Truncated Power Law Distribution Research Articles

Competition among recombination pathways in single FAPbBr3 nanocrystals.

Single particle level microscopy of immobilized FAPbBr3 nanocrystals (NCs) has elucidated the involvement of different processes in their photoluminescence (PL) intermittency. Four different blinking patterns are observed in the data from more than 100 NCs. The dependence of PL decays on PL intensities brought out in fluorescence lifetime intensity distribution (FLID) plots is rationalized by the interplay of exciton- and trion-mediated recombinations along with hot carrier (HC) trapping. The high intensity-long lifetime component is attributed to neutral exciton recombination, the low intensity-short lifetime component is attributed to trion assisted recombination, and the low intensity-long lifetime component is attributed to hot carrier recombination. Change-point analysis (CPA) of the PL blinking data reveals the involvement of multiple intermediate states. Truncated power law distribution is found to be more appropriate than power law and lognormal distribution for on and off events. Probability distributions of PL trajectories of single NCs are obtained for two different excitation fluences and wavelengths (λex = 400, 440nm). Trapping rate (kT) prevails at higher power densities for both excitation wavelengths. From a careful analysis of the FLID and probability distributions, it is concluded that there is competition between the HC and trion assisted blinking pathways and that the contribution of these mechanisms varies with excitation wavelength as well as fluence.

Power Law in Deep Neural Networks: Sparse Network Generation and Continual Learning With Preferential Attachment.

Training deep neural networks (DNNs) typically requires massive computational power. Existing DNNs exhibit low time and storage efficiency due to the high degree of redundancy. In contrast to most existing DNNs, biological and social networks with vast numbers of connections are highly efficient and exhibit scale-free properties indicative of the power law distribution, which can be originated by preferential attachment in growing networks. In this work, we ask whether the topology of the best performing DNNs shows the power law similar to biological and social networks and how to use the power law topology to construct well-performing and compact DNNs. We first find that the connectivities of sparse DNNs can be modeled by truncated power law distribution, which is one of the variations of the power law. The comparison of different DNNs reveals that the best performing networks correlated highly with the power law distribution. We further model the preferential attachment in DNNs evolution and find that continual learning in networks with growth in tasks correlates with the process of preferential attachment. These identified power law dynamics in DNNs can lead to the construction of highly accurate and compact DNNs based on preferential attachment. Inspired by the discovered findings, two novel applications have been proposed, including evolving optimal DNNs in sparse network generation and continual learning tasks with efficient network growth using power law dynamics. Experimental results indicate that the proposed applications can speed up training, save storage, and learn with fewer samples than other well-established baselines. Our demonstration of preferential attachment and power law in well-performing DNNs offers insight into designing and constructing more efficient deep learning.

Segmental estimation and testing method for power-law distributions and some extensions

For discrete segmental power-law distributions, the probability ratio ft/ft+1 is a linear function of the exponent parameter. Based on this property, the estimation of the exponent parameter and a goodness-of-fit testing method are provided. The proposed testing method is parameter-independent and the testing statistic is proved to asymptotically follow a chi-square distribution. In the region where power-law properties exist, the testing method and the estimation method can be applied by segments, so they can also be used to determine interval endpoints. These methods can also be extended to other discrete distributions such as Yule distribution, Poisson distribution, Geometry distribution and so on. Some simulation results of synthetic truncated power-law distributions provide support for the effectiveness of the proposed methods. To demonstrate the applicability of the method, two empirical examples, word frequencies of the novel Moby Dick and US casuality numbers in the American Indian War, are analyzed.

Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowding.

We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of hard spheres in d = 3 dimensions and, thus, obtain an estimate of the random close packing volume fraction, ϕRCP, as a function of size polydispersity. We first consider mixtures of particle sizes with discrete distributions. For binary systems, we show agreement between our predictions and simulations using both our own results and results reported in previous studies, as well as agreement with recent experiments from the literature. We then apply our approach to systems with continuous polydispersity using three different particle size distributions, namely, the log-normal, Gamma, and truncated power-law distributions. In all cases, we observe agreement between our theoretical findings and numerical results up to rather large polydispersities for all particle size distributions when using as reference our own simulations and results from the literature. In particular, we find ϕRCP to increase monotonically with the relative standard deviation, sσ, of the distribution and to saturate at a value that always remains below 1. A perturbative expansion yields a closed-form expression for ϕRCP that quantitatively captures a distribution-independent regime for sσ < 0.5. Beyond that regime, we show that the gradual loss in agreement is tied to the growth of the skewness of size distributions.

