A high sensitivity ultra-low temperature RF conductance and noise measurement setup

We report on the realization of a high sensitivity RF noise measurement scheme to study small current fluctuations of mesoscopic systems at milliKelvin temperatures. The setup relies on the combination of an interferometric ampli- fication scheme and a quarter-wave impedance transformer, allowing the mea- surement of noise power spectral densities with GHz bandwith up to five orders of magnitude below the amplifier noise floor. We simultaneously measure the high frequency conductance of the sample by derivating a portion of the signal to a microwave homodyne detection. We describe the principle of the setup, as well as its implementation and calibration. Finally, we show that our setup allows to fully characterize a subnanosecond on-demand single electron source. More generally, its sensitivity and bandwith make it suitable for applications manipulating single charges at GHz frequencies.Comment: The following article has been submitted to Review of Scientific Instrument

Multiscale Analysis of Microvascular Blood Flow: A Multiscale Entropy Study of Laser Doppler Flowmetry Time Series

Processes regulating the cardiovascular system (CVS) are numerous. Each possesses several temporal scales. Their interactions lead to interdependences across multiple scales. For the CVS analysis, different multiscale studies have been proposed, mostly performed on heart rate variability signals (HRV) reflecting the central CVS; only few were dedicated to data from the peripheral CVS, such as laser Doppler flowmetry (LDF) signals. Very recently, a study implemented the first computation of multiscale entropy for LDF signals. A nonmonotonic evolution of multiscale entropy with two distinctive scales was reported, leading to a markedly different behavior from the one of HRV. Our goal herein is to confirm these results and to go forward in the investigations on origins of this behavior. For this purpose, 12 LDF signals recorded simultaneously on the two forearms of six healthy subjects are processed. This is performed before and after application of physiological scales-based filters aiming at isolating previously found frequency bands linked to physiological activities. The results obtained with signals recorded simultaneously on two different sites of each subject show a probable central origin for the nonmonotonic behavior. The filtering results lead to the suggestion that origins of the distinctive scales could be dominated by the cardiac activity

Laser speckle contrast imaging: Multifractal analysis of data recorded in healthy subjects

Purpose: The monitoring of microvascular blood flow can now be performed with laser specklecontrastimaging (LSCI), a new noninvasive laser-based technique. LSCI images have good spatial and temporal resolutions. Nevertheless, from now, few processing of these data have been performed to have a better knowledge on their properties. We herein propose a multifractal analysis of LSCI data recorded in the forearm of healthy subjects, based on the method from Halseyet al., one of the popular methods using the box-counting technique. Methods: In laser specklecontrastimage time sequences, we studied time evolution of pixel values, as well as time evolution of pixel values averaged in regions of interest (ROI) of different sizes. The results are compared with the ones obtained with single-point laser Doppler flowmetry (LDF) signals recorded simultaneously to LSCI images. Results: Our work shows that, for the range of scales studied and with the method from Halseyet al., time evolution of pixel values present narrow multifractal spectra, reminding the ones of monofractal data. However, we observe that when LSCI pixel values are averaged in ROI large enough and followed with time, the multifractal spectra become larger and closer to the ones of LDF signals. Conclusions: Single pixels from laser specklecontrastimages may not possess the same multifractal properties as LDF signals. These findings could now be compared with the ones obtained with other ranges of scales and with data recorded from pathological subjects

Study of time reversibility/irreversibility of cardiovascular data: theoretical results and application to laser Doppler flowmetry and heart rate variability signals

Time irreversibility can be qualitatively defined as the degree of a signal for temporal asymmetry. Recently, a time irreversibility characterization method based on entropies of positive and negative increments has been proposed for experimental signals and applied to heart rate variability (HRV) data (central cardiovascular system (CVS)). The results led to interesting information as a time asymmetry index was found different for young subjects and elderly people or heart disease patients. Nevertheless, similar analyses have not yet been conducted on laser Doppler flowmetry (LDF) signals (peripheral CVS). We first propose to further investigate the above-mentioned characterization method. Then, LDF signals, LDF signals reduced to samples acquired during ECG R peaks (LDF_RECG signals) and HRV recorded simultaneously in healthy subjects are processed. Entropies of positive and negative increments for LDF signals show a nonmonotonic pattern: oscillations—more or less pronounced, depending on subjects—are found with a period matching the one of cardiac activity. However, such oscillations are not found with LDF_RECG nor with HRV. Moreover, the asymmetry index for LDF is markedly different from the ones of LDF_RECG and HRV. The cardiac activity may therefore play a dominant role in the time irreversibility properties of LDF signals

Multifractal analysis of heart rate variability and laser Doppler flowmetry fluctuations:comparison of results from different numerical methods

