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In this work, we propose novel offline and online Inverse Differential Game (IDG) methods for nonlinear Differential Games (DG), which identify the cost functions of all players from control and state trajectories constituting a feedback Nash equilibrium. The offline approach computes the sets of all equivalent cost function parameters that yield the observed trajectories. Our online method is guaranteed to converge to cost function parameters of the offline calculated sets. For both methods, we additionally analyze the case where the cost and value functions are not given by known parameterized structures and approximation structures, like polynomial basis functions, need to be chosen. Here, we found that for guaranteeing a bounded error between the trajectories resulting from the offline and online IDG solutions and the observed trajectories an appropriate selection of the cost function structures is required. They must be aligned to assumed value function structures such that the coupled Hamilton-Jacobi-Bellman equations can be fulfilled. Finally, the theoretical results and the effectiveness of our new methods are illustrated with a numerical example.

This paper explores cooperative trajectory planning approaches within the context of human-machine shared control. In shared control research, it is typically assumed that the human and the automation use the same reference trajectory to stabilize the coupled system. However, this assumption is often incorrect, as they usually follow different trajectories, causing control conflicts at the action level that have not been widely researched. To address this, it is logical to extend shared control concepts to include human-machine interaction at the trajectory-level before action execution, resulting in a unified reference trajectory for both human and automation. This paper begins with a literature overview on approaches of cooperative trajectory planning. It then presents an approach of finding a joint trajectory by modelling cooperative trajectory planning as an agreement process. A generally valid system structure is proposed for this purpose. Finally, it proposes concepts to implement cooperative trajectory planning as an agreement process.

Broad application of human-machine interaction (HMI) demands advanced and human-centered control designs for the machine's automation. Human natural motor action shows stochastic behavior, which has so far not been respected in HMI control designs. Using a previously presented novel human-variability-respecting optimal controller we present a study design which allows the investigation of respecting human natural variability and its effect on human interaction experience. Our approach is tested in simulation based on an identified real human subject and presents a promising approach to be used for a larger subject study.

Understanding causal relationships within a system is crucial for uncovering its underlying mechanisms. Causal discovery methods, which facilitate the construction of such models from time-series data, hold the potential to significantly advance scientific and engineering fields. This study introduces the Cross-Mapping Coherence (CMC) method, designed to reveal causal connections in the frequency domain between time series. CMC builds upon nonlinear state-space reconstruction and extends the Convergent Cross-Mapping algorithm to the frequency domain by utilizing coherence metrics for evaluation. We tested the Cross-Mapping Coherence method using simulations of logistic maps, Lorenz systems, Kuramoto oscillators, and the Wilson-Cowan model of the visual cortex. CMC accurately identified the direction of causal connections in all simulated scenarios. When applied to the Wilson-Cowan model, CMC yielded consistent results similar to spectral Granger causality. Furthermore, CMC exhibits high sensitivity in detecting weak connections, demonstrates sample efficiency, and maintains robustness in the presence of noise. In conclusion, the capability to determine directed causal influences across different frequency bands allows CMC to provide valuable insights into the dynamics of complex, nonlinear systems.

In this paper, a method for a cooperative trajectory planning between a human and an automation is extended by a behavioral model of the human. This model can characterize the stubbornness of the human, which measures how strong the human adheres to his preferred trajectory. Accordingly, a static model is introduced indicating a link between the force in haptically coupled human-robot interactions and humans's stubbornness. The introduced stubbornness parameter enables an application-independent reaction of the automation for the cooperative trajectory planning. Simulation results in the context of human-machine cooperation in a care application show that the proposed behavioral model can quantitatively estimate the stubbornness of the interacting human, enabling a more targeted adaptation of the automation to the human behavior.

Physical Human-Machine Interaction plays a pivotal role in facilitating collaboration across various domains. When designing appropriate model-based controllers to assist a human in the interaction, the accuracy of the human model is crucial for the resulting overall behavior of the coupled system. When looking at state-of-the-art control approaches, most methods rely on a deterministic model or no model at all of the human behavior. This poses a gap to the current neuroscientific standard regarding human movement modeling, which uses stochastic optimal control models that include signal-dependent noise processes and therefore describe the human behavior much more accurate than the deterministic counterparts. To close this gap by including these stochastic human models in the control design, we introduce a novel design methodology resulting in a Human-Variability-Respecting Optimal Control that explicitly incorporates the human noise processes and their influence on the mean and variability behavior of a physically coupled human-machine system. Our approach results in an improved overall system performance, i.e. higher accuracy and lower variability in target point reaching, while allowing to shape the joint variability, for example to preserve human natural variability patterns.

