Producing indices composed of multiple input variables has been embedded in some data processing and analytical methods. We aim to test the feasibility of creating data-driven indices by aggregating input variables according to principal component analysis (PCA) loadings. To validate the significance of both the theory-based and data-driven indices, we propose principles to review innovative indices. We generated weighted indices with the variables obtained in the first years of the two-year panels in the Medical Expenditure Panel Survey initiated between 1996 and 2011. Variables were weighted according to PCA loadings and summed. The statistical significance and residual deviance of each index to predict mortality in the second years was extracted from the results of discrete-time survival analyses. There were 237,832 surviving the first years of panels, represented 4.5 billion civilians in the United States, of which 0.62% (95% CI = 0.58% to 0.66%) died in the second years of the panels. Of all 134,689 weighted indices, there were 40,803 significantly predicting mortality in the second years with or without the adjustment of age, sex and races. The significant indices in the both models could at most lead to 10,200 years of academic tenure for individual researchers publishing four indices per year or 618.2 years of publishing for journals with annual volume of 66 articles. In conclusion, if aggregating information based on PCA loadings, there can be a large number of significant innovative indices composing input variables of various predictive powers. To justify the large quantities of innovative indices, we propose a reporting and review framework for novel indices based on the objectives to create indices, variable weighting, related outcomes and database characteristics. The indices selected by this framework could lead to a new genre of publications focusing on meaningful aggregation of information. An index or composite measure can be used to represent an idea or an outcome. Many of the weighted indices or composite measures are the summation of the products of variables values and equal or variable-specific weights. AlthougThe generation of weighted or unweighted indices has been important to operationalize abstract subjects or create new research tools. However, the use of indices or composite measures is more prevalent than many may expect. The process of producing indices that are composed of a subset of variables from a database has been embedded in several data processing and analytical methods. For example, principal components (PCs) are the linear combinations of the variables according to principal component analysis (PCA). PartialCombining the conventional view that takes statistical significance as the criteria for the validity of indices and the prevalent use of data aggregation and implicit weighting of input variables, we aim to propose and test a data-driven procedure of “index mining” or a systematic search for optimal variable aggregation. By taking PCA as an example to assign weights to input variables, the procedures to aggregate input variables are according to PCA loadings and a PCA-based method to generate statistically significant mortality indices is developed. After index mining, we also propose a review framework to examine the validity of newly generated indices according to the differences we identify between the data-driven approach and prevalent theory-based index-generating methods.This secondary data analysis study was approved by the ethics committee of the Centre hospitalier de l'Université de Montréal. We generated weighted indices with the variables from the first years of the two-year Medical Expenditure Panel Survey (MEPS) panels according to PCA loadings to predict mortality in the second years ; see This study first selected features with a correlation-based method proposed for the purpose of removing redundant variables and increasing computational feasibility, 19. TheSpearman’s rank-order correlation was used to create a correlation matrix of all variables, categorical or continuous, 19. ForOf the 71 categorical variables, three ordinal variables that ranked poverty categories (povcaty1), difficulty in using fingers to grasp (fngrdf1), and a summary measure of vision impairment (vision2) were not transformed. Other 68 nominal variables were replaced with 184 binominal variables. This led to 367 variables available for PCA and 15 variables used for personal identification and control for survey design.PCA, PC for principal component, was proven useful for dimension reduction or data pre-processing. AlthougN. In pc, was the sum of all input variables, denoted by x, weighted by PC-specific loadings, denoted by L.The indices were generated according to PCA loadings. Each PC was a linear combination of all input variables and could be seen as a weighted sum of all variables after input variables being catered and scaled. The numIndexpc.n, was the product of the leading variable, in terms of absolute values of loadings, and its PC-specific loading, denoted by Lixi while pc referring the PC that was used to produce indices, n specifying the numbers of input variables required for the index in n equalling one. The second one was the sum of the products of the first two leading variables weighted by PC-specific loadings, denoted by The process of PCA-based index generation was described as follows. The first index of each PC, denoted by The outcome of interest was mortality in the second years. The survival function of the MEPS interviewees was estimated with Kaplan-Meier method and adjuThe deaths in the second years were modelled in four three-month periods or quarters: January to March, April to June, July to September, and October to December. Each individual was duplicated for each quarter if they remained alive. For example, an individual that survived throughout the second years of the MEPS panels would have four data entries representing four quarters. Each data entry was labelled alive. If someone died in the third quarter, July to September, they would only have three observations for non-existence in the fourth quarter and the third entry was labelled dead.survey package[The survival of the MEPS participants in the second year of each panel was modelled with discrete-time event history analysis for the violation of the proportional hazard assumption in Cox model by generated indices. We triey package availably package and RStuy package.Because of the large number of significant indices generated from the MEPS data alone, we would like to estimate the impact of new indices on academic publishing and knowledge translation, assuming three steps required within three-month periods of index mining: generation of weighted indices, formation of theories and methods, and comparisons across databases . In eachThe average number of articles published in an academic journal was about 64 to 68 annually in 2012, 1.8 to 1.9 million articles by 28,100 active journals. We assuth MEPS panels. There were 237,832 surviving the first years of panels. This represented 4.5 billion civilians in the United States, of which 0.62% (95% CI = 0.58% to 0.66%) died in the second years of the panels. The demographic characteristics were listed in There were 244,089 individuals surveyed throughout the two-year panels in the first to 16The leading variables contributing the most to the first five PCs were listed in The p values of all 134,689 weighted indices with or without the adjustment of age, sex and races were plotted in Following the proposed publication cycles in There are opportunities and challenges identified from the data-driven index mining process. There are several important points learned from the process and results of data-driven index mining. First, the number of significant innovative indices composing multiple input variables is large and the proportion is beyond the probability that we may expect, one out of 20, if aggregating variables according to PCA loadings. In addition to PCs that are often used in PC regression and other models, we findSecond, all of the significant indices compose input variables of unequal weights. This contrasts the usual practice of assigning equal weights to all input variables, 8. In aIn this empirical study, using equal weights in most indices is not the best method to aggregate information or augment signal in this data set. Compared to the loadings obtained from PCA in βindex) regarding a hypothetical outcome (y) can be transmitted to all input variables (xi)[βindexwi for each xi.Third, using equal weights is a strong and possibly arbitrary assumption for the relationships between input variables and their predictive power. In bles (xi). The inpwi) links the relative scales of predictive power of all input variables and assumes the regression coefficients of the input variables regarding the outcome should not be estimated individually. The coefficients should be set collectively (βindexwi for each xi). For another outcome, the same restriction applies and the actual coefficients of the input variables simultaneously change in the same relative scales, as a new βindex for all input variables regarding the new outcome.This means that the weighting scheme  if there are sufficient numbers of sample sizes, how to interpret the composite coefficients (βindexwi for each xi) derived from the index coefficients, how much of the outcome variability can be explained by each input variable and how the outcome may change with the alteration of one input variable if controlling for another input variable of the index, will not be easy to answer. If these questions are the major concern for researchers, using indices as proxies to predict outcomes may not be ideal.For indices frequently used as proxy predictors, the restriction on the relationships and relative scales of all input variables by enforcing an index coefficient may not be ideal. Questions, like why not directly use single variables as predictors to obtain variable coefficients  transformation. By applFifth, our results support that weak classifiers can be combined to form stronger classifiers. We findLastly, the publication of new indices may help to secure academic tenure and journal publication. The is because of the fact that the number of publications is significantly associated with tenure decisions. The larWith sufficient sources of publication materials, the focus may soon become how to improve the publication quality or ask authors to comply with review frameworks designed for innovative indices, such as the one we propose in To deal with the identified problems and questions to the newly generated mortality indices in a single data set, we suggest the index creators or readers to assess these problems according to research objectives and through analytical methods. Based on our experiences in generating PCA-based indices, it is important to first understand the problems or questions researchers may encounter while mining indices, listed in the Problems box in In the Assessment box in After reviewing potential problems, assessment results, and important issues in the data set, there are several options toward the data set or weighting schemes, listed in the Actions to be justified section in However, there are other considerations that also matter in the aggregation of information and the generation of index in the last section, Other considerations, in Second, whether the sample sizes of the databases that researcher may use to generate or test new indices are large enough for PCA or other methods is also a key issue. PCA becomes unstable if the number of observations is less than the number of variables. With smLastly, the role of the newly generated indices is also important to consider. For the indices that are treated as outcomes, the theories or existing evidence to combine the indices may be more important than other data objectives. For indices that serve as predictors, proxy indices, the reason why and how to combine input variables are the key to choose the weighting schemes and the methods to generate new indices.There are several limitations to this study. First, computing power is important for index mining. The creation of a complete matrix of significance in The weighting and summation of variables based on PCA loadings can lead to a large number of significant weighted indices regarding important outcomes, such as mortality in this study. However, the numbers of publishable indices may be less than those of significant indices due to several reasons. The first is that the adjacent indices produced according to the loadings of the same principal components may be quite similar because some of the loadings can be close to zero. There are currently no methods or algorithms to estimate the exact numbers of publishable indices. We are currently developing several methods to prioritize the significant indices for publication, some of which are computationally intensive. One option is to first examine the significant indices with insignificant neighbouring indices. Another is to use explicit criteria to prioritize indices relative to the neighbouring indices and among the others created based on the same principal components. The criteria can be p values, model fit statistics, or effect sizes regarding specific outcomes. The chosen ones can be those with much lower p values than the neighbouring ones. Other computationally intensive methods we are developing aims to directly interpret the derived indices and select those interpretable and significant ones for publication. This involves algorithms to interpret the derived indices and select based on the similarity between indices and input variables in terms of certain information criteria. The methods to select the best method to aggregate information into indices remains to be further developed and justified.PCA loadings can be used to assign weights to input variables and generate innovative indices. With data from 16 longitudinal 2-year MEPS panels, there are 134,689 indices derived from 251 non-redundant variables. Of all indices, there are 40,803 indices significantly associated with mortality in the second years of the MEPS panels with or without the adjustment of age, sex and races. We find that assigning equal weights to variables requires justification and clear objectives. The results help us to develop a preliminary data-driven framework to review the process of index generation. In this framework, the objectives and rationales to combine information from input variables are important issues to consider, as well as the characteristics of the databases. In the face of the possible deluge of innovative indices, we suggest the development of a standard reporting system for the publication of indices and the creation of publication channels for further discussion of information aggregation or variable stacking.S1 Table(XLSX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S1 Equation(DOCX)Click here for additional data file.


