All 3D isocentric errors in the study were 0.3 mm or less. The median x and y laser alignment coordinate error was 0.09 mm, and 94% of the time the x and y laser error was ≤0.25 mm. A phantom test showed that the system can make submillimeter end‐to‐end accuracy achievable, making a conventional linac a “Submillimeter Knife”.The Stereotactic Alignment for Linear Accelerator (S. A. Linac) system is developed to conveniently improve the alignment accuracy of a conventional linac equipped with stereotactic cones. From the Winston‐Lutz test, the SAlinac system performs three‐dimensional (3D) reconstruction of the quality assurance (QA) ball coordinates with respect to the radiation isocenter, and combines this information with digital images of the laser target to determine the absolute position of the room lasers. A handheld device provides near‐real‐time repositioning advice to enable the user to align the QA ball and room lasers to within 0.25 mm of the centroid of the radiation isocenter. The results of 37 Winston‐Lutz tests over 68 days showed that the median 3D QA ball alignment error was 0.09 mm, and 97% of the time the 3D error was PACS numbers: 87.53.Ly, 87.55.Qr For normal clinical use, the XKnife System accuracy requirement is a radial distance of 1.5 mm for the couch mount Winston‐Lutz test. Radial distance is only in two dimensions (2D), so the corresponding three‐dimensional (3D) requirement may be 2.1 mm . This is seven times greater than the theoretical result. Was the theoretical result too optimistic? Since the standard deviation of the Low study was twice as large as the actual result, there must be significant variation even in the research setting. It is possible to meet the specification and still be misaligned by 2 mm in just the isocenter alignment QA test alone. Therefore the end‐to‐end misalignment could be substantially greater than 2 mm due to various parameters like misalignment between laser target pointer (LTP) and laser target localizer frame (LTLF), misalignment of head frames, uncertainty in the CT scan, couch axis wobble, gantry skew, gantry lean, laser divergence, misalignment of ion chamber during commissioning, and other factors. Such a large misalignment could undermine the accuracy needed for SRS.The difference between theoretical accuracy that research papers present and the actual accuracy achieved in normal clinics may sometimes be too large. For example, Low et al.1 showThe situation can be exacerbated when physicians draw extremely tight margins with the high expectation of accuracy in the stereotactic system. Furthermore, the penumbra of stereotactic cones is a lot sharper than a multileaf collimator or jaws, so the dosimetric impact of geometric misses is more severe than for conventional radiation therapy treatments. There is not as much blurry penumbra in the treatment that could at least provide some amount of dose to the missed part of the tumor. For extremely small cones like 5 mm, if the alignment is off by more than 2 mm, the treatment could be much less than optimal.(–) there has been continual progress toward developing systems with improved accuracy.(–) In addition, a few authors have shown that with some of the stereotactic systems it is possible for diligent physicists to beat the system specifications.(–) This is a remarkable achievement, but it doesn't imply that other clinics can routinely achieve better accuracy than the system specifications. If the isocentric alignment specification of the XKnife system could be tightened from 1.5 mm to 0.25 mm, it should make a submillimeter end‐to‐end specification possible. Therefore, the goal of this research is to develop a method that can inexpensively, conveniently and reliably enable users to achieve submillimeter (0.25 mm) radiation isocenter alignment accuracy in a normal clinical setting with minimal changes to the existing hardware and procedures, while providing explicit, concise feedback that clearly warns if the desired accuracy specification is not being met.Since the inception of linac‐based stereotactic systems–4 thThe Stereotactic Alignment for Linear Accelerator (S. A. Linac) system is designed to work with any conventional gantry mounted linac with stereotactic cones. A Radionics XKnife system  was used to test the SAlinac system in this study. It is assumed the reader has familiarity with stereotactic systems; therefore, only components of XKnife necessary to understand the new modifications are discussed in detail. Winston‐Lutz films were scanned with a Microtek ArtixScan 1800f flatbed scanner . The ArtixScan 1800f is a 48‐bit scanner with a glassless film tray, which suspends the film in a holder so there is no chance of artifacts reflecting from a glass tray. The SAlinac program estimates the 2D ball coordinates of each shot from the scanned film, and performs 3D reconstruction of the ball coordinates. A 12.5 mm cone was used because it is easier to visualize QA ball misalignments manually, although the SAlinac program can process results for larger cones.Three Canon PowerShot S3 cameras are used in the SAlinac system to capture digital images of the lasers impinging the laser target. The cameras are mounted near the room lasers on the left wall, the right wall and the ceiling. A laser target cube (LTC) was constructed, which is similar to the Radionics LTP except it has a laser target on three sides so that all three cameras can see the lasers simultaneously. The SAlinac program estimates the 2D laser coordinates relative to the target from the images captured with the digital cameras.A Dell Precision Workstation with the Microsoft Windows operating system is used as the server and, for convenience, the results are transmitted from the server via an 802.11 wireless network to an HP iPAQ or Dell Axim handheld unit. The Winston‐Lutz test usually takes less than a minute to process, and each laser image takes a second or two to process.The SAlinac system was first used on a Varian 600C linac  at Mercy Hospital in Scranton, Pennsylvania. At that stage of the research we did not yet have the laser alignment portion of the system, so although the Winston‐Lutz analysis was very accurate, it was inconvenient to try to manually position the laser target and QA ball more accurately at the isocenter, and there was nothing to help align the lasers to the isocenter. The system was also tested briefly on a Varian 2100C/D at Albert Einstein Medical Center in Philadelphia, Pennsylvania. The results presented in this study are all from a Siemens Mevatron MXE 2  at Christiana Care Hospital in Newark, DE. We began a study with GAFCHROMIC EBT film , but it requires at least 200 to 300 MU to obtain a reasonable image, and the scanned image was not as good as for XV film. For the Winston‐Lutz tests in this study, we exclusively used XV film and 50 MU per shot to first discover the best attainable accuracy with the system. Subsequent studies can be performed to determine if 0.25 mm accuracy is also consistently attainable with other media, especially GAFCHROMIC film and the EPID.The SAlinac system was tested with various forms of radiographic media. The best accuracy was obtained with Kodak XV film and 50 monitor units (MU) per shot. In the past we did some Winston‐Lutz tests with TL film exposed with 5 to 10 MU per shot, but the images from TL film were noticeably grainier, which tends to degrade accuracy. Occasionally we have used EDR2 film, which provided similar accuracy as the XV film, but required about 200 MU for a good image. For convenience, the algorithms could be generalized to process an image from an electronic portal imaging device (EPID) instead of data from the film scanner.,13 WThe coordinate system is defined with respect to a supine patient with the head towards the gantry. Consistent with the Radionics XKnife notation, we define a right‐handed 3D coordinate system with origin at the linac's radiation isocenter, such that the positive x‐axis is toward the patient's left, the positive y‐axis is superior (towards the gantry), and the positive z‐axis is anterior (towards the ceiling). Consequently, the acquired 2D laser target images and Winston‐Lutz shots are in beam's eye view (BEV) orientation, with the positive y‐axis toward the gantry. When the gantry is in the anterior to posterior (AP) position, the 2D positive x‐axis of the BEV coincides with the x‐axis of the 3D coordinate system.The Winston‐Lutz tests in this study are all taken with default collimator and couch angles, because during treatment we correct for couch axis wobble by realigning the ceiling laser to the LTLF frame at each couch angle. Residual couch axis misalignments are beyond the scope of this study, although the SAlinac program does have a freestyle mode, which will estimate the x and y ball coordinates of each shot for any combination of gantry and couch angles; the user can manually determine the interpretation of the x and y ball coordinates for each individual shot. Whenever one of the four predefined “Shot Styles” listed in Table The simplest Winston‐Lutz test is a three‐shot test consisting of a shot from the patient's left (LT), AP, and the patient's right (RT). Even though linacs typically have a counterweight to offset the weight of the collimator, on some older linacs there is measurably greater wobble in the AP position than in the posterior to anterior (PA) position. For this reason, whenever possible we use the “Laterals + AP/PA” shot style from Table Bx, By, and Bz, and the 2D x and y coordinates of each shot of the Winston‐Lutz tests are defined as in Fig. The 3D QA ball coordinates with respect to the radiation isocenter are denoted Based on the orientation described in the preceding section, we define the gantry skew about the axis of gantry rotation ascX over AP and PA as well. However, the potential wobble on the AP shot could induce more error instead of improving the estimate. Furthermore, the definition in Eq. Since we usually also include a PA shot, we could have averaged cY asWe also compute another gantry skew parameter along the y‐axis cY skew, we monitor cY as a measure of consistency of the individual y‐axis shot coordinate measurements. The sag due to gravity on the gantry could be denoted cZ, but instead it is just labeled “sag,” which is a more descriptive name. We define AP sag and PA sag asSince we have not yet encountered a linac with a significant  For simplicity, we define the desired target point within this trajectory as the “isocenter.” The primary deviation from the isocenter along the x‐ and z‐axes is due to cone misalignment or gantry skew, which may be correctable, as shown in the Results section below. The primary deviation from the isocenter along the y‐axis is gantry sag due to gravity, which cannot be easily changed. Some controversy exists regarding where the QA ball should be placed along the y‐axis; it could be either: a) centered at the lateral shots, b) centered between sagAP and sagPA, c) centered between the lateral shots and sagAP, or d) wherever else along the y‐axis the physicist desires. To accommodate all these opinions we define an additional parameter, sagcenter, that provides the physicist with the flexibility to center By anywhere along the y‐axis.To measure the isocenter with a resolution of 0.1 mm, the definition of “isocenter” must be properly qualified. It has been shown that the focal point of the linac is actually a trajectory as a function of gantry angle, rather than a single point.15 ForBx, By, and Bz will inherently measure ball position from the centroid of the linac radiation isocenter, adjusted by the desired sagcenter:err3d is the 3D Euclidean distance corresponding to the three components Bx, By, and Bz.The definitions we use for ball coordinates Bx, By, and Bz, but we have found these definitions to be more stable over the range of shot styles we use. For the three‐shot test without a PA shot, Eq. Bx=BxAP−cX, but for all other shot styles