Objective. To investigate quantitatively and objectively the effects of repeated muscle vibration (rMV) of triceps surae on the gait pattern in a 5-year-old patient with Cerebral Palsy with equinus foot deformity due to calf spasticity. Methods. The patient was assessed before and one month after the rMV treatment using Gait Analysis. Results. rMV had positive effects on the patient's gait pattern, as for spatio-temporal parameters  and kinematics. The pelvic tilt reduced its anteversion and the hip reduced the high flexion evidenced at baseline; the knee and the ankle gained a more physiological pattern bilaterally. The Gillette Gait Index showed a significant reduction of its value bilaterally, representing a global improvement of the child's gait pattern. Conclusions. The rMV technique seems to be an effective option for the gait pattern improvement in CP, which can be used also in very young patient. Significant improvements were displayed in terms of kinematics at all lower limb joints, not only at the joint directly involved by the treatment  but also at proximal joints . Cerebral palsy (CP) is the most common cause of physical disability in children, with a reported incidence of 2.0 ± 2.5 per 1000 live births. Children with CP may present a variety of motor problems. Some are directly related to the lesion in the central nervous system, influencing muscle tone, balance, strength, and selectivity (primary problems), whereas static muscle contractures and bony deformities (secondary problems) develop slowly over time in response to the primary problems and to growth [Recently, a study based on Transcranial Magnetic Stimulation (TMS) demonstrated that a repeated muscle vibration (rMV) intervention can modify primary motor cortex (M1) plasticity, inducing an increase in short intracortical inhibition (SICI) of the vibrated muscle and an inverse pattern in its antagonist , 4. SincSince rMV technique resulted to be safe and comfortable in adults –11 and aThe patient was a male affected by tetraplegic CP, bilateral, neurological signs in four limbs with minimal functional involvement of upper limbs associated with no mental retardations. He was born at the 31st week of gestation; at birth 1 minute and 5 minute Apgar scores were 8. The birth weight was 1790 gr, and the length was 43 cm. He has respiratory distress for which he was kept in an incubator for 26 days after birth. The MRI showed a periventricular leukomalacia. At the moment of the intervention he was 5 years old . He was able to walk on toes with a pattern of increasing hip and knee flexion for the spasticity at the adductor muscles, flexor, and triceps surae; no contractures were present on the lower limbs. He was level II of the Gross Motor Function Classification System: he walks without devices and is limited in walking outdoors and in the community, with no ability to perform gross motor skills. No antispasticity drugs or restraint therapy had been done in the previous six months, and he did not undergo surgical treatment on the lower limbs. He did physiotherapy five times a week. Throughout all the experiment duration, no antispasticity drugs were administered.The study was approved by the Ethics Research Committee of the Institute. His parents gave their informed consent to the child's participation in the study.The gait pattern of the subject was compared to an aged matched normality band composed of 20 healthy subjects . Selection criteria for nondisabled subjects included no prior history of cardiovascular, neurological, or musculoskeletal disorders. They exhibited normal motor and intellectual development.The patient underwent the rMV treatment and was examined with clinical assessment and with gait analysis (GA) before (PRE session) and one month after the treatment (POST session).GA was conducted using a 12-camera optoelectronic system  for the evaluation of movement kinematics and a synchronic video system . After collection of the anthropometric measures , passive markers were placed at special points of reference, directly on the subject's skin. The passive markers were positioned as described by Davis et al. . Vibration intervention was applied over 3 consecutive days, one session a day consisting of 3 × 10 min applications, separated by 1-minute interval. During the rMV the child was required to make a voluntary isometric contraction of vibrated muscle, against the hand of the assessor, to obtain about 30–50% of his plantarflexion. The clinical assessment was performed by the measurement of the dynamic ankle range of motion and passive range of motion in the supine position with the knee flexed to 90° and fully extended as assessed by the modified Tardieu Scale (MTS) . The angFor this measurement, the child laid supine with the knee in full extension, and the subtalar joint stabilized. The ankle joint was flexed as fast as possible, and the first catch angle was measured by a manual goniometry. The degrees of dorsiflexion from the joint's neutral position were recorded as a positive number and the degrees of plantarflexion as a negative number. The results of the clinical assessment are displayed in Some parameters were identified and calculated from kinematic data: spatiotemporal parameters and joint-angles values at specific instants of the gait cycle and range of motions (ROMs), calculated as difference between maximum and minimum values of a specific angle plot. In addition, in order to quantify globally the gait pattern of the subject, the Gillette Gait Index (GGI) or Normalcy Index (NI) , 15 was U tests. Null hypotheses were rejected when probabilities were below 0.05.All the previously defined parameters were computed for all trials of the patient, and then the mean values and standard deviations of all indexes were calculated for the patient in each session and for the CG. Data of the first (PRE) and the second (POST) session were compared with the Wilcoxon tests, in order to detect significant changes in patient's gait pattern. The patient's and the controls' data were compared with Mann-Whitney In PRE session the child was characterised by low ROM values of ankle passive dorsi-plantarflexion and of Tardieu test; the right side displayed less physiological values than the left one. One month later, in POST session, some improvements appeared mainly at the right side which gained higher joint excursion and more symmetric condition.As concerns spatiotemporal parameters, before intervention the child walked with a lower velocity of progression, longer stance time, in particular on the right side, and reduced anterior step length, if compared to normal values: this condition was likely due to the search for better stability and equilibrium during gait. In the POST session these parameters, although far from normality, improved in terms of duration of right % stance, reducing the asymmetry present in the PRE session, and in terms of the bilateral anterior step length.Statistically significant improvements were observed in the main joints kinematics. The pelvic tilts, which were characterised by an anterior position on the sagittal plane  and the presence of a double bump with a higher range of motion (ROM index), reduced the anteversion, getting closer to the control group values. However, the pelvic path maintained the double bump, and the range of motion (ROM index) remained unchanged.As concerns the hip joint, before treatment it appeared flexed during the whole gait cycle, especially on the right side; it displayed an excessive right flexion at initial contact (IC index) and reduced bilateral extension ability in midstance (min in St); the maximum values in swing (Max Sw index) were higher than normal in both limbs. In POST session the IC and min St indices decreased at both limbs, and particularly on the right side. The maximum value in the swing phase (Max Sw index) improved bilaterally, even though the hyperflexion remained. The knee joint in PRE session was characterised by high flexion during the stance (IC and min St indices) and swing (Max Sw index) phases for the right limb, while the left knee was characterised by hyperextension during the stance phase and a reduced flexion ability in swing phase, showing a limited range of motion (ROM index). The intervention lead to bilateral positive effects: the right side reduced its high flexion in the stance phase (IC and min St indices), while the left one reached more physiological values at the initial contact and in swing phase (Max Sw index). On the left side the tendency to hyperextension persisted with an extension value (min St index) far from normality. The knee range of motion improved bilaterally. The effects of the treatment on ankle joints was a significant reduction of the plantarflexion on the left side during the whole gait cycle; on the right side, a better dorsiflexion ability in the swing phase (Max Sw index) was displayed. In terms of ankle joint, both feet were plantarflexed during the whole duration of the gait cycle  with a more severe equinus foot at the left limb. The range of motion (ROM index) was higher than normality on the right side and limited on the left one.P < .05).The GGI data  showed tThe present research shows that a treatment based on short-term vibratory applications on calf muscle can induce a 1-month effect on the gait pattern of a very young child affected by CP. In our case study the evaluation of the rMV effectiveness on the gait patterns of a 5-year-old child with tetraplegia secondary to CP has been documented and quantified through the comparison of the child's gait before (PRE session) and one month after (POST session) the treatment. The examination of the PRE session data showed a severe alteration of the gait pattern bilaterally, both at proximal and distal joints. The child walked very slowly, with long stance duration and short step length. The pelvis was in an anterior position on the sagittal plane with high excursion during the gait cycle; the hip joint was shifted towards flexion, particularly for the right limb. The knee showed a strong asymmetric strategy: while the right side was characterised by a high flexion during the gait cycle, the left side displayed a hyperextended pattern in midstance. Both ankles were plantarflexed, and the left side showed a less physiological position than the other limb. The GGI mean values confirmed the global alteration of gait pattern for both sides. One month after the rMV therapy performed on the calf muscles (POST session) our data demonstrated a significant improvement in terms of spatiotemporal parameters and kinematics. Although far from normality, the duration of stance phase and step length improved, displaying a more symmetric gait pattern. The ankle improved mainly on the left side, approaching normality. At the proximal joints, the pelvic tilt and the hip pattern also improved, reasonably because of an increased ankle control. In particular the hip joint reduced its excessive flexion at the initial contact on the right side, and better extension ability in midstance was reached bilaterally. The strong asymmetry between the right and the left knees was reduced: while the left limb improved, maintaining the tendency to hyperextension in midstance, the right side reduced its excessive flexion during stance. As a result, the knee paths gained a quite physiological pattern.Global improvements were confirmed by the GGI index, which reduced significantly its values bilaterally, showing a more physiological gait strategy. In conclusion, this paper demonstrated quantitatively and objectively the positive effects of the rMV application on gait pattern in a child with CP. In particular, GA showed that the effectiveness appeared on all lower limbs joints, not only at the joints directly involved in the treatment  but also at the proximal joints . In particular the main improvement was noted at the left side which was characterised by the most severe equinus foot; as the treatment was applied with the same procedure and vibratory parameters, our results may demonstrate that the improvements appeared to be wider in presence of the highest degree of functional limitation.The study has some limitations. Only one single case is reported, and this resulted in limited strength of the clinical and statistical findings. However, this paper represents the first attempt of rMV application in a child. Over the last few years, rMV procedure has received increasing scientific attention as a promising rehabilitation technique for adult chronic stroke , 7, althThen only a muscles group, the TS, has been treated in this case report, being ankle dorsi-plantarflexion the most relevant deficit; obviously further researches may be conducted considering more muscle groups in patients with more complex functional limitation, where more than one muscle should be treated.