This paper introduces a novel model-based adaptive shared control to allow for the identification and design challenge for shared-control systems, in which humans and automation share control tasks. The main challenge is the adaptive behavior of the human in such shared control interactions. Consequently, merely identifying human behavior without considering automation is insufficient and often leads to inadequate automation design. Therefore, this paper proposes a novel solution involving online identification of the human and the adaptation of shared control using Linear-Quadratic differential games. The effectiveness of the proposed online adaptation is analyzed in simulations and compared with a non-adaptive shared control from the state of the art. Finally, the proposed approach is tested through human-in-the-loop experiments, highlighting its suitability for real-time applications.

In this work, we analyze the applicability of Inverse Dynamic Game (IDG) methods based on the Minimum Principle (MP). The IDG method determines unknown cost functions in a single- or multi-agent setting from observed system trajectories by minimizing the so-called residual error, i.e. the extent to which the optimality conditions of the MP are violated with a current guess of cost functions. The main assumption of the IDG method to recover cost functions such that the resulting trajectories match the observed ones is that the given trajectories are the result of a Dynamic Game (DG) problem with known parameterized cost function structures. However, in practice, when the IDG method is used to identify the behavior of unknown agents, e.g. humans, this assumption cannot be guaranteed. Hence, we introduce the notion of the trustworthiness of the residual error and provide necessary conditions for it to define when the IDG method based on the MP is applicable to such problems. From the necessary conditions, we conclude that the MP-based IDG method cannot be used to validate DG models for unknown agents but can yield under certain conditions robust parameter identifications, e.g. to measurement noise. Finally, we illustrate these conclusions by validating a DG model for the collision avoidance behavior between two mobile robots with human operators.

In this paper, we propose a new algorithm to solve the Inverse Stochastic Optimal Control (ISOC) problem of the linear-quadratic sensorimotor (LQS) control model. The LQS model represents the current state-of-the-art in describing goal-directed human movements. The ISOC problem aims at determining the cost function and noise scaling matrices of the LQS model from measurement data since both parameter types influence the statistical moments predicted by the model and are unknown in practice. We prove global convergence for our new algorithm and at a numerical example, validate the theoretical assumptions of our method. By comprehensive simulations, the influence of the tuning parameters of our algorithm on convergence behavior and computation time is analyzed. The new algorithm computes ISOC solutions nearly 33 times faster than the single previously existing ISOC algorithm.

Telemanipulation has become a promising technology that combines human intelligence with robotic capabilities to perform tasks remotely. However, it faces several challenges such as insufficient transparency, low immersion, and limited feedback to the human operator. Moreover, the high cost of haptic interfaces is a major limitation for the application of telemanipulation in various fields, including elder care, where our research is focused. To address these challenges, this paper proposes the usage of nonlinear model predictive control for telemanipulation using low-cost virtual reality controllers, including multiple control goals in the objective function. The framework utilizes models for human input prediction and taskrelated models of the robot and the environment. The proposed framework is validated on an UR5e robot arm in the scenario of handling liquid without spilling. Further extensions of the framework such as pouring assistance and collision avoidance can easily be included.

Hexapeptides are increasingly applied as model systems for studying the amyloidogenecity properties of oligo- and polypeptides. It is possible to construct 64 million different hexapeptides from the twenty proteinogenic amino acid residues. Today's experimental amyloid databases contain only a fraction of these annotated hexapeptides. For labeling all the possible hexapeptides as "amyloidogenic" or "non-amyloidogenic" there exist several computational predictors with good accuracies. It may be of interest to define and study a simple graph structure on the 64 million hexapeptides as nodes when two hexapeptides are connected by an edge if they differ by only a single residue. For example, in this graph, HIKKLM is connected to AIKKLM, or HIKKNM, or HIKKLC, but it is not connected with an edge to VVKKLM or HIKNPM. In the present contribution, we consider our previously published artificial intelligence-based tool, the Budapest Amyloid Predictor (BAP for short), and demonstrate a spectacular property of this predictor in the graph defined above. We show that for any two hexapeptides predicted to be "amyloidogenic" by the BAP predictor, there exists an easily constructible path of length at most 6 that passes through neighboring hexapeptides all predicted to be "amyloidogenic" by BAP. For example, the predicted amyloidogenic ILVWIW and FWLCYL hexapeptides can be connected through the length-6 path ILVWIW-IWVWIW-IWVCIW-IWVCIL-FWVCIL-FWLCIL-FWLCYL in such a way that the neighbors differ in exactly one residue, and all hexapeptides on the path are predicted to be amyloidogenic by BAP. The symmetric statement also holds for non-amyloidogenic hexapeptides. It is noted that the mentioned property of the Budapest Amyloid Predictor \url{https://pitgroup.org/bap} is not proprietary; it is also true for any linear Support Vector Machine (SVM)-based predictors.