A mathematical scheme is proposed here to model a damaged mechanical configuration for laminated and sandwich structures. In particular, two kinds of functions defined in the reference domain of plates and shells are introduced to weaken their mechanical properties in terms of engineering constants: a two-dimensional Gaussian function and an ellipse shaped function. By varying the geometric parameters of these distributions, several damaged configurations are analyzed and investigated through a set of parametric studies. The effect of a progressive damage is studied in terms of displacement profiles and through-the-thickness variations of stress, strain, and displacement components. To this end, a posteriori recovery procedure based on the three-dimensional equilibrium equations for shell structures in orthogonal curvilinear coordinates is introduced. The theoretical framework for the two-dimensional shell model is based on a unified formulation able to study and compare several Higher-order Shear Deformation Theories (HSDTs), including Murakami’s function for the so-called zig-zag effect. Thus, various higher-order models are used and compared also to investigate the differences which can arise from the choice of the order of the kinematic expansion. Their ability to deal with several damaged configurations is analyzed as well. The paper can be placed also in the field of numerical analysis, since the solution to the static problem at issue is achieved by means of the Generalized Differential Quadrature (GDQ) method, whose accuracy and stability are proven by a set of convergence analyses and by the comparison with the results obtained through a commercial finite element software. Shell structures are becoming very popular due to their typical curved shapes that can characterize the structural behavior of these elements. For instance, the capability of transferring and holding external loads is substantially different from the one of a flat panel. Analogously, the free vibrations, stresses and strains, as well as the buckling loads, are highly affected by the shell curvature ,2. It shThe mechanical behavior of these structures is even more intriguing to analyze if composite materials are introduced ,4. IndeeIn recent years, the idea of variable mechanical properties for a composite medium has begun to spread in order to optimize the structural performances and reach the best mechanical responses towards the environmental demands. Firstly, the well-known class of functionally graded materials (FGMs) should be mentioned ,58,59,60The present paper also falls within the topic of variable stiffness structures, since it aims to investigate the static behavior of composite plates and shells with variable mechanical properties. Nevertheless, this variation is concentrated in some delimited areas of the composite to model a sudden deterioration of the material properties. The weakening at issue can occur when damage spreads within the medium that composes the structure. Consequently, the elastic properties of the structure are considerably reduced only in limited zones, whereas the undamaged areas of the structure present unchanged features. This configuration can be mathematically achieved by assigning particular smooth functions, such as the well-known two-dimensional Gaussian distribution or an ellipse shaped law, to the elastic parameters that define the mechanical properties of the structure. As highlighted in the paper by Ladevèze and Le Dantec , a generOnce the constitutive laws are specified, the governing equations are obtained in the framework of higher-order shear deformation theories (HSDTs), since these peculiar mechanical configurations could be ineffectively studied through the well-known first-order shear deformation theory (FSDT), as highlighted in many works during the last decades ,125,126.In this paper, differential geometry is used to evaluate those geometric parameters needed for the description of the shell middle surface, which are required in the fundamental operators of the governing equations ,3. Let uThe coordinate describe ,93,94. AP’ of the shell middle surface is located by the position vector Each point The normal direction Once the position vector Definitions (4) are based on differential geometry principles. It should be noted that the scalar parameters in (4) are clearly physical quantities whose magnitude depends on the coordinates For a doubly-curved surface, the principal radii of curvature In case of a singly-curved shell or a degenerate shell (which corresponds to a plate), one radius of curvature (or both of them for a flat structure) tends to infinite value. Finally, the geometric quantities The displacement field of a generic laminated composite shell is defined by the three-dimensional displacements shown in . In thisThis function could be required to capture the so-called zig-zag effect that could happen when peculiar lamination schemes are considered. Further details concerning the Murakami’s function can be found in ,129,130.N defines the structural model. Consequently, the acronyms It is clear that the maximum order of expansion s papers ,94,95, tThe generalized strains of the middle surface For the sake of completeness, the quantities collected in the generalized strain vector are shown belowThe complete treatise concerning the generalized strains and their definitions in extended notation can be found in the book by Tornabene et al. . The meaAs far as the linear elastic constitutive relations are concerned, the stress components The elements of the constitutive matrix Conversely, they are set equal to the non-reduced coefficientsIt should be noted that the normal stress  account , the elaThe following expression must be introduced instead for the non-reduced coefficientsWith reference to definitions (26)–(28), all the remaining engineering constants can be deduced by means of the following relationsIn addition, the orientation of the material properties tructure . For comIt should be noted that such variations are applied at the point Once the generalized strain components 15) are evaluated, it is possible to compute also the stress resultants 5 are evaThe constitutive operator In extended notation, relation (36) can be written as follows for a generic HSDT whose maximum order of expansion is given by With reference to the well-known FSDT, the following correspondences can be deduced,      A0=B,      he works ,94,95. S(+) specifies that the top surface is loaded, whereas the superscript (−) is used to identify a load applied on the other external surface. On the other hand, the subscript represents the coordinate along which the force is applied. The static equivalence principle is employed to evaluate the generalized load components acting on the shell middle surface, given by By means of Hamilton’s variational principle ,4, a setThe following expressions can be used to define each quantity in (43) for each order of kinematic expansionBy means of relations (36) and (15), the equilibrium equations can be written as a function of the generalized displacements of the middle surfaceThe GDQ technique is used to obtain and solve the discrete form of the governing equations. Indeed, the present numerical method provides the solution of the strong formulation of the fundamental Equation (47) by approximating the partial derivatives. For completeness purposes, the main aspects of this technique are presented briefly . Let us Thus, the order of the point is given by d) from the ones related to the boundary nodes (b). As a consequence, all the quantities in (65) are evaluated to consider this classification as followsThe static solution of the problem is obtained applying the GDQ technique, which allows the following discrete form of the governing equations to be writtenThe generalized displacements of the boundary points It can be observed that the size of the problem turns out to be ed edges  are compOnce the static solution is obtained, the three-dimensional elasticity equations in terms of stresses can be used to evaluate the through-the-thickness variation of all these quantities. In fact, the three indefinite equilibrium equations of elasticity written in an orthogonal curvilinear coordinate system allows the three-dimensional profiles of stresses and strains to be obtained, consequently, even if the higher-order structural model illustrated above is two-dimensional. The following treatise presents the main aspects of the recovery procedure at issue. Once the generalized displacements of the middle surface are computed, the kinematic model (10) is employed to obtain the three-displacements of the solid medium in each point By means of the GDQ technique, the generalized strains (15) can be computed in each grid point. As a consequence, the three-dimensional strain components related to each discrete point of the middle surface can be evaluated by using expression (18). The strains at issue assume the following aspectIn particular, quantities The GDQ method is employed to approximate the partial derivatives of the membrane stresses as followsConditions (80) are imposed through the following expressions, which represent the effective through-the-thickness variations of the shear stresses in each point of the domainEquation (78) can be now employed to obtain the normal stress by applying the corresponding boundary condition at the bottom surfaceAnalogously, another boundary condition must be introduced at the external surface of the top layerIt should be noted that the quantity in (89) is evaluated neglecting the hypothesis of plane stress, thus the non-reduced elastic coefficients are employed. Moreover, the strain components (87)–(89) could be discontinuous at the layer interfaces since no compatibility interlaminar conditions are enforced.Finally, the actual through-the-thickness variations of the membrane stresses As mentioned in the previous sections, the integrals which appear in the definitions of the elastic coefficients The procedure to compute the weighting coefficients for the integration purposes . The weiA generic element of the matrix The present GDQ based approach is implemented in MATLAB code developed by the authors , which iAll the mechanical and geometric characteristics of these structures are summarized in ified in ,93,94,95The convergence analyses are performed for a simply supported (SSSS) square plate a, considFrom the various plots depicted in Finally, it should be highlighted that a good convergence is reached by using many sampling points. Nevertheless, the test at issue is characterized by a noticeable mechanical discontinuity. For this reason, the value The same flat structure of the convergence analysis is also used in this application, assuming completely clamped boundary conditions (CCCC). Two damage configurations are considered: Gau-2 and Gau-3. The former provides the increase of damage intensity As expected, the displacements increase when the damage grows or when it involves a bigger area of the domain. The