In this work we attempt to find out the extent to which realistic prebiotic compartments, such as fatty acid vesicles, would constrain the chemical network dynamics that could have sustained a minimal form of metabolism. We combine experimental and simulation results to establish the conditions under which a reaction network with a catalytically closed organization (more specifically, an ( Biochemistry, however, takes place within compartments. All known metabolisms are co-evolutionary scenario can be envisioned in which reaction networks would very early be hosted within protocell compartments, becoming increasingly both interdependent and complex thereafter.Until recently, self-assembling compartments  have been regarded as a challenge for the development of any complex chemistry, due to the barrier to the free diffusion of solutes they represent and the corresponding reduction of the molecular precursor accessibility to the inner aqueous core of the system. Therefore, some authors have shown preference for a scheme of prebiotic transitions in which (bio-)chemistry develops without lipid compartments soft interfaces; see Note 2 in The role of lipid phases and compartments that likely preceded bio-membranes must have gone beyond their primary anti-dilution effects of preventing the irreversible loss of soluble, non-abundant–but often essential–organic compounds. For example, lipid bilayer and multilayer structures have been reported to assist polymerization of both nucleic acids and peptides in various experimental conditions In this context, it would be of great interest to determine the conditions for viability of cyclic reaction networks  within vesicles made of prebiotically plausible amphiphilic molecules. Although several interesting results have been recently obtained on those lines , with concentrations that are assumed to have fixed values in that medium . In addition, there is a system containing a protometabolic reaction network limited or enclosed by a semi-permeable primitive membrane. With these premises, the membrane is considered to be permeable to the small precursors, but impermeable to the bulkier metabolic intermediates produced by the internal reaction network The protometabolic model we will explore  consistsAs mentioned at the end of the Introduction, the metabolic model has already been analyzed in homogeneous conditions All rate constants are treated as invariant, with the fixed values shown in Notice from  that, quThe restriction of constant concentrations of S, T and U in the external environment (Stationary state solutions (i.e. states with invariant concentrations of intermediates) were calculated see  and explWe first analyzed the possible steady-state solutions under the extreme assumption of non-limiting diffusion of precursors, i.e. immediate supply of feeding molecules S, T and U. This situation is equivalent to the assumption of instantaneous uptake of precursors from the external reservoir  were surely absent in the early stages of the emergence of life, thus inter-conversion rates were also probably much slower in prebiotic conditions; i.e. generally speaking, longer time scales than those characteristic of present biochemistry should be considered. However, even without taking into account how the progressive development of catalysis could accelerate the general pace of protometabolic reactions, permeability values in a compartmentalized system, like ours, will already define important restrictions on the time scale of the encapsulated chemistry. As the maintenance of the system in a functional steady state has been shown to be at risk for relatively low values of the incorporation rate constants , a fairly general conclusion may be drawn from our analysis: it makes little sense to investigate separately the properties of compartments and the chemistries that take place within and around them. From our perspective, it is dangerous to neglect the problem of the encapsulation of complex reaction pathways , and to consider their appearance independent from the development of compartments. Indeed, a highly efficient protometabolism  would most probably perish by self-suffocation, as its need for nutrients and raw materials might not be satisfied by the passive influx of substrates. Conversely, the control of the properties and dynamic plasticity of the boundary of a system becomes really significant when the amphiphilic or lipidic compounds of the membrane are endogenously synthesized , rather than directly taken from the set of molecules available from the environment. The latter side of the coin becomes more obvious in the context of the transition from Here we have mainly dealt with the former issue: the viability conditions that compartmentation imposes on reaction networks and, more precisely, with the problem of how membrane permeability to nutrients may limit the characteristic time scale of the protometabolic processes taking place within a prebiotic vesicle. This problem, theoretically posed and discussed in This scenario accords quite well with recent experiments on the relative leakiness of prebiotic, fatty acid compartments In the present work, the focus has been set on the problem of nutrient accessibility to a compartmentalized protometabolism. We have limited the analysis to a simple, abstract (rac-1-Oleoylglycerol (GMO) was obtained from Sigma, USA.Lauric acid (LA), oleic acid (OA), bicine, carboxyfluorescein (CF) and Triton X-100 were purchased from Fluka, Switzerland. Vesicle suspensions were prepared by adding the fatty acid, LA, melted in advance, to a preheated 100 mM bicine buffer solution containing 8 mM CF and following the pH vesiculation method Vesicles were extruded with a small extruder from Avanti Polar Lipids, USA, passing vesicle suspensions (21 times) through polycarbonate filters with either 50 (for the OA/GMO system) or 400 nm  pore diameter. Non-encapsulated CF was removed by size-exclusion chromatography, on an agarose column (Bio-Gel A1.5) previously equilibrated with 100 mM bicine buffer at the corresponding pH. To avoid vesicular disruption during separation, this buffer contained a concentration of amphiphile close to the CVC in the case of LA (for OA/GMO vesicles this was not necessary). A set of ordinary differential equations was defined to describe the system dynamics see . StationThe stability of each of the stationary states found was checked by means of variational analysis: the Jacobian matrix was evaluated at the particular steady-state values, and the eigenvalues and eigenvectors calculated. Those steady-state solutions having all eigenvalues with negative real parts were identified as asymptotically stable, whereas those with at least one eigenvalue with positive real part correspond to unstable steady states.Matlab was used for the previously detailed calculations as well as for dynamical simulations, which consisted in experiments of numerical integration of the set of ordinary differential equations and were thus deterministic.Text S1Notes from the text.(PDF)Click here for additional data file.Text S2Permeability calculation.(PDF)Click here for additional data file.Text S3Set of ordinary differential equations of the model protometabolism.(PDF)Click here for additional data file.


