Multifractality in the stock market: price increments versus waiting times

By applying the multifractal detrended fluctuation analysis to the high-frequency tick-by-tick data from Deutsche B\"orse both in the price and in the time domains, we investigate multifractal properties of the time series of logarithmic price increments and inter-trade intervals of time. We show that both quantities reveal multiscaling and that this result holds across different stocks. The origin of the multifractal character of the corresponding dynamics is, among others, the long-range correlations in price increments and in inter-trade time intervals as well as the non-Gaussian distributions of the fluctuations. Since the transaction-to-transaction price increments do not strongly depend on or are almost independent of the inter-trade waiting times, both can be sources of the observed multifractal behaviour of the fixed-delay returns and volatility. The results presented also allow one to evaluate the applicability of the Multifractal Model of Asset Returns in the case of tick-by-tick data.Comment: Physica A, in prin

Focal osteoporosis defects play a key role in hip fracture

$\textbf{BACKGROUND}$: Hip fractures are mainly caused by accidental falls and trips, which magnify forces in well-defined areas of the proximal femur. Unfortunately, the same areas are at risk of rapid bone loss with ageing, since they are relatively stress-shielded during walking and sitting. Focal osteoporosis in those areas may contribute to fracture, and targeted 3D measurements might enhance hip fracture prediction. In the FEMCO case-control clinical study, Cortical Bone Mapping (CBM) was applied to clinical computed tomography (CT) scans to define 3D cortical and trabecular bone defects in patients with acute hip fracture compared to controls. Direct measurements of trabecular bone volume were then made in biopsies of target regions removed at operation. $\textbf{METHODS}$: The sample consisted of CT scans from 313 female and 40 male volunteers (158 with proximal femoral fracture, 145 age-matched controls and 50 fallers without hip fracture). Detailed Cortical Bone Maps (c.5580 measurement points on the unfractured hip) were created before registering each hip to an average femur shape to facilitate statistical parametric mapping (SPM). Areas where cortical and trabecular bone differed from controls were visualised in 3D for location, magnitude and statistical significance. Measures from the novel regions created by the SPM process were then tested for their ability to classify fracture versus control by comparison with traditional CT measures of areal Bone Mineral Density (aBMD). In women we used the surgical classification of fracture location ('femoral neck' or 'trochanteric') to discover whether focal osteoporosis was specific to fracture type. To explore whether the focal areas were osteoporotic by histological criteria, we used micro CT to measure trabecular bone parameters in targeted biopsies taken from the femoral heads of 14 cases. $\textbf{RESULTS}$: Hip fracture patients had distinct patterns of focal osteoporosis that determined fracture type, and CBM measures classified fracture type better than aBMD parameters. CBM measures however improved only minimally on aBMD for predicting any hip fracture and depended on the inclusion of trabecular bone measures alongside cortical regions. Focal osteoporosis was confirmed on biopsy as reduced sub-cortical trabecular bone volume. $\textbf{CONCLUSION}$: Using 3D imaging methods and targeted bone biopsy, we discovered focal osteoporosis affecting trabecular and cortical bone of the proximal femur, among men and women with hip fracture.Arthritis Research UK (grant no. ARC17822) and Cambridge National Institute for Health Research (NIHR) Biomedical Research Centre

Electrospun nanosized cellulose fibers using ionic liquids at room temperature

Aiming at replacing the noxious solvents commonly employed, ionic-liquid-based solvents have been recently explored as novel non-volatile and non-flammable media for the electrospinning of polymers. In this work, nanosized and biodegradable cellulose fibers were obtained by electrospinning at room temperature using a pure ionic liquid or a binary mixture of two selected ionic liquids. The electrospinning of 8 wt% cellulose in 1-ethyl-3-methylimidazolium acetate medium (a low viscosity and room temperature ionic liquid capable of efficiently dissolving cellulose) showed to produce electrospun fibers with average diameters within (470 ± 110) nm. With the goal of tailoring the surface tension of the spinning dope, a surface active ionic liquid was further added in a 0.10 : 0.90 mole fraction ratio. Electrospun cellulose fibers from the binary mixture composed of 1-ethyl-3-methylimidazolium acetate and 1-decyl-3-methylimidazolium chloride ionic liquids presented average diameters within (120 ± 55) nm. Scanning electron microscopy, X-ray diffraction analysis, nuclear magnetic resonance spectroscopy, Fourier transform infrared spectroscopy, and thermogravimetric assays were used as core methods to evaluate the structural integrity, morphology and crystallinity of the raw, electrospun, and regenerated samples of cellulose. Moreover, the photoluminescence spectra of both raw and electrospun fibers were acquired, and compared, indicating that the cellulose emitting centers are not affected by the dissolution of cellulose in ionic liquids. Finally, the use of non-volatile solvents in electrospinning coupled to a water coagulation bath allows the recovery of the ionic fluid, and represents a step forward into the search of environmentally friendly alternatives to the conventional approaches

