Multiscale sampling model for motion integration

Biologically plausible strategies for visual scene integration across spatial and temporal domains continues to be a challenging topic. The fundamental question we address is whether classical problems in motion integration, such as the aperture problem, can be solved in a model that samples the visual scene at multiple spatial and temporal scales in parallel. We hypothesize that fast interareal connections that allow feedback of information between cortical layers are the key processes that disambiguate motion direction. We developed a neural model showing how the aperture problem can be solved using different spatial sampling scales between LGN, V1 layer 4, V1 layer 6, and area MT. Our results suggest that multiscale sampling, rather than feedback explicitly, is the key process that gives rise to end-stopped cells in V1 and enables area MT to solve the aperture problem without the need for calculating intersecting constraints or crafting intricate patterns of spatiotemporal receptive fields. Furthermore, the model explains why end-stopped cells no longer emerge in the absence of V1 layer 6 activity (Bolz & Gilbert, 1986), why V1 layer 4 cells are significantly more end-stopped than V1 layer 6 cells (Pack, Livingstone, Duffy, & Born, 2003), and how it is possible to have a solution to the aperture problem in area MT with no solution in V1 in the presence of driving feedback. In summary, while much research in the field focuses on how a laminar architecture can give rise to complicated spatiotemporal receptive fields to solve problems in the motion domain, we show that one can reframe motion integration as an emergent property of multiscale sampling achieved concurrently within lamina and across multiple visual areas.This work was supported in part by CELEST, a National Science Foundation Science of Learning Center; NSF SBE-0354378 and OMA-0835976; ONR (N00014-11-1-0535); and AFOSR (FA9550-12-1-0436). (CELEST, a National Science Foundation Science of Learning Center; SBE-0354378 - NSF; OMA-0835976 - NSF; N00014-11-1-0535 - ONR; FA9550-12-1-0436 - AFOSR)Published versio

Three-Dimensional Stress-Strain State of a Pipe with Corrosion Damage Under Complex Loading

Formation of wall friction force by turbulent oil flow and resulting change of pipe’s stress-strain state are studied. Three-dimensional model of stress-strain state of pipe with internal corrosion defect loaded by internal pressure, friction caused by motion of oil and by temperature is presented. Analysis of main results of computer simulations is given

Computational principles for an autonomous active vision system

Vision research has uncovered computational principles that generalize across species and brain area. However, these biological mechanisms are not frequently implemented in computer vision algorithms. In this thesis, models suitable for application in computer vision were developed to address the benefits of two biologically-inspired computational principles: multi-scale sampling and active, space-variant, vision. The first model investigated the role of multi-scale sampling in motion integration. It is known that receptive fields of different spatial and temporal scales exist in the visual cortex; however, models addressing how this basic principle is exploited by species are sparse and do not adequately explain the data. The developed model showed that the solution to a classical problem in motion integration, the aperture problem, can be reframed as an emergent property of multi-scale sampling facilitated by fast, parallel, bi-directional connections at different spatial resolutions. Humans and most other mammals actively move their eyes to sample a scene (active vision); moreover, the resolution of detail in this sampling process is not uniform across spatial locations (space-variant). It is known that these eye-movements are not simply guided by image saliency, but are also influenced by factors such as spatial attention, scene layout, and task-relevance. However, it is seldom questioned how previous eye movements shape how one learns and recognizes an object in a continuously-learning system. To explore this question, a model (CogEye) was developed that integrates active, space-variant sampling with eye-movement selection (the where visual stream), and object recognition (the what visual stream). The model hypothesizes that a signal from the recognition system helps the where stream select fixation locations that best disambiguate object identity between competing alternatives. The third study used eye-tracking coupled with an object disambiguation psychophysics experiment to validate the second model, CogEye. While humans outperformed the model in recognition accuracy, when the model used information from the recognition pathway to help select future fixations, it was more similar to human eye movement patterns than when the model relied on image saliency alone. Taken together these results show that computational principles in the mammalian visual system can be used to improve computer vision models