Salmonella enterica subspecies 1 serovar Typhimurium (S. Tm) in the streptomycin mouse model for diarrhea. We focused on the first step on the way to systemic infection — the colonization of the cecal lymph node (cLN) from the gut — and studied roles of inflammation, dendritic cells and innate immune effectors in the colonization process. To this end, we inoculated mice with mixtures of seven wild type isogenic tagged strains (WITS) of S. Tm. The experimental data were analyzed with a newly developed mathematical model describing the stochastic immigration, replication and clearance of bacteria in the cLN. We estimated that in the beginning of infection only 300 bacterial cells arrive in the cLN per day. We further found that inflammation decreases the net replication rate in the cLN by 23%. In An understanding of how pathogens colonize their hosts is crucial for the rational design of vaccines or therapy. While the molecular factors facilitating the invasion and systemic infection by pathogens are a central focus of research in microbiology, the population biological aspects of colonization are still poorly understood. Here, we investigated the early colonization dynamics of  Salmonella bacteria after oral infection in a mouse model for complicated Salmonella diarrhea. To estimate migration and replication rates, we infected the mice with mixtures of identical, but distinguishable strains of the bacterium and analyzed the results with a mathematical model that describes the demography of the bacterial population. Random loss of some of these strains during colonization of the mice allows us to estimate migration rates between anatomical compartments. We find that approximately 300 bacteria migrate per day from the gut to the cecal lymph node – the first step towards systemic infection. We further investigate how bacterial migration and replication is affected by inflammation and various agents of the immune system. Our study provides unprecedented information on the colonization dynamics of this bacterial infection and introduces a framework for further improving therapy and vaccination.Like humans, pathogens have a demography. Within their hosts, they migrate, replicate, and die. Understanding these processes quantitatively can help designing vaccines and treatment by identifying vulnerabilities of the pathogen population. For most pathogens, however, quantitative information on how they replicate and spread in their hosts is lacking. Here, we investigate the early colonization of hosts by  Understanding the population biological aspects of how a pathogen colonizes its host is crucial for prevention of infection. Only if we know where a pathogen enters, which anatomical compartments it colonizes, where and how fast it replicates, migrates, and gets killed, will we be able to optimally design interventions that block this process. Just as there are molecular Achilles' heels of pathogens, population dynamical parameters exist that characterize vulnerabilities of the infection process. Combining the knowledge of molecular mechanisms with an understanding of the population dynamics of an infection thus holds great promise for the design of vaccines and therapy. For most pathogens, however, the population biological aspects of infection are not well understood.The population dynamics of pathogens within the host has been investigated most extensively for viruses, in particular for Human and Simian Immunodeficiency Viruses. We know how this virus enters Salmonella to investigate if bacterial cells initiate an infection independently of each other Haemophilus influenzae The study of the colonization dynamics of bacterial pathogens has an impressive early history. Meynell & Stocker used pairs or triplets of differentially marked strains of Today we have much better tools to monitor bacterial spread and replication at our disposal, and advanced population dynamical methods are being used to understand how infections unfold within their hosts Yersinia pseudotuberculosis has been investigated qualitatively H. influenzae. Lastly, Grant et al. presented a quantitative study on the dynamics of Salmonella infection following intravenous inoculation of mice Nevertheless, there are a few notable studies on the colonization of host by bacterial pathogens. Recently, Margolis & Levin Salmonella diarrhea In the present study, we define the early population dynamics in a mouse model for S. Tm with well characterized virulence defects and different mice strains with known deficiencies in pathogen handling.We were primarily interested in the rate at which the bacteria migrate from the gut to the cLN, and in the growth rate of the bacterial population in that compartment. To estimate these key population biological parameters we used inocula containing multiple wild type isogenic tagged strains (WITS) that have been used to elucidate population biological characteristics of bacterial pathogens in other systems in vivo constitutes a challenge. While the bacterial population size can be measured in many anatomical compartments, this measure is a complex composite of migration, replication and clearance, and hence does not allow quantifying the rates at which these processes occur. Therefore, we have developed a novel approach combining experimental infection with mixed inocula and mathematical modeling to determine bacterial migration to and replication with-in the cLN.Determining the migration, replication and clearance rates of bacteria S. Tm strains, each carrying a unique, 40 base pair long tag in the chromosome S. Tm. The rationale for using mixed inocula was to reveal the stochasticity of the colonization process: for an appropriate mixing ratio, only some of the strains in the mix arrive in the cLN. The stochastic loss of WITS on their way to the cLN enables us to estimate the rate at which they immigrate. The strains that successfully enter the cLN subsequently increase in numbers. From these numbers, we can infer the growth rate of the bacterial population in the cLN.The infection experiments were performed using a mixture of seven Before we present our findings, let us elaborate the advantages of using mixed inocula for studying of the colonization dynamics of the cLN. As we stated above, if we simply measure the bacterial population size in the cLN it is difficult to disentangle immigration from replication. In these simulations, the variation of the bacterial population size arises only from the intrinsic stochasticity of bacterial division, clearance  and immigration from the gut. In real mice, the distinction between the two scenarios would be blurred even more because there would be larger variation in the time courses of the bacterial population size due to biological differences between mice and experimental sources of error. As a consequence, it is not feasible to distinguish the two scenarios on the basis of measurements of the bacterial population size alone.With mixed inocula, on the other hand, the distinction between the two scenarios is clear-cut. Assume we inoculate with a mix containing seven WITS at a frequency of 1% and 93% untagged bacteria. In the scenario with low immigration, an individual WITS will fail to colonize the cLN in 37% of the cases. Thus, on average more than half of the WITS will be recovered from the cLN one day after inoculation. If immigration is high, however, WITS will fail to colonize in only 2.5% of the cases, i.e. all WITS will be recovered from the cLN in most animals. Using mixed inocula is therefore a much more sensitive approach to determining immigration and growth rates.The mathematical model we employed to analyze these infection data is a stochastic birth-death process extended by immigration see . It predFrom measurements of the population size of differently tagged bacteria recovered from the lymph node at a given time point, we can estimate the migration rate of bacterial cells from the gut to the cLN, and the net growth rate, odel see . Unfortuodel see . We stilodel see . Lastly,S. Tm, and 5% WITS , this corresponds to a migration rate of 298 cells per day. Given that the population size in the gut is approximately From these numbers, we estimated that the net growth rate, ours see . The migVisualizing the agreement between the observed and predicted number of WITS in the cLN is not straight-forward. The reason for this is that our model formalizes migration and division as stochastic processes, and therefore does not make a deterministic prediction on the population size of WITS in the cLN. Rather, our model gives us the probability to observe a certain population size. For example, with the best estimates for our parameters, the predicted probability to observe 1 CFU of a single WITS in the cLN 24 hours after the infection is 0.085. The probability to observe 0 CFU, i.e. not to recover a WITS, is 0.12.Moreover, the space of potential population sizes  is large compared to the number of observations. In the present case, for example, we have measured the population sizes of seven WITS in 11 mice. Thus, we have 77 observations. More than half of these observations are population sizes below 10 CFU, the rest is scattered between 10 and 47. The sparseness of the observations gives rise to seeming discrepancies between the predicted and observed population sizes of WITS in the cLN 24 hours after infection see .These difficulties in visualizing the quality of the model fit can be overcome by plotting the cumulative distribution function of predicted and observed population sizes of WITS. The cumulative distribution function describes the fraction of observed or predicted measurements less than or equal to some population size. For example, we mentioned above that more than half of our observations are less than 10 CFU. This can be seen from the cumulative distribution function plotted in To statistically test for the goodness of fit, we apply a As an independent validation of our model, we can predict the total bacteria population size in the cLN see . This vaS. Tm and a non-invasive mutant S. Tm To investigate the role of inflammation, we compared the infection dynamics of wild type S. Tm. The reduction of the migration rate is consistent with the key role of the SPI-1 encoded type III secretion system in traversing the gut epithelial barrier, a key step for reaching the cLN S. Tm the net replication rate of For the  day see . Thus thThe black and grey lines in 1640 see .S. Tm and S. Tm but the WITS lacked SPI-1. We have shown earlier that this type of infection elicits gut inflammation S. Tm carried the tag, we could analyze the population of wild type S. Tm in a healthy, non-inflamed gut environment To investigate the cause of these differences in the immigration and net replication rates, we conducted experiments in which the inoculum consisted of wild type S. Tm, i.e. inflammation was induced, the population of WITS that lacked SPI-1 increased with a net doubling time of 6.5 hours  and performed according to local guidelines  and the Swiss animal protection law (TschG).S. enterica subspecies 1 serovar Typhimurium) and the avirulent mutant The wild type strain SB300 -Ccr7tm1Rfor/J S. Tm, we developed a simple stochastic model that describes the immigration of bacterial cells into the cecal lymph node (cLN) and their replication and clearance in that compartment.To model the colonization of mice by S. Tm migrate from the gut to the cLN at a constant rate S. Tm population in the cLN (when we simulate the colonization dynamics).The model assumes that To be able to describe the event that the cLN is not colonized by WITS, we formulate the model as a continuous-time Markov process. This process has the following transition probabilities:These transition probabilities lead to the following master equations for the state probabilities, Analogously to the birth-death process, we can derive the probability generating function that is defined as From the probability generating function we can obtain the state probabilities Assume we conduct an experiment involving One day after inoculation, the population sizes of WITS are determined. We denote this population size as Maximizing this expression for the log-likelihood allows us to obtain best estimates for the parameters of our model from experimental data on the population sizes of each WITS in each mouse, S. Tm strains and mice genotypes. It is clear that the likelihood functions are well behaved and that there is only one maximum in the biologically relevant parameter range.Since it is impossible to estimate all three parameters of our model, we set the clearance rate constant of bacterial cells in the cLN If we set  one see . Becausezero see .From our estimates of S. Tm mixed with The quality of the fits were assessed with a The goodness of fit test compares the number of observations in the bins to the number of observations predicted by the birth-death-immigration model with the maximum likelihood parameter estimates. The null hypothesis of this test is that there is no significant discrepancy between observations and model prediction. This null hypothesis was not rejected for any of the datasets we analyzed.All the probability generating functions and likehoods described here were implemented in the R language of statistical computing Figure S1Relative frequency of each WITS in the cecum 24 hours after infection. Measurements for three representative mice are shown. All WITS strains are present at approximately equal frequencies.(PDF)Click here for additional data file.Figure S2WITS at various dilutions can be detected with our protocol that involves overnight culture and rtqPCR. There is no bias against detecting WITS at low frequencies.(PDF)Click here for additional data file.Figure S3State probabilities  as functions of time. For this figure we assumed (PDF)Click here for additional data file.Figure S4Contour plots of likelihood for the different experiments. The red dots indicate the maximum of the likelihood.(PDF)Click here for additional data file.Figure S5Relation between assumed clearance rate constant, , and our parameter estimates.A. The relation to the estimate of the replication rate constant, B. The relation to the estimate of the migration rate constant of WITS, (PDF)Click here for additional data file.