Size Polydispersity Tunes Slip Avalanches of Granular Gouge

AbstractGranular materials have frequently been used as representations of natural fault gouges. Although they can reproduce proper avalanche behaviors, the universality of the scaling exponent of avalanche size remains debatable. As a core issue in both amorphous plasticity and geophysics, avalanche universality may help reconcile the avalanche behaviors of earthquake and granular materials into the same universality class. We examine numerically the signatures of stress avalanches emerging from quasi‐static shear of granular materials with different size polydispersity. A persistent serrated plastic flow phenomenon is observed in our models with varying polydispersity. The stress drop is well defined by a truncated power law distribution P(s) ~ s−τexp(−s/smax). The exponent τ and cutoff stress drop smax show a clear dependence on polydispersity, which reflects a tuned criticality. We further calculate the effective temperature from the statistics of energy fluctuations. The effective temperature volatility can be used to explain the tuned critical behaviors of granular gouge.

Study of the School–Residence Spatial Relationship and the Characteristics of Travel-to-School Distance in Shenyang

The school–residence spatial relationship is a key factor in understanding urban spatial structure and travel-to-school behavior of students. Analyzing the change law and the spatial characteristics of travel-to-school distance can provide a basis for improved accessibility of urban educational facilities and enable enrolment of students from the neighborhood. Based on one complete month of mobile phone signaling data for May 2018, the changes in student density with the travel-to-school distance was analyzed using MATLAB and Mann–Kendall Trend Test, and the pattern and the spatial structure of travel-to-school were explored. The results revealed that: (1) With increase in travel-to-school distance, the student density showed a decrease in truncated power law distribution, and it is concentrated within the travel-to-school distance of 5.0 km; (2) According to the sudden change points of the student density growth rate, the threshold distance for travel to kindergartens is 1.30 km, and for primary schools and secondary schools is 1.50 km. The school–residence spatial structure is divided according to the threshold of travel-to-school distance and the scope of attendance; (3) The dominant flow of travel-to-school is generally from urban peripheral and marginal areas to the urban core area, and partly from marginal areas to peripheral areas; (4) The pattern of travel-to-school is polycentric, and the study centers are mainly located in the urban central district north of the Hun River. The urban core area has the strongest attraction of students, while the marginal area has the weakest.

Transforming Mesoscale Granular Plasticity Through Particle Shape

When an amorphous material is strained beyond the point of yielding it enters a state of continual reconfiguration via dissipative, avalanche-like slip events that relieve built-up local stress. However, how the statistics of such events depend on local interactions among the constituent units remains debated. To address this we perform experiments on granular material in which we use particle shape to vary the interactions systematically. Granular material, confined under constant pressure boundary conditions, is uniaxially compressed while stress is measured and internal rearrangements are imaged with x-rays. We introduce volatility, a quantity from economic theory, as a powerful new tool to quantify the magnitude of stress fluctuations, finding systematic, shape-dependent trends. For all 22 investigated shapes the magnitude $s$ of relaxation events is well-fit by a truncated power law distribution $P(s)\sim {s}^{-\tau} exp(-s/s^*)$, as has been proposed within the context of plasticity models. The power law exponent $\tau$ for all shapes tested clusters around $\tau=$ 1.5, within experimental uncertainty covering the range 1.3 - 1.7. The shape independence of $\tau$ and its compatibility with mean field models indicate that the granularity of the system, but not particle shape, modifies the stress redistribution after a slip event away from that of continuum elasticity. Meanwhile, the characteristic maximum event size $s^*$ changes by two orders of magnitude and tracks the shape dependence of volatility. Particle shape in granular materials is therefore a powerful new factor influencing the distance at which an amorphous system operates from scale-free criticality. These experimental results are not captured by current models and suggest a need to reexamine the mechanisms driving mesoscale plastic deformation in amorphous systems.