Easy-plane antiferromagnet in tilted field: gap in magnon spectrum and susceptibility

Motivated by recent experimental data on dichloro-tetrakis thiourea-nickel (DTN) [T.A. Soldatov $\textit{et al}$, Phys. Rev. B ${\bf 101}$, 104410 (2020)], a model of antiferromagnet on a tetragonal lattice with single-ion easy-plane anisotropy in the tilted external magnetic field is considered. Using the smallness of the in-plane field component, we analytically address field dependence of the energy gap in ``acoustic'' magnon mode and transverse uniform magnetic susceptibility in the ordered phase. It is shown that the former is non-monotonic due to quantum fluctuations, which was indeed observed experimentally. The latter is essentially dependent on the ``optical'' magnon rate of decay on two magnons. At magnetic fields close to the one which corresponds to the center of the ordered phase, it leads to experimentally observed dynamical diamagnetism phenomenon

Vibro-impact in rolling contact

Irregular wavy residual damages (troppy phenomenon) occur in the contact area in rolling friction as the result of a nonstationary process of cyclic deformation. They initiate vibro-impact loading of an active system. The results of experimental study of these damages are given. Theoretical model satisfactory describing troppy phenomenon is developed

The concept of damaged material

Дано краткий обзор известных понятий повреждаемости материалов при сопротивлении усталости. Разработан новый подход к оценке повреждаемости трибофатических систем, работающих в сложных условиях одновременного действия контактных и объемных нагрузок.The short review of known concepts of damageability of materials in fatigue resistance is given. The new approach to a damageability of tribo-fatigue systems working in difficult conditions of simultaneous action contact and extracontact loadings is stated

When environmental changes do not cause geographic separation of fauna: differential responses of Baikalian invertebrates

<p>Abstract</p> <p>Background</p> <p>While the impact of climate fluctuations on the demographic histories of species caused by changes in habitat availability is well studied, populations of species from systems without geographic isolation have received comparatively little attention. Using CO1 mitochondrial sequences, we analysed phylogeographic patterns and demographic histories of populations of five species (four gastropod and one amphipod species) co-occurring in the southwestern shore of Lake Baikal, an area where environmental oscillations have not resulted in geographical isolation of habitats.</p> <p>Results</p> <p>Species with stronger habitat preferences (gastropods <it>B. turriformis</it>, <it>B. carinata </it>and <it>B. carinatocostata</it>) exhibit rather stable population sizes through their evolutionary history, and their phylogeographic pattern indicates moderate habitat fragmentation. Conversely, species without strong habitat preference (gastropod <it>M. herderiana </it>and amphipod <it>G. fasciatus</it>) exhibit haplotype networks with a very abundant and widespread central haplotype and a big number of singleton haplotypes, while their reconstructed demographic histories show a population expansion starting about 25-50 thousand years ago, a period marked by climate warming and increase in diatom abundance as inferred from bottom-lake sedimentary cores.</p> <p>Conclusions</p> <p>In agreement with previous studies, we found that species reacted differently to the same environmental changes. Our results highlight the important role of dispersal ability and degree of ecological specialization in defining a species' response to environmental changes.</p