in Table Bx. For the five‐shot test with obliques, the BxPA parameter is approximated byθ=40° is sufficient to avoid collisions for most tumor locations. For consistency we always use θ=40° for five‐shot tests even though a smaller angle would often work.There are many other possible ways to define the ball coordinates sagcenter=(sagAP−sagPA)/2 to center By between sagAP and sagPA, which helps minimize the maximal radial distance over all shots. In clinics where only three‐shot Winston‐Lutz tests are used, it may be tempting to use sagcenter=sagAP/2, because this would make the three‐shot tests look better. However, that would push more of the error from sag to the PA shot, which would cause any treatment arcs below the horizontal plane to be further misaligned.We use This set of QA ball equations has been found to offer flexibility in Winston‐Lutz tests for virtually all cranial tumor locations, while maximizing consistency from one shot style to another. A consistent set of measurements is important, because the goal of the SAlinac system is to track and compensate for miniscule changes in gantry, collimator and laser positions.Rx, Ry, and Rz can be reconstructed as:The 2D and 3D laser coordinates are defined similarly to the QA ball coordinates. The 2D coordinates of laser position relative to the target are defined in Fig. W is to account for the fact that the ceiling laser is typically closer to the target than the wall lasers. Consequently the AP laser line is thinner, yielding better accuracy. Ideally, the variance of each laser position estimate should be measured over time and all lasers weighted appropriately. However, for this phase of the study we simply use W=3.The weighting factor The laser position relative to the target is not the desired quantity for alignment because the target is never exactly at the radiation isocenter. This fact confounds all efforts to align lasers to an intermediate reference point like the mechanical isocenter standard (MIS). Even if it were possible to perfectly align the lasers to the LTP on the MIS, the MIS is never exactly at the isocenter, so the lasers would still be misaligned. What we really want to minimize is the absolute laser position with respect to the radiation isocenter. In a manual alignment system, only relative laser position can be seen, which makes determination of the absolute laser position with respect to isocenter almost impossible. However, with computer‐assisted alignment, the 2D absolute laser positions can easily be determined as:The 3D absolute laser positions can be obtained by using these values as in Eq. Tx, Ty, and Tz:Equations The equations from the preceding sections would be sufficient if nothing ever moved. Instead of attempting to construct a more rigid mechanical system to reduce movement, a computer‐guided system to track slight laser, collimator and gantry movements and to provide the user with near‐real‐time repositioning advice to adapt to all these movements was created. This is accomplished through the use of state variables, which remember prior QA ball and absolute laser positions, and adaptively track them as the system components are being repositioned.τx, τy, τz are a memory of the previous target position Tx, Ty, Tz. Likewise the state variables αx, αy, αz and αxRT, αyRT, αzAP, αyAP, αxLT, αyLT are a memory of the previous absolute laser position Ax, Ay, Az and AxRT, AyRT, AxAP, AyAP, AxLT, AyLT.The state variables Typically the user starts a session in AlignTarget mode, in which the SAlinac program calculatesThe 2D relative laser positions as defined in Fig. If any lasers are out of alignment or if they had started to approach the 0.25 mm alignment goal in previous sessions, the user can switch to AlignLaser mode. At this point the QA ball position from the previous Winston‐Lutz test becomes irrelevant because the target has been moved. Therefore Eq. The state variables are a one‐step delayed estimate of their corresponding parameters. They are saved to disk as a backup after each new laser image or Winston‐Lutz test is processed.Whenever a Winston‐Lutz test is analyzed, the ball position is estimated as in Eqs. The SAlinac Winston‐Lutz analysis algorithm automatically finds the radiation shots and pinhole. The full width at half maximum (FWHM) contour around each shot is automatically generated, as well as a contour around each ball shadow. The 2D x, y QA ball coordinates of each shot are defined as the x, y coordinates of the centroid of the beam contour subtracted from the x, y coordinates of the centroid of the ball contour. The 3D QA ball coordinates and gantry parameters are then estimated as in Eqs. RGB=[0 0 0]) scribe lines and red (RGB=[255 0 0]) laser lines, and then automatically calibrates to the color of the closest lines it finds. The initial black and red colors are variables; so conceptually the program should also be able to blindly adapt to green (RGB=[0 255 0]) lasers, although green lasers were not available for this study. After the colors have been calibrated, the image is transformed into color distance space, where color distance is the square root of the sum of the squares of the color of each pixel relative to a reference color. The FWHM edges of lasers and scribe lines are measured in terms of color distance and from this the relative laser positions are estimated. The zero point used as the reference for the images is the centroid of the scribe lines. Equations (10) to (15) are then used to compute target position or absolute laser position, depending on whether the program is in AlignTarget or AlignLaser mode. Numerous safety checks are employed .For AlignTarget and AlignLaser modes, the algorithm automatically finds the laser target and lasers in the image. The red, green and blue (RGB) values of the image depend on the room lighting conditions which may vary from day to day, so the algorithm was designed to be adaptive. The algorithm initially looks for black  provides near‐real‐time repositioning advice over a wireless network, as shown in Fig. The PDA only shows information for the current selected mode. However, the widescreen monitor on the server is much larger, so the server's graphical user interface (GUI) shows QA ball position and measured gantry parameters, along with laser target position and the position of each laser. The server GUI also displays the results from Fig. www.DiversiLabs.com/radonc/stereotaxy/indexData.html to facilitate verification of the results. An evaluation version of the software may also be downloaded from the www.DiversiLabs.com website.It is difficult to verify the accuracy claims of various authors without access to the raw data. One of the benefits of the SAlinac system is that all images and results are archived in standard formats for easy access. The data for the series presented in this study is posted at The first step in preparing the Mevatron MXE 2 at Christiana Hospital for this research was to reduce the gantry skew. Many linear accelerators have a threaded cross‐brace that can be adjusted to tune out gantry skew. This type of adjustment should only be attempted by trained professionals, and an extremely accurate Winston‐Lutz analysis tool should be employed to ensure the effort is successful.The three‐shot Winston‐Lutz test in Fig. cX is still consistently less than 0.1 mm, as may be seen in Figs. We then placed the QA ball near the centroid of the isocenter as shown Fig. cX, cY, sagAP and sagPA are plotted in Fig. −0.004 mm, 0.04 mm, 0.36 mm, and 0.19 mm, respectively, all with standard deviations of 0.05 mm or less. Position of the QA ball is presented in Fig. ±1.5 mm to facilitate visual comparison of the new results to the existing 1.5 mm radial distance specification. The dashed grid lines represent the 0.2 mm accuracy goal.Gantry parameters Two series of results spanning 68 days are presented in this study. The first series began on 5/21/2007 after version 1.0 of the software was installed on a new computer and a few preliminary Winston‐Lutz tests had been done. A couch mount Winston‐Lutz test is shown for each patient; on days with more than one patient, there is more than one alignment test. The gaps in data in the figures are due to the fact that there were no SRS or stereotactic radiotherapy (SRT) patients in those time periods, so the system was not used. The second series began on 8/28/2007, after treatments resumed and the system was recalibrated. The first series of data includes 13 Winston‐Lutz tests with four orthogonal angles, and the second series of data includes 24 Winston‐Lutz tests with five shots, including the posterior oblique angles. The results of both series are very similar.It may be seen from the x‐axis of Figs. Absolute laser position estimates of all the lasers are presented in Fig. Estimator accuracy is difficult to determine when the exact location of the QA ball is not known. However, it is relatively straightforward to estimate precision and systematic error of the estimator, and these should help provide insight regarding the accuracy of the algorithm.cX and cY values are each an average of two estimates, so the standard deviation of the individual x, y estimates of each shot should be 2 times the standard deviation of the cX and cY estimates. The standard deviation of gantry skew parameters over the 37 trials was 0.044 mm for cX and 0.017 mm for cY. It is conceivable that some of the 0.044 mm variation in cX was actually due to the mechanical precision of this 15‐year‐old linac, and not entirely from algorithmic uncertainty. Therefore, the deviation of the cY estimates is probably a better indication of estimator precision, which is 0.017*2=0.024 mm.Precision of the algorithm can be estimated from a) the redundancy of the calculation of gantry parameters, and b) the mechanical precision of the gantry, as follows. The −0.04 mm over the 344 x and y values of the shots of these 37 Winston‐Lutz tests. Estimated bias is shown in Fig. −0.04 mm and the standard deviation of the x, y shot values is approximately ±0.024 mm. This −0.04 mm systematic error is consistent enough that it could be simply subtracted from the results to remove it, or subsequent versions of the algorithm may be able to reduce it.Systematic error (or bias) of the algorithm was estimated by processing all the Winston‐Lutz tests in this study upside down and backwards, and comparing the inverted results to the corresponding proper orientation results. The estimated bias is half the average difference of the inverted results, which was a median of Since the SAlinac system makes it possible to achieve 0.25 mm isocentric alignment accuracy using the couch mount, the MIS could now become optional. This could save 10–15 minutes of daily clinical time while still exceeding the accuracy of the MIS based system. from Standard Imaging  was used to assess the end‐to‐end accuracy of the SAlinac system. The Lucy phantom was loaded with 2.5 inch by 2.5 inch pieces of GAFCHROMIC film and CT scanned in the Radionics Brown–Robert–Wells (BRW) frame and localizer rods, as is done for patients. The CT was imported into the XKnife treatment planning system and the GAFCHROMIC film was contoured. An isocentric arc plan was generated, targeting the center of the film. The SAlinac system was used to align the QA ball and room lasers to within 0.25 mm of the radiation isocenter, as normally performed for patients. The Lucy phantom was attached to the LCMA, still in the BRW frame, and the SAlinac system was used to guide the LTLF frame to the isocenter. At each couch angle, the SAlinac system was used to realign the LTLF frame to the ceiling laser. The GAFCHROMIC films were scanned with the Microtek ArtixScan 1800f flatbed scanner at 300 dots per inch (DPI) and the results were analyzed in MATLAB . By comparing the beam center to the film center in Fig. x=−0.73 mm, y=0.27, mm, and z=−0.41 mm. The total 3D error is 0.87 mm.The Lucy phantom,16 fAligning the QA ball and room lasers to within 0.25 mm of the radiation isocenter can provide a substantial improvement in stereotactic alignment accuracy. However, there are still many other sources of alignment error that the SAlinac system has potential to solve. In the following sections, we discuss how the system can serve as the foundation for achieving submillimeter end‐to‐end accuracy.From a technical perspective, since now one can align the laser target and QA ball to within 0.25 mm of the isocenter, it is very straightforward to align the patient's tumor to the isocenter using a similar algorithm with the LTLF frame. The program tracks and compensate for misalignments between the LTLF frame and the LTC analogously to the way it tracks and compensates for misalignments of the lasers. This part of the system has not yet been used on patients, but phantom testing has proven the concept. The end‐to‐end phantom test of the SAlinac system with the Lucy phantom from Standard Imaging did achieve submillimeter end‐to‐end alignment accuracy as shown in Fig. For many linacs, the couch axis is the largest source of error in stereotactic treatments. Because of this, it is recommended to go back into the treatment room for each couch angle and realign the LTLF back to the ceiling laser. When the SAlinac system is used to align the LTLF to the isocenter, it could also be used to more accurately realign the LTLF back to the ceiling laser at each couch angle, as we did for the phantom test. When this technique is employed, great care must be taken to ensure that only the desired shift is made and that the tilt adjustment is not changed, especially for stereotactic systems that do not have a tilt lock.