Generation of 3D shape, density, cortical thickness and finite element mesh of proximal femur from a DXA image Areal bone mineral density (aBMD), as measured by dual-energy X-ray absorptiometry (DXA), predicts hip fracture risk only moderately. Simulation of bone mechanics based on DXA imaging of the proximal femur, may help to improve the prediction accuracy. Therefore, we collected three (1-3) image sets, including CT images and DXA images of 34 proximal cadaver femurs (set1, including 30 males, 4 females), 35 clinical patient CT images of the hip (set 2, including 27 males, 8 females) and both CT and DXA images of clinical patients (set 3, including 12 female patients). All CT images were segmented manually and landmarks were placed on both femurs and pelvises. Two separate statistical appearance models (SAMs) were built using the CT images of the femurs and pelvises in sets 1 and 2, respectively. The 3D shape of the femur was reconstructed from the DXA image by matching the SAMs with the DXA images. The orientation and modes of variation of the SAMs were adjusted to minimize the sum of the absolute differences between the projection of the SAMs and a DXA image. The mesh quality and the location of the SAMs with respect to the manually placed control points on the DXA image were used as additional constraints. Then, finite element (FE) models were built from the reconstructed shapes. Mean point-to-surface distance between the reconstructed shape and CT image was 1.0mm for cadaver femurs in set 1 (leave-one-out test) and 1.4mm for clinical subjects in set 3.The reconstructed volumetric BMD showed a mean absolute difference of 140 and 185mg/cm 3 for set 1 and set 3 respectively. The generation of the SAM and the limitation of using only one 2D image were found to be the most significant sources of errors in the shape reconstruction. The noise in the DXA images had only small effect on the accuracy of the shape reconstruction. DXA-based FE simulation was able to explain 85% of the CT-predicted strength of the femur in stance loading. The present method can be used to accurately reconstruct the 3D shape and internal density of the femur from 2D DXA images. This may help to derive new information from clinical DXA images by producing patient-specific FE models for mechanical simulation of femoral bone mechanics. 3D shape, vBMD, cortical thickness and FE mesh of the proximal femur were reconstructed from a DXA image  Surface reconstruction error was 1.0-1.4mm  Use of DXA, instead of projected CT images, had no significant effect on the reconstruction accuracy  DXA-based FE agreed well with CT-based FE analysis (stiffness r 2 =0.85, MAC=0.977) DXA-based FE analysis may help to simulate patient-specific bone mechanics Osteoporosis is a disease characterized by reduced mineral density and inferior bone quality. Therefore, bone fracture risk increases with osteoporosis (Kanis et al., 1994; WHO, 1994) . It is estimated that 30% of all women over 50 years of age in Europe are affected by osteoporosis (Melton et al., 1992) . The number of osteoporotic fractures in Europe was estimated in year 2000 to be 3.1-3.7 million, and their direct cost €32 billion (Kanis and Johnell, 2005) . These costs are expected to rise to €76.8 billion per year in 2050 (Kanis and Johnell, 2005) .. Bone mineral density (BMD) measurement using dual-energy x-ray absorptiometry (DXA) at the hip is most commonly used to diagnose osteoporosis (Link, 2012) . The patient's BMD value is compared with the mean BMD value of the reference population of healthy young women. The result is reported as a T-score, which is the number of standard deviations (SD) from the mean population (WHO, 1994) . A patient is defined as osteoporotic if the T-score value is below -2.5 SD. However, BMD alone can explain less than one third of all low trauma fractures (Pasco et al., 2006) . This is partly due to facts that BMD does not account for the geometry and internal architecture of the bone. Hip structural analysis (HSA) measures geometric features of the femoral shape e.g. femoral neck length and cross-sectional moment of inertia from a DXA image. Although HSA structural parameters are highly correlated with BMD, they are not better predictors of fracture risk than BMD (Bonnick, 2007) . Finite element (FE) modelling based on quantitative CT (QCT) images has been shown to explain at least 20% more of the strength of the femur (Cody et al., 1999) . With QCT-based FE modelling, additional factors that help explaining femoral strength can be taken into account. These include e.g. shape and structure of the trabecular bone (Larsson et al., 2014) , the effect of the loading direction (Grassi et al., 2012; Trabelsi and Yosibash, 2011) and the thickness of the cortical bone (Chevalier et al., 2009 ). It has also enabled prediction of the fracture location (Schileo et al., 2014) . However, CT imaging is more expensive and induces larger radiation dose on the patients than DXA (Kanis, 2002) . This impairs the use of CT-based FE models for fracture risk prediction in the clinics.. Two-dimensional FE models can be built from DXA images (Luo et al., 2013; Naylor et al., 2013; Sarkalkan et al., 2014) . Femoral strength computed with 2D FE models was shown to be an independent predictor of fracture risk (Naylor et al., 2013) . However, 2D FE analysis was also shown to be sensitive to the patient's position (Luo et al., 2013) . It is also intrinsically not able to account for the impact in the anteriorposterior direction, which is known to significantly affect femur's load-bearing ability (Ford et al., 1996) .. DXA-based 3D FE analyses could overcome these limitations.. If the shape and internal density of a bone could be reconstructed from one or a few 2D radiographs, it would provide information about the 3D bone geometry and architecture for the assessment of the fracture risk. Thus, the concept of shape reconstruction has been studied intensively (Ahmad et al., 2010; Chernoff and Nielsen, 2009; Galibarov et al., 2010; Iwashita et al., 2007; Knaan and Joskowicz, 2003; Kurazume et al., 2009; Langton et al., 2009; Markelj et al., 2012; Whitmarsh et al., 2013 Whitmarsh et al., , 2011a Zheng, 2009 ). Most of the previous methods use several 2D images, and only a few studies reconstructed both shape and internal density of the proximal femur using one 2D radiograph (Galibarov et al., 2010; Thevenot et al., 2013; Väänänen et al., 2012b) . Two of them used a single 2D DXA image Väänänen et al., 2012c) . However, these methods do not automatically yield the 3D mesh for the FE simulation. Further, the methods do not distinguish between trabecular and cortical bone (Thevenot et al., 2013) . This is a limitation since the geometry and thickness of the cortical bone play an essential role in determining the strength of the total femur (Holzer et al., 2009; Koivumäki et al., 2012a) . Therefore, an automatic method that accurately estimates bone 3D shape and internal density and generates FE meshes from a single clinical 2D DXA image is still missing.. The aim of the present study was to develop an automatic method to reconstruct the 3D shape, internal volumetric BMD (vBMD) and cortical thickness of the proximal femur from a single hip DXA image. Further, the outcome should be directly suitable for FE simulations. The method could subsequently be used to calculate bone strength and predict patient's susceptibility to fractures. We assessed the major sources of error and how the errors accumulated during each step of the shape reconstruction. Especially, we evaluated the effect of noise and spatial resolution in DXA imaging on the accuracy of the reconstruction by comparing it to the reconstruction from a projected CT image. We also assessed the suitability of the generated FE-mesh for mechanical evaluation. Finally, the effect of shape reconstruction on the results of the FE models was assessed. An automatic method was developed to reconstruct the 3D shape and internal architecture of the proximal femur using only one 2D clinical DXA image. This was done by aligning a 3D statistical appearance model of the femur and pelvis with the DXA image. The outcome of the reconstruction is directly suitable for FE modelling since it produces good quality tetrahedral mesh including BMD values which can further be converted to Young's modulus. In