Multiscale sampling model for motion integration

Biologically plausible strategies for visual scene integration across spatial and temporal domains continues to be a challenging topic. The fundamental question we address is whether classical problems in motion integration, such as the aperture problem, can be solved in a model that samples the visual scene at multiple spatial and temporal scales in parallel. We hypothesize that fast interareal connections that allow feedback of information between cortical layers are the key processes that disambiguate motion direction. We developed a neural model showing how the aperture problem can be solved using different spatial sampling scales between LGN, V1 layer 4, V1 layer 6, and area MT. Our results suggest that multiscale sampling, rather than feedback explicitly, is the key process that gives rise to end-stopped cells in V1 and enables area MT to solve the aperture problem without the need for calculating intersecting constraints or crafting intricate patterns of spatiotemporal receptive fields. Furthermore, the model explains why end-stopped cells no longer emerge in the absence of V1 layer 6 activity Introduction Visual scene integration is a well-studied topic, yet there is still little consensus about the necessary and sufficient network that affords the function observed. Historically, the classical view of visual processing is a local to global approach whereby earlier visual areas serve as edge and orientation detectors that pass on information to higher-order areas that perform more complex processing to complete the 3-D representation of the visual scene In this paper, we explore whether a classic problem in visual motion integration-the aperture problemcan be solved with a simple model that samples the visual scene at different spatial and temporal scales in parallel. To frame what is meant by aperture problem, we note that a neuron&apos;s receptive field acts as a viewing aperture and only detects components of motion visible to its field of view (often not the same as the true global Citation: Sherbakov, L., &amp; Yazdanbakhsh, A. (2013 Downloaded from jov.arvojournals.org on 07/01/2019 motion). Due to the difference in size between stimulus and receptive fields (the latter being smaller), the true motion of a line viewed from this aperture is only unambiguous at line endings (assuming no significant texture is present); the rest of the cells only have view access to the perpendicular component of motion-this is commonly understood as the aperture problem Historically, three broad classes of solutions have been proposed to explain how the aperture problem is solved: (a) intersection of constraints, (b) vector averaging of motion direction, and (c) feature tracking. The intersection of constraints method uses the normal components of velocity and predicts the perceived direction of motion from where those velocity-space lines intersect Our approach differs from the above three in several ways: (a) We de-emphasize intra-areal processing as the central mechanism that propagates the relevant information to solve the aperture problem, (b) fast interareal and interlaminar connections between V1 and MT feed back information onto V1, and (c) the computation done in our model areas V1 and MT is essentially identical with the only difference being spatial sampling scales. Henceforth, we use the terms &apos;&apos;spatial sampling scale&apos;&apos; and &apos;&apos;multiscale sampling&apos;&apos; to mean the integration of information from neural populations with heterogeneous receptive field sizes wherein some populations have receptive fields as much as an order of magnitude larger than other populations. This type of heterogeneity is well documented in biology More recently, other models have suggested that multiscale sampling and feedback are the critical components to quickly and successfully solve the aperture problem in area MT There has also been an increased interest in statistical models that explain how and under what conditions the aperture problem is solved. Most of these models rely on a Bayesian framework in which the local motion is represented by likelihood functions of the line&apos;s position and velocity. Global motion is then inferred by introducing prior constraints and computing the posterior distribution Methods In this work, we develop a computational model that simulates the response of three visual areas (LGN, V1 layers 4 and 6, and MT) to a vertically oriented bar moving at a 458 angle The model The model consists of LGN cells, V1 layer 6 neurons, V1 layer 4 interneurons, V1 layer 4 excitatory neurons, and MT cells ( To simulate direction-selective V1 neurons, we introduce the concept of a direction-selective mask