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We study various fluctuation and correlation signals of the deconfined state using a dynamical recombination approach (quark Molecular Dynamics, qMD). We analyse charge ratio fluctuations, charge transfer fluctuations and baryon-strangeness correlations as a function of the center of mass energy with a set of central Pb+Pb/Au+Au events from AGS energies on (Elab = 4 AGeV) up to the highest RHIC energy available (V sNN = 200 GeV) and as a function of time with a set of central Au+Au qMD events at V sNN = 200 GeV with and without applying our hadronization procedure. For all studied quantities, the results start from values compatible with a weakly coupled QGP in the early stage and end with values compatible with the hadronic result in the final state. We show that the loss of the signal occurs at the same time as hadronization and trace it back to the dynamical recombination process implemented in our model.
To investigate the formation and the propagation of relativistic shock waves in viscous gluon matter we solve the relativistic Riemann problem using a microscopic parton cascade. We demonstrate the transition from ideal to viscous shock waves by varying the shear viscosity to entropy density ratio n/s. Furthermore we compare our results with those obtained by solving the relativistic causal dissipative fluid equations of Israel and Stewart (IS), in order to show the validity of the IS hydrodynamics. Employing the parton cascade we also investigate the formation of Mach shocks induced by a high-energy gluon traversing viscous gluon matter. For n/s = 0.08 a Mach cone structure is observed, whereas the signal smears out for n/s >=0.32.
Gamma synchronization has generally been associated with grouping processes in the visual system. Here, we examine in monkey V1 whether gamma oscillations play a functional role in segmenting surfaces of plaid stimuli. Local field potentials (LFPs) and spiking activity were recorded simultaneously from multiple sites in the opercular and calcarine regions while the monkeys were presented with sequences of single and superimposed components of plaid stimuli. In accord with the previous studies, responses to the single components (gratings) exhibited strong and sustained gamma-band oscillations (30–65 Hz). The superposition of the second component, however, led to profound changes in the temporal structure of the responses, characterized by a drastic reduction of gamma oscillations in the spiking activity and systematic shifts to higher frequencies in the LFP (~10% increase). Comparisons between cerebral hemispheres and across monkeys revealed robust subject-specific spectral signatures. A possible interpretation of our results may be that single gratings induce strong cooperative interactions among populations of cells that share similar response properties, whereas plaids lead to competition. Overall, our results suggest that the functional architecture of the cortex is a major determinant of the neuronal synchronization dynamics in V1. Key words: attention , gamma , gratings , oscillation , visual cortex
Human Transformer2-beta (hTra2-beta) is an important member of the serine/arginine-rich protein family, and contains one RNA recognition motif (RRM). It controls the alternative splicing of several pre-mRNAs, including those of the calcitonin/calcitonin gene-related peptide (CGRP), the survival motor neuron 1 (SMN1) protein and the tau protein. Accordingly, the RRM of hTra2-beta specifically binds to two types of RNA sequences [the CAA and (GAA)2 sequences]. We determined the solution structure of the hTra2-beta RRM (spanning residues Asn110–Thr201), which not only has a canonical RRM fold, but also an unusual alignment of the aromatic amino acids on the beta-sheet surface. We then solved the complex structure of the hTra2-beta RRM with the (GAA)2 sequence, and found that the AGAA tetra-nucleotide was specifically recognized through hydrogen-bond formation with several amino acids on the N- and C-terminal extensions, as well as stacking interactions mediated by the unusually aligned aromatic rings on the beta-sheet surface. Further NMR experiments revealed that the hTra2-beta RRM recognizes the CAA sequence when it is integrated in the stem-loop structure. This study indicates that the hTra2-beta RRM recognizes two types of RNA sequences in different RNA binding modes.
The goal of this project is to develop a framework for a cell that takes in consideration its internal structure, using an agent-based approach. In this framework, a cell was simulated as many sub-particles interacting to each other. This sub-particles can, in principle, represent any internal structure from the cell (organelles, etc). In the model discussed here, two types of sub-particles were used: membrane sub-particles and cytosolic elements. A kinetic and dynamic Delaunay triangulation was used in order to define the neighborhood relations between the sub-particles. However, it was soon noted that the relations defined by the Delaunay triangulation were not suitable to define the interactions between membrane sub-particles. The cell membrane is a lipid bilayer, and does not present any long range interactions between their sub-particles. This means that the membrane particles should not be able to interact in a long range. Instead, their interactions should be confined to the two-dimensional surface supposedly formed by the membrane. A method to select, from the original three-dimensional triangulations, connections restricted to the two-dimensional surface formed by the cell membrane was then developed. The algorithm uses as starting point the three-dimensional Delaunay triangulation involving both internal and membrane sub-particles. From this triangulation, only the subset of connections between membrane sub-particles was considered. Since the cell is full of internal particles, the collection of the membrane particles' connections will resemble the surface to be obtained, even though it will still have many connections that do not belong to the restricted triangulation on the surface. This "thick surface" was called a quasi-surface. The following step was to refine the quasi-surface, cutting out some of the connections so that the ones left made a proper surface triangulation with the membrane points. For that, the quasi-surface was separated in clusters. Clusters are defined as areas on the quasi-surface that are not yet properly triangulated on a two-dimensional surface. Each of the clusters was then re-triangulated independently, using re-triangulation methods also developed during this work. The interactions between cytosolic elements was given by a Lennard-Jones potential, as well as the interactions between cytosolic elements and membrane particles. Between only membrane particles, the interactions were given by an elastic interaction. For each particle, the equation of motion was written. The algorithm chosen to solve the equations of motion was the Verlet algorithm. Since the cytosol can be approximated as a gel, it is reasonable to suppose that the sub-cellular particles are moving in an overdamped environment. Therefore, an overdamped approximation was used for all interactions. Additionally, an adaptive algorithm was used in order to define the size of the time step used in each interaction. After the method to re-triangulate the membrane points was implemented, the time needed to re-triangulate a single cluster was studied, followed by an analysis on how the time needed to re-triangulate each point in a cluster varied with the cluster size. The frequency of appearance for each cluster size was also compared, as this information is necessary to guarantee that the total time needed by to re-triangulate a cell is convergent. At last, the total time spent re-triangulating a surface was plotted, as well as a scaling for the total re-triangulation time with the variation. Even though there is still a lot to be done, the work presented here is an important step on the way to the main goal of this project: to create an agent-based framework that not only allows the simulation of any sub-cellular structure of interest but also provides meaningful interaction relations to particles belonging to the cell membrane.