In response to the urging need of fire managers for timely information on fire location and extent, the SITHON system was developed. SITHON is a fully digital thermal imaging system, integrating INS/GPS and a digital camera, designed to provide timely positioned and projected thermal images and video data streams rapidly integrated in the GIS operated by Crisis Control Centres. This article presents in detail the hardware and software components of SITHON, and demonstrates the first encouraging results of test flights over the Sithonia Peninsula in Northern Greece. It is envisaged that the SITHON system will be soon operated onboard various airborne platforms including fire brigade airplanes and helicopters as well as on UAV platforms owned and operated by the Greek Air Forces. Fast fire detection and real time monitoring of fire parameters, such as fire spread and location of hot spots, are crucial for the success of the initial attack on and containment of a fire. For this purpose, thermal infrared sensors and airborne infrared line scanners or frame cameras should be regarded as components of such a detection and monitoring system. These can provide fundamental information on fire extent and intensity, as well as rate of progress, which are of vital importance for tactical suppression actions.strategic level, information on the fuel load, the assets and land cover distribution at different regions is needed to allocate national and regional priorities and to support decisions such as the regional distribution of budgets, personnel and equipment as well as to establish and maintain initial attack capabilities, and weather and fire monitoring systems. At the same time, at a management level, information is needed to support fire occurrence monitoring, fire behaviour process models and fire occurrence prediction systems. Finally, at an operational level, especially during a crisis, tactical observations are those that provide detailed, frequent, and repetitive views of specific fire events. Added-value products from these observations include the fire perimeter, fire front, and isolated hot spots and they are used to support decision making for initial attack response, logistical and tactical planning and sustained action operations [Information is required at different levels, and should be customised to user needs. For instance, at a erations . However1.1.fixed platforms can make use of cameras on towers, buildings or masts with good visibility of the surveyed terrain. The sensor technologies used in today's automatic ground detection systems are mainly infrared cameras, but in some cases optical cameras may be used. Autonomous detection of hot spots in the thermal infrared (TIR) part of the electromagnetic (E/M) spectrum is the basis for several commercial systems, such as BOSQUE (IZAR-FABA) and BSDS (Teletron). The images are sent to a central control unit via a radio communication system [Automatic detection systems mounted on n system , 3.satellite technology. Satellite systems are by far the mostly developed fire remote sensing tools. Satellites providing information in the infrared spectrum by deploying TIR imaging spectrometers are suitable for fire detection. Satellites and sensors with such capabilities include MSG-SEVIRI and GOES, NOAA –AVHRR, TRMM-VIRS, METOP-AVHRR-3, TERRA-MODIS, AQUA-MODIS, ERS2-ATSR, ENVISAT-AATSR, LANDSAT-TM/ETM+ and TERRA-ASTER. However, none of them has been used operationally for fire detection, mainly due to insufficient revisiting time . It is noteworthy that these satellites can be used in a multi-sensor approach to improve the temporal resolution and may also be used in a complementary way with other surveillance systems. Near real time monitoring to support civil protection services as well as regional and national authorities has been implemented in the framework of RISK-EOS, a service element within the Global Monitoring for Environment and Security (GMES) program funded by European Space Agency and the European Commission.Major fires are detectable from space and their progress can be monitored using Apart from the operational satellites, whose primary task, however, is not fire detection, there are plans for certain satellite missions dedicated to fire detection. For instance, FUEGO  is plannAircraft (manned or unmanned) are manoeuvrable and may very quickly revisit the critical areas providing rapid response for emergency situations. Airborne TIR sensors  can detect new hot spots that develop rapidly into wildland fires. Besides aircrafts equipped with TIR sensors can be used for supporting fire-fighters in safety tasks, and for detecting escape routes or security zones, in areas where the human visibility is restricted due to the smoke.The fixed orbit of satellite platforms applies a restraint in revisiting capability both in tactical operations during the crisis that require frequent and repetitive observations, and in surveillance of vulnerable areas under high-risk conditions. In the 1980s the first research and development activities on infrared fire imaging from aircraft started at the National Interagency Fire Center (NIFC). These activities included the use of forward looking infrared (FLIR) systems , and devOther systems used in different countries incorporating thermal infrared technology to assist forest fires fighting include surveillance and co-ordination airplane ACO , Daedalus System , Wildfire Airborne Sensor Programme WASP (Rochester Technology Institute) and Airborne Wildfire Intelligence System AWIS . A review of airborne infrared systems is conducted by Rodriguez Y Silva .This brief review proves that in the last decade there have been advancements in technologies supporting wild land fire management and tactical emergency response , 9, 10. The present paper introduces SITHON, a complete system tailored to the unique requirements of the wildland fire fighting community. Section 2 presents the system in detail, whilst Section 3 demonstrates the results of a test flight. In Section 4 the main conclusions are drawn.2.2.1.The SITHON Project was funded in 2003 under the Operational Program of Competitiveness of the Greek Ministry of Development-General Secretariat for Research and Technology . The project lasted three years and was initiated in July 2003. The main objectives of the project were to foster collaboration between the private service sector, technological partners and research community, to demonstrate the synergy of evolving technologies  for increasing the information content of data collected, and enhancing the timeliness in data collection, processing and transition towards an effective detection, monitoring and management of wildfire suppression actions.in-situ optical cameras, and an airborne fire detection system based on a fully digital thermal imaging sensor. The network of sensors is linked to an integrated GIS environment in order to facilitate the fire fighting management and support the decision making process during crisis. The GIS data bases incorporates qualitative and quantitative information layers needed to estimate the fire risk, such as the vegetation types and quantity of fuel matter, the road network for accessing the active fires, the area's morphology, the sensitive and endangered locations , the high danger infrastructures , the natural or artificial water reservoirs, etc. The platform of SITHON includes a Crisis Operating Centre, which receives information in the form of images and data from the wireless sensor detection systems, displays it on wide screen monitors and analyses it to derive the dynamic picture of fire evolution. In the following sections a detail description of the airborne thermal imaging part of the SITHON system is given.It is well known that time is a crucial parameter in fire combating and fire containment. The level of efficiency depends on the availability of fire fighting resources, the firemen endurance, as well as the knowledge of the terrain, the fire location and the ways to access to it. For this purpose the SITHON project applied remote sensing systems of terrestrial and airborne detection sensors for the localization, notification and monitoring of the active forest fires. The whole SITHON system comprises a wireless network of 2.2.The SITHON project aimed at conducting further R&D in the area of using new smaller and less expensive IR uncooled cameras for fire detection and monitoring purposes, and post-fire management . SITHON also focused in the area of image processing coupled with Geographic Information System (GIS), Global Positioning System (GPS) and Inertial Navigation System (INS) technologies to assist in the dynamic translation of the raw image data collected  to usable products. The SITHON airborne system was designed to offer high quality colour (video RGB) and infrared imagery. Each frame acquisition is coupled with kinematic GPS and inertial platform data ingested by a precise MIDG II Inertial Measuring Unit (IMU) on board the airplane. The integration of the GPS, the IMU and camera data along with a digital elevation model (DEM) allows for real time orthorectification and geo-positioning of the acquired frames without using ground surveyed control points.hot spot identification, geo-positioning and alarm generation,fire front location and representation on a map,isothermal contour lines generation and mapping,geo-referenced video (RGB) and thermal image frames projected to the Hellenic Geodetic Reference System (EGSA87) or any other cartographic projection system used by the fire managers in the area of interest,synthetic cartographic products integrating georeferenced thermal and/or video images with existing background maps of assets, transportation networks and facilities situated in the area of operations.The ultimate aims in SITHON system design were directed to meet operational tactical requirements and products generation which are useful for crisis management including:Timeliness is of paramount importance for the success of such a system. The system is designed to ensure automatic fire detection. It is mountable on any airborne platform and can be operated within 15 to 20 minutes after the first fire announcement. Once on the platform, SITHON is supported by a fully automated control system, which manages the frame acquisition, the radiometric image calibration and thresholding, as well as the dynamic hot spot/fire front identification and geo-positioning within 50-100 m error with the lack of any operating GPS station on the ground. To be noted that the off-line processing of stereo pairs of images with the incorporation of GPS ground reference data, improves the geo-positioning accuracy up to the order of 1-3 m . Clearly, the post-processing of stereo pairs of images is useful only for post-crisis management to allow precise mapping and assessment of the damages in the impacted zones. During crisis, the imaging system is integrated with telemetry equipment ready to transmit the output products to fire-fighting forces in real-time. The platform of SITHON was a CESSNA 