that is applied to neurons of a given selectivity after they receive the LGN input. Model areas V1 layer 6, V1 layer 4 interneurons, and V1 layer 4 excitatory cells each have three motion direction-selective layers: rightward, upward, and right-up (458). The rightward direction cells, for example, respond best to LGN input at the center of the moving bar where the only component of motion that is visible to the cell&apos;s receptive field is horizontal (for more detail, see Direction mask section). Model LGN synapses onto three V1 populations: V1 layer 6 cells, V1 layer 4 interneurons, and V1 layer 4 excitatory cells. These synapses are not only well documented in physiology studies of area V1 Journal of Vision Journal of Vision (2013) 13(11):18, 1-14 Sherbakov &amp; Yazdanbakhsh 4 Downloaded from jov.arvojournals.org on 07/01/2019 Model area MT is similarly split into three populations that inherit their motion-direction selectivity from V1: rightward-selective MT cells, upward-selective MT cells, and right-up selective MT cells. MT only receives input from V1 layer 4 cells of the same direction selectivity; no cross-orientation interactions are modeled in either area V1 or MT. MT receptive field sizes are simulated as roughly 10 times that of V1 layer 4 receptive field sizes The feedback connections in our model consist of MT onto V1 layer 6 and MT onto V1 layer 4 excitatory cells All excitatory and inhibitory inputs to the model are driving (additive) and shunted (modulated by the cell&apos;s own activity) with the exception of V1 layer 6 synapses, which are modulatory (see Appendix). All visual areas (with the exception of LGN) are modeled with distance-dependent shunting with oncenter-off-surround intra-areal connections: where x ij is the model cell at location (i, j), A is the membrane potential decay rate, B stands for the depolarization threshold, I(t) is the driving input to the cell at time t, C is a kernel for distance-dependent excitation, D is a surrogate for the hyperpolarization threshold, E is a kernel for distance-dependent inhibition, and F is a kernel for on-center-off-surround intraareal interactions. The * operation denotes a convolution with the respective kernel. The parameters B ¼ 90 and D ¼ 60 are kept constant for all simulated brain regions. The decay rate, A, and the kernel sizes C, E, and F are varied as described in the section Parameter selection. LGN is similar to other model areas with the simplification that it does not have any intra-areal interactions. For a detailed summary of the equations, see Appendix. Direction mask To address how our model neurons detect direction of motion, we introduce the direction-selective mask abstraction. The direction mask functions as a rudimentary Reichardt detector or any other mechanism that extracts &apos;&apos;first-order&apos;&apos; motion. We do not address how this direction mask emerges in a biological system; rather, the goal of this paper is to focus on multiscale sampling of the motion stimulus. Motion direction selectivity is achieved in area V1 by introducing a direction mask over LGN cells that modulate the sampled activity based on which spatial region the V1 cells can perceive The stimulus The stimulus we use is a vertically oriented bar 100 units in length and 1 unit in width, moving at a 458 angle relative to the horizontal Analysis of simulations To determine whether the aperture problem was present in our simulation, we defined the solution to the aperture problem to be the case when, at some time t, the vector average of the preferred direction of motion pointed toward the pattern motion (458 from the horizontal) as opposed to the component direction of motion. The expected vector average component direction of motion was 28 from the horizontal for area V1 layer 4, 48 for V1 layer 6, and 188 for area MT. The expected component direction of motion is not uniquely 08 from the horizontal because cells that could see the bar ends and therefore the correct direction of motion Parameter selection To find the appropriate parameter range for our model, we attempted to match our LGN, V1, and MT cells to known latencies, peak response profiles, and spike distributions from available data in the macaque visual system. For LGN dynamics, our target cell was tuned to have a latency of roughly 20 ms (Schmolesky et al., 1998), a peak response at 50 ms, and complete response decay by 300 ms To enforce the notion of different sized receptive fields in LGN, V1 layer 6, V1 layer 4, and MT, we used two-dimensional Gaussians to simulate the amount of excitatory and inhibitory influence of neighboring cells both within (intra-) and between (inter-) lamina and visual areas. We up-sampled or down-sampled the excitatory