≤0.2 mm.Even when the lasers are aligned well at the isocenter, in most clinics they typically diverge from each other noticeably when measured a few centimeters out from the isocenter because they are not mounted perfectly onto the walls and ceiling. In this situation, aligning the LTLF to the lasers could induce a tilt such that realigning the LTLF back to the ceiling laser for each couch angle can actually misalign the patient's tumor away from isocenter. For this reason we precisely remounted our room lasers such that at 200 mm from the isocenter the laser divergence is smaller than our measurement ability – probably  Following the strategy of the rest of the SAlinac system, instead of trying to reposition the patient in the frame, we could compensate for the alignment error when positioning the LTLF frame to isocenter. Yaw can be compensated for by the appropriate couch rotation, and there is already a pitch microadjustment knob on the Radionics LCMA; a roll adjustment could also be added. Since the patient's skin is deformable, it would be best to make the measurements with a spring‐loaded digital gauge probe like the Gamma Knife Extend repositioning check tool , to ensure maximum reproducibility.Prior to every treatment with frame‐based stereotactic systems, we recorded a set of depth helmet measurements to ensure the patient has not moved. Since we have still never seen a set of depth helmet measurements that had all errors equal to zero, it is reasonable to conclude that the patient always does move at least slightly. It would be just as easy to enter these measurements into a computer program instead of writing them down in the chart, and a program could calculate x, y, z, and roll, pitch, yaw offsets.17 FolNo couch mount stereotactic system can avoid gantry sag, but the SAlinac system can at least center the treatment between the AP and PA sag. The residual misalignment is much less than one millimeter and, when properly centered, sag will tend to average out; our phantom test still achieved submillimeter end‐to‐end alignment despite the gantry sag.We have developed a new quality assurance system called SAlinac for precision stereotactic radiation therapy delivery. The SAlinac system demonstrates that, with the right combination of digital electronics and algorithms, it is possible to consistently achieve 0.25 mm isocenter alignment on a conventional linear accelerator in a normal clinical setting. This provides a systematic and convenient way to improve stereotactic alignment. Straightforward extensions of the system can provide comprehensive improvement of patient alignment in the future, and the phantom test shows that submillimeter end‐to‐end alignment can be achieved with this system.


We reverse engineer dynamics of financial contagion to find the scenario of smallest exogenous shock that, should it occur, would lead to a given final systemic loss. This reverse stress test can be used to identify the potential triggers of systemic events, and it removes the arbitrariness in the selection of shock scenarios in stress testing. We consider in particular the case of distress propagation in an interbank market, and we study a network of 44 European banks, which we reconstruct using data collected from banks statements. By looking at the distribution across banks of the size of smallest exogenous shocks we rank banks in terms of their systemic importance, and we show the effectiveness of a policy with capital requirements based on this ranking. We also study the properties of smallest exogenous shocks as a function of the parameters that determine the endogenous amplification of shocks. We find that the size of smallest exogenous shocks reduces and that the distribution across banks becomes more localized as the system becomes more unstable. This research began in the year 2000 with the work of Allen and Gale, who showed that the topology of financial networks influences financial contagion4. Many different algorithms have since then been developed to model the propagation of distress between banks under different assumptions as well as to study the relation between the structure of a financial network and its stability (see for instance21). In this respect, significant progress has been made in the identification of the main drivers of financial contagion and in the design of new stress test frameworks that, at odds with standard micro-prudential tools, do account for interactions between banks26.Systemic risk – the risk associated with the occurrence of a catastrophic breakdown of the financial system – arises endogenously from interactions between the participants that operate in financial markets. Because some types of interactions between financial institutions (in the following banks for brevity) can be modeled in terms of dynamical processes on networks, a growing body of literature has focused on the study of contagion and distress propagation in financial networksWhile the focus of research carried out so far has been mainly that of developing models to understand how exogenous shocks are amplified by the endogenous dynamics of the system, here we look at the reverse problem. We compute the time trajectories of smallest shocks that need to affect banks to produce a final loss of equity larger than a given threshold, which we therefore refer to as worst case shocks. The solution of this reverse problem is useful to identify stress scenarios whose occurrence would lead to systemic events, thus identifying the vulnerabilities of a financial system.At the level of individual institutions, reverse stress testing is a regulatory requirement in the United Kingdom (UK) and the European Union. The Financial Services Authority, one of the UK’s financial regulators, describes it as a complementary exercise to general stress and scenario testing. In standard stress testing a forward-looking methodology is employed, in which scenarios are selected to predict their potential impact upon the financial health of banks. Reverse stress testing on the other hand looks backward by identifying the scenarios that cause a specific loss to a bank. This way of identifying stress scenarios is the major advantage of reverse stress testing. Instead of relying on the judgement of experts to select scenarios, the most dangerous scenarios are automatically identified.27. Some studies are dedicated to optimizing scenario selection, and defining probability distributions of the numerous intertwined driving variables across asset classes. For two recent reviews see28 and for a mathematical approach to worst case scenario selection see29. However, we were not able to find any previous research on reverse stress testing in interbank networks that investigates systemic risk.Previous work in this area has focused on developing reverse stress testing frameworks that are intended to be used for the risk analyses of individual institutions rather than of the financial system as a whole30 to reconstruct the matrix of interbank exposures. We then computed the worst case shocks under a linear model of distress propagation, the so-called DebtRank13. We chose this contagion algorithm because of its simplicity and because it can be considered a first-order approximation for a more generic class of contagion algorithms32.In this paper we present as a case study a reverse stress test analysis of a system composed of the 44 European banks that are the constituents of the STOXX Europe 600 Banks index. This index is the major equity benchmark of the most significant financial institutions in Europe. For each bank we collected data on total interbank lending, total interbank borrowing and Tier 1 equity capital. We used the RAS algorithm34. In spite of this there still are valid reasons to look at interbank exposures networks. First of all, they can amplify contagion due to other mechanism36. Second, the result about the limited effect of interbank exposure refers to the situation in which stress is propagated from a borrower to the lender only after the default of the borrower. However in practice, as pointed out in34, losses can occur even in absence of defaults because of credit quality devaluation – the situation in which lenders revalue their interbank assets because they perceive a decline in the ability of their counterparties to repay their debt – which DebtRank aims at capturing in a crude way37.It must be noted that the importance of interbank exposures for financial contagion has been questionedWe show that as the largest eigenvalue of the matrix of interbank leverages increases the worst case shocks become smaller and concentrated in a smaller set of banks;We compute the distribution across banks of worst case shock sizes, thus providing a ranking of banks in terms of their systemic importance;We show that the obtained ranking can be used to make the system more robust through the implementation of targeted capital requirement policies.Our main results are the following:38. This implies that the worst case shocks that we compute are the smallest across the different contagion algorithms and could be used to provide lower bounds for the size of the exogenous shocks needed to produce systemic events.It must be stressed that all our results are derived using a very specific mechanics of distress propagation, the so-called DebtRank, and as such they are affected by this choice. In particular, the linear assumption of DebtRank tends to overestimate losses with respect to other contagion mechanisms proposed in the literature39. In control theory the goal is to drive a system (in our case a network representing interbank lending between banks) from an initial state to a desired target state  with the least effort .Beyond the specific results we obtain, we regard as the main contribution of the paper that of employing contagion algorithms to reverse engineer contagion dynamics in complex systems. This approach is inspired by (network) control theory, which is a methodology from engineering recently applied to complex systemsN banks that interact through a network of mutual exposures (interbank assets and liabilities). A bank is financially characterised through numerous positions on its balance sheet, the three most important positions for our study are the