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Early diagnosis of sepsis enables timely resuscitation and antibiotics and prevents subsequent morbidity and mortality. Clinical approaches relying on point-in-time analysis of vital signs or lab values are often insensitive, non-specific and late diagnostic markers of sepsis. Exploring otherwise hidden information within intervals-in-time, heart rate variability (HRV) has been documented to be both altered in the presence of sepsis, and correlated with its severity. We hypothesized that by continuously tracking individual patient HRV over time in patients as they develop sepsis, we would demonstrate reduced HRV in association with the onset of sepsis. We monitored heart rate continuously in adult bone marrow transplant (BMT) patients (n = 21) beginning a day before their BMT and continuing until recovery or withdrawal (12+/-4 days). We characterized HRV continuously over time with a panel of time, frequency, complexity, and scale-invariant domain techniques. We defined baseline HRV as mean variability for the first 24 h of monitoring and studied individual and population average percentage change (from baseline) over time in diverse HRV metrics, in comparison with the time of clinical diagnosis and treatment of sepsis (defined as systemic inflammatory response syndrome along with clinically suspected infection requiring treatment). Of the 21 patients enrolled, 4 patients withdrew, leaving 17 patients who completed the study. Fourteen patients developed sepsis requiring antibiotic therapy, whereas 3 did not. On average, for 12 out of 14 infected patients, a significant (25%) reduction prior to the clinical diagnosis and treatment of sepsis was observed in standard deviation, root mean square successive difference, sample and multiscale entropy, fast Fourier transform, detrended fluctuation analysis, and wavelet variability metrics. For infected patients (n = 14), wavelet HRV demonstrated a 25% drop from baseline 35 h prior to sepsis on average. For 3 out of 3 non-infected patients, all measures, except root mean square successive difference and entropy, showed no significant reduction. Significant correlation was present amongst these HRV metrics for the entire population. Continuous HRV monitoring is feasible in ambulatory patients, demonstrates significant HRV alteration in individual patients in association with, and prior to clinical diagnosis and treatment of sepsis, and merits further investigation as a means of providing early warning of sepsis.

There is growing interest in the relation between the brain and music. The appealing similarity between brainwaves and the rhythms of music has motivated many scientists to seek a connection between them. A variety of transferring rules has been utilized to convert the brainwaves into music; and most of them are mainly based on spectra feature of EEG. In this study, audibly recognizable scale-free music was deduced from individual Electroencephalogram (EEG) waveforms. The translation rules include the direct mapping from the period of an EEG waveform to the duration of a note, the logarithmic mapping of the change of average power of EEG to music intensity according to the Fechner's law, and a scale-free based mapping from the amplitude of EEG to music pitch according to the power law. To show the actual effect, we applied the deduced sonification rules to EEG segments recorded during rapid-eye movement sleep (REM) and slow-wave sleep (SWS). The resulting music is vivid and different between the two mental states; the melody during REM sleep sounds fast and lively, whereas that in SWS sleep is slow and tranquil. 60 volunteers evaluated 25 music pieces, 10 from REM, 10 from SWS and 5 from white noise (WN), 74.3% experienced a happy emotion from REM and felt boring and drowsy when listening to SWS, and the average accuracy for all the music pieces identification is 86.8%(kappa = 0.800, P<0.001). We also applied the method to the EEG data from eyes closed, eyes open and epileptic EEG, and the results showed these mental states can be identified by listeners. The sonification rules may identify the mental states of the brain, which provide a real-time strategy for monitoring brain activities and are potentially useful to neurofeedback therapy.

The evolution of vocabulary in academic publishing is characterized via keyword frequencies recorded in the ISI Web of Science citations database. In four distinct case-studies, evolutionary analysis of keyword frequency change through time is compared to a model of random copying used as the null hypothesis, such that selection may be identified against it. The case studies from the physical sciences indicate greater selection in keyword choice than in the social sciences. Similar evolutionary analyses can be applied to a wide range of phenomena; wherever the popularity of multiple items through time has been recorded, as with web searches, or sales of popular music and books, for example.