310Q two-engine aircraft own and operated by AEROPHOTO Ltd .2.3.2.3.1.f) of 20 mm.The integration of the camera was simplified due to existing design elements of the plane. For instance, the aircraft was equipped with a gyro-stabilized camera mount, on which the infrared camera body was mounted and fixed. The Thermovision R 570 camera used is a light-weight high performance uncooled forward looking infrared camera. It uses advanced uncooled Focal Plane Array (FPA) micro-bolometer technology and stores images and data to memory cards. The detector consists of a cavity with 77 760 microbolometers made of Si-elements coated with a thermal resistance layer. The microbolometers are thermal detectors and are operated without cooling. But besides the thermal radiance of the target, the radiation of internal camera components may be detected by the uncooled detector arrays, and this can decrease the measurement accuracy. To tackle this problem the inside case temperature is measured at several locations and these measurements are used in the automatic re-calibration of the camera at predefined time intervals. In addition, in order to avoid any convective heat transfer to the detector elements, the bolometers are placed in a vacuum chamber and their temperature is kept close to the ambient temperature using Peltier elements. Although the response time of bolometers is remarkably longer than quantum detectors, an image frequency of 60 Hz is achievable with this system. The absence of moving parts makes the operation of the Thermovision R 570 IR-camera of AGEMA more comfortable and safe. Bolometers are not selective with respect to the spectral range, therefore optical filters are used with this camera to optimise response at a spectral range of 7.5-13 μm. The camera optical system is using lenses with a focal length , the camera underwent an analytical 3-D calibration , using the 3-D calibration test field of the Laboratory of Photogrammetry [shown in p, ypx and camera constant c, have been expressed in pixel units with respect to FPA dimensions (320×240 pixels). The best value for the calibrated camera constant c was estimated to be 763,871 pixels, which is equivalent to a focal length of 19,86 mm, given that the physical dimension of pixel is 26 μm. This calibration procedure is repeated annually prior to fire season and camera deployment.In order to recover precisely the camera's internal characteristics, that are the coordinates of the principal point shown in  belonginshown in , is repoV is the velocity of the platform (aircraft), f is the camera focal length, H is the flight height above ground level, Δt is the time for exposure and θ is the off nadir angle. The SITHON imaging system has been designed as to avoid blurring effects on the acquired images. Taking as example the height and aircraft velocity conditions during SITHON demonstration, mounted on a CESSNA 310Q airplane flying at 160 km/h and 7500 ft (∼2300 m) above the ground, and considering that the camera is looking at nadir (θ= ∼ 0°) with lenses of 19,86 mm focal length and exposure time of 1/60 sec, the blur parameter is estimated to be of 0,006 mm or 6μm. Therefore, the effect of blur is about the 1/5 of pixel's physical dimension, which is not discernible by human eye. It should be noted that the FPA detector size of the Thermovision R 570 IR-camera of AGEMA is 0.026 mm or 26μm . The forward motion of the aircraft during camera operation may result in a blurring effect of the acquired image. The image blur parameter is defined as:2.3.2.. The IMU device operated by the SITHON system is the MIDG II of Microbotics  and position o, Yo, Zo) is shown in l is the FPA physical dimension (mm) along the flight axis (l = 6.24 mm), V is the velocity of aircraft, f is the camera focal length, H is the flight height above ground level, and OV is the percentage overlap, which equals to 0% for monoscopic view or at least 60% for a stereoscopic one. The payload components  are controlled by a laptop PC  onboard the airplane. The camera and the IMU are rigidly attached and oriented to the camera opening at the bottom of the aircraft . The sysDuring the operations the payload engineer is provided with several interfaces showing dynamically (i) the status of system's components and subcomponents, (ii) the data input to the system , (iii) the status of communication between the system controller (onboard) and data server (on the ground), and (iv) the output products .2.3.4.data package. The data package is forwarded to a server PC system , installed on the ground station or on board the aircraft (depending on the chosen communication architecture). The data package is decoded on the server PC, and transformed to useful products before the next camera frame is captured. The following operations are carried out on the server station in real time:image geo-rectification and projection,identification of temperature alarms (image processing),display of the geographic coordinates of detected hot spots and fire fronts.For every camera exposure the corresponding GPS and IMU data are automatically registered together with the image data to create a new Direct image geo-referencing is based on a) the combination of the GPS data for the positioning of the camera exposure centre, and b) the inertial measurements returning the camera's orientation angles at the time of exposure. The restored and ortho-rectified thermal or video images are projected to the reference cartographic projection system, and undergo a number of additional processing operations including global image thresholding, in order to detect areas with temperatures exceeding a predetermined value (hot spots). The generated temperature and hot spots map products are then combined with existing background and asset maps of the area under monitoring.3.Several demonstrations of the SITHON airborne imaging platform have been conducted during the project lifecycle. The first experiments were carried out in May 2005. During these operations new requirements for additional R&D developments were identified for enhancing system's capabilities meeting operational functionality needs. The system in its final configuration was flown over the Sithonia Peninsula of Chalkidiki in May 2006 . The sysDuring the demonstration campaigns the entire study area was surveyed by the SITHON system by capturing and processing acquisitions every 5-7 seconds. The exact time interval between successive acquisitions depended on the flying conditions . The computer system controlling the image capture during the flight was calculating and automatically adjusting the time interval between the successive frames. For as long as the level of recorded temperatures was within ordinary values the system was remaining in the so-called ‘silent mode’ sending to the server PC every processed and geo-referenced thermal image frame.2 on the ground as detected from 2,000 m and 1,000 m ASL is given in As long as the first hot spot event with a temperature above the predefined threshold limit was detected, the system turned immediately to ‘alarm mode’ and the aircraft staff was alerted to the danger by a sound alarm. At the same time, the geographic coordinates of the fire event were shown on the display, indicating the existence and location of the fire as in 4.The design and operation of SITHON, a fully digital airborne thermal imaging system integrating INS/GPS and a digital camera has been described and its demonstration results have been discussed. During the operations it was demonstrated the system's configuration robustness for secure processing and provision of results in real time while it is in the air, supporting the fire managers and fire fighters. Yet, most of the airborne platforms are mainly being used to drop water and retardant on top of fires. The present developments allow the command and operations control centre to pinpoint the path of the airborne sensor on a map and depict the evolution on the fire fronts during fire fighting. During system development the motivation behind engineering design was to meet the need of fire managers to follow in detail the magnitude of emergency, and also to run battling scenario online. For this purpose timely positioned and projected thermal images as well as video data streams rapidly integrated in the GIS systems operated by the Crisis Control Centres have to be available in an efficient manner. These issues were well solved and demonstrated by operating SITHON.Some other issues still lay on the data link communication, which needs to be solved independently from place to place, as the legislation framework, and bandwidth permissions for establishing adequate air-ground data links between the airborne platform and the Crisis Control Centres vary with the country/region. Another remaining issue is the integration of cartographic projection systems, which are used in the various countries/regions wishing to operate the system. It is considered that both issues are easily resolvable in collaboration with the Authorities wishing to operate the system, by licensing the deployment of common wireless air-ground communication and providing access to the full set of their cartographic projection systems used .The conducted experiments have also shown that ortho-rectification in the air for real-time transfer of thermal images to the ground does not require any precise and fine resolution elevation model (DEM) of the observed area, considering also the rough positioning accuracy of the thermal sensor (∼50 m) provided by the single use of the camera GPS receiver. If this operation mode is selected, the use of a globally available DEM such as the SRTM data with a cell size of 90 m and cell height accuracy of ∼10-15 m is considered sufficient. However, if off-line stereo-pair image processing is requested for burn scar mapping and damage assessment using data from a GPS base station operated on the ground, then it is of utmost importance to use high quality DEMs in order to obtain the appropriate mapping accuracies.Today the disaster management and social security community can profit from the technological advancements, enabled by the combined use of image processing, navigation, and Earth Observation technologies, with the existing and planned sensor systems of high observing sensitivity, and airborne platforms in particular UAVs. For these purposes it is envisaged that the SITHON system will be operated onboard multitude airborne platforms including the fire brigade airplanes and helicopters as well as the UAV platforms owned and operated by the Greek Air Forces. In this context the authors are in discussion with the Civil Protection and Air Forces authorities in Greece and other south European Mediterranean countries, for flying the SITHON airborne system during the crisis situations imposed by wildfires and flooding. Through national and European projects the authors are committed to assisting and improving the development of these supporting technologies so that they are operationally used by the disaster management community.