Although models based on independent component analysis (ICA) have been successful in explaining various properties of sensory coding in the cortex, it remains unclear how networks of spiking neurons using realistic plasticity rules can realize such computation. Here, we propose a biologically plausible mechanism for ICA-like learning with spiking neurons. Our model combines spike-timing dependent plasticity and synaptic scaling with an intrinsic plasticity rule that regulates neuronal excitability to maximize information transmission. We show that a stochastically spiking neuron learns one independent component for inputs encoded either as rates or using spike-spike correlations. Furthermore, different independent components can be recovered, when the activity of different neurons is decorrelated by adaptive lateral inhibition.
Understanding the dynamics of recurrent neural networks is crucial for explaining how the brain processes information. In the neocortex, a range of different plasticity mechanisms are shaping recurrent networks into effective information processing circuits that learn appropriate representations for time-varying sensory stimuli. However, it has been difficult to mimic these abilities in artificial neural network models. Here we introduce SORN, a self-organizing recurrent network. It combines three distinct forms of local plasticity to learn spatio-temporal patterns in its input while maintaining its dynamics in a healthy regime suitable for learning. The SORN learns to encode information in the form of trajectories through its high-dimensional state space reminiscent of recent biological findings on cortical coding. All three forms of plasticity are shown to be essential for the network's success. Keywords: synaptic plasticity, intrinsic plasticity, recurrent neural networks, reservoir computing, time series prediction
In the present work, the problem of protein folding is addressed from the point of view of equilibrium thermodynamics. The conformation of a globular protein in solution at common temperatures is quite complicated without any geometrical symmetry, but it is an ordered state in the sense of its biological activity. This complicated conformation of a single protein molecule is destroyed upon increasing the temperature or by the addition of appropriate chemical agents, as is revealed by the loss of its activity and change of the physical properties, and so on. Once the complicated native structures having biological activity are lost, it would be natural to suppose that the native structure could hardly be restored. Nevertheless, pioneers, such as Anson and Mirsky, recognized as early as in 1925 that this was not always the case. If one defines the folded and unfolded states of a protein as two distinct phases of a system, then under the variation of temperature the system is transformed from one phase state into another and vice versa. The process of protein folding is accompanied by the release or absorption of a certain amount of energy, corresponding to the first-oder-type phase transitions in the bulk. Knowing the partition function of the system one can evaluate its energy and heat capacity under different temperatures. This task was performed in this work. The results of the developed statistical mechanics model were compared with the results of molecular dynamic simulations of alanine poylpeptides. In particular, the dependencies on temperature of the total energy of the system and heat capacity were compared for alanine polypeptides consisting of 21, 30, 40, 50 and 100 amino acids. The good correspondence of the results of the theoretical model with the results of molecular dynamics simulations allowed to validate the assumptions made about the system and to establish the accuracy range of the theory. In order to perform the comparison of the results of theoretical model and the molecular dynamics simulations it is necessary to perform the efficient analysis of the results of molecular dynamics simulations. This task was also addressed in the present work. In particular, different ways to obtain dependence of the heat capacity on temperature from molecular dynamics simulations are discussed and the most efficient one is proposed. The present thesis reports the result of molecular dynamic simulations for not only alanine polypeptides by also for valine and leucine polypeptides. In valine and leucine polypeptides, it is also possible to observe the helix↔random coil transitions with the increase of temperature. The current thesis presents a work that starts with the investigation of the fundamental degrees of freedom in polypeptides that are responsible for the conformational transitions. Then this knowledge is applied for the statistical mechanics description of helix↔coil transitions in polypeptides. Finally, the theoretical formalism is generalized for the case of proteins in water environment and the comparison of the results of the statistical mechanics model with the experimental measurements of the heat capacity on temperature dependencies for two globular proteins is performed. The presented formalism is based on fundamental physical properties of the system and provides the possibility to describe the folding↔unfolding transitions quantitatively. The combination of these two facts is the major novelty of the presented approach in comparison to the existing ones. The “transparent” physical nature of the formalism provides a possibility to further apply it to a large variety of systems and processes. For instance, it can be used for investigation of the influence of the mutations in the proteins on their stability. This task is of primary importance for design of novel proteins and drug delivering molecules in medicine. It can provide further insights into the problem of protein aggregation and formation of amyloids. The problem of protein aggregation is closely associated with various illnesses such as Alzheimer and mad cow disease. With certain modifications, the presented theoretical method can be applied to the description of the protein crystallization process, which is important for the determination of the structure of proteins with X-Rays. There many other possible applications of the ideas described in the thesis. For instance, the similar formalism can be developed for the description of melting and unzipping of DNA, growth of nanotubes, formation of fullerenes, etc.
Short-term memory requires the coordination of sub-processes like encoding, retention, retrieval and comparison of stored material to subsequent input. Neuronal oscillations have an inherent time structure, can effectively coordinate synaptic integration of large neuron populations and could therefore organize and integrate distributed sub-processes in time and space. We observed field potential oscillations (14–95 Hz) in ventral prefrontal cortex of monkeys performing a visual memory task. Stimulus-selective and performance-dependent oscillations occurred simultaneously at 65–95 Hz and 14–50 Hz, the latter being phase-locked throughout memory maintenance. We propose that prefrontal oscillatory activity may be instrumental for the dynamical integration of local and global neuronal processes underlying short-term memory.