and inhibitory Gaussians by the same amount, which was determined by the relative receptive field size of the given visual area to the LGN receptive field size. All excitatory Gaussian kernels had a standard deviation ¼ 0.15 and peak ¼ 18, representing the spatial spread and amplitude of the outgoing signals passed from one visual area to another. The inhibitory Gaussians contributing to the off-surround had a standard deviation ¼ 1.2 and peak ¼ 0.5. These parameters were chosen for consistency with other models that use the shunting equation to represent the membrane potential of cell populations The LGN receptive field was used as the baseline receptive field, which was then up-sampled to simulate the receptive fields of V1 and MT. The excitatory portion of the LGN Gaussian had a radius of 2 units (cells), and the inhibitory portion had a radius of 5 units. V1 layer 6 was modeled as having twice the receptive field of LGN (excitatory radius ¼ 4 units, inhibitory radius ¼ 10 units). Our model V1 layer 4 had the same receptive field size as LGN, consistent with data that suggests layer 4 has smaller receptive fields than layer 6 of V1 The intra-areal sampling was simulated by a difference of Gaussians (excitatory-inhibitory), whose excitatory and inhibitory regions were down-sampled by two, relative to the cell&apos;s interareal sampling kernel (for example, MT&apos;s intra-areal sampling kernel had an excitatory radius of 10 units and an inhibitory radius of 25 units). This relatively smaller receptive field was meant to simulate slower intra-areal communication when compared to its interareal counterpart. All simulations were performed in MATLAB 2009b. All equations and stimuli were modeled in 2-D in their differential equation form (see Appendix). Results Our simulation results show that the aperture problem can be solved in area MT with this relatively simple multiscale sampling model Journal of Vision (2013) 13(11):18, 1-14 Sherbakov &amp; Yazdanbakhsh 6 Downloaded from jov.arvojournals.org on 07/01/2019 V1 layer 6 responds mostly to component motion throughout the simulation (vector average ¼ 218 early in the simulation and 258 later in the simulation). V1 layer 4, however, begins to shift more strongly toward pattern motion as the simulation progresses (vector average ¼ 228 early in the simulation and 338 later in the simulation). This phenomenon of V1 neurons being caught between component and pattern motion has been documented in end-stopped cells (most of which are coincidentally found in layer 4 of V1) When we analyzed the dynamics of our model cells, we discovered that a strong end-stopping phenomenon emerged in our V1 layer 4 cells (and to a lesser extent in our V1 layer 6 cells) Lastly, when we deactivated V1 layer 6 in our model ( Discussion Our simulations show that it is indeed possible to solve the aperture problem through multiscale sampling between different lamina and visual areas. Our results are consistent with physiology, which shows that MT resolves the aperture problem while V1 continues to respond largely to the components of motion despite direct feedback from MT. We believe that multiscale sampling (with or without feedback) is the key ingredient to the emergence of endstopped cells in V1 layer 4, which, in turn, greatly facilitates the solution of the aperture problem in area MT. To give an intuitive explanation of why multiscale sampling works, consider a moving bar that elicits activity from LGN cells, which then synapse onto rightward direction-selective V1 cells. The activity in the rightward direction V1 cells is greatest in the middle of the bar where the receptive fields only perceive the horizontal component of motion. Now suppose these rightward-selective cells sample the LGN input at two different spatial scales and that the activity from the larger spatial scale is subtracted from the activity of the smaller spatial scale (this corresponds to V1 L4 cells receiving inhibition from V1 L4 interneurons, which receive their input from V1 L6 cells with larger receptive fields). The region that will be most suppressed because of this (smaller -larger receptive field) activity difference is precisely the middle of the bar. For this reason, we see that the strongest end-stopping occurs in our rightward-selective cells in V1 although some end-stopping can also be seen in right-up direction-selective cells. While we find that feedback is not necessary for a successful solution to the aperture problem in area MT, it facilitates strong end-stopping in area V1 by providing a third spatial sampling scale. We hypothesize that the more spatial sampling scales the system is exposed to, the easier it becomes to suppress activity that does not agree between scales