all cases, over 99% of the elements had scaled minimum solid angle above 0.5, indicating good or excellent element quality. In addition, most of the elements with lower quality were located at the minor trochanter region, whose biomechanical relevance is minor when predicting bone strength.. Those few distorted elements were automatically fixed. This means that mesh quality is not a restricting factor for the accuracy of the mechanical simulation. The presented method is also able to estimate the cortical thickness and to account for the overlaying acetabulum on the femoral head in a DXA image.. In literature, when only one DXA or X-ray image was used for the reconstruction, the mean point-tosurface reconstruction error generally ranged between 1.1 and 3.0 mm (Galibarov et al., 2010; Hurvitz and Joskowicz, 2008; Langton et al., 2009a; Thevenot et al., 2013; . Thus, the current findings (1.0 and 1.4 mm) are among the most accurate reported. Compared to our earlier method (Väänänen et al., 2012b) the mean point-to-surface distance during reconstruction of cadaver femurs was slightly increased (from 0.88 mm to 1.02 mm), although in general SAM-based methods (Hurvitz and Joskowicz, 2008; Whitmarsh et al., , 2010 seem to perform the reconstruction more accurately than general template-based methods (Galibarov et al., 2010; Langton et al., 2009a; Thevenot et al., 2013) . The advantages in our current method compared to our earlier ones (Väänänen et al., 2012b (Väänänen et al., , 2011 are that: 1) it accounts for that the acetabulum covers the femur in the DXA images and thus removes the error; 2) it automatically accounts for the orientation of the femur in the 2D DXA image since the rotations of the femur are among the optimized parameters, and 3) the outcome is directly applicable for FE simulations.. The accuracy of the vBMD density was 185mg/cm 3 which is approximately 13% of the total variation of the vBMD. The vBMD was evaluated element-by-element between the mesh of the original CT images and reconstructed shape. Our average element volume was less than one tenth of the voxel volume used earlier in the voxel-by-voxel comparison . This partly explains the larger variation in vBMD compared to what has been reported earlier. Standardized evaluation protocols would help to compare the methods more consistently (Markelj et al., 2012) . In the DXA images from clinical patients, potential additional sources of errors are lower signal-to-noise ratio due to soft tissue coverage, and the pelvis which covers the femoral head. In our study, also the demographics parameters (age and sex) differed between the training sets and the test set. In addition, the resolution, to which the reconstructed shape is compared, was lower in the original CT images of the clinical subjects (restriction in our ethical permission) than in the CT images of the training set. The number of subjects in both training and evaluations sets were relatively low (34 and 12). However, the method shows promising performance already with these limited sets. Therefore, to improve the training of SAMs, it is necessary in the future to collect more femurs from patients with similar ethnical parameters as the patients in our clinical test set. Now it remains unclear if the difference in the reconstruction accuracy between our method and the most accurate one reported earlier was due to the gender differences between the test and train sets, the lower resolution in the CT images of the test set, or due to differences between the methods.. Adding SAM of the pelvis to the reconstruction of the shape positively influenced the accuracy in the femoral head, as compared to that of earlier studies . The head and neck were the most accurately reconstructed regions in our study. The head was estimated with 40% higher accuracy than that reported by . These authors accounted for the overlaying pelvis in DXA images by extrapolating the femoral head region based on the other regions. Adding the pelvis to the reconstruction has also another benefit since it allows more realistic boundary conditions in the FE simulations in the future.. Correlation of the stiffness between the QCT-based and DXA-based models was r 2 =0.85. This is in agreement or better than earlier findings (Langton et al., 2009b; Väänänen et al., 2012b) and shows good agreement between the models. The MAC value between the models was 0.977, which manifests good agreement between the predicted local displacements. Therefore, the present results are encouraging and suggest close agreement between the FE models of the reconstructed shapes and the results from experimental tests in the future (Grassi et al., 2013; Väänänen et al., 2013) .. Modelling of the cortical bone separately in the FE model, based on direct segmentation from clinical CT images, has earlier been shown to improve the prediction of the experimental femoral strength (Koivumäki et al., 2012a (Koivumäki et al., , 2012b . Our study demonstrates that the 3D cortical thickness can be reconstructed from one DXA image with good accuracy. However, since a threshold value was given for the minimum cortical thickness, current methodology may slightly overestimate the reconstruction accuracy of the cortical thickness at regions with very thin cortex such as in the region of the femoral head. The overestimation could be resolved in the future by utilizing cortex-thickness mapping and estimation algorithms (Treece et al., 2010 (Treece et al., , 2012 .. A few manual landmarks were needed on the reference image. Placing these landmarks takes in all cases less than half a minute for an image, and the method is robust against small differences in the position of these landmarks. However, our future goal is still to make the manual positioning of these landmarks unnecessary.. Calculation time for a clinical DXA-based reconstruction was on one core of Intel Sandy Bridge 2,6 GHz processor around 40 hours. Solving one FE simulation on Intel Core i7-3770 CPU @ 3.40 GHz took around 20 minutes. In the future, computation time can be substantially reduced by e.g. using graphical processor unit calculations in the generation of DRR (Ehlke et al., 2013) .. In conclusion, the presented method was able to reconstruct the femoral shape, cortical thickness and internal density based on one clinical DXA image with high accuracy (e.g. shape error of 1.4mm). It was also able to automatically generate 3D meshes which are suitable for FE analysis. DXA-based FE analyses agreed well with CT-based FE analyses (i.e., the warped models).. Step-by-step evaluation of the reconstruction of the 3D shape showed that the generation of the SAM, reconstruction based on 2D image and utilizing clinical DXA images where the most significant sources of error in the reconstruction, whereas use of noisier DXA images instead of projection of CT images as reference image seemed to have only minor effects. The method was able to reconstruct the shape based on the DXA image of a clinical subject with an average accuracy of 1.42 mm ( Table 2 , Fig. 4 and 5) and with an average volumetric difference with respect to the original shape of 7%. Use of different reference images, i.e., DXA image or projected CT image, did not affect the accuracy markedly. For example, the average surface reconstruction accuracy changed with only 0.00-0.08 mm. The 3D distribution of the vBMD, based on one DXA image from clinical subjects, was reconstructed with an average difference of 0.19g/cm 3 (Table 2 , Fig. 6, supplementary figure S3 ). The cortical thickness was estimated with an average accuracy of 0.37mm (Table 2 , Fig. 7, supplementary figure S3 ). The produced FE meshes were suitable for FE simulations, since over 99 % of the elements had an element quality higher than 0.5 as measured with the scaled minimum solid angle. The linear correlation between the stiffnesses from the warped FE models and the projected CT-based FE models was r 2 =0.81. The correlation between the stiffnesses from the warped and DXA-based FE models was even higher (r 2 =0.85) (Fig. 8 ). BMD measured with DXA was also directly compared with the stiffness of the warped FE model when the resulting correlation was lower (r 2 =0.72). The MAC correspondence between the warped and CT projection-based FE models was 0.984 ± 0.011, and warped and DXA-based models was 0.977 ± 0.016.