The frequent appearance of empirical rank-frequency laws, such as Zipf’s law, in a wide range of domains reinforces the importance of understanding and modeling these laws and rank-frequency distributions in general. In this spirit, we utilize a simple stochastic cascade process to simulate several empirical rank-frequency distributions longitudinally. We focus especially on limiting the process’s complexity to increase accessibility for non-experts in mathematics. The process provides a good fit for many empirical distributions because the stochastic multiplicative nature of the process leads to an often observed concave rank-frequency distribution  and the finiteness of the cascade replicates real-world finite size effects. Furthermore, we show that repeated trials of the process can roughly simulate the longitudinal variation of empirical ranks. However, we find that the empirical variation is often less that the average simulated process variation, likely due to longitudinal dependencies in the empirical datasets. Finally, we discuss the process limitations and practical applications. Rank-frequency laws, such as Zipf’s law and more generally power laws, have been observed in a multitude of domains ranging from the intensity of wars to the populations of major cities Historically, empirical rank-frequency distributions became a focus of research as the ubiquity of the power law in many of these distributions became apparent. A famous example being Zipf’s observations relating word frequency to word rank in natural language texts However, as far as we know these novel approaches have not examined the longitudinal variation of empirical rank-frequency distributions. Furthermore, many of these approaches understandably focus on rank-frequency distributions with power law like bodies . In contrast, we simulate several empirical rank-frequency distributions by using a simple stochastic cascade process (hereafter the fracturing (FT) process). The FT process is a stochastic multiplicative process that produces a concave rank-frequency distribution , due to an underlying relationship with the gamma distribution. In addition, the FT process cascades a fixed finite number of times and contains a minimum size constraint thus replicating finite size effects. Finally, we show that the FT process can roughly simulate the longitudinal variation of empirical ranks through repeated trials of the process. In other words, each FT process trial can represent an observation of the dataset at a specific point in time.Importantly, we emphasize the practical application of the FT process rather than detailed mathematical derivations. Furthermore, we hope that the process’s simplicity will allow non-experts to understand the process and help illustrate how even a simple process can give rise to a variety of rank-frequency shapes.To start we give a brief overview of the FT process. Essentially the process simulates the repeated fracturing of an interval . The process begins with a single unit interval at time step 0, and at every time step The FT process is highly related to fracturing  processes studied extensively by physicists and mathematicians We utilize the FT process to simulate six empirical datasets to illustrate the types of datasets well represented by the process. The empirical datasets focus mostly on consumer popularity and are as follows:French book sales volumes in 2003 US theatrical earnings in 2002 US last name frequency of census respondents in the 2000 census Artist play frequency of Audioscrobbler music plugin as of May 2005 YouTube video request frequency originating from the University of Massachusetts Amherst campus network during several dispersed observation periods in fall 2007 to spring 2008 US magazine circulation revenue estimates in 2000 Furthermore, in order to establish the strengths of the FT process in relation to other popular models, we also fit a classical one parameter power law model and the previously mentioned novel discrete generalized beta distribution (DGBD). The power law and DGBD models were fit using multiple linear regression on the log-log transform of the models, in an approach similar to Similarly, the log-log transform of the FT process was fit to the datasets by manually maximizing the coefficient of determination  at each rank over the entire data period. The coefficient of variation is a common normalized variation (or dispersion) measure defined as the ratio of the standard deviation to the mean. In cases where the number of ranks varied during different years, the CV was calculated only up to maximum common rank of all observations. In both the empirical distributions and FT process, the very high variation of the initial ranks is due to large outliers which, by definition, should appear at the head of rank distributions. Often these outliers are the combined result of several rare conditions or factors. For example, the movie Avatar earned significantly more than any other movie released between 2002 and 2012 due to a combination of excellent release timing, weak competition, 3D technology hype, higher 3D tickets prices, and a world famous director In contrast, in empirical distributions small outliers at the bottom ranks are generally limited by the data collection methodology or limits of the real-world process. Whereas, in the FT process small outliers are limited by the underlying gamma distribution skewness and the minimum interval size constraint. Furthermore, the slow increase in variation throughout the middle ranks is due to the differences in the mean and standard deviation slopes. In general, the variations of the empirical datasets are lower than the average FT process variations. Broadly, we can categorize these empirical dependencies into either direct or indirect dependencies. A direct dependency implies that the same rank value spans several longitudinal observations. A notable example is the first rank of the US magazine circulation revenue dataset, which In any case, the magnitude of the empirical variation will generally be smaller than the FT process average variation and this should be taken into account when utilizing the FT process.A significant limitation of the FT process is that the process can only create rank-frequency distributions with reciprocal head and tail slopes (ignoring the minimum size limit). This limitation is inherent in the FT process itself due to the process’s common fracturing point distribution. This limitation could be addressed by utilizing different fracturing point distributions for different fractures depending on the magnitude of the interval. However, this addition would add significant complexity to the process, thus potentially undermining the processes strengths of simplicity and understandability. We leave this exploration for future work.An important question is whether the FT process roughly mirrors the real-world processes of the studied datasets or whether the process merely happens to produce similar rank-frequency distributions.Historically, researchers have described many different processes that produce particular rank-frequency distributions. Ref. In the case of US theatrical earnings, each process cascade could be interpreted as an individual (supply side) business decision or event that determines the combination of resources  devoted to each movie. For example, the initial cascade could represent the division of gross movie industry resources into movie studio alliances. A similar argument can be made for the French book sales data and music popularity data and several other datasets.Realistically though, many of these behavioral based databases might be more accurately represented by a (demand side) detailed preferential attachment process. Such processes have been used utilized extensively to model human social networks The definition of the FT process ranks as a set of goods in a single marketplace, as in the French book market, allows for experiments in market dynamics. For example, we simulated the merger of four identical French book markets, with each market based on the 2003 French book dataset, into a single large market. In practical terms, we compared the combined and resorted ranks of four FT process simulations against a single larger FT process simulation. These results align with theories that postulate that market integration will increase the so called “superstar” effect. From an FT process viewpoint, this integration implies a larger overall market and several additional fracturing steps. If the fracturing process remains unchanged, increasing inequality is an inevitable consequence.Often in practice, the full set of empirical ranks is not available due to, for example, privacy concerns or business confidentiality reasons. In cases where only the head ranks are available the decision over which model or process to utilize becomes much more difficult. In economic situations, the underlying supply and demand side effects can give hints as to the tail behavior. For instance, the French book sales and US theatrical earnings datasets both have significantly truncated tails. This tail behavior is potentially related to physical distribution bottlenecks and high marginal inventory costs.  