results are compared with the solution obtained with a finite element commercial software (Strand 7) for the undamaged case, by using a three-dimensional model (3D-FEM). The profiles in hand are shown in the graphs through a dotted notation and match perfectly with the corresponding GDQ curves. The through-the-thickness variations of strain, stress, and displacement components are presented in A completely clamped (CCCC) laminated plate is considered in this paragraph. The geometric features are the same as of the previous test, but the lamination scheme is given by rial see . Two damA FCFC sandwich structure with a central soft-core is investigated in this paragraph. The shell geometry is given by the singly-curved cylindrical surface with parabolic profile depicted in The deterioration of the mechanical properties involves only the external layers and the elliptic shape describes a damage that affects the shell along all its length along the coordinate ny works ,94,95, Mained in ,94,95. Tn [u1(0) a and the) (u3(0) b increasA branch of a parabolic arch is employed to describe the meridian curve of a CCCF doubly-curved panel of revolution c. As illThe effect of the damage parameters on the strain, stress, and displacement profile along the shell thickness is investigated in The results were presented in terms of displacement profiles related to the shell middle surface and through-the-thickness variations of strain, stress, and displacement components at specific points of the domain. It was proven that the damage affects all these static quantities.The numerical approach shows a convergent behavior when applied to this kind of structural problems.It was proven that the damage modifies the structural response. In general, the displacement increases when the damage intensity grows or when it involves a bigger area of the domain; analogously, the overall displacement is greater when the damage spreads to the adjacent layers.As far as stresses and strains are concerned, the effects of the damage on their through-the-thickness profiles are lower than the effects caused on the corresponding displacements; nevertheless, it is possible to observe noticeable differences between the profiles which are related respectively to the minimum and maximum values of the parameters used in the parametric analyses to model the deterioration of the mechanical properties.Similar profiles in terms of strains, stresses, and displacements are obtained by means of different HSDTs. Consequently, all these enriched kinematic models are able to deal with damaged composite plates and shells.No significant differences are observable between a higher-order model and the corresponding one embedded with the Murakami’s function when a laminated composite is analyzed. On the other hand, the Murakami’s function is required to deal with sandwich structures with an inner soft-core.A numerical analysis was proposed in the paper to deal with the linear static behavior of damaged plates and shells. The solutions were obtained through the application of the GDQ method, which was also employed to evaluate the through-the-thickness variations of stress and strain components by means of a recovery procedure based on the three-dimensional equilibrium equations for a shell structure. Several boundary conditions, geometric shapes, stacking sequences, and load combinations were considered and investigated through a variety of higher-order structural models, including the Murakami’s function for the zig-zag effect when needed. The mechanical properties of the shells were taken as variable to model a damaged configuration. In particular, the two-dimensional Gaussian function and an elliptic expression were introduced to model a damage which affects all the engineering constants of the corresponding medium in concentrated areas of the shell domain. Several parametric investigations were carried out to study the effect of the various parameters that describe those functions. The following observations are noted:As a future development, the authors believe that the present damage model should be also employed in the dynamic field to investigate how the deterioration of the mechanical properties of a generic medium affects the corresponding structural response. In addition, the authors will attempt to compare the present approach with some experimental and numerical tests available in the literature.


Here, we present a concept based on the realization that a complex medium can be used as a simple interferometer. Changes in the wavefront of an incident coherent beam can be retrieved by analyzing changes in speckle patterns when the beam passes through a light diffuser. We demonstrate that the spatial intensity correlations of the speckle patterns are independent of the light diffusers, and are solely determined by the phase changes of an incident beam. With numerical simulations using the random matrix theory, and an experimental pressure-driven wavefront-deforming setup using a microfluidic channel, we theoretically and experimentally confirm the universal sensitivity of speckle intensity correlations, which is attributed to the conservation of optical field correlation despite multiple light scattering. This work demonstrates that a light diffuser works as a simple interferometer, and presents opportunities to retrieve phase information of optical fields with a compact scattering layer in various applications in metrology, analytical chemistry, and biomedicine. Speckle is a granular pattern that appears when highly coherent light is scattered by a random structure23491012One of the advantages of speckle metrology is its utility in phase-measurement interferometry20Despite the high resolution gained from the broad range of spatial frequencies in speckle, the implementation of phase-sensing methods requires both an interferometric setup with precise alignment and careful analysis of the diffraction patternsHere, we demonstrate the universal response of the diffusive scattering media to the phase changes of an incident light field. We numerically and experimentally studied how the spatial intensity correlation coefficient of a speckle field after a diffuser is solely determined by the wavefront of a beam impinging on the diffuser. The results validated our proposed method retrieving a single parameter determining optical phase information of the beam of interest. Finally, the universal decorrelation relationship regardless of the scattering media in diffusive regime was investigated.The basic principles of the phase sensitivity of speckle patterns and its universal behaviors over diffusive layers are illustrated in a priori information, or calibrated information about the scattering layer is required. Somewhat intriguingly, a universal relationship exists between the phase change of an incident light and the correlated spatial intensity after a scattering layer, which is independent of the properties of the scattering media  and x2(r′) impinge onto the scattering layer, and corresponding scattered fields are y1(r) and y2(r), respectively.We first mathematically formulate the intensity cross-correlation coefficient G to describe the scattering layer related to the incident and output fields, the exact form of the output scattered field is given as,Using a Green’s function Because an image sensor measures the scattered intensity image rather than field the intensity correlation, r space.where r space. Then, according to the Reed’s moment theorem27To progress beyond this point, an important assumption is required: all the scattered field exhibit complex Gaussian distribution over which is the well-known Siegert relation applied in spatial domainr space, Since where any diffusive scattering layer that satisfies the Reed’s theorem, the speckle correlation directly represents the field correlation of incident fields, which verifies the field sensing ability of speckle metrology.where In order to identify when the scattering layer would satisfy the Reed’s theorem, we employed a numerical simulation which emulates the transmission matrices (TMs) of scattering media. The sets of TMs of scattering media was obtained with an approach used in disordered metallic systems1331323334L/ls, or the ratio of the thickness of a layer L to its scattering mean free path ls. In our numerical simulations, a TM relates 1024 input modes of the incident field to 1024 output modes of a scattered field in the diffusive regime.The scattering strength of a medium was controlled by changing the optical thickness L/ls is 1, 8, and 20. In a weakly scattering media  was used as a coherent light source. The laser beam impinges onto the surface of the microfluidic channel. The beam which is transmitted through the channel encounters a scattering layer after a propagation of 2 cm. Speckle pattern formed by the scattering layer is recorded with a CCD image sensor . The separation between the layer and the image sensor was adjusted to achieve the highest signal-to-noise ratio.In the optical setup, a diode-pumped solid state laser  , ten layIn addition, we applied a continuous increase of pressure and calculated the variation of output intensity correlation . The preP. P is 3.2 kPa, The curves in We note that in our experiment the scattered field can be affected by other factors such as a distance between the layer and the image sensor due to diffraction. However, since the measured intensity probability distribution follows Rayleigh statistics, it is inferred that the field probability distribution follows complex Gaussian, which allows the application of Reed’s theorem.In this letter, we present the universal sensitivity of speckle intensity correlations to wavefront deformation in light diffusers. When the alteration in speckle intensities is expressed as the correlation coefficient, it was analytically shown that the speckle change is relevant to just the wavefront deformation whenever a scattering layer belongs to the diffusive regime. Employing a numerical simulation using a TM, we found that the saturated value of speckle intensity correlation is consistent with the modulus square of the incident field correlation. With a wavefront-deforming setup using a deformable microchannel, we experimentally confirmed the universality of the spatial intensity correlation to the changes in the wavefront of a beam passing through various scattering layers, regardless of the type and thickness of the scattering layer.The present work may open new avenues for optical metrology and interferometry because it directly enables a simple speckle-based approach for the detection of wavefront change using a scattering layer. Importantly, the present work provides a theoretical framework and experimental verification for general speckle metrology. In particular, the present work provides a means to retrieve phase images directly regardless of scattering media and without any calibration or characterization of the scattering media in use. From a practical point of view, our concept is easily implemented with the insertion of a scattering medium in the midst of a beam trajectory, without the need for a reference beam, to obtain the interference pattern between speckles. It also provides a method of cost-effective remote sensing, because the setup only requires an ordinary scattering layer, like the translucent Scotch tape we used. Our principle is applicable independent of the choice of scattering medium, guaranteeing that any diffusive layer always gives the same expected performance at given conditions. We expect this approach will find direct applications in various applications where the optical phase change is of interest, ranging from metrology, analytical chemistry, sensing, and biomedical optics.How to cite this article: Kim, K. D. et al. Universal sensitivity of speckle intensity correlations to wavefront change in light diffusers. Sci. Rep.7, 44435; doi: 10.1038/srep44435 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