interbank assets and liabilities as well as the equity. The interbank assets correspond to the total sum of loans that a bank extended to other banks (its interbank counterparties), whereas interbank liabilities are the total sum of loans borrowed from other banks. The equity is the difference between assets and liabilities and describes the capital buffer that can be used to absorb losses. In the case of systemic risk one of the most common losses is that due to the default of a borrower, that is the inability of a bank to repay (part of) its loans.We consider a system of Aij(t) the value of the exposure of bank i to bank j at time t, by Ei(t) the equity of bank i at time t, by i at time t, and finally by Li the liabilities of bank i, that we assume to be constant over time. A further assumption is that banks do not rebalance their portfolio (i.e. the number of shares they own of an asset is assumed to be constant), so that the changes in the balance sheet of a bank are only due to changes in the price of the bank’s assets.In the following we consider a discrete time dynamic for the value of banks’ portfolios, and we denote by From the balance sheet identity we have thatt depends on the equity of its counterparties at time t − 1. Following21 we assume that the relative devaluation of an interbank asset is proportional to the relative devaluation of the equity of the counterparty:β ∈  is a positive constant related to the strength of contagion between counterparties. More specifically, β represents the percentage loss experienced by a lender when the corresponding borrower looses 1% of its equity. This also means that β is the fraction of interbank loan that is lost upon the default of the borrower, i.e. the loss given default. Therefore the equity of bank i evolves in discrete time according toWe now consider a situation in which the value of external assets is subject to random market fluctuations, while the value of the interbank assets of a bank at time 21 we now define ij represents the importance for bank i of its interbank asset associated with bank j, as measured in terms of i’s equity. In particular, if the value of the interbank asset drops by 1%, bank i would experience a loss of Λij% of its equity. For this reason, Λij is referred to as the matrix of interbank leverages21.Following40 or overlapping portfolios24. In the case of rollover risk, internal assets would be short term interbank assets, and the matrix of interbank leverage would be replaced by its transpose. In the case of overlapping portfolios, internal assets would instead be assets that can be liquidated by banks during a fire sale, external assets would be very illiquid assets that are not marketable, and the matrix of interbank leverage would be replaced by the matrix of overlaps between banks portfolios.In this paper we focus on direct exposures as a means of financial contagion. However, we note that our framework could be extended to other cases, like those of rollover riski due to shocks to its external assets between times 0 and t, so that41 we can thus measure the impact of shocks on the capital of each bank and compute their propagation across time. We now imagine a situation in which we want to reverse stress test the system over a time horizon T. In particular, we assume to be at time t = 0 and we look for trajectories of shocks T to losses equal or greater than a given threshold, i.e. such thati ∈ {1, 2, …, n}, and where we have denoted by i. We also note that 0 is the identity matrix. There are clearly many possible trajectories that satisfy the constraints  = ui(t) − ui(t − 1) and assumed ui(0) = 0 for all i. Δui(t) represents the loss due to shocks on external assets experienced by bank i between times t − 1 and t. The optimization problem can be more conveniently written in terms of the only variables Δu’s asIn the following we will also refer to the contribution of a bank c, i.e. we assume that the matrix Λ is such that i. In this case all banks are the same, they are subject to the same dynamic and to the same constraint. Therefore, by symmetry, also the trajectories of worst case shocks are the same for all banks. The optimization problem (λ = βc and Δu(t) = u(t) − u(t − 1), as before we set u(0) = 0, and, with respect to , which is the target state of the optimized dynamics;The minimal financial loss T.The time horizon We discuss an empirical application of the optimization problem  to an inβλmax is the one that determines the stability of the DebtRank dynamics42. When βλmax < 1 an exogenous shock is progressively dampened by the dynamic, while when βλmax > 1 shocks are amplified42. We note that usually β is set to one in the literature on DebtRank37, while λmax depends on the specific pattern of interbank loans and is usually between zero and two. Here we consider only one snapshot of interbank exposures at a given time, so that λmax is fixed and equal to 1.38. In order to explore the relevant range of values we therefore vary the parameter β.The quantity β would normally have an upper bound of one, so that the maximum value for product βλmax would be 1.38. In the following we also show results for higher values of βλmax, corresponding to values of β larger than one. The results obtained for β > 1 should therefore be interpreted as an exploration of hypothetical scenarios of a higher leveraged system.Because of its interpretation in terms of loss given default, the parameter K as a function of βλmax for different time horizons and for i. It can be seen that the size of exogenous shocks decreases as a function of βλmax across all T. As βλmax increases the endogenous dynamics of the network lead to a larger amplification of the distress, such that a lower size of external shocks is required to reach the target loss Figure T result in smaller K independently of the value of βλmax. The endogenous network dynamics propagate the distress of the previous time step, thereby implying a lower external shock requirement as T is increased. Because the iteration map (5) does not reach a fixed point when βλmax > 1, even in the absence of external shocks beyond the first time step (i.e. u(t) = 0 for any t > 1), we expect the size of the exogenous shocks K to go towards zero exponentially fast in the limit T → ∞. This is indeed the case, as shown in the inset of Fig. For a similar reason larger K as a function of βλmax and T = 20. From this figure we see that when βλmax is large enough the shock needed to cause the sought final losses is relatively independent of βλmax < 1.The behavior is qualitatively similar for any value of final losses entclass1pt{minimaT = 20 as a function of βλmax and 43, equating to a loss of about 26%. UBS devalued its assets by CHFm 18,240  and had an equity capital at the beginning of 2008 of CHFm 43,82644, implying a loss of about 42%.The cost function is related to the fluctuations over time of the value of external assets along the trajectory of shocks. Another quantity that can be used to characterize the properties of exogenous shocks is βλmax42, and it is derived under some assumptions: that banks do not react to changing market conditions, that the recovery rate is zero, and that no policy intervention is in place. These are all strong assumptions, and relaxing them would curb the extent of contagion. Nevertheless, the model still provides an upper bound to systemic losses and a simple criterion to discriminate between stable and potentially unstable regions in the space of parameters.Figure 45.We have so far looked at the aggregate properties of worst case shocks, however the methodology we propose allows to obtain the distribution of shocks across banks in the system. This information is useful as it enables us to rank banks in terms of their contribution to the aggregate shock, and to identify potential concentrations of vulnerability in the system: If the worst case aggregate shock is uniformly distributed across all banks, then we would expect the system to be more resilient with respect to idiosyncratic failures of individual banks ; if the shock is instead highly concentrated in a few banks, the system is vulnerable with respect to the failure of those banksi. The IPR has a lower bound of 1 when the shock is concentrated in one node, and an upper bound of n when the shock is equally spread across all nodes. As it can be seen in Fig. βλmax approaches 1, and it becomes constant for βλmax > 1.The extent of concentration of systemic risk can be quantified by computing the inverse participation ratio (IPR), defined asλmax leads to a reduction of the aggregate size of the shock K needed to drive the system towards a certain loss and to a concentration of shocks upon a smaller set of banks. We stress here that these two behaviors have different roots. The reduction of K is due to the fact that the system becomes more unstable as leverage increases. The concentration of risk is due to the heterogeneity of leverage across banks. In fact, in the homogeneous system considered above this concentration does not occur. The heterogeneity of banks’ leverages, shown in Supplementary Fig. We have seen that increasing βλmax < 1 a large fraction of nodes need to experience stress in order for the system to observe significant losses, when βλmax > 1 only a few nodes are sufficient to cause significant losses. In the next section we will use this insight to devise a policy experiment to reduce the observed system losses.The observed concentration of risk as measured by the IPR is one of the most significant findings of this study. It indicates that as the pace of the dynamic in an interbank market increases, a decreasing number of nodes in the system can cause systemic events. In other words, while for small βλmax) where systemic vulnerabilities can be associated with a small set of banks, those where the aggregate shock is concentrated.The trajectories of worst case shocks that we have computed correspond to the least extreme scenario that leads to a prescribed final loss equal or greater than To show that this is the case we run the dynamics  forward βλmax when the stressed banks are those with the highest values of Ki. We also report the results for the benchmark case in which stressed banks are randomly selected. As expected, deviations from the benchmark case become larger as the system becomes more unstable. The concentration of systemic risk in the system can be seen particularly when βλmax = 1.5 (black line), in which case the exogenous shock of 5 banks can lead to roughly 70% of all observed final losses. Note that when banks are randomly selected then no such concentration is observed .Figure These insights can be used for a policy experiment on the equity capital requirements of individual banks, that aims to reduce the observed financial losses under the scenario identified through the reverse stress test. In fact the contribution of each bank to the aggregate shock can be used to rank banks in terms of their systemic impact.i receives a proportion Ki/K of the total additional capital. We then compare this policy with a benchmark according to which the equity of each bank is increased by 5% of its current value. This benchmark mimics the case of a homogeneous (relative) increase in the capital requirement of banks. For both policies, we compute the total relative losses R0.The results of a policy exercise in which capital is allocated depending on this ranking are shown in Fig. 46. Put together these requirements are referred to as the Common Equity Tier 1 ratio. The definition of risk-weighted assets is thus a crucial factor in determining the level of equity capital. In brief, each asset held by a bank is given a factor based on its riskiness, which scales its weight in the aggregation of total assets. Our policy approach of increasing the equity capital is thus different to current regulations. The focus of this section is to identify whether this difference is warranted, by testing whether