Characterization of Sleep Stages by Correlations of Heartbeat Increments

We study correlation properties of the magnitude and the sign of the increments in the time intervals between successive heartbeats during light sleep, deep sleep, and REM sleep using the detrended fluctuation analysis method. We find short-range anticorrelations in the sign time series, which are strong during deep sleep, weaker during light sleep and even weaker during REM sleep. In contrast, we find long-range positive correlations in the magnitude time series, which are strong during REM sleep and weaker during light sleep. We observe uncorrelated behavior for the magnitude during deep sleep. Since the magnitude series relates to the nonlinear properties of the original time series, while the signs series relates to the linear properties, our findings suggest that the nonlinear properties of the heartbeat dynamics are more pronounced during REM sleep. Thus, the sign and the magnitude series provide information which is useful in distinguishing between the sleep stages.Comment: 7 pages, 4 figures, revte

Effect of Trends on Detrended Fluctuation Analysis

Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the DFA method become difficult to analyze. We systematically study the effects of three types of trends -- linear, periodic, and power-law trends, and offer examples where these trends are likely to occur in real data. We compare the difference between the scaling results for artificially generated correlated noise and correlated noise with a trend, and study how trends lead to the appearance of crossovers in the scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the ``apparent'' scaling of the trend. We study how the characteristics of these crossovers depend on (i) the slope of the linear trend; (ii) the amplitude and period of the periodic trend; (iii) the amplitude and power of the power-law trend and (iv) the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws -- i.e. long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend, assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superimposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise.Comment: 20 pages, 16 figure

Thermal Resonance in Signal Transmission

We use temperature tuning to control signal propagation in simple one-dimensional arrays of masses connected by hard anharmonic springs and with no local potentials. In our numerical model a sustained signal is applied at one site of a chain immersed in a thermal environment and the signal-to-noise ratio is measured at each oscillator. We show that raising the temperature can lead to enhanced signal propagation along the chain, resulting in thermal resonance effects akin to the resonance observed in arrays of bistable systems.Comment: To appear in Phys. Rev.

Solutions of ionic liquids with diverse aliphatic and aromatic solutes – Phase behavior and potentials for applications:A review article

This article principally reviews our research related to liquid–liquid and solid–liquid phase behavior of imidazolium- and phosphonium-based ionic liquids, mainly having bistriflamide ([NTf2]−) or triflate ([OTf]−) anions, with several aliphatic and aromatic solutes (target molecules). The latter include: (i) diols and triols: 1,2-propanediol, 1,3-propanediol and glycerol; (ii) polymer poly(ethylene glycol) (PEG): average molecular mass 200, 400 and 2050 – PEG200 (liquid), PEG400 (liquid) and PEG2050 (solid), respectively; (iii) polar aromatic compounds: nicotine, aniline, phenolic acids (vanillic, ferulic and caffeic acid,), thymol and caffeine and (iv) non-polar aromatic compounds (benzene, toluene, p-xylene). In these studies, the effects of the cation and anion, cation alkyl chain and PEG chain lengths on the observed phase behaviors were scrutinized. Thus, one of the major observations is that the anion – bistriflamide/triflate – selection usually had strong, sometimes really remarkable effects on the solvent abilities of the studied ionic liquids. Namely, in the case of the hydrogen-bonding solutes, the ionic liquids with the triflate anion generally exhibited substantially higher solubility than those having the bistriflamide anion. Nevertheless, with the aromatic compounds the situation was the opposite – in most of the cases it was the bistriflamide anion that favoured solubility. Moreover, our other studies confirmed the ability of PEG to dissolve both polar and non-polar aromatic compounds. Therefore, two general possibilities of application of alternative, environmentally acceptable, solvents of tuneable solvent properties appeared. One is to use homogeneous mixtures of two ionic liquids having [NTf2]− and [OTf]− anions as mixed solvents. The other, however, envisages the application of homogeneous and heterogeneous (PEG + ionic liquid) solutions as tuneable solvents for aromatic solutes. Such mixed solvents have potential applications in separation of the aforesaid target molecules from their aqueous solutions or in extraction from original matrices. From the fundamental point of view the phase equilibrium studies reviewed herein and the diversity of the pure compounds – ionic liquids and target molecules – represent a good base for the discussion of interactions between the molecules that exist in the studied solutions