A coronary fistula (CF) is a rare congenital cardiac anomaly in which there is a connection between the coronary artery and a cardiac chamber or a great vessel. In the paediatric population, a CF is usually asymptomatic. While the circumflex coronary artery (Cx) is the least common source of a CF, the right heart chambers are the most common location of drainage. Herein, we present a symptomatic 10-month-old boy with an atrial septal defect (ASD) in whom we incidentally detected a CF, which stemmed from the Cx and drained to the right atrium. Because the patient was symptomatic and his small size was not appropriate for percutaneous closure of the ASD, surgical closure of the ASD and CF was performed. A coronary fistula (CF) is a rare congenital cardiac anomaly in which there is a connection between one or more coronary arteries and a cardiac chamber or great vessel.In the follow up of a 10-month-old boy (weight 8 kg and height 70 cm) with a prenatal diagnosis of atrial septal defect (ASD), apart from the fixed splitting of the second heart sound, a prominent increase in the severity of the mid-systolic murmur at the pulmonary auscultation area was incidentally detected. On echocardiography, a new continuous jet flow into the RA indicative of a CF was detected.His history showed he had had recurrent upper respiratory infection and failure to thrive so that both the weight and height of the patient were within the third and 10th percentiles. There was no evidence of myocardial ischaemia on electrocardiography. On echocardiography, the ASD (5 mm) was secundum type. The opening of the jet was sited adjacent to the superior cavo-atrial junction . PosteriIn contrast-enhanced computed tomography, the left main and circumflex coronary arteries were dilated . The CF originated from the proximal Cx and coursed posterior to the aorta before draining into the RA . BecauseAfter a median sternotomy and pericardiotomy, the CF was located adjacent to the posterior part of the superior cavo-atrial junction. Under cardiopulmonary bypass (CPB), the aorta was cross-clamped and cardiac electromechanical quiescence was established. Through a right atriotomy, the secundum ASD was primarily closed.It was detected under cardioplegic wash-out that the opening of the CF was located inferior to the cavo-atrial junction and it had multiple openings, which were connected with a loose membrane . FollowiThe postoperative course was uneventful. In postoperative echocardiography, the atrial septum was intact and no turbulent flow in the right atrium was detected. Aspirin was given for three months. At the six-month follow-up visit, he was found to have gained weight (12 kg). Additionally, no turbulent flow within the atrium or posterior to the aorta was detected in echocardiographic evaluation.As the use of selective coronary angiography became widespread, recognition of a CF has been improving since the 1950s.In the literature, while the Cx was the least common source of a CF, the right heart chambers were the most common location of drainage.7Contrary to our case, nine of 10 CFs were asymptomatic in an evaluation of CFs in paediatric cases, and surgical ligation under CPB support without application of an aortic crossclamp was performed in four cases.In our opinion, based on the clinical presentation and coexistent cardiac pathology, the choice of therapeutic management strategy should be individualised. Because of the possibility of the development of complications in the future, we successfully operated on a symptomatic paediatric case in whom the CF was incidentally diagnosed in association with an ASD.


Despite the impact of hypertension and widely accepted target values for blood pressure (BP), interventions to improve BP control have had limited success.We describe the design of a 'translational' study that examines the implementation, impact, sustainability, and cost of an evidence-based nurse-delivered tailored behavioral self-management intervention to improve BP control as it moves from a research context to healthcare delivery. The study addresses four specific aims: assess the implementation of an evidence-based behavioral self-management intervention to improve BP levels; evaluate the clinical impact of the intervention as it is implemented; assess organizational factors associated with the sustainability of the intervention; and assess the cost of implementing and sustaining the intervention.e.g., qualitative analyses--pattern matching; quantitative methods--linear mixed models).The project involves three geographically diverse VA intervention facilities and nine control sites. We first conduct an evaluation of barriers and facilitators for implementing the intervention at intervention sites. We examine the impact of the intervention by comparing 12-month pre/post changes in BP control between patients in intervention sites versus patients in the matched control sites. Next, we examine the sustainability of the intervention and organizational factors facilitating or hindering the sustained implementation. Finally, we examine the costs of intervention implementation. Key outcomes are acceptability and costs of the program, as well as changes in BP. Outcomes will be assessed using mixed methods (The study results will provide information about the challenges and costs to implement and sustain the intervention, and what clinical impact can be expected. Controlling hypertension improves cardiovascular and renal outcomes, and the mechanisms for achieving control including diet, exercise, and medications are well known and accepted. Despite the increased incidence of hypertension-related diseases, well-established evidence-based guidelines, and the availability of over 100 antihypertensive medications, approximately 25% to 40% of veterans with hypertension in 2007 did not have adequate blood pressure (BP) control (≥140/90 mmHg) . B-6. B3-6]The intervention is a nurse-delivered tailored telephone intervention that was developed and previously evaluated in the Veteran-Study To Improve The Control of Hypertension (V-STITCH) ,8, and rThe intervention uses a behavioral-educational approach to enhance hypertensive patients' self-management capability and is organized around telephone encounters that occur approximately once every 4 to 5 weeks for 12 months. During the phone calls, trained nurses use the intervention software to gather medical and behavioral information. Patient responses to these questions activate a set of behavioral and educational modules within the intervention software that address such issues as social support, knowledge, health behaviors including smoking, weight loss, diet, alcohol use, stress, and participatory decision making ,10,12.We have included three intervention sites located in three separate Veterans Integrated Service Networks (VISNs). Intervention facilities were selected based on four criteria. First, these facilities perceived that they could further benefit from improving the level of BP control at their facilities. Second, their patient demographics  vary, which increases the generalizability of evaluation results. Third, the investigators have established collaboration with the leaders of these VISNs. Finally, the intervention sites agreed to leverage resources and funds to support a nurse (or nurses) required to implement the intervention. Each intervention site is matched to three control sites  based on the level of VA organizational complexity and VISN affiliation.Organizations often find it necessary and desirable to adapt evidence-based interventions to facilitate implementation, encourage ownership, and enhance acceptability among target populations . The chaWe sought to balance the competing demands of adaptation and fidelity by requiring intervention sites to use certain intervention features and implementation processes while allowing them the flexibility to tailor other aspects of the intervention and the implementation process to local conditions, and providing intervention sites with centralized implementation support Table . This apIntervention facilities are required to commit at least four staff members in this partnership to ensure open communication among site participants and increase the likelihood of effective implementation: nurse interventionist, site principal investigator (physician), representative of the nursing administration, and information technology (IT) support staff. Each site has to agree to fund at least one-half of a full-time equivalent (FTE) nurse position, filled by one or more individuals. The nurse(s) will need to implement the program for two years--one year of enrollment and one year of follow-up. The facilities are responsible for determining nursing resources available to deliver the intervention, so these individuals may include both primary care staff nurses and individuals with experience as case managers.The facility also is required to identify a specific site principal investigator, who leads the implementation effort at the facility and acts as a conduit between the facility and the centralized implementation support team. In the case of the present study, this person is typically a physician. In addition, participation requires the support of the director of nursing, who has the authority to dedicate nursing time for the intervention. Lastly, the site has to designate an information technology staff to be a contact and troubleshooter for the roll-out and use of the intervention software.Each intervention facility has the goal of enrolling 500 patients during the 12-month implementation period. Patients can be referred to the intervention in any of the following three ways, depending on the preferences of the primary care providers at each intervention site:1. For VA patients with a diagnosis of hypertension and last BP reading of >140/90 mmHg, primary care providers receive a reminder that the patient has poorly controlled hypertension that includes an option to place an order for the behavioral-educational intervention.2. An item has been added to the