and reciprocal head and tail slopes. Furthermore, the FT process can simulate the longitudinal variation of empirical datasets since the process’s longitudinal variation roughly follows the same shape as many empirical datasets variations.In terms of further practical applications, rank-frequency models are increasingly being applied in empirical economics research For instance, predicting the magnitude of the first few rank elements is typically difficult due to high variation. As mentioned, by definition, the outliers of the underlying size-frequency distribution will be placed at the ends of the related rank-frequency distribution. However, an accurate prediction of these first ranks is useful in, for example, quantitative financial risk analysis and supply/capacity management. Imagine a situation with only two previous longitudinal observations, an obvious method to predict future ranks is to average the previous two observations.The confidence placed in these predictions should be based on the expected variation of these ranks. In the absence of variation information from a similar business sector, a general variation estimate based on the FT process could be utilized as a starting point. We leave these additional examples and methods for future work.With regard to overall understandability, the FT process has real-world analogues such as the repeated fracturing of rocks into sediment that are easily observed and understood. Furthermore, the fitting parameter can be understood as an analogue to the physical distribution of force causing the fracturing. In other words, the fracture will probably (though not certainly) occur where there is the greatest application of force over area (pressure).Finally, in terms of transparency, a formal and full mathematical treatment of the FT process is still needed.The FT process starts with a single unit interval which is then fractured into two intervals with size R is the standard uniform random variable. Each of these two intervals is then similarly fractured into two smaller intervals to create four intervals. This recursion continues until the final time step after which there are where The shape of the resultant rank-frequency distribution is determined by the fitting parameter, The FT process also imposes a minimum size for the generated intervals. This constraint helps simulate real-world limitations and is specific to the empirical dataset being fit. For example, a bookstore does not typically sell fractions of a single book. In In practical computational terms, the FT process naturally lends itself to a recursive implementation. We provide a simple recursive open source licensed implementation in Perl as a supporting information file (Supporting Code S2).The discrete generalized beta distribution represents a useful comparison and reference point. Ref. where The power law model represents a classic one parameter model. The parameter fitting was performed through a similar multiple linear regression method as the DGBD fitting and the natural log transformation iswhere The weighted coefficient of determination  of interval sizes from a single FT process trial (since the rank function is a simple transform of the corresponding cumulative distribution function (hereafter CDF)). Unfortunately, the resultant interval sizes from a single FT process trial are by definition interdependent. This interdependence results in a non-standard distribution  where Interestingly, this form shows that, in this special case, the natural logarithm of the size of an interval Click here for additional data file.Code S1Recursive Implementation of FT Process in Perl.(PL)Click here for additional data file.


This research is concerned with a methodology for automated generation of polyhedral building models for complex structures, whose rooftops are bounded by straight lines. The process starts by utilizing LiDAR data for building hypothesis generation and derivation of individual planar patches constituting building rooftops. Initial boundaries of these patches are then refined through the integration of LiDAR and photogrammetric data and hierarchical processing of the planar patches. Building models for complex structures are finally produced using the refined boundaries. The performance of the developed methodology is evaluated through qualitative and quantitative analysis of the generated building models from real data. Hence, the generation of a Digital Building Model (DBM) has been one of the key research topics in both the photogrammetric and computer vision communities. Significant research related to this topic has been implemented for the last two decades. Aerial imagery has traditionally been one of the preferred data sources for DBM generation, where a variety of approaches have been investigated and developed using either single image, stereo-image pair, or multiple images. The approaches utilizing single images are only effective for simple buildings ,2. Thus,LiDAR (Light Detection and Ranging) systems, on the other hand, directly provide accurate and highly dense surface information without the need for feature matching in overlapping strips. Thus, several researchers have been interested in the utilization of LiDAR data for DBM generation –14. In sIt is well known that image and LiDAR data have complementary characteristics, which would lead to a higher level of automation and more reliable DBM generation . TherefoThis paper proposes a new methodology for automated DBM generation while overcoming the problems in the previous research. Complex building structures, whose rooftops can be represented by several planar patches bounded by straight lines, will be the main focus in this research. The planar patches might have different slopes and aspects. Since it is hard to represent complex building structures by pre-defined building models or building parts, this research will reconstruct polyhedral models through a data-driven approach. To achieve reliable building models for complex structures, this research focuses on the solutions of several problems. More specifically, geometric and spectral constraints are introduced to determine precise boundary segments. Moreover, a solution for the occlusion problem in large scale imagery over urban environment is suggested through hierarchical processing of building primitives . A flow diagram of the proposed DBM generation procedure is depicted in 2.The proposed method starts with building hypothesis generation  which differentiates buildings from other objects  within the dataset. Since elevation data is directly acquired by a LiDAR system, the degree of automation in building detection using this type of data is higher when compared to that using imagery . Hence, A generated building hypothesis might be composed of several connected planar patches. Therefore, the segmentation procedure suggested by  is carriHence, there is need for the improvement of the initial boundaries of the building primitives to acquire a precise building model. Since the building primitives produced have accurate plane parameters, a precise boundary segment for a ridge line can be generated by intersecting two adjacent building primitives if any exist. The intersection of the building primitives that are almost parallel and/or coplanar is avoided by checking the angles between the surface normal vectors of the primitives since this would lead to a weak intersection. 3.Precise boundary segments for the remaining portions of the building boundaries will be derived through the integration of LiDAR data and stereo imagery. This procedure will be carried out through several steps: 1) Co-registration of LiDAR and image data; 2) Warped image generation; 3) Straight line detection; 4) 3D line matching; 5) Grouping of matched 3D lines; and 6) Precise boundary segment selection. These steps will be explained in the following paragraphs.3.1.As a prerequisite of the integration procedure, the co-registration of the imagery and LiDAR data to a common reference frame is carried out. To ensure the best quality of the co-registration procedure, the LiDAR data is utilized as the source of control for the image geo-referencing. Since it is almost impossible to identify distinct LiDAR points, which can be recognized in the imagery, segmented planar patches and extracted linear features from the LiDAR data are utilized as the source of control for the geo-referencing of the aerial imagery .3.2.It is well know that large scale imagery over urban areas has significant relief displacement and geometric distortions which are factors that make image matching difficult and unreliable. To resolve this problem, we decided to incorporate LiDAR data into the matching procedure as a constraint. Let us assume at this stage that two orthophotos are generated by using a stereo-image pair and LiDAR data . Since the ortho-rectification procedure eliminates perspective distortions, features in one orthophoto will be directly compatible with their conjugate features in the other orthophoto. Hence, the feature matching process using these orthophotos will be much easier and more reliable compared to the process using the original imagery. However, this research will not generate a complete orthophoto for each of the images of a stereo-pair. Instead, we will generate pseudo-orthophotos that only rectify a portion of the image that includes the building primitive under consideration. These pseudo orthophotos will be denoted as “warped imagery”. In this case, the agreement of the features in the warped imagery will exist only along the rooftop patch.l, dl, el, and fl); see r, dr, er, and fr). Then, the grey value at the projected image location  at the position, dl in the left image) is assigned to the corresponding location of the object point  on the building primitive plane  beyond the derived initial boundary while considering the resolution of the LiDAR data. Object points, which are regularly spaced according to the nominal Ground Sampling Distance (GSD) of the aerial images, within the range of the building primitive plane in question are then projected onto the corresponding image plane using the collinearity equations and the established geo-referencing parameters. For example, the object points, B, D, E, and F along the LiDAR plane are projected onto the corresponding image points in the left image  & g(dr), g(el) & g(er), and g(fl) & g(fr)). The degree of similarity for a point that does not physically belong to the building rooftop  and (br) in As can be seen in the figure, the degree of similarity between the two warped images  for a location on the rooftop of a building primitive will be high since the corresponding points in the left and right images are conjugate; refer to points D, E and F and their grey values on the warped images  and the normal distance (nd) between these segments are smaller than given thresholds  on either side of each of the group members in the left and right warped images is investigated. The precise boundary segment will be defined as the line segment where we have the biggest transition from high to low spectral similarity measures among the line segments in each group. In other words, the line segment which has the largest difference between a high spectral similarity measure on one side and a low spectral similarity measure on the other side will be chosen to be the precise boundary segment.2 is bounded by L1 and L2. Also r3 is bounded by L2 and L3. Additionally, two more regions, r1 and r4, are defined by outermost lines and pre-determined buffers . Afterwards, each line segment divides the aggregated regions  into two parts. For example, L1 defines two regions, R1_In (= r1) and R1_Out (= r2 + r3 + r4), as shown in i_In and Ri_Out (for the ith line segment), using i_RASSM is the average spectral similarity measure for a region on either side of the ith line segment in the group under consideration. tSSM is the spectral similarity measure for a certain point. m is the total number of cells in a certain region along the building primitive plane (or warped image plane). n is the total number of line segments in the same group.More specifically, the spectral similarity measure at a given location along the building primitive plane (or warped image plane) is defined as the cosine of the angle between the Red Green Blue (RGB) colour vectors  at the sOne should note that some of the building boundary portions might not have precise boundary segments from the integration process due to the failure of 3D line matching process. Such a failure comes from the occlusions where other higher building primitives or trees might hide the building primitive in question either partially or fully. 