our policy is effective in stabilising the system. The European Banking Authority (EBA) reported after its 2016 stress test exercise of the 51 largest banking institutions in Europe, that the average Common Equity Tier 1 ratio increased from 8.9% at the end of 2010 to 13.2% at the end of 2015. This corresponds to an increase of about 50% in equity capital across these banks47. In this respect our suggested 5% capital increase is quite small. The fact that such small increase of equity can lead to a significant reduction of losses is due to the linear assumption of DebtRank. We note however that our focus here is not on the absolute performance of our policy, but rather on its performance relative to the benchmark. We also note that there is a large overlap between the banks involved in the stress tests of the EBA and the STOXX index used in this paper. In fact 10 out of the 15 European banks classified as global systemically important banks in 2015 are in the top 15 of our ranking of banks based on their systemic importance Ki48.Currently the Basel III capital regulations stipulate a minimum level of equity capital of 4.5% plus an additional conservation buffer 2.5% of a bank’s total risk-weighted assets. Moreover national regulators may require an addition capital increase of up to 2.5% if an increase in risk is observed across the systemβλmax < 1 the two policies achieve a similar reduction of total losses, while the policy based on the reverse stress test becomes more effective when βλmax > 1. The reason for this result is that the explosive dynamics when βλmax > 1 lead to a concentration of systemic risk in a few banks on which an effective policy should concentrate.As it can be seen in Fig. Figure The decreasing returns of scale of our policy are of high relevance to financial regulators. Higher capital requirements come at large costs to banks, not only due to the costs involved in raising the additional capital but also in terms of lower returns. The fact that equity capital requirements beyond a certain level lead to drastically diminished marginal reductions in risk, points towards an optimal trade-off between the costs of increasing equity capital requirements and their effectiveness in reducing risk.K and its related measures such as the IPR display the same behavior across the three years. Furthermore the ranking of nodes is very robust across time, such that the results of the equity capital policy are very similar in 2014 and 2016 compared to those of 2015 presented here. The correlation between nodal shocks across different years is always larger than 0.9. The strong similarity between the years is due to the relative stability of equity, interbank assets and liabilities of individual banks.To test the robustness of our results we collected data of the previous year (2014) and following year (2016) to compare to the simulations undertaken in this paper, which are based on 2015 data. The results are very similar across the years (see Supplementary Information). The cost function K, the IPR and the policy very similar. We show the corresponding plots in the supplementary information, together with a characterization of the cost function and the IPR as a function of the network density.We additionally tested the influence of our choice to study only the complete STOXX network on our results. We therefore redid the entire analysis presented in the paper by using the RAS algorithm to construct a network with density of 60%. We found the behavior of the total shock We have introduced a simple reverse stress testing methodology to reverse engineer distress contagion in financial networks. We reversed the standard stress testing approach by setting a specific outcome, the loss of a certain fraction of the equity of each bank, and looking for the scenario with smallest shocks that could lead to such outcome over a given time horizon.λmax increases, but that at the same time the shock gets concentrated in a smaller number of banks. On the basis on this concentration of worst case shocks, we ranked banks in terms of their systemic impact. Based on this ranking we suggested a simple policy of capital allocations that significantly reduces the vulnerability of the system with respect to the identified scenario in the regime of high endogenous amplification.We considered a system of interbank relationships based on 2015 annual data of the equity, interbank lending and borrowing of the largest 44 stock exchange listed European banks. We found that at the aggregate level the size of the worst case shock decreases as the largest eigenvalue 36. Two specific contagion channels are overlapping portfolio risk35 and liquidity risk, that may result in fire-sales50. Extending the reverse stress testing framework to these types of contagion is left for future work. Indeed further studies of different channels of contagion should also take into account the specific characteristics of individual institutions that play a large role in the concentration of risk34. A third limitation of our analysis is the fact that we only considered direct long exposures between banks. Banks interact in many ways in the real world, and a more realistic scenario would consider a multilayer description of the network of interbank interactions. In this respect, our present analysis corresponds to an aggregation of the multilayer structure into a single layer53. However, it would be important to look also at the disaggregated multilayer structure because the properties of aggregated and non-aggregated systems have been shown to differ in some cases52. Fourth, we considered the case of banks as passive investors. This is certainly a useful benchmark, but a more realistic scenario would also account for the reaction of banks to changing market conditions.Our analysis can be improved in several directions: First of all, we considered a simple linear dynamical rule of distress propagation. Although common in the literature of financial contagion, this assumption can at best be considered only an approximation of the true dynamics. In a more general case, it is still possible to write an optimization problem analogous to  to perfoIn spite of all the present limitations, our analysis suggests that reverse stress testing is a useful tool for the identification of vulnerabilities at the systemic level, and we believe this is an interesting avenue of future investigation with potentially relevant policy implications.30. If no further constraints are added, the outcome of the RAS algorithm is a complete weighted network of interbank claims. Although real interbank networks are far from complete57, here for simplicity we focus on this limiting case which allows us to focus on the mechanics of reverse stress testing only, rather than on the interplay between network topology and contagion. In order to test how much our results are driven by the fact that the network we consider is complete, we have replicated our analysis for an incomplete network with density 60%. The results of this analysis are reported in the Supplementary Information, section We collected data of the 44 banks belonging to the STOXX Europe 600 Banks index, ticker symbol: SX7P. In particular, for each bank we collected information on its equity, total interbank assets (advances and loans to banks) and total interbank liabilities (deposits due to other banks) for the entire year of 2015. Note that we converted all values to Euros using the prevailing foreign exchange rates on November 11th 2016. We then used the RAS algorithm to reconstruct a matrix of interbank liabilities to represent an interbank lending network. Starting from total interbank assets and liabilities of each bank, the RAS algorithm allows an allocation of interbank loans across counterpartiesSupplementary information


With the continuous expansion of the cloud computing platform scale and rapid growth of users and applications, how to efficiently use system resources to improve the overall performance of cloud computing has become a crucial issue. To address this issue, this paper proposes a method that uses an analytic hierarchy process group decision (AHPGD) to evaluate the load state of server nodes. Training was carried out by using a hybrid hierarchical genetic algorithm (HHGA) for optimizing a radial basis function neural network (RBFNN). The AHPGD makes the aggregative indicator of virtual machines in cloud, and become input parameters of predicted RBFNN. Also, this paper proposes a new dynamic load balancing scheduling algorithm combined with a weighted round-robin algorithm, which uses the predictive periodical load value of nodes based on AHPPGD and RBFNN optimized by HHGA, then calculates the corresponding weight values of nodes and makes constant updates. Meanwhile, it keeps the advantages and avoids the shortcomings of static weighted round-robin algorithm. With the extensive applications of cloud computing, open-source projects of cloud computing platform construction such as Hadoop, Eucalyptus, CloudStack, and OpenStack are also increasing  static load balancing and dynamic load balancing, in which dynamic load balancing There are many the common load balancing algorithms in cloud computing environments: Round-Robin Scheduling (RR) Hahne , Weighte2.Equally Spread Current Execution Load (ESCEL)RR Scheduling Hahne  is to di3.Throttled load balancing algorithm (Throttled)ESCEL is a dynamic load balancing algorithm that requires a load balancer to monitor tasks to be addressed  which is put forward by Saaty Saaty , is a toAHP requires dividing decision problems into the destination layer, criterion layer and project layer in accordance with their nature and affiliation to the establishment of a hierarchical structure. Among all levels, in order to avoid difficulties caused by the pairwise comparison of elements, the number of elements in the next layer dominated by a single element is generally no more than nine Srdjevic . Based oIn Fig. Judgment matrix construction is a critical step of AHP, and after the establishment of hierarchical structure, the relationship between various elements  is determined. A judgment matrix is for a certain element of the upper layer, and evaluates the relative superiority degree between this layer and its associated elements. In order to have a certain degree of recognition and quantitative results, the general scale could be adopted to quantify the relative superiority degree of various elements, and thus a pairwise comparison judgment matrix will be constructed.The comparison judgment matrix has the following three features:aij often take the reciprocals of the scales, and the meaning of each scale is shown in Table The scale values Since the integer and reciprocal between meet the mental habits of people when they are making judgment, and just as many psychology researches show that when comparing certain property of a set of things, and if being satisfied with the judgment, average people can generally and correctly identify the grade of property or the amount of things between  as a quantity standard of the consistency degree of the judgment matrix.In the analytic hierarchy process, the corresponding comparative judgment matrix of each criterion can be obtained by factors at their disposal. The single factor weight is obtained mainly through the ordering vector of solving matrix. Calculation steps are as follows:Equation  shows thB2, thus the relative weight vectors (eigenvectors) and consistency index CI are shown as follows:Calculating according to the steps on the basis of the judgment matrix obtained above, we can get the eigenvalue maximum through RI, thereby knowing that Matrix B1 satisfying the following consistency by the CR value:From Table B2, thus its relative weight vector and consistency index CI are shown as follows:We can get the eigenvalue maximum through RI, thereby knowing Matrix B2 satisfying the following consistency by the CR value:From Table