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Recovery of rhythmic activity in a central pattern generator: analysis of the role of neuromodulator and activity-dependent mechanisms Abstract The pyloric network of decapods crustaceans can undergo dramatic rhythmic activity changes. Under normal conditions the network generates low frequency rhythmic activity that depends obligatorily on the presence of neuromodulatory input from the central nervous system. When this input is removed (decentralization) the rhythmic activity ceases. In the continued absence of this input, periodic activity resumes after a few hours in the form of episodic bursting across the entire network that later turns into stable rhythmic activity that is nearly indistinguishable from control (recovery). It has been proposed that an activity-dependent modification of ionic conductance levels in the pyloric pacemaker neuron drives the process of recovery of activity. Previous modeling attempts have captured some aspects of the temporal changes observed experimentally, but key features could not be reproduced.Here we examined a model in which slow activitydependent regulation of ionic conductances and slower neuromodulator-dependent regulation of intracellular Ca 2+ concentration reproduce all the temporal features of this recovery. Key aspects of these two regulatory mechanisms are their independence and their different kinetics. We also examined the role of variability (noise) in the activitydependent regulation pathway and observe that it can help to reduce unrealistic constraints that were otherwise required on the neuromodulator-dependent pathway. We conclude that small variations in intracellular Ca 2+ concentration, a Ca 2+ uptake regulation mechanism that is directly targeted by neuromodulator-activated signaling pathways, and variability in the Ca 2+ concentration sensing signaling pathway can account for the observed changes in neuronal activity. Our conclusions are all amenable to experimental analysis. Neural networks that produce rhythmic patterns of activity are commonly involved in behaviors serving basic biological functions, including breathing, heartbeat, locomotion, digestion, etc. (Frere et al. 2004; Golowasch and Marder 1992; MacKay-Lyons 2002; Marder 2000) and most of our understanding derives from work on central pattern generators (CPGs) (Marder and Calabrese 1996; McCrea and Rybak 2008; Selverston 2010) . CPGs are often capable of generating robust activity but can also adapt to drastically changing environments. This is accomplished by a readjustment of neuronal intrinsic and synaptic properties (Bucher et al. 2005; Marder and Bucher 2001; Tryba et al. 2003) . One example of such a system is the pyloric network localized in the stomatogastric ganglion (STG) of the crustacean central nervous system (Selverston and Moulins 1986) .. Under normal circumstances the rhythmic activity of the pyloric network depends obligatorily on neuromodulatory substances released by terminals of axons entering the STG via a single input nerve. If action potential transmission along this nerve is blocked (i.e. the STG is 'decentralized'), rhythmic pyloric activity ceases (Russell 1979) . However, a pattern of activity closely resembling the original pyloric pattern recovers spontaneously in the absence of neuromodulatory input within several hours (Golowasch et al. 1999; Luther et al. 2003; Thoby-Brisson and Simmers 1998) . In the crab Cancer borealis, this recovery follows a complex temporal dynamical process that involves the alternating onset and termination of the rhythm, or 'bouting' (Luther et al. 2003) . This bouting activity can last several hours, after which a stable pyloric pattern emerges that distinguishes itself from the control pattern only by its somewhat lower frequency (Golowasch et al. 1999; Luther et al. 2003) .. We have previously shown that the bouting phase of the recovery of rhythmic pyloric activity after decentralization can be accounted for by the relatively fast activity-dependent regulation of voltage-gated calcium and potassium currents (Golowasch et al. 1999) , or even only of voltage-gated calcium currents (Zhang et al. 2009 ). In these studies we used conductance-based models to further show that, whether only calcium currents or both calcium and potassium currents are regulated, no transition to a stable pattern of activity can be observed in the absence of an additional regulatory mechanism that operates at a much slower time scale (Zhang and Golowasch 2007; Zhang et al. 2009 ). Under these conditions, the resulting recovery process meets most of the signature features of recovery in biological preparations (Luther et al. 2003) . Nevertheless, these models show two important attributes that are not observed in biological preparations (Luther et al. 2003) : 1) individual bout durations gradually increased until stable recovery, 2) a correlation is observed between the extent of bouting activity and delay to stable recovery. In this paper, we used a modified version of our original model (Zhang and Golowasch 2007) to examine the process of functional recovery of the rhythmic activity of a pacemaker cell using phase plane analysis. In order to accomplish this, this model was modified to both remove non-essential elements for the recovery process, thus reducing it to a two dimensional system. It was additionally modified to reproduce experimentally observed features. The results of this study confirm that activity-dependent feedback to a single conductance, that need not be a calcium conductance, is a sufficient condition to elicit bouting activity, and that the rate of intracellular Ca 2+ sequestration plays a critical role in controlling the appearance of a stable pyloric rhythm. We find that during bouting, the system alternates its behavior between a limit cycle (within bouts) and a stable fixed point (within interbouts). The switch between these two states occurs via a subcritical Hopf bifurcation, while the transition to the stable recovery occurs as the Ca 2+ pump rate increases, making the system transition to a state from which it cannot switch back to the stable fixed point. Our results show that, as observed experimentally, the stable recovery of rhythmic activity is fully decoupled from the appearance of bouting. Nevertheless, bouting always precedes the stable recovery. In our model this is forced by the slow nature of the mechanism controlling the stable recovery. Finally, the introduction of low level noise into the system reduces constraints on slow regulatory processes, making the model more physiologically realistic. We discuss possible biological mechanisms that may mediate these two regulatory pathways. It is important to understand to what extent neurons and networks can recover their normal function if it is lost due to trauma, disease or other perturbations, and to identify the mechanisms that allow this to happen. Rhythmic neuronal activity patterns are typically found to be involved in basic biological functions, such as breathing, heartbeat, digestion, locomotion, etc. (Frere et al. 2004; Golowasch and Marder 1992; MacKay-Lyons 2002; Marder 2000) . Thus, recovery of activity is all the more crucial. The pyloric network located in the stomatogastric ganglion of decapods crustaceans is capable of just such a recovery when its rhythmic activity is disrupted as a consequence of the loss of central neuromodulatory input (Luther et al. 2003; Thoby-Brisson and Simmers 1998) and may provide insights that may be applicable to other systems. Here we propose a model to account for some important features observed experimentally that we could not reproduce with previous models (Golowasch et al. 1999; Zhang and Golowasch 2007; Zhang et al. 2009 ), suggesting possible line for experimental work aimed at understanding the mechanisms involved. The most important difference with previous models is the uncoupling of the activity-dependent regulation of ionic conductances from the neuromodulator-dependent regulation of intracellular Ca 2+ concentration (cf. (Zhang and Golowasch 2007; Zhang et al. 2009) ). This allowed us to eliminate the dependency of the recovery of stable periodic activity from the duration of episodic (bouting) activity that ensues soon after decentralization. Furthermore, the added assumption that low level noise is present along the biochemical pathway(s) underlying activity-dependent regulation of conductances allows the relaxation of a major (and biologically unrealistic) restriction in the kinetics of the neuromodulator-sensitive