4.The remaining portions of the initial boundary corresponding to the occlusion areas caused by higher building primitives sharing vertical walls with the ones in question see  can be pAt this stage, one should note that there might be portions of the initial boundaries which have not been refined. This might happen when higher building primitives or trees partially or fully hide lower and non-adjacent building primitives in the imagery see . The rig5.So far, precise boundary segments have been established through the procedures mentioned above. One should note that the established segments are not connected to each other. This section will, hence, introduce a procedure to make a closed polygon using these segments. This procedure begins by establishing the proper sequence of the established boundary segments for each building primitive, by investigating their proximity to the ordered chain of vertices along the initial boundary for that primitive. To construct a closed-polygon for a given building primitive, an intersection procedure is implemented to connect neighbouring boundary segments according to their established sequence. The boundary refinement and closed-polygon generation procedures are carried out for the individual building primitives one by one starting from the highest building primitives and proceeding to lower ones. The automatically generated DBM might include incorrectly detected boundary segments. Two examples of erroneous boundary segments are shown in To edit incorrectly established boundary segments from the automated process, a manual mono-plotting procedure is introduced. The operator interactively deletes or adds boundary segments to acquire complete building models. More specifically, the measurements of the end points for the erroneous boundary segments are done in one image and a mono-plotting procedure is used to directly project these measurements onto the plane of building primitives using the established geo-referencing parameters. It should be noted that the operator does not need to precisely measure the end points of the boundary segments . The end points of the boundary segments will be precisely defined through the automated closed-polygon generation procedure.6.Experiments with real LiDAR and image data are carried out to evaluate the performance of the proposed methodology. The LiDAR dataset and a stereo-pair were acquired by an Optech 3100 system and RC30 analog camera, respectively. The stereo-pair has a scale of 1:5,000 and was digitally scanned at a resolution of 12 microns, resulting in a Ground Sampling Distance (GSD) of 6 cm. The Interior Orientation Parameters (IOPs) were provided in a Camera Calibration Certificate (CCC) and the Exterior Orientation Parameters (EOPs) were determined through the proposed co-registration procedures in Section 3. The average point spacing for the LiDAR data is approximately 0.75 m (about 1.3 points per square meter). In the next processing phase, the initial boundaries of the building primitives are refined through the precise boundary segment derivation. The precise boundary segments are derived from the integration of LiDAR and photogrammetric data and hierarchical processing of the building primitives. Once all the boundary segments for a building primitive have been generated, a closed-polygon is generated using these boundary segments. Finally, all the boundary segments of the closed-polygons in the study area are aligned simultaneously. The descriptions, values, and justifications for the utilized thresholds in the precise boundary segment derivation are listed in The performance of the proposed precise boundary segment derivation procedures can be verified by visually checking the closeness of the automatically produced boundaries to the actual building primitive boundaries. Three building primitives are selected to assess the performance of the boundary refinement procedure for different levels of building complexity. This part of the experimental results provides a quantitative evaluation of the correctness, completeness, and accuracy of the proposed automated DBM generation process. The correctness and completeness measures, The correctness measure evaluates the percentage of erroneous boundary segments among the established boundary segments. On the other hand, the completeness measure gives an indication of the percentage of missing or erroneously established boundary segments. The study area has a total of 40 building primitives, which are represented by 291 boundary segments. The proposed procedure produced 311 boundary segments for all the building primitives. Among the boundary segments produced, 276 boundary segments were correctly established. Based on these numbers, the correctness and completeness measures for this study area are 89% (276/311) and 95% (276/291), respectively. Several researchers have used the correctness and completeness measures to evaluate the quality of their DBM reconstruction. The correctness of 80% and the completeness of 94% in a per-pixel evaluation were achieved by . MoreoveAs for assessing the accuracy of the automatically established DBM, the coordinates of the DBM corner points are compared with those derived manually using a photogrammetric reconstruction procedure. To get an idea of the quality of the manually derived coordinates, two operators were asked to derive the 3D coordinates of the vertices of the building rooftops in the study area. The second column in Having established the expected accuracy from a manual operation, the coordinates derived from the proposed procedure were compared with the average of the coordinates determined by the two operators. The statistics derived from this comparison are reported in the third column of The heights of these fences range from 0.5 m to 1.0 m. The operators defined the corners of the DBM on top of the fences (the figure shows the points selected by the operators), whereas the proposed procedure placed the corners on the rooftop plane, as defined by the segmented LiDAR data. Therefore, the mean comparison shows a Z-bias between the manually and automatically generated vertices . The standard deviation in the Z-direction reveals good compatibility between the manual and automated procedures.7.This research proposed a new methodology for automated generation of polyhedral building models for complex structures with horizontal and tilted rooftops, which are bounded by straight lines. The key contributions of this research in the building reconstruction procedure are the precise boundary segment derivations from two processes, namely, one through the integration of photogrammetric and LiDAR data; and the other one through the hierarchical processing of building primitives.An object-based integration of photogrammetric and LiDAR data has been carried out in one-step by introducing warped imagery without handling photogrammetric and LiDAR data separately. The image matching ambiguity was significantly reduced by utilizing warped imagery since such imagery does not have relief displacement and geometric distortions. Moreover, the utilization of warped imagery for feature matching process took an advantage of both higher planimetric accuracy of the image-based reconstruction and higher vertical accuracy of LiDAR data. In addition, spectral similarity transitions across the matched line segments in the warped imagery were investigated to select precise boundary segments. The hierarchical processing of building primitives was proposed to reconstruct boundary segments in occluded areas where higher building primitives hide lower and neighbouring primitives. Precise boundary segments have been acquired for such occluded areas by projecting the boundary segments constructed for higher building primitives onto the lower and neighbouring ones.Qualitative analysis was performed by visually inspecting the constructed boundary results. The visual inspection proved that the proposed building reconstruction procedure performs well for complex and connected buildings. Quantitative analysis was also carried out based on the completeness, correctness, and RMSE analysis. The correctness and completeness ratios for the study area were 89% and 95%, respectively. The performance of this research is slightly higher compared to other studies. Missing or erroneous line segments can be edited through an introduced simple manual mono-plotting work; then, complete building models can be easily acquired. In addition, the coordinates of the DBM corner points were compared with those derived manually using a photogrammetric reconstruction procedure to assess the accuracy of the established DBM. The RMSE analysis found that the DBM produced was quite close to the results obtained manually.Future work will focus on the alleviation of the effects of shadow and uniform textures on both sides of a boundary segment. Moreover, the building reconstruction procedure will be expanded to incorporate more than two images. Finally, this approach will be extended to manipulate non-planar surfaces, which might not be bounded by straight lines.