providers' primary care screen in the VA electronic medical record that will allow a patient's provider to order the intervention even if the hypertension reminder has not been triggered for the patient.3. If few intervention orders are received, the nurse is able to access a pre-populated list of patients who meet the same criteria as the hypertension care reminder. Starting with the patient with the most recent outpatient BP record, the nurse would contact the patient's primary care provider regarding the intervention.Facilities can use one of two approaches to scheduling patients. In some cases, facilities have developed a specific nurse telephone hypertension self-management clinic established for the purpose of delivering the intervention. Like other healthcare appointments, the clerk receives an order from a primary care provider to schedule a specific time for the nurse to call the patient. The other option allows facilities to develop an alert that goes to the nurse indicating that a new patient is in the queue to be called. Upon calling the patient, the ordering provider is notified.The nurse must place a note in the VA electronic medical record, the Computerized Patient Record System (CPRS), to describe any patient concerns. The nurse is responsible for addressing serious patient needs during the call following standard facility/clinic operating procedures.i.e., behind the VA firewall) using a point-to-point connection between the user's computer and a centralized server as the user goes through each screen that corresponds to call script and data collection.The intervention software is a distributed application built using the Microsoft .net framework. Users navigate to a VA intranet web page to launch the software. Using this system, nurses are able to access records from their site only. Data are transmitted within the VA protected computer environment  , includiPart of the implementation process consists of presentations of our intervention to an expert panel and our key stakeholders for review and comments. This implementation process (and its study) is being conducted with support of the VA Quality Enhancement Research Initiative (QUERI)) -23 progrThe remainder of this article describes four different components of the evaluation project that address implementation, clinical impact, sustainability, and costs of the behavioral-educational intervention. Table Study one addresses the first specific aim: to assess organizational factors associated with the successful implementation of an evidence-based behavioral intervention to control BP. For this study, successful implementation of the intervention is defined by the degree to which patients receive scheduled phone calls that include presentation of content outlined by the intervention software. Informed by the conceptual model, study one research questions include: how do VA site leaders foster organizational readiness to implement the intervention; what VA clinic policies and practices are needed to support intervention use; and do VA clinics with a stronger implementation climate show more consistent, high-quality, appropriate intervention use as indicated by proxies such as patient retention, BP levels, and medication adherence? This component also seeks to describe the use of implementation approaches. While there are a number of methods available for implementing interventions, there is no consensus on the most efficient methods and dose of support for effectively implementing interventions .i.e., the cases). Quantitative data from the nine VA clinics in the comparison group account for secular trends in hypertension management practices and clinical outcomes.Study one employs a case study design involving the collection and analysis of both qualitative and quantitative data. Case study methods are well-suited for studying implementation processes, which tend to be fluid, non-linear, and context-sensitive ,26. In aStudy one draws upon primary data collected from multiple sources using multiple methods to analyze potential facilitators and barriers to implementing the intervention, including site visits, semi-structured interviews, phone calls, e-mail exchanges, and standardized surveys. Prior to the launch of the intervention, we conduct interviews with the clinic director, physicians, nurses, IT staff, and office staff identified by the local site principal investigator who are involved in or affected by the implementation of the intervention  Table . We use In addition to the wealth of qualitative data we plan to collect, we administer two surveys. The Assessment of Chronic Illness Care (ACIC) is implemented at baseline and 12 months at both the implementation clinics. The ACIC is developed to allow healthcare teams to evaluate the degree to which their organization has implemented practices suggested by the Chronic Care Model ,29. The e.g., coordinating implementation activities), perceived commitment of the core implementation group to implement the intervention, and perceived commitment of the user group to support and use the intervention.At the same time the ACIC is administered, the Organization Readiness to Change Survey is administered. Twelve items assess perceived efficacy of the core implementation group to carry out critical implementation tasks effectively . If the patterns match, the predicted pattern is said to receive support. If the patterns do not, the investigator reformulates the predicted pattern by developing and investigating alternative predictions.Consistent with a case study research design, we use pattern-matching logic to guide data analysis . In pattProcedurally, qualitative data analysis involves three phases: data coding, within-case analysis, and between-case analysis. In the first phase, we use qualitative data analysis software (ATLAS.ti 5.2) to code the study data. The conceptual model provides a starting list of codes, which we supplement with emergent codes as needed. In the second phase, we conduct a within-case analysis of each VA clinic implementing the intervention. Using ATLAS.ti, we generate reports of all text segments for each code. We assess the degree to which the construct appears in the data (its 'strength'), the degree to which the construct positively or negatively affects implementation , and the degree to which relationships among constructs match the conceptual model.Consistent with the organization-level focus of the conceptual model, we aggregate and analyze quantitative data at the VA clinic level (three intervention sites and nine control sites). We then analyze the quantitative data in conjunction with the qualitative data using the pattern-matching logic described above. For example, using the ACIC data, we examine whether VA clinics with more developed organizational infrastructures and climates supporting chronic care delivery at baseline exhibit greater management support, stronger implementation climates, better innovation-values fit, and more effective implementation. These data also help us gauge whether implementing the BP control intervention stimulated or facilitated more systemic changes in chronic care organization and delivery within the implementing clinic, or whether secular trends within the VA represent a plausible rival explanation for the results that we see.Study one is expected to produce a theoretically informed, empirically grounded organizational model of implementation suitable for complex innovations and adapted to the context of clinical practice. An additional product of this phase of the study is an evaluation of approaches to implementation of the behavioral intervention.Study two seeks to assess the clinical impact of the implemented behavioral self-management intervention in order to assess the effectiveness of the intervention outside the supportive context of a randomized controlled trial. The population of interest is veterans with hypertension who meet criteria for the behavioral intervention and visit their primary care clinic at the VA for routine care. The two primary research questions are:i.e., clinical-level) program?1. What is the impact, in terms of average systolic BP improvement, of having implemented the behavioral intervention versus not having implemented the intervention as a facility-wide ?Question one is an organizational (or policy) question that addresses the impact of rolling out the intervention facility-wide by comparing facilities implementing the behavioral intervention (implementation facilities) versus those that do not (control facilities). Question two addresses the impact of the intervention from the perspective of the patient by comparing patients receiving the intervention versus those that do not within facilities/clinics that implemented the intervention. Figure i.e., observational, non-equivalent groups) design with repeated measures [i.e., hospital director approval, FTE requirements), for question one, clinics are not randomly assigned to implement versus not implement the behavioral intervention. Similarly, for question two, patients within facilities implementing the behavioral intervention are not randomly assigned to receive the intervention versus not receive the intervention.The study design is a clustered quasi-experimental  at least three times in prior two years, and who have a BP measurement taken during the first visit. For question two, the study sample used to address question one is restricted to patients at implementation facilities.For both questions, the primary outcome is systolic BP, a continuous variable. Time is measured continuously in weeks since the first time a patient visits a participating facility during the implementation roll-out. For question one, the primary predictor variable is the implementation indicator variable . For question two, the primary predictor variable is the treatment received indicator variable .This study relies primarily on data from the Veterans Health Information Systems and Technology Architecture (VistA), the electronic medical record system used to support both inpatient and outpatient care in the VA. Specifically, BP measurements (the primary outcome variable for both questions) and other covariates will be obtained from the Health Data Repository (HDR) for patients in our target population of interest. BP measurements in the HDR are date-stamped, allowing us to derive time (as defined above) for data analysis. The treatment received indicator variable (for question two) will be obtained from the software used by the study nurse to administer the behavioral self-management intervention.Because facilities are not randomized to implement or not implement the behavioral intervention (question one), and patients within implementation facilities are not randomized to receive or not receive the intervention (question two), an important challenge is the potential presence of confounding variables. A confounder variable is related to the outcome and is unevenly distributed between 'treatment' conditions , but is not in the causal