Multiscale sampling model for motion integration

Biologically plausible strategies for visual scene integration across spatial and temporal domains continues to be a challenging topic. The fundamental question we address is whether classical problems in motion integration, such as the aperture problem, can be solved in a model that samples the visual scene at multiple spatial and temporal scales in parallel. We hypothesize that fast interareal connections that allow feedback of information between cortical layers are the key processes that disambiguate motion direction. We developed a neural model showing how the aperture problem can be solved using different spatial sampling scales between LGN, V1 layer 4, V1 layer 6, and area MT. Our results suggest that multiscale sampling, rather than feedback explicitly, is the key process that gives rise to end-stopped cells in V1 and enables area MT to solve the aperture problem without the need for calculating intersecting constraints or crafting intricate patterns of spatiotemporal receptive fields. Furthermore, the model explains why end-stopped cells no longer emerge in the absence of V1 layer 6 activity Introduction Visual scene integration is a well-studied topic, yet there is still little consensus about the necessary and sufficient network that affords the function observed. Historically, the classical view of visual processing is a local to global approach whereby earlier visual areas serve as edge and orientation detectors that pass on information to higher-order areas that perform more complex processing to complete the 3-D representation of the visual scene In this paper, we explore whether a classic problem in visual motion integration-the aperture problemcan be solved with a simple model that samples the visual scene at different spatial and temporal scales in parallel. To frame what is meant by aperture problem, we note that a neuron&apos;s receptive field acts as a viewing aperture and only detects components of motion visible to its field of view (often not the same as the true global Citation: Sherbakov, L., &amp; Yazdanbakhsh, A. (2013 motion). Due to the difference in size between stimulus and receptive fields (the latter being smaller), the true motion of a line viewed from this aperture is only unambiguous at line endings (assuming no significant texture is present); the rest of the cells only have view access to the perpendicular component of motion-this is commonly understood as the aperture problem Historically, three broad classes of solutions have been proposed to explain how the aperture problem is solved: (a) intersection of constraints, (b) vector averaging of motion direction, and (c) feature tracking. The intersection of constraints method uses the normal components of velocity and predicts the perceived direction of motion from where those velocity-space lines intersect Our approach differs from the above three in several ways: (a) We de-emphasize intra-areal processing as the central mechanism that propagates the relevant information to solve the aperture problem, (b) fast interareal and interlaminar connections between V1 and MT feed back information onto V1, and (c) the computation done in our model areas V1 and MT is essentially identical with the only difference being spatial sampling scales. Henceforth, we use the terms &apos;&apos;spatial sampling scale&apos;&apos; and &apos;&apos;multiscale sampling&apos;&apos; to mean the integration of information from neural populations with heterogeneous receptive field sizes wherein some populations have receptive fields as much as an order of magnitude larger than other populations. This type of heterogeneity is well documented in biology More recently, other models have suggested that multiscale sampling and feedback are the critical components to quickly and successfully solve the aperture problem in area MT There has also been an increased interest in statistical models that explain how and under what conditions the aperture problem is solved. Most of these models rely on a Bayesian framework in which the local motion is represented by likelihood functions of the line&apos;s position and velocity. Global motion is then inferred by introducing prior constraints and computing the posterior distribution ables, which is not only time consuming on a single computer but also biologically questionable. A last distinguishing feature of our model is the emergence of several observable cell properties that we did not explicitly set out to simulate. End-stopping, a phenomenon observed in area V1 and MT whereby cells develop suppressed responses to long but not short bar lengths Methods In this work, we develop a computational model that simulates the response of three visual areas (LGN, V1 layers 4 and 6, and MT) to a vertically oriented bar moving at a 458 angle The model The model consists of LGN cells, V1 layer 6 neurons, V1 layer 4 interneurons, V1 layer 4 excitatory neurons, and MT cells ( To simulate direction-selective V1 neurons, we introduce the concept of a direction-selective mask that is applied to neurons of a given selectivity after they receive the LGN input. Model areas V1 layer 6, V1 layer 4 interneurons, and V1 layer 4 excitatory cells each have three motion direction-selective layers: rightward, upward, and right-up (458). The rightward direction cells, for example, respond best to LGN input at the center of the moving bar where the only component of motion that is visible to the cell&apos;s receptive field is horizontal (for more detail, see Direction mask section). Model LGN synapses onto three V1 populations: V1 layer 6 cells, V1 layer 4 interneurons, and V1 layer 4 excitatory cells. These synapses are not only well documented in physiology studies of area V1 Journal of Vision Journal of Vision (2013) 13(11):18, 1-14 Sherbakov &amp; Yazdanbakhsh 4 Model area MT is similarly split into three populations that inherit their motion-direction selectivity from V1: rightward-selective MT cells, upward-selective MT cells, and right-up selective MT cells. MT only receives input from V1 layer 4 cells of the same direction selectivity; no cross-orientation interactions are modeled in either area V1 or MT. MT receptive field sizes are simulated as roughly 10 times that of V1 layer 4 receptive field sizes The feedback connections in our model consist of MT onto V1 layer 6 and MT onto V1 layer 4 excitatory cells All excitatory and inhibitory inputs to the model are driving (additive) and shunted (modulated by the cell&apos;s own activity) with the exception of V1 layer 6 synapses, which are modulatory (see Appendix). All visual areas (with the exception of LGN) are modeled with distance-dependent shunting with oncenter-off-surround intra-areal connections: where x ij is the model cell at location (i, j), A is the membrane potential decay rate, B stands for the depolarization threshold, I(t) is the driving input to the cell at time t, C is a kernel for distance-dependent excitation, D is a surrogate for the hyperpolarization threshold, E is a kernel for distance-dependent inhibition, and F is a kernel for on-center-off-surround intraareal interactions. The * operation denotes a convolution with the respective kernel. The parameters B ¼ 90 and D ¼ 60 are kept constant for all simulated brain regions. The decay rate, A, and the kernel sizes C, E, and F are varied as described in the section Parameter selection. LGN is similar to other model areas with the simplification that it does not have any intra-areal interactions. For a detailed summary of the equations, see Appendix. Direction mask To address how our model neurons detect direction of motion, we introduce the direction-selective mask abstraction. The direction mask functions as a rudimentary Reichardt detector or any other mechanism that extracts &apos;&apos;first-order&apos;&apos; motion. We do not address how this direction mask emerges in a biological system; rather, the goal of this paper is to focus on multiscale sampling of the motion stimulus. Motion direction selectivity is achieved in area V1 by introducing a direction mask over LGN cells that modulate the sampled activity based on which spatial region the V1 cells can perceive The stimulus The stimulus we use is a vertically oriented bar 100 units in length and 1 unit in width, moving at a 458 angle relative to the horizontal Analysis of simulations To determine whether the aperture problem was present in our simulation, we defined the solution to the aperture problem to be the case when, at some time t, the vector average of the preferred direction of motion pointed toward the pattern motion (458 from the horizontal) as opposed to the component direction of motion. The expected vector average component direction of motion was 28 from the horizontal for area V1 layer 4, 48 for V1 layer 6, and 188 for area MT. The expected component direction of motion is not uniquely 08 from the horizontal because cells that could see the bar ends and therefore the correct direction of motion Parameter selection To find the appropriate parameter range for our model, we attempted to match our LGN, V1, and MT cells to known latencies, peak response profiles, and spike distributions from available data in the macaque visual system. For LGN dynamics, our target cell was tuned to have a latency of roughly 20 ms (Schmolesky et al., 1998), a peak response at 50 ms, and complete response decay by 300 ms To enforce the notion of different sized receptive fields in LGN, V1 layer 6, V1 layer 4, and MT, we used two-dimensional Gaussians to simulate the amount of excitatory and inhibitory influence of neighboring cells both within (intra-) and between (inter-) lamina and visual areas. We up-sampled or down-sampled the excitatory and inhibitory Gaussians by the same amount, which was determined by the relative receptive field size of the given visual area to the LGN receptive field size. All excitatory Gaussian kernels had a standard deviation ¼ 0.15 and peak ¼ 18, representing the spatial spread and amplitude of the outgoing signals passed from one visual area to another. The inhibitory Gaussians contributing to the off-surround had a standard deviation ¼ 1.2 and peak ¼ 0.5. These parameters were chosen for consistency with other models that use the shunting equation to represent the membrane potential of cell populations The LGN receptive field was used as the baseline receptive field, which was then up-sampled to simulate the receptive fields of V1 and MT. The excitatory portion of the LGN Gaussian had a radius of 2 units (cells), and the inhibitory portion had a radius of 5 units. V1 layer 6 