A, thus its relative weight vector and consistency index CI are shown as follows:We can get the eigenvalue maximum through CI = 0, we can get that matrix A has consistency.By Based on the relative weight of each factor, we assume the data vectors of performance index and time index collected at the service nodes are S is, the heavier the node load will be. Conversely, the smaller the value of S is, the lighter the node load will be.As we can see from the equation above, the larger the load evaluation metric Here, we combine AHP group decision making with RBF neural networks effectively to make RBF neural networks become a neural network with the experience of experts in related fields through training. Training data are from the load evaluation framework of AHP group decision making. When a new evaluation process proceeds, we can obtain a comprehensive evaluation value, thus effectively reduce the complexity of the computation process simply through modifying the trained and mature input parameter RBFNN  represents the output of the ith hidden layer node; x is the n-dimensional input vector; m is the number of hidden layer neurons; ci is the basis function center; σi is the basis width of the ith hidden layer node. Each neuron node of hidden layer has a radial basis function center vector ci, this vector and the input sample “x” have the same dimension and m” neurons, it has “m” radial basis function centers.Wherein, ||x − The output layer of RBF network is a linear combination of hidden layer node outputs, and the output expression is shown as follows:ωi is the weight from the ith hidden layer node to the output layer node, and p is the number of neurons at the output layer. In a RBF neural network, the output of hidden layer node represents the degree of departure of input sample “X” from radial basis function center “Ci” of hidden layer node. The network input layer implements non-linear mapping and the output layer implements linear mapping.Wherein, The load prediction model based on RBF neural networks is shown as Fig. Previously, Sharifian and Motamedi compared the WRR, RBF and ANFIS on load balancing, the result show that RBF was better than others on convergence rate and prediction accuracy   to train RBF neural networks, namely to combine the HGA with the recursive least-squares method. The HGA can only determine the structure of RBF neural networks, the center and width of the hidden layer nodes, so this paper combines the HGA with the recursive least-squares method to construct connection weights between the hidden layer and the output layer. Determining the weights between the hidden layer and the output layer by the recursive least-squares method can ensure high convergence speed 19):\docuyi and the expected output di, refer to reference (Chen et al. Step 5 Evaluate the performance of RBF neural networks and calculate the individual fitness degree.The train data mentclass2pt{minimConsidering that the objective of training RBF neural networks is to make it the simplest network structure while meet certain precision requirements, that is to make the approximation error precision and the complexity of the neural network in comprehensive index reach the minimum, in which the network approximation error precision objective function is represented by error sum of squares, and the network complexity is represented by the node number of the hidden layer, this paper adopts the fitness function as follows:N is the number of samples, M is the number of nodes in the hidden layer, n is the number of neural network input nodes, yi is the network output corresponding to the ith input sample, di is the desired output, a, b, and d is constant.Step 6 Judge whether it meets the termination condition or not. If meet, then end it; otherwise, continue to the next step.Step 7 Select individual as parent based on individual fitness.In Eq. , N is thi being selected, where fi is the fitness value of individual i, and denotes the sum of individual fitness values of the population.Step 8 The parent generation generates new individuals through cross and mutation, and parents are new individuals form new population.This paper adopts the selection operation which is based on the proportion of adaptation value, the probability of individual Step 9 Return to Step 3 to continue.In a hierarchical genetic strategy, it is necessary to do the crossover and mutation operations simultaneously with the controlling genes and parameter genes. The crossover probability and mutation probability adopt adaptive crossover and mutation probability. The crossover operation of the controlling genes follows the binary-coded cross rules. In order to make the real number coding of parameter genes produce new parameter genes through crossover operations, parameter genes generate a new parameter gene string by using a linear combination of the value of cross-bit corresponding to two parameter gene strings. The mutation operation of the controlling genes is a complementary operation of themselves with a certain probability. While the parameter genes follow an offset mutation, which is to add a random offset value to the mutation bit with a certain probability.Request tasks in a cloud computing environment are mutually independent. We use the HHGA-RBFNN model described above to predict the load of the current cloud computing system, and use the prediction result to calculate the polling weight of the cloud computing nodes periodically, and form a new dynamic load balancing algorithm—DPWRR through the combination with weighted round-robin algorithm.The cloud computing load balancing center nodes predict the load of service nodes as per periodic time T;Calculating a corresponding polling weight value for each back-end service node according to the prediction results by using HHGA-RBF model;The central node allocates based on the polling weight value after receiving the request tasks.The dynamic load balancing algorithm proposed here belongs to a centralized algorithm, which is to allocate the request tasks and deal with load balancing issues through a central node. When users issue a request, the load balancing policy of the central node decides which node to handle this task. The centralized load balancing algorithm mainly contains three steps:After a period T, re-predict the load of nodes and calculate the corresponding polling weights. This method turns the static weight of the weighted polling algorithm to a dynamic adjustment one.Processes of load balancing algorithm based on load prediction are shown in Fig. In an arithmetic process, the pseudo code of nodes which allocate tasks according to the weights of each node is shown in Algorithm 1.The information policy in this paper adopts the periodic collection methods and collects load index information on time, and the triggering policy is triggered by the central control node, that is to use the sender initiative. The algorithm proposed in this paper is focused on positioning strategy, and mainly considers the allocation of user request tasks, and it does not involve the migration strategy, thus involving no migration of virtual machines in cloud computing.Node load information monitoring moduleSeveral major modules of algorithm design is shown in Fig. 2.Load prediction moduleIn order to grasp the node load condition more accurately, solve the problem of node load prediction, and then calculate the polling weights of back-end service node according to the node load prediction results, we adopt the indexes chosen by the AHP group decision making and load evaluation method: performance index B1 and time index B2. The time period T which is related to the node load information collection is set in this module. And when the periodic time is reached, the node load information monitoring will be informed to collect the load information of the back-end node. Time period T must be set reasonably. Theoretically, the shorter the cycle time is, the more frequently the node load information collection will be, thus it is more able to reflect the node load condition, but if the node load information collection frequency is too high, it will cause unnecessary overhead and aggravation load. Generally, the collected time period T is set in 5–10 s (Drougas et al. 3.Request scheduling moduleBefore performing load prediction, first we used group decision making AHP to make a load quantification of the index information collected by nodes. After collecting sufficient data, we can take them as the sample data to train the RBF neural network. Meanwhile we perform parameter optimization to RBF neural network with hierarchical genetic algorithm and recursive least square method. After obtaining the prediction model, the load prediction module predicts the load of data provided by the load information monitoring module.Wi is the weights of node i, Wi is the load prediction of node i, C adjusts constant in order to get an integer Wi. When request scheduling module is in the initial state, all the polling weights of each node can be set as 1.We can first calculate the polling weights of the back-end service nodes and dynamically adjust the node weights as per the node load prediction value provided by the load prediction module, select the appropriate node to deal with tasks received following the weighted polling algorithm. The calculation formula of node polling weights is:MATLAB software was used for doing a simulation experiment. Firstly, we can collect 1000 sets of data on the host of server, in which the parameter data under the performance indicators B1 as training samples to train RBFNN1 in the upper left corner of Fig. The normalization formula is shown as follows:In Eq. , \documeAccording to Qiang et al. , we set Figures The comparison of the prediction results of the total index A is shown in Fig. In a CloudAnalyst simulation platform (Wickremasinghe et al. The transmission delay and bandwidth between regional locations are shown in Tables In the cloud computing data center DC1 formed by CDC1, the simulation results of RR, ESCEL, Throttled and DPWRR load balancing algorithm proposed in this paper are shown in Tables In the cloud computing data center formed by DC1, DC2 and DC3, the simulation results of RR, ESCEL, Throttled and DPWRR load balancing algorithm proposed in this paper are shown in Tables The comparison of the average response time of user groups between the load balancing algorithm DPWRR designed by this paper and RR, ESCEL, Throttled under different configurations of CDC1 and CDC2 is shown in Fig. The comparison of the average processing time of data center among the four kinds of load balancing algorithms—DPWRR, RR, ESCEL and Throttled under cloud computing data centers of CDC1 and CDC2 is shown in Fig. This paper presents a dynamic load algorithm based on AHPGD and HHGA-RBF neural networks under the cloud computing environment, in order to solve the problem of load balancing of the allocation of user request tasks in cloud computing environment. It describes the basic idea and design of the algorithm based on the load prediction model, that constructed in the load prediction process uses a HGA and the recursive least-squares method to train parameters of RBF neural networks. The algorithm combines with weighted round-robin algorithm and dynamically updates the weights of each node within the time period. In the design details of the algorithm, we propose three modules of the algorithm: node load information monitoring module, load prediction module and request scheduling module; meanwhile this paper also designs the time period T and the calculation method of node weights. Finally, we further describe the simulation experiments of the proposed algorithm conducted with CloudAnalyst, and analyze its comparison with the algorithms of RR, ESCEL and Throttled, the results of which show that the algorithm is slightly better than the other three load balancing algorithms, which is effective and feasible.