mechanism. With these changes, we can now account for all the kinetic features observed experimentally (Luther et al. 2003) during the entire process of recovery: loss of activity immediately after decentralization, appearance of slow bouting activity after a long silent period, and the delayed transition from bouting to a stable rhythmic state that does not involve a progressive reduction in the bout duration, which was a major shortcoming in previous models. The uncoupling of the two regulatory pathways allowed us also to account for an additional feature observed during the recovery of a stable rhythmic state that previous model could not explain: the transition to a stable state almost always follows a period of bouting activity but it does not depend on any property of the bouting phase (such as bout or interbout durations). We propose that this is simply due to the very different time scales of the activity-dependent mechanisms, which are relatively fast, and the neuromodulator-dependent mechanisms, which are slower. This could explain why on rare occasions a preparation will recover a stable pyloric rhythm without first undergoing bouting, or sometimes express an overlap of bouting and of the onset of steady rhythmic activity, as a consequence of different relative kinetics of the neuromodulatory-and the activity-dependent pathways.. Our assumption that the activity-dependent regulatory pathway, represented in our model by an activity sensor that regulates the maximal conductance of one ionic current, could have variable activity may be the result of stochastic fluctuations in biochemical pathways as has been proposed for many molecular systems in recent years (Levine and Hwa 2007; Shahrezaei and Swain 2008) . This can easily arise from the operation of pathways in which certain molecules are maintained at very low concentrations (Cao and Liang 2007) . We modeled such source of variability by adding noise to the maximal conductance of I Ca . This has two consequences that mirror experimental observations: it makes the bouting activity more variable, and it greatly relaxes the biologically unrealistic constraints otherwise necessary on the separate and independent biochemical pathway regulated by neuromodulators.. What biologically plausible mechanisms could underlie the activity-dependent regulation of ion channels and the activity-independent regulation of a Ca 2+ pump? Because stable recovery from decentralization is a very slow process that expresses itself only after a long delay (many hours), direct regulation of channels and pumps by second messengers or enzymes is deemed unlikely. However, regulation of protein synthesis and/or transcription are possible mechanisms, especially since transcription has been shown to be involved in the control of recovery from decentralization in a related species (Thoby-Brisson and Simmers 2000) . Additionally, it has been shown that neuronal activity can control (i.e. switch) the expression of calcium ATPase isoforms in axons of a different crustacean species, crayfish (Lnenicka et al. 1998) as well as in vertebrate muscle (Briggs et al. 1990; Leberer et al. 1989 ) with time courses comparable to those of the phenomenon we study (many hours). Ca 2+ pumps (e.g. SERCA) are regulated by the protein phospholamban (Simmerman and Jones 1998) , whose expression also appears to be transcriptionally regulated and to participate in activity-dependent muscle type switching with similar time course (Hu et al. 1995) . Several mechanisms have been identified in different systems that can mediate activity-dependent transcriptional regulation of these proteins (Mellstrom et al. 2008) . Other, non-activitydependent, regulatory mechanisms that can be linked to neuromodulator receptor activation have been characterized as well (Gudi et al. 2002) . Specifically for instance, it has been reported that both phospholamban and a Ca 2+ ATPase are controlled by thyroid hormone in heart, with hormonal concentration changes leading to very large changes in expression in mRNA levels of both molecules over the course of days (Nagai et al. 1989 ). Long-term adenylyl cyclase regulation (Sugano et al. 2011) has also been shown to regulate sarcoplasmic calcium in heart via several different components, including phospholamban phosphorylation. cGMP, a molecule that is regulated by a number of modulators, is also known to regulate transcription of different molecules in several systems (Gudi et al. 2002; Martel et al. 2010; Ota et al. 2010; Pilz and Casteel 2003) . Additional intracellular signaling pathways have been shown to regulate SERCA2 expression, such as calcineurin A (Prasad and Inesi 2011) , which is also known to be regulated by several neuromodulatory systems. Finally, neuromodulator-mediated regulation of other types of pumps, i.e. Na + /K + ATPase are known to exist in vertebrate as well as invertebrates (Aizman et al. 2000; Catarsi and Brunelli 1991; Catarsi et al. 1993; Therien and Blostein 2000; Tobin and Calabrese 2005) . Although these are all short-term regulatory processes, it is not inconceivable that they may also mediate long-term processes such as the one proposed here given that pathways know to activate transcription are involved in many of them (i.e. cyclic nucleotides). In sum, although direct information for our system is clearly lacking at this time, there are a number of possible paths through which, Ca 2+ pumps or their regulatory proteins can themselves be regulated by products of G-protein coupled receptors, which the neuropeptide receptors in the STG are likely to be, and the intracellular signaling molecules activated by them. Furthermore, a time course of many hours is possible (even likely) if transcription and translation of pumps and regulating molecules are involved. A sudden increase in molecular activity, such as that of an ATPase, could also be expected after a slow buildup of several independent interacting regulatory components past a threshold. In the absence of detailed experimental evidence, we propose that such a mechanism may be at work here.. Episodic activity somewhat similar to bouting activity has been characterized in other systems, particularly in developing networks of the spinal cord, retina, neocortex and hippocampus (O'Donovan 1999; O'Donovan et al. 1998; Vladimirski et al. 2008; Yuste et al. 1995) . Such episodic activity depends on network interactions via depressing excitatory synapses or via gap junctions, which sometimes determine temporal relationships between episodes and interepisodic silent activity. While the pyloric network's recovery of activity does not appear to require synaptic modifications (Luther et al. 2003 ) and we do not observe such temporal relationships during the bouting phase, one feature that appears common to both phenomena is that intracellular Ca 2+ concentration changes are involved (Garaschuk et al. 1998; Gu et al. 1994; Yuste et al. 1995) . Our results suggest that intracellular Ca 2+ concentration changes may be necessary. This is directly supported by the observation of Ca 2+ -dependent ionic conductance regulation in cultured pyloric neurons (Haedo and Golowasch 2006) , crayfish neurons (Hong and Lnenicka 1995) , as well as in numerous other systems. We propose that, similar to what is observed in developing vertebrate networks, the episodic activity of the pyloric network requires intracellular Ca 2+ concentration changes, which regulate ionic conductances, and that the system is extremely sensitive to these changes. Our model shows oscillations of G Ca of no more than 1% being sufficient to explain all the temporal changes observed. However, the model predicts intracellular Ca 2+ concentration changes of over 100% (not shown). While 1% changes in G Ca would be extremely hard to resolve, 100% changes in intracellular Ca 2+ concentration changes should be relatively easy to detect. These predictions can be experimentally tested.. Our results suggest that the Ca 2+ current conductance does not need to be the sole target of activity-dependent regulation. Although we show that G Ca regulation is sufficient for the recovery process, other currents can equally mediate the effects of an activity sensor in generating temporal changes of the rhythmic pattern characteristic of the pyloric network. In fact, it has been shown before that the conductance of multiple ionic currents, including Ca 2+ and K + conductances, undergoes changes during the process of recovery from decentralization (Khorkova and Golowasch 2007; Thoby-Brisson and Simmers 2002) . Our conclusions do not exclude