pathway between the intervention and the outcome . For queFor both questions, a linear mixed modeling (LMM)  strategyi.e., repeated systolic BP measurements on patients nested within clinics), clustering by clinic and within-person correlations must be taken into account in both the data analysis and power calculations. Following Donner and Klar [Statistical power considerations are based on question one. Based on previous data ,36, we aand Klar , we use and Klar . Assuminand Klar ), a two-and Klar  for the and Klar ,40, a miWe anticipate one major product of the study to demonstrate improved systolic BP in clinics using the intervention relative to clinics who did not receive the intervention.Study three assesses the sustainability of the behavioral-educational self-management intervention to control BP. Just as it is necessary to study the processes through which patients must make a long-term commitment to self-management of hypertension, we study the ability of VA facilities to make long-term commitments to support the intervention. In this study, sustainability is operationalized as the willingness and capacity of VA facilities to maintain intervention use beyond the initial 12-month period in which new patients are enrolled and existing patients continue to receive the intervention. Specifically, three research questions are examined: How do the benefits and costs of the intervention as perceived by various stakeholders affect the sustained use of the intervention by VA clinics? What policies and practices are necessary to support sustained use by clinics? And how do organizational factors like staff turnover, competing priorities, and organizational changes affect sustained use by clinics?i.e., the cases). The focus is on the three VA clinics implementing the intervention. Data from the nine VA clinics in the comparison group are used to account for secular trends in hypertension management practices and clinical outcomes.Study three employs a case study design involving the collection and analysis of both qualitative and quantitative data. VA clinics serve as the units of analysis , and a third type of costs not assessed in randomized trials that relate to intervention dissemination to the clinics, which involves initial time costs of study investigators and clinic leadership in the buy-in and planning phases of the study . TogetheThe study sample for the cost analysis includes the matched cohorts of 6,000 veterans with hypertension who meet criteria for the behavioral self-management intervention and have at least one visit to the participating clinics during the intervention roll-out period and have a BP measurement taken during the first visit .e.g., planning, intervention training, nurse time) [This includes three costs: study investigator time modifying the intervention in preparation for the roll-out period; study investigator and clinic staff time spent during the buy-in phase developing trust and commitment to the implementation study; and study investigator and clinic staff time spent on implementing the intervention (se time) . We are Inpatient utilization data from the patient treatment file (PTF) data and outpatient utilization data from the Outpatient Care File (OPC) are to be merged with VA Decision Support System (DSS) data on VA expenditures for all trial participants to compare VA resource utilization of veterans randomized to treatment clinics and veterans randomized to control clinics before and during intervention roll-out. The outcome of interest is annual healthcare costs over the 12-month period, and the patient is the unit of analysis. A VA payor perspective is applied. All costs are to be valued in 2010 US dollars, based on the Current Price Index-Medical (CPI-M).We anticipate a major product of the study to outline the full range of costs required to implement and sustain the intervention in the six intervention clinics relative to clinics who did not receive the intervention.Conducting implementation research can be challenging and because of initial IRB challenges, we had to modify the study from six intervention sites and six control sites to the current three intervention sites compared to nine usual care sites.The prevalence of hypertension has increased to 29.3% in 2003 to 2004 , resultiDespite solid evidence of efficacy, there has long been a knowledge-practice gap in implementing hypertension interventions . In addiThe clinical strengths of our evaluation project include: building upon previously successful interventions that have resulted in improved BP control; an intervention that uses resources already available in primary care clinics and that could be redeployed in new ways to achieve higher quality of care for patients with hypertension; and assessing the costs associated with implementation of the intervention. Demonstrating the costs of the intervention will help ensure the dissemination of the intervention.This implementation study capitalizes on the national healthcare system of the VA to systematically examine the local adoption of an effective program aimed to manage veterans' hypertension while informing implementation science. The goals of the intervention are aligned with the performance goals of the hospital administration as demonstrated with the leveraging of facility resources. Nonetheless, implementation of evidence based practices requires changes across the system, and this study is designed to facilitate and evaluate such changes.The magnitude of the gap between discovery and delivery cannot be understated. Nor can we underestimate the gap between what we know and what we need to know in terms of promoting the use of evidence-based guidelines in primary care settings. Given the magnitude of the 'systems change' that may be required to meet hypertension guidelines, the project may also have a significant impact on veteran's health by helping the VA to accelerate the translation of scientific advances into large-scale improvements in health and substantial reductions in health disparities. Findings from the current endeavor may transcend the VA into other healthcare settings.The authors declare that they have no competing interests.HBB and GLJ were responsible for obtaining funding. All authors contributed to the design of the study, implementation of the project, design and coordination of the study, and helped to draft the manuscript. All authors read and approved the final manuscript.


Detecting objects is an important task when moving through a natural environment. Flies, for example, may land on salient objects or may avoid collisions with them. The neuronal ensemble of Figure Detection cells (FD-cells) in the visual system of the fly is likely to be involved in controlling these behaviours, as these cells are more sensitive to objects than to extended background structures. Until now the computations in the presynaptic neuronal network of FD-cells and, in particular, the functional significance of the experimentally established distributed dendritic processing of excitatory and inhibitory inputs is not understood.We use model simulations to analyse the neuronal computations responsible for the preference of FD-cells for small objects. We employed a new modelling approach which allowed us to account for the spatial spread of electrical signals in the dendrites while avoiding detailed compartmental modelling. The models are based on available physiological and anatomical data. Three models were tested each implementing an inhibitory neural circuit, but differing by the spatial arrangement of the inhibitory interaction. Parameter optimisation with an evolutionary algorithm revealed that only distributed dendritic processing satisfies the constraints arising from electrophysiological experiments. In contrast to a direct dendro-dendritic inhibition of the FD-cell (Direct Distributed Inhibition model), an inhibition of its presynaptic retinotopic elements (Indirect Distributed Inhibition model) requires smaller changes in input resistance in the inhibited neurons during visual stimulation.Distributed dendritic inhibition of retinotopic elements as implemented in our Indirect Distributed Inhibition model is the most plausible wiring scheme for the neuronal circuit of FD-cells. This microcircuit is computationally similar to lateral inhibition between the retinotopic elements. Hence, distributed inhibition might be an alternative explanation of perceptual phenomena currently explained by lateral inhibition networks. Moving through an environment requires gathering information about the spatial properties of the surroundings. Collisions with obstacles have to be avoided and objects that may serve as landmarks for orientation need to be detected. Collision avoidance does not require detailed information about the object properties. Rather, it may be sufficient to know that there is an object no matter what it is.In a wide range of species visual interneurons have been found which preferentially respond to small objects in their receptive field  There is now good evidence for spatially distributed interactions in the input circuit or on the dendrite of the FD-cells The above mentioned models were recently modified to allow a simulated fly to track a small moving target in a virtual environment Using model simulations we analyse three different wiring schemes with respect to their ability to comply with the two above mentioned experimentally established constraints. For all wiring schemes we assume the same receptive field for the inhibitory neuron and the FD-cell. To adjust the models to the constraints imposed by the electrophysiological data, we optimised the model parameters by means of an optimisation method.The aim of the study is to unravel fundamental computational principles underlying object sensitivity of FD-cells and putting forward electrophysiologically checkable predictions, but not to mimic the detailed neuronal circuitry. Therefore, we chose a new paradigm which relies on only few free model parameters and allows us to model dendritic signal spread within a dendro-dendritic wiring scheme at a relatively abstract level by spatial lowpass convolution : = {n∶i−σ/2≤n≤i+σ/2; 1≤n≤W}Accordingly, we implemented the spatially distributed processing of the retinotopic input in the inhibitory part of the FD-cell circuit, consisting of HS-cells and the vCH-cell, as a single spatial lowpass filter. In the model these two cells are lumped into a single inhibitory element. In a first approximation, a rectangular filter kernel was used to spatially convolve the input signal. This approximation saves computation time since the filter can be calculated as a running average:V is the input signal and I the convolved output signal. i and n denote the position along the dendrite. W is the width of the receptive field and σ is the width of the filter kernel.m of the FD-cell that results from spatial dendritic pooling:I and EE denote the reversal potentials of ion channels with the associated inhibitory (gI) and excitatory (gE) conductances, respectively. E0 is the resting potential of the cell. The inhibitory and excitatory conductances will be calculated from the respective input using functions specifying synaptic transmission between the presynaptic input and the corresponding postsynaptic cell (see below). The reversal potentials are fixed parameters. If the reversal potential of an ion channel is more positive than the resting potential E0 of the FD-cell, this channel is excitatory. A reversal potential more negative than the resting potential denotes an inhibitory channel.To unravel the significance of the spatially distributed processing in the neural circuit presynaptic to the FD-cell, the FD-cell is considered to be isopotential. The equivalent electrical circuit of a one-compartment passive membrane patch is used to calculate the membrane potential U0 to 1. The other conductances are thus given relative to the leak conductance. The electrical equivalent circuit delivers a membrane potential Um as a result.We set the leak conductance gSynapses were often found to transform the presynaptic signal nonlinearly into postsynaptic responses The Direct Pooled Inhibition (DPI) model does not comply with the anatomical constraint of the inhibitory element conveying its signal in a distributed fashion to its postsynaptic targets. Nonetheless, this model will serve as a reference to understand the importance of a distributed processing. The FD-cell receives its excitatory and inhibitory input as a one-compartment passive membrane patch as described above. The FD-Cell is directly excited by the vector V(i) of retinotopically distributed velocity values .Vsyn, into a conductance gV(i)  from each spatial position i is transformed, via the synaptic transmission function ce gV(i) . All locI of inhibitory FD-cell ion channels. As these channels are supposed to be inhibitory, their reversal potential has to be equal to or more negative than the resting potential. The case of a reversal potential equal to the resting potential represents so-called shunting inhibition. The reversal potentials are free model parameters. Hence, optimisation of the model will constrain the values of these potentials. gI is calculated as the spatial average of V(i) transformed by the synaptic transmission function synI (equation 4). Therefore, all spatial information is lost in the inhibitory signal. Note that in the inhibitory pathway the synaptic transmission function is applied after spatial integration, whereas this function is applied to the excitatory input before integration.The FD-cell receives its inhibitory input from a neuron which has the same receptive field as the FD-cell itself . After cVg(i) = Vsyn(V(i))In terms of spatial pooling this model is similar to a previous model of the FD-cells V, Ei and, for both functions of synaptic transmission, the three parameters characterising saturation, slope and position of the transmission characteristic (see above). For optimisation some parameters had to be constrained to ensure they are within a biologically realistic range. Thus, in the optimisation process, the reversal potential Ee is kept smaller than 100 mV whilst the reversal potential of the inhibitory ion channel Ei is held at the level of the resting potential (shunting inhibition) or at a more negative level (though not below −120 mV). It is obvious that the synaptically inducted conductances are biologically limited. Since we do not know the upper limit, we choose a wide range: The maximum of the excitatory and the inhibitory conductance are limited each to 10,000-times the leak conductance.The DPI model has 8 free parameters: the reversal potentials EV of excitatoy ion channels. However, DDI differs from DPI with respect to the inhibitory pathway  is transformed into an array of conductances gI(i) of the FD-cell (The Direct Distributed Inhibition (DDI) model uses the same activation of the FD-cell as the DPI model: the retinotopic velocity information V(i) is transformed into a sum of conductances g pathway . DDI tak pathway . Dendrit FD-cell . In cont FD-cell  and 4B.V(i) and gI(i), respectively. gV(i) and gI(i) are the conductances of the synaptically controlled ion channels with the reversal potentials EV and EI, respectively:Ig(i) = Isyn(I(i)), Vg(i) = Vsyn(V(i)) and I(i) as defined in eq. (1)The FD-cell integrates the velocity information in terms of the conductances gV, EI, the width sigma of the filter kernel and, for both functions of synaptic transmission, the three parameters characterising saturation, the slope and the position of the transmission characteristic (see above). Here again the optimal values have been determined by optimisation (see below). The value ranges which are set to be valid for the optimisation are the same as for the DPI model.The model has 9 free parameters: the reversal potentials EFrom an abstract point of view, DPI is only a special version of DDI. If the inhibitory neuron of the FD-cell circuit were electrically compact, this neuron would have exactly the same potential along the entire dendrite. For the DDI model this situation is given for an infinite width of the spatial filter kernel averaging the signal across the entire receptive field.i = E0.in is the input signal, shunt denotes the strength of the shunt.The Indirct Distributed inhibition (IDI) model differs from the other models in one essential aspect: the inhibition of the FD-Cell is indirect, since it is mediated via its presynaptic retinotopic input elements. Here, not the FD-cell itself is inhibited, but its input elements. As a first approximation, the inhibition is implemented as a pure shunting inhibition, i.e. EI as specified above, the lowpass-filtered signal I(i) is transformed entry-wise into the shunting signal (see equation 7). This signal shunts the retinotopic input of the FD-cell according to Equation 6. Employing the synaptic transmission function synV the resulting signal is transformed into the array of local conductances gv(i) of the FD-Cell (V(i) reflects the total conductance of the FD-cell corresponding to ion channels with the reversal potential EV. The FD-cell has no direct inhibitory input.Vg(i) = Vsyn(presyn(V(i), Isyn(I(i)))) and I(i) as defined in eq. (1)The inhibitory element contacts the output area of the local movement detectors and shunts them before they reach the FD-cell . The shu FD-Cell . SimilarV, the width sigma of the spatial filter kernel and, for both functions of synaptic transmission, the three parameters characterising saturation, the slope and the position of the transmission characteristic. Again the optimal values have been determined by optimisation (see below). The value ranges which are set to be valid for the optimisation are the same as for the previous models.The model has 8 free parameters: the reversal potential EThe model parameters were optimised to mimic the experimentally determined velocity and size dependences of the FD-cell response. Since only spike rates were available from the extracellular recordings of FD-cell activity, these had to be transformed into membrane potentials. Based on a previous study, the membrane potential was assumed to be proportional to the spike rate rms root mean squared was chosen:rms if a parameter is beyond the valid value range (see above) ensured the parameters to stay within this ranges.Our aim was to account for both the size dependence and the velocity dependence of the FD-cell response in each model using only a single set of parameters. Therefore, it was essential to optimise the models simultaneously with respect to both criteria. Since the experimentally determined dependence of the FD response on object and background velocity comprises more data points than the size dependence results compare , the forrms distance to the biological data as one reference. This reference assumes that the neuronal response does not depend at all on the tested stimulus parameters. The standard error of the mean (SEM) of the data from the velocity dependence experiments To asses the significance of the smallest distance values obtained by the optimisation procedure we used a constant artificial response which has the smallest drms as a function of the model parameters. Consequently, we expect Differential Evolution to be an appropriate optimisation method.We applied “Differential Evolution” as an automatic stochastic optimisation method rms as a function of 8 (DPI and IDI models) or 9 (DDI model) parameters. Since Differential Evolution is a stochastic optimisation method, finding the global optimum is not guaranteed, as it is possible to get stuck in a local optimum. Initially, the optimisation was performed several times in preliminary tests with different initial parameters of the search algorithm. The set of these parameters performing best was chosen for the final optimisation .The algorithm searches for the global optimum of the function to be analysed. In our case we want to find the optimum of the distance measure drms in the last 10,000 steps of searching was negligible (<0.01 mV). Each of the 1,000 runs delivers one set of model parameters as a solution which is a candidate for the global optimum.The optimisation procedure was repeated 1,000 times for each model. Each run was stopped after a fixed number of iterations  or if the improvement in terms of dSince the optimisation procedure may return only a local optimum as a solution, more than one optimum was found for each model. Each of the optima was found several times. Hence, the algorithm did not get stuck in a single local optimum and the different optima were found reliably. However, there is no guarantee that we found all local optima including the global optimum. Systematic variations of the model parameters around the best found solution ensured that the algorithm did not get stuck between optima as solutions actually turned out to be local optima.rms is most interesting. However, since also qualitative properties are important, good solutions in terms of the distance measure drms may also be interesting, even if they are not the best.In the following we evaluate the different solutions for each of the three models. At first the solution with the best drms of 2.1 mV. This is beyond the SEM  of the corresponding experimental data rms of 3.7 mV for the constant response reference assuming that the response does not depend on the tested stimuli at all.None of the solutions found for the DPI model mimics the size dependence of the FD responses: only for high object velocities the DPI responses decrease with an increasing object size. For small and medium object velocities, the model responses do not show any preference for small objects and the response is the same for all object sizes. On the other hand, all solutions for the DPI model mimic the velocity dependence quite well. The deviations are in the range of the SEM of the experimental data. Only at high background and object speeds do we find a big difference . The disIt was surprising that no pronounced