Experience-driven formation of parts-based representations in a model of layered visual memory
(2009)
Growing neuropsychological and neurophysiological evidence suggests that the visual cortex uses parts-based representations to encode, store and retrieve relevant objects. In such a scheme, objects are represented as a set of spatially distributed local features, or parts, arranged in stereotypical fashion. To encode the local appearance and to represent the relations between the constituent parts, there has to be an appropriate memory structure formed by previous experience with visual objects. Here, we propose a model how a hierarchical memory structure supporting efficient storage and rapid recall of parts-based representations can be established by an experience-driven process of self-organization. The process is based on the collaboration of slow bidirectional synaptic plasticity and homeostatic unit activity regulation, both running at the top of fast activity dynamics with winner-take-all character modulated by an oscillatory rhythm. These neural mechanisms lay down the basis for cooperation and competition between the distributed units and their synaptic connections. Choosing human face recognition as a test task, we show that, under the condition of open-ended, unsupervised incremental learning, the system is able to form memory traces for individual faces in a parts-based fashion. On a lower memory layer the synaptic structure is developed to represent local facial features and their interrelations, while the identities of different persons are captured explicitly on a higher layer. An additional property of the resulting representations is the sparseness of both the activity during the recall and the synaptic patterns comprising the memory traces. Keywords: visual memory, self-organization, unsupervised learning, competitive learning, bidirectional plasticity, activity homeostasis, parts-based representation, cortical column
We suggest a new method to compute the spectrum and wave functions of excited states. We construct a stochastic basis of Bargmann link states, drawn from a physical probability density distribution and compute transition amplitudes between stochastic basis states. From such transition matrix we extract wave functions and the energy spectrum. We apply this method toU(1)2+1 lattice gauge theory. As a test we compute the energy spectrum, wave functions and thermodynamical functions of the electric Hamiltonian and compare it with analytical results. We find excellent agreement. We observe scaling of energies and wave functions in the variable of time. We also present first results on a small lattice for the full Hamiltonian including the magnetic term.
Poster Presentation from Nineteenth Annual Computational Neuroscience Meeting: CNS*2010 San Antonio, TX, USA. 24-30 July 2010 Statistical models of neural activity are at the core of the field of modern computational neuroscience. The activity of single neurons has been modeled to successfully explain dependencies of neural dynamics to its own spiking history, to external stimuli or other covariates [1]. Recently, there has been a growing interest in modeling spiking activity of a population of simultaneously recorded neurons to study the effects of correlations and functional connectivity on neural information processing (existing models include generalized linear models [2,3] or maximum-entropy approaches [4]). For point-process-based models of single neurons, the time-rescaling theorem has proven to be a useful toolbox to assess goodness-of-fit. In its univariate form, the time-rescaling theorem states that if the conditional intensity function of a point process is known, then its inter-spike intervals can be transformed or “rescaled” so that they are independent and exponentially distributed [5]. However, the theorem in its original form lacks sensitivity to detect even strong dependencies between neurons. Here, we present how the theorem can be extended to be applied to neural population models and we provide a step-by-step procedure to perform the statistical tests. We then apply both the univariate and multivariate tests to simplified toy models, but also to more complicated many-neuron models and to neuronal populations recorded in V1 of awake monkey during natural scenes stimulation. We demonstrate that important features of the population activity can only be detected using the multivariate extension of the test. ...
This thesis is dedicated to the study of fluctuation and correlation observables of hadronic equilibrium systems. The statistical hadronization model of high energy physics, in its ideal, i.e. non-interacting, gas approximation will be investigated in different ensemble formulations. The hypothesis of thermal and chemical equilibrium in high energy interaction will be tested against qualitative and quantitative predictions.
It is currently not known how distributed neuronal responses in early visual areas carry stimulus-related information. We made multielectrode recordings from cat primary visual cortex and applied methods from machine learning in order to analyze the temporal evolution of stimulus-related information in the spiking activity of large ensembles of around 100 neurons. We used sequences of up to three different visual stimuli (letters of the alphabet) presented for 100 ms and with intervals of 100 ms or larger. Most of the information about visual stimuli extractable by sophisticated methods of machine learning, i.e., support vector machines with nonlinear kernel functions, was also extractable by simple linear classification such as can be achieved by individual neurons. New stimuli did not erase information about previous stimuli. The responses to the most recent stimulus contained about equal amounts of information about both this and the preceding stimulus. This information was encoded both in the discharge rates (response amplitudes) of the ensemble of neurons and, when using short time constants for integration (e.g., 20 ms), in the precise timing of individual spikes (<= ~20 ms), and persisted for several 100 ms beyond the offset of stimuli. The results indicate that the network from which we recorded is endowed with fading memory and is capable of performing online computations utilizing information about temporally sequential stimuli. This result challenges models assuming frame-by-frame analyses of sequential inputs.
Information sent to and received by cells is essential for a homeostatic development of tissues and organs. These same signals are responsible for the good functioning of lymphatic organs and therefore govern the immune response. Dysfunctioning of the signaling networks is related to pathological situations, among which one can find cancer and auto-immune diseases. Intercellular communication involves the synthesis and the adjustment of signals by the secreting/emitting cell in order to reach the needed threshold. Diffusion of the signal to the target cell in addition to its interpretation lead to functional changes like cell migration and aggregation. Individual cells such as bacteria find food or increase their virulence through taxis (directional stimulus) and/or kinesis (speed stimulus). Immune cells appear to use the same processes to find bacteria and cellular debris, as well as to perform the cellular dance observed in germinal centers. This behavior is a result of an up or down regulation of specific signals that suggest to B and T-cells the paths to follow. Furthermore, cell segregation in the white pulp of the spleen, was also shown to be a result of a tight adjustment of T-cell kinesis. Restriction to cellular tracks and other experimentally provided measurements does not ensure a full comprehension of the observed cellular behavior. Thus, the study of patterns opens new gates to our understanding of the immune system. With the help of the agent-based modeling technique, cellular migration and aggregation are investigated in response to various cell-cell interactions. This work aims to explore different mechanisms that lead to cellular migration and aggregation, by defining the emergent properties of interest and that will help distinguish between interactions, starting by a simple look at the emergent patterns, followed by an analysis of their size, their degree of aggregation and the effective communication distances. Finally, the results obtained from the in silico experiments provided a guideline to differentiate between many cell-cell interactions under specific circumstances. Chemotaxis and phototaxis with and without diffusive cellular motion were shown to be distinguishable through an analysis of the emerging aggregation profiles.
Malignant neoplasms are one of the top causes of death in all developed countries around the world and account for almost one quarter of all deaths. An individual cell based computational model with strong connections to the experimental data through lattice free, newtonian interaction could be used to validate experimental results and eventually make predictions guiding further experiments. This model was build as a part of the thesis and shall be extended to the modelling of the effects of ionic radition on the vascularised tumour as a possible treatment for inoperable tumours.