To contribute to the understanding of the complex dynamics in the cardiovascular system (CVS), the central CVS has previously been analyzed through multifractal analyses of heart rate variability (HRV) signals that were shown to bring useful contributions. Similar approaches for the peripheral CVS through the analysis of laser Doppler flowmetry (LDF) signals are comparatively very recent. In this direction, we propose here a study of the peripheral CVS through a multifractal analysis of LDF fluctuations, together with a comparison of the results with those obtained on HRV fluctuations simultaneously recorded. To perform these investigations concerning the biophysics of the CVS, first we have to address the problem of selecting a suitable methodology for multifractal analysis, allowing us to extract meaningful interpretations on biophysical signals. For this purpose, we test four existing methodologies of multifractal analysis. We also present a comparison of their applicability and interpretability when implemented on both simulated multifractal signals of reference and on experimental signals from the CVS. One essential outcome of the study is that the multifractal properties observed from both the LDF fluctuations (peripheral CVS) and the HRV fluctuations (central CVS) appear very close and similar over the studied range of scales relevant to physiology

Multifractal analysis of central (electrocardiography) and peripheral (laser Doppler flowmetry) cardiovascular time series from healthy human subjects

Analysis of the cardiovascular system (CVS) activity is important for several purposes, including better understanding of heart physiology, diagnosis and forecast of cardiac events. The central CVS, through the study of heart rate variability (HRV), has been shown to exhibit multifractal properties, possibly evolving with physiologic or pathologic states of the organism. An additional viewpoint on the CVS is provided at the peripheral level by laser Doppler flowmetry (LDF), which enables local blood perfusion monitoring. We report here for the first time a multifractal analysis of LDF signals through the computation of their multifractal spectra. The method for estimation of the multifractal spectra, based on the box method, is first described and tested on a priori known synthetic multifractal signals, before application to LDF data. Moreover, simultaneous recordings of both central HRV and peripheral LDF signals, and corresponding multifractal analyses, are performed to confront their properties. With the scales chosen on the partition functions to compute Renyi exponents, LDF signals appear to have broader multifractal spectra compared to HRV. Various conditions for LDF acquisitions are tested showing larger multifractal spectra for signals recorded on fingers than on forearms. The results uncover complex interactions at central and peripheral CVS levels

Multiscale entropy of laser Doppler flowmetry signals in healthy human subjects

Purpose: The cardiovascular system (CVS) regulation can be studied from acentral viewpoint, through heart rate variability (HRV) data, and from a peripheral viewpoint, through laser Doppler flowmetry (LDF) signals. Both the central and peripheral CVSs are regulated by several interacting mechanisms, each having its own temporal scale. The central CVS has been the subject of many multiscale studies. By contrast, these studies at the level of the peripheral CVS are very recent. Among the multiscale studies performed on the central CVS data, multiscale entropy has been proven to give interesting physiological information for diagnostic purposes. However, no multiscale entropyanalysis has been performed on LDF signals. The authors’ goal is therefore to propose a first multiscale entropy study of LDF data recorded in healthy subjects. Methods: The LDF signals recorded in the forearm of seven healthy subjects are processed. Their period sampling is T = 50 ms , and coarse-graining scales from T to 23 T are studied. Also, for validation, the algorithm is first tested on synthetic signals of known theoretical multiscale entropy. Results: The results reveal nonmonotonic evolution of the multiscale entropy of LDF signals, with a maximum at small scales around 7 T and a minimum at longer scales around 18 T , singling out in this way two distinctive scales where the LDF signals undergo specific changes from high to low complexity. This also marks a strong contrast with the HRV signals that usually display a monotonic increase in the evolution of the multiscale entropy. Conclusions: Multiscale entropy of LDF signals in healthy subjects shows variation with scales. Moreover, as the variation pattern observed appears similar for all the tested signals, multiscale entropy could potentially be a useful stationary signature for LDF signals, which otherwise are probe-position and subject dependent. Further work could now be conducted to evaluate possible diagnostic purposes of the multiscale entropy of LDF signals

On the Pierce-Birkhoff Conjecture

International audienceThis paper represents a step in our program towards the proof of the Pierce--Birkhoff conjecture. In the nineteen eighties J. Madden proved that the Pierce-Birkhoff conjecture for a ring A$is equivalent to a statement about an arbitrary pair of points$\alpha,\beta\in\sper\ A$and their separating ideal$$; we refer to this statement as the Local Pierce-Birkhoff conjecture at$\alpha,\beta$. In this paper, for each pair$(\alpha,\beta)$with$ht()=\dim A$, we define a natural number, called complexity of$(\alpha,\beta)$. Complexity 0 corresponds to the case when one of the points$\alpha,\beta$is monomial; this case was already settled in all dimensions in a preceding paper. Here we introduce a new conjecture, called the Strong Connectedness conjecture, and prove that the strong connectedness conjecture in dimension n-1 implies the connectedness conjecture in dimension n in the case when$ht()$is less than n-1. We prove the Strong Connectedness conjecture in dimension 2, which gives the Connectedness and the Pierce--Birkhoff conjectures in any dimension in the case when$ht()$less than 2. Finally, we prove the Connectedness (and hence also the Pierce--Birkhoff) conjecture in the case when dimension of A is equal to$ht()=3$, the pair$(\alpha,\beta)$is of complexity 1 and$A$ is excellent with residue field the field of real numbers