Polycyclic aromatic hydrocarbons (PAHs) are highly toxic, carcinogenic substances. On soils contaminated with PAHs, crop cultivation, animal husbandry and even the survival of microflora in the soil are greatly perturbed, depending on the degree of contamination. Most microorganisms cannot tolerate PAH-contaminated soils, however, some microbial strains can adapt to these harsh conditions and survive on contaminated soils. Analysis of the metagenomes of contaminated environmental samples may lead to discovery of PAH-degrading enzymes suitable for green biotechnology methodologies ranging from biocatalysis to pollution control. In the present study, our goal was to apply a metagenomic data search to identify efficient novel enzymes in remediation of PAH-contaminated soils. The metagenomic hits were further analyzed using a set of bioinformatics tools to select protein sequences predicted to encode well-folded soluble enzymes. Three novel enzymes (two dioxygenases and one peroxidase) were cloned and used in soil remediation microcosms experiments. The novel enzymes were found to be efficient for degradation of naphthalene and phenanthrene. Adding the inorganic oxidant CaO2 further increased the degrading potential of the novel enzymes for anthracene and pyrene. We conclude that metagenome mining paired with bioinformatic predictions, structural modelling and functional assays constitutes a powerful approach towards novel enzymes for soil remediation.

This letter presents an extended analysis and a novel upper bound of the subclass of Linear Quadratic Near Potential Differential Games (LQ NPDG). LQ NPDGs are a subclass of potential differential games, for which a distance between an LQ exact potential differential game and the LQ NPDG. LQ NPDGs exhibit a unique characteristic: the smaller the distance from an LQ exact potential differential game, the closer their dynamic trajectories. This letter introduces a novel upper bound for this distance. Moreover, a linear relation between this distance and the resulting trajectory errors is established, opening the possibility for further application of LQ NPDGs., Comment: This work has been submitted to Elsevier for possible publication

In this paper, a cooperative decision-making is presented, which is suitable for intention-aware automated vehicle functions. With an increasing number of highly automated and autonomous vehicles on public roads, trust is a very important issue regarding their acceptance in our society. The most challenging scenarios arise at low driving speeds of these highly automated and autonomous vehicles, where interactions with vulnerable road users likely occur. Such interactions must be addressed by the automation of the vehicle. The novelties of this paper are the adaptation of a general cooperative and shared control framework to this novel use case and the application of an explicit prediction model of the pedestrian. An extensive comparison with state-of-the-art algorithms is provided in a simplified test environment. The results show the superiority of the proposed model-based algorithm compared to state-of-the-art solutions and its suitability for real-world applications due to its real-time capability.

This paper introduces two new identification methods for linear quadratic (LQ) ordinal potential differential games (OPDGs). Potential games are notable for their benefits, such as the computability and guaranteed existence of Nash Equilibria. While previous research has analyzed ordinal potential static games, their applicability to various engineering applications remains limited. Despite the earlier introduction of OPDGs, a systematic method for identifying a potential game for a given LQ differential game has not yet been developed. To address this gap, we propose two identification methods to provide the quadratic potential cost function for a given LQ differential game. Both methods are based on linear matrix inequalities (LMIs). The first method aims to minimize the condition number of the potential cost function's parameters, offering a faster and more precise technique compared to earlier solutions. In addition, we present an evaluation of the feasibility of the structural requirements of the system. The second method, with a less rigid formulation, can identify LQ OPDGs in cases where the first method fails. These novel identification methods are verified through simulations, demonstrating their advantages and potential in designing and analyzing cooperative control systems., Comment: This paper has been accepted for publication in Computational and Applied Mathematics, Springer

This paper presents a white-box intention-aware decision-making for the handling of interactions between a pedestrian and an automated vehicle (AV) in an unsignalized street crossing scenario. Moreover, a design framework has been developed, which enables automated parameterization of the decision-making. This decision-making is designed in such a manner that it can understand pedestrians in urban traffic and can react accordingly to their intentions. That way, a human-like response to the actions of the pedestrian is ensured, leading to a higher acceptance of AVs. The core notion of this paper is that the intention prediction of the pedestrian to cross the street and decision-making are divided into two subsystems. On the one hand, the intention detection is a data-driven, black-box model. Thus, it can model the complex behavior of the pedestrians. On the other hand, the decision-making is a white-box model to ensure traceability and to enable a rapid verification and validation of AVs. This white-box decision-making provides human-like behavior and a guaranteed prevention of deadlocks. An additional benefit is that the proposed decision-making requires low computational resources only enabling real world usage. The automated parameterization uses a particle swarm optimization and compares two different models of the pedestrian: The social force model and the Markov decision process model. Consequently, a rapid design of the decision-making is possible and different pedestrian behaviors can be taken into account. The results reinforce the applicability of the proposed intention-aware decision-making.