Background: In this interdisciplinary project, the biological effects of heavy ions are compared to those of X-rays using tissue slice culture preparations from rodents and humans. Advantages of this biological model are the conservation of an organotypic environment and the independency from genetic immortalization strategies used to generate cell lines. Its open access allows easy treatment and observation via live-imaging microscopy. Materials and methods: Rat brains and human brain tumor tissue are cut into 300 micro m thick tissue slices. These slices are cultivated using a membrane-based culture system and kept in an incubator at 37°C until treatment. The slices are treated with X-rays at the radiation facility of the University Hospital in Frankfurt at doses of up to 40 Gy. The heavy ion irradiations were performed at the UNILAC facility at GSI with different ions of 11.4 A MeV and fluences ranging from 0.5–10 x 106 particles/cm². Using 3D-confocal microscopy, cell-death and immune cell activation of the irradiated slices are analyzed. Planning of the irradiation experiments is done with simulation programs developed at GSI and FIAS. Results: After receiving a single application of either X-rays or heavy ions, slices were kept in culture for up to 9d post irradiation. DNA damage was visualized using gamma H2AXstaining. Here, a dose-dependent increase and time-dependent decrease could clearly be observed for the X-ray irradiation. Slices irradiated with heavy ions showed less gamma H2AX-positive cells distributed evenly throughout the slice, even though particles were calculated to penetrate only 90–100 micro m into the slice. Conclusions: Single irradiations of brain tissue, even at high doses of 40 Gy, will result neither in tissue damage visible on a macroscopic level nor necrosis. This is in line with the view that the brain is highly radio-resistant. However, DNA damage can be detected very well in tissue slices using gamma H2AX-immuno staining. Thus, slice cultures are an excellent tool to study radiation-induced damage and repair mechanisms in living tissues.
There is little doubt that Quantumchromodynamics (QCD) is the theory which describes strong interaction physics. Lattice gauge simulations of QCD predict that in the m,T plane there is a line where a transition from confined hadronic matter to deconfined quarks takes place. The transition is either a cross over (at low m) or of first order (at high m). It is the goal of the present and future heavy ion experiment at RHIC and FAIR to study this phase transition at different locations in the m,T plane and to explore the properties of the deconfined phase. It is the purpose of this contribution to discuss some of the observables which are considered as useful for this purpose.
Poster presentation: How can two distant neural assemblies synchronize their firings at zero-lag even in the presence of non-negligible delays in the transfer of information between them? Neural synchronization stands today as one of the most promising mechanisms to counterbalance the huge anatomical and functional specialization of the different brain areas. However, and albeit more evidence is being accumulated in favor of its functional role as a binding mechanism of distributed neural responses, the physical and anatomical substrate for such a dynamic and precise synchrony, especially zero-lag even in the presence of non-negligible delays, remains unclear. Here we propose a simple network motif that naturally accounts for zero-lag synchronization of spiking assemblies of neurons for a wide range of temporal delays. We demonstrate that when two distant neural assemblies do not interact directly but relaying their dynamics via a third mediating single neuron or population and eventually achieve zero-lag coherent firing. Extensive numerical simulations of populations of Hodgkin-Huxley neurons interacting in such a network are analyzed. The results show that even with axonal delays as large as 15 ms the distant neural populations can synchronize their firings at zero-lag in a millisecond precision after the exchange of a few spikes. The role of noise and a distribution of axonal delays in the synchronized dynamics of the neural populations are also studied confirming the robustness of this sync mechanism. The proposed network module is densely embedded within the complex functional architecture of the brain and especially within the reciprocal thalamocortical interactions where the role of indirect pathways mimicking direct cortico-cortical fibers has been already suggested to facilitate trans-areal cortical communication. In summary the robust neural synchronization mechanism presented here arises as a consequence of the relay and redistribution of the dynamics performed by a mediating neuronal population. In opposition to previous works, neither inhibitory, gap junctions, nor complex networks need to be invoked to provide a stable mechanism of zero-phase correlated activity of neural populations in the presence of large conduction delays.
Poster presentation: Background To test the importance of synchronous neuronal firing for information processing in the brain, one has to investigate if synchronous firing strength is correlated to the experimental subjects. This requires a tool that can compare the strength of the synchronous firing across different conditions, while at the same time it should correct for other features of neuronal firing such as spike rate modulation or the auto-structure of the spike trains that might co-occur with synchronous firing. Here we present the bi- and multivariate extension of previously developed method NeuroXidence [1,2], which allows for comparing the amount of synchronous firing between different conditions. ...
Poster presentation: Coordinated neuronal activity across many neurons, i.e. synchronous or spatiotemporal pattern, had been believed to be a major component of neuronal activity. However, the discussion if coordinated activity really exists remained heated and controversial. A major uncertainty was that many analysis approaches either ignored the auto-structure of the spiking activity, assumed a very simplified model (poissonian firing), or changed the auto-structure by spike jittering. We studied whether a statistical inference that tests whether coordinated activity is occurring beyond chance can be made false if one ignores or changes the real auto-structure of recorded data. To this end, we investigated the distribution of coincident spikes in mutually independent spike-trains modeled as renewal processes. We considered Gamma processes with different shape parameters as well as renewal processes in which the ISI distribution is log-normal. For Gamma processes of integer order, we calculated the mean number of coincident spikes, as well as the Fano factor of the coincidences, analytically. We determined how these measures depend on the bin width and also investigated how they depend on the firing rate, and on rate difference between the neurons. We used Monte-Carlo simulations to estimate the whole distribution for these parameters and also for other values of gamma. Moreover, we considered the effect of dithering for both of these processes and saw that while dithering does not change the average number of coincidences, it does change the shape of the coincidence distribution. Our major findings are: 1) the width of the coincidence count distribution depends very critically and in a non-trivial way on the detailed properties of the inter-spike interval distribution, 2) the dependencies of the Fano factor on the coefficient of variation of the ISI distribution are complex and mostly non-monotonic. Moreover, the Fano factor depends on the very detailed properties of the individual point processes, and cannot be predicted by the CV alone. Hence, given a recorded data set, the estimated value of CV of the ISI distribution is not sufficient to predict the Fano factor of the coincidence count distribution, and 3) spike jittering, even if it is as small as a fraction of the expected ISI, can falsify the inference on coordinated firing. In most of the tested cases and especially for complex synchronous and spatiotemporal pattern across many neurons, spike jittering increased the likelihood of false positive finding very strongly. Last, we discuss a procedure [1] that considers the complete auto-structure of each individual spike-train for testing whether synchrony firing occurs at chance and therefore overcomes the danger of an increased level of false positives.