A neuron embedded in an intact brain, unlike an isolated neuron, participates in network activity at various spatial resolutions. Such multiple scale spatial dynamics is potentially reflected in multiple time scales of temporal dynamics. We identify such multiple dynamical time scales of the inter-spike interval (ISI) fluctuations of neurons of waking/sleeping rats by means of multiscale analysis. The time scale of large non-Gaussianity in the ISI fluctuations, measured with the Castaing method, ranges up to several minutes, markedly escaping the low-pass filtering characteristics of neurons. A comparison between neural activity during waking and sleeping reveals that non-Gaussianity is stronger during waking than sleeping throughout the entire range of scales observed. We find a remarkable property of near scale independence of the magnitude correlations as the primary cause of persistent non-Gaussianity. Such scale-invariance of correlations is characteristic of multiplicative cascade processes and raises the possibility of the existence of a scale independent memory preserving mechanism.

Photosensitive epilepsy is a type of reflexive epilepsy triggered by various visual stimuli including colourful ones. Despite the ubiquitous presence of colorful displays, brain responses against different colour combinations are not properly studied. Here, we studied the photosensitivity of the human brain against three types of chromatic flickering stimuli by recording neuromagnetic brain responses (magnetoencephalogram, MEG) from nine adult controls, an unmedicated patient, a medicated patient, and two controls age-matched with patients. Dynamical complexities of MEG signals were investigated by a family of wavelet entropies. Wavelet entropy is a newly proposed measure to characterize large scale brain responses, which quantifies the degree of order/disorder associated with a multi-frequency signal response. In particular, we found that as compared to the unmedicated patient, controls showed significantly larger wavelet entropy values. We also found that Renyi entropy is the most powerful feature for the participant classification. Finally, we also demonstrated the effect of combinational chromatic sensitivity on the underlying order/disorder in MEG signals. Our results suggest that when perturbed by potentially epileptic-triggering stimulus, healthy human brain manages to maintain a non-deterministic, possibly nonlinear state, with high degree of disorder, but an epileptic brain represents a highly ordered state which making it prone to hyper-excitation. Further, certain colour combination was found to be more threatening than other combinations.

In this paper, time changes of the Brownian motions on generalized Sierpinski carpets including

X and the City, a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow through tunnels? Can you predict whether a traffic light will stay green long enough for you to cross the intersection? And what is the likelihood that your city will be hit by an asteroid? Every math problem and equation in this book tells a story and examples are explained throughout in an informal and witty style. The level of mathematics ranges from precalculus through calculus to some differential equations, and any reader with knowledge of elementary calculus will be able to follow the materials with ease. There are also some more challenging problems sprinkled in for the more advanced reader. Filled with interesting and unusual observations about how cities work,X and the Cityshows how mathematics undergirds and plays an important part in the metropolitan landscape.

Felix Klein, one of the great nineteenth-century geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple coexisting symmetries. For a century, these images barely existed outside the imagination of mathematicians. However, in the 1980s, the authors embarked on the first computer exploration of Klein's vision, and in doing so found many further extraordinary images. Join the authors on the path from basic mathematical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can follow the step-by-step instructions for writing programs that generate the images. Others can see how the images relate to ideas at the forefront of research.

Brownian motion is the incessant motion of small particles immersed in an ambient medium. It is due to fluctuations in the motion of the medium particles on the molecular scale. The name has been carried over to other fluctuation phenomena. This book treats the physical theory of Brownian motion. The extensive mathematical theory, which treats the subject as a subfield of the general theory of random processes, is touched on but not presented in any detail. Random or stochastic process theory and statistical mechanics are the primary tools. The first eight chapters treat the stochastic theory and some applications. The next six present the statistical mechanical point of view. Then follows chapters on applications to diffusion, noise, and polymers, followed by a treatment of the motion of interacting Brownian particles. The book ends with a final chapter treating simulation, fractals, and chaos.

Wavelets are spatially localized functions whose amplitude drops off exponentially outside a small “window”. They are used to magnify experimental or numerical data and have become powerful tools in signal processing and other computational sciences. This book gives scientists and engineers a practical understanding of wavelets--their origins, their purpose, their use, and their prospects. It covers the applications of wavelets as a diagnostic tool and the use of wavelet basis functions to solve differential equations. Each chapter was written by one of five lecturers of a course sponsored by the Institute of Computer Applications in Science and Engineering (ICASE) and the NASA Langley Research Center. Not only does this book treat the latest advances on the subject, but it also attempts to impart practical knowledge to allow scientists and engineers to evaluate objectively where these tools stand in relation to their needs.