L\xe9vy-like movement patterns of metastatic cancer cells revealed in microfabricated systems and implicated in vivo

Metastatic cancer cells differ from their non-metastatic counterparts not only in terms of molecular composition and genetics, but also by the very strategy they employ for locomotion. Here, we analyzed large-scale statistics for cells migrating on linear microtracks to show that metastatic cancer cells follow a qualitatively different movement strategy than their non-invasive counterparts. The trajectories of metastatic cells display clusters of small steps that are interspersed with long “flights”. Such movements are characterized by heavy-tailed, truncated power law distributions of persistence times and are consistent with the Lévy walks that are also often employed by animal predators searching for scarce prey or food sources. In contrast, non-metastatic cancerous cells perform simple diffusive movements. These findings are supported by preliminary experiments with cancer cells migrating away from primary tumors in vivo. The use of chemical inhibitors targeting actin-binding proteins allows for “reprogramming” the Lévy walks into either diffusive or ballistic movements.

Seismicity induced by longwall coal mining at the Thoresby Colliery, Nottinghamshire, U.K.

The U.K. has a long history of deep coal mining, and numerous cases of mining-induced seismicity have been recorded over the past 50 years. In this study we examine seismicity induced by longwall mining at one of the U.K.’s last deep coal mines, the Thoresby Colliery, Nottinghamshire. After public reports of felt seismicity in late 2013 a local seismic monitoring network was installed at this site, which provided monitoring from February to October 2014. This array recorded 305 seismic events, which form the basis of our analysis. Event locations were found to closely track the position of the mining face within the Deep Soft Seam, with most events occurring up to 300 m ahead of the face position. This indicates that the seismicity is being directly induced by the mining, as opposed to being caused by activation of pre-existing tectonic features by stress transfer. However, we do not observe correlation between the rate of excavation and the rate of seismicity, and only a small portion of the overall deformation is being released as seismic energy. Event magnitudes do not follow the expected Gutenberg-Richter distribution. Instead, the observed magnitude distributions can be reproduced if a Truncated Power Law distribution is used to simulate the rupture areas. The best-fit maximum rupture areas correspond to the distances between the Deep Soft Seam and the seams that over- and underlie it, which have both previously been excavated. Our inference is that the presence of a rubble-filled void (or goaf) where these seams have been removed is preventing the growth of larger rupture areas. Source mechanism analysis reveals that most events consist of dip-slip motion along near-vertical planes that strike parallel to the orientation of the mining face. These mechanisms are consistent with the expected deformation that would occur as a longwall panel advances, with the under- and over-burdens moving upwards and downwards respectively to fill the void created by mining. This further reinforces our conclusion that the events are directly induced by the mining process. Similar mechanisms have been observed during longwall mining at other sites.

The evolutionary origins of Lévy walk foraging.

We study through a reaction-diffusion algorithm the influence of landscape diversity on the efficiency of search dynamics. Remarkably, the identical optimal search strategy arises in a wide variety of environments, provided the target density is sparse and the searcher’s information is restricted to its close vicinity. Our results strongly impact the current debate on the emergentist vs. evolutionary origins of animal foraging. The inherent character of the optimal solution (i.e., independent on the landscape for the broad scenarios assumed here) suggests an interpretation favoring the evolutionary view, as originally implied by the Lévy flight foraging hypothesis. The latter states that, under conditions of scarcity of information and sparse resources, some organisms must have evolved to exploit optimal strategies characterized by heavy-tailed truncated power-law distributions of move lengths. These results strongly suggest that Lévy strategies—and hence the selection pressure for the relevant adaptations—are robust with respect to large changes in habitat. In contrast, the usual emergentist explanation seems not able to explain how very similar Lévy walks can emerge from all the distinct non-Lévy foraging strategies that are needed for the observed large variety of specific environments. We also report that deviations from Lévy can take place in plentiful ecosystems, where locomotion truncation is very frequent due to high encounter rates. So, in this case normal diffusion strategies—performing as effectively as the optimal one—can naturally emerge from Lévy. Our results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks.

Big data analyses reveal patterns and drivers of the movements of southern elephant seals.