Poster presentation: Characterizing neuronal encoding is essential for understanding information processing in the brain. Three methods are commonly used to characterize the relationship between neural spiking activity and the features of putative stimuli. These methods include: Wiener-Volterra kernel methods (WVK), the spike-triggered average (STA), and more recently, the point process generalized linear model (GLM). We compared the performance of these three approaches in estimating receptive field properties and orientation tuning of 251 V1 neurons recorded from 2 monkeys during a fixation period in response to a moving bar. The GLM consisted of two formulations of the conditional intensity function for a point process characterization of the spiking activity: one with a stimulus only component and one with the stimulus and spike history. We fit the GLMs by maximum likelihood using GLMfit in Matlab. Goodness-of-fit was assessed using cross-validation with Kolmogorov-Smirnov (KS) tests based on the time-rescaling theorem to evaluate the accuracy with which each model predicts the spiking activity of individual neurons and for each movement direction (4016 models in total, for 251 neurons and 16 different directions). The GLMs that considered spike history of up to 35 ms, accurately predicted neuronal spiking activity (95% confidence intervals for KS test) with a performance of 97.0% (3895/4016) for the training data, and 96.5% (3876/4016) for the test data. If spike history was not considered, performance dropped to 73,1% in the training and 71.3% in the testing data. In contrast, the WVF and the STA predicted spiking accurately for 24.2% and 44.5% of the test data examples respectively. The receptive field size estimates obtained from the GLM (with and without history), WVF and STA were comparable. Relative to the GLM orientation tuning was underestimated on average by a factor of 0.45 by the WVF and the STA. The main reason for using the STA and WVF approaches is their apparent simplicity. However, our analyses suggest that more accurate spike prediction as well as more credible estimates of receptive field size and orientation tuning can be computed easily using GLMs implemented in Matlab with standard functions such as GLMfit.
Poster presentation: Introduction Rhythmic synchronization of neural activity in the gamma-frequency range (30–100 Hz) was observed in many brain regions; see the review in [1]. The functional relevance of these oscillations remains to be clarified, a task that requires modeling of the relevant aspects of information processing. The temporal correlation hypothesis, reviewed in [2], proposes that the temporal correlation of neural units provides a means to group the neural units into so-called neural assemblies that are supposed to represent mental objects. Here, we approach the modeling of the temporal grouping of neural units from the perspective of oscillatory neural network systems based on phase model oscillators. Patterns are assumed to be stored in the network based on Hebbian memory and assemblies are identified with phase-locked subset of these patterns. Going beyond foregoing discussions, we demonstrate the combination of two recently discussed mechanisms, referred to as "acceleration" [3] and "pooling" [4]. The combination realizes in a complementary manner a competition for activity on a local scale, while providing a competition for coherence among different assemblies on a non-local scale. ...
Poster presentation: Introduction Adequate anesthesia is crucial to the success of surgical interventions and subsequent recovery. Neuroscientists, surgeons, and engineers have sought to understand the impact of anesthetics on the information processing in the brain and to properly assess the level of anesthesia in an non-invasive manner. Studies have indicated a more reliable depth of anesthesia (DOA) detection if multiple parameters are employed. Indeed, commercial DOA monitors (BIS, Narcotrend, M-Entropy and A-line ARX) use more than one feature extraction method. Here, we propose TESPAR (Time Encoded Signal Processing And Recognition) a time domain signal processing technique novel to EEG DOA assessment that could enhance existing monitoring devices. ...
Poster presentation: Functional connectivity of the brain describes the network of correlated activities of different brain areas. However, correlation does not imply causality and most synchronization measures do not distinguish causal and non-causal interactions among remote brain areas, i.e. determine the effective connectivity [1]. Identification of causal interactions in brain networks is fundamental to understanding the processing of information. Attempts at unveiling signs of functional or effective connectivity from non-invasive Magneto-/Electroencephalographic (M/EEG) recordings at the sensor level are hampered by volume conduction leading to correlated sensor signals without the presence of effective connectivity. Here, we make use of the transfer entropy (TE) concept to establish effective connectivity. The formalism of TE has been proposed as a rigorous quantification of the information flow among systems in interaction and is a natural generalization of mutual information [2]. In contrast to Granger causality, TE is a non-linear measure and not influenced by volume conduction. ...
Poster presentation: Our work deals with the self-organization [1] of a memory structure that includes multiple hierarchical levels with massive recurrent communication within and between them. Such structure has to provide a representational basis for the relevant objects to be stored and recalled in a rapid and efficient way. Assuming that the object patterns consist of many spatially distributed local features, a problem of parts-based learning is posed. We speculate on the neural mechanisms governing the process of the structure formation and demonstrate their functionality on the task of human face recognition. The model we propose is based on two consecutive layers of distributed cortical modules, which in turn contain subunits receiving common afferents and bounded by common lateral inhibition (Figure 1). In the initial state, the connectivity between and within the layers is homogeneous, all types of synapses – bottom-up, lateral and top-down – being plastic. During the iterative learning, the lower layer of the system is exposed to the Gabor filter banks extracted from local points on the face images. Facing an unsupervised learning problem, the system is able to develop synaptic structure capturing local features and their relations on the lower level, as well as the global identity of the person at the higher level of processing, improving gradually its recognition performance with learning time. ...
Poster presentation: Introduction We study the problem of object recognition invariant to transformations, such as translation, rotation and scale. A system is underdetermined if its degrees of freedom (number of possible transformations and potential objects) exceed the available information (image size). The regularization theory solves this problem by adding constraints [1]. It is unclear what constraints biological systems use. We suggest that rather than seeking constraints, an underdetermined system can make decisions based on available information by grouping its variables. We propose a dynamical system as a minimum system for invariant recognition to demonstrate this strategy. ...
Poster presentation: Introduction Dopaminergic neurons in the midbrain show a variety of firing patterns, ranging from very regular firing pacemaker cells to bursty and irregular neurons. The effects of different experimental conditions (like pharmacological treatment or genetical manipulations) on these neuronal discharge patterns may be subtle. Applying a stochastic model is a quantitative approach to reveal these changes. ...
