback-Global-Cascade Model for Hierarchical l Heart Rate Variability in Healthy Humans

A broad view on Heart Rate Variability (HRV) study is made and the hierarchical structure is shown in Local-Feedback-Global-Cascade (LFGC) model, which is built to explore the role of reflex feedback. This feedback, which integrates additive and multiple functionalities in multifractal cascade models, functions on the She-Waymire (SW) form of the hierarchical structure so that the concept of defect dynamics can be applied to LFGC model. The experimental evidence verified the existence of the hierarchical structure and showed discrete scale invariance in data supported the additive feedback law, which may exist in the cardiovascular system in harmony with this dynamical cascade model.

A Local-Feedback-Global-Cascade Model for Hierarchical l Heart Rate Variability in Healthy Humans

A broad view on Heart Rate Variability (HRV) study is made and the hierarchical structure is shown in Local-Feedback-Global-Cascade (LFGC) model, which is built to explore the role of reflex feedback. This feedback, which integrates additive and multiple functionalities in multifractal cascade models, functions on the She-Waymire (SW) form of the hierarchical structure so that the concept of defect dynamics can be applied to LFGC model. The experimental evidence verified the existence of the hierarchical structure and showed discrete scale invariance in data supported the additive feedback law, which may exist in the cardiovascular system in harmony with this dynamical cascade model.

Tunable discrete scale invariance in transition-metal pentatelluride flakes

Log-periodic quantum oscillations discovered in transition-metal pentatelluride give a clear demonstration of discrete scale invariance (DSI) in solid-state materials. The peculiar phenomenon is convincingly interpreted as the presence of two-body quasi-bound states in a Coulomb potential. However, the modifications of the Coulomb interactions in many-body systems having a Dirac-like spectrum are not fully understood. Here, we report the observation of tunable log-periodic oscillations and DSI in ZrTe5 and HfTe5 flakes. By reducing the flakes thickness, the characteristic scale factor is tuned to a much smaller value due to the reduction of the vacuum polarization effect. The decreasing of the scale factor demonstrates the many-body effect on the DSI, which has rarely been discussed hitherto. Furthermore, the cut-offs of oscillations are quantitatively explained by considering the Thomas-Fermi screening effect. Our work clarifies the many-body effect on DSI and paves a way to tune the DSI in quantum materials.

Magnetotransport signatures of Weyl physics and discrete scale invariance in the elemental semiconductor tellurium

The study of topological materials possessing nontrivial band structures enables exploitation of relativistic physics and development of a spectrum of intriguing physical phenomena. However, previous studies of Weyl physics have been limited exclusively to semimetals. Here, via systematic magnetotransport measurements, two representative topological transport signatures of Weyl physics, the negative longitudinal magnetoresistance and the planar Hall effect, are observed in the elemental semiconductor tellurium. More strikingly, logarithmically periodic oscillations in both the magnetoresistance and Hall data are revealed beyond the quantum limit and found to share similar characteristics with those observed in ZrTe5and HfTe5. The log-periodic oscillations originate from the formation of two-body quasi-bound states formed between Weyl fermions and opposite charge centers, the energies of which constitute a geometric series that matches the general feature of discrete scale invariance (DSI). Our discovery reveals the topological nature of tellurium and further confirms the universality of DSI in topological materials. Moreover, introduction of Weyl physics into semiconductors to develop “Weyl semiconductors” provides an ideal platform for manipulating fundamental Weyl fermionic behaviors and for designing future topological devices.