small-field tuning has been obtained with DPI, since this distinguishing characteristic of FD-cells was previously obtained with a similar model rms is not sufficient for a model to be acceptable, it is also necessary that their optimised parameter values have biological plausibility. Three parameters of the best solution of the DPI model are at the border of the permitted range (see above). This is the case in one parameter vector for the parameter determining the slope of the synaptic transmission function and in another vector for the reversal potential of the inhibitory ion channels EI. Allowing values beyond this range did not noticeably improve the model. The third critical parameter is the level of saturation S of the synaptic transmission functions which is determined by the ratio between the synaptically induced conductance and the leak conductance of the FD-cell. With an increasing conductance ratio, the performance of the model increases slightly, but is no longer much affected for ratios above approximately 100 . Hence, the drms is close to the SEM of 1.2 mV as obtained for the corresponding experimental data. As for the DDI model, we observe a major deviation between the model and the experimental results only at the highest tested background and object velocities  are characterised by a nearly linear transmission of the inhibitory synapses, whereas the excitatory synapses have an expansive characteristic. Nevertheless, small field tuning may be obtained even with linear transmission characteristics at both excitatory and inhibitory synapses. This is illustrated here for a simplified model variant of IDI. It consists of a spatial low pass filter mimicking, as in IDI, the dendritic signal spread in the inhibitory neuron (see eq. 1), a shunting inhibition as given by eq. 6 and a linear summation accounting for both linear transmission of the input signals and the dendritic integration by the model FD-cell (model(input)):The entries of a spatially distributed signal input(i) account for the numerator of the fraction. The denominator consists of the entries of the spatially blurred input signal and a term accounting for the cells leak conductance. The leak parameter was arbitrarily set to 1.The model simulations reveal that just a spatial low-pass filter combined with a presynaptic shunting inhibition  are sufficient to produce a preference for small objects . For numShunting inhibition of the retinotopic elements is by itself not sufficient to ensure small-field tuning of the model: Without spatial blurring the response of the inhibitory neuron the FD-cell response is proportional to object size . With inIt has been the objective of this modelling study to challenge different model circuits with respect to their ability to account for a preference of FD-cells in the blowfly visual system for small moving objects as well as the characteristic dependence of their responses on object and background velocity In all tested models small-field tuning is accomplished by inhibiting the FD-cell either directly or indirectly via another motion sensitive cell. Issues were the functional consequences of different architectures of the neuronal microcircuits. In particular we assessed the impact of localised inhibition after spatial pooling of retinotopic motion information versus distributed dendritic inhibition as well as pre- and postsynaptic synaptic interactions. We did this by employing a new approach of modelling the signal spread in a passive dendritic tree by spatial filtering of the cell's input activity pattern rather than by detailed compartmental models. The parameters characterising the three analysed model circuits were automatically optimised with respect to the most characteristic electrophysiological properties of FD-Cells. In contrast to inhibition after spatial pooling, circuits based on spatially distributed inhibition can approximate the preference of FD-cells for small objects and their dependence on object and background velocity so well that we are, in most cases, not able to clearly distinguish the experimental data from the model responses.In the Direct Pooled Inhibition (DPI) model, the inhibitory element spatially integrates the motion signals before inhibiting the FD-cell directly. With appropriate parameter constellations it satisfies either the characteristic size dependence or the velocity dependence, but not both with the same parameter setting. Hence, this model cannot account for the characteristic features of the FD-cells.With a spatially distributed interaction between the inhibitory element and the FD-cell or its input elements the performance improves significantly. In the model “Direct Distributed Inhibition” (DDI), the inhibitory element interacts with the FD-cell dendro-dendritically, whereas in the model “Indirect Distributed Inhibition” (IDI) it interacts presynaptically to the FD-cell with its retinotopic input elements. The two distributed models approximate quite well both the dependence of the FD responses on pattern size as well as its dependence on object and background velocity. At most data points are the model data within the standard error of the mean of the experimental data.This good performance of the distributed models relies on a spatial blurring of the retinotopically mediated velocity signal in the dendrite of the inhibitory neuron. Hence, we can conclude that a distributed interaction which preserves the spatially distributed retinotopic velocity signal in the inhibitory neuron, though in a blurred form, is an essential part of the circuitry of object detection in the visual system of the fly.This conclusion is in good accordance with the available experimental data: (1) elimination of the inhibitory vCH-cell eliminates the preference of the FD-cell for small objects As a potential advantage of a circuit relying on spatially distributed inhibition the inhibitory signal has more computational degrees of freedom than a pooled signal. In the latter case, only the signal strength can be varied as a function of time, whereas in the former situation the spatial domain can also be used. Hence, in the case of a distributed interaction the inhibitory signal may depend in different ways on object size as well as on the contrast and speed of the stimuli There might be another advantage of distributed models (DDI and IDI) over a model where the signal in the inhibitory element is spatially pooled prior to its interaction with the FD-cell (DPI). Unlike the DPI model, when tuned to the size dependence of the FD-cell the responses of the DDI and IDI models do not confound two objects moving in the receptive field with a single object of twice the size in their responses. A second object has only a small effect on the response of the models with distributed inhibition, whereas the response of the DPI model decreases. This means that spatially distributed inhibition cannot be disturbed as easily as an inhibition after spatial pooling by a second object which turns up in the receptive field of the FD-cell. Although this prediction has not been tested in FD-cells so far, a similar effect was found in an object-sensitive cell of dragonflies It is not known so far whether the spatially distributed inhibition operates directly on the dendrite of the FD-cell or indirectly via its retinotopic input elements. Both DDI and IDI are able to mimic similarly well all considered response properties of FD-cells. However, the synaptic conductance changes required for this performance differ for the two wiring schemes. IDI achieves the required performance with conductance changes which are by magnitudes smaller than the ones necessary for DDI. The performance of IDI does not improve further with increasing conductances. In contrast, DDI requires not only much higher conductance changes than IDI to satisfy the constraints, but gets continually better with growing conductance changes.Measurements of input resistance in the axon of blowfly motion sensitive neurons without and during visual motion stimulation reveal a ratio of less than 2∶1 between the total synaptically induced conductance and the leak conductance Nevertheless, independent of the biophysical details of the synaptic interaction between inhibitory neuron and FD-cell two advantages of a distributed indirect inhibition make this wiring scheme currently the most plausible one: Since IDI performs well for much smaller conductances than DDI, it is likely to be much less demanding with respect to energy expenditure. This is because, large synaptic currents require much more ions to be actively transported to the other side of the cell membrane. Furthermore IDI is less demanding with respect to the biophysical and geometrical properties of the FD-cell, because in DDI the very simple approximation of the model FD-cell operates sufficiently well only for very large synaptically controlled conductance. Only additional biophysical and geometric assumptions may – if at all - improve DDI in this respect.The two distributed models might be directly distinguished by experimental analysis. Due to an indirect inhibition the overall conductance of the FD-cell should decrease with increasing object size. The overall conductance depends, apart from the leak conductance, on the excitatory synaptic conductances. Therefore, a decreasing cellular response with increasing object size is predicted to lead to a decreasing overall conductance. In the case of direct inhibition of the FD-cell however, motion in the receptive field would also lead to an opening of inhibitory ion channels in the FD-cell dendrite. With increasing object size, the inhibitory currents are predicted to overcompensate the excitatory input currents. Thus, in the case of a direct inhibition, the overall conductance of an FD-cell should increase with increasing object size, in contrast to an indirect inhibition.Despite the good overall agreement of the models based on distributed inhibition and the experimental data, there are some differences for spatially extended objects and at high velocities.The difference obtained for large objects may be caused by the very simplistic receptive field structure of the model cells. In the models we assumed the same sensitivity across the entire receptive field, although the sensitivity of real cells building the circuit declines towards the receptive field edges Two aspects may be responsible for the difference of the model performance and the experimental data at high velocities. (1) Velocity coding by biological motion detectors, as found in the fly visual system, is not linear Spatial blurring of the retinotopic input resulting from dendritic signal spread in the inhibitory neuron is restricted to the neighbourhood of an activated input element. This is also true for the mechanism of lateral inhibition. A lateral inhibition circuit and the IDI model also show a structural similarity. In the case of lateral inhibition, a layer of interneurons is laterally inhibited by neighbouring input elements . Assumin