NeuroXidence: reliable and efficient analysis of an excess or deficiency of joint-spike events
(2009)
Poster presentation: We present a non-parametric and computationally-efficient method named NeuroXidence (see http://www.NeuroXidence.com ) that detects coordinated firing within a group of two or more neurons and tests whether the observed level of coordinated firing is significantly different from that expected by chance. NeuroXidence [1] considers the full auto-structure of the data, including the changes in the rate responses and the history dependencies in the spiking activity. We demonstrate that NeuroXidence can identify epochs with significant spike synchronisation even if these coincide with strong and fast rate modulations. We also show, that the method accounts for trial-by-trial variability in the rate responses and their latencies, and that it can be applied to short data windows lasting only tens of milliseconds. Based on simulated data we compare the performance of NeuroXidence with the UE-method [2,3] and the cross-correlation analysis. An application of NeuroXidence to 42 single-units (SU) recorded in area 17 of an anesthetized cat revealed significant coincident events of high complexities, involving firing of up to 8 SUs simultaneously (5 ms window). The results were highly consistent with those obtained by traditional pair-wise measures based on cross-correlation: Neuronal synchrony was strongest in stimulation conditions in which the orientation of the sinusoidal grating matched the preferred orientation of most of the SUs included in the analysis, and was the weakest when the neurons were stimulated least optimally. Interestingly, events of higher complexities showed stronger stimulus-specific modulation than pair-wise interactions. The results suggest strong evidence for stimulus specific synchronous firing and, therefore, support the temporal coding hypothesis in visual cortex. ...
Poster presentation: Introduction We here focus on constructing a hierarchical neural system for position-invariant recognition, which is one of the most fundamental invariant recognition achieved in visual processing [1,2]. The invariant recognition have been hypothesized to be done by matching a sensory image of a particular object stimulated on the retina to the most suitable representation stored in memory of the higher visual cortical area. Here arises a general problem: In such a visual processing, the position of the object image on the retina must be initially uncertain. Furthermore, the retinal activities possessing sensory information are being far from the ones in the higher area with a loss of the sensory object information. Nevertheless, with such recognition ambiguity, the particular object can effortlessly and easily be recognized. Our aim in this work is an attempt to resolve such a general recognition problem. ...
Poster presentation: Introduction We here address the problem of integrating information about multiple objects and their positions on the visual scene. A primate visual system has little difficulty in rapidly achieving integration, given only a few objects. Unfortunately, computer vision still has great difficultly achieving comparable performance. It has been hypothesized that temporal binding or temporal separation could serve as a crucial mechanism to deal with information about objects and their positions in parallel to each other. Elaborating on this idea, we propose a neurally plausible mechanism for reaching local decision-making for "what" and "where" information to the global multi-object recognition. ...
Poster presentation: Introduction The brain is a highly interconnected network of constantly interacting units. Understanding the collective behavior of these units requires a multi-dimensional approach. The results of such analyses are hard to visualize and interpret. Hence tools capable of dealing with such tasks become imperative. ....
Recently, two-photon imaging has allowed intravital tracking of lymphocyte migration and cellular interactions during germinal center (GC) reactions. The implications of two-photon measurements obtained by several investigators are currently the subject of controversy. With the help of two mathematical approaches, we reanalyze these data. It is shown that the measured lymphocyte migration frequency between the dark and the light zone is quantitatively explained by persistent random walk of lymphocytes. The cell motility data imply a fast intermixture of cells within the whole GC in approximately 3 h, and this does not allow for maintenance of dark and light zones. The model predicts that chemotaxis is active in GCs to maintain GC zoning and demonstrates that chemotaxis is consistent with two-photon lymphocyte motility data. However, the model also predicts that the chemokine sensitivity is quickly down-regulated. On the basis of these fi ndings, we formulate a novel GC lymphocyte migration model and propose its verifi cation by new two-photon experiments that combine the measurement of B cell migration with that of specifi c chemokine receptor expression levels. In addition, we discuss some statistical limitations for the interpretation of two-photon cell motility measurements in general.
The dissertation deals with the general problem of how the brain can establish correspondences between neural patterns stored in different cortical areas. Although an important capability in many cognitive areas like language understanding, abstract reasoning, or motor control, this thesis concentrates on invariant object recognition as application of correspondence finding. One part of the work presents a correspondence-based, neurally plausible system for face recognition. Other parts address the question of visual information routing over several stages by proposing optimal architectures for such routing ('switchyards') and deriving ontogenetic mechanisms for the growth of switchyards. Finally, the idea of multi-stage routing is united with the object recognition system introduced before, making suggestions of how the so far distinct feature-based and correspondence-based approaches to object recognition could be reconciled.
We argue that Clustering in heavy ion collisions could be the missing element in resolving the socalled HBT puzzle, and briefly discuss the different physical situations where clustering could be present. We then propose a method by which clustering in heavy ion collisions could be detectedin a model-independent way.
We calculate leading-order dilepton yields from a quark-gluon plasma which has a time-dependent anisotropy in momentum space. Such anisotropies can arise during the earliest stages of quark-gluon plasma evolution due to the rapid longitudinal expansion of the created matter. A phenomenological model for the proper time dependence of the parton hard momentum scale, p_hard, and the plasma anisotropy parameter, xi, is proposed. The model describes the transition of the plasma from a 0+1 dimensional collisionally-broadened expansion at early times to a 0+1 dimensional ideal hydrodynamic expansion at late times. We find that high-energy dilepton production is enhanced by pre-equilibrium emission up to 50% at LHC energies, if one assumes an isotropization/thermalization time of 2 fm/c. Given sufficiently precise experimental data this enhancement could be used to determine the plasma isotropization time experimentally.
Synchronisierte Antworten aus der Großhirnrinde : ein Lösungsvorschlag für das Bindungsproblem
(2005)
The interplay of charmonium production and suppression in In+In and Pb+Pb reactions at 158 AGeV and in Au+Au reactions at sqrt(s)=200 GeV is investigated with the HSD transport approach within the hadronic comover model' and the QGP melting scenario'. The results for the J/Psi suppression and the Psi' to J/Psi ratio are compared to the recent data of the NA50, NA60, and PHENIX Collaborations. We find that, at 158 AGeV, the comover absorption model performs better than the scenario of abrupt threshold melting. However, neither interaction with hadrons alone nor simple color screening satisfactory describes the data at sqrt(s)=200 GeV. A deconfined phase is clearly reached at RHIC, but a theory having the relevant degrees of freedom in this regime (strongly interacting quarks/gluons) is needed to study its transport properties.
This thesis contributes to the field of soft matter research and studies the importance of hydrodynamic interactions during free-solution electrophoresis of linear polyelectrolytes by means of coarse-grained molecular dynamics simulations including full electro-hydrodynamic interactions. The center of attention is the specific role of hydrodynamic interactions on the electrophoretic behaviour of charged macromolecules. Points of interest are the dependence of hydrodynamic interactions on the chain length, the chain flexibility and the surrounding counterions, and their combined influence on important observables such as the static chain conformations and the dynamic transport coefficients, i.e., the diffusion and the electrophoretic mobility. These problems are addressed by extensive computer simulations that are quantitatively matched with experimental results. Existing theoretical predictions are carefully examined and are augmented by the observations in this thesis.