possible synaptic changes within the pyloric network or ionic conductance changes of non-pacemaker neurons of the network. Both of these types of changes could act synergistically to modify the properties of the network, and need to be examined experimentally. Here we have aimed to show that all the changes necessary to account for the temporal features of pyloric activity observed during the recovery of function after decentralization can be accounted for by excitability and intracellular Ca 2+ regulation changes in the pacemaker neuron.. Our phase plane analysis shows that the critical fixed point located near the knee between the left and middle branches of the V-nullcline alone can generate the bifurcations needed for the model neuron to switch between bouting and interbout silence. Our model however, shows three fixed points. The possible roles of the additional two fixed points located along the middle branch of the Vnullcline are unclear. Although they are not required for the generation of the bouting activity and stable recovery, they may play roles in other attributes of neuronal activity. For instance, in the biological system the onset of individual bouts is characterized by a rapid acceleration of the pyloric rhythm and typically a slow decay to the interbout low frequency or silence (Luther et al. 2003) . This is not captured in our simplified model neuron. It is possible that while I Ca plays a crucial role in the activation of the bouts, other currents control their oscillation frequency and/or termination. A full model neuron, perhaps including axonal compartments, might be required to explain such details of neuronal activity, including the predicted small oscillations of the neuron's voltage at both the beginning and at the end of each bout (Fig. 4(a) ), which we have never observed in the biological system.. In a previous study we explored the effects on the pyloric activity of disrupting its activity prior to decentralization (Zhang et al. 2009) . A model was proposed to explain the observed responses in which both an activitydependent signaling pathway and a neuromodulatordependent pathway regulate ionic conductances directly. In order to attempt to dissect out the possible mechanisms that explain the temporal properties of the network activity recovery process in the present study we did not incorporate the neuromodulator-dependent regulatory pathway of ionic conductances. It would be interesting to now combine the two approaches by adding a direct neuromodulatordependent regulation path of ionic conductances to the present model with the goal of obtaining a full account of all the currently known responses of the system to decentralization. Electrophysiological recordings were carried out exactly as described before (Luther et al. 2003) . Pyloric rhythm activity was measured from extracellular recordings of motor nerves ( Fig. 1(a) ).. We built a pacemaker neuron with only a soma/neurite (S/N) compartment generating slow-wave oscillations. Since it has been observed that action potentials produced by an axonal compartment (Zhang and Golowasch 2007; Zhang et al. 2009 ) does not make a significant contribution to the recovery process, no axonal compartment was added and only the following currents necessary for slow wave oscillations were included in the S/N compartment: leakage current (I leak ), voltage-gated Ca 2+ current (I Ca ), voltage-gated delayed rectifier K + current (I Kd ), transient A-type K + current (I A ), and a voltage-gated, neuromodulator-dependent, inward current found in pyloric neurons in crab STG, I MI , which represents the neuromodulator input from adjacent ganglia (Swensen and Marder 2000) . Decentralization is implemented by turning G MI to zero.. The equations were adapted from those described by Zhang and Golowasch (2007) and Zhang et al. (2009) for the pacemaker neuron. The parameters describing these currents are included in Table 1 . A schematic diagram of the intracellular signaling mechanisms is shown in Fig. 1(b) , and the parameters that determine these mechanisms are given in . S A is the maximal value of S A , and M thr_A represents the [Ca] cyt for half maximal activation of M A . Although [Ca] cyt dynamics in biological neurons is regulated by many components, its major changes were here assumed to be due to two main processes: calcium influx via I Ca , and calcium uptake by an intracellular calcium pump located in the endoplasmic reticulum membrane, ER. This is described by:. where γ is the current-to-concentration conversion factor. R pump is the activity rate of the calcium pump in the ER (in μM msec ─1 ). α pump is the [Ca] cyt for half maximal pump rate (Zhang and Golowasch 2007) .. As in our previous model, the activity sensor S A regulates the maximal calcium conductance G Ca (Fig. 1(b) ).. t A is the time constant of Ca 2+ conductance regulation and G Ca min represents the minimal value of G Ca , which is determined by the intrinsic properties of Ca 2+ channels in the plasma membrane and the Ca 2+ pump activity in the ER. G S_Ca represents the portion of G Ca that is activity sensor-dependent, and is a decreasing function of S A . S thr_A is the half maximal value of G S_Ca and r S represents the steepness of G S_Ca regulation. G S Ca represents the maximal value that G Ca can achieve via activity-dependent regulation.. The regulation of R pump ( Fig. 1(b) ) has been modified relative to previous versions of our model for two main reasons. First, although we have already established that the increase of R pump plays a critical role in the emergence of stable recovery (but lesser or none on bouting properties) (Zhang and Golowasch 2007; Zhang et al. 2009 ), previous models show a gradual increase in the duration of both individual bouts and interbouts with time until stable recovery is achieved, which is not a behavior that is observed experimentally (Luther et al. 2003) . Second, experimental observations have not revealed evidence of correlations between duration of bouting activity and overall time to stable recovery (Luther et al. 2003) , while our previous models do (Zhang and Golowasch 2007; Zhang et al. 2009 ). In order to account for these . R pump depends on two components: R pump_min , the minimal value of R pump (determined by the intrinsic properties of the Ca 2+ pump), and F(M) representing the portion of R pump sensitive to modulator receptor regulation via some second messenger pathway. M represents the activation of such a second messenger pathway, and F(M) is a decreasing sigmoid function of M. M thr is the value of M for half maximal activation of F(M), and r M is the steepness of F (M). R pump_M is the maximal value of the modulatordependent portion of R pump . Hence, R pump is bounded by R pump_min and R pump_min +R pump_M . The time constant t M , the rate of change of M, determines the time for stable recovery. A large value of t M ensures that R pump changes slowly (and remains near its low initial value of 10 −5 ) for a long time after decentralization ( Fig. 2(c) ). For simplicity, M directly detects the changes of G MI , which represents the neuromodulatory input, including neuromodulator receptors, but receptor activation is not explicitly represented, and G MI activation is assumed to be (Fig. 1c) , bouting ensued after a silent period followed by a stable rhythm (vertical arrow). (b) G Ca changes in the simplified model with E Ca fixed at +128 mV. Horizontal arrow point at a baseline G Ca =0.069 μS. Inset: Magnified V m and G Ca changes during bouting. Arrows point at V m = −70 mV, and G Ca = 0.08845 and 0.08895 μS (min and max, respectively). (c) R pump activity in the simplified model. Notice that stable neuronal activity coincides with the abrupt increase of R pump at around 1.4 h (vertical arrows in A-C). Decentralization is indicated by the time=0 marks, and corresponds to setting G MI =0 Table 2 Conductance and calcium pump regulation very fast. M is 1 when G MI is turned on. After G MI turns to zero, M gradually decreases towards zero until it crosses M thr making F(M) increase abruptly.. For the purpose of speeding the computations, t A and t M were adjusted so that the time course of recovery is scaled down by approximately 30 to 50-fold compared to that observed in the biological system (Luther et al. 2003) . No differences in general behavior of the model were observed when the time constants were given more realistic values.. The model neuron was built using XPP. The phase plane and bifurcation analysis were performed using the XPP/ Auto software (Ermentrout 2002) .