was modeled as having twice the receptive field of LGN (excitatory radius ¼ 4 units, inhibitory radius ¼ 10 units). Our model V1 layer 4 had the same receptive field size as LGN, consistent with data that suggests layer 4 has smaller receptive fields than layer 6 of V1 The intra-areal sampling was simulated by a difference of Gaussians (excitatory-inhibitory), whose excitatory and inhibitory regions were down-sampled by two, relative to the cell&apos;s interareal sampling kernel (for example, MT&apos;s intra-areal sampling kernel had an excitatory radius of 10 units and an inhibitory radius of 25 units). This relatively smaller receptive field was meant to simulate slower intra-areal communication when compared to its interareal counterpart. All simulations were performed in MATLAB 2009b. All equations and stimuli were modeled in 2-D in their differential equation form (see Appendix). Results Our simulation results show that the aperture problem can be solved in area MT with this relatively simple multiscale sampling model Journal of Vision (2013) 13(11):18, 1-14 Sherbakov &amp; Yazdanbakhsh 6 V1 layer 6 responds mostly to component motion throughout the simulation (vector average ¼ 218 early in the simulation and 258 later in the simulation). V1 layer 4, however, begins to shift more strongly toward pattern motion as the simulation progresses (vector average ¼ 228 early in the simulation and 338 later in the simulation). This phenomenon of V1 neurons being caught between component and pattern motion has been documented in end-stopped cells (most of which are coincidentally found in layer 4 of V1) When we analyzed the dynamics of our model cells, we discovered that a strong end-stopping phenomenon emerged in our V1 layer 4 cells (and to a lesser extent in our V1 layer 6 cells) Lastly, when we deactivated V1 layer 6 in our model ( Discussion Our simulations show that it is indeed possible to solve the aperture problem through multiscale sampling between different lamina and visual areas. Our To get a global view of direction coding in our model visual areas, the last column shows the average PD for the cells that see the line end and those that don&apos;t, together, in areas V1 L6 (first row), V1 L4 (second row), and MT (third row). The dotted blue lines indicate the PD early in the simulation (,60 ms), and the solid blue lines show the PD of the cells after 60 ms. Simulation area V1 L6 responds most to the component direction of motion and changes the least throughout the simulation. Area V1 L4 first responds to the component direction of motion but shifts closer toward the pattern direction of motion later in the simulation, such that the vector average of the PD is between the two extremes. Area MT responds to the component direction of motion at the beginning; however, after 60 ms, MT responds entirely to the pattern. While the expected pattern motion is the same for all cells (458), the component motion is different based on the size of the receptive field of the model area. The expected component direction of motion is not uniquely 08 from the horizontal because cells that can see the bar ends and therefore whose component motion is the correct direction of motion (458) are averaged with cells that can only see the middle of the bar (08 from the horizontal). The expected PD for component motion is 28 from the horizontal for V1 L4, 48 from the horizontal for V1 L6, and 188 from the horizontal for MT. Journal of Vision (2013) 13(11):18, 1-14 Sherbakov &amp; Yazdanbakhsh 8 results are consistent with physiology, which shows that MT resolves the aperture problem while V1 continues to respond largely to the components of motion despite direct feedback from MT. We believe that multiscale sampling (with or without feedback) is the key ingredient to the emergence of endstopped cells in V1 layer 4, which, in turn, greatly facilitates the solution of the aperture problem in area MT. To give an intuitive explanation of why multiscale sampling works, consider a moving bar that elicits activity from LGN cells, which then synapse onto rightward direction-selective V1 cells. The activity in the rightward direction V1 cells is greatest in the middle of the bar where the receptive fields only perceive the horizontal component of motion. Now suppose these rightward-selective cells sample the LGN input at two different spatial scales and that the activity from the larger spatial scale is subtracted from the activity of the smaller spatial scale (this corresponds to V1 L4 cells receiving inhibition from V1 L4 interneurons, which receive their input from V1 L6 cells with larger receptive fields). The region that will be most suppressed because of this (smaller -larger receptive field) activity difference is precisely the middle of the bar. For this reason, we see that the strongest end-stopping occurs in our rightward-selective cells in V1 although some end-stopping can also be seen in right-up direction-selective cells. While we find that feedback is not necessary for a successful solution to the aperture problem in area MT, it facilitates strong end-stopping in area V1 by providing a third spatial sampling scale. We hypothesize that the more spatial sampling scales the system is exposed to, the easier it becomes to suppress activity that does not agree between scales