This paper presents the development of a real-time simulator for the validation of controlling a large vehicle manipulator. The need for this development can be justified by the lack of such a simulator: There are neither open source projects nor commercial products, which would be suitable for testing cooperative control concepts. First, we present the nonlinear simulation model of the vehicle and the manipulator. For the modeling MATLAB/Simulink is used, which also enables a code generation into standalone C++ ROS-Nodes (Robot Operating System Nodes). The emerging challenges of the code generation are also discussed. Then, the obtained standalone C++ ROS-Nodes integrated in the simulator framework which includes a graphical user interface, a steering wheel and a joystick. This simulator can provide the real-time calculation of the overall system's motion enabling the interaction of human and automation. Furthermore, a qualitative validation of the model is given. Finally, the functionalities of the simulator is demonstrated in tests with a human operators., Comment: in German language

Autonomous driving is a popular research area within the computer vision research community. Since autonomous vehicles are highly safety-critical, ensuring robustness is essential for real-world deployment. While several public multimodal datasets are accessible, they mainly comprise two sensor modalities (camera, LiDAR) which are not well suited for adverse weather. In addition, they lack far-range annotations, making it harder to train neural networks that are the base of a highway assistant function of an autonomous vehicle. Therefore, we introduce a multimodal dataset for robust autonomous driving with long-range perception. The dataset consists of 176 scenes with synchronized and calibrated LiDAR, camera, and radar sensors covering a 360-degree field of view. The collected data was captured in highway, urban, and suburban areas during daytime, night, and rain and is annotated with 3D bounding boxes with consistent identifiers across frames. Furthermore, we trained unimodal and multimodal baseline models for 3D object detection. Data are available at \url{https://github.com/aimotive/aimotive_dataset}., Comment: The paper was accepted to ICLR 2023 Workshop Scene Representations for Autonomous Driving

Methods from artificial intelligence (AI), in general, and machine learning, in particular, have kept conquering new territories in numerous areas of science. Most of the applications of these techniques are restricted to the classification of large data sets, but new scientific knowledge can seldom be inferred from these tools. Here we show that an AI-based amyloidogenecity predictor can strongly differentiate the border- and the internal hexamers of $\beta$-pleated sheets when screening all the Protein Data Bank-deposited homology-filtered protein structures. Our main result shows that more than 30\% of internal hexamers of $\beta$ sheets are predicted to be amyloidogenic, while just outside the border regions, only 3\% are predicted as such. This result may elucidate a general protection mechanism of proteins against turning into amyloids: if the borders of $\beta$-sheets were amyloidogenic, then the whole $\beta$ sheet could turn more easily into an insoluble amyloid-structure, characterized by periodically repeated parallel $\beta$-sheets. We also present that no analogous phenomenon exists on the borders of $\alpha$-helices or randomly chosen subsequences of the studied protein structures.

Hexapeptides are widely applied as a model system for studying amyloid-forming properties of polypeptides, including proteins. Recently, large experimental databases have become publicly available with amyloidogenic labels. Using these datasets for training and testing purposes, one may build artificial intelligence (AI)-based classifiers for predicting the amyloid state of peptides. In our previous work (Biomolecules, 11(4) 500, (2021)) we described the Support Vector Machine (SVM)-based Budapest Amyloid Predictor (\url{https://pitgroup.org/bap}). Here we apply the Budapest Amyloid Predictor for discovering numerous amyloidogenic and non-amyloidogenic hexapeptide patterns with accuracy between 80\% and 84\%, as surprising and succinct novel rules for further understanding the amyloid state of peptides. For example, we have shown that for any independently mutated residue (position marked by ``x''), the patterns CxFLWx, FxFLFx, or xxIVIV are predicted to be amyloidogenic, while those of PxDxxx, xxKxEx, and xxPQxx non-amyloidogenic at all. We note that each amyloidogenic pattern with two x's (e.g.,CxFLWx) describes succinctly $20^2=400$ hexapeptides, while the non-amyloidogenic patterns comprising four point mutations (e.g.,PxDxxx) gives $20^4=160,000$ hexapeptides in total. To our knowledge, no similar applications of artificial intelligence tools or succinct amyloid patterns were described before the present work.

This paper presents a systematic method for the design of a limited information shared control (LISC). LISC is used in applications where not all system states or reference trajectories are measurable by the automation. Typical examples are partially human-controlled systems, in which some subsystems are fully controlled by automation while others are controlled by a human. The proposed systematic design method uses a novel class of games to model human-machine interaction: the near potential differential games (NPDG). We provide a necessary and sufficient condition for the existence of an NPDG and derive an algorithm for finding a NPDG that completely describes a given differential game. The proposed design method is applied to the control of a large vehicle-manipulator system, in which the manipulator is controlled by a human operator and the vehicle is fully automated. The suitability of the NPDG to model differential games is verified in simulations, leading to a faster and more accurate controller design compared to manual tuning. Furthermore, the overall design process is validated in a study with sixteen test subjects, indicating the applicability of the proposed concept in real applications., Comment: This work has been submitted to the IEEE for possible publication