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Development of a piezo-driven 3-DOF stage with T-shape flexible hinge mechanism full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP url' above for details on accessing the published version and note that access may require a subscription. proposed to eliminate the nonlinear hysteresis, the trajectory tracking performances and to reduce external disturbance of the 3-DOF stage. The roles of precision positioning technology have become increasingly important in various industry fields, such as micro/nano manipulation system, microelectronics processing, optical instruments and measurement systems. A precision positioning system mainly composed of actuation device, guide mechanism and end effector. The guide mechanism is one of the key factors to determine the static and dynamic performance of the positioning system. In order to guarantee positioning accuracy, one of the best choices is to utilized flexure based mechanism for guidance of the motion. The flexure based mechanism is capable of improving the motion accuracy due to the advantages of flexure hinges including no backlash, free of wear, no lubrication, and low friction.. Several studies have focused on the design and control of precision positioning systems with flexure-based mechanisms. In order to improve the motion accuracy, there are a variety of flexure hinges have been proposed and utilized in the positioning system, including notch-type hinge [1] [2] [3] , leaf-spring hinge [4] [5] [6] , right elliptical hinge [7] , V-shape flexure hinge [8] , cross-axis flexural pivots [9] [10] [11] , split-tube flexural pivots [12] , cartwheel hinges [13] [14] [15] [16] [17] , and so on. Among the proposed flexure hinges, the notch-type hinge and leaf-spring hinge are the most popular and widely utilized in precision positioning system. Particularly, the leaf-spring hinges possess the capability of large working range.. Recent research efforts have been directed towards the development of high performance positioning mechanisms for bio-nanotechnology, AFM (atomic force microscope) and confocal microscopes [18] [19] [20] . These advanced applications bring a number of tremendous challenges for the mechanical design and optimization of positioning mechanisms. In order to implement the positioning and orientation of the sample for the precision measurement and characterisation, it is necessary to develop a 3-DOF positioning stage which can be utilized to conduct the in-plane motion. Tian et al. have designed a 3-DOF flexure-based mechanism for micro/nano manipulation [21] . In order to improve the stiffness of the moving platform, a monolithic flexure-based 3-RRR parallel mechanism is utilized to implement planar motions. Hwang et al. presented a novel ultra-precision in-plane XYθ positioning stage with kinematic decoupling between translational motion and rotational motion components [22] , Qin et al. proposed the design of a novel 3-DOF monolithic manipulator with three improved Scott-Russell (ISR) mechanisms [23] . In these developed mechanisms, a series of the notch-type hinges have been adopted as a guide mechanism.. However, the mechanical design of the 3-DOF positioning system with combination of the notch type and leaf-spring hinges has also been provided by Kim et al. [24] and Bhagat et al. [25] . In addition, Kim et al. presented the mechanical design of a 3-DOF flexure-based parallel compliant mechanism for the hollow type biomedical specimen stage base on notch-type hinges and cartwheel hinges [26] . This paper presents a novel 3-DOF precision positioning stage featured with three symmetric T-shape flexure hinges design. The T-shape flexure hinge is composed of three leaf-spring hinge subsections connected at the together like a T-joint. Thus, the T-shape flexure hinge can provide the in plane motion with relatively large out-of-plane stiffness, and meanwhile the proposed T-shape flexure hinge has the capability of compact structural design for such kinds of micro/nano positioning stages. It is demonstrated from the computational analyses that the proposed T-shape flexure hinge can provide high natural frequency, large working range and high motion dexterity.. The mechanical design of the flexure-based mechanism using parallel motion and actuation configuration is provided. The monolithic mechanism is manufactured using the WEDM technique to guarantee the machining accuracy and motion precision. The analytical models of the developed mechanism have been established to investigate the static and dynamic characteristics of the entire system. Both the stiffness and working space of the moving platform have been analyzed. The FEA (finite element analyse) has also been conducted to obtain further insights into the performance of the developed flexure-based mechanism. A number of experiments have been performed to verify the established models and characteristics of the flexure-based mechanism. This paper is organized as follows: Section II introduces mechanical design of the stage, and analytic models have established in section III. Section IV provides the kinematic analysis of the stage. In Section V, FEA has been performed to validate the static and dynamic characteristics of the flexure-based mechanism. The experimental setup and results have been provided in section VI. Conclusions are presented in Section VII.

O O O O O B O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Equity in access to fortified maize flour and corn meal Mass fortification of maize flour and corn meal with a single or multiple micronutrients is a public health intervention that aims to improve vitamin and mineral intake, micronutrient nutritional status, health, and development of the general population. Micronutrient malnutrition is unevenly distributed among population groups and is importantly determined by social factors, such as living conditions, socioeconomic position, gender, cultural norms, health systems, and the socioeconomic and political context in which people access food. Efforts trying to make fortified foods accessible to the population groups that most need them require acknowledgment of the role of these determinants. Using a perspective of social determinants of health, this article presents a conceptual framework to approach equity in access to fortified maize flour and corn meal, and provides nonexhaustive examples that illustrate the different levels included in the framework. Key monitoring areas and issues to consider in order to expand and guarantee a more equitable access to maize flour and corn meal are described. Micronutrient malnutrition (MNM) affects all regions of the world. Countries in every region face deficiencies in individual or multiple vitamins and minerals (iron, folic acid, vitamin A, vitamin B12, or zinc). It is estimated that micronutrient deficiencies may currently affect one-third of the world's population. 1 The consequences of MNM are generally well documented. 2, 3 It has been calculated that 53 million disability-adjusted life years and 1.5 million deaths of children who are under 5 years of age are linked to MNM. 4 The negative impact of MNM on people's productivity, opportunities, and health outcomes make them more vulnerable to impoverishment. 5 MNM is also associated with morbidity and mortality, and hinders improvements in maternal health. [6] [7] [8] [9] [10] [11] Fortification of foods with vitamins and minerals as a public health intervention aims to increase the micronutrient content in staple foods or condiments at the processing stage, before they are introduced to the market, as a means to improve the nutritional quality of the population's diet. 12 Targeted fortification is commonly directed to specific subpopulations, for example, fortified complementary foods to be consumed by infants and young children 13 or supplementary food for people living in emergency settings.. 14 Mass fortification, often market driven, involves fortifying staple foods that are consumed by a large sector of the population. Mass fortification can be voluntary or mandatory; in the former, food manufacturers decide to fortify their product for business reasons (e.g., ready-to-eat breakfast cereals), while mandatory mass fortification is a public health intervention enforced by a government to ensure the population receives adequate amounts of vitamins and minerals. 12, 15 Mass fortification of staple foods is a longstanding public health intervention that plays an important role in the effective and timely intention of the United Nations Millennium Development Goals (MDGs). 16, 17 Wheat flour fortification with iron or salt iodization, for example, has proved to be an effective intervention with a high effectiveness-to-cost ratio.. America. Estimates suggest that maize provides approximately 20% of the calories consumed in the world. 