Saprinus planiusculus on a rat carrion as a beetle species of forensic importance in Khuzestan province.Medico legal forensic entomology is the science and study of cadaveric arthropods related to criminal investigations. The study of beetles is particularly important in forensic cases. This can be important in determining the time of death and also obtain qualitative information about the location of the crime. The aim of this study was to introduce the This study was carried out using a laboratory bred rat (Wistar rat) as a model for human decomposition. The rat was killed by contusion and placed in a location adjacent to the Karun River. Observations and collections of beetles were made daily during May to July 2015.S. planiusculus was seen in the fresh to post decay stages of body decomposition and the largest number of this species caught in the decay stage.Decomposition time for rat carrion lasted 38 days and The species of beetle found in this case could be used in forensic investigations, particularly during the warm season in the future. Medico legal forensic entomology is the science and study of cadaveric arthropods related to criminal investigations  in Ahvaz city‚ Iran. Ahvaz is the capital of Khuzestan Province, located in the southern part of the country and bordering Iraq and the Persian Gulf Fig. . The cliThis study was carried out using a laboratory bred rat (Wistar rat) weighing 352 g as a model for human decomposition Fig. .Fig. 3WSaprinus planiusculus adults were collected only during the night. Decomposition time for the mouse lasted 38 days. S. planiusculus was seen in the fresh to post decay stages of body decomposition and the largest number of this species caught in the decay stage.In this period of time‚ two guilds of carrion-dwelling insects; adult beetles in the family of Histerida (Coleoptera) and fly maggots of the Calliphoridae family were collected from the soil surface near the carrion. Nearly throughout the Palaearctic Region (Daria et al. Saprinus planiusculus resembles Saprinus niponicus, with which it is to a great extent sympartic; however, it can be distinguished from the latter by the shortened third dorsal elytral stria and the shape of the 8th sternum of the male genitalia (Ohara Body length‚ male: 3.95-5.66 mm, female: 4.09-6.33 mm. Top of pronotum without punctures or only with very small punctures, color black‚ frontal stria of head weakly carinate and complete (Fig. ia Ohara .Fig. 4ThSince insect live on decomposing body tissues both as a food source and/or habitat they could be manipulated to estimate the postmortem interval in line with the data on species of insect, their growth rates and fluctuating environmental temperatures (Byrd and Castner Predatory insects can intercept intraspecific pheromones to discover necrophagous species on the same odors of decomposition used by saprophagous insects to find the carrion that is home to thousands of individuals that may well become their next meal or host (Rivers and Dahlem S. planiusculus has been recorded from carrions in Poland and Turkey (Matuszewski et al. Hister abbreviatus (Summerlin et al. planiusculus lifecycle. Based on our observations, this insect is active at night and during the day hiding in the soil and feed on the insects that are present on the body. Therefore, in forensic entomology studies, behavior and food habits of S. planiusculus should be considered.The study on the life history patterns of insects with forensic importance is essential and plays a important role in forensic entomology field for PMI determination (Keshavarzi et al. planiusculus, in order to determine the exact length of each life cycle stages, which will be of great value to the further improvement of the PMI estimation and other forensic implications.This beetle is active in fresh to post decay stages of body decomposition and can be helpful for the development of forensic entomology field in Iran. Future research will be needed on the biology and ecology of S.


We believe that it is important that governments understand the reliability of the mortality data which they have at their disposable to guide policy debates. In many instances, verbal autopsy (VA) will be the only source of mortality data for populations, yet little is known about how the accuracy of VA diagnoses is affected by the reliability of the symptom responses. We previously described the effect of the duration of time between death and VA administration on VA validity. In this paper, using the same dataset, we assess the relationship between the reliability and completeness of symptom responses and the reliability and accuracy of cause of death (COD) prediction.The study was based on VAs in the Population Health Metrics Research Consortium (PHMRC) VA Validation Dataset from study sites in Bohol and Manila, Philippines and Andhra Pradesh, India. The initial interview was repeated within 3–52 months of death. Question responses were assessed for reliability and completeness between the two survey rounds. COD was predicted by Tariff Method.kappa = 0.447): 42.5 % of responses positive at the first interview were negative at the second, and 47.9 % of responses positive at the second had been negative at the first. Question reliability was greater for the short form of the PHMRC instrument (kappa = 0.497) and when analyzed at the level of the individual decedent (kappa = 0.610). Reliability at the level of the individual decedent was associated with COD predictive reliability and predictive accuracy.A sample of 4226 VAs was collected for 2113 decedents, including 1394 adults, 349 children, and 370 neonates. Mean question reliability was unexpectedly low  systems.The online version of this article (doi:10.1186/s12963-016-0104-2) contains supplementary material, which is available to authorized users. Good quality data about the distribution of cause of death (COD) in a population in the context of well-functioning civil registration and vital statistics (CRVS) systems is fundamental to good public health practice , 2. IdeaIn an earlier paper, we described the effect of the duration of time between death and VA administration  on VA validity. The analysis was based on a study of pairs of verbal autopsies for 2113 decedents collected at various time periods after death from field sites in Andhra Pradesh in India, and in Bohol and Manila in the Philippines. The data were entered into the PHMRC VAI and analysed using the Tariff Method . Tariff We believe that it is important that governments understand the reliability of the mortality data which they have at their disposable to guide policy debates. In many instances, VA will be the only source of mortality data for populations, yet little is known about how the accuracy of VA diagnoses is affected by the reliability of the symptom responses. We are aware of only one publication which examines a small number of maternal deaths in Burkina Faso and Indonesia. Repeatability  was found to be moderate in interview material and lower in terms of individual deaths .reliability as “the degree to which the results obtained by a measurement can be replicated,” and accuracy as the ability of the VA “to correctly identify a person who did or did not have [die from] the disease of interest” [In this paper, based on the same dataset as described above, we assess the relationship between the consistency of individual symptom responses and the reliability and accuracy of COD prediction. We define nterest” .VAs for this study were collected for deaths occurring from 2007 to 2010 in Bohol, Manila, and Andhra Pradesh. VAs were administered in two separate rounds. The first round was collected between 6 days and 5 months after death as a part of the PHMRC Gold Standard Verbal Autopsy Validation Study (PHMRC study) [The general methodology of the PHMRC study has been described in detail elsewhere and is summarized here for convenience . Gold stThe PHMRC VAI includes both closed-ended questions and an open-ended narrative. Close-ended questions concern symptoms of the terminal illness, details of underlying disease conditions that had been obtained from health service providers, risk behaviors , and details of interaction with health services. Questions collected either as continuous or categorical variables were transformed into dichotomous variables which we refer to as question items. Text items, also dichotomous variables, were derived from an open-ended narrative using a text mining procedure that identifies keywords and word groups .The VAI was applied in two lengths: long form and short form. The long form is the original PHMRC VAI which was used in this study . The shotariff score for each COD. The tariff score depends on the strength of association between a single symptom and a particular COD and on its distribution across all causes. In effect, the tariff score normalizes the symptom distribution across causes. Prediction of COD in an individual decedent is based on a summation of tariff scores for that death. COD lists by module (age group) are shown in Additional file Data collected for this study were analysed using Tariff Method , 13. TheThe tariff scores for a symptom strongly associated with a particular COD will have high standard deviations, and tariff scores for symptoms more common across many different CODs will have low standard deviations. The short form of the PHMRC VAI was created by first ranking all question items in the long form and then successively deleting low-ranking symptoms, simultaneously observing the effect of deletions on the performance characteristics (COD predictive accuracy) of the instrument using formal item-reduction methods . The shoThe Tariff Method has been shown to have a high level of validity at both the individual and population levels when compared with other methods of VA analysis . BecauseVA performance in assigning COD to an individual decedent was assessed using chance-corrected concordance (CCC) which measures sensitivity adjusted for chance . The CCCThe data set was structured in the form of a matrix. Each cell of the matrix contains two numbers which