The growing number of large databases of animal tracking provides an opportunity for analyses of movement patterns at the scales of populations and even species. We used analytical approaches, developed to cope with “big data”, that require no ‘a priori’ assumptions about the behaviour of the target agents, to analyse a pooled tracking dataset of 272 elephant seals (Mirounga leonina) in the Southern Ocean, that was comprised of >500,000 location estimates collected over more than a decade. Our analyses showed that the displacements of these seals were described by a truncated power law distribution across several spatial and temporal scales, with a clear signature of directed movement. This pattern was evident when analysing the aggregated tracks despite a wide diversity of individual trajectories. We also identified marine provinces that described the migratory and foraging habitats of these seals. Our analysis provides evidence for the presence of intrinsic drivers of movement, such as memory, that cannot be detected using common models of movement behaviour. These results highlight the potential for “big data” techniques to provide new insights into movement behaviour when applied to large datasets of animal tracking.

Fracture size and transmissivity correlations: Implications for transport simulations in sparse three‐dimensional discrete fracture networks following a truncated power law distribution of fracture size

AbstractWe characterize how different fracture size‐transmissivity relationships influence flow and transport simulations through sparse three‐dimensional discrete fracture networks. Although it is generally accepted that there is a positive correlation between a fracture's size and its transmissivity/aperture, the functional form of that relationship remains a matter of debate. Relationships that assume perfect correlation, semicorrelation, and noncorrelation between the two have been proposed. To study the impact that adopting one of these relationships has on transport properties, we generate multiple sparse fracture networks composed of circular fractures whose radii follow a truncated power law distribution. The distribution of transmissivities are selected so that the mean transmissivity of the fracture networks are the same and the distributions of aperture and transmissivity in models that include a stochastic term are also the same. We observe that adopting a correlation between a fracture size and its transmissivity leads to earlier breakthrough times and higher effective permeability when compared to networks where no correlation is used. While fracture network geometry plays the principal role in determining where transport occurs within the network, the relationship between size and transmissivity controls the flow speed. These observations indicate DFN modelers should be aware that breakthrough times and effective permeabilities can be strongly influenced by such a relationship in addition to fracture and network statistics.

Human-Mobility-Based Spray and Wait: Efficient Routing Protocol for Pocket Switched Networks

Delay and/or Disruption-Tolerant Networking (DTN) is a novel communication prototype that can span across multiple networks and deal with unpredicted conditions in the Internet model. Pocket Switched Networks (PSN) are delay tolerant networks with hand held devices. Nodes in a PSN make use of a store-carry-and-forward paradigm to communicate along with themselves. The routing protocols performances that have been developed for DTN based on the movement pattern of the nodes. We propose a Human Mobility based Spray & Wait Routing protocol (HMSaW). This protocol makes use of truncated power law distribution of pause time and flight length of human mobility to smartly forward data in DTN and PSN. Simulation results show that the proposed HMSaW shows better delivery ratio and the communication overhead, with marginal reduction in average delay compared to existing PROPHET and Spray & Wait Routing protocol.

Analyses of characetristics of air passenger group mobility behaviors

In this paper, we use the civil aviation passenger reservation record data to analyze the characteristics of air passenger group mobility behaviors. We find that the airline network has restriction on passengers traveling, which causes the group travel length distribution to be more consistent with the stretched exponential distribution and to have no scale-free property. The passenger travel interval time satisfies a truncated power law distribution rather than the power law distribution. Meanwhile, holidays have a great influence on passengers traveling. In particular, during the Spring Festival, the summer vacation, and National Day, the number of traveling passengers is far more than at any other time. And passengers who will travel during the holidays prefer to book tickets in advance. By analyzing the throughput, we find that it has a periodicity and is easy to be affected by festival and holidays. Moreover, the throughput of the airport is greatly related to the number of cities which are navigable to each other.

Precipitation as Meteoric Sediment and Scaling Laws of Bedrock Incision: Assessing the Sadler Effect