The timing of feedback to early visual cortex in the perception of long-range apparent motion
(2008)
When 2 visual stimuli are presented one after another in different locations, they are often perceived as one, but moving object. Feedback from area human motion complex hMT/V5+ to V1 has been hypothesized to play an important role in this illusory perception of motion. We measured event-related responses to illusory motion stimuli of varying apparent motion (AM) content and retinal location using Electroencephalography. Detectable cortical stimulus processing started around 60-ms poststimulus in area V1. This component was insensitive to AM content and sequential stimulus presentation. Sensitivity to AM content was observed starting around 90 ms post the second stimulus of a sequence and most likely originated in area hMT/V5+. This AM sensitive response was insensitive to retinal stimulus position. The stimulus sequence related response started to be sensitive to retinal stimulus position at a longer latency of 110 ms. We interpret our findings as evidence for feedback from area hMT/V5+ or a related motion processing area to early visual cortices (V1, V2, V3).
What is the energy function guiding behavior and learningµ Representationbased approaches like maximum entropy, generative models, sparse coding, or slowness principles can account for unsupervised learning of biologically observed structure in sensory systems from raw sensory data. However, they do not relate to behavior. Behavior-based approaches like reinforcement learning explain animal behavior in well-described situations. However, they rely on high-level representations which they cannot extract from raw sensory data. Combinations of multiple goal functions seems the methodology of choice to understand the complexity of the brain. But what is the set of possible goals. ...
A small-world network has been suggested to be an efficient solution for achieving both modular and global processing-a property highly desirable for brain computations. Here, we investigated functional networks of cortical neurons using correlation analysis to identify functional connectivity. To reconstruct the interaction network, we applied the Ising model based on the principle of maximum entropy. This allowed us to assess the interactions by measuring pairwise correlations and to assess the strength of coupling from the degree of synchrony. Visual responses were recorded in visual cortex of anesthetized cats, simultaneously from up to 24 neurons. First, pairwise correlations captured most of the patterns in the population´s activity and, therefore, provided a reliable basis for the reconstruction of the interaction networks. Second, and most importantly, the resulting networks had small-world properties; the average path lengths were as short as in simulated random networks, but the clustering coefficients were larger. Neurons differed considerably with respect to the number and strength of interactions, suggesting the existence of "hubs" in the network. Notably, there was no evidence for scale-free properties. These results suggest that cortical networks are optimized for the coexistence of local and global computations: feature detection and feature integration or binding.
Poster presentation A central problem in neuroscience is to bridge local synaptic plasticity and the global behavior of a system. It has been shown that Hebbian learning of connections in a feedforward network performs PCA on its inputs [1]. In recurrent Hopfield network with binary units, the Hebbian-learnt patterns form the attractors of the network [2]. Starting from a random recurrent network, Hebbian learning reduces system complexity from chaotic to fixed point [3]. In this paper, we investigate the effect of Hebbian plasticity on the attractors of a continuous dynamical system. In a Hopfield network with binary units, it can be shown that Hebbian learning of an attractor stabilizes it with deepened energy landscape and larger basin of attraction. We are interested in how these properties carry over to continuous dynamical systems. Consider system of the form Math(1) where xi is a real variable, and fi a nondecreasing nonlinear function with range [-1,1]. T is the synaptic matrix, which is assumed to have been learned from orthogonal binary ({1,-1}) patterns ξμ, by the Hebbian rule: Math. Similar to the continuous Hopfield network [4], ξμ are no longer attractors, unless the gains gi are big. Assume that the system settles down to an attractor X*, and undergoes Hebbian plasticity: T´ = T + εX*X*T, where ε > 0 is the learning rate. We study how the attractor dynamics change following this plasticity. We show that, in system (1) under certain general conditions, Hebbian plasticity makes the attractor move towards its corner of the hypercube. Linear stability analysis around the attractor shows that the maximum eigenvalue becomes more negative with learning, indicating a deeper landscape. This in a way improves the system´s ability to retrieve the corresponding stored binary pattern, although the attractor itself is no longer stabilized the way it does in binary Hopfield networks.
In this work the nuclear structure of exotic nuclei and superheavy nuclei is studied in a relativistic framework. In the relativistic mean-field (RMF) approximation, the nucleons interact with each other through the exchange of various effective mesons (scalar, vector, isovector-vector). Ground state properties of exotic nuclei and superheavy nuclei are studied in the RMF theory with the three different parameter sets (ChiM, NL3, NL-Z2). Axial deformation of nuclei within two drip lines are performed with the parameter set (ChiM). The position of drip lines are investigated with three different parameter sets (ChiM, NL3, NL-Z2) and compared with the experimental drip line nuclei. In addition, the structure of hypernuclei are studied and for a certain isotope, hyperon halo nucleus is predicted.
Spatio-temporal dynamics of primary lymphoid follicles during organogenesis and lymphneogenesis
(2007)
Primary lymphoid follicles are structures which are important for adaptive immune responses in mammals. Within the follicles follicular dendritic cells (FDC) are maintained by constant stimuli provided by B cells. It is thought that the FDC are important for immune response. It is of interest to know how lymphoid follicles are regulated in order to understand their role in various autoimmune diseases in which these follicles are created ectopically. With the help of a tissue simulation relying on an agent-based cell model on top of a regular triangulation various scenarios suggested by the available experimental data have been investigated. In order to cope with the complexity in the simulation of immune tissue the regular triangulation has been implemented for the use on parallel computers. The algorithms for kinetic and dynamic regular triangulation have been created newly. Also the cell model underlying the simulation has been designed newly in many aspects. The simulations allowed to identify common factors that regulate the formation of lymphoid follicles normally during organogenesis in development and lymphneogenesis in the course of diseases. The generation of FDC from local stromal populations under the influence of B cell aggregates is shown to be possible with the given experimental parameters. The sequence of the organogenesis and lymphneogenesis can be described with regard to the morphology of the B and T zone. Tests for the stability of the primary lymphoid follicle system constraints the regulation of the B cell efflux. The required lymphatic vessels around the lymphoid follicle are shown to be negatively correlated with the FDC network. Moreover it is shown that the adjacent T zone consisting of its own stromal population and T cells has similar regulation principles. This easily explains the intermediate ring of B cells found around the T zone during development and certain signaling molecule deficiencies. A major result of this thesis is that the generation of FDC needs negative regulation while a number of other possible mechanisms is incompatible with the available experimental data. Moreover the observed microanatomy was brought into a functional relationship with data on the cellular level finally culminating in the proposal of new experiments that shed light on the dynamics of the primary lymphoid follicle. One conclusion is that the FDC directly or indirectly influence the angiogenesis and lymphangiogenesis processes in secondary lymphoid tissues. The work presented here may help to guide experiments with the help of computers in order to reduce the amount of experiments and design them in a way to maximize the amount of information about biological systems.