Determining important vertices in large graphs (e.g., Google's PageRank in the case of the graph of the World Wide Web) facilitated the construction of excellent web search engines, returning the most important hits corresponding to the submitted user queries. Interestingly, finding important edges -- instead of vertices -- in large graphs has received much less attention until now. Here we examine the human structural braingraph (or connectome), identified by diffusion magnetic resonance imaging (dMRI) methods, with edges connecting cortical and subcortical gray matter areas and weighted by fiber strengths, measured by the number of the discovered fiber tracts along the edge. We identify several "single" important edges in these braingraphs, whose high or low weights imply the sex or the age of the subject observed. We call these edges implicator edges since solely from their weight, one can infer the sex of the subject with more than 67 \% accuracy or their age group with more than 62\% accuracy. We argue that these brain connections are the most important ones characterizing the sex or the age of the subjects. Surprisingly, the edges implying the male sex are mostly located in the anterior parts of the brain, while those implying the female sex are mostly in the posterior regions. Additionally, most of the inter-hemispheric implicator edges are male ones, while the intra-hemispheric ones are predominantly female edges. Our pioneering method for finding the sex- or age implicator edges can also be applied for characterizing other biological and medical properties, including neurodegenerative- and psychiatric diseases besides the sex or the age of the subject, if large and high-quality neuroimaging datasets become available.

The amyloid state of proteins is widely studied with relevancy in neurology, biochemistry, and biotechnology. In contrast with amorphous aggregation, the amyloid state has a well-defined structure, consisting of parallel and anti-parallel $\beta$-sheets in a periodically repeated formation. The understanding of the amyloid state is growing with the development of novel molecular imaging tools, like cryogenic electron microscopy. Sequence-based amyloid predictors were developed by using mostly artificial neural networks (ANNs) as the underlying computational techniques. From a good neural network-based predictor, it is a very difficult task to identify those attributes of the input amino acid sequence, which implied the decision of the network. Here we present a Support Vector Machine (SVM)-based predictor for hexapeptides with correctness higher than 84\%, i.e., it is at least as good as the published ANN-based tools. Unlike the artificial neural networks, the decision of the SVMs are much easier to analyze, and from a good predictor, we can infer rich biochemical knowledge. Availability and Implementation: The Budapest Amyloid Predictor webserver is freely available at https://pitgroup.org/bap.

Gaussian blurring is a well-established method for image data augmentation: it may generate a large set of images from a small set of pictures for training and testing purposes for Artificial Intelligence (AI) applications. When we apply AI for non-imagelike biological data, hardly any related method exists. Here we introduce the "Newtonian blurring" in human braingraph (or connectome) augmentation: Started from a dataset of 1053 subjects, we first repeat a probabilistic weighted braingraph construction algorithm 10 times for describing the connections of distinct cerebral areas, then take 7 repetitions in every possible way, delete the lower and upper extremes, and average the remaining 7-2=5 edge-weights for the data of each subject. This way we augment the 1053 graph-set to 120 x 1053 = 126,360 graphs. In augmentation techniques, it is an important requirement that no artificial additions should be introduced into the dataset. Gaussian blurring and also this Newtonian blurring satisfy this goal. The resulting dataset of 126,360 graphs, each in 5 resolutions (i.e., 631,800 graphs in total), is freely available at the site https://braingraph.org/cms/download-pit-group-connectomes/. Augmenting with Newtonian blurring may also be applicable in other non-image related fields, where probabilistic processing and data averaging are implemented.

The human brain is the most complex object of study we encounter today. Mapping the neuronal-level connections between the more than 80 billion neurons in the brain is a hopeless task for science. By the recent advancement of magnetic resonance imaging (MRI), we are able to map the macroscopic connections between about 1000 brain areas. The MRI data acquisition and the subsequent algorithmic workflow contain several complex steps, where errors can occur. In the present contribution, we describe and publish 1064 human connectomes, computed from the public release of the Human Connectome Project. Each connectome is available in 5 resolutions, with 83, 129, 234, 463, and 1015 anatomically labeled nodes. For error correction, we follow an averaging and extreme value deleting strategy for each edge and for each connectome. The resulting 5320 braingraphs can be downloaded from the \url{https://braingraph.org} site. This dataset makes possible the access to these graphs for scientists unfamiliar with neuroimaging- and connectome-related tools: mathematicians, physicists, and engineers can use their expertize and ideas in the analysis of the connections of the human brain. Brain scientists also have a robust and large, multi-resolution set for connectomical studies.