Although it has been several decades since Sadler (1981) first showed that sediment accumulation rates exhibit a negative power law dependence on measurement interval (i.e., the Sadler effect), only recently has a manifestation of covariance in rate with duration become more widely appreciated in degradational settings. Because our collective understanding of rates of deposition and erosion are widely utilized to constrain the importance of active tectonism and climate forcing in shaping the surface of our planet, cognizance of the dependence of rate on duration of observation is of critical importance. Relations between elevation change (deposition, erosion) and rate scaling laws have often been examined by stochastic random walk simulations, but this approach is generally confounded by insufficient data on amounts of land-surface change, on durations of land-surface change, and on hiatal durations separating time intervals of change. Deposition or erosion rates measured over short intervals, such as during floods, are usually too large to be sustained over geologic timescales, and this difference implies that hiatuses of consequential duration must separate intervals of incision and/or deposition. While it has been argued that hiatuses may have a truncated power law distribution (reflecting the largely stochastic nature of processes in time and space), we (collectively) lack adequate data on magnitudes and temporal distributions of natural depositional and/or erosional events in many geologic systems to fully understand their relations. Abundantly available data on meteoric precipitation (rainfall), comprising precipitation amounts, precipitation durations, and drought durations at different timescales and from different climatic settings, are an attractive analogue for longer-term processes of deposition and erosion that can only be inferred from incomplete geologic data. Here, manifestations and reasons for the Sadler effect are examined in a region of relatively discontinuous meteoric sedimentation as recorded by 2,311 precipitation (and intervening hiatus) events over the past 63 yr in Las Vegas, Nevada. Collectively, these data suggest several conclusions. (1) Frequencies of rainfall magnitude, rainfall duration, and intervening hiatuses are closely approximated by exponential amount and duration frequency distributions; quantities and lengths of precipitation are more or less randomly partitioned in length-time space. (2) The negative power law dependence of precipitation rate on measurement interval is largely unrelated to the progressive inclusion or exclusion of longer or shorter intervals of precipitation or drought over longer or shorter durations of consideration. (3) Dependence of precipitation rate on total (rainfall plus hiatal) duration, manifested as positive covariance in total duration and amount, only becomes apparent among the Las Vegas data when durations span more than several years. Over shorter time spans, the stochastic nature of synoptic weather systems imparts steep negative power law covariance to duration versus rate relations; over longer durations, the influence of Las Vegas climate becomes increasingly apparent as variation in precipitation amounts is increasingly explained by total duration. (4) Actuality of the Sadler effect in Las Vegas rainfall data, manifested as the negative dependence of log-scaled rate on measurement duration, primarily reflects the degree of correspondence between amount and duration. These tenets are further examined in light of recently published data on cumulative durations and rates of bedrock incision. These degradational systems largely exhibit negative power law rate duration slopes, a trend previously interpreted as reflecting some sort of dependence of incision rate on measurement interval. However, when viewed in a context of precipitation as meteoric sediment, these erosional data are more readily understood as largely reflecting the degree of correlation between per-event durations and amounts of incision among the various river systems under consideration.

Motile male gametes of the araphid diatom Tabularia fasciculata search randomly for mates.

Sexuality in the marine araphid diatom Tabularia involves an unusual type of gamete, not only among diatoms but possibly in all of nature. The non-flagellated male gamete is free and vigorously motile, propelled by pseudopodia. However, the cues (if any) in their search for compatible female gametes and the general search patterns to locate them are unknown. We tracked and compared male gamete movements in the presence and absence of receptive female gametes. Path linearity of male movement was not affected by presence of female gametes. Male gametes did not move towards female gametes regardless of their proximity to each other, suggesting that the detection range for a compatible mate is very small compared to known algal examples (mostly spermatozoids) and that mate recognition requires (near) contact with a female gamete. We therefore investigated how male gametes move to bring insight into their search strategy and found that it was consistent with the predictions of a random-walk model with changes in direction coming from an even distribution. We further investigated the type of random walk by determining the best-fit distribution on the tail of the move length distribution and found it to be consistent with a truncated power law distribution with an exponent of 2.34. Although consistent with a Lévy walk search pattern, the range of move lengths in the tail was too narrow for Lévy properties to emerge and so would be best described as Brownian motion. This is somewhat surprising because female gametes were often outnumbered by male gametes, thus contrary to the assumption that a Brownian search mode may be most optimal with an abundant target resource. This is also the first mathematically analysed search pattern of a non-flagellated protistan gamete, supporting the notion that principles of Brownian motion have wide application in biology.