represent responses to a question which has been asked twice Table . The rowAn endorsed question is one to which the respondent answered “Yes.” The endorsement ratio is the proportion of questions that have been endorsed.kappa, which adjusts proportion agreement for chance. Proportion agreement has been included here for the sake of completeness. Tariff Method makes use only of endorsed questions. When, as in this study, endorsement ratios are low, proportion agreement puts undue emphasis on negative responses. Two other metrics examine the reliability of positive responses; a) the proportion of questions endorsed in the first round of VA that were not endorsed in the second round, and b) the proportion of questions not endorsed at the first round that were endorsed at the second round. We refer to these as question proportion loss and question proportion gain, respectively.The two common measures of reliability are proportion agreement (the proportion of questions with the same “Yes” and “No” answers at two interviews) and kappa [Decedent question kappa  measuresprediction match,” measures whether predictions of the COD were the same at the first and second round of interviews.To quantify the reliability of individual COD assignments, a dichotomous variable, labeled “decedent question kappa = β0 + β1respondent match + β2interviewer match + β3recall period 6–11 months + β4recall period 12–23 months + β5recall period ≥ 24 months + β6module + β7siteUsing linear regression, we examined the effects on question reliability of changes between survey rounds in the respondent or in the interviewer, of time between survey rounds, and of module and site. Because of co-linearity, Bohol (1) and Bohol (2) were combined into a single reference group.We then examined the effects of question reliability on COD prediction reliability using logistic regression. Because each individual death in the data set has two VAs, a correct assignment was significantly more likely in the second VA if it had also been selected in the first VA (correlation coefficient of 0.485). We therefore relaxed the assumption of independence between observations for verbal autopsy diagnoses from the same decedent. Setting a fixed effect that differentiated between first and second round VAs would detract from measuring the effect of the true predictor of interest: COD prediction match. We employed a clustered sandwich variance estimator  using thP(prediction match) = logit(β0 + β1(decedent question kappa*10))Decedent question kappa is the independent variable in the regression. Because kappa is bound between zero and one, we multiplied decedent question kappa by ten to make odds ratios more intuitively understandable.A convenience sample of 4226 VAs was collected for 2113 decedents Table ; 13.4 % Table Endorsement ratios for text items were, in general, less than for question items. A table showing reliability metrics for both question and text items, i.e., for the instrument as a whole, is to be found in Additional file Table Decedent question kappa is the dependent variable in Regression 1, a linear regression, which uses contextual factors as independent variables. Table Prediction match was the dependent variable in Regression 2, a logistic regression. The odds ratio for the independent variable (decedent question kappa)*10 was 1.421 . This can be interpreted as meaning that an increase of 0.1 in mean decedent question kappa would make COD prediction match between first- and second-round VAs 42.1 % more likely.Estimates of COD prediction reliability and validity in Table What benchmarks are there for the levels of predictive accuracy described in this study? The two major sources for COD statistics in resource-poor countries are medical certificates of COD for hospital deaths and VA for non-hospital deaths. Table Table This study was initially designed to determine the effect of the duration of time since death on VA symptom recall . Our aimvice versa.There are four key attributes of VA question responses: 1) reliability, 2) completeness, 3) the contribution the symptom response makes to diagnosis, , and 4) the accuracy with which responses reflect the real-life experience of the terminal illness. The last attribute could not be measured in the current database. Note also that although reliability and completeness are related, responses to a question can be reliable but not complete, and We make a number of observations. First, levels of question reliability were unexpectedly low Table . Mean quSecond, the structured VAI was introduced in the first place to ensure completeness of question responses. Yet 42.5 % of positive responses at the first interview were negative at the second and 47.9 % of positive responses at the second had been negative at the first. By this measure alone, the subset of responses obtained at each of the interviews was incomplete.On the other hand, the measures of question reliability and completeness improved when applied to the short form of the VAI which contained the questions which contributed most to the accuracy of prediction as measured by Tariff Table . We concDifferences between the long and short forms were preserved when the data were analyzed at the level of the individual. Mean decedent question kappa was 0.610 in the long form and 0.676 in the short form. In comparing question kappa with decedent question kappa we interpret kappa not only as a measure of agreement beyond chance but as an intraclass correlation coefficient . In otheContextual factors, operating at the level of individual decedents, explained 30 % of the variation in decedent question kappa (Regression 1). Variation between modules was responsible for approximately 15–16 % of the variation; non-matching of respondents was responsible for 6 % and of interviewers for 3 %. These are not large effects. It should be remembered, however, that the study was conducted in a research environment and much care had been taken in the selection of respondents and in the training of interviewers.A hierarchy of effects of reliability/non-reliability has now been established. An increase of 0.1 in mean decedent question kappa would make a COD prediction match between the first and second round VAs 42.1 % more likely (Regression 2). COD prediction match, in turn, was strongly associated with the accuracy of prediction of COD Table .per se, they are also attributes of responses to questions about individual deaths. VAs of deaths in infants and small children conform more closely to the clinical encounter than do VAs in adults. The former rely on caretaker observations of clinical signs, whereas the latter are a mix of observations of signs and of secondhand accounts of conversations about symptoms. The level of detail in the communication between caretaker and decedent will have depended in part on their personalities and in part on the nature of their relationship. A woman, for example, might give quite different accounts of menstrual irregularity to her sister and to her husband.Reliability and completeness are not only attributes of question responses We conclude from the foregoing remarks that a VA, based as it is on the recollections of family members weeks or months after the event, is not and cannot be as accurate as a hospital diagnosis based not only on a clinical history but also on clinical examination and investigation. However, at the population level, automated VA is a very useful and cost-effective approach to determining the cause composition of mortality.Two further issues deserve consideration in seeking to answer the question of why Tariff Method is as accurate as it is. The first relates to the characteristics of the open-ended narrative and the second to the nature of Tariff Method itself.At the end of interview, in the long form of the PHMRC VAI, the respondent is asked, “Could you please summarize, or tell us in your own words, any additional information about the illness and/or death of your loved one?” This is referred to as the “open narrative.” The text items referred to in the preceding sections were extracted from this narrative. It was noted that the endorsement ratio for text items was lower than for question items, i.e., responses in the open-ended narrative were less complete and less reliable than in the questionnaire. The tariff score for a symptom question mentioned spontaneously was frequently higher than when elicited through the questionnaire . This isIt was noted earlier that each COD is associated with a set of symptoms. The full set of symptoms as recorded for the hospital gold standard cases could be regarded as the ideal for a particular COD. The individual death from a particular cause is likely to be associated with a subset of those symptoms but not the full set, and different individual deaths are likely to be associated with different subsets. Caretakers were reporting aspects of the terminal illness. Accuracy in assigning COD is dependent on the reliability of the prediction but is not so dependent on the reliability of responses to symptom questions.The paradox of low levels of reliability and completeness in response to symptom questions in association with high levels of predictive accuracy of VAs  is, in our view, resolved. We conclude that although informants may report different aspects of the same illness on different occasions – that is, their reports may be unreliable and incomplete – they still reflect a sufficient number of symptoms sufficiently accurately for the Tariff Method to make an accurate diagnosis. This finding adds further support to the basic philosophy of the short-form VA questionnaire, namely that only items are being retained that are robust and have sufficient discriminatory power for major causes of death.Question reliability at the level of the individual – decedent question kappa – is an important factor in COD prediction reliability and hence of COD predictive accuracy. It follows that predictive accuracy is dependent on the quality of interview – a most important conclusion to keep in mind as VAs progressively move from a research environment to routine CRVS systems.