Measure Of Burstiness Research Articles

Evolving Patterns in Irrational Numbers Using Waiting Times between Digits

There is an increasing interest in determining if there exist observable patterns or structures within the digits of irrational numbers. We extend this search by investigating the interval in position between two consecutive occurrences of the same digit, a kind of waiting time statistics. We characterise these by the burstiness measure which distinguishes if the inter-event times are periodic, bursty, or Poisson processes. Furthermore, the complexity–entropy plane was used to determine if the intervals are stochastic or chaotic. We analyse sequences of the first 1 million digits of the numbers π, e, 2, and ϕ. We find that the intervals between single, double, and triple digits are Poisson processes with a burstiness measure in the range −0.05≤B≤0.05 for the four numbers studied. This result is supported by a complexity–entropy plane analysis, which shows that the time intervals have the same characteristics as Gaussian noise. The four irrational numbers have identical degrees of complexity and burstiness in their inter-event analysis.

Using bursty announcements for detecting BGP routing anomalies

Despite the robust structure of the Internet, it is still susceptible to disruptive routing updates that prevent network traffic from reaching its destination. Our research shows that BGP announcements that are associated with disruptive updates tend to occur in groups of relatively high frequency, followed by periods of infrequent activity. We hypothesize that we may use these bursty characteristics to detect anomalous routing incidents. In this work, we use manually verified ground truth metadata and volume of announcements as a baseline measure, and propose a burstiness measure that detects prior anomalous incidents with high recall and better precision than the volume baseline. We quantify the burstiness of inter-arrival times around the date and times of four large-scale incidents: the Indosat hijacking event in April 2014, the Telecom Malaysia leak in June 2015, the Bharti Airtel Ltd. hijack in November 2015, and the MainOne leak in November 2018; and three smaller scale incidents that led to traffic interception: the Belarusian traffic direction in February 2013, the Icelandic traffic direction in July 2013, and the Russian telecom that hijacked financial services in April 2017. Our method leverages the burstiness of disruptive update messages to detect these incidents. We describe limitations, open challenges, and how this method can be used for routing anomaly detection.

A Mortality Study for ICU Patients using Bursty Medical Events.

The study of patients in Intensive Care Units (ICUs) is a crucial task in critical care research which has significant implications both in identifying clinical risk factors and defining institutional guidances. The mortality study of ICU patients is of particular interest because it provides useful indications to healthcare institutions for improving patients experience, internal policies, and procedures (e.g. allocation of resources). To this end, many research works have been focused on the length of stay (LOS) for ICU patients as a feature for studying the mortality. In this work, we propose a novel mortality study based on the notion of burstiness, where the temporal information of patients longitudinal data is taken into consideration. The burstiness of temporal data is a popular measure in network analysis and time-series anomaly detection, where high values of burstiness indicate presence of rapidly occurring events in short time periods (i.e. burst). Our intuition is that these bursts may relate to possible complications in the patient's medical condition and hence provide indications on the mortality. Compared to the LOS, the burstiness parameter captures the temporality of the medical events providing information about the overall dynamic of the patients condition. To the best of our knowledge, we are the first to apply the burstiness measure in the clinical research domain. Our preliminary results on a real dataset show that patients with high values of burstiness tend to have higher mortality rate compared to patients with more regular medical events. Overall, our study shows promising results and provides useful insights for developing predictive models on temporal data and advancing modern critical care medicine.

Measuring burstiness for finite event sequences.

Characterizing inhomogeneous temporal patterns in natural and social phenomena is important to understand underlying mechanisms behind such complex systems and, hence, even to predict and control them. Temporal inhomogeneities in event sequences have been described in terms of bursts that are rapidly occurring events in short time periods alternating with long inactive periods. The bursts can be quantified by a simple measure, called the burstiness parameter, which was introduced by Goh and Barabási [Europhys. Lett. 81, 48002 (2008)EULEEJ0295-507510.1209/0295-5075/81/48002]. The burstiness parameter has been widely used due to its simplicity, which, however, turns out to be strongly affected by the finite number of events in the time series. As the finite-size effects on burstiness parameter have been largely ignored, we analytically investigate the finite-size effects of the burstiness parameter. Then we suggest an alternative definition of burstiness that is free from finite-size effects and yet simple. Using our alternative burstiness measure, one can distinguish the finite-size effects from the intrinsic bursty properties in the time series. We also demonstrate the advantages of our burstiness measure by analyzing empirical data sets.

Burst firing of single neurons in the human medial temporal lobe changes before epileptic seizures.

To better understand the mechanisms that lead to the sudden and unexpected occurrence of seizures, with the neuronal correlate being abnormally synchronous discharges that disrupt neuronal function. To address this problem, we recorded single neuron activity in epilepsy patients during the transition to seizures to uncover specific changes of neuronal firing patterns. We focused particularly on neurons repeatedly firing discrete groups of high-frequency action potentials (so called bursters) that have been associated with ictogenesis. We analyzed a total of 459 single neurons and used the mean autocorrelation time as a quantitative measure of burstiness. To unravel the intricate roles of excitation and inhibition, we also examined differential contributions from putative principal cells and interneurons. During interictal recordings, burstiness was significantly higher in the seizure onset hemisphere, an effect found only for principal cells, but not for interneurons, and which disappeared before seizures. These findings deviate from conventional views of ictogenesis that propose slowly-increasing aggregates of bursting neurons which give rise to seizures once they reach a critical mass. Instead our results are in line with recent hypotheses that bursting may represent a protective mechanism by preventing direct transmission of postsynaptic high-frequency oscillations.

A Study on the Spiking Pattern in a Neuron Model Based on the Burstiness Measure

A Study on the Spiking Pattern in a Neuron Model Based on the Burstiness Measure

Modeling multipath fading channel dynamics for packet data performance analysis

The multipath fading channel modeling traditionally focuses on physical level dynamics such as signal strength and bit error rate. In this paper we characterize multipath fading channel dynamics at the packet level and analyze the corresponding data queueing performance in various environments. The integration of wireless channel modeling and data queueing analysis provides us a unique way to capture important channel statistics with respect to various wireless network factors such as channel bandwidth, mobile speed and channel coding. The second order channel statistics, i.e. channel power spectrum, is found to play an important role in the modeling of multipath fading channels. The data queueing performance is largely dependent on the interaction between the channel power spectrum and the data arrival power spectrum; whichever has lower frequency power will have more impact on queueing performance. Note that the data arrival power spectrum provides a measure of burstiness and correlation behavior of data packet arrivals. Throughout the paper, we use the Markov chain modeling technique to match the measured important channel statistics for both channel modeling and queueing analysis.