Nestedness in bipartite networks of Thuja plicata, Prunus laurocerasus and Buxus sempervirens and their pathogens

The trade with cultivated plants is one of the major pathways for the introduction of invasive species, pathogens included. Based on network analysis, the present study aimed the interaction between several species of cultivated woody perennials found in gardening outlets and nurseries trading with ornamental species and their documented pathogens. Focal species of the host list were Thuja plicata, Buxus sempervirens and Prunus laurocerasus, the selection being based on reported bestselling figures. Bipartite, qualitative, undirected networks were constructed to incorporate woody perennials as hosts and their documented pathogens. The tested network properties were: connectance, node degree distribution, web asymmetry and nestedness. Cluster analysis using Euclidian distance and niche overlap index of Pianka were employed as additional pattern description metrics. The main network containing 33 host species and 112 pathogens was characterized by truncated power law distribution fitting the observed degree distribution of hosts and power law distribution fitting the observed degree distribution of pathogens, low connectance (C = 0.12), intermediate web asymmetry (W = 0.54) and high significant nestedness (N = 0.94). The network containing three focal hosts showed significant lower nestedness (N = 0.54), higher asymmetry (W = 0.94) and higher connectance (C = 0.38). Cluster analysis revealed the separation of focal species distinctly, the majority of other hosts merging in one cluster. Due to the prevalence of specialized pathogens the niche breadth was narrow, with small overlap in resources’ partition (Pianka index = 0.31). Our results showed that a random assembly of hosts (woody ornamentals displayed for sale in retail centers and nurseries) could harbor pathogens which attached in a non-random manner, generating a characteristic pathosystem, with distinctive topology. The possible implications of the study consisted in a new insight in invasive spread and the inclusion of new pathogens in local pathogen communities using network analysis as a powerful investigation tool.

Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions

Recently, Clauset, Shalizi, and Newman have proposed a systematic method to find over which range (if any) a certain distribution behaves as a power law. However, their method has been found to fail, in the sense that true (simulated) power-law tails are not recognized as such in some instances, and then the power-law hypothesis is rejected. Moreover, the method does not work well when extended to power-law distributions with an upper truncation. We explain in detail a similar but alternative procedure, valid for truncated as well as for non-truncated power-law distributions, based in maximum likelihood estimation, the Kolmogorov-Smirnov goodness-of-fit test, and Monte Carlo simulations. An overview of the main concepts as well as a recipe for their practical implementation is provided. The performance of our method is put to test on several empirical data which were previously analyzed with less systematic approaches. We find the functioning of the method very satisfactory.

Temporal dynamics and impact of event interactions in cyber-social populations

The advance of information technologies provides powerful measures to digitize social interactions and facilitate quantitative investigations. To explore large-scale indoor interactions of a social population, we analyze 18 715 users' Wi-Fi access logs recorded in a Chinese university campus during 3 months, and define event interaction (EI) to characterize the concurrent interactions of multiple users inferred by their geographic coincidences-co-locating in the same small region at the same time. We propose three rules to construct a transmission graph, which depicts the topological and temporal features of event interactions. The vertex dynamics of transmission graph tells that the active durations of EIs fall into the truncated power-law distributions, which is independent on the number of involved individuals. The edge dynamics of transmission graph reports that the transmission durations present a truncated power-law pattern independent on the daily and weekly periodicities. Besides, in the aggregated transmission graph, low-degree vertices previously neglected in the aggregated static networks may participate in the large-degree EIs, which is verified by three data sets covering different sizes of social populations with various rendezvouses. This work highlights the temporal significance of event interactions in cyber-social populations.

Human-Mobility-Based Sensor Context-Aware Routing Protocol for Delay-Tolerant Data Gathering in Multi-Sink Cell-Phone-Based Sensor Networks

Ubiquitous use of cell phones encourages development of novel applications with sensors embedded in cell phones. The collection of information generated by these devices is a challenging task considering volatile topologies and energy-based scarce resources. Further, the data delivery to the sink is delay tolerant. Mobility of cell phones is opportunistically exploited for forwarding sensor generated data towards the sink. Human mobility model shows truncated power law distribution of flight length, pause time, and intercontact time. The power law behavior of inter-contact time often discourages routing of data using naive forwarding schemes. This work exploits the flight length and the pause time distributions of human mobility to design a better and efficient routing strategy. We propose a Human-Mobility-based Sensor Context-Aware Routing protocol (HMSCAR), which exploits human mobility patterns to smartly forward data towards the sink basically comprised of wi-fi hot spots or cellular base stations. The simulation results show that HMSCAR significantly outperforms the SCAR, SFR, and GRAD-MOB on the aspects of delivery ratio and time delay. A multi-sink scenario and single-copy replication scheme is assumed.