20 In countries where maize is a staple, corn flour or maize meal tends to be consumed by population groups across the social gradient, irrespective of age, sex, socioeconomic position, or place of resident. However, populations in a lower socioeconomic position and living in less urbanized areas are more likely to have a heavy reliance on maize (flour or meal) as a dietary staple. [21] [22] [23] [24] By 2013, 12 countries had a policy to fortify maize flour with at least one micronutrient: five countries in Africa (Kenya, Nigeria, South Africa, Tanzania, and Uganda) and seven in the Americas (Brazil, Costa Rica, El Salvador, Guatemala, Mexico, United States of America, and Venezuela). 25 Fortified foods do not always reach the population groups most in need of this intervention, 26 and maize flour or corn meal is no exception. Inequity in access to fortified foods needs to be locally researched and contextually understood, just as food fortification needs to be understood and analyzed in country-specific contexts. 27 The global public health community agrees that such inequity is socially determined and must be analyzed through a perspective of social determinants of health (SDH). 28, 29 This article on equity in access to fortified maize flour and corn meal draws on such a perspective, as well as on well-established analytical public health models, such as the World Health Organization (WHO) framework of analysis to approach equity, social determinants, and public health, 30 which has been used to better understand other nutritional problems, such as the lack of consumption of fruits and vegetables in Chile 31 and child malnutrition in Iran. 32 Some implications of this analysis for program monitoring and policy are also presented. In this article, maize flour and corn meal are used as a generic term that comprises various types of maize flour and corn meals produced and consumed in different countries or regions of the world (e.g., nixtamalized or precooked flour). The evidence and examples presented in this article suggest that incorporating an SDH and equity approach can contribute to increasing and guaranteeing access to fortified maize flour and corn meal. However, this approach is not yet common.. Food fortification is a complex public health intervention, and so strategies for fortification need to be intersectorally aligned, especially with poverty reduction programs and other social intervention schemes. Although it has been suggested that the long-term sustainability of fortification programs can be ensured when consumers are willing and able to bear the additional cost of fortified foods, this is exceptionally difficult in contexts of extreme and extended poverty and lack of opportunities. Thus, guaranteeing access to fortified foods requires that the reasons for the causes be addressed, that is, the factors that allow for the reproduction of exclusion and poverty that are socially determined and therefore modifiable.. Inequities in access to fortified maize flour and corn meal, where these are staples, can perpetuate inequalities among communities and individuals with respect to cognitive abilities, work skills, or capacities for self-protecting one's health and that of one's family. For the 900 million people that consume maize and maize-based products as their main staple food, it is crucial that the scientists, program implementers, and policy makers understand and intervene in the barriers that prevent access to fortified maize flour and corn meal.. oversight of the scientific merit of each article. The authors alone are responsible for the views expressed in this article; they do not necessarily represent the views, decisions, or policies of the institutions with which they are affiliated or the decisions, policies, or views of the World Health Organization. The opinions expressed in this publication are those of the authors and are not attributable to the sponsors, publisher, or editorial staff of Annals of the New York Academy of Sciences.

B O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O B O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O B O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Remarks on Context-free Parallel Communicating Grammar Systems Generating Crossed Agreements Abstract. When modeling natural languages, three phenomena should be considered: the so-called multiple agreements, crossed agreements and replication. These aspects are represented by the three languagesrespectively. In the present paper, we give parallel communicating grammar systems (PC grammar systems) that are context-free and that generate the non-context-free language K 2 but have less components than those systems published so far. In two cases, the results are optimal. This paper follows [5] , where linear and right-linear systems have been considered for generating the language K 2 , besides systems for the languages K 1 and K 3 .

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Brushing with additional cleaning restrictions Abstract. In graph cleaning problems, brushes clean a graph by traversing it subject to certain rules. We consider the process where at each time step, a vertex that has at least as many brushes as incident, contaminated edges, sends brushes down these edges to clean them. Various problems arise, such as determining the minimum number of brushes (called the brush number) that are required to clean the entire graph. Here, we study a new variant of the problem in which no more than k brushes can be sent at any time step. Imagine a network of pipes that must be periodically cleaned of a regenerating contaminant, say algae. In cleaning such a network (see [11] for a paper that introduced this process), there is an initial configuration of brushes on vertices; every vertex and edge is initially regarded as dirty. A vertex is ready to be cleaned if it has at least as many brushes as incident dirty edges. When a vertex is cleaned, it sends one brush along each incident dirty edge; these edges are now said to be clean. (No brush ever traverses a clean edge.) The vertex is also deemed clean. Excess brushes remain on the clean vertex and take no further part in the process. (In fact, for our purpose in this paper, we may think about clean vertices as if they were removed from the graph.) Figure 1 illustrates the cleaning process for a graph G where there are initially two brushes at vertex b and one brush at vertex c. The solid edges indicate dirty edges while the dashed edges indicate clean edges. For example, the process starts with vertex b being cleaned, sending a brush to each of vertices a and d.. This model, perhaps surprisingly, corresponds to the minimum total imbalance of the graph which is used in graph drawing theory [5] and is well-studied, in particular, for random graphs [1, 15] . (See also [9] for algorithmic aspects, [12, 14] for a related model of cleaning with brooms, [4] for a variant with no edge capacity restrictions, [7] for a combinatorial game, and [13] for a relation to more general family of perfect vertex elimination schemes leading to upper-locally distributed lattices.) Having been inspired by chip firing processes [3, 10] , the manner in which brushes disperse from an individual vertex is such that they do so in unison, provided that their vertex meets the criteria to be cleaned. Models in which multiple vertices may be cleaned simultaneously are called parallel cleaning models (see [6] for more details). In contrast, sequential cleaning models mandate that vertices are cleaned one at a time. The variant considered in [11] and the one we consider in this paper are sequential in nature.. Key words and phrases. graph searching, brush number, chip firing. The first author was partially supported by National Science Centre grant DEC-2011/02/A/ST6/00201. The second author was partially supported by National Science Centre grant DEC-2011/02/A/ST6/00201 and a scholarship for outstanding young researchers founded by the Polish Ministry of Science and Higher Education.. The third author was supported by NSERC and Ryerson University. In this paper, we consider the variant of the process in which there is one additional restriction, namely, it is not allowed to clean vertices with more than k dirty neighbours (k is a fixed parameter). For example, 3 brushes were enough to clean the graph presented on Figure 1 . However, if at most k = 2 brushes can be sent in each time step, vertex d cannot be cleaned; one additional brush has to be introduced (say, at vertex e) and our task can be accomplished with 4 brushes in total.. The formal definition of the k-restricted process and th k-brush number, b k (G), is introduced in Section 2 (b(G) denotes the original brush number introduced in [11] and also defined in Section 2). In Section 3, we characterize graphs that can be cleaned in this process. Moreover, we show that for any k ∈ N, x ∈ [1, 2], and ε > 0, there exists a tree T such that |b k (T )/b(T ) − x| < ε. This result is sharp, that is, this property does not hold for other values of x. Similarly, it is shown that for any k ∈ N \ {1}, x ∈ [1, ∞), and ε > 0, there exists a graph G such that |b k (G)/b(G) − x| < ε. In Section 4, we study a polynomial-time algorithm that, given any tree T and any k ∈ N, computes the k-brush number of T . The paper is concluded with a few open problems (see Section 5) .. Throughout, we consider only finite, simple, undirected graphs in the paper. For background on graph theory, the reader is directed to [16] .