For more than a decade now, we can discover and study thousands of cerebral connections with the application of diffusion magnetic resonance imaging (dMRI) techniques and the accompanying algorithmic workflow. While numerous connectomical results were published enlightening the relation between the braingraph and certain biological, medical, and psychological properties, it is still a great challenge to identify a small number of brain connections, closely related to those conditions. In the present contribution, by applying the 1200 Subjects Release of the Human Connectome Project (HCP), we identify just 102 connections out of the total number of 1950 connections in the 83-vertex graphs of 1065 subjects, which -- by a simple linear test -- precisely, without any error determine the sex of the subject. Very surprisingly, we were able to identify two graph edges out of these 102, if, whose weights, measured in fiber numbers, are all high, then the connectome always belongs to a female subject, independently of the other edges. Similarly, we have identified 3 edges from these 102, whose weights, if two of them are high and one is low, imply that the graph belongs to a male subject -- again, independently of the other edges. We call the former 2 edges superfeminine and the first two of the 3 edges supermasculine edges of the human connectome. Even more interestingly, one of the edges, connecting the right Pars Triangularis and the right Superior Parietal areas, is one of the 2 superfeminine edges, and it is also the third edge, accompanying the two supermasculine connections, if its weight is low; therefore it is also a "switching" connection.

The human connectome has become the very frequent subject of study of brain-scientists, psychologists, and imaging experts in the last decade. With diffusion magnetic resonance imaging techniques, unified with advanced data processing algorithms, today we are able to compute braingraphs with several hundred, anatomically identified nodes and thousands of edges, corresponding to the anatomical connections of the brain. The analysis of these graphs without refined mathematical tools is hopeless. These tools need to address the high error rate of the MRI processing workflow, and need to find structural causes or at least correlations of psychological properties and cerebral connections. Until now, structural connectomics was only rarely able identifying such causes or correlations. In the present work, we study the frequent neighbor sets of the most deeply investigated brain area, the hippocampus. By applying the Frequent Network Neighborhood mapping method, we identified frequent neighbor-sets of the hippocampus, which may influence numerous psychological parameters, including intelligence-related ones. We have found neighbor sets, which have significantly higher frequency in subjects with high-scored Penn Matrix tests, and with low-scored Penn Word Memory tests. Our study utilizes the braingraphs, computed from the imaging data of the Human Connectome Project's 414 subjects, each with 463 anatomically identified nodes.

While it is still not possible to describe the neural-level connections of the human brain, we can map the human connectome with several hundred vertices, by the application of diffusion-MRI based techniques. In these graphs, the nodes correspond to anatomically identified gray matter areas of the brain, while the edges correspond to the axonal fibers, connecting these areas. In our previous contributions, we have described numerous graph-theoretical phenomena of the human connectomes. Here we map the frequent complete subgraphs of the human brain networks: in these subgraphs, every pair of vertices is connected by an edge. We also examine sex differences in the results. The mapping of the frequent subgraphs gives robust substructures in the graph: if a subgraph is present in the 80% of the graphs, then, most probably, it could not be an artifact of the measurement or the data processing workflow. We list here the frequent complete subgraphs of the human braingraphs of 414 subjects, each with 463 nodes, with a frequency threshold of 80%, and identify 812 complete subgraphs, which are more frequent in male and 224 complete subgraphs, which are more frequent in female connectomes.

In the study of the human connectome, the vertices and the edges of the network of the human brain are analyzed: the vertices of the graphs are the anatomically identified gray matter areas of the subjects; this set is exactly the same for all the subjects. The edges of the graphs correspond to the axonal fibers, connecting these areas. In the biological applications of graph theory, it happens very rarely that scientists examine numerous large graphs on the very same, labeled vertex set. Exactly this is the case in the study of the connectomes. Because of the particularity of these sets of graphs, novel, robust methods need to be developed for their analysis. Here we introduce the new method of the Frequent Network Neighborhood Mapping for the connectome, which serves as a robust identification of the neighborhoods of given vertices of special interest in the graph. We apply the novel method for mapping the neighborhoods of the human hippocampus and discover strong statistical asymmetries between the connectomes of the sexes, computed from the Human Connectome Project. We analyze 413 braingraphs, each with 463 nodes. We show that the hippocampi of men have much more significantly frequent neighbor sets than women; therefore, in a sense, the connections of the hippocampi are more regularly distributed in men and more varied in women. Our results are in contrast to the volumetric studies of the human hippocampus, where it was shown that the relative volume of the hippocampus is the same in men and women.

The Protein Data Bank (PDB) contains more than 135 000 entries today. From these, relatively few amyloid structures can be identified, since amyloids are insoluble in water. Therefore, mostly solid state NMR-recorded amyloid structures are deposited in the PDB. Based on the geometric analysis of these deposited structures we have prepared an automatically updated webserver, which generates the list of the deposited amyloid structures, and, additionally, those globular protein entries, which have amyloid-like substructures of a given size and characteristics. We have found that applying only the properly chosen geometric conditions, it is possible to identify the deposited amyloid structures, and a number of globular proteins with amyloid-like substructures. We have analyzed these globular proteins and have found that many of them are known to form amyloids more easily than many other globular proteins. Our results relate to the method of (Stankovic, I. et al. (2017): Construction of Amyloid PDB Files Database. Transactions on Internet Research. 13 (1): 47-51), who have applied a hybrid textual-search and geometric approach for finding amyloids in the PDB. If one intends to identify a subset of the PDB for some applications, the identification algorithm needs to be re-run periodically, since in 2017, on average, every day 30 new entries were deposited in the data bank. Our webserver is updated regularly and automatically, and the identified amyloid- and partial amyloid structures can be viewed or their list can be downloaded from the site https://pitgroup.org/amyloid.