This work is devoted to the description of mechanisms that might be responsible for avian magnetoreception. Two possible theoretical concepts underlying this phenomenon are formulated and their functionality is proven in realistic geomagnetic fields. It has been suggested that the "magnetic sense" in birds may be mediated by the blue light receptor protein- cryptochrome- which is known to be localized in the retinas of migratory birds. Cryptochromes are a class of photoreceptor signaling proteins that are found in a wide variety of organisms and which primarily perform regulatory functions, such as the entrainment of circadian rhythm in mammals and the inhibition of hypocotyl growth in plants. Recent experiments have shown that the activity of cryptochrome-1 in Arabidopsis thaliana is enhanced by the presence of a weak external magnetic field, confirming the ability of cryptochrome to mediate magnetic field responses. Cryptochrome's signaling is tied to the photoreduction of an internally bound chromophore, flavin adenine dinucleotide (FAD). The spin chemistry of this photoreduction process, which involves electron transfer from a chain of three tryptophans, is modulated by the presence of a magnetic field in an effect known as the radical pair mechanism. Cryptochrome was suggested as a possible magnetoreceptor for the first time in 2000. However, no realistic calculations of the magnetic field effect in cryptochrome were performed. One of the goals of the present thesis is computationally to study the electron spin dynamics in cryptochrome and to show the feasibility of a cryptochrome-based compass in birds. In particular, the activation yield of cryptochrome was studied as a function of an external magnetic field and it was shown that the activation of the protein can be influenced by the geomagnetic field. In the work it has also been proven that cryptochrome provides an inclination compass, which is necessary for bird orientation. The evolution of spin densities as a function of time is also discussed. An alternative mechanism of avian magnetoreception discussed in the thesis is based on the interaction of two iron minerals (magnetite and maghemite) which were only recently found in subcellular compartments within the sensory dendrites of the upper beak of several bird species. The iron minerals in the beak form platelets of crystalline maghemite and assemblies of magnetite nanoparticles (magnetite clusters). The interaction between these particles can be manipulated by an external magnetic field inducing a primary receptor potential via strain-sensitive membrane channels that lead to a certain bird orientation effect. Various properties of the magnetite/maghemite magnetoreceptor system have been considered: the potential energy surface of the magnetite cluster has been calculated and analyzed as a function of the orientation of an external magnetic field; the forces acting on the magnetite cluster were calculated and analyzed; the force differences caused by the change of the direction of external magnetic field were established; the probability of opening the mechanosensitive ion channel was calculated. Finally it has been demonstrated that the iron-mineral based magnetoreceptor provides a polarity magnetic compass. Various conditions at which the magnetoreception process is violated are outlined.
I investigate some of the inert phases in three-flavor, spin-zero color-superconducting quark matter: the CFL phase (the analogue of the B phase in superfluid 3He), the A and A* phases, and the 2SC and sSC phases. I compute the pressure of these phases with and without the neutrality condition. Without the neutrality condition, after the CFL phase the sSC phase is the dominant phase. However, including the neutrality condition, the CFL phase is again the energetically favored phase except for a small region of intermediate densities where the 2SC/A* phase is favored. It is shown that the 2SC phase is identical to the A* phase up to a color rotation. In addition, I calculate the self-energies and the spectral densities of longitudinal and transverse gluons at zero temperature in color-superconducting quark matter in the CFL phase. I find a collective excitation, a plasmon, at energies smaller than two times the gap parameter and momenta smaller than about eight times the gap. The dispersion relation of this mode exhibits a minimum at some nonzero value of momentum, indicating a van Hove singularity.
In this thesis we investigate the role played by gauge fields in providing new observable signatures that can attest to the presence of color superconductivity in neutron stars. We show that thermal gluon fluctuations in color-flavor locked superconductors can substantially increase their critical temperature and also change the order of the transition, which becomes a strong first-order phase transition. Moreover, we explore the effects of strong magnetic fields on the properties of color-flavor locked superconducting matter. We find that both the energy gaps as well as the magnetization are oscillating functions of the magnetic field. Also, it is shown that the magnetization can be so strong that homogeneous quark matter becomes metastable for a range of parameters. This points towards the existence of magnetic domains or other types of magnetic inhomogeneities in the hypothesized quark cores of magnetars. Obviously, our results only apply if the strong magnetic fields observed on the surface of magnetars can be transmitted to their inner core. This can occur if the superconducting protons expected to exist in the outer core form a type-I I superconductor. However, it has been argued that the observed long periodic oscillations in isolated pulsars can only be explained if the outer core is a type-I superconductor rather than type-I I. We show that this is not the only solution for the precession puzzle by demonstrating that the long-term variation in the spin of PSR 1828-11 can be explained in terms of Tkachenko oscillations within superfluid shells.
Background Objects in our environment are often partly occluded, yet we effortlessly perceive them as whole and complete. This phenomenon is called visual amodal completion. Psychophysical investigations suggest that the process of completion starts from a representation of the (visible) physical features of the stimulus and ends with a completed representation of the stimulus. The goal of our study was to investigate both stages of the completion process by localizing both brain regions involved in processing the physical features of the stimulus as well as brain regions representing the completed stimulus. Results Using fMRI adaptation we reveal clearly distinct regions in the visual cortex of humans involved in processing of amodal completion: early visual cortex - presumably V1 - processes the local contour information of the stimulus whereas regions in the inferior temporal cortex represent the completed shape. Furthermore, our data suggest that at the level of inferior temporal cortex information regarding the original local contour information is not preserved but replaced by the representation of the amodally completed percept. Conclusion These findings provide neuroimaging evidence for a multiple step theory of amodal completion and further insights into the neuronal correlates of visual perception.