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I B I B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Extended difference-of-Gaussians model incorporating cortical feedback for relay cells in the lateral geniculate nucleus of cat Abstract A striking feature of the organization of the early visual pathway is the significant feedback from primary visual cortex to cells in the dorsal lateral geniculate nucleus (LGN). Despite numerous experimental and modeling studies, the functional role for this feedback remains elusive. We present a new firing-rate-based model for LGN relay cells in cat, explicitly accounting for thalamocortical loop effects. The established DOG model, here assumed to account for the spatial aspects of the feedforward processing of visual stimuli, is extended to incorporate the influence of thalamocortical loops including a full set of orientation-selective cortical cell populations. Assuming a phase-reversed push-pull arrangement of ON and OFF cortical feedback as seen experimentally, this extended DOG (eDOG) model exhibits linear firing properties despite non-linear firing characteristics of the corticothalamic cells. The spatiotemporal receptive field of the eDOG model has a simple algebraic structure in Fourier space, while the real-space receptive field, as well as responses to visual stimuli, are found by evaluation of an integral. As an example application we use the eDOG model to study effects of cortical feedback on responses to flashing circular spots and patch-grating stimuli and find that the eDOG model can qualitatively account for experimental findings. A striking feature of the early visual pathway is the significant feedback from primary visual cortex to cells in the dorsal lateral geniculate nucleus (LGN). This cortical feedback has been shown to switch LGN relay cells from burst to tonic firing modes (McCormick and von Krosigk 1992; Godwin et al. 1996) and to modify the response properties of LGN cells to visual stimuli both in cat (Geisert et al. 1981; Vidyasagar and Urbas 1982; Murphy and Sillito 1987; Sillito et al. 1993 Sillito et al. , 1994 Cudeiro and Sillito 1996; Wörgötter et al. 1998; Wang et al. 2006; Andolina et al. 2007 ) and monkey (Marrocco et al. 1982; McClurkin and Marrocco 1984; McClurkin et al. 1994; Marrocco et al. 1996) . These studies reported both enhanced and reduced responses of LGN neurons due to cortical feedback, and the identification of a particular functional role of this feedback has been difficult Usrey 2008, 2011) . Cortical feedback has been shown to affect the length tuning of relay-cell responses (Murphy and Sillito 1987) and the response to patch-grating stimuli (Sillito et al. 1993; Cudeiro and Sillito 1996; Sillito and Jones 2002) .. Relay cells receive synaptic inputs from a variety of sources (Sherman and Guillery 2001) : excitatory input from retinal ganglion cells, feedforward inhibition from intrageniculate interneurons, inhibitory feedback from the thalamic reticular nucleus (TRN) and excitatory feedback from the striate cortex. Intrageniculate interneurons and TRN cells also receive feedback from cortex. When trying to decipher the properties of such a complex neural network, mathematical modeling is an essential tool, and a few mathematical models have been constructed to elucidate effects of cortical feedback on LGN neurons. They have focused on the effect of cortical feedback on visual latency (Köhn and Wörgötter 1996) , synchronization of thalamocortical oscillations (Destexhe et al. 1998; Destexhe 2000; Mayer et al. 2007) , temporal structure of spike trains (Wörgötter et al. 1998 ), synchronization of LGN-cell firing (Kirkland and Gerstein 1998; Kirkland et al. 2000) , object segmentation based on motion cues (Hillenbrand and van Hemmen 2000) , LGN responses to bipartite drifting grating stimuli (Hayot and Tranchina 2001) , and on LGN impulse responses (Yousif and Denham 2007) . These modeling efforts have typically been based on grids of neurons representing the different populations in the early visual pathway (retinal, LGN, TRN, and cortical cells), and results for the question at hand have been found by numerical simulations.. In this article we present a new firing-rate-based model of spatiotemporal LGN relay-cell responses to visual stimuli incorporating cortical feedback. In this extended DOG model (eDOG) the feedforward response is modeled by means of the standard difference-of-Gaussians (DOG) model (Rodieck 1965) , and the corticothalamic feedback is assumed to have a phase-reversed push-pull organization (Wang et al. 2006 ): e.g., inhibitory feedback influence from a cortical ON-cell onto an LGN cell is accompanied by an excitatory feedback influence from a cortical OFF cell. While the resulting model has a more complicated mathematical structure than the DOG model, it is still linear. This means that responses to arbitrary visual stimuli can be calculated by evaluating integrals, though numerical evaluation is generally required. In the eDOG model, characteristics of cortical feedback such as strength, spatial spread and temporal properties are parameterized in a straightforward manner, and possible effects on LGN cells from cortical feedback can be studied more easily-both conceptually and methodologically-than with extensive numerical simulations of networks of neurons.. In section ''Impulse response and receptive field'' we introduce impulse-response functions and receptive fields. In section ''Receptive-field models incorporating phasereversed push-pull cortical feedback'' a general expression for the linear response of relay cells incorporating cortical feedback from a full set of orientation-selective cortical populations is derived, while the eDOG model is presented in section ''Extended difference-of-Gaussians model''. An example application is given in section ''Example application: patch-grating stimuli'' where we use the eDOG model to describe the effects of cortical feedback on responses to flashing circular spots and patch-grating stimuli and compare with experimental findings (Sillito et al. 1993; Cudeiro and Sillito 1996; Sillito and Jones 2002) . We discuss our findings in the final section.. Preliminary accounts of some of the results presented here have been presented in abstract form previously (Einevoll and Plesser 2003) .

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Design, navigation, and structure of a hypermedia application for the teaching-learning of pneumatic engineering design drawing This article presents a hypermedia application used to study pneumatics that serves to support the lecturer in the lecture hall and as a self-study tool for the student. The reasoning behind the creation of this application is as follows: currently, there is no application on the market, which is equipped with a navigational system to guide the student through this subject matter, which has a system for self-assessment, and a system to identify those concepts that are of greatest interest or difficulty for the student. The proposed system monitors the time each user spends studying each section, as well as the dates on which each they are studied. Moreover, students are able to monitor their progress in learning the subject matter and identify those areas in which they have to improve. They are also able to simulate any pneumatic circuit in order to check its feasibility or detect any errors. The application has an open, modular structure, which enables changes to be made without its structure being affected. Use of the hypermedia application has supported the tutorial work of lecturers and reduced time spent elaborating on subject matter in the lecture hall, at the same time as facilitating its study. Technical drawing for industrial purposes, according to [1, is a means of written communication used by technicians to lay out and convey the information needed for the design, construction, operation and verification of every type of material used in industry. Technical drawing is able to represent mechanical, electric and electronic installations as well as each of their respective components.. Pneumatic systems are found within mechanical systems and they are widely used in productive processes for the manufacture, transport and handling of products.. The difficulties experienced by the great majority of students, associated with visualising and representing the pneumatic systems, which are displayed by means of slides or drawings on a blackboard, lead in the first instance to a search for programmes on the market that will help improve the effectiveness of the teaching/learning of pneumatics. Among others, such programmes include Neusim [2, which is a programme that simulates pneumatic circuits and FluidSim-3-Pneumatics [3, which in addition to simulation contains explanations that refer to its animated components, examples of their applications and didactic videos. These help the student to learn more about pneumatic components, as well as how to establish the necessary connections to achieve a desired sequence of operations. However, the navigational structure is based on drop-down menus, lacks any system for the students to evaluate their own progress in learning the subject matter and lacks a system that assists in the identification of those areas of the subject matter in which the student is experiencing most difficulty.. The reasons described above have led to the design of the pneumatic engineering design drawing hypermedia. Our aims have been to facilitate navigation, guide students through their studies, synthesize the course contents, avoid excessive time spent tracing out complex drawings on the blackboard, avoid improvisations by the teacher and present the subject matter through pictures, videos and animations. These aspects, in conjunction with explanatory texts, form part of the interconnected information that will improve the learning of pneumatics.

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