In mapping the human structural connectome, we are in a very fortunate situation: one can compute and compare graphs, describing the cerebral connections between the very same, anatomically identified small regions of the gray matter among hundreds of human subjects. The comparison of these graphs has led to numerous recent results, as the (i) discovery that women's connectomes have deeper and richer connectivity-related graph parameters like those of men, or (ii) the description of more and less conservatively connected lobes and cerebral regions, and (iii) the discovery of the phenomenon of the Consensus Connectome Dynamics. Today one of the greatest challenges of brain science is the description and modeling of the circuitry of the human brain. For this goal, we need to identify sub-circuits that are present in almost all human subjects and those, which are much less frequent: the former sub-circuits most probably have functions with general importance, the latter sub-circuits are probably related to the individual variability of the brain structure and functions. The present contribution describes the frequent connected subgraphs (instead of sub-circuits) of at most 6 edges in the human brain. We analyze these frequent graphs and also examine sex differences in these graphs: we demonstrate numerous connected sub-graphs that are more frequent in female or the male connectome. While our results describe subgraphs, instead of sub-circuits, we need to note that all macroscopic sub-circuits correspond to an underlying connected subgraph. Our data source is the public release of the Human Connectome Project, and we are applying the data of 426 human subjects in this study.

Deep, classical graph-theoretical parameters, like the size of the minimum vertex cover, the chromatic number, or the eigengap of the adjacency matrix of the graph were studied widely by mathematicians in the last century. Most researchers today study much simpler parameters of braingraphs or connectomes which were defined in the last twenty years for enormous networks -- like the graph of the World Wide Web -- with hundreds of millions of nodes. Since the connectomes, describing the connections of the human brain, typically contain several hundred vertices today, one can compute and analyze the much deeper, harder-to-compute classical graph parameters for these, relatively small graphs of the brain. This deeper approach has proven to be very successful in the comparison of the connectomes of the sexes in our earlier works: we have shown that graph parameters, deeply characterizing the graph connectivity are significantly better in women's connectomes than in men's. In the present contribution we compare numerous graph parameters in the three largest lobes --- frontal, parietal, temporal --- and in both hemispheres of the brain. We apply the diffusion weighted imaging data of 423 subjects of the NIH-funded Human Connectome Project, and present some findings, never described before, including that the right parietal lobe contains significantly more edges, has higher average degree, density, larger minimum vertex cover and Hoffman bound than the left parietal lobe. Similar advantages in the deep graph connectivity properties are hold for the left frontal vs. the right frontal and for the right temporal vs. the left temporal lobes.

Based on the data of the NIH-funded Human Connectome Project, we have computed structural connectomes of 426 human subjects in five different resolutions of 83, 129, 234, 463 and 1015 nodes and several edge weights. The graphs are given in anatomically annotated GraphML format that facilitates better further processing and visualization. For 96 subjects, the anatomically classified sub-graphs can also be accessed, formed from the vertices corresponding to distinct lobes or even smaller regions of interests of the brain. For example, one can easily download and study the connectomes, restricted to the frontal lobes or just to the left precuneus of 96 subjects using the data. Partially directed connectomes of 423 subjects are also available for download. We also present a GitHub-deposited set of tools, called the Brain Graph Tools, for several processing tasks of the connectomes on the site \url{http://braingraph.org}.

Here we show a method of directing the edges of the connectomes, prepared from diffusion tensor imaging (DTI) datasets from the human brain. Before the present work, no high-definition directed braingraphs (or connectomes) were published, because the tractography methods in use are not capable of assigning directions to the neural tracts discovered. Previous work on the functional connectomes applied low-resolution functional MRI-detected statistical causality for the assignment of directions of connectomes of typically several dozens of vertices. Our method is based on the phenomenon of the "Consensus Connectome Dynamics" (CCD), described earlier by our research group. In this contribution, we apply the method to the 423 braingraphs, each with 1015 vertices, computed from the public release of the Human Connectome Project, and we also made the directed connectomes publicly available at the site \url{http://braingraph.org}. We also show the robustness of our edge directing method in four independently chosen connectome datasets: we have found that 86\% of the edges, which were present in all four datasets, get the very same directions in all datasets; therefore the direction method is robust, it does not depend on the particular choice of the dataset. We think that our present contribution opens up new possibilities in the analysis of the high-definition human connectome: from now on we can work with a robust assignment of directions of the connections of the human brain.

In the applications of the graph theory it is unusual that one considers numerous, pairwise different graphs on the very same set of vertices. In the case of human braingraphs or connectomes, however, this is the standard situation: the nodes correspond to anatomically identified cerebral regions, and two vertices are connected by an edge if a diffusion MRI-based workflow identifies a fiber of axons, running between the two regions, corresponding to the two vertices. Therefore, if we examine the braingraphs of $n$ subjects, then we have $n$ graphs on the very same, anatomically identified vertex set. It is a natural idea to describe the $k$-frequently appearing edges in these graphs: the edges that are present between the same two vertices in at least $k$ out of the $n$ graphs. Based on the NIH-funded large Human Connectome Project's public data release, we have reported the construction of the Budapest Reference Connectome Server \url{http://connectome.pitgroup.org} that generates and visualizes these $k$-frequently appearing edges. We call the graphs of the $k$-frequently appearing edges "$k$-consensus connectomes" since an edge could be included only if it is present in at least $k$ graphs out of $n$. Considering the whole human brain, we have reported a surprising property of these consensus connectomes earlier. In the present work we are focusing on the frontal lobe of the brain, and we report here a similarly surprising dynamical property of the consensus connectomes when $k$ is gradually changed from $k=n$ to $k=1$: the connections between the nodes of the frontal lobe are seemingly emanating from those nodes that were connected to sub-cortical structures of the dorsal striatum: the caudate nucleus, and the putamen. We hypothesize that this dynamic behavior copies the axonal fiber development of the frontal lobe.

Graph theory in the last two decades penetrated sociology, molecular biology, genetics, chemistry, computer engineering, and numerous other fields of science. One of the more recent areas of its applications is the study of the connections of the human brain. By the development of diffusion magnetic resonance imaging (diffusion MRI), it is possible today to map the connections between the 1-1.5 cm$^2$ regions of the gray matter of the human brain. These connections can be viewed as a graph: the vertices are the anatomically identified regions of the gray matter, and two vertices are connected by an edge if the diffusion MRI-based workflow finds neuronal fiber tracts between these areas. This way we can compute 1015-vertex graphs with tens of thousands of edges. In a previous work, we have analyzed the male and female braingraphs graph-theoretically, and we have found statistically significant differences in numerous parameters between the sexes: the female braingraphs are better expanders, have more edges, larger bipartition widths, and larger vertex cover than the braingraphs of the male subjects. Our previous study has applied the data of 96 subjects; here we present a much larger study of 426 subjects. Our data source is an NIH-founded project, the "Human Connectome Project (HCP)" public data release. As a service to the community, we have also made all of the braingraphs computed by us from the HCP data publicly available at the \url{http://braingraph.org} for independent validation and further investigations., Comment: arXiv admin note: substantial text overlap with arXiv:1512.01156, arXiv:1501.00727

Connections of the living human brain, on a macroscopic scale, can be mapped by a diffusion MR imaging based workflow. Since the same anatomic regions can be corresponded between distinct brains, one can compare the presence or the absence of the edges, connecting the very same two anatomic regions, among multiple cortices. Previously, we have constructed the consensus braingraphs on 1015 vertices first in five, then in 96 subjects in the Budapest Reference Connectome Server v1.0 and v2.0, respectively. Here we report the construction of the version 3.0 of the server, generating the common edges of the connectomes of variously parameterizable subsets of the 1015-vertex connectomes of 477 subjects of the Human Connectome Project's 500-subject release. The consensus connectomes are downloadable in csv and GraphML formats, and they are also visualized on the server's page. The consensus connectomes of the server can be considered as the "average, healthy" human connectome since all of their connections are present in at least $k$ subjects, where the default value of $k=209$, but it can also be modified freely at the web server. The webserver is available at \url{http://connectome.pitgroup.org}.

We analyzed correlations between more than 700 psychological-, anatomical- and connectome--properties, originated from the Human Connectome Project's (HCP) 500-subject dataset. Apart from numerous natural correlations, which describe parameters computable or approximable from one another, we have discovered numerous significant correlations in the dataset, never described before. We also have found correlations described very recently independently from the HCP-dataset: e.g., between gambling behavior and the number of the connections leaving the insula.

In our previous study we have shown that the female connectomes have significantly better, deep graph-theoretical parameters, related to superior "connectivity", than the connectome of the males. Since the average female brain is smaller than the average male brain, one cannot rule out that the significant advantages are due to the size- and not to the sex-differences in the data. To filter out the possible brain-volume related artifacts, we have chosen 36 small male and 36 large female brains such that all the brains in the female set are larger than all the brains in the male set. For the sets, we have computed the corresponding braingraphs and computed numerous graph-theoretical parameters. We have found that (i) the small male brains lack the better connectivity advantages shown in our previous study for female brains in general; (ii) in numerous parameters, the connectomes computed from the large-brain females, still have the significant, deep connectivity advantages, demonstrated in our previous study., Comment